In the North Area Mall, 18 of the 90 stores sell shoes. If that same ratio holds true for the University Mall and 9 stores there sell shoes, how many stores are at University Mall?

Answer:

[tex]Probability = \frac{3\\}{14}[/tex]

Step-by-step explanation:

Given

Republicans = 10

Democrats = 6

Total = Republicans + Democrats = 10 + 6 = 16

Selection = 3

Required

Probability that all selected members are Republicans

This implies that all selected members are republicans and none are republicans

This is calculated by (Number of ways of selecting 3 republicans * Number of ways of selecting 0 Democrats) / (Total number of possible selections)

First; the number of ways the 3 republicans from 10 can be selected needs to be calculated;

[tex]^{10}C_3 = \frac{10!}{(10-3)!3!}[/tex]

[tex]^{10}C_3 = \frac{10!}{7!3!}[/tex]

[tex]^{10}C_3 = \frac{10*9*8*7!}{3!7!}[/tex]

Divide numerator and denominator by 7!

[tex]^{10}C_3 = \frac{10*9*8}{3*2*1}[/tex]

[tex]^{10}C_3 = \frac{720}{6}[/tex]

[tex]^{10}C_3 = 120[/tex]

Next, the number of ways that 0 republicans can be selected from 6 will be calculated

[tex]^6C_0 = \frac{6!}{(6-0)!0!}[/tex]

[tex]^6C_0 = \frac{6!}{6!0!}[/tex]

[tex]^6C_0 = 1[/tex]

Next, the total number of possible selection will be calculated; In other words number of ways of selecting 3 politicians fro a group of 16

[tex]^{16}C_3 = \frac{16!}{(16-3)!3!}[/tex]

[tex]^{16}C_3 = \frac{16!}{13!3!}[/tex]

[tex]^{16}C_3 = \frac{16*15*14*13!}{13!3!}[/tex]

[tex]^{16}C_3 = \frac{16*15*14}{3!}[/tex]

[tex]^{16}C_3 = \frac{16*15*14}{3*2*1}[/tex]

[tex]^{16}C_3 = \frac{3360}{6}[/tex]

[tex]^{16}C_3 = 560[/tex]

Lastly, the probability is calculated as follows;

[tex]Probability = \frac{^{10}C_3\ *\ ^6C_0}{^{16}C_3}[/tex]

[tex]Probability = \frac{120\ *\ 1}{560}[/tex]

[tex]Probability = \frac{120\\}{560}[/tex]

Simplify fraction to lowest term

[tex]Probability = \frac{3\\}{14}[/tex]

Answer: 6 + 3 = 9

Step-by-step explanation:

5.5 does not equal to 20

Answer:

Mean: 8.28

Standard deviation: 2.84

Step-by-step explanation:

This random variable "number of Billy Ripken error cards found" can be described by the binomial distribution, with sample size n=360 (number of packs) and probability of success p=0.023 (probabillity of a pack containing the coveted Billy Ripken error card).

Then, the mean and standard deviation are calculate as for the binomial distribution:

[tex]\mu=np=360\cdot 0.023=8.28\\\\\sigma=\sqrt{np(1-p)}=\sqrt{360\cdot 0.023\cdot 0.977}=\sqrt{8.08956}\approx2.84[/tex]

Answer:

f(x) is not a function meaning this is false.

Step-by-step explanation:

One input, can only have one output. In this case 5 has two outputs, 1 and 3. This statement is false.

Hope this helped! :)

Answer:  6x² + 11

Step-by-step explanation:

  24x³ - 54x²    +    44x - 99

=  6x²(4x - 9)     +    11(4x - 9)

=  (6x² + 11) (4x - 9)

This can be rewritten as: 4x(6x² + 11) - 9(6x² + 11)

This is the answer to your problem.

Answer:

A. Lines a and b are pa because their corresponding angles are congruent.

Step-by-step explanation:

The corresponding angles are both 110 degrees.

the answer is 3y+2x+8

Answer:

Step-by-step explanation:

Hello!

