Find the area of the shaded part ! ​

Find The Area Of The Shaded Part !

Answers

Answer 1

Answer:

Step-by-step explanation:

Semicircle:

Shaded area of semicircle = area of outer semicircle - area of inner semicircle

Outer semicircle:

d = 40 m  r = 40/2 = 20m

Area of outer semicircle = πr²

                                        = 3.14*20*20

                                        =    1256 m²

Inner semicircle:

d = 30 m  r = 30/2 = 15 m

Area of outer semicircle = πr²

                                        = 3.14*15*15

                                        =  706.5 m²

Shaded area of semicircle = 1256 - 706.5 = 549.5 m²

Shaded area of semicircle in both sides = 2 * 549.5 = 1099 m²

Rectangle on both sides:

Length = 50 m

width = 30 m

Area of shaded rectangles on both sides = 2* (length *width)

                                                                      = 2* 50 * 30

                                                                       = 3000 m²

Shaded area = 1099 + 3000 = 4099 m²


Related Questions

In 5 days she made 80 sandcastles. Each day she made 4 fewer castles than the day before. How many castles did she make each day?

Answers

Answer:

Castles made:    N         day 1

                           N - 4    day 2

                           N - 8     day 3

                           N - 12     day 4

                           N - 16      day 5

Total   5 N - 40 = 80

              N = 24  total  castles day 1

Total castles = 24 + 20 + 16 + 12 + 8 = 80

-1/2(6x-10)=1/3(6x+9)

Answers

Answer:

x = 2/5

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

-1/2(6x - 10) = 1/3(6x + 9)

Step 2: Solve for x

[Distributive Property] Distribute parenthesis:                                               -3x + 5 = 2x + 3[Subtraction Property of Equality] Subtract 2x on both sides:                      -5x + 5 = 3[Subtraction Property of Equality] Subtract 5 on both sides:                        -5x = -2[Division Property of Equality] Divide -5 on both sides:                                x = 2/5

Last year, the CDC claimed there were 1700 different strains of a virus around the
world. Since then, numbers have increased by 9.7% more than what the scientists
originally estimated. How many strains are estimated currently? Round to the nearest
number.

Answers

Answer: 1865

Step-by-step explanation:

Given

Claimed strains of virus is 1700

If it is increased by 9.7%

Estimated value can be given by

[tex]\Rightarrow 1700+1700\times 9.7\%\\\Rightarrow 1700(1+0.097)\\\Rightarrow 1700\times 1.097\\\Rightarrow 1864.9\approx 1865[/tex]

Thus, the estimated number is [tex]1865[/tex]

Which graph represents the function f (x) = StartFraction 1 Over x + 3 EndFraction minus 2?

Answers

Given:

The function is:

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

To find:

The graph of the given function.

Solution:

We have,

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

It can be written as:

[tex]f(x)=\dfrac{1-2(x+3)}{x+3}[/tex]

[tex]f(x)=\dfrac{1-2x-6}{x+3}[/tex]

[tex]f(x)=\dfrac{-2x-5}{x+3}[/tex]

Putting [tex]x=0[/tex] to find the y-intercept.

[tex]f(0)=\dfrac{-2(0)-5}{(0)+3}[/tex]

[tex]f(0)=\dfrac{-5}{3}[/tex]

So, the y-intercept is [tex]\dfrac{-5}{3}[/tex].

Putting [tex]f(x)=0[/tex] to find the x-intercept.

[tex]0=\dfrac{-2x-5}{x+3}[/tex]

[tex]0=-2x-5[/tex]

[tex]2x=-5[/tex]

[tex]x=\dfrac{-5}{2}[/tex]

[tex]x=-2.5[/tex]

So, the x-intercept is [tex]-2.5[/tex].

For vertical asymptote, equate the denominator and 0.

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

So, the vertical asymptote is [tex]x=-3[/tex].

The degrees of numerator and denominator are equal, so the horizontal asymptote is the ratio of leading coefficients.

[tex]y=\dfrac{-2}{1}[/tex]

[tex]y=-2[/tex]

So, the horizontal asymptote is [tex]y=-2[/tex].

