A college graduate is curious about the proportion of graduates who have loan debt 20 years after graduating. Let the proportion of graduates who have loan debt 20 years after graduating be p. If the college graduate wishes to know if the proportion of graduates who have loan debt 20 years after graduating is less than 18%, what are the null and alternative hypotheses?

Answer:

Step-by-step explanation:

From the information given:

mean life span of a brand of automobile = 35,000

standard deviation of a brand of automobile = 2250 miles.

the z-score that corresponds to each life span are as follows.

the standard z- score formula is:

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

For x = 34000

[tex]z = \dfrac{34000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-1000}{2250}[/tex]

z = −0.4444

For x = 37000

[tex]z = \dfrac{37000 - 35000}{2250}[/tex]

[tex]z = \dfrac{2000}{2250}[/tex]

z = 0.8889

For x = 3000

[tex]z = \dfrac{30000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-5000}{2250}[/tex]

z = -2.222

From the above z- score that corresponds to their life span; it is glaring  that the tire with the life span 30,000 miles has an unusually short life span.

For x = 30,500

[tex]z = \dfrac{30500 - 35000}{2250}[/tex]

[tex]z = \dfrac{-4500}{2250}[/tex]

z = -2

P(z) = P(-2)

Using excel function (=NORMDIST -2)

P(z) = 0.022750132

P(z) = 2.28th percentile

For x =  37250

[tex]z = \dfrac{37250 - 35000}{2250}[/tex]

[tex]z = \dfrac{2250}{2250}[/tex]

z = 1

Using excel function (=NORMDIST 1)

P(z) = 0.841344746

P(z) = 84.14th percentile

For x = 35000

[tex]z = \dfrac{35000- 35000}{2250}[/tex]

[tex]z = \dfrac{0}{2250}[/tex]

z = 0

Using excel function (=NORMDIST 0)

P(z) = 0.5

P(z) = 50th percentile

a.  The z score of each life span should be -0.4444, 0.889, and 2.2222.

b.  The percentile of each life span should be 0.0228, 0.8413 and  0.5000.

Given that,

(a)

The z score should be

[tex]Z1 = \frac{34000-35000}{2250} = -0.4444\\\\Z2 = \frac{37000-35000}{2250} = 0.8889\\\\Z3 = \frac{30000-35000}{2250} = -2.2222\\\\[/tex]

The tire with life span of 30000 miles would be considered unusual

(b)

The percentile should be

[tex]Z1 = \frac{30500-35000}{2250} = -2[/tex]

p(Z1 < -2) = NORMSDIST(-2) = 0.0228

[tex]Z2 = \frac{37250-35000}{2250} = 1[/tex]

p(Z2 < 1) = NORMSDIST(1) = 0.8413

[tex]Z3 = \frac{35000-35000}{2250} = 0[/tex]

p(Z3 < 0) = NORMSDIST(0) = 0.5000

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Answer:

The standard deviation of the sample mean is  [tex]\sigma _ {\= x } = 2.711[/tex]

Step-by-step explanation:

From the question we are told that

   The mean is  [tex]\= x = 60[/tex]

    The standard deviation is  [tex]\sigma = 21[/tex]

     The sample size is [tex]n = 60[/tex]

Generally the standard deviation of the sample mean is mathematically represented as  

               [tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]

               [tex]\sigma _ {\= x } = 2.711[/tex]

Answer: Reject the null hypothesis because the p-value =0.025 is less than the significance level α=0.05.

Step-by-step explanation: Trust me

Answer:

x = [tex]\frac{3}{4}(n-1)[/tex]

Step-by-step explanation:

It's given in the question that '' The number is 75% of one less than a number n"

Let the number is 'x'.

One less than a number 'n' will be = (n - 1)

75% of one less than a number will be = 75% of (n -1)

                                                                = [tex]\frac{75}{100}(n-1)[/tex]

                                                                = [tex]\frac{3}{4}(n-1)[/tex]

Therefore, the desired expression to get the number 'x' will be,

x = [tex]\frac{3}{4}(n-1)[/tex]

Answer:

3/4(n-1)

Step-by-step explanation:

did it in rsm

Answer:

120

Step-by-step explanation:

Let's say you put them on the shelf one by one, from left to right.

