A rabbit eats turnips and radishes. The number of turnips is four more then twice the number of radishes. Let n represent the number of radishes. Write the expression that gives the number of turnips

Alan made an error in subtracting the x-coordinates without considering their signs. The correct method to find the distance between two points on the same horizontal line is taking the absolute value of the difference of the x-coordinates. Thus, the actual distance from point A to point B is 11 units.

Alan made an error in calculating the distance between point A(-8,-4) and point B(3,-4). The error is in the subtraction, as he should have taken the absolute value of the difference of the x-coordinates of points A and B because the y-coordinates are the same. To find the distance between two points on a coordinate plane, the correct formula when points lie on the same horizontal line (same y-coordinates) is the absolute difference of the x-coordinates. Therefore, the actual distance is calculated as follows:

|x2 - x1| = |3 - (-8)| = |3 + 8| = 11 units

So, the actual distance from point A to point B is 11 units.

Answer:

[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value using the alternative hypothesis is given by:

[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]  

Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge

Step-by-step explanation:

Information provided

4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9

We can find the sample mean and deviation with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]\bar X=3.76[/tex] represent the sample mean

[tex]s=0.241[/tex] represent the sample standard deviation

[tex]n=10[/tex] sample size  

[tex]\mu_o =3.5[/tex] represent the value to check

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

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test  if the new design increased the absorption amount of the sponge (3.5), the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 3.5[/tex]  

Alternative hypothesis:[tex]\mu > 3.5[/tex]  

Since we don't know the deviation the statistic is given by:

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

Replacing the info given we got:

[tex]t=\frac{3.76-3.5}{\frac{0.241}{\sqrt{10}}}=3.407[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

And the p value using the alternative hypothesis is given by:

[tex]p_v =P(t_{(9)}>3.407)=0.0039[/tex]  

Since the p value is lower than the significance level provided of 0.10 we have enough evidence to reject the null hypothesis and we can conclude that the new design increased the absorption amount of the sponge

Answer: 8.5%

Step-by-step explanation:

This is simple interest.

The formula fie finding simple interest is

I = principal × rate × time

-------------------------------

100

I = PRT/100

From the given values,

P = $5,500, T = 4years, R = ?, I = $1,870

Now we shall change the formula which is fundamental or in situ to suit the rate R.we now have

I = PRT

----

100

PRT = I × 100

R. = I × 100

---------

P × T

= 1,870 × 100

---------------

5,500 × 4

= 1,870 × 25

------------

5,500

= 187000/4

-----------

5500

= 46750/5500

= 8.5%

Therefore, the imtetest rate at which the loan was calculated is

8.5%.

Answer:

1) A. H0: μ ≥ 7.2; H1: μ < 7.2

2) D. Reject H0 if z < –1.645

3) [tex]t=\frac{6.2-7.2}{\frac{0.9}{\sqrt{35}}}=-6.573[/tex]  

4) [tex]p_v =P(z<-6.573)=2,47x10^{-11}[/tex]  

Step-by-step explanation:

Information provided  

[tex]\bar X=6.2[/tex] represent the sample mean for the number of movies watched last month

[tex]\sigma=0.9[/tex] represent the population deviation

[tex]n=35[/tex] sample size selected

[tex]\mu_o =7.2[/tex] represent the value that we want to test    

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

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

1) System of hypothesis

We want to check if college students watch fewer movies a month than high school students, and the best system of hypothesis are:

Null hypothesis:[tex]\mu \geq 7.2[/tex]      

Alternative hypothesis:[tex]\mu < 7.2[/tex]      

A. H0: μ ≥ 7.2; H1: μ < 7.2

2) Decision rule

For this case we are ocnduting a left tailed test so then we need to find a critical value in the normal standard distribution who accumulates 0.05 of the area in the left and we got:

[tex]z_{crit}= -1.645[/tex]

And the rejection zone would be:

D. Reject H0 if z < –1.645

3) Statistic

Since we know the population deviation the statistic is given by:

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

Replacing we got:

[tex]t=\frac{6.2-7.2}{\frac{0.9}{\sqrt{35}}}=-6.573[/tex]      

4) P value

We have a left tailed test then the p value would be:      

[tex]p_v =P(z<-6.573)=2,47x10^{-11}[/tex]  

Final answer:

The correct null and alternate hypotheses are H0: μ ≥ 7.2 and H1: μ < 7.2, respectively. Reject the null hypothesis if z < -1.645. The computed test statistic is approximately -7.378, suggesting a p-value near zero and thus, we can conclude that college students watch fewer movies on average.

Explanation:

In order to determine whether college students watch fewer movies a month than high school students, we should set up a hypothesis test comparing the college students' mean number of movies watched to the known population mean for high school students.

