Please answer this correctly

Answer: D

Step-by-step explanation:

Since we are not given the height of the trapezoid, we can split this into a triangle and a rectangle. We find the area of each and then add them together. In order to do so, we must use Pythagorean Theorem to find the missing length so that we can find the area.

a²+b²=c²

a²+4²=8²

a²+16=64

a²=48

a=√48

a=4√3

Now that we know the missing length of the triangle, we can find the area of the triangle and the rectangle.

Triangle

A=1/2bh

A=1/2(4)(4√3)

A=8√3

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

Rectangle

A=lw

A=7(4√3)

A=28√3

With our areas, we can add them together.

4√3+28√3=36√3 cm²

Answer:

The calculated value t = 4.976 > 2.6264 at 0.01 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

The  mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012

Step-by-step explanation:

Given Mean of the population μ = $53,900

Given sample size 'n' = 100

Mean of the sample size x⁻ = 55,144

Sample standard deviation 'S' = 5200

Null hypothesis:H₀: There is no difference between the means

Alternative Hypothesis :H₁: The  mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012

Test statistic

[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

[tex]t = \frac{55144-53900}{\frac{5200}{\sqrt{100} } }[/tex]

t = 4.976

Degrees of freedom

ν = n-1 = 100-1 =99

t₀.₀₁ = 2.6264

The calculated value t = 4.976 > 2.6264 at 0.01 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

Final answer:-

The  mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012

Answer:

We conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.

Step-by-step explanation:

We are given that the Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012.

A sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200.

Let [tex]\mu[/tex] = mean starting salary for business majors in 2013.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] $53,900     {means that the mean starting salary for business majors in 2013 is smaller than or equal to the mean starting salary in 2012}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $53,900     {means that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012}

The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;

                               T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean starting salary = $55,144

            s = sample standard deviation = $5,200

            n = sample of business majors = 100

So, the test statistics  =  [tex]\frac{55,144-53,900}{\frac{5,200}{\sqrt{100} } }[/tex]  ~ [tex]t_9_9[/tex]

                                     =  2.392

The value of t-test statistic is 2.392.

Now, at 0.01 significance level the t table gives a critical value of 2.369 at 99 degree of freedom for right-tailed test.

Since our test statistic is more than the critical value of t as 2.392 > 2.369, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.

Answer:

68 miles per hour.

Step-by-step explanation:

The time taken for the driver to drive 119 miles is 105 minutes.

The average speed is equal to distance divided by the time taken.

105 minutes is equal to 1.75 hours.

[tex]S=119/1.75[/tex]

[tex]S =68[/tex]

The driver's average speed is 68 miles per hour.

Answer:

Speed = 68 mph

Step-by-step explanation:

Given:

Distance = 119 miles

Time = 1 hour 45 minutes = 1.75 hours

Required:

Speed = ?

Formula:

Average Speed = Total Distance Covered / Total Time Taken

Solution:

Speed = 119/1.75

Speed = 68 mph

Answer:

$783.46

Step-by-step explanation:

Compounded interest rate (quarterly) formula: A = P(1 + r/4)^4t

Simply plug in our known variables and solve:

910 = P(1 + 0.015/4)^4(10)

910 = P(1.00375)^40

910 = 1.16151P

P = 783.464

Answer: 783

Step-by-step explanation:

Answer:

C. with 3000 successes of 5000 cases sample

Step-by-step explanation:

Given that we need to test if the proportion of success is greater than 0.5.

From the given options, we can see that they all have the same proportion which equals to;

Proportion p = 30/50 = 600/1000 = 0.6

p = 0.6

But we can notice that the number of samples in each case is different.

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size

po = Null hypothesized value

p^ = Observed proportion

Since all other variables are the same for all the cases except sample size, from the formula for the test statistics we can see that the higher the value of sample size (n) the higher the test statistics (z) and the highest z gives the strongest evidence for the alternative hypothesis. So the option with the highest sample size gives the strongest evidence for the alternative hypothesis.