The given data corresponds to the variables

Y:  Annual Maintenance  Expense ($100s)

X: Weekly Usage  (hours)

n= 10

∑X= 253; ∑X²= 7347; [tex]\frac{}{X}[/tex]= ∑X/n= 253/10= 25.3 Hours

∑Y= 346.50; ∑Y²= 13010.75; [tex]\frac{}{Y}[/tex]= ∑Y/n= 346.50/10= 34.65 $100s

∑XY= 9668.5

a)

To estimate the slope and y-intercept you have to apply the following formulas:

[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{9668.5-\frac{253*346.5}{10} }{7347-\frac{(253)^2}{10} }= 0.95[/tex]

[tex]a= \frac{}{Y} -b\frac{}{X} = 34.65-0.95*25.3= 10.53[/tex]

^Y= a + bX

^Y= 10.53 + 0.95X

b)

H₀: β = 0

H₁: β ≠ 0

α:0.05

[tex]F= \frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg}; Df_{Error}}[/tex]

F= 47.62

p-value: 0.0001

To decide using the p-value you have to compare it against the level of significance:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The decision is to reject the null hypothesis.

At a 5% significance level you can conclude that the average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.

b= 0.95 $100s/hours is the variation of the estimated average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.

a= 10.53 $ 100s is the value of the average annual maintenance expense of the computer wheel alignment and balancing machine when the weekly usage is zero.

c)

The value that determines the % of the variability of the dependent variable that is explained by the response variable is the coefficient of determination. You can calculate it manually using the formula:

[tex]R^2 = \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]} = \frac{0.95^2[7347-\frac{(253)^2}{10} ]}{[13010.75-\frac{(346.50)^2}{10} ]} = 0.86[/tex]

This means that 86% of the variability of the annual maintenance expense of the computer wheel alignment and balancing machine is explained by the weekly usage under the estimated model ^Y= 10.53 + 0.95X

d)

Without usage, you'd expect the annual maintenance expense to be $1053

If used 100 hours weekly the expected maintenance expense will be 10.53+0.95*100= 105.53 $100s⇒ $10553

If used 1000 hours weekly the expected maintenance expense will be $96053

It is recommendable to purchase the contract only if the weekly usage of the computer is greater than 100 hours weekly.

Answer:

^Y= 26.72 + 0.0547Xi

^Y/[tex]_{X=3000}[/tex]= 190.82ºF

B. It is unrealistically high.

Step-by-step explanation:

Hello!

*Full text*

The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of .05. What is wrong with this predicted value?

Chirps in 1 min.     929    854    771    1004    1201    1027

Temperature (F)     81.3    77.3    64.8    80.3    92.2    80.9

What is the regression equation?

^y= _____ + _____

(Round the x-coefficient to four decimal places as needed. Round the constant to two decimals as needed)

What is the predicted value? ^y= _____ (Round to one decimal places as needed)

What is wrong with this predicted value?

A. The first variable should have been the dependent variable

B. It is unrealistically high.

C. It is only an approximation

D. Nothing is wrong with this value

To calculate the regression equation you have to estimate the slope and the y-intercept.

^Y= a + bX

Estimate of the slope:

[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]

n= 6

∑X= 5786 ∑X²= 5691944 [tex]\frac{}{X}[/tex]= 964.33

∑Y= 476.80 ∑Y²= 38277.76 [tex]\frac{}{Y}[/tex]= 79.47

∑XY= 465940.4

[tex]b= \frac{465940.4-\frac{5786*476.80}{6} }{5691944-\frac{(5786)^2}{6} }= 0.0547[/tex]

Estimate of the Y-intercept:

[tex]a= \frac{}{Y} -b*\frac{}{X}[/tex]

[tex]a= 79.47 -0.0547*964.33= 26.696= 26.72[/tex]

The estimated regression equation is:

^Y= 26.72 + 0.0547Xi

^Y/[tex]_{X=3000}[/tex]= 26.72 + 0.0547*3000= 190.82ºF

At the rate of 3000 chirps per minute it is expected a temperature of 190.82ºF

As you can see it is unrealistic to think that the chirping rate of bugs will have any effect over the temperature. For what is known about bugs, they tend to be more active to higher temperatures.

