A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds that the data was normally distributed and average jail time was 15.5 months with a standard deviation of 5.7 months. Is the reported claim correct? (use a 0.05 level of significance)

Answer:

[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]  

Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges

Step-by-step explanation:

Data given

[tex]\bar X_{1}=15[/tex] represent the mean for sample A

[tex]\bar X_{2}=20[/tex] represent the mean for sample B  

[tex]s_{1}=5[/tex] represent the sample standard deviation for A

[tex]s_{f}=4[/tex] represent the sample standard deviation for B  

[tex]n_{1}=500[/tex] sample size for the group A

[tex]n_{2}=400[/tex] sample size for the group B  

[tex]\alpha=0.01[/tex] Significance level provided

t would represent the statistic

System of hypothesis

The system of hypothesis is the true difference in the time students spent for online assignments between the two colleges, the system of hypothesis would be:  

Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]  

Alternative hypothesis:[tex]\mu_{1} - \mu_{2}\neq 0[/tex]  

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

[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)  

The degrees of freedom are given by [tex]df=n_1 +n_2 -2=500+400-2=898[/tex]  

Replacing the info given we got:

[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]  

Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges

The cost of the fabric per yard is approximately $6.39.

To find the cost of the fabric per yard, we need to first calculate the cost per foot and then convert it to yards.

Step 1: Calculate the cost per foot of fabric.

[tex]Cost per foot = Total cost / Total feet[/tex]

[tex]Cost per foot = $9.60 / 4.5 feet[/tex]

[tex]Cost per foot = $2.13[/tex]

Step 2: Convert the cost per foot to cost per yard.

Since there are 3 feet in a yard, we can find the cost per yard by multiplying the cost per foot by 3.

[tex]Cost per yard = Cost per foot * 3[/tex]

[tex]Cost per yard ≈ $2.13 * 3[/tex]

[tex]Cost per yard = $6.39[/tex]

Complete correct question:

Alvin makes pillows for his room he buys 4.5 feet of fabric for 9.60 what is the cost of the fabric per yard?

Answer:

13/15

Step-by-step explanation:

First, you find a common denominator. 10 x 3 and 6 x 5 both equal 30, so 30 can be used as a common denominator. You also have to multiply the numerator by the same number you multiplied in the denominator. Since we did 10 x 3, do 7 x 3, and with the other fraction we did 6 x 5, so do 1 x 5. You should get 21/30 + 5/30. Since they have the same denominator, you can add them. You'll get 26/30, which can still be simplified. 30 divided by 2 is 15, and 26 divided by 2 is 13. The final answer is 13/15.

Answer:

gergverkngvneropgeronhnernih[eh[neirvhier,hn[eriin[hnerohper'her

Step-by-step explanation:

Answer:

Common Examples of Negative Correlation. A student who has many absences has a decrease in grades. As weather gets colder, air conditioning costs decrease. If a train increases speed, the length of time to get to the final point decreases.

Answer:

The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]

Step-by-step explanation:

Suppose we have a quadratic equation in the following format:

[tex]y = f(x) = ax^{2} + bx + c[/tex]

The vertex of the function is the point [tex](x_{v}, f(x_{v})[/tex], in which

[tex]x_{v} = -\frac{b}{2a}[/tex]

In this problem:

[tex]f(x) = x^{2} - x + 2[/tex]

This means that [tex]a = 1, b = -1, c = 2[/tex]

So

[tex]x_{v} = -\frac{-1}{2} = \frac{1}{2}[/tex]

[tex]f(x_{v}) = f(\frac{1}{2}) = (\frac{1}{2})^{2} - \frac{1}{2} + 2 = \frac{1}{4} - \frac{1}{2} + 2 = \frac{1 - 2 + 8}{4} = \frac{7}{4}[/tex]

The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]

Answer:

116°

Step-by-step explanation:

Given that :

∠ ABD measures (4x + 10)

∠ ACD measures  (5x - 2)