Therefore, option C with sample size 5000 and proportion 0.6 has the highest sample size. Hence, option C gives the strongest evidence for the alternative hypothesis

Answer:

[tex]n=\frac{0.04(1-0.04)}{(\frac{0.03}{1.64})^2}=114.76[/tex]  

And rounded up we have that n=115

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]

Solution to the problem

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

The proportion of defectives is estimated as: [tex]\hat p=0.04[/tex]. And on this case we have that the margin of error is [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.04(1-0.04)}{(\frac{0.03}{1.64})^2}=114.76[/tex]  

And rounded up we have that n=115

Answer:

CICI

Step-by-step explanation: NO cici

Christian, Iris and Morgan each get an equal share of 1/2 of the pizza and the model 1/6 represent the fraction of the ​pizza each person gets.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Christian, Iris and Morgan each get an equal share of 1/2 of the pizza.

To find the fraction of the ​pizza each person gets:

Divide the amount of pizza by the number of people.

There are 3 people and 1/2 pizza.

The fraction of the pizza each person gets

= The amount of pizza / number of people

The fraction of the pizza each person gets

= (1/2) / 3

Simplifying into multiplication,

The fraction of the pizza each person gets = 1/2 x 1/3

The fraction of the pizza each person gets

= 1/(2x3)

= 1/6

Therefore, the model that represents the requirement is 1/6.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ5

Answer:

2/7

Step-by-step explanation:

Seven employees can be arranged in 7! ways. n(S) = 7!

Two adjacent desks for married couple can be selected in 6 ways viz.,(1, 2), (2, 3), (3,4), (4, 5), (5,6),(6,7).

This couple can be arranged in the two desks in 2! ways. Other five persons can be arranged in 5! ways.

So, number of ways in which married couple occupy adjacent desks

= 6×2! x 5! =2×6!

so, the probability that the married couple will have adjacent desks

[tex]\frac{n(A)}{n(s)} =\frac{2\times6!}{7!} \\=\frac{2}{7}[/tex]

Answer:

We want a line that passes through the point (4, 7/2)

and we have no other information of this line, so we can not fully find it, but we can find a general line.

We know that a line can be written as:

y = a*x + b.

Now we want that, when x = 4, we must have y = 7/2.

7/2 = a*4 + b

b = -a*4 + 7/2

Then we can write this line as:

y = a*x - a*4 + 7/2.

Where a can take any value, and it is the slope of our line.

Answer:

A

Step-by-step explanation:

Answer:

There are 10 teams.

Step-by-step explanation:

Given that the question wants at least 48 swimmers so any numbers above 47 are counted.

In this diagram, there are 10 teams consisting 48 swimmers and above, 48, 52, 53, 63, 76, 79, 82, 84, 85 and 86.

Answer:

10 teams have 48 or more swimmers.

Step-by-step explanation:

If we look at stem 4 there is one team with 48 members.

So counting from there we  have:

1 + 2 + 1 + 2 + 4

= 10 teams.

Answer:

(a) 2.81%

(b) 0.5%

Step-by-step explanation:

We have the following information from the statement:

P = 64 + - 0.9

(a) We know that the perimeter is:

P = 2 * pi * r

if we solve for r, we have to:

r = P / 2 * pi

We have that the formula of the area is:

A = pi * r ^ 2

we replace r and we are left with:

A = pi * (P / 2 * pi) ^ 2

A = (P ^ 2) / (4 * pi)

We derive with respect to P, and we are left with:

dA = 2 * P / 4 * pi * dP

We know that P = 64 and dP = 0.9, we replace:

dA = 2 * 64/4 * 3.14 * 0.9

dA = 9.17

The error would come being:

dA / A = 9.17 / (64 ^ 2/4 * 3.14) = 0.02811

In other words, the error would be 2.81%

(b) tell us that dA / A <= 0.01

we replace:

[P * dP / 2 * pi] / [P ^ 2/4 * pi] <= 0.01

solving we have:

2 * dP / P <= 0.01

dP / P <= 0.01 / 2

dP / P <= 0.005

Which means that the answer is 0.5%

EASY!

