1. Ryan budgets $35 a week for lunch for 5 days. What
is his average lunch expense each day?

Answer:

a) CI = (113,637.5  ,  124,672.5)

b) CI = (112,581  ,  125,729)

c) CI = (110,501.4  ,  127,808.6)

Step-by-step explanation:

You have the following information:

[tex]\overline{x}[/tex]: mean annual household income = 119,155

σ: standard deviation = 30,000

n: sample = 80

The interval of confidence is given by the following expression:

[tex]\overline{x}\pm Z_{\alpha/s}(\frac{\sigma}{\sqrt{n}})[/tex]

Z_α/2: distribution density factor

where α and Z_α/2 are given by the range of the confidence interval.

a) For a 90% confidence interval you have:

α = 1 - 0.9 = 0.1

Z_0.1/2 = Z_0.05 = 1.645   (found in a table of normal distribution)

You replace in the equation (1) to obtain the confidence interval:

[tex]119,155\pm (1.645)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm5,517.5[/tex]

Then, the confidence interval is (119,155 + 5,517.5 , 119,155 - 5,517.5  )

= (113,637.5  ,  124,672.5)

b) For a 95% confidence interval you have:

α = 1 - 0.95 = 0.05

Z_0.05/2 = Z_0.025 = 1.96

[tex]119,155\pm (1.96)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 6,574.0[/tex]

The confidence interval is (112,581  ,  125,729)

c) For a 99% confidence interval:

α = 1 - 0.99 = 0.01

Z_0.01/2 = Z_0.005 = 2.58

[tex]119,155\pm (2.58)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 8,653.6[/tex]

The confidence interval is (110,501.4  ,  127,808.6)

d) When the confidence level increases the width of the confidence increases too. This can be noticed in the normal distribution, when the confidence level is higher, the area of the tails is reduced, and so, the confidence interval is higher.

Answer:

D is 10

b/12

Step-by-step explanation:

Answer:

Both F and Z have symmetry.

Answer:

87°

Step-by-step explanation:

In the given figure, a quadrilateral is inscribed in a circle. Therefore, it is a cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

[tex] \therefore \: z + 93 \degree = 180 \degree \\ \therefore \: z = 180 \degree - 93 \degree \\ \huge \red{ \boxed{\therefore \: z = 87 \degree}}[/tex]

Answer:

#1

Step-by-step explanation:

The four yellow boxes represent x so together they are 4 * x or 4x. The blue boxes seem to represent -1 and since there are three of them together they are -1 * 3 = -3. 4x + (-3) = 4x - 3.

Answer: choice B

Step-by-step explanation:

The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x-axis.

Answer: B

Step-by-step explanation:

Answer:

a) H0: [tex]\sigma = 1.34[/tex]

H1: [tex]\sigma \neq 1.34[/tex]

b) [tex] df = n-1= 10-1=9[/tex]

And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:

[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]

c) [tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]

d) For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34

Step-by-step explanation:

Information provided

n = 10 sample size

s= 1.186 the sample deviation

[tex]\sigma_o =1.34[/tex] the value that we want to test

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

t represent the statistic  (chi square test)

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

Part a

On this case we want to test if the true deviation is 1,34 or no, so the system of hypothesis are:

H0: [tex]\sigma = 1.34[/tex]

H1: [tex]\sigma \neq 1.34[/tex]

The statistic is given by:

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

Part b

The degrees of freedom are given by:

[tex] df = n-1= 10-1=9[/tex]

And the critical values with [tex]\alpha/2=0.005[/tex] on each tail are:

[tex] \chi_{\alpha/2}= 1.735, \chi_{1-\alpha/2}= 23.589[/tex]

Part c

Replacing the info we got:

[tex] t=(10-1) [\frac{1.186}{1.34}]^2 =7.05[/tex]

Part d

For this case since the critical value is not higher or lower than the critical values we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not significantly different from 1.34

Answer:

The correct answer is letter c. Josh had 24 games and Peter had 32 by the end of the week.

