Suppose that nine bats was used. For each trail, the zoo keeper pointed to one of two "feeders" Suppose that the bats went to the correct feeder (the one that the zoo keeper pointed at) 7 times. Find the 95% confidence interval for the population proportion of times that the bats would follow the point.

A. (0.59, 1.05)

B. (0.44,0.94)C. (0.51, 1.0)

Answer:

The height of the pile is increasing [tex]\frac{20}{49\pi}[/tex] a minute when the pile is 14ft high.

Step-by-step explanation:

The volume of a cone is given by the following formula:

[tex]V = \frac{\pi r^{2}h}{3}[/tex]

We have that the diameter and the height are equal, so [tex]r = \frac{h}{2}[/tex]

So

[tex]V = \frac{\pi h^{3}}{12}[/tex]

Let's derivate this equation, using implicit derivatives.

[tex]\frac{dV}{dt} = \frac{\pi h^{2}}{4}\frac{dh}{dt}[/tex]

In this problem, we have to:

Find [tex]\frac{dh}{dt}[/tex], when [tex]\frac{dV}{dt} = 20, h = 14[/tex]. So

[tex]\frac{dV}{dt} = \frac{\pi h^{2}}{4}\frac{dh}{dt}[/tex]

[tex]20 = \frac{196\pi}{4}\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt} = \frac{20}{49\pi}[/tex]

The height of the pile is increasing [tex]\frac{20}{49\pi}[/tex] a minute when the pile is 14ft high.

This involves relationship between rates using Calculus.

dh/dt = 0.13 ft/min

Volumetric rate; dv/dt = 20 ft³/min

height of pile; h = 14 ft

We are not given the diameter here but as we are dealing with a right circular cone, we will assume that the diameter is equal to the height.

Thus; diameter; d = 14 ft

radius; r = h/2 = d/2 = 14/2

radius; r= 7 ft

Plugging in the relevant values, we have;

20 = ¹/₄π × 14² × (dh/dt)

dh/dt = (20 × 4)/(π × 14²)

dh/dt = 0.13 ft/min

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Two right triangles are congruent if the corresponding altitudes and angle bisectors through the right angles are congruent.

In order to prove that two right triangles are congruent if the corresponding altitudes and angle bisectors through the right angles are congruent, we can use the side-side-side (SSS) congruence theorem. This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

In this case, we can show that the corresponding altitudes and angle bisectors through the right angles are congruent for both triangles. Since both triangles have congruent corresponding altitudes and congruent angle bisectors through the right angles, we can conclude that the triangles are congruent.

Therefore, the statement is proven.

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Answer:

d) [-16.03,-3.97]

[tex]-16.03 \leq \mu_A -\mu_B \leq -3.97[/tex].

Step-by-step explanation:

Notation and previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]n_A=18[/tex] represent the sample of A

[tex]n_B =13[/tex] represent the sample of B

[tex]\bar x_A =39[/tex] represent the mean sample  for A

[tex]\bar x_B =49[/tex] represent the mean sample for B  

[tex]s_A =8[/tex] represent the sample deviation for A

[tex]s_B =4[/tex] represent the sample deviation for B

[tex]\alpha=0.01[/tex] represent the significance level

Confidence =99% or 0.99

The confidence interval for the difference of means is given by the following formula:  

[tex](\bar X_A -\bar X_B) \pm t_{\alpha/2}\sqrt{(\frac{s^2_A}{n_A}+\frac{s^2_B}{n_B})}[/tex] (1)  

The point of estimate for [tex]\mu_A -\mu_B[/tex] is just given by:  

[tex]\bar X_A -\bar X_B =39-49=-10[/tex]  

The appropiate degrees of freedom are [tex]df=n_1+ n_2 -2=18+13-2=29[/tex]

Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,29)".And we see that [tex]t_{\alpha/2}=2.756[/tex]  

The standard error is given by the following formula:  

[tex]SE=\sqrt{(\frac{s^2_A}{n_A}+\frac{s^2_B}{n_B})}[/tex]  

And replacing we have:  

[tex]SE=\sqrt{(\frac{8^2}{18}+\frac{4^2}{13})}=2.188[/tex]  

Confidence interval  

Now we have everything in order to replace into formula (1):  

[tex]-10-2.756\sqrt{(\frac{8^2}{18}+\frac{4^2}{13})}=-16.03[/tex]  

[tex]-10+2.756\sqrt{(\frac{8^2}{18}+\frac{4^2}{13})}=-3.97[/tex]  

So on this case the 99% confidence interval for the differences of means would be given by [tex]-16.03 \leq \mu_A -\mu_B \leq -3.97[/tex].

d) [-16.03,-3.97]

The 99% confidence interval for the difference in the true means of items sold at location A and B is [-15.64, -4.36], therefore the correct answer is F. None of the above.