Step 1: State the null and alternate hypotheses.

The correct hypotheses would be A. H0: μ ≥ 7.2; H1: μ < 7.2 since we are testing if the college students watch fewer movies, which is a one-tailed test.

Step 2: State the decision rule.

The correct decision rule at the 0.05 significance level for a left-tailed test would be D. Reject H0 if z < – 1.645.

Step 3: Calculate the test statistic.

Using the formula for the z-test, z = (sample mean - population mean) / (population standard deviation / √ sample size), we calculate z = (6.2 - 7.2) / (0.9 / √35) ≈ – 7.378. Thus, the test statistic z is approximately -7.378.

Step 4: Find the p-value.

With a z-score as extreme as – 7.378, the p-value is near zero, implying strong evidence against the null hypothesis.

Answer:

  π/2 or 1.57 square units

Step-by-step explanation:

The area of a sector with central angle θ is given by the formula ...

  A = (1/2)r²θ

Filling in the given value, we find the area to be ...

  A = (1/2)(3²)(π/9) = π/2 . . . . square units

Using 3.14 for π, this is ...

  A = 3.14/2 = 1.57 . . . . square units

Answer:

f(x) + g(x)  =  -2x^2 - 2x + 8

Step-by-step explanation:

Given:  f(x) = 3x+5 and g(x) = -2x^2-5x+3

Find  f(x) + g(x)

f(x) + g(x)  = 3x + 5 + (-2x^2 - 5x + 3)

f(x) + g(x)  =  5 + -2x^2 - 2x + 3

f(x) + g(x)  =  -2x^2 - 2x + 8

Answer:

  (f+g)(x) = -2x^2 -2x +8

Step-by-step explanation:

(f+g)(x) = f(x) +g(x)

  = (3x +5) +(-2x^2 -5x +3)

(f+g)(x) = -2x^2 -2x +8

Answer:

both

Step-by-step explanation:

Answer:

The number is 30

Step-by-step explanation:

Let x be the number

2/3 x = 20

Multiply each side by 3/2 to isolate x

3/2 *2/3x = 20*3/2

x = 30

Answer:

[tex]Length\hspace{3}of\hspace{3}the\hspace{3}beam=y=21.3ft[/tex]

Step-by-step explanation:

Look the picture I attached you. As you can see the beam against the wall form a right triangle. The trigonometry functions on a right triangle are:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\hspace{10}csc(\theta)=\frac{hypotenuse}{opposite}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\hspace{10}sec(\theta)=\frac{hypotenuse}{adjacent} \\\\tan(\theta)=\frac{opposite}{adjacent} \hspace{20}cot(\theta)=\frac{adjacent}{opposite}[/tex]

The problem give us the following data:

[tex]y=9sec(\theta)[/tex]

Using the previous information about the trigonometry functions on a right triangle and the data provided by the problem you can conclude:

[tex]y=Hypotenuse\\Adjacent=9\\\theta=65^{\circ}[/tex]

Therefore:

[tex]y=9sec(65^{\circ})=9*(2.366201583)=21.29581425\approx21.3ft[/tex]

The length of the beam for the given situation is 21.3 ft.

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles.

Here, given function

y = 9. sec θ

put, θ = 65⁰

then, y = 9 X sec 65⁰

        y = 9 X 2.366

        y = 21.294 ft. ≈ 21.3 ft.

Thus, the length of the beam for the given situation is 21.3 ft.

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Answer:

10,000

Step-by-step explanation:  

10 x 10 = 100 when you do the power of 2, you multiply that number by itself.

Answer:

8x = 24

Step-by-step explanation:

[tex]x = \text{The fabric he used to make the seat cover}[/tex]

Then, since he used 8 times as much fabric to make the tent then

[tex]\text{Fabric needed for the tent} = 8x = 24[/tex]

Therefore your equation would be [tex]8x = 24[/tex]

To find the amount of fabric Carl used for the seat cover, the equation is 8x = 24. The variable x represents the amount of fabric for the seat cover, and 24 is the total yards of fabric used for the tent.

Carl used some fabric to make a seat cover. Then he used 8 times as much fabric to make a tent. He used 24 yards for the tent. To write an equation to represent this situation, let's designate the amount of fabric used for the seat cover as x.

According to the problem statement, the tent required 8 times more fabric than the seat cover. Therefore, we can write the equation as:

8x = 24

Where:

This equation can now be solved to find out the amount of fabric Carl used to make the seat cover.

you will need

2 gallons lime soda

1 gallon icecream

and 4 gallons lemonade

Answer:

1.12 meters

Step-by-step explanation:

Answer:

1.12

Step-by-step explanation:

each week it grows 0.16 m

so,in 7 weeks it will grow 0.16*7m

Answer:

you live on the 21st floor

Step-by-step explanation:

46-4=42 (level -2 to ground level)

42÷2=21

You first calculate the sample mean, or μ_bar, of the data. Given it's a Poisson distribution, the mean is equal to the variance, giving your standard deviation. Finally, for a 95% CI, you apply the Z score to the formula μ_bar ± Z*(sqrt(μ_bar/n)) to obtain your confidence interval.