Step-by-step explanation:

We know that Josh has a total of 32 games, while that value is 133% as many as Peter's, therefore the number of games Peter had at the beginning of the week is:

[tex]josh = \frac{133}{100}*peter\\peter = \frac{josh}{1.33}\\peter = \frac{32}{1.33}\\peter = 24.06[/tex]

At the beginning of the week Peter had 24 games. At the end of the week Josh gave Peter 25% of his games, therefore Peter's total is:

[tex]peter = 24 + 0.25*josh\\peter = 24 + 0.25*32\\peter = 24 + 8 = 32[/tex]

While Josh had:

[tex]josh = 32 - 8 = 24[/tex]

The correct answer is letter c.

Answer:

30%

Step-by-step explanation:

fat ÷ total

15 ÷ 50

.3

30%

Answer:

30%

Step-by-step explanation:

To find the percent from fat, take the calories from fat and divide by the total

15/50

.3

Multiply by 100%

30%

Answer:

In the figure ∠ABO and ∠BCO have measures equal to 35°.

Step-by-step explanation:

Measure of arc AD = 180-measure of arc CD= 180-125 =55

m<AOB= 55 ( measure of central angle is equal to intercepted arc)

<OAB= 90 degrees (Tangent makes an angle of 90 degrees with the radius)

In triangle AOB ,

< AB0 = 180-(90+55)= 35 degrees( angle sum property of triangle)

In triange BOC ,< BOC=125 ,

m<, BCO=35 degrees

Answer:

∠ABO and ∠BCO

Step-by-step explanation:

Answer:

Dear Laura Ramirez

Answer to your query is provided below

Option D is correct.

Reason - Because of Hinge and Converse of Hinge theorem

Answer:

Part a

Null hypothesis: [tex] \mu = 69.3[/tex]

Alternative hypothesis: [tex]\mu \neq 69.3[/tex]

Part b

[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]

Step-by-step explanation:

For this case we have the following info given :

[tex] \bar X = 69.8[/tex] the sample mean

[tex] n= 140[/tex] represent the sample size

[tex] s = 11.2[/tex] represent the standard deviation

Part a

And we want to test if the true mean is equal to 69.3 so then the system of hypothesis:

Null hypothesis: [tex] \mu = 69.3[/tex]

Alternative hypothesis: [tex]\mu \neq 69.3[/tex]

Part b: Find the statistic

The statistic is given by:

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

And replacing the info we got:

[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]

Answer:

1.08

Step-by-step explanation:

If Romeo earns 8% more than Juliet,

Example?

If Juliet earns $80

80x8% = 6.40  So his pay would be 80 + 6.40

If you times 80 by 1.08 (this would also be 108%) you would get $86.40

Answer:

1674 ft²

Step-by-step explanation:

Area S = 65*30

Area A = (65 - x)(30 - x) = (65 - 3)(30 - 3) = 62*27= 1674 ft²

Answer:

4cos=2X

X=3-4COS

X=-1

Answer:

50π cm²

Step-by-step explanation:

In this case we have that the area of the boomerang has been the area of the largest semicircle minus the area of the smaller semicircles.

We know that the radius is half the diameter:

r = d / 2 = 20/2

r = 10

Now we have to:

Alargest = π · r²

Alargest = π · (10 cm) ²

Alargest = 100π cm²

Asmaller = π · r²

Asmaller = π · (5 cm) ²

Asmaller = 25π cm²

Finally, the boomerang area has been:

Aboomerang = 100π cm² - 2 · (25π cm²)

Aboomerang = 50π cm²

Answer:

6

Step-by-step explanation:

Let's call the number of pairs of socks he buys s.

[tex]12.50+2.50s=27.50[/tex]

Subtract 12.50 from both sides:

[tex]2.50s=15[/tex]

Divide both sides by 2.5 to isolate s:

[tex]s=6[/tex]

Hope this helps!

