Exhibit 11-2 We are interested in determining whether the variances of the sales at two music stores (A and B) are equal. A sample of 25 days of sales at store A has a sample standard deviation of 30, while a sample of 16 days of sales from store B has a sample standard deviation of 20. At 95% confidence, the null hypothesis _____. a. should not be rejected b. should be revised c. should be rejected d. None of these answers are correct.

Answer:

3rd option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{5}{3}[/tex] and c = - 3 , then

y = - [tex]\frac{5}{3}[/tex] x - 3 ← equation of line

Answer:

we use side of triangle to find area and divide by 2 so first one is 15*15+ 8*15/2 225+60=285

Answer:

a) cosA=5/13   b) sinA=12/13

Step-by-step explanation:

Look at the needed angle, then use SOHCAHTOA!

Answer:

cos A = 5/13,  sin A = 12/13

Step-by-step explanation:

Watch the picture for help.

sin A = a/c (According to the picture)

cos A = b/c (According to the picture)

Step-by-step explanation:

Math is a language

say you plant two posts that are 5ft apart and you want to get up to 60ft

right now you've covered 5ft and now have 60 - 5 = 55ft to go.

you plant the next one: 55 - 5 = 50ft to go

instead of subtracting many times and counting hiw many times we've subtracted, we can use division

60ft / 5ft = 12 posts

to verify, you can multiply 5 and 12 which is the same as adding 5 + 5 + 5 + 5 +... + 5 = 5ft x 12 Posts= 60ft in total length

There are 12 posts for 60 feet of straight line fence.

Here,

Given that,

Post are space 5 feet apart.

We have to find number of posts for 60 feet of straight line fence.

What is Division method?

This method of distributing a group of things into equal parts is termed as division.

Now,

We can division method to find number of posts for 60 feet of straight line fence.

Here, Post are space 5 feet apart.

Number of posts = [tex]\frac{60}{5} = 12[/tex]

Hence, There are 12 posts for 60 feet of straight line fence.

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Answer:

[tex]2*\pi *10=62.83185307[/tex]

[tex]20/2 = 10[/tex]

[tex](Radius)[/tex][tex]Or the C = \pi*d[/tex]

62.83185307 is the answer

Answer:

C≈60

Step-by-step explanation:

remember circumference formula

[tex] \displaystyle C = 2\pi r[/tex]

given that,d=20 therefore r would be 20/2=10 thus substitute:

[tex] \displaystyle C = 2\pi .10[/tex]

simplify mutilation:

[tex] \displaystyle C = 20\pi [/tex]

substitute the given value of π:

[tex] \displaystyle C = 20.3[/tex]

simplify multiplication:

[tex] \displaystyle C = 60[/tex]

and we are done!

Answer: t = 5

Step-by-step explanation:

If 2t = 10, then we divide 10 by 2. The answer is 5.

Answer:

The expected dollar value for a person playing this game is -$1, that is, a loss of $1.

Step-by-step explanation:

Expected dollar value:

Probability of each outcome multiplied by it's monetary outcome.

Outcomes:

45% probability of winning $100.

45% probability of losing $100.

10% probability of losing $10.

What is the expected dollar value for a person playing this game?

[tex]E = 0.45*100 - 0.45*100 - 0.1*10 = -1[/tex]

The expected dollar value for a person playing this game is -$1, that is, a loss of $1.

Answer:

The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women

Step-by-step explanation:

Before solving the question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Test if a lower proportion of men favor stricter gun control than women:

At the null hypothesis, we test if the proportion is the same, that is, the difference of the proportions if 0. So

[tex]H_0: p_M - p_W = 0[/tex]

At the alternative hypothesis, we test if it is less, that is, the subtraction of the proportions is negative. So

[tex]H_1: p_M - p_W < 0[/tex]

The test statistic is:

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

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

In a recent survey of gun control laws, a random sample of 564 women, 313 favored stricter gun control laws.

This means that:

[tex]p_W = \frac{313}{564} = 0.555[/tex]

[tex]s_W = \sqrt{\frac{0.555*0.445}{564}} = 0.0209[/tex]

In a random sample of 588 men, 307 favored stricter gun control laws.