Considering the value obtained, as it is incredible high, if this regression was correct, every time the chirping rate of bugs increases, the ambient temperature would rise to levels incompatible with life.

I hope this helps!

Answer:

The sales tax is 2.10

Step-by-step explanation:

Take the price of the item and multiply by the sales tax rate to determine the tax

30 * 7%

30 * .07

2.10

The sales tax is 2.10

Answer:

Option D (20) is the right answer.

Step-by-step explanation:

The given values are:

Length of wood,

= 78 inches

Wood pieces,

=  [tex]3\frac{3}{4} \ inches[/tex]

On converting this in proper fraction, we get

=  [tex]3\frac{3}{4}[/tex]

=  [tex]\frac{15}{4}[/tex]

=  [tex]3.75 \ inches[/tex]

Now,

On dividing "78" from "3.78", we get

=  [tex]\frac{78}{3.75}[/tex]

=  [tex]20.8 \ pieces[/tex]

So we got "20 pieces".

Answer:

7 seconds

Step-by-step explanation:

Given the height equation of the motion;

s = -16t^2 + 256t

At s = 1008 ft

The equation becomes;

1008 = -16t^2 + 256t

16t^2 - 256t + 1008 = 0

Solving the quadratic equation for t;

Factorising, we have;

16(t-7)(t-9) = 0

t = 7 or t = 9

When the ball is going up it would reach the given height at time t = 7 seconds.

When it is coming down it would reach the given height at time t = 9 seconds.

Answer:

C. x < 25 and x ≥ 0

Step-by-step explanation:

Fastest and easiest way to do this is to graph the inequality and find out the lines.

answer:

0.25 miles/sec, i hope this helps

Step-by-step explanation:

Answer:

0.9^10

Step-by-step explanation:

The probability to make an error in 1 question =0.1 => The probability that this one particular question will be answered correctly is P=1-0.1=0.9

There are 10 questions  that are independent from each other .

The probability to be answered correctly is 0.9  each.  So the probability to answer correctly to all of them is

P(10quest=correct) =0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9*0.9=0.9^10

Answer: 2.04÷ 4= 0.51

4.68÷9= 0.52

4 pack is better value by 0.01

The tangent vector to r(t) at any t in the domain is

[tex]\mathbf T(t)=\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}=2\cos t\,\mathbf i-7\sin t\,\mathbf j[/tex]

At t = π/6, the tanget vector is

[tex]\mathbf T\left(\dfrac\pi6\right)=\sqrt3\,\mathbf i-\dfrac72\,\mathbf j[/tex]

To get the unit tangent, normalize this vector by dividing it by its magnitude:

[tex]\left\|\mathbf T\left(\dfrac\pi6\right)\right\|=\sqrt{(\sqrt3)^2+\left(-\dfrac72\right)^2}=\dfrac{\sqrt{61}}2[/tex]

So the unit tangent at the given point is

[tex]\dfrac{\mathbf T\left(\frac\pi6\right)}{\left\|\mathbf T\left(\frac\pi6\right)\right\|}=2\sqrt{\dfrac3{61}}\,\mathbf i-\dfrac7{\sqrt{61}}\,\mathbf j[/tex]

Applying derivatives, the tangent vector of unit length at the point given is:

[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]

The vector function is:

[tex]r(t) = 2\sin{(t)}i + 7\cos{(t)}j[/tex]

The tangent vector is it's derivative, which is given by:

[tex]r^{\prime}(t) = 2\cos{(t)}i - 7\sin{(t)}j[/tex]