This question is about computing a confidence interval for the difference of two sample means. The formula for the 99% confidence interval for the difference between two means is:

(X1 - X2) ± Z * sqrt [s1^2/n1 + s2^2/n2]

Where X1 and X2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and Z is the Z-score for the desired confidence level. For a 99% confidence level, the Z-score is approximately 2.576. We plug the given values into the equation to calculate:

(39 - 49) ± 2.576 * sqrt [(8^2 / 18) + (4^2 / 13)] => -10 ± 2.576 * sqrt [3.56 + 1.23] => -10 ± 2.576 * sqrt [4.79] => -10 ± 2.576 * 2.19 => -10 ± 5.64

This means the 99% confidence interval for the difference in the true means of items sold at location A and B is [-15.64, -4.36], which is not among the given options, so the correct answer is F. None of the above.

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Answer:

Confidence interval for the population mean lifetime of the Amazon Kindle DX is (33.30 months to 42.70 months)

Step-by-step explanation:

Given;

Mean lifespan x = 38 months

Standard deviation r = 12 months

Number of kindle selected n = 25

Confidence range = 95%

Z*(95%) = 1.96

Confidence interval = x+/-Z*(r/√n)

= 38 +/- 1.96(12/√25)

= 38 +/- 4.70

Confidence interval = (33.30 months to 42.70 months)

Answer:

a) The 90% confidence interval would be given by (721.716;790.724)  

b) We are 90% confident that the true mean for the true speed of light is between (721.716;790.724)  

c) We assume the following conditions:

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Part a

[tex]\bar X=756.22[/tex] represent the sample mean  

[tex]\mu[/tex] population mean (variable of interest)  

[tex]s=100.89[/tex] represent the sample standard deviation  

n=25 represent the sample size  

90% confidence interval  

The confidence interval for the mean is given by the following formula:  

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)  

The degrees of freedom are given by:

[tex]df=n-1=25-1=24[/tex]

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,24)".And we see that [tex]t_{\alpha/2}=1.71[/tex]  

Now we have everything in order to replace into formula (1):  

[tex]756.22-1.71\frac{100.89}{\sqrt{25}}=721.716[/tex]  

[tex]756.22+1.71\frac{100.89}{\sqrt{25}}=790.724[/tex]  

So on this case the 90% confidence interval would be given by (721.716;790.724)  

Part b

We are 90% confident that the true mean for the true speed of light is between (721.716;790.724)  

Part c

We assume the following conditions:

Final answer:

The 90% confidence interval for the true speed of light is between 299,723.02683 km/sec and 299,789.41317 km/sec. This interval suggests we can be 90% confident that the constant speed of light falls within this range, with the understanding that the true speed of light is approximately 299,792,458 m/s.

Explanation:

The sample mean is 756.22, and the standard deviation is 100.89 with 25 trials.

First, add 299,000 km/sec to the sample mean to revert to the actual speed of light. Adjusted mean = 756.22 + 299,000 = 299,756.22 km/sec.

Since the sample size (25) is greater than 30, we use the z-score for a 90% confidence interval, which is 1.645.

To find the margin of error (ME), use the formula ME = z * (σ/√n), where σ is the standard deviation and n is the sample size. ME = 1.645 * (100.89/√25)= 1.645 * 20.178 = 33.19317 km/sec.

The confidence interval is then mean ± ME. That gives us the interval: [299,756.22 - 33.19317, 299,756.22 + 33.19317] or [299,723.02683, 299,789.41317] km/sec.

Interpretation: We are 90% confident that the true speed of light lies within the interval of 299,723.02683 to 299,789.41317 km/sec.

The samples are independent and randomly selected.

The data reported is accurate and measured without systematic errors.

The data is normally distributed or the sample size is large enough for the Central Limit Theorem to apply.

These results align with the known fact that the speed of light is a constant at approximately 299,792,458 meters/second, and any deviations observed in the experiment are likely due to measurement error or experimental uncertainties.

Answer:

3.216%

Step-by-step explanation:

This bond sells at a higher price or value, which means that its coupon is bogus of market interest rate. Therefore, the minimum yield rate that accounts for the possibility of the bond being called is calculated at the earliest possible call date. Let say exactly 15 years from the date of purchase, because that would be the most disadvantageous date for the bondholder for the call to occur.