The subject is related to Poisson distribution and the calculation of a confidence interval (CI) for the population mean (µ).

Firstly, we calculate the sample mean that is the total number of instances divided by the number of days:

This gives us the sample mean, µ_bar.

Given the data follows a Poisson distribution, the mean and the variance are equal (µ = variance). For a Poisson distribution, the variance is equal to µ divided by n, hence we get the standard deviation as sqrt(µ/n).

For a 95% CI, Z = 1.96 (from the standard normal table). Our CI will therefore be µ_bar ± Z*(sqrt(µ_bar/n)).

Since n is large, the distribution can be assumed to be approximately normal and the CI can be treated as reliable.

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To calculate a 95% confidence interval for a Poisson distributed data set, first calculate the sample mean. Consider the variance of Poisson equals to its mean, the standard error would be square-root of (mean divided by sample size). Using z-score of ±1.96 for 95% confidence level, solve for mean in both inequalities will give the interval.

The question pertains to deriving a 95% confidence interval for the mean (µ) of a Poisson distributed data set. In this case, the data set provided represents the number of teacher absences in a school district over 50 days.

Firstly, you will need to calculate the sample mean by multiplying each absence by its frequency, sum those up, then divide the sum by the total number of observations. This serves as an estimator for the Poisson mean µ.

Considering that the variance of a Poisson variable equals to its mean µ. The standard error would then be √(µ/n), where n is the number of observations. For a 95% interval, Z should be approximately ±1.96.

The confidence interval can be calculated using the standard formula for a large sample size:

Z = ±1.96 = (X - µ)/√(µ/n)

Solving for µ in both inequalities will give you the confidence interval.

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Answer:

percentage error = 11.11 %

Step-by-step explanation:

Brandon poured w hat he estimated to be 32 ounces of oil into his car's engine . He later determined that he has actually poured 36 ounces from the marking on the container . The percentage error is computed below.

percentage error = approximate value - exact value/exact value × 100

approximate value = 32 ounces

exact value = 36 ounces

percentage error = |32 - 36| / | 36 | × 100

note we used the absolute value to eliminate negative signs

percentage error = 4/36 × 100

percentage error = 400/36

percentage error = 11.11 %

Answer:

[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]    

[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]

3.49 < u < 4.37

Step-by-step explanation:

Data provided

3.6​, 3.1​, 4.0​, 4.9​, 3.0​, 4.3​, 3.6​, 4.6​, 4.6​, 4.0​, 4.4​, 3.6​, 3.3​, 4.2​, 3.7

The sample mean and deviation can be calculated with the following formulas

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex]

[tex]\bar X=3.93[/tex] represent the sample mean

[tex]\mu[/tex] population mean

s=0.574 represent the sample standard deviation

n=15 represent the sample size  

Confidence interval

The confidence interval for the true mean is given by:

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

The degrees of freedom, given by:

[tex]df=n-1=15-1=114[/tex]

The Confidence is 0.99 or 99%, the significance is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical value would be[tex]t_{\alpha/2}=2.977[/tex]

Replacing we got:

[tex]3.93-2.977\frac{0.574}{\sqrt{15}}=3.49[/tex]    

[tex]3.93+2.977\frac{0.574}{\sqrt{15}}=4.37[/tex]

3.49 < u < 4.37

Answer:

y=50x

Step-by-step explanation:

For every additional 2 hours (x), there are 100 bricks laid.

This means the slope is 50 (100/2)(200/4)etc.

50*2=100

50*4=200

50*6=300

50*8=400

Answer:

Step-by-step explanation:

Answer:

272

Step-by-step explanation:

Answer:

is D

Step-by-step explanation:

for egny

Principal Balance: 2000

Compound Interest: 3%

Type: Yearly

2000 x 1.03 = 2060

Year 1 : £2060

2060 x 1.03 = 2121.8

Year 2: £2121.8

There will be £2,121.80 in the account after 2 years.

Answer:okStep-by-step explanation:

Answer:

b 2.50 per 2 bottles of sprite

Step-by-step explanation:

Answer:

The answer is B.

2.50 per 2 bottles of sprite

Step-by-step explanation:

Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for detailed and step by step solution of the given problem.

a. The critical number of f is -5

b. The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).

c.  There is no relative extremum at x = -5.

d. Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).