At point [tex]t = \frac{\pi}{6}[/tex], we have that:

[tex]r^{\prime}(\frac{\pi}{6}) = 2\cos{(\frac{\pi}{6})}i - 7\sin{(\frac{\pi}{6})}j[/tex]

[tex]r^{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{2}i - \frac{7}{2}[/tex]

[tex]r^{\prime}(\frac{\pi}{6}) = \sqrt{3}i - \frac{7}{2}[/tex]

The norm of the vector is:

[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\sqrt{3}^2 + (-\frac{7}{2})^2}[/tex]

[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\frac{61}{4}}[/tex]

[tex]|r^{\prime}(\frac{\pi}{6})| = \frac{\sqrt{61}}{2}[/tex]

The unit vector is given by each component divided by the norm, thus:

[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{\sqrt{3}}{\frac{\sqrt{61}}{2}}i - \frac{7}{2\frac{\sqrt{61}}{2}}j[/tex]

[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]

A similar problem is given at https://brainly.com/question/20733439

Answer:

First term a = 41

Step-by-step explanation:

Arithmetic Progression:

Common differences d = -2

[tex]S_{n}=\frac{n}{2}(2a+[n-1]d)\\\\S_{20}=\frac{20}{2}(2a+19*[-2])\\\\[/tex]

  = 10*(2a - 38)

 = 10*2a - 10*38

=20a - 380

[tex]S_{22}=\frac{22}{2}(2a+21*[-2])\\\\[/tex]

= 11 (2a -42)

=11*2a - 11*42

= 22a - 462

[tex]S_{22}=S_{20}\\\\[/tex]

22a - 462 = 20a - 380

22a = 20a - 380 + 462

22a = 20a + 82

22a - 20a = 82

2a = 82

a = 82/2

a = 41

First term a = 41

Answer:

Hey there!

3/2 and 3/4 can be written as decimals that terminate.

Hope this helps :)

Answer:

C

Step-by-step explanation:

A terminating decimal is usually defined as a decimal number that contains a finite number of digits after the decimal point.

3/2=1.5

3/4= 0.75 (It ends after division)

Answer:

a) 8.23% probability that a piece of pottery will be finished within 95 minutes

b) 0.28% probability that it will take longer than 110 minutes.

Step-by-step explanation:

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Two variables:

Means [tex]\mu_{a}, \mu_{b}[/tex]

Standard deviations [tex]\sigma_{a}, \sigma_{b}[/tex]

Sum:

[tex]\mu = \mu_{a} + \mu_{b}[/tex]

[tex]\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}}[/tex]

In this question:

[tex]\mu_{a} = 40, \mu_{b} = 60, \sigma_{a} = 2, \sigma_{b} = 3[/tex]

So

[tex]\mu = \mu_{a} + \mu_{b} = 40 + 60 = 100[/tex]

[tex]\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}} = \sqrt{4 + 9} = 3.61[/tex]

A) What is the probability that a piece of pottery will befinished within 95 minutes?

This is the pvalue of Z when X = 95.

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

[tex]Z = \frac{95 - 100}{3.61}[/tex]

[tex]Z = -1.39[/tex]

[tex]Z = -1.39[/tex] has a pvalue of 0.0823

8.23% probability that a piece of pottery will befinished within 95 minutes.

B) What is the probability that it will take longer than 110 minutes?

This is 1 subtracted by the pvalue of Z when X = 110.

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

[tex]Z = \frac{110 - 100}{3.61}[/tex]

[tex]Z = 2.77[/tex]

[tex]Z = 2.77[/tex] has a pvalue of 0.9972

1 - 0.9972 = 0.0028

0.28% probability that it will take longer than 110 minutes.

Graph the line using the slope and y-intercept, or two points.

Slope: -7/3

y-intercept: 2

Please mark me as brainliest if possible. Stay safe and God bless you!!