You can pick 1 of the 5 for the first position.

5

Now you have 4 books left. You pick one out of those 4 for the second position.

5 * 4

There are 3 choices left for the 3rd position.

5 * 4 * 3

2 left for the 4th position.

5 * 4 * 3 * 2

Finally, there is one book left for the 5th position.

5 * 4 * 3 * 2 * 1

Now we multiply:

5 * 4 * 3 * 2 * 1 = 120

Answer:

27°

Step-by-step explanation:

D is 72° because it alternates with B, alternate angles are equal.

2x+72°+2x= 180° because it is a straight line.

4x+72°=180°

4x=108°

x=27°

Answer:

a) the angle of ascent is 8.2°

b) the horizontal distance traveled is 4375 m

Step-by-step explanation:

depth of ocean = 626 m

distance traveled in the ascent = 4420 m

This is an angle of elevation problem with

opposite side to the angle = 626 m

hypotenuse side = 4420 m

a) angle of ascent ∅ is gotten from

sin ∅ = opp/hyp = 626/4420

sin ∅ = 0.142

∅ = [tex]sin^{-1}[/tex] 0.142

∅ = 8.2°  this is the angle of ascent of the submarine.

b) The horizontal distance traveled will be gotten from Pythagoras theorem

[tex]hyp^{2}[/tex] = [tex]opp^{2}[/tex] + [tex]adj^{2}[/tex]

The horizontal distance traveled will be the adjacent side of the right angle triangle formed by these distances

[tex]4420^{2}[/tex] = [tex]626^{2}[/tex] + [tex]adj^{2}[/tex]

adj = [tex]\sqrt{4420^{2}-626^{2} }[/tex]

adj = 4375 m  this is the horizontal distance traveled.

Answer:

A. 9

Step-by-step explanation:

Well if you go to 190 on the y-axis and go all the way to the right you can see according to the line of best fit A. 9 should be the correct answer.

Thus,

A.9 is the correct answer.

Hope this helps :)

Answer:

A. 9

Step-by-step explanation:

A line of best fit is a line that goes through a scatter plot that will express the relationship between those points. So, if we look at 190 on the y-axis, we can approximate that on the line of best fit it would be closest to 9 on the x-axis.

Answer:

The Taylor series is   [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Step-by-step explanation:

From the question we are told that

      The function is  [tex]f(x) = sin (x)[/tex]

This is centered at  

       [tex]a = 2 \pi[/tex]

Now the next step is to represent the function sin (x) in it Maclaurin series form which is  

          [tex]sin (x) = \frac{x^3}{3! } + \frac{x^5}{5!} - \frac{x^7}{7 !} +***[/tex]

=>       [tex]sin (x) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

   Now since the function is centered at  [tex]a = 2 \pi[/tex]

We have that

           [tex]sin (x - 2 \pi ) = (x-2 \pi ) - \frac{(x - 2 \pi)^3 }{3 \ !} + \frac{(x - 2 \pi)^5 }{5 \ !} - \frac{(x - 2 \pi)^7 }{7 \ !} + ***[/tex]

This above equation is generated because the function is not centered at the origin but at [tex]a = 2 \pi[/tex]

           [tex]sin (x-2 \pi ) = $$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x - 2 \pi)^{2n+1}][/tex]

Now due to the fact that [tex]sin (x- 2 \pi) = sin (x)[/tex]

This because  [tex]2 \pi[/tex] is a constant

   Then it implies that the Taylor series of the function centered at [tex]a = 2 \pi[/tex] is

             [tex]$$\sum_{n=0}^{\infty} [\frac{(-1)^n}{(2n +1)!} (x)^{2n+1}][/tex]

Answer:

See the attachment for sketch

Thr region is unbounded

DNE

Step-by-step explanation:

y≤ -2x + 10

The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.

The slope would be 4/3 and the y-intercept is 1

Create a table x and y and in x there is -3/4 and 0 and for the y side is 0 and 1. The line would be in the 2 quadrant with 2 points on on the y axis 1 and the other on the x axis 0.9 and that would be the graphed description of the line. Sorry if this is hard to understand i don’t have a access to draw or insert an image.

The graph of the linear equation is on the image at the end.