The minimum semiannual yield:

j= i²/2

i² = 2j

which therefore satisfies the expression below for the worst possible case scenario yield:

1722.25 = 0.04*1100*[tex]a]_30[/tex]+[tex]\frac{1100}{(1+j)^30}[/tex]

Also, with the use of a financial calculator (making sure that the calculator is not in BGN mode)

1722.25 PV, -44 PMT, -1100 FV, 30 N, CPT 1/Y.

j can be found to be 1.608245%. The corresponding nominal annual rate compounded semiannually is (X) = i² = 2j =3.216%

Answer:

[tex] t=(25-1) [\frac{0.141}{0.1}]^2 =47.71[/tex]

Step-by-step explanation:

Data given

[tex]\bar X=20[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

[tex]s^2=0.02[/tex] represent the sample variance

[tex]s=0.141[/tex] represent the sample deviation

n=25 represent the sample size  

State the null and alternative hypothesis

On this case we want to check if the population standard deviation is more than 0.01, so the system of hypothesis are:

H0: [tex]\sigma \leq 0.1[/tex]

H1: [tex]\sigma >0.1[/tex]

In order to check the hypothesis we need to calculate the statistic given by the following formula:

[tex] t=(n-1) [\frac{s}{\sigma_o}]^2 [/tex]

This statistic have a Chi Square distribution distribution with n-1=25-1=24 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

[tex] t=(25-1) [\frac{0.141}{0.1}]^2 =47.71[/tex]

What is the critical value for the test statistic at an α = 0.05 significance level?

Since is a right tailed test the critical zone it's on the right tail of the distribution. On this case we need a quantile on the chi square distribution with 24 degrees of freedom that accumulates 0.05 of the area on the right tail and 0.95 on the left tail.  

We can calculate the critical value in excel with the following code: "=CHISQ.INV(0.95,24)". And our critical value would be [tex]\chi^2 =36.415[/tex]

Since our calculated value is higher than the critical value we reject the null hypothesis at 5% of significance.

The variance hypothesis test for a cancer treatment drug with a sample mean of 20 mg and sample variance of 0.02 mg results in a chi-square test statistic of 48. This test statistic will be used to determine if the drug's variance exceeds the acceptable limit.

The question at hand is concerning a hypothesis test of the variance in dosage of a cancer treatment drug. The null hypothesis (H0) claims that the standard deviation of the drug content is not more than 0.1 mg, which corresponds to a variance of 0.01 mg² since variance = standard deviation². The alternative hypothesis (Ha) is that the variance is greater than 0.01 mg². Given the sample variance as 0.02 mg² and a sample size of 25, the test statistic for the chi-square test can be calculated using the formula:

Test statistic (chi-square) = (n - 1)*sample variance / hypothesized variance

Test statistic = (25 - 1) * 0.02 / 0.01 = 24 * 2 = 48

The calculated test statistic is 48. Since the sample variance is greater than the hypothesized variance, we have a test statistic that would fall in the rejection region based on the selected significance level in a Chi-square distribution, suggesting that the drug dosage may indeed have greater variability than the company's standard.

Answer:

Step 2 involved distributive property and the value of y is equal to 8.

Step-by-step explanation:

In step 2, there has been an error in applying the Distributive Property correctly.

Distributive Property-  a(b+c)

                                       = a x b + a x c

Step 2: [tex]2y+16=4y[/tex]

Step 3:[tex]2y=16[/tex]

Step 4: [tex]y=8[/tex]

y=8

Answer:

2 should be distributed as 2y + 16; y + 8

Answer:

y = -4/6x - 4

Step-by-step explanation:

y = m(x - x₁) + y₁

You're given m=-4/6 and (0,-4) ←x₁=0, y₁=-4

so just plug it into the point-slope equation.

y = (-4/6)(x - (0)) + (-4)

y = (-4/6)(x) + (-4)

y = -4/6x - 4

Answer:y = -4x/6 - 4

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The slope,m of the given line is -4/6

To determine the intercept, we would substitute m = -4/6, x = 0 and y = -4 into y = mx + c. It becomes

- 4 = -4/6 × 0 + c = 0 + c

c = - 4

The equation becomes

y = -4x/6 - 4

Answer:

[tex]t=\frac{0.505-0.49}{\frac{0.12}{\sqrt{51}}}=0.893[/tex]  

[tex]p_v =P(t_{50}>0.893)=0.1881[/tex]  

If we compare the p value and a significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean is not significantly higher than 0.49 units.  

Step-by-step explanation:

Data given and notation

[tex]\bar X=0.505[/tex] represent the sample mean  

[tex]s=0.12[/tex] represent the standard deviation for the sample

[tex]n=51[/tex] sample size  

[tex]\mu_o =0.49[/tex] represent the value that we want to test  

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses to be tested  

We need to conduct a hypothesis in order to determine if the average nitrogen level dos not exced 0.49 units, the system of hypothesis would be:

Null hypothesis:[tex]\mu \leq 0.49[/tex]  

Alternative hypothesis:[tex]\mu > 0.49[/tex]  

Compute the test statistic  

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

We can replace in formula (1) the info given like this:  

[tex]t=\frac{0.505-0.49}{\frac{0.12}{\sqrt{51}}}=0.893[/tex]  

Now we need to find the degrees of freedom for the t distirbution given by:

[tex]df=n-1=51-1=50[/tex]

What do you conclude?  