Answer: 17/16 or 1 1/16

Step-by-step explanation:

BRO IT'S ELEMANTARY FRACTIONS!!!!

Answer:

Look below

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

c. 13.5 cm

Step-by-step explanation:

In the right triangle formed by the main sail.

Using the trigonometric function

[tex]\tan \theta =\dfrac{\text{Opposite}}{\text{Adjacent}} \\\tan 52^\circ =\dfrac{x}{9} \\x=9 \times \tan 52^\circ\\x=11.52$ cm[/tex]

Therefore:

Height of the mast = 2+11.5=13.5 cm

The height of the mast is 13.5 cm.

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Translate this sentence into an equation. The product of Holly's height and 3 is 39. Use the variable h to represent Holly's height.

Let holly's savings be h. If the  product of Holly's savings and 3 is 39, this can be represented mathematically as h*3 = 39

To get holly's savings "h', we will divide both sides of the equation by 3

h*3 = 39

h*3/ 3= 39/3

h = 13*3/ 3

h = 13 * 3/3

h = 13*1

h = 13

Holly's savings is 13 and the required equation is 3h =39

Answer:

At first it increases by 25%, then you have 1.25x the original temp. A drop of 40% gives you .6 x 1.25, or 75% of the original temperature

Step-by-step explanation:

found that on the web for yuh. I really hope it helped.

Answer:

decreased by 25%

Step-by-step explanation:

Answer:

is m= 10.5 espero que te ayude

Answer:

The null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.

A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).

The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have.

Step-by-step explanation:

This hypothesis test will test the claim that the compensation plan increases the average sales per salesperson. This claim will be stated in the alternative hypothesis, and will state that, with the compensation plan, the sales are significantly higher than without the compensation plan.

The null hypothesis, that Steve wants to falsify, will state that the sales will not differ with or withour compensation plan.

We can write this hypothesis as:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.

A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).

The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have. The sales would be expected to increase due to this implementation, and they will not increase, at least, not for the compensation plan.

Answer:

a. P(x=0)=0.2967

b. P(x=1)=0.4444

c. P(x=2)=0.2219

d. P(x=3)=0.0369

Step-by-step explanation:

The variable X: "number of meals that exceed $50" can be modeled as a binomial random variable, with n=3 (the total number of meals) and p=0.333 (the probability that the chosen restaurant charges mor thena $50).

The probabilty p can be calculated dividing the amount of restaurants that are expected to charge more than $50 (5 restaurants)  by the total amount of restaurants from where we can pick (15 restaurants):

[tex]p=\dfrac{5}{15}=0.333[/tex]

Then, we can model the probability that k meals cost more than $50 as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{3}{k} 0.333^{k} 0.667^{3-k}\\\\\\[/tex]

a. We have to calculate P(x=0)

[tex]P(x=0) = \dbinom{3}{0} p^{0}(1-p)^{3}=1*1*0.2967=0.2967\\\\\\[/tex]

b. We have to calculate P(x=1)

[tex]P(x=1) = \dbinom{3}{1} p^{1}(1-p)^{2}=3*0.333*0.4449=0.4444\\\\\\[/tex]

c. We have to calcualte P(x=2)

[tex]P(x=2) = \dbinom{3}{2} p^{2}(1-p)^{1}=3*0.1109*0.667=0.2219\\\\\\[/tex]

d. We have to calculate P(x=3)

[tex]P(x=3) = \dbinom{3}{3} p^{3}(1-p)^{0}=1*0.0369*1=0.0369\\\\\\[/tex]

Answer:

y+1=3(x-1), D.

Step-by-step explanation:

Parallel lines have the same slope: Slope should be 3.

y+1=3(x-1)

If we spin the spinner 11 times, 4 is the best prediction possible for the number of times it will land on pink.