Then

∠ABD = ∠ACD  ( rule : angle by same chord AD )

∠ABD =   (4x + 10)°

∠ACD =   (5x - 2)°

so we can as well say that :

(4x + 10)° = (5x - 2)°

4x - x = -10 -2

- x = - 12

x   = 12

∠ABD = (4x + 10)°

= ( 4 × 12 + 10)°

= 58°

∠ACD = (5x - 2)°

= ( 5 * 12 - 2)°

= 58°

∠AOD = 2∠ABD = 2∠ACD   ( since angle by arc AD at  center is  twice the  angle by same arc AC in other arc segment)

 ∠AOD =  2 × 58°

∠AOD = 116°

Measure of arc AD = 116°

Answer:

4

Step-by-step explanation:

n/6+2

Let n = 12

12/6 +2

Division first

2 +2

4

Answer:

4

Step-by-step explanation:

plug in 12 for n and you get :: 12/6 + 2

PEMDAS says to divide first, 12/6 is 2. you add 2 next and you get 4

thank me and rate me 5 pls :)

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

a) For the null hypothesis,

P = 0.55

For the alternative hypothesis,

P > 0.55

Considering the population proportion, probability of success, p = 0.55

q = probability of failure = 1 - p

q = 1 - 0.55 = 0.45

Considering the sample,

Probability of success, P = 0.62

Number of samples, n = 1810

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.62 - 0.55)/√(0.55 × 0.45)/1810 = 5.98

Since this is a right tailed test, the critical value would be the p value to the right of z = 5.98

p value = 0.00001

Since alpha, 0.02 > than the p value, 0.00001, then we would reject the null hypothesis.

Using the critical value approach, By using the critical region method,

the calculated test statistic is 5.98 for the right tail and - 5.98 for the left tail

Since α = 0.02, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.02/2 = 0.01

The z score for an area to the left of 0.01 is - 2.325

For the right, α/2 = 1 - 0.01 = 0.99

The z score for an area to the right of 0.995 is 2.325

In order to reject the null hypothesis, the test statistic must be smaller than - 2.325 or greater than 2.325

Since - 5.98 < - 2.325 and 5.98 > 2.325, we would reject the null hypothesis.

Therefore, it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%.

Answer:

solve for x

x   ≤  −  7

Answer:

C=2πr

Step-by-step explanation:

Answer:

a) At least 842 adults must be surveyed.

b) At least 1068 adults must be surveyed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

a) 73% of adults used the Internet.

At least n adults must be surveyed.

n is found when [tex]M = 0.03, \pi = 0.73[/tex]

So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.73*0.27}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.73*0.27}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.73*0.27}}{0.03}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.73*0.27}}{0.03})^{2}[/tex]

[tex]n = 841.3[/tex]

Rounding up

At least 842 adults must be surveyed.

b. No known possible value of the proportion.

Same as above, the difference as the since we do not know the value of the proportion, we use [tex]\pi = 0.5[/tex], which is when the largest sample size is going to be needed.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.5*0.5}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.5*0.5}}{0.03}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.5*0.5}}{0.03})^{2}[/tex]

[tex]n = 1067.11[/tex]

Rounding up

At least 1068 adults must be surveyed.

To be 95% confident that the sample percentage of U.S. adults who use the Internet is in error by no more than 3 percentage points, a total of 1068 adults must be surveyed.

To estimate the current percentage of U.S. adults who use the Internet with a 95 percent confidence level and an error margin of no more than three percentage points, we must determine the sample size we need to survey. We'll follow the formula below for estimating the sample size:

n = (Z² * p(1-p)) / E^2

Where n is the sample size, Z is the z-score associated with our desired confidence level (for a 95% confidence level, Z is about 1.96), p is the estimated proportion of the population (based on the 2006 data, we'll use 0.73), and E is the margin of error (which we want to be 0.03).