Answer:

z(65) = (65-64.2)/[2.81/sqrt(60)] = 0.8/(0.3279)

Step-by-step explanation:

Using the normal probability distribution and the central limit theorem, it is found that there is a 0.0154 = 1.54% probability that the mean height for the sample is greater than 65 ​inches.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

In this problem:

The probability that the mean height for the sample is greater than 65 ​inches is 1 subtracted by the p-value of Z when X = 65, thus:

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{65 - 64.3}{\frac{2.81}{\sqrt{75}}}[/tex]

[tex]Z = 2.16[/tex]

[tex]Z = 2.16[/tex] has a p-value of 0.9846.

1 - 0.9846 = 0.0154

0.0154 = 1.54% probability that the mean height for the sample is greater than 65 ​inches.

A similar problem is given at https://brainly.com/question/24663213

Answer:

18 + 81 = 9(x² + 6x + 9)

11 = (x + 3)²

When we are completing the square, we are going to move the value of c across the equals.  We will do that by adding, and end up with

18=9(x²+6x)

We take the value of b (the coefficient of x), divide it by 2 and square it:

(6/2)²=3²=9

This is the value that completes the square.  However, since the entire square is multiplied by 9, this value must be multiplied by 9 before we can add it across the equals:

18+9(9) = 9(x²+6x+9)

18+81=9(x²+6x+9)

99=9(x²+6x+9)

Dividing both sides by 9, we have:

11=x²+6x+9

11=(x+3)²

Answer:

18 + 81 = 9(x2 + 6x + 9) and 11 = (x + 3)2

Step-by-step explanation:

EDG

Answer:

y + 6 = -3(x - 1) - Point Slope

y=-x+8 - Slope Intercept

2x - 5y = 9 - Standard

Step-by-step explanation:

Point Slope Form is: [tex]y-y_1=m(x-x_1)[/tex]

y + 6 = -3(x - 1) would be in point slope form, where the point is (1,-6) and the slope is '-3'.

Slope-intercept form is: [tex]y=mx+b[/tex]

y=-x+8 is in slope intercept form, where '-1' is the slope and '8' is the y-intercept.

This only leaves 2x - 5y = 9, which is in standard form.

All the correct linear equation with the name of its form are,

1) y = -x + 8   =   Slope-intercept form

2) 2x - 5y = 9  =  Standard form

3) y + 6 = -3(x - 1)  =  Point-slope form

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

All the expressions are,

1) y = -x + 8  

2) 2x - 5y = 9  

3) y + 6 = -3(x - 1)

Now, All the correct linear equation with the name of its form are,

1) y = -x + 8   =   Slope-intercept form

2) 2x - 5y = 9  =  Standard form

3) y + 6 = -3(x - 1)  =  Point-slope form

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Answer:

-3

Step-by-step explanation:

Answer:

This has multiple answers, A, C, And D

Step-by-step explanation:

Answer:

It is definitely A, C, and D.

Step-by-step explanation:

I just answered this question and got it right. I hope this helps and please mark brainliest!

Answer:

8x/5

There’s a 1 in front of the x also remember to always simplify

3/5x + 1x

Answer:8x/5

Step-by-step explanation:

Answer:

b = -18

Step-by-step explanation:

(3 + 4i) (-3-2i)

When we foil:

-9 + -6i + -12i + -8i^2

-8i^2 = +8

Combine like terms:

-1 + -18i

Answer:

-5.7° C

Step-by-step explanation:

-2.7 °C (degrees Celsius) - 3 °C (degrees Celsius) = -5.7° C

Answer:

[tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex].

Step-by-step explanation:

The given expression is

[tex]\log_84a\left(\dfrac{b-4}{c^4}\right)[/tex]

Using the properties of logarithm, we get

[tex]\log_84+\log_8a+\log_8\left(\dfrac{b-4}{c^4}\right)[/tex]     [tex][\because \log_a mn=\log_a m+\log_a n][/tex]

[tex]\log_84+\log_8a+\log_8(b-4)-\log_8c^4[/tex]     [tex][\because \log_a \frac{m}{n}=\log_a m-\log_a n][/tex]

[tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex]     [tex][\because \log_a x^n =n\log_a x][/tex]

Therefore, the required expression is [tex]\log_84+\log_8a+\log_8(b-4)-4\log_8c[/tex].

