A random sample of 100 cars was taken and data were recorded on the miles per gallon (mpg) in the city and on the highway. The mean city mpg was 28 with a standard deviation of 9.2. The mean highway mpg was 35 with a standard deviation of 8.6. The correlation coefficient between city mpg and highway mpg is 0.95. Although a scatterplot is not show, it has been determined that a linear equation is appropriate for the data. Determine the correct value of the slope for the linear model that predicts highway mpg based on city mpg and interpret it in context.

To find the inverse, interchange the variables and solve for y. f−^1(x)=−3x/2−7/4

To find the inverse, interchange the variables and solve for  

f − 1 ( x ) = − 3 x 2 − 7 4

hope  this helped and I know this is the answer

Answer:327412000

Step-by-step explanation:

Answer: Two-way frequency tables are especially important because they are often used to analyze survey results. Two-way frequency tables are also called contingency tables. Two-way frequency tables are a visual representation of the possible relationships between two sets of categorical data.

Step-by-step explanation:

=======================================================

Explanation:

If order mattered, then we'd have 17*16*15 = 4080 different permutations. Notice how I started with 17 and counted down 1 at a a time until I had 3 slots to fill. We count down by 1 because each time we pick someone, we can't pick them again.

So we have 4080 different ways to pick 3 people if order mattered. But again order doesn't matter. All that counts is the group itself rather than the individual or how they rank. There are 3*2*1 = 6 ways to order any group of three people, which means there are 4080/6 = 680 different combinations possible.

An alternative is to use the nCr formula with n = 17 and r = 3. That formula is

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

where the exclamation marks indicate factorials

The number of different ways that are there to select 3 players is 680.

Since there is A team of 17 softball players need to choose three players to refill the water cooler.

So here we can say there are [tex]17\times 16\times 15 = 4080[/tex]

And, since we have to select 3 people so the no of ways should be [tex]3\times 2\times 1 = 6\ ways[/tex]

So, here the number of different ways should be

[tex]= 4080\div 6[/tex]

= 680

Therefore, The number of different ways that are there to select 3 players is 680.

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Answer:

The answer is below

Step-by-step explanation:

a)Given that the length of fencing available is 400 yards. This means that the perimeter of the rectangle is 400 yards.

the perimeter of a rectangle is given as:

Perimeter = 2(length + width) = 2(l + w)

Hence;

400 = 2(l + w)

200 = l + w

l = 200 - w

The area of a rectangle is given as:

Area = length × width

Area = (200 - w) × w

Area = 200w - w²

b) For a quadratic equation y = ax² + bx + c. it has a maximum at x = -b/2a

Hence, for the area = 200w - w² a=-1, b = 200, the maximum width is at:

w = -b/2a = -200/2(-1) = -200/-2 = 100

A width of 100 yard has the largest area

c) l = 200 - w = 200 - 100 = 100 yards

Area = l × w = 100 × 100 = 10000 yd²

The maximum area is 10000 yd²

Answer:

The answer for both apples and bananas is 21

The answer for only apples or only bananas is 45

Step-by-step explanation:

36 plus 30 minus 45

50-5 is 45

only apples or bananas is 15 + 9

Answer:

A) 58

Step-by-step explanation:

Mean = Sum of all the data ÷  total number of data

         [tex]=\frac{52+70+88+15+65}{5}\\\\\\=\frac{290}{5}\\\\\\= 58[/tex]

Answer:

rational numbers

Step-by-step explanation:

Answer:

53.5 DEGREES

Step-by-step explanation:

90 + 36.5 = 125.6

180 - 126.5 = 53.5 degrees

The measure of the other small angle will be 53.5 degree.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In a right triangle, One angle measures 36.5 degrees.

Now,

Since, The triangle is a right triangle.

So, One of the angle = 90 degree

And, One angle measures 36.5 degrees.

Let the measure of the other small angle = x degree

Since, The sum of all the interior angles in a triangle = 180 degree

So, We can formulate;

⇒ x + 90 + 36.5 = 180

⇒ x + 126.5 = 180

⇒ x = 180 - 126.5

⇒ x = 53.5 degree.

Thus, The measure of the other small angle will be 53.5 degree.

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Answer:

715,340 > 715,034

Step-by-step explanation:

Answer:

.18n+2400-.06n=6000

.12n=3600

n=3600/.12=$30000 at 18%, $10000 at 6%

Step-by-step explanation:

Answer:

  all real numbers except x=2

Step-by-step explanation:

We assume you intend c(x) = 5/(x-2), rather than c(x) = (5/x) -2 as written.

__

The domain of c(x) is real numbers, excluding 2. Multiplying c(x) by d(x) doesn't change that.

The domain of (cd)(x) = c(x)×d(x) = 5(x+3)/(x-2) is "all real numbers except 2".