To do it, we need to find two points on the line, so let's evaluate it.

When x = 0

y = (4/3)*0 + 1 = 1 ----> (0, 1)

When x = 3

y = (4/3)*3 + 1 = 5 ---> (3 , 5)

Now just graph these two points and connect them with a line, that will be the graph of the linear equation.

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Ans   k = 4

Step-by-step explanation:

Here g(x) =[tex]\frac{-1}{3}x + 1[/tex] and

        f(x) = [tex]\frac{-1}{3} x -3[/tex]

Now,  g(x) = f(x) + k

    or,      [tex]\frac{-1}{3}x + 1[/tex]  =  [tex]\frac{-1}{3} x -3 + k[/tex]

    or,      1 + 3 = k

    So,  k = 4   Answer.

Answer:

The probability is 0.04746

Step-by-step explanation:

Firstly, we calculate the z-score here

Mathematically;

z-score = x-mean/SD/√n

Where from the question;

x = 85, mean = 90 , SD = 15 and n = 25

Plugging these values into the equation, we have;

Z = (85-90)/15/√25 = -5/15/5 = -1.67

So the probability we want to calculate is ;

P(z > -1.67)

We use the standard normal distribution table for this;

P(z > -1.67) = 0.04746

Answer:

[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]

Step-by-step explanation:

Hello

[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]

So values of x which is not in this domain is

[tex]-7\leq x\leq 0[/tex]

which is [-7,0]

hope this helps

Answer:

[tex]\boxed{\sf \ \ \ 10^2+11^2+12^2=13^2+14^2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's note a a positive integer

5 consecutive integers are

a

a+1

a+2

a+3

a+4

so we need to find a so that

[tex]a^2+(a+1)^2+(a+2)^2=(a+3)^2+(a+4)^2\\<=>\\a^2+a^2+2a+1+a^2+4a+4=a^2+6a+9+a^2+8a+16\\<=>\\3a^2+6a+5=2a^2+14a+25\\<=>\\a^2-8a-20=0\\<=>\\(a+2)(a-10)=0\\<=>\\a = -2 \ or \ a = 10\\[/tex]

as we are looking for positive integer the solution is a = 10

do not hesitate if you have any question

Answer:

D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Answer:

there are 620 comic books

Step-by-step explanation:

let number of comic books be x

total books=3x+x

2480=4x

2480/4=x

620=x

Answer:

Step-by-step explanation:

Let comic books be ' X '

Let Novels be ' 3x '

Now, finding the value of X

According to Question,

[tex]3x + x = 2480[/tex]

Collect like terms

[tex]4x = 2480[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{2480}{4} [/tex]

Calculate

[tex]x = 620[/tex]

Thus, There are 620 comic books in the book store.

Hope this helps...

Best regards!!

Answer:

b. 0.585

Step-by-step explanation:

According to Bayes' theorem:

[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]

Let A = Person is infected, and B = Person tested positive. Then:

P(B|A) = 93.9%

P(A) = 5.8%

P(B) = P(infected and positive) + P(not infected and positive)

[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]

Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:

[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]

The probability is 0.585.

Answer:

C. x+4y=-8

Step-by-step explanation:

The standard form of an equation is Ax+Bx=C

y= -[tex]\frac{1}{4}[/tex]x-2

Multiply 4 by both sides

4y= -x-8

1+4y= -8

Answer:

see graph

Step-by-step explanation:

A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.

Answer:

The 95% confidence interval for the mean score, , of all students taking the test is

        [tex]28.37< L\ 30.63[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is [tex]n = 59[/tex]

    The mean score is  [tex]\= x = 29.5[/tex]

     The standard deviation [tex]\sigma = 5.2[/tex]

Generally the standard deviation of mean is mathematically represented as

                [tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]

             [tex]\sigma _{\= x} = 0.677[/tex]

The degree of freedom is mathematically represented as

          [tex]df = n - 1[/tex]

substituting values

        [tex]df = 59 -1[/tex]

        [tex]df = 58[/tex]

Given that the confidence interval is 95%  then the level of significance is mathematically represented as

         [tex]\alpha = 100 -95[/tex]

        [tex]\alpha =[/tex]5%

        [tex]\alpha = 0.05[/tex]

Now the critical value at  this significance level and degree of freedom is

       [tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]

Obtained from the critical value table  

    So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as

      [tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]

substituting value

      [tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]

       [tex]28.37< L\ 30.63[/tex]

Answer:

x = 1

Step-by-step explanation:

Set up the rational expression with the same denominator over the entire equation.