Plug in the values:

n = (1.96² * 0.73 * 0.27) / 0.03² = 1067.14

Since we cannot survey a fraction of a person, we round up to the next whole number. Therefore, the manager would need to survey 1068 adults in order to be 95 percent confident that the sample percentage is in error by no more than three percentage points.

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Answer:

H0:μ=10.6

Ha:μ≠10.6

Step-by-step explanation:

you do not find out about the 12.9 until after stating the hypothesis.

The correct hypothesis set for testing whether the mean number of sick days has changed is H0: μ = 10.6 against Ha: μ ≠ 10.6, which represents a two-tailed test.

The correct set of hypotheses for the city administrator to test whether the mean number of sick days this year is

different from last year would be:

This is because the administrator is investigating if there is a change in either direction (increase or decrease), which is

considered a two-tailed test.

The null hypothesis (H0) always states that there is no difference or no effect, while the alternative hypothesis (Ha)

suggests that there is a difference from the norm, in that the mean is not equal to 10.6 days.

Based on the information given, the correct answer would be:

B. H0: μ = 10.6
Ha: μ ≠ 10.6

Answer:

Substitute the slope and the coordinate of D into the equations and solve for b for each equation

Step-by-step explanation:

The equation for a line is y = mx+b

where m is the slope and b is the y intercept

We know m

We have a point (x,y)

We can substitute into the equation and solve for b

Answer:

First option

Step-by-step explanation:

In y = mx + b, m is the slope and b is the y-intercept

Plug in m, and coordinates of D and solve for b

Answer:

They now should survey 800 people.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem:

Same level of confidence, so same z

Same proportion, so same [tex]\pi[/tex]

We have to change n

We want to reduce the margin of error by half.

M is inverse proportion to the square root of n. That is, as n increases, M decreases.

We want to decrese M by half. So we need to increase n by a factor of 2^2 = 4

The first survey had a sample of 200 people

Increasing by a factor of 4.

200*4 = 800

They now should survey 800 people.

Answer:

Step-by-step explanation:

Lines A B, C D, and D P intersect at point P. Angle A P C is 65 degrees, Angle C P E is blank, angle E P B is 90 degrees, and angle B P D is blank.

Determine the measures of the unknown angles in the figure.

m∠APD =  

✔ 115°

m∠CPE =  

✔ 25°

m∠BPD =  

✔ 65°

The measure of unknown angles

m∠APD = 115

m∠CPE = 25

m∠BPD = 65

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. They are also referred to as additional angles. Angles that share a vertex are said to be neighbouring. Hence, the linear angles have a common vertex in this instance as well.

Using Linear Pair

<APC + <CPE + <EPB = 180

65 + <CPE + 90 = 180

<CPE = 180 - 155

<CPE = 25

So, <APD = 90 + 25 = 115 degree

<CPE = 25 degree

<BPD = <APC = 65 degree (Vertically opposite angle)

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Answer:

  14 units

Step-by-step explanation:

Both points lie on the vertical line x=32, so the distance between them is the difference of their y-coordinates:

  29 -15 = 14 . . . . units

The two points are 14 units apart.

Answer:

[tex] d = \sqrt{(32-32)^2 +(15-29)^2} = \sqrt{196}= 14[/tex]

So then we can conclude that the smallest distance between the point A (32,15) and the point B(32,39) is 14

Step-by-step explanation:

When we have a two points on a dimensional space A and B we can find the distance between the two points with the following formula:

[tex] d= \sqrt{(x_A -x_B)^2 +(y_A -y_B)^2}[/tex]

Where (x_A,y_A) represent the coordinates for the point A and (x_B,y_B) represent the coordinates for the point B. And we know that the coordinates are :

A= (32,15) and B= (32,29)

And replacing in the formula for the distance we got:

[tex] d = \sqrt{(32-32)^2 +(15-29)^2} = \sqrt{196}= 14[/tex]

So then we can conclude that the smallest distance between the point A (32,15) and the point B(32,39) is 14

Answer:

Step-by-step explanation:

.7104

The probability that the difference in sample means (males – females) is greater than 20 cm is; 0.7088

The formula for z-score of difference between two means is;

z = (x₁' - x₂' - Δ)/√[(√σ₁²/n₁) + (σ₂²/n₂)]

We are given;

Sample mean 1; x₁' = 180 cm

Sample mean 2; x₂' = 158 cm

Standard deviation 1; σ₁ = 7 cm

Standard Deviation 2; σ₂ = 9 cm

hypothesized difference; Δ = 20 cm

Sample size; n₁ = n₂ = 10

Thus;

z = (180 - 158 - 20)/√[(7²/10) + (9²/10)]

z = 0.55

From online z-score table, we have;

p = 0.71

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Answer: player A = 11/16 and player B = 5/16

Step-by-step explanation:

If a coin was to be tossed to determine the winner possible outcomes using arithmetical triangle.

Player A needs 2 points = 11

Player B needs 3 points = 5

Total outcome of tossing a coin = 16

Player A = 11/16 = 0.6875

Player B = 5/16 = 0. 3125

Or

Using the fifth roll of the pascal triangle (2+3) outcome

( 1, 4, 6, 4, 1 )

Addition of the first 3 represent Player A chances of winning = ( 1+ 4 + 6 ) = 11

And the last two = ( 1 + 4 ) = 5 represents the chances of team B winning

Total number of outcome = ( 1 + 4 + 6 + 4 + 1 ) = 16

Answer:

The forumula for finding area of the circle is  \pi r^2.

Step-by-step explanation:

Let's find the radius of the mug:

r=\frac{d}{2}=\frac{8}{2}=4

Now, we can to express the area of each cookie in terms of pi:

Area= \pi *4^2=16\pi

Answer:

29.3

Step-by-step explanation:

For Ice-cream Cone

height (h) = 7 cm

diameter (d) = 4 cm

radius (r) = diameter/2 = 4/2 cm

radius (r) = 2 cm

Volume Of A Cone

= π * r^2 * h/3

= 22/7 * 2 * 2 * 7/3

= 22 * 4 * 1/3 cm

= 88/3 cm

= 29.3 cm^3

Thus, the Volume of the cone would be 29.3 cm^3

Answer:

The correct option is option 2.

Step-by-step explanation:

In this case we need to test whether the previous data for the proportion of Americans who favored mandatory testing of students in public schools as a way to rate the school has decreased this year or not.

The hypothesis can be defined as follows:

H₀: The proportion supporting mandatory testing is not less than 74% this year, i.e. p ≥ 0.74.

Hₐ: The proportion supporting mandatory testing is less than 74% this year, i.e. p < 0.74.

It is provided that the p-value of the test is,

p-value = 0.015

The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

The p-value of 0.015 or 1.5% implies that, if it is true that 74% of Americans still favor mandatory testing this year, then the probability that the poll results will show that 71% or less with the same opinion is 1.5%.

Thus, the correct option is option 2.

Answer:

L = 2 m

The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m

Step-by-step explanation:

Given;

Speed of sound v = 340 m/s

Frequency of sound f = 170 hz

The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is;

Length L = v/f = speed/frequency

L = 340/170

L = 2 m

The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m

Answer:

its 6

just simplify the expression.

-Hops

Answer: 6

Divide

18÷9=2

Multiply

2×3=6

Answer:

63.

Step-by-step explanation:

To solve this equation, we will first need to multiply both sides by 8 to get rid of the coefficient:

8×[tex]\frac{1}{8}[/tex](x-56)=[tex]\frac{7}{8}[/tex]×8

Now, this will get rid of the fractions, giving us:

x-56= 7

Next, simply add 56 to both sides:

x-56+56= 7+56

This results in:

x=63.

Answer:

Step-by-step explanation:

Originally, there were 47 ducks.  After the dog jumped in, there were 29.  This means there were 18 ducks.