Answer:

B on edge

Step-by-step explanation:

Answer:

[tex]\mathbf{\dfrac{e^{2t}}{36} + \dfrac{e^{3t}}{18} + \dfrac{e^{4t}}{12} +\dfrac{e^{5t}}{9} + \dfrac{5e^{6t}}{36} + \dfrac{7e^{7t}}{6} + \dfrac{5e^{8t}}{36} + \dfrac{e^{9t}}{9} + \dfrac{e^{10t}}{12} + \dfrac{e^{11t}}{18} + \dfrac{e^{12t}}{36} }[/tex]

Step-by-step explanation:

The objective is to find the moment generating  function of  [tex]M_{X+Y}(t) \ of \ X+Y[/tex].

We are being informed that the fair die is rolled twice;

So; X to be the value for the  first roll

Y to be the value of the second roll

The outcomes  of X are:  X = {1,2,3,4,5,6}

Where ;

[tex]P (X=x) = \dfrac{1}{6}[/tex]

The outcomes  of Y are:  y = {1,2,3,4,5,6}

Where ;

[tex]P (Y=y) = \dfrac{1}{6}[/tex]

The outcome of Z = X+Y

[tex]= \left[\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\ (2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\ (3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6) \\ (4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6) \\ (5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6) \\ (6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6) \end{array}\right][/tex]

= [2,3,4,5,6,7,8,9,10,11,12]

Here;

[tex]P (Z=z) = \dfrac{1}{36}[/tex]

∴ the moment generating function [tex]M_{X+Y}(t) \ of \ X+Y[/tex]is as follows:

[tex]M_{X+Y}(t) \ of \ X+Y[/tex] = [tex]E(e^{t(X+Y)}) = E(e^{tz})[/tex]

⇒ [tex]\sum \limits^{12}_ {z=2 } et ^z \ P(Z=z)[/tex]

= [tex]\mathbf{\dfrac{e^{2t}}{36} + \dfrac{e^{3t}}{18} + \dfrac{e^{4t}}{12} +\dfrac{e^{5t}}{9} + \dfrac{5e^{6t}}{36} + \dfrac{7e^{7t}}{6} + \dfrac{5e^{8t}}{36} + \dfrac{e^{9t}}{9} + \dfrac{e^{10t}}{12} + \dfrac{e^{11t}}{18} + \dfrac{e^{12t}}{36} }[/tex]

Answer:

  44x +56y = 95

Step-by-step explanation:

To write the equation of the perpendicular bisector, we need to know the midpoint and we need to know the differences of the coordinates.

The midpoint is the average of the coordinate values:

  ((-2.5, -2) +(3, 5))/2 = (0.5, 3)/2 = (0.25, 1.5) = (h, k)

The differences of the coordinates are ...

  (3, 5) -(-2.5, -2) = (3 -(-2.5), 5 -(-2)) = (5.5, 7) = (Δx, Δy)

Then the perpendicular bisector equation can be written ...

  Δx(x -h) +Δy(y -k) = 0

  5.5(x -0.25) +7(y -1.5) = 0

  5.5x -1.375 +7y -10.5 = 0

Multiplying by 8 and subtracting the constant, we get ...

  44x +56y = 95 . . . . equation of the perpendicular bisector

Answer:

The answer is 508

Step-by-step explanation:

Solution

First of all, the proportion of B is exceeds 0.5 in total.

Now,

To find the total of A it we have A =314 +512 = 826

The number of employed that choose B = 356

For us to have the proportion of B to be higher than the 0.5, the unemployed B from what is shown here should exceed the difference between total A and B employed

what this suggest is that the employed B is greater than 826-356 = 470

So,

The respondent that are unemployed that choose B  must be greater than 470

Thus,

We recall that the B proportion among the unemployed respondent is lesser than .50

Thus suggests that the respondent that are unemployed who choose be is lesser than 512

The conditions becomes

470 lesser than the number of unemployed respondents who selected B lesser than 512

Hence  the needed number of the number of unemployed respondents who chose B should be between 470 and 512

So, possible answer here is 508.