To calculate the expected value of a random variable, simply multiply it with the respective probability and sum the respective products.

Given, total number of outcomes=11.

Total number of pink colored spin= 4

Probability of a spin resulting pink color=4/11

Expected number of spins of pink color= [tex]\sum xp(x)[/tex]

=(1×4/11)+(2×4/11)+(3×4/11)+(4×4/11)

=4/11(1+2+3+4)

=40/11

=3.63 ≈ 4

Thus, the best prediction possible for the number of times it will land on pink is 4.

Learn more about expected value, here:

https://brainly.com/question/28197299

#SPJ12

Incomplete:

Image of spinner is missing in the question, Therefore attaching it below:

Answer:

  A) 10, -3.73, -6.035, -6.259 . . . cm/s

  B) -6.2832 cm/s

Step-by-step explanation:

A) For problems like this, where repeated evaluation of a function is required, I find a graphing calculator or spreadsheet to be an appropriate tool. The attached shows that we defined the position function ...

  p(t) = 2sin(πt) +5cos(πt)

and a function for computing the average velocity from t=1. For some time interval ending at t2, the average velocity is ...

  Va(t2) = Δp/Δt = (p(t2) -p(1))/(t2 -1)

Then, for example, for t2 = 2, the average velocity on the interval [1, 2] is ...

  Va(2) = (p(2) -p(1))/(2 -1) = ((2sin(2π) +5cos(2π)) -(2sin(π) +5cos(π)))/(1)

  = (2·0+5·1 -(2·0 +5·(-1)) = 10 . . . . matches the table value for x1 = 2.

Then the average velocity values for the intervals of interest are ...

  1) [1, 2]   Va = 10

  2) [1, 1.1]   Va = -3.73

  3) [1, 1.01]   Va = -6.035

  4) [1, 1.001]   Va = -6.259

__

B) Sometimes a better estimate is obtained when the interval is centered on the point of interest. Here, we can compute the average velocity on the interval [0.999, 1.001] as a better approximation of the instantaneous velocity at t=1. That value is ...

  [0.999, 1.001]   Va = -6.283175*

Our estimate of V(1) is -6.2832 cm/s.

The exact value is -2π ≈ -6.2831853... cm/s

__

* This is the average of the Va(0.999) and Va(1.001) values in the table.

Answer:

x < -4/7

Step-by-step explanation:

X + 5/7 < 1/7

Subtract 5/7 from each side

X + 5/7  -5/7 <1/7-5/7

x < -4/7

Answer:

Option B

Step-by-step explanation:

When A and B are independent events:

P(A and B) = P(A) * P(B)

OR

P(A|B) = P(A) * P(B)

Answer:

9 people

Step-by-step explanation:

37, 39, 41, 46, 61, 63, 69, 77, 80

9 people waited more than 36 minutes.

Answer:

Pillows:

Blankets:

Pet Beds:

Step-by-step explanation:

18 + 45 + 27 = 90 (there are 90 students)

18 out of 90 = 20%

45 out of 90 = 50%

27 out of 90 = 30%

Hope this helps!

Step-by-step explanation:

Joe mama

Answer:

[tex]\dfrac{15}{19}[/tex]

Step-by-step explanation:

The soccer player so far has made 15 penalty kicks in 19 attempts.

Therefore:

Total Number of trials =19

Number of Successes =15

Therefore, the relative frequency probability that she will make her next penalty​ kick is:

[tex]=\dfrac{\text{Number of Successes}}{\text{Total Number of Trials}} \\=\dfrac{15}{19}[/tex]

Answer:

x^2

Step-by-step explanation:

[tex]x^4\cdot x^{-2}= \\\\x^{4-2}= \\\\x^2[/tex]

Hope this helps!

Answer:

[tex]x^{2}[/tex]

Step-by-step explanation:

[tex]x^4 \times x^{-2}[/tex]

[tex]x^{4+-2}[/tex]

[tex]x^{4-2}[/tex]

[tex]x^{2}[/tex]