Compute the p-value  

Since is a right tailed test the p value would be:  

[tex]p_v =P(t_{50}>0.893)=0.1881[/tex]  

If we compare the p value and a significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean is not significantly higher than 0.49 units.  

Answer:

effective memory access = 658 ns

Step-by-step explanation:

GIven data:

Effective memory access time is given as

[tex] = [H_1*T_1]+[(1-H_1)*H_2*T_2]+[(1-H_1)(1-H_2)*H_m*T_m][/tex]

from the data given above we have

[tex]H_1 = 0.1[/tex]

[tex]H_2 = 0.3[/tex]

[tex]T_1 = 10 ns[/tex]

[tex]T_2 = 100 ns[/tex]

hit rate, [tex]H_m = 1 ns[/tex]

access time [tex]= T_m = 1000 ns[/tex]

Plugging all information in above formula to get the effective memory access

[tex]= 0.1\times 10 + 0.9\times 100+ 0.9 \times 0.7\times 1 \times 1000[/tex]

= 1+27+ 630

=658 ns

The expected value of the received voltage is 4. The variance of the received voltage is 64/3. The covariance of the transmitted and received voltage is 0.

(a) To find the expected value of the received voltage, we need to use the linearity property of the expectation and the fact that V and X are independent. The expected value of R is given by:

E[R] = E[V+X] = E[V] + E[X]

Since V and X are independent, we have E[X] = 4 and E[V] = 0 (by symmetry of the uniform distribution). Therefore, E[R] = 0 + 4 = 4.

(b) To find the variance of the received voltage, we can use the properties of variance. Variance is additive for independent random variables, so:

Var[R] = Var[V+X] = Var[V] + Var[X]

Since V and X are independent, we have Var[X] = 4^2 = 16 and Var[V] = (16^2)/12 = 64/12 = 16/3. Therefore, Var[R] = 16/3 + 16 = 64/3.

(c) The covariance of the transmitted and received voltage is given by:

Cov[V, R] = E[(V - E[V])(R - E[R])]

Since E[V] = 0 and E[R] = 4, this simplifies to:

Cov[V, R] = E[VR] - E[V]E[R]

Since V and R are independent, we have Cov[V, R] = E[V]E[R] - E[V]E[R] = 0.

(d) The optimal linear estimate VL(R) is given by:

VL(R) = E[V] + Cov[V, R]/Var[R] * (R - E[R])

Since Cov[V, R] = 0, the optimal linear estimate becomes:

VL(R) = E[V] + 0/Var[R] * (R - E[R]) = E[V] = 0.

(e) The minimum mean square error of the estimate is given by:

e* = Var[V - VL(R)]

Since VL(R) = E[V] = 0, this simplifies to:

e* = Var[V] = 16/3.

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Answer: E , You will lose 5.6 cents

Step-by-step explanation:

Because with two dice, there are 36 possible outcomes, 21 are 7 or less, 14 are 8 through 11, and 1 is twelve.

Also when you have a total of 8,9,10 or 11, you gain $1 deducing the $1 you bet. The same with when you have 12 you gain $5.

Average $ to gain when total is 8,9,10 or 11 = P(8,9,10,11)

P(8,9,10,11) = ($2-$1)(14/36) = $14/36 gain

P(12) = ($6-$1)(1/36) = $5/36 gain

P(7 or less) = (0-$1)(21/36) = -$21/36 loss

P(loss or gain)= P(8,9,10,11) + P(12) + P(7 or less)

P(loss or gain) = $( 14/36 + 5/36 - 21/36) = -$2/36

P(loss or gain) = -$0.056 = -5.6 cents loss

Therefore, For every $1 bet you will lose 5.6 cents.

Answer: Addie weighs 4 ounces

Missy weighs 14 ounces

Corky weighs 8 ounces

Step-by-step explanation:

Let a represent the weight of Addie.

Let m represent the weight of Missy.

Let c represent the weight of Corky.

Together Addie and Missy weigh 18 ounces. This means that

a + m = 18 - - - - - - - - - 1

Missy and Corky weigh 22 ounces. This means that

m + c = 22

m = 22 - c - - - - - - - - - - 2

Addie and Corky weigh 12 ounces. This means that

a + c = 12

a = 12 - c - - - - - - - - - - - 3

Substituting equation 2 and equation 3 into equation 1, it becomes

22 - c + 12 - c = 18

34 - 2c = 18

- 2c = 18 - 34 = - 16

c = - 16/ - 2 = 8

Substituting c = 8 into equation 2, it becomes

m = 22 - 8

m = 14

Substituting c = 8 into equation 3, it becomes

a = 12 - 8

a = 4

Answer: It's attached.