47 - 29 = 18

After the dog got out 5 groups of 3 ducks came.  This means that 15 ducks came back.

5 × 3 = 15

To find the total amount of ducks, add the ducks together.

18 + 15 = 33

To find the number of ducks remaining in the pond, subtract the 29 ducks scared away from the initial 47, then add the 15 ducks that returned in 5 groups of 3, resulting in 33 ducks now present in the pond.

The student has asked a question related to a basic arithmetic problem involving ducks in a pond. Initially, there were 47 ducks in the pond. A dog scares 29 ducks away. After the dog leaves, 5 groups of 3 ducks each return to the pond. To solve this, we perform two main steps:

Answer: it will trave 56.89 meters before coming to rest.

Step-by-step explanation:

This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as

S = a/(1 - r)

where

S = sum of the distance travelled by the ball

a = initial distance or height of the ball

r = common ratio

From the information given,

a = 128/9

r = (32/3)/(128/9) = 0.75

Therefore,

S = (128/9)/(1 - 0.75) = 56.89 meters

The distance travelled is an illustration of the sum to infinity of a geometric sequence.

The ball will a travel 56.89 meters before coming to rest

The sequence is given as:

[tex]\mathbf{128/9, 32/3, 8, 6....}[/tex]

From the sequence above, we have:

[tex]\mathbf{a = 128/9}[/tex] --- the first term

[tex]\mathbf{r = 6/8 = 3/4}[/tex] -- the common ratio

The sum to infinity of a geometric progression is:

[tex]\mathbf{S_{\infty} = \frac{a}{1-r}}[/tex]

So, we have:

[tex]\mathbf{S_{\infty} = \frac{128/9}{1-3/4}}[/tex]

[tex]\mathbf{S_{\infty} = \frac{128/9}{1/4}}[/tex]

Divide

[tex]\mathbf{S_{\infty} = \frac{128}{9} \times 4}[/tex]

[tex]\mathbf{S_{\infty} = \frac{128\times 4}{9} }[/tex]

[tex]\mathbf{S_{\infty} = \frac{512}{9} }[/tex]

[tex]\mathbf{S_{\infty} = 56.89}[/tex]

Hence, the ball will a travel 56.89 meters before coming to rest

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Answer:

a) [tex]\mu = 3500 gr, \sigma = 500g[/tex]

[tex]X \sim N(\mu =3500, \sigma =500)[/tex]

b) For this case we want to find this probability:

[tex] P(X< 3110)[/tex]

And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.

c) For this case the z score is defined as:

[tex] z =\frac{X-\mu}{\sigma}[/tex]

And replacing we got:

[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]

And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8

d) We can find this probability using the normal standard distribution or excel and we got:

[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]

Step-by-step explanation:

For this problem we define the random variable of interest X defined as "the birth weigth of babies" and the distribution for this variable is normal

Part a

The parameters are given:

[tex]\mu = 3500 gr, \sigma = 500g[/tex]

[tex]X \sim N(\mu =3500, \sigma =500)[/tex]

Part b

For this case we want to find this probability:

[tex] P(X< 3110)[/tex]

And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.

Part c

For this case the z score is defined as:

[tex] z =\frac{X-\mu}{\sigma}[/tex]

And replacing we got:

[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]

And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8

Part d

We can find this probability using the normal standard distribution or excel and we got:

[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]

Answer:

56

Step-by-step explanation:

Just took the quiz

Hope this helps!

Answer:

The volume of the sphere is 972π mm³

Step-by-step explanation:

To calculate the volume of a sphere we have to use the following formula:

V = volume

r = radius  = 9mm

π = pi

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * π * (9mm)³

V = π * ⁴⁄₃ *729mm³

V = π * 972mm³

V = 972π mm³

The volume of the sphere is 972π mm³

Answer:

Step-by-step explanation: Opposite sides of a parallelogram are equal.

Answer:

The opposite sides of the parallelogram have equal lengths.

Step-by-step explanation:

PLATO SAMPLE