Since the expression on each side of the equation has the same denominator, the numerators must be equal

5x =4x+1

Move all terms containing x to the left side of the equation.

Hope this can help you

Answer:

6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.

Step-by-step explanation:

Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.

Answer:

I think it is

Step-by-step explanation:

Answer:

5n√2m^ - 3mn

Step-by-step explanation:

Answer:

A =625 ft^2

Step-by-step explanation:

The perimeter of a square is

P = 4s where s is the side length

100 =4s

Divide each side by 4

100/4 = 4s/4

25 = s

A = s^2 for a square

A = 25^2

A =625

Answer:

The speed of the first train is 70 km/hr

The speed of the second train is 60 km/hr

Step-by-step explanation:

For the first train:

Travel time = 2 hours

The speed = ?

we designate the speed as V

For the second train:

The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)

speed = 10 km/hr slower than that of the first train, we can then say

the speed = V - 10

The total distance traveled by both trains in the opposite direction of one another is 215 km

we can put this problem into an equation involving the distance covered by the trains.

we know that distance = speed x time

the distance traveled by the first train will be

==> 2 hrs x V = 2V

the distance traveled by the second train will be

==> 1.25 hrs x (V - 10) = 1.25(V - 10)

Equating the above distances to the total distance between the trains, we'll have

2V + 1.25(V - 10) = 215

2V + 1.25V - 12.5 = 215

3.25V = 215 + 12.5

3.25V = 227.5

V = 227.5/3.25 = 70 km/hr     this is the speed of the first train

Recall that the speed of the second train is 10 km/hr slower, therefore

speed of the second train = 70 - 10 = 60 km/hr

The speed of the trains are 70km/hr and 60km/hr respectively.

The distance of the first train will be represented by: = 2 × D = 2D

The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).

Based on the information given in the question, the equation to solve the question will be:

2D + 1.25(D - 10) = 215

Collect like terms

2D + 1.25D - 12.5 = 215

3.25D = 215 + 12.5

3.25D = 227.5

D = 227.5/3.25

D = 70km/hour

The speed of the second train will be:

= 70 - 10 = 60km per hour.

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Answer: The machine depreciates during the fifth year by $4000.

Step-by-step explanation:

Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.

When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.

Then, the machine depreciates A(x) during the fifth year as

[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]

Hence, the machine depreciates during the fifth year by $4000.

Answer:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Step-by-step explanation:

For this case we have the following function:

[tex] y= x^4 -36x^2[/tex]

We can find the first derivate and we got:

[tex] y' = 4x^3 -72x[/tex]

In order to find the concavity we can find the second derivate and we got:

[tex] y'' = 12x^2 -72[/tex]

We can set up this derivate equal to 0 and we got:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Answer:

Step-by-step explanation:

Question:

4(y - 3) = 48

1. Distribute

4y - 12 = 48

2. Simplify Like terms

4y - 12 = 48

    + 12 + 12

4y = 60

3. Solve

4y = 60

/4       /4

y = 15

4. Check:

4(y - 3) = 48

4((15) - 3) = 48

4(12) = 48

48 = 48     Correct!

Hope this helped,

Kavitha

Answer:

[tex]y=15\\[/tex]

Step 1:

To find y, we first have to multiply [tex]4(y-3)[/tex]. When we do that (4 * y, 4 * - 3), we get [tex]4y-12[/tex].

Step 2:

Our equation looks like this now:

[tex]4y-12=48[/tex]

To solve this equation, we have to add 12 on both sides so we can cancel out the -12 on the left side of the equation.

[tex]4y-12(+12)=48(+12)[/tex]

[tex]4y=60[/tex]

Now, we can divide 4 on both sides to get y  by itself.

[tex]4y/4\\60/4[/tex]

[tex]y=15[/tex]

Answer:

75

Step-by-step explanation:

x = 75°

yes x = 75°(OPPOSITE ANGLES ARE EQUAL)

..