Step-by-step explanation:

The table is attached.

The ratio is:

[tex]ratio=\frac{24}{8}\\\\ratio=3[/tex]

Knowing tha ratio, you can complete the table.

The steps are:

1. Multiply the number of panes given in the table by the ratio find above, in order to find the number of windows.

3. Divide the number of windows given in the table by the ratio find above, in order to find the number of panes.

Given [tex]Panes=3[/tex]:

[tex]Windows=3*3=9[/tex]

 Given [tex]Windows=3[/tex]:

[tex]Panes=\frac{3}{3}=1[/tex]

Given [tex]Windows=5[/tex]:

[tex]Panes=\frac{5}{3}[/tex]

Given [tex]Panes=18[/tex]:

[tex]Windows=18*3=54[/tex]

Answer:windows x6

Step-by-step explanation:

Answer:

a) [tex]A(t=0)= 23.1 e^{0.0152(0)}=23.1e^0 =23.1[/tex]

b) [tex]t = \frac{ln(\frac{28.3}{23.1})}{0.0152}=13.357 years[/tex]

So for this case the answer would be 13.347 years, the population will be 28.3 million and ye year would be 2000+13.347 and that would be approximately in 2014

Step-by-step explanation:

For this case we assume the following model:

[tex]A(t)= 23.1 e^{0.0152 t}[/tex]

Where t is the number of years after 2000/

Part a

For this case we want the population for 2000 and on this case the value of t=0 since we have 0 years after 2000. If we rpelace into the model we got:

[tex]A(t=0)= 23.1 e^{0.0152(0)}=23.1e^0 =23.1[/tex]

So then the initial population at year 2000 is 23.1 million of people.

Part b

For this case we want to find the time t whn the population is 28.3 million.

So we need to solve this equation:

[tex]28.3= 23.1 e^{0.0152(t)}[/tex]

We can divide both sides by 23.1 and we got:

[tex]\frac{28.3}{23.1}= e^{0.0152t}[/tex]

Now we can apply natural log on both sides and we got:

[tex]ln(\frac{28.3}{23.1})= 0.0152 t[/tex]

And then for t we got:

[tex]t = \frac{ln(\frac{28.3}{23.1})}{0.0152}=13.357 years[/tex]

So for this case the answer would be 13.347 years, the population will be 28.3 million and ye year would be 2000+13.347 and that would be approximately in 2014

Answer:

The area of this revolted surface is 36π

Step-by-step explanation:

To obtain the area of a revolted surface, you have to define:

1) which is the axis on which the surface is revolted: this defines the limits on that axis or hight of the surface. In this case x∈[0;2]

2) which is the expression of the radius of the revolted surface and its dependence with the hight. In this case, the radius expression could be Y=4x+5

3) Define the angular variable: If this is a fully revolted surface, the angular variable will go from 0 to 2π

Now we can obtain the area with a double integral:

[tex]A=\int\limits^{2}_0 { \int\limits^{2\pi}_0 {r} \, d \varphi } \, dx =\int\limits^{2}_0 { \int\limits^{2\pi}_0 {4x+5} \, d \varphi } \, dx =\int\limits^{2}_0 { (2\pi)(4x+5)} \, dx=36\pi[/tex]

Answer:

A. 2 hours walking; 12 hours running

Step-by-step explanation:

The combination of hours walking and running has to respect both these inequalities:

[tex]3w + 6r \geq 36[/tex]

[tex]3w + 6r \leq 90[/tex]

A. 2 hours walking; 12 hours running

3w + 6r = 3*2 + 6*12 = 6+72 = 78.

Ok, it is larger than 35 and smaller than 91.

B. 4 hours walking; 3 hours running

3w + 6r = 3*4 + 6*3 = 12 + 18 = 30.

Invalid. Lesser than 36.

C. 9 hours walking; 12 hours running

3w + 6r = 3*9 + 6*12 = 27 + 72 = 99

Larger than 90. Invalid

D. 12 hours walking; 10 hours running

3w + 6r = 3*12 + 6*10 = 96

Larger than 90. Invalid

The combination of hours Keitaro can walk and run in a month to reach his goal is 2 hours walking; 12 hours running

3w + 6r ≥ 36. (1)

3w + 6r ≤ 90. (2)

substitute each option into the equation

A. 2 hours walking; 12 hours running

3w + 6r ≥ 36

3(2) + 6(12) ≥ 36

6 + 72 ≥ 36

78 ≥ 36

True

3w + 6r ≤ 90

3(2) + 6(12) ≤ 90

6 + 72 ≤ 90

78 ≤ 90

True

B. 4 hours walking; 3 hours running

3w + 6r ≤ 90

3(4) + 6(3) ≤ 90

12 + 18 ≤ 90

30 ≤ 90

True

B. 4 hours walking; 3 hours running

3w + 6r ≥ 36

3(4) + 6(3) ≥ 36

12 + 18 ≥ 36

30 ≥ 36

False

C. 9 hours walking; 12 hours running

3w + 6r ≥ 36

3(9) + 6(12) ≥ 36

27 + 72 ≥ 36

99 ≥ 36

True

3w + 6r ≤ 90

3(9) + 6(12) ≤ 90

27 + 72 ≤ 90

99 ≤ 90

False

D. 12 hours walking; 10 hours running

3w + 6r ≥ 36

3(12) + 6(10) ≥ 36

36 + 60 ≥ 36

96 ≥ 36

True

3w + 6r ≤ 90

3(12) + 6(10) ≤ 90

36 + 60 ≤ 90

96 ≤ 90

False.

Therefore, the combination of hours Keitaro can walk and run in a month to reach his goal is 2 hours walking; 12 hours running

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Answer:

[tex]P(X\geq 2)=1-P(X\leq 1)=1-[0.054294+0.167762]=0.777944[/tex]

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: [tex]P(A)+P(A') =1[/tex]

Find the probability that at least 2 of the women sampled have been the victim of domestic abuse.

On this case we want to find this probability

[tex]P(X\geq 2) =1-P(X<2)=1-P(X\leq 1)= 1-[P(X=0)+P(X=1)][/tex]

And we can find the individual probabilities like this:

[tex]P(X=0)=(25C0)(0.11)^0 (1-0.11)^{25-0}=0.054294[/tex]  

[tex]P(X=1)=(25C1)(0.11)^1 (1-0.11)^{25-1}=0.167762[/tex]  

[tex]P(X\geq 2)=1-P(X\leq 1)=1-[0.054294+0.167762]=0.777944[/tex]

Using the binomial distribution, it is found that there is a 0.287825 = 28.7825% probability that at least 2 of the women sampled have been the victim of domestic abuse.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that at least 2 of the women sampled have been the victim of domestic abuse is given by:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which:

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

Hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{25,0}.(0.1111)^{0}.(0.8889)^{25} = 0.052641[/tex]

[tex]P(X = 1) = C_{25,1}.(0.1111)^{1}.(0.8889)^{24} = 0.164484[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.052641 + 0.164484 = 0.217125[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.217125 = 0.782875[/tex]

0.287825 = 28.7825% probability that at least 2 of the women sampled have been the victim of domestic abuse.

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Answer:

Null hypothesis: [tex]p\leq 0.3[/tex]

Alternative hypothesis: [tex]p > 0.3[/tex]

Step-by-step explanation:

1) Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

2) Solution to the problem

On this case we want to test is [tex]p>0.3[/tex] since we want to check if the new model has improved the warranty rate, we can express it like this:

[tex]p-0.3<0[/tex] since are equivalent expressions.

And the alternative hypothesis should be the complement:

Null hypothesis: [tex]p\leq 0.3[/tex] or [tex]p=0.3[/tex]

So the correct system of hypothesis for this case would be:

Null hypothesis: [tex]p\leq 0.3[/tex]

Alternative hypothesis: [tex]p > 0.3[/tex]

The alternative way should be:

Null hypothesis: [tex]p = 0.3[/tex]

Alternative hypothesis: [tex]p > 0.3[/tex]

Answer:

False. The products from cross multiplication are different.

Step-by-step explanation:

To know if a pair of ratios form a proportion, cross multiply. If the products are equal, they are a proportion.

Write like this to see top (numerator) and bottom (denominator) clearly.

[tex]\frac{4}{5} =\frac{5}{6}[/tex]

Multiply each numerator with the other side's denominator:

4 X 6 = 24

5 X 5 = 25

Are they equal? No. 24 ≠ 25

Therefore it's not a proportion.

Answer:

Ray Flagg will pay $5,272 at the time of his 30th installment.

Step-by-step explanation:

Ray took $12,000 load for 60 months. As he paid no amount as down payment so his monthly payment will be $200:

[tex]=12000/60\\=200[/tex]

Instead of $200 per month, he used to pay $232 per month. So, before his 30th installment, he paid 29 installments each of $232 which is $6,728:

[tex]=232*29\\=6728[/tex]

As the business does better, he wishes to payback remaining amount at once so he will pay $5,272 as:

[tex]12000-6728\\=5272[/tex]

To calculate the remaining balance of a fixed installment loan after a certain number of payments, use the formula provided in the detailed answer.

Ray Flagg took out a 60-month fixed installment loan of $12,000 to open a new pet store. He paid no money down and began making monthly payments of  $232. Ray's business does better than expected and instead of making his 30th payment, Ray wishes to repay his loan in full.

To calculate the remaining balance after 29 months, we can use the formula for the remaining balance of a fixed installment loan:

Remaining Balance = Balance × (1 + Monthly Interest Rate)Number of Payments Made - (Monthly Payment × ((1 + Monthly Interest Rate)Number of Payments Made - 1) / Monthly Interest Rate)

Using the given values, the monthly interest rate can be calculated by dividing the annual interest rate by 12 and converting it to a decimal.

Finally, substitute the values into the formula to find the remaining balance after 29 months.

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Answer:

The probability of drawing a heart or diamond is 1/2 or 0.5

The probability that the card is not a spade is 3/4 or 0.75

Step-by-step explanation:

Consider the provided information.

Part (a) Find the probability of drawing a heart or diamond.

There are 13 cards of heart and 13 cards of diamond.

We need to find the probability of drawing a heart or diamond.

[tex]P(\text{Heart or Diamond})=P(\text{Heart card Drawn})+P(\text{Diamond card Drawn})[/tex]

[tex]P(\text{Heart or Diamond})=\frac{13}{52}+\frac{13}{52}[/tex]

[tex]P(\text{Heart or Diamond})=\frac{26}{52}=\frac{1}{2}=0.5[/tex]

Hence, the probability of drawing a heart or diamond is 1/2 or 0.5

(b) Find the probability that the card is not a spade.

Out of 52 cards 13 are spade,

That means 52 - 13 = 39 cards are not a spade.

[tex]P(\text{Not spade})=\frac{39}{52}=\frac{3}{4}=0.75[/tex]

Hence, the probability that the card is not a spade is 3/4 or 0.75

Answer:

Step-by-step explanation:

Answer:

Percentage score will be 83.33 %

Step-by-step explanation:

We have given Antonette gets 70 % on 10 problem test

Let consider here here total problem = total marks

So marks get 10 10 problem test = 10×0.7 = 7

Marks get in 20 problem test = 20×0.8 = 16

And marks get in 30 problem test = 30×0.9 = 27

Now total marks get get by Antonette = 7 +16 + 27 = 50

And total marks = 60

So percentage score of Antonette [tex]=\frac{50}{60}\times 100=83.33[/tex] %

In a game of choice and payoff, Nick's dominant strategy is to choose 'Right', while Rosa lacks a dominant strategy. The Nash equilibrium is when Nick chooses 'Right' and Rosa chooses either 'Left' or 'Right' because changing their decisions would not lead to higher payoff.

The subject of this question is about a concept from game theory known as dominant strategies and the Nash equilibrium. Nick and Rosa are playing a game where they each simultaneously choose an action (Left or Right) and receive a payoff that depends on both their choices. To find the dominant strategy for each player, we need to identify what action that player would take, regardless of the other player's choice.

For Nick, the dominant strategy is to choose Right because his payoff (5 when Rosa picks Left, 6 when Rosa picks Right) is higher than when he picks Left (8 when Rosa picks Left, 4 when Rosa picks Right). For Rosa, she has no dominant strategy because her payoff is the same (4) whether she chooses Left or Right if Nick is choosing Left, and the same holds if Nick is choosing Right.

The Nash equilibrium is a situation where neither player can benefit by changing their strategy, assuming the other player stays the same. Here, the Nash equilibrium occurs when Nick chooses Right and Rosa chooses Left or Right, because neither player can gain a higher payoff by unilaterally changing their strategy.

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Answer

The answer and procedures of the exercise are attached in the following archives.

Step-by-step explanation:

You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.  

The correct statement is that the middle 50% of personal injury claim costs fall between $989.72 and $1,088.18, which represents the interquartile range. This range and the standard deviation are key in evaluating the distribution of claim costs.

The statement that the middle 50% of the costs are between $989.72 and $1,088.18 is correct in reference to the provided summary statistics of personal injury claims. This range is defined by the first and third quartiles, also known as the interquartile range (IQR). The IQR is a measure of variability and represents the span between the 25th percentile (first quartile) and the 75th percentile (third quartile), which indeed encompasses the middle 50% of data in a given sample.

In the context of personal injury claims costs at your firm, this means that half of the claim costs fall within that range, with fewer costs being less than $989.72 (the lower 25%) and fewer costs being more than $1,088.18 (the upper 25%). This can be useful information for assessing claims costs and preparing for future claims expenses. The provided standard deviation of $89.50 indicates the average amount that claim costs vary from the mean ($1,040.47).

Answer:

[tex](0,0.75) \:or\:(0,\frac{3}{4})[/tex]

Step-by-step explanation:

Hi there!

1) Firstly, connect the points to draw a triangle.