This means that:

[tex]p_M = \frac{307}{588} = 0.522[/tex]

[tex]s_M = \sqrt{\frac{0.522*0.478}{588}} = 0.0206[/tex]

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_M - p_W = 0.522 - 0.555 = -0.033[/tex]

[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0206^2+0.0209^2} = 0.029[/tex]

Value of the test statistic:

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

[tex]z = \frac{-0.033 - 0}{0.029}[/tex]

[tex]z = -1.12[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion difference greater than 0.033, which is the p-value of z = -1.12.

Looking at the z-table, z = -1.12 has a p-value of 0.1314.

The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women

Answer:

see below

Step-by-step explanation:

y = x²-8x+ 15

Let x = -2

y = (-2)²-8(-2)+ 15

  = 4 +16 +15

   = 35

Let x = 1

y = (1)²-8(1)+ 15

     1 -8+15

   =8

The vertex is (4,-1)

Answer:

option D

because every length is one fifth of the corresponding length of the bigger triangle

Answer:

y=-1x+5

Step-by-step explanation:

answer

A. - ( -13) = 13

thank. u

Answer:

b

Step-by-step explanation:

A is incorrect cause it would be a negative

C would also be a negative

D is a positive

so yea

Cora, her sister, and four friends. So there are 6 people, 120 candies are divided equally in the bag, so each person gets 20 candies

Each person will get 20 candles.

The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.

Now it is given that,

Number of candles in the bag = 120

Cora, her sister, and four friends are going to share.

So, Number of person = 6

Thus, candles each person gets = Number of candles in the bag / Number of person

⇒ candles each person gets = 120 / 6

⇒ candles each person gets = 20

Thus, each person will get 20 candles.

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Answer:

i got (-10/7, -44/7)

Answer:

7 DAYS IN A WEEK

Step-by-step explanation:

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDA

7 DAYS

Answer:

it depends... What is X in this situation?

Step-by-step explanation:

A week has seven days.

A day has one day..?

I dont know how to help you, Sorry

Answer:

D

Step-by-step explanation:

shaped like a cone

Cone = 1/3

v = 1/3 x 3.14 x 2.5^2 x 4.2

v =27.475

The equation should the artist use to calculate the volume of the

cone is, 4. V=1/3π (2.5)²(4.2)

A cone is a three-dimensional geometric object with a smooth, curved top and a flat base. As a cone's height increases, its radius gradually decreases until it reaches a particular point.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, An artist is making a sculpture shaped like a cone having a radius of 2.5 inches and a height of 4.2 inches.

We know The volume of a cone is (1/3)πr²h.

Therefore, The volume of the cone would be,

= (1/3)π(2.5)²×4.2 cubic inches.

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Answer:

45 mph

251 ft

Step-by-step explanation:

[tex] s = \sqrt{30fl} [/tex]

a.)

[tex] s = \sqrt{30(0.85)(80)} [/tex]

[tex] s = \sqrt{2040} [/tex]

[tex] s = 45 [/tex]

Answer: 45 mph

b.)

[tex] 80 = \sqrt{30(0.85)l} [/tex]

[tex] 80^2 = (\sqrt{25.5l})^2 [/tex]

[tex] 25.5l = 6400 [/tex]

[tex] l = 251 [/tex]

Answer: 251 ft

Answer:

A = $29,201.97

A = P + I where

P (principal) = $20,000.00

I (interest) = $9,201.97

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 9.5/100

r = 0.095 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 20,000.00(1 + 0.095/12)(12)(4)

A = 20,000.00(1 + 0.007916667)(48)

A = $29,201.97

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $20,000.00 at a rate of 9.5% per year compounded 12 times per year over 4 years is $29,201.97

Answer:

[tex] x_{1} = 3 + \sqrt {6} [/tex]

[tex] x_{2} = 3 - \sqrt {6} [/tex]

Step-by-step explanation:

Given the quadratic equation;

x² - 6x + 3 = 0

To find the roots of the quadratic equation, we would use the quadratic formula;