<3

- Eli

Answer:

57

Step-by-step explanation:

Area of rectangle:

4 x 12

=48

Area of left triangle:

2 x 3 / 2

=3

Area of right triangle:

6 x 2 / 2

=6

Total Area:

48 + 3 + 6 = 57

Answer: 100

Step-by-step explanation: 4 * 12 = 48     6 * 2 / 0.5 = 24    3 * 2 / 0.5 = 12

48+24+12=84 84 to the nearest hundred is 100.

Answer:

Step-by-step explanation:

First of all, we need to define the image and pre-image.

Second, let's write down the coordinates of each rectangle.

ABCD coordinates:

A(-6,5)

B(-1,5)

C(-1,1)

D(-6,1)

A'B'C'D' coordinates:

A'(5,-1)

B'(5,-6)

C'(1,-6)

D'(1,-1)

The first rule we need to apply is the 90° clockwise rotation which is

[tex](x,y) \implies (y,-x)[/tex]

Which gives us (5,6), (5,1), (1,1), (1,6).

Then, we use the 7 units-down rule

[tex](x,y) \implies (x,y-7)[/tex]

Which gives us (5,-1), (5,-6), (1,-6) and (1,-1).

Therefore, the right answer is the third choice.

Answer:

A 90° clockwise rotation about the origin and a translation of 7 units down.

Answer:

Always true

Step-by-step explanation:

Trust me

Answer:

true

Step-by-step explanation:

Answer:

x = 36

Step-by-step explanation:

x/3 - 14 = -2

x - 42 = -6

x = -6 + 42

x = 36

Hope this helps! :)

Answer:

x= 36

Step-by-step explanation:

X/3 - 14 = -2

Add 14 to each side

X/3 - 14+14 = -2+14

x/3 = 12

Multiply each side by 3

x/3 * 3 = 12*3

x = 36

Answer:

12.5

Step-by-step explanation:

to find the length of one side of the hexagon, draw diagonal lines, which will be six diagonals, this will divide the hexagon into, 6 equilateral triangles. The diagonals are equal in length to the side of the square (25 cm.) and the sides of the equilateral triangles are just half of this (12.5 cm.)

25/2=12.5

Answer:

Convert [tex]\frac{2}{3}[/tex] to an improper fraction.

So your answer is [tex]\frac{11}{3}[/tex]

Step-by-step explanation:

Hope this helped you!!

━━━━━━━☆☆━━━━━━━

▹ Answer

[tex]\frac{11}{3}[/tex]

▹ Step-by-Step Explanation

3 * 3 = 9

9 + 2 = 11

Therefore, the answer is 11/3.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

f(-1) = -8

f(1) =  -12

Complete Question

Express the confidence interval 0.555 less than p less than  0.777 in the form Modifying above p with caret plus or minus Upper E.

Answer:

The modified representation is [tex]\r p \pm E = 0.666 \pm 0.111[/tex]

Step-by-step explanation:

From the question we are told that

    The  confidence interval interval is  [tex]0.555 < p < 0.777[/tex]

Now looking at the values that make up  the up confidence interval we see that this is a symmetric  confidence interval(This because the interval covers 95%  of the area under the normal curve which mean that the probability of a value falling outside the interval is 0.05 which is divided into two , the first half on the left -tail and the second half on the right tail  as shown on the figure in the first uploaded image(reference - Yale University ) ) which means

     Now  since the confidence interval is  symmetric , we can obtain the sample proportion as follows

             [tex]\r p = \frac{0.555 + 0.777}{2}[/tex]

            [tex]\r p =0.666[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = \frac{1}{2} * K[/tex]

Where  K is the length of the confidence interval which iis mathematically represented as

           [tex]K = 0.777 -0.555[/tex]

         [tex]K = 0.222[/tex]

Hence  

          [tex]ME = \frac{1}{2} * 0.222[/tex]

           [tex]ME = 0.111[/tex]

So the confidence interval can now be represented as

        [tex]\r p \pm E = 0.666 \pm 0.111[/tex]