2) From each vertex either with a pair of square or with a software trace a perpendicular line to the opposite side.

3) The concurrent point, i.e. the intersection point of these three altitudes is the orthocenter. Orthocenter means the the right center.

In equilateral triangles the Orthocenter coincides with the Centroid.

4) Finally, the coordinates of the Orthocenter found is (0,0.75)

Answer:

a) [tex]\mu_1 -\mu_2[/tex] parameter of interest.

Where [tex]\mu_1[/tex] represent the mean response for adults

[tex]\mu_2[/tex] represent the mean response for teenegers

b) The best estimate is given by [tex]\bar X_1 -\bar X_2[/tex]

Since the best estimator for the true mean is the sample mean [tex]\hat \mu = \bar X[/tex]

c) The best estimate is given by [tex]\bar X_1 -\bar X_2 =0.225-0.059=0.166[/tex]

d) The 95% confidence interval would be given by [tex]-0.012 \leq \mu_1 -\mu_2 \leq 0.344[/tex]  

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Let group 1 be adults and group 2 be teenagers.

[tex]\bar X_1 =0.225[/tex] represent the sample mean 1

[tex]\bar X_2 =0.059[/tex] represent the sample mean 2

n1 represent the sample 1 size  

n2 represent the sample 2 size  

[tex]s_1 [/tex] sample standard deviation for sample 1

[tex]s_2 [/tex] sample standard deviation for sample 2

SE =0.091 represent the standard error for the estimate

(a) Give notation for the quantity that is being estimated.

[tex]\mu_1 -\mu_2[/tex] parameter of interest.

(b) Give notation for the quantity that gives the best estimate.

[tex]\mu_1 -\mu_2[/tex] parameter of interest.

The best estimate is given by [tex]\bar X_1 -\bar X_2[/tex]

Since the best estimator for the true mean is the sample mean [tex]\hat \mu = \bar X[/tex]

(c) Give the value for the quantity that gives the best estimate.

The best estimate is given by [tex]\bar X_1 -\bar X_2 =0.225-0.059=0.166[/tex]

(d) Give a confidence interval for the quantity being estimated. Assuming 95% of confidence

The confidence interval for the difference of means is given by the following formula:  

[tex](\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex] (1)  

The point of estimate for [tex]\mu_1 -\mu_2[/tex] is just given by:

[tex]\bar X_1 -\bar X_2 =0.225-0.059=0.166[/tex]

We can assume that since we know the standard error the deviations are known and we can use the z distribution instead of the t distribution for the confidence interval.

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]  

The standard error is given by the following formula:

[tex]SE=\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}=0.091[/tex]

Given by the problem

Now we have everything in order to replace into formula (1):  

[tex]0.166-1.96(0.091)=-0.012[/tex]  

[tex]0.166+1.96(0.091)=0.344[/tex]  

So on this case the 95% confidence interval would be given by [tex]-0.012 \leq \mu_1 -\mu_2 \leq 0.344[/tex]  

Final answer:

The quantity being estimated in the study is the difference in mean response to unlearn fear associations between adults and teenagers, denoted by Δμ = μ1 - μ2, where μ1 and μ2 represent the mean responses for adults and teenagers, respectively. This study contributes to understanding how fear associations are formed and unlearned, with implications on evolutionary predisposition towards certain fears.

Explanation:

The quantity being estimated in the study between adolescents and adults regarding their ability to unlearn fear associations tied to a specific sound is captured by the notation Δμ = μ1 - μ2. Here, μ1 represents the mean response for adults, and μ2 represents the mean response for teenagers. In this context, a higher physiological measure indicates less fear, with adults showing a mean response of 0.225 and teenagers showing a mean response of 0.059. The standard error of the estimate provided is 0.091, which helps in understanding the variability or precision of our estimated difference between the two groups' mean responses.

This study hints at the broader theory of preparedness, suggesting that humans are evolutionarily predisposed to easily associate certain stimuli with fear. Notably, the differentiation in fear response unlearning between age groups aligns with observations in social and developmental psychology about the specificity of fear acquisition and the challenges in modify these responses once established, especially during the teenage years.

Answer:

Standard error of the estimate of the difference between the two proportions=0.0259

Step-by-step explanation:

Given that the following data collected in two recent surveys of whether voters in cities A and B favor a ballot proposition in the next election.

City                         A                  B            Total

Sample size          615            585             1200

Favour X               463           403               866

Proportion p         0.7528     0.6889        0.7217

Std error for difference

= [tex]\sqrt{p(1-p)(\frac{1}{n_1} }+ \frac{1}{n_2} \\[/tex]

p =0.7217

1-p = 0.2783

by substituting p and n1 = 615 and n2 = 585 we get

Std error = 0.0259

Standard error of the estimate of the difference between the two proportions=0.0259