Note: the standard form of a quadratic equation is ax² + bx + c = 0

a = 1, b = -6 and c = 3

The quadratic equation formula is;

[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]

Substituting into the formula, we have;

[tex] x = \frac {-(-6) \; \pm \sqrt {-6^{2} - 4*1*(3)}}{2*1} [/tex]

[tex] x = \frac {6 \pm \sqrt {36 - (12)}}{2} [/tex]

[tex] x = \frac {6 \pm \sqrt {36 - 12}}{2} [/tex]

[tex] x = \frac {6 \pm \sqrt {24}}{2} [/tex]

[tex] x = \frac {6 \pm 2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = \frac {6 + 2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = \frac {6}{2} + \frac {2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = 3 + \sqrt {6} [/tex]

Or

[tex] x_{2} = \frac {6 - 2 \sqrt {6}}{2} [/tex]

[tex] x_{2} = \frac {6}{2} - \frac {2 \sqrt {6}}{2} [/tex]

[tex] x_{2} = 3 - \sqrt {6} [/tex]

Answer:

The rate of change of volume of the cone with respect to radius is [tex]\frac{2}{3}\pi\times rh\\[/tex].

Step-by-step explanation:

radius of come = r

height of cone = h

Volume of cone

[tex]V = \frac{1}{3}\pi\times r^2 h[/tex]

As the height is constant, the rate of change of volume with respect to radius is given by the derivative of volume with respect to radius.  

[tex]\frac{dV}{dr}=\frac{1}{3}\pi\times {2r}h\\\\\frac{dV}{dr}=\frac{2}{3}\pi\times rh\\\\[/tex]

Answer:

A and E

Step-by-step explanation:

There is no solution.

Step-by-step explanation:

Given:

y = 2x + 1

4x - 2y = 4

Substitute y = 2x + 1 into 4x - 2y = 4

4x - 2(2x + 1) = 4

4x - 4x - 2 = 4

0x = 4 + 2

0x = 6

Anything to the multiple of zero is zero. Hence 0x = 0, and 0 ≠ 6

So there is no solution to the equation.

Answer:

snafnjnfnEWfnwenlfnwenflwenlfewfwefư

Answer:3

Step-by-step explanation:

Answer:

90% confidence interval is ( -149.114, -62.666   )

Step-by-step explanation:

Given the data in the question;

Sample 1                                Sample 2

x"₁ = 259.23                            x"₂ = 365.12

s₁  = 34.713                              s₂ = 48.297

n₁ = 5                                       n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

[tex]S_p^2[/tex] = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

[tex]S_p^2[/tex] = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

[tex]S_p^2[/tex] = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [  4 + 9 ]

[tex]S_p^2[/tex] = [ 4819.9692 + 20993.4 ] / [  13 ]

[tex]S_p^2[/tex] = 25813.3692 / 13

[tex]S_p^2[/tex] = 1985.64378

Now the Standard Error will be;

[tex]S_{x1-x2[/tex] = √[ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]

we substitute

[tex]S_{x1-x2[/tex] = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

[tex]S_{x1-x2[/tex] = √[ 397.128756 + 198.564378 ]

[tex]S_{x1-x2[/tex] = √595.693134

[tex]S_{x1-x2[/tex] = 24.4068

Critical Value = [tex]t_{\frac{\alpha }{2}, df[/tex] = [tex]t_{0.05, df=13[/tex] = 1.771  { t-table }

So,

Margin of Error E =  [tex]t_{\frac{\alpha }{2}, df[/tex] × [ ( [tex]S_p^2[/tex] / n₁ ) + ( [tex]S_p^2[/tex] / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666   )

Answer:

B) 12

Step-by-step explanation:

2/7 is the original ratio

7 × 6 = 42

2 × 6 = 12

Answer:

B = 31.6

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan B = opp / adj

tan B = 28.2 / 45.8

taking the inverse tan of each side

tan ^ -1 ( tan B) = tan ^-1 (28.2/45.8)

B =31.62145

Rounding to the nearest tenth

B = 31.6