(a) To find the critical numbers of the function,  find where the derivative is 0 or undefined.

To find the derivative of f(x):

[tex]f'(x) = (2/3)(x + 5)^(-1/3)[/tex]

The derivative is undefined at x = -5, since[tex](x + 5)^(1/3)[/tex] would be 0 in the denominator.

So -5 is a critical number of f.

(b) To find the intervals on which the function is increasing or decreasing,  examine the sign of the derivative on each interval.

Since f'(x) is always positive (except at x = -5, where it is undefined),

The function is increasing on the interval (-5, infinity) and decreasing on the interval (-infinity, -5).

(c) To apply the First Derivative Test, look at the sign of the derivative near the critical point x = -5.

The derivative is undefined at x = -5, so the test is not applicable

Therefore, there is no relative extremum at x = -5.

Since f(x) is increasing for x > -5 and decreasing for x < -5, there is no relative minimum or maximum in the interval (-infinity, infinity).

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Answer:

The answer is 16 ft

Step-by-step explanation:

The shape with the smallest possible perimeter for a given area is a circle but among quadrilaterals, it's a square. Given an area of 15 square feet, the length of each side of the square would be approximately 3.87 feet, and the perimeter would be approximately 15.49 feet.

The disciplines specified here is Mathematics, and the question is related to the correlation between an area and perimeter of a shape. In this case, the shape with the smallest possible perimeter for a given area would be a circle. However, if we only examine quadilateral shapes, then the shape with the minimum possible perimeter would be a square because a square is the quadrilateral that has the maximum area for a given perimeter.

If the area of the square is 15 square feet, then you can determine each side of the square by taking the square root of the area. The square root of 15 is approximately 3.87 feet. Now, to determine the perimeter of the square, you multiply this value by 4 because a square has four sides of equal length, hence perimeter is ~15.49 feet.

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Answer:

x = 5 (check the diagram included)

Step-by-step explanation:

The question is incomplete, I have included a diagram to aid the understanding of the question

Parallelograms are quadrilaterals which have their opposite sides parallel and equal. This also means that the opposite angles in a parallelogram are equal

From the attached figure, we have:

|FG| = 3x + 10, |HE| = 7x - 30

To calculate for the value of x that makes the quadrilateral a parallelogram, we have:

Remember the opposite sides of a parallelogram are equal

3x + 10 = 7x - 30

3x - 7x = 10 - 30

-4x = -20

x = 20 ÷ 4

x = 5

x = 5 makes the quadrilateral a parallelogram

Answer:

[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]  

[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]  

We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]  

Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs

Step-by-step explanation:

Information given

[tex]p_1[/tex] represent the real population proportion of males with tattoos

[tex]\hat p_1 =\frac{190}{1231}=0.154[/tex] represent the estimated proportion of males with tattos

[tex]n_1=1231[/tex] is the sample size for males

[tex]p_2[/tex] represent the real population proportion of female with tatto

[tex]\hat p_2 =\frac{143}{1067}=0.134[/tex] represent the estimated proportion of females with tattos

[tex]n_2=1067[/tex] is the sample size of female

[tex]z[/tex] represent the critical value

Confidence intrval

The confidence interval for the difference of two proportions would be given by this formula  

[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]  

For the 90% confidence interval the value of [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2=0.05[/tex], and the critical value for this case would be:  

[tex]z_{\alpha/2}=1.64[/tex]  

Replacing the info given we got:

[tex](0.154-0.134) - 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=-0.00402[/tex]  

[tex](0.154-0.134) + 1.64 \sqrt{\frac{0.154(1-0.154)}{1231} +\frac{0.134(1-0.134)}{1067}}=0.044[/tex]  

We are confident at 95% that the difference between the two proportions is [tex]-0.00402 \leq p_1 -p_2 \leq 0.044[/tex]  

Since the confidence interval contains the value 0 we can conclude that at 10% of significance we don't have enough evidence to conclude that the true proportions for female and male with tattos differs

Answer:

In geometry, the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

Step-by-step explanation:

Answer:

In geometry, the  theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

Step-by-step explanation:

Answer:

82 divided by 5 = 16.4

Step-by-step explanation:

you divide 82 by 5 and get 16.4 or 82 divided by 10= 8.2

They do first they split up the ten bills and it is 8.0.

We have given that,

Five friends are sharing 82 dollars they keep a record

82 divided by 5

[tex]\frac{82}{5} = 16.4[/tex]

You divide 82 by 5 and get 16.4,

After the split up to ten bills is given by,

A split is a situation in a particular frame of a ten-pin bowling game where the player throws the ball and knocks the headpin

82 divided by 10

[tex]\frac{80}{10} =8.0[/tex]

They do first they split up the ten bills.

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