__

2 is excluded because c(x) is undefined for that value.

Answer:

123.76

Step-by-step explanation:

a negative times a negative is a positive

22.1 times 5.6 is 123.76

Answer:

- 1/2

Step-by-step explanation:

(-4/5) × (- 5/8)

- 4/5 × - 5/8

First we mulitply across

The top and the bottom.

- 20 / 40

because -4 × -5 = +20

and -5 × -8 = +40

Now we simplify the fraction

- 20 / 40

= - 2 /4

= - 1/2

Because we have to simplify it and so I divided it by 10 first.

-20 ÷ 10 = -2 and -40 ÷ 10 = -4

Then I simplified it again by dividing it by 2.

-2 ÷ 2 = -1 and -4 ÷ 2 = -2

So finally we have:

-1/2

And we cannot simplify that anymore so that is the answer.

Hope that helped!

Answer:

1/2

Step-by-step explanation:

since negative * negative= positive we multiply the top and bottom to get. 20/40 which simplifies

Answer:

[tex]\Huge \boxed{-2.3, \ \frac{-1}{3} , \ \sqrt{3} , \ \sqrt{7} , \ 5.1}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

We will convert the values into decimals for simplicity.

[tex]\sqrt{7} = 2.64575131106...[/tex]

[tex]-2.3=-2.3[/tex]

[tex]\sqrt{3} = 1.73205080757...[/tex]

[tex]5.1=5.1[/tex]

[tex]\displaystyle \frac{-1}{3} =-0.333333333...[/tex]

Arranging from least to greatest:

[tex]\displaystyle -2.3, \ \frac{-1}{3} , \ \sqrt{3} , \ \sqrt{7} , \ 5.1[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

37

Step-by-step explanation:

The calculation of size for a new television is shown below:-

With the help of Pythagoras theorem

[tex]h^2 = b^2 + p^2[/tex]

where

h indicates hypotenuse which is the diagonal length

b indicates the base which is the length of the horizontal side

p indicates perpendicular which is the TV length of the vertical side.

[tex]h^2 = \sqrt{b^2 + p^2}[/tex]

now, we will put the values into the above formula

[tex]= \sqrt{32^2 + 18^2} \\\\ = \sqrt{1024 + 324} \\\\ = \sqrt{1348}[/tex]

Which gives result

= 36.7

or

= 37

Answer:

  see below

Step-by-step explanation:

Each age bracket defines a domain of the function. The function value is constant for that domain. This function gives admission price (P) as a function of age (a).

  [tex]P(a)=\left\{\begin{array}{ccl}0&\text{for}&a\le5\\3&\text{for}&5<a\le18\\5&\text{for}&18<a<65\\4&\text{for}&a\ge65\end{array}\right.[/tex]

Answer:

Hi

Step-by-step explanation:

Hi

Step-by-step explanation:

Part 1

To find out the amount of water ten big water bottles can hold, we have to find out how much water is in each water bottle. To do this, we divide the amount we are looking for by the number of items.

8 ÷ 4 = 2

Part 1 answer: Each water bottle can hold 2 gallons of water.

Part 2

Now that we know the amount of water in each water bottle, we can find out how much water 10 water bottles can hold. To do so, we multiply our previous answer, 2, by the number of items (10).

2 • 10 = 20

Part 2 answer: 10 water bottles can hold 20 gallons of water.

Our final answer: 20 gallons

I hope this helps you!

Answer:

-12

Step-by-step explanation:

Answer:

x=0

Step-by-step explanation:

First, we distribute on both sides

6x+6-5x=8+2x-2

simplify

x+6=2x+6

subtract x from both sides

6=x+6

subtract 6 from both sides

x=0

(plz give brianliest ty)

Answer:

x = 0

Step-by-step explanation:

6 ( x + 1 ) -5x = 8 + 2 ( x - 1 ) (Distribute)

6x + 6 - 5x = 8 + 2x - 2 (Rearrange expression)

6x - 2x - 5x = 8 - 6 - 2 (Combine like terms)

-1x = 0 (Divide)

x = 0

Answer:

Step-by-step explanation:

Ordered pair (0, 0) & (0.5, 2.5)  will fall on the line of graph

Step-by-step explanation:

Megan expects to save an average of 5 dollars per week from her babysitting earnings.

=> Saving Per  week  = 5 $

Saving in 0.5 Week = 0.5 * 5 = 2.5 $

hence ordered pair (0.5, 2.5)  will fall on the line of graph

Saving in 3 Week = 3 * 5 = 15 $

Hence (3, 18) will not fall on  line

Saving in 0 Week = 0.5 * 0 = 0 $

hence ordered pair (0, 0)  will fall on the line of graph

Saving in 4.5 Week = 4.5 * 5 = 22.5 $

Hence (4.5, 30) will not fall on  line

Ordered pair (0, 0) & (0.5, 2.5)  will fall on the line of graph

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

Megan expects to save an average of 5 dollars per week from her babysitting earnings.