End behavior of the given function:

[tex]f(x)\to -2[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to -3^-[/tex]

[tex]f(x)\to \infty[/tex] as [tex]x\to -3^+[/tex]

[tex]f(x)\to -2[/tex] as [tex]x\to \infty[/tex]

Using all these key features, draw the graph of given function as shown below.

Answer:

The Answer Is A.

Step-by-step explanation:

A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?​

Answers

Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.

He wants to end up with a 44 mL solution, so

x + y = 44 mL

Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain

0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL

of acid.

Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives

0.04x + 0.15 (44 mL - x) = 5.28 mL

0.04x + 6.6 mL - 0.15x = 5.28 mL

1.32 mL = 0.19x

x ≈ 6.95 mL

==>   y ≈ 37.05 mL

Critical Thinking: Empirical/Quantitative Skills
United flight 15 from New York's JFK to San Francisco uses a Boeing 757-200 with 180 seats. Because some
people with tickets don't show up. United will overbook by selling more than 180 tickets. If the flight is not
overbooked, the airline will lose revenue due to empty seats, but if too many tickets are sold and some
passengers are denied seats, the airline loses money from the compensation that must be given to bumped
passengers. Assume that there is a 0.905 probability that a passenger with a ticket will show up for the
flight. Also assume that the airline sells 200 tickets for the 180 seats that are available.
1. When 200 tickets are sold, calculate the probability that exactly 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Show your calculation (ie. what you put in the calculator) and round to 4 decimals.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.

Answers

Answer:

1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using 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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Assume that there is a 0.905 probability that a passenger with a ticket will show up for the  flight.

This means that [tex]p = 0.905[/tex]

Also assume that the airline sells 200 tickets

This means that [tex]n = 200[/tex]

Question 1:

Exactly, so we can use the P(X = x) formula, to find P(X = 180).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910[/tex]

0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.

Now we have to use the approximation.

Mean and standard deviation:

[tex]\mu = E(X) = np = 200*0.905 = 181[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15[/tex]

Using continuity correction, this is [tex]P(X \leq 180 + 0.5) = P(X \leq 180.5)[/tex], which is the p-value of Z when X = 180.5. Thus

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

[tex]Z = \frac{180.5 - 181}{4.15}[/tex]

[tex]Z = -0.12[/tex]

[tex]Z = -0.12[/tex] has a p-value of 0.4522.

0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.

Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So

[tex]p + 0.4522 = 1[/tex]

[tex]p = 1 - 0.4522 = 0.5478[/tex]

0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

Evaluate the given expression for x = 5 and y=5. 6x2 + 7xy + 3y?​

Answers

Step-by-step explanation:

Given, x = 5

y = 5

= 6(5)^2 +7(5)(5) +3(5)

= 6(25)+7(25) +15

= 150+175 + 15

= 150 + 190

=340

Answer:

x = 12 y = 7

Step-by-step explanation:

6x^2 + 7xy + 3y

6(5)^2+ 7(5) + 7(8)y

6(5+5)+25+35 + 7(8)-7y

60+25+35+ 56-7y

y - 5 = 120 + 35 - 5 (+49y)

sqrt 150 + sqrt 49

x = 12 y = 7

A boy's mother was 32 years old when he was born. Let a represent the boy's age and m represent the mother's age.

Complete the table using the relationship between a and m.

PLEASE ANSWER!!!!

Answers

see the picture attached

Which word phrases represent the variable expression m – 11? Choose all answers that are correct. A. 11 more than a number B. the difference of a number and 11 C. the quotient of a number and 11 D. 11 less than a number

Answers

Answer: D

Step-by-step explanation:

m – 11

A. 11 more than a number ( m+11 )

B. the difference of a number and 11 ( 11/m )

C. the quotient of a number and 11  ( m/11 )

D. 11 less than a number ( m-11 )

Write the sum using summation notation, assuming the suggested pattern continues.

2, -10, 50, -250, +…

Is this sequence arithmetic or geometric? How do you know?

Answers

Answer:

[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]

Step-by-step explanation:

An arithmetic sequence is of the form:

[tex]A_n = A_{n-1} + d[/tex]

While a geometric sequence is of the form:

[tex]A_n = A_{n-1}*r[/tex]

notice that first, we have a change of sign in our sequence, so we already can discard the arithmetic sequence.

In fact, the pattern is kinda easy to see.

The first term is:

A₁ = 2

the second term is:

A₂ = -10

notice that:

A₂/A₍ = r = -10/2 = -5

The third term is:

A₃ = 50

the quotient between the third term and the second term is:

A₃/A₂ = 50/-10 = -5

Whit this we can already conclude that the n-th term of our sequence will be:

[tex]A_n = A_{n-1}*(-5)[/tex]

Then the summation will be something like:

[tex]\sum_{n = 1} A_n = A_1 + A_2 + A_3 + ... = 2 - 10 + 50 - ...[/tex]

We can write:

[tex]A_n = A_{n-1}*(-5) = (A_{n-2}*(-5))*(-5)) = A_1*(-5)^{n-1} = 2*(-5)^{n-1}[/tex]

Then the summation is just:

[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]

Is the answer right?

Answers

Answer:

one solution.. your answer is correct

Step-by-step explanation:

discriminate = 900 - (4*9*25)  = 0

thus only one solution

your answer is correct

f(x) = −16x2 + 24x + 16
what is the vertex

Answers

Answer:

VERTEX: (0.75,25)    

Step-by-step explanation:

the vertex will be at [-b/2a, f(-b/2a)]

−16x2 + 24x + 16

4(-4x^2 + 6x +4)

a = -4, b=6,c=4

-6/-8 = 3/4

f(3/4) = 25

Equation?
Slope?
Y-intercept?

Answers

Answer:

see explanation

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 )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (4, 2) ← 2 points on the line

m = [tex]\frac{2-(-3)}{4-0}[/tex] = [tex]\frac{2+3}{4}[/tex] = [tex]\frac{5}{4}[/tex]

The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = [tex]\frac{5}{4}[/tex] - 3 ← equation of line

Pleasant help me out explanation need it

Answers

Answer:

for which question???????????????

Answer:

Ok please tell me your question because you forgotten the question your asking dor

REVISED 2/3/
the following using the picture below.
4
a) Two pairs of supplementary angles:
b) A pair of complementary angles:







Please explain this! Thank you!

Answers

Supplementary angles are those angles which make a sum of 180°.

Complementary angles are those angles which make a sum of 90°.

The supplementary angles are given by the straight lines making angles of 180°.

There are two straight lines CB and DE

The angles DAF and FAE are the two angles making a straight line DE

The angles CAF and FAB are the two angles making a straight line CB

The complementary angles are given by angles formed between the perpendicular lines making angles of 90°.

Angle BAF is formed by angle BAE and angle AEF

Supplementary Angle given by the straight line DE is formed by the angles DAF and FAE.

Complementary Angle BAF is formed by angle BAE and angle AEF.

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Use a calculator to find the mean of the data. {21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}

Answers

Answer:

The mean of the data is 21.41

Step-by-step explanation:

To find the mean of a data set you must...

Add up all data values to get the sum

Count the number of values in your data set

Divide the sum by the count

The mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.

What is mean?

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

We have a data set:

{21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}

As we know from the definition of the mean:

The mean can be calculated using the formula:

Mean = sum of the data set/number of the data in the data set

Mean = 471/22

Mean = 21.409  ≈ 21.41

Thus, the mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.

Learn more about the mean here:

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f(x) = x2
g(x) = (x +4)^2 - 1
We can think of g as a translated (shifted) version of f.
Hurry I am in summer school and almost done I need help ASAP!

Answers

Answer:

down by 1 unit and left by 4 units

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift left of a units

• If a < 0 then a shift right of a units

Then

g(x) = (x + 4)² - 1

is f(x) shifted down by 1 unit and shifted left by 4 units

In a class of 5 , there are 3 students who have done their homework. If the teacher 2 chooses 2 2 students, what is the probability that none of them have done their homework?

Answers

Answer:

2 over 5

Step-by-step explanation:

This means out of 5 students only three did their work so 5-3=2

And the number of students who did their work over the total number of students in the class to find the probability

The probability that none of them have done their homework is 0.57%

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that there are 3 students who have done their homework.

If the teacher 2 chooses 2 students, then;

Total no. of Outcomes= 5

Students who did their homework = 3

Students who didn't do their homework is 5-3 = 2

Probability of no. of students who haven't done their homework.

P(e)= 2/5

Thus P(students who haven't done homework) P(e)=0.57%

Learn more about probability here;

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There are about 320 million people living in the United States. Of these, how many would you predict wear corrective lenses?

Answers

Answer:

243840000 people

Step-by-step explanation:

The total sample size = 1000

Samole proportion of those who wear corrective lenses :

p = x / n ; n = sample size

p = 762 / 1000 = 0.762

To predict the number of people who wear corrective lenses :

Total population * p

320,000,000 * 0.762

= 243840000 people

Answer:

243840000

Step-by-step explanation:

11) 161.3 is what percent of 177.2?

Answers

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Answer:

it's 91.027%

Step-by-step explanation:

I hope i helped

Mr. Johnson took up an appointment with Nestle Ghana as an accountant with an annual salary of $164 million. as part of his appointment, he was promised a yearly increment of $24 million. Mr Johnson got promoted to chief accountant after six years of work with an annual salary of $300 million and yearly increment of$36 million.
calculate a) Mr. Johnson's salary in the tenth year of service.
b). Mr. Johnson's total earnings at the end of the tenth year of service.

Answers

Good luck you’re going to need it

Answer:

300 million(1+ 36 million) y

Step-by-step explanation:

A laptop was originally sold for $975. The laptop is now on sale for $828.75.The percent markdown must have been...

Answers

Answer:

15% markdown

Step-by-step explanation:

To find the percent markdown

Take the original price minus the new price

975-828.75

146.25

Divide by the original price

146.25/975

.15

Change to percent form

15% markdown

Please Help!! much appreciated! :D

Find the value of y.

Answers

In the largest triangle, the missing side has length

√((11 + 5)² - x ²) = √(256 - x ²)

But it's also the hypotenuse of the triangle with side lengths 11 and y, so that its length can also be written as

√(11² + y ²) = √(121 + y ²)

so that

√(256 - x ²) = √(121 + y ²)

or, by taking the squares of both sides,

256 - x ² = 121 + y ²

y ² = 135 - x ²

In the smallest triangle, you have

5² + y ² = x ²   ==>   x ² = 25 + y ²

Substitute this into the previous equation and solve for y :

y ² = 135 - (25 + y ²)

y ² = 110 - y ²

2y ² = 110

y ² = 55

y = √55

Find the value of x and y.
60°
6

Answers

Answer:

b .

x = 3

y = 3[tex]\sqrt3[/tex]

Step-by-step explanation:

Using the pythagorean identities for 30-60-90° triangle,

we know the ratio of the sides is    x - x√3 - 2x

Since 2x = 6

Then smallest side is x (opposite ∠30°) = 6/2 = 3

The other side y , opposite ∠60° will be x√3 or 3√3.

9514 1404 393

Answer:

  B. x = 3; y = 3√3

Step-by-step explanation:

You only need to use your sense of triangles to choose the correct answer:

  x < y < 6

This relation fits only one answer choice:

  x = 3, y = 3√3

_____

Additional comment

For multiple choice questions, it isn't always about working the problem. Usually, it is about knowing what the answer has to look like. The usual criteria are (a) is the answer true; (b) does the answer make sense in the context of the problem statement; (c) can you get this answer if you work the problem in detail. More often than not, the first two criteria will let you choose the correct answer without doing any detailed solving.

A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 110 feet. The smallest path bordering the patch of grass measures 55 feet. The smallest angle formed by the paths bordering the patch of grass measures 29º.
What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest
degree. Show all your work.

Answers

Answer:

76 degrees

Step-by-step explanation:

First, we can draw a picture. Two of the sides are 110 feet and 55 feet. In a triangle, the smallest angle is opposite the smallest side and vice versa. Therefore, if I have my triangle arranged in the way shown, the smallest angle of 29 degrees will be opposite of the smallest side of 55 feet.

The law of sines states that a/sinA=b/sinB=c/sinC , with corresponding angles being opposite of its corresponding side. Therefore, we can say that

55 feet/ sin(29 degrees) = 110 / sin(largest angle).

If we say that the largest angle is equal to x, we can say

55 / sin(29°) = 110/sin(x)

multiply both sides by x to remove a denominator

55 * sin(x)/ sin(29°) = 110

multiply both sides by sin(29°) to remove the other denominator

55 * sin(x) = 110 * sin(29°)

divide both sides by 55 to isolate the sin(x)

sin(x) = 110 * sin(29°) / 55

For an angle, if sin(x) = y, we can say that arcsin(y) = x. Therefore, we can say

x = arcsin(110 * sin(29°)/55)

x ≈ 76 degrees

triangle ABC is reflected about the line Y equals negative X to give triangle ABC with vertices A (-1, 1), B (-2, -1), C (-1,0). What are the vertices of triangle ABC?

Answers

9514 1404 393

Answer:

A'(-1, 1)B'(1, 2)C'(0, 1)

Step-by-step explanation:

Reflection across the line y = -x is accomplished by the transformation ...

  (x, y) ⇒ (-y, -x)

Then the images of the given points are ...

  A(-1, 1) ⇒ A'(-1, 1) . . . . this point is on the line of reflection, so doesn't move

  B(-2, -1) ⇒ B'(1, 2)

  C(-1, 0) ⇒ C'(0, 1)

3.3 A circle has a radius of 12cm. An angle of 3.2 radians is subtended at the centre by an arc. Calculate the length of the arc. (3)​

Answers

Answer:

S = 38.4 centimeters.

Step-by-step explanation:

Given the following data;

Radius, r = 12 cmAngle = 3.2 rads

To find the length of the arc of a circle;

A full circle measures an angle of 360 degrees.

π = 180°

So; Angle, A = 360° = 2π

Therefore, a full circle is equal to 2π in terms of radians (rads).

Also, the circumference (the length of an arc) of a circle is equal to 2πr or Ar.

Mathematically, the length of the arc of a circle is given by the formula;

S = rA

Where;

S is the length of the arc.A is the angle measured in radians.

Substituting into the formula, we have;

S = 12 * 3.2

S = 38.4 centimeters.

11 + box equals 19 find box​

Answers

Answer:

8

Step-by-step explanation:

11 + x = 19

Subtract 11 from each side

11+x -11 = 19-11

x = 8

Answer:

8

Step-by-step explanation:

11 + box = 19

=> box = 19 - 11

.°. box = 8

Hans rented a truck for one day. There was a base fee of $15.95, and there was an additional charge of 77 cents for each mile driven. Hans had to pay
$207,68 when he returned the truck. For how many miles did he drive the truck?

Answers

Answer: 249 miles

Step-by-step explanation:

First write a function that represents the amount paid for renting a truck:

Set x as each mile driven.Set y as the total amount paid.$15.95 is the base fee paid no matter the mile, meaning the rent start at $15.95, not 0.

Function: y = mx + b

m = slope = amount paid for each mile driven = 77¢ = $0.77b = y-intercept = amount paid when 0 miles driven = base fee = $15.95

y = 0.77x + 15.95

He paid a total of $207.68, therefore y = 207.68:

207.68 = 0.77x + 15.95

Solve the equation for x:

207.68 - 15.95 = 0.77x

191.73 = 0.77x

x = 249 miles driven

A manager records the repair cost for 14 randomly selected dryers. A sample mean of $88.34 and standard deviation of $19.22 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the dryers. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer:

Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]

Step-by-step explanation:

Given that,  

Point estimate = sample mean = [tex]\bar x[/tex] = 88.34  

sample standard deviation = s = 19.22  

sample size = n = 14  

Degrees of freedom = df = n - 1 = 13  

Critical value =[tex]t\alpha /2,[/tex] df = 1.771

 

Margin of error

[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]  

Margin of error = E = 9.10  

The 90% confidence interval estimate of the population mean is,  

[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]

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