=> Saving Per  week  = 5 $

Saving in 0.5 Week = 0.5 * 5 = 2.5 $

hence ordered pair (0.5, 2.5)  will fall on the line of graph

Saving in 3 Week = 3 * 5 = 15 $

Hence (3, 18) will not fall on  line

Saving in 0 Week = 0.5 * 0 = 0 $

hence ordered pair (0, 0)  will fall on the line of graph

Saving in 4.5 Week = 4.5 * 5 = 22.5 $

Hence (4.5, 30) will not fall on line

Hence, Ordered pair (0, 0) & (0.5, 2.5)  will fall on the line of graph.

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Answer:

FG = 39

Step-by-step explanation:

From the question given:

FH = 9x + 15

GH = 5x + 4

FG = ?

From the question given above, we can say that G is the midpoint of FH. This implies that:

FH = FG + GH

With the above idea in mind, we can obtain FG as follow:

FH = 9x + 15

GH = 5x + 4

FG = ?

FH = FG + GH

9x + 15 = FG + 5x + 4

Rearrange

FG = 9x + 15 - 5x - 4

FG = 9x - 5x + 15 - 4

FG = 4x + 11

Next, we shall determine the value of x. This can be obtained as follow:

Since G is the midpoint of FH, it therefore means that FG and GH are equal i.e

FG = GH

With the above idea in mind, we can obtain the value of x as follow:

FG = 4x + 11

GH = 5x + 4

FG = GH

4x + 11 = 5x + 4

Collect like terms

11 - 4 = 5x - 4

7 = x

x = 7

Thus, we can obtain the value of FG as follow:

FG = 4x + 11

x = 7

FG = 4x + 11

FG = 4(7) + 11

FG = 28 + 11

FG = 39

***Check ***

FH = 9x + 15

x = 7

FH = 9(7) + 15 = 63 + 15 = 78

GH = 5x + 4

x = 7

GH = 5(7) + 4 = 35 + 4 = 39

FG = 4x + 11

x = 7

FG = 4(7) + 11 = 28 + 11 = 39

FH = FG + GH

FH = 78

FG = 39

GH = 39

FH = FG + GH

78 = 39 + 39

78 = 78

Answer:

as we know, the integral of [tex]x^{n}[/tex] is [tex]\frac{x^{n+1} }{n+1}[/tex]

so, the integral of x.[tex]2^{x}[/tex] will be found as follows:

here, we will use a trick called 'integration by parts'

let x = u and [tex]2^{x}[/tex] = v

∫uv dx = u∫v dx - ∫[(du/dx)* ∫v dx] dx

∫x.[tex]2^{x}[/tex] dx = x∫[tex]2^{x}[/tex] - ∫[(dx/dx) * ∫[tex]2^{x}[/tex] dx ] dx

∫x.[tex]2^{x}[/tex] dx = x*[tex]\frac{2^{x+ 1}}{x+ 1}[/tex] - 1 * [tex]\frac{2^{x + 1} }{x + 1}[/tex]

= [tex]\frac{2^{x} }{x + 1}[/tex]( x - 1 )

Answer:

(a)   x follows a poisson distribution with parameter λ = 8 / hour

(b)   P( X = 5 ) = 0.09160

      P( X ≥ 5 ) = 0.9004

(c)   the expected value  of the number of nonconforming parts produced during a 120-min period = 16 nonconforming parts per 120 minutes

The standard deviation = 4

(d)   P(X ≥ 20) = 0.5297

      P( X ≤  10) = 0.0108

Step-by-step explanation:

Suppose nonconforming parts are produced with a rate = 8 / hour (i.e. on average, 8 nonconforming parts will be made during a production period of one hour).

(a)  If x denotes the number of nonconforming parts made during one hour, then : x follows a poisson distribution with parameter λ = 8 / hour

(b)

What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?

the probability that exactly 5 nonconforming parts are produced during a 1-hour period can  be computed as:

P( X = 5 ) = [tex]e^{- \lambda } \lambda^x /x![/tex]

P( X = 5 ) = [tex]e^{- 8 }(8)^5 /5![/tex]

P( X = 5 ) = 0.09160

the probability that at least 5 nonconforming parts are produced during a 1-hour period

P( X ≥ 5 ) = 1 -  P( X ≤ 4)

[tex]P( X \geq 5 ) = 1 - \sum \limits ^4_{x=0} e^{-\lambda} \lambda ^x/x![/tex]

[tex]P( X \geq 5 ) = 1 - (e^{-8} 8 ^4/4! + e^{-8} 8 ^3/3! + e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]

[tex]P( X \geq 5 ) = 1 - 0.0996[/tex]

P( X ≥ 5 ) = 0.9004

c)  What are the expected value and standard deviation of the number of nonconforming parts produced during a 120-min period?

the expected value  of the number of nonconforming parts produced during a 120-min period [tex]\lambda = 8 \times \dfrac {120}{60}[/tex]

= 16 nonconforming parts per 120 minutes

The standard deviation = [tex]\lambda^{1/2}[/tex]

The standard deviation = [tex](16)^{1/2}[/tex]

The standard deviation = 4

(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?

During a 2.5 - hour period , the expected value = 8 × 2.5 = 20

As such, the probability  that at least 20  nonconforming parts produced during a 2.5-hour period is:

P(X ≥ 20) = 1 - P(X ≤ 19)

[tex]P( X \geq 20 ) = 1 - \sum \limits ^{19}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]

[tex]P( X \geq 20 ) = 1 - (e^{-8} 8 ^{19}/19! + e^{-8} 8 ^{18}/{18}! + e^{-8} 8 ^{17}/17!+...+e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]

P(X ≥ 20) = 1 -  0.4703

P(X ≥ 20) = 0.5297

Probability that at most  10 nonconforming parts produced during this period is:

P( X ≤  10) = [tex]\sum \limits ^{10}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]

[tex]P( X \leq 10) = e^{8} 8 ^{10}/{10}! + e^{8} 8 ^{9}/{9}! + e^{8} 8 ^{8}/{8}! + ...+ e^{8} 8 ^{2}/{2}!+ e^{8} 8 ^{1}/{1}! + e^{8} 8 ^{0}/{0}![/tex]

P( X ≤  10) = 0.0108

Following are the calculation to the given points:

For point a)

With parameter, x follows the poisson distribution is [tex]\lambda=\frac{8}{hour}[/tex]

For point b)

The probability that exactly 5 nonconforming parts are generated in a one-hour period.

[tex]\to P(X=5)=e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0916[/tex]

There is a good chance that at least 5 nonconforming parts exist.

[tex]\to P(X\geq 5) =1-P(X\leq 4)[/tex]

                 [tex]=1 -\sum_{x=0}^{4} \ e^{-\lambda } \frac{\lambda ^{x}}{x!} \\\\=1-0.0996\\\\=0.9004[/tex]

For point c)

Expected value for 120-minute period [tex]\lambda=8\times \frac{120}{60} =16[/tex] 120 minutes of nonconforming sections

[tex]\to \sigma ==(\lambda)^{\frac{1}{2} =(16)^{\frac{1}{2}} =4[/tex]

For point d)

Expected value for 2.5 hours

[tex]\to \lambda =8\times 2.5=20[/tex]

As a result, there is a good chance that at least 20 nonconforming items were manufactured.

[tex]\to P(X\geq 20)=1-P(X\leq 19)[/tex]

                   [tex]=1-\sum_{x=0}^{19}\ e^{-\lambda }\frac{\lambda^{x}}{x!}\\\\=1-0.4703\\\\=0.5297[/tex]

There is a chance that no more than 10 nonconforming parts were created.

[tex]\to P(X\leq 10)=\sum_{x=0}^{10}e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0108[/tex]

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add 6 plus 33 then do x+1 then you divide

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

Answer: 32/3

Step-by-step explanation:

To find the area of the region between the curves, you first want to find the interval of both curves. You can do that by setting both curves equal to each other.

[tex]-\frac{1}{2}x^2+2=\frac{1}{2} x^2-2[/tex]                   [subtract both sides by 2]

[tex]-\frac{1}{2}x^2= \frac{1}{2} x^2-4[/tex]                         [subtract both sides by [tex]\frac{1}{2} x^2[/tex]]

[tex]-x^2=-4\\x=2,-2[/tex]        

Now that we know the interval, we set this into an integral and subtract the top curve by the bottom curve. *Note: I can't type in -2 into the interval, therefore only a "-" will be displayed.

[tex]\int\limits^2_- {|-\frac{1}{2}x^2+2-(\frac{1}{2}x^2-2) | } \, dx[/tex]                     [distribute -1]

[tex]\int\limits^2_-{|-\frac{1}{2}x^2+2-\frac{1}{2}x^2+2 |} \, dx[/tex]                       [combine like terms]

[tex]\int\limits^2_- {|-x^2+4|} \, dx[/tex]                                          [solve integral]

[tex]\frac{32}{3}[/tex]

The area between the curves is 32/3. This was also the reason why we had the absolute values because area can never be negative.

Answer:

Line Segment

Step-by-step explanation:

Because the start on a line and end on a line.

Answer:

line segment

Step-by-step explanation: