2) a truck rental company rents a moving truck one day by charging $31 plus $0.13 per mile. write a linear equation that relates the cost c, in dollars, of renting the truck to the number x of miles driven. what is the cost of renting the truck if the truck is driven 180 miles? a) c(x)

The linear regression equation that represents this data is given as follows: y = 22x - 518.

Using this equation, when 38 passes are thrown, the expected yardage is of 318 yards.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

In the context of this problem, the input and output are given as follows:

The points to be inserted in the calculator are given as follows:

(39, 360), (35, 235), (35, 262), (37, 249), (40, 338).

Hence the equation is given by:

y = 22x - 518.

With 38 passes, the expected yardage is calculated as follows:

y = 22(38) - 518 = 318 yards.

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After solving the given equation using quadratic formula we gat solutions as 0.83 and 0.169

What is quadratic formula?

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b±√(b²-4ac))/(2a).

On simplifying the given equation we get,

(2x-3)²=4x

4x²+9-12x = 4x

4x²-16x+9 = 0

Comparing with ax²+bx+c = 0

a = 4, b = -16, c = 9

Quadratic formula is:

[tex]\frac{-b +- \sqrt{b^2-4ac} }{2a}[/tex]

putting the values from question we get,

[tex]\frac{16 +- \sqrt{16^2-4(4)(9)} }{216}[/tex]

[tex]\frac{16 +- \sqrt{256-144} }{32}[/tex]

[tex]\frac{16 +- \sqrt{112} }{32}[/tex]

[tex]Solution 1 = \frac{ 16+ 10.58 }{32} = 0.83[/tex]

[tex]Solution 2 = \frac{16 - 10.58}{32} = 0.169[/tex]

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Complete question

(2x-3)²=4x solve using quadratic formula

Answer:

The answer is B.

Step-by-step explanation:

I remember this question.

Answer:

c

Step-by-step explanation:

The width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200.

A rectangular garden has a length of 60 feet (ft)

a width of w ft

and a perimeter of 200 ft.

The formula of perimeter of a rectangle is 2(lenght + width)

The equation that represents the garden's perimeter is 2(60 + w) = 200

2(60 + w) = 200

120 + 2w = 200

2w = 200 - 120

2w = 80

w = 40

Therefore, width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200

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The age of the radioactive artifact is approximately 19029.6 years old

Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.

To solve this problem, we have to find the disintegration constant and we can use the formula of half-life of the sample to do that.

The half-life of a sample is given as;

[tex]T_\frac{1}{2}=\frac{ln}{\lambda}\\T_\frac{1}{2} =\frac{ln}{5715} \\ T_\frac{1}{2} = 0.000121\\[/tex]

The formula of radioactivity is given as

[tex]N = N_oe^(^-^\lambda ^t)[/tex]

Substituting the values into the equation

[tex]N = N_oe^(^-^\lambda ^t)\\\frac{N}{N_o} = e^-^(^\lambda ^t)\\0.1 = e^-^(^0^.^0^0^0^1^2^1^*^t^)\\t = 19029.6 years[/tex]

The artifact is approximately 19029.6 years.

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Step-by-step explanation:

100% = $250

1% = 100%/100 = 250/100 = $2.50

the price decreased by

250 - 180 = $70

how many % are $70 ?

as many as how many times 1% ($2.50) fits into $70 :

70 / 2.50 = 28%

it changed (decreased) by 28%.

The problem says you have 10 books arranged on a shelf and then you are choosing 4 books in alphabetical order.

Given that you are choosing books with an order (alphabetical) it means the order does matter, then it is a permutation (which is an ordered combination).

In this case, no repetitions are allowed because you can't repeat a book in the selection, they'll be 4 different books from the shelf, the formula you have to use is:

Then n=10 and r=4, replace these values:

Then, can be chosen 5040 different groups of books.

The answer is option D.

The number of pounds when company A and B have same amount is 16 pounds.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.

In this case, shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound.

Let each pound be represented by p.

Company A will be 7 + 0.50p

Company B will be 11 + 0.25p

We will equate both equations.

7 + 0.50p = 11 + 0.25p

Collect like terms

0.50p - 0.25p = 11 - 7

0.25p = 4

Divide

p = 4 / 0.25

p = 16

The number of pounds is 16 pounds.

The complete information is given below.

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shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound. How many pounds will give an equal amount?

Answer:negative

Step-by-step explanation:

Because it should be on the bottom left corner if you are using a graph it is different in each corners of the graph. There is four sides for the graph.

Solution

- The rule for this transformation is given below:

- Based on this rule, f(x + 8) will shift the graph 8 units to the left

Final Answer

Shifted left (OPTION B)

Answer:

x = 11

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = 4 , b₁ = x , b₂ = 6 and A = 34 , then

[tex]\frac{1}{2}[/tex] × 4 × (x + 6) = 34

2(x + 6) = 34 ( divide both sides by 2 )

x + 6 = 17 ( subtract 6 from both sides )

x = 11

Answer:

A. 1/6 would be the answer I think

The mistake that Dolly have in her conclusion is A. Her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks. That her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks.

An experiment is carried out in order to get more information about a particular thing.

In this case, at the end of the 10 weeks, she graphed her weight over time and noticed that for the two weeks she didn't write down anything she lost weight.

Therefore, this caused the mistake that was noticed.

In conclusion, the correct option is A.

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An equation for the line of best fit for a men's height, y, based on her shoe size, x is; y = 0.25x + 66.6

A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

In this scenario, the men's shoe size would be plotted on the x-axis of the scatter plot while her height would be plotted on the y-axis.

By critically observing the scatter plot (see attachment) which models the data, we can reasonably deduce that an equation for the line of best fit is given by:

y = 0.25x + 66.6

Interpret the meaning of the residual from part B is given below.

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lets remember what it means compound continuously,

the interest never stopped, the balance is earning interest at all time

Joseph is 22 and he wants to know how much money he will have at 55

55-22=33

his balance will gain interest for 33 years, this is our time

there is a 7% rate

the formula is

P(t)= P(0) e ^rt

our t is 33

rate=7%

Joseph will have a balance at age 55, 45,334.99 dollars

[tex]p =( 1.5x - 3) + (1.5x - 3) + (0.75x - 1) \\ = 1.5x + 1.5x + 0.75x - 3 - 3 - 1 \\ p= 3.75x - 7[/tex]

ABOVE IS THE SIMPLIFIED PERIMETER OF THE TRIANGLE.

1. The pairs for each tent, based on common factors of 40, are given as follows (1, 40), (2, 20), (4, 10), (5, 8), (8, 5), (10, 4), (20, 2), and (40, 1).

2. Matching the number of tents with the number of boys is as follows:

     1                                          40

    2                                          20

    3                                          No match

    4                                          10

    5                                          8

    6                                          No match

    7                                          No match

The factors of a number are the numbers that can divide it exactly or without a remainder.

For instance, the factors of the number, 40, are 1, 2, 4, 5, 8, 10, 20, and 40.

Thus, there are 8 ways that the tents can be arranged to accommodate the campers (boys) based on the factors of 40.

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The graphed function in the slope-intercept form can be written as:

y = -4*x - 2

A general linear function in the slope-intercept form is written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

On the graph, we can see that our line intercepts the y-axis at y = -2, so the y-intercept is b = -2, replacing that we get:

y = m*x - 2

We also can see that the line passes through (-1, 2), replacing these values on the linear equation we get:

2 = m*(-1) - 2

m = -2 - 2

m = -4

Thus, the linear function in the graph is:

y = -4*x - 2

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The probability that the mean daily revenue for the next 30 days will be less than $7000 IS 0.7333

Standard deviation of the sample is equal to the population's Standard Deviation divided by the square root of the sample's item count.

Standard Deviation of the sample = [tex]1200/\sqrt{30} = 219.09[/tex]

SD of the sample is equal to the population's Standard Deviation divided by the square root of the sample's item count.

To reach a result of 300, divide 7500 by the mean of 7200. 300 divided by the sample's SD (219.09) yields a result of 1.37. A z-table search for +1.37 returns a result of 0.9147. Accordingly, there is a 0.9147 percent chance that the average daily revenue over the following 30 days will be less than $7500.

To get a result of -200, divide 7000 by the mean of 7200. Divide -200 by the sample's standard deviation (219.09), and you'll get -0.91. search for -0.91 in a z-table receive a score of 0.1814. The likelihood that the mean daily revenue for the following 30 days would be less than $7000 is therefore 0.1814.

Simply subtract the likelihood that the mean daily revenue is less than $7000 (0.1814) from the likelihood that the mean daily revenue is less than $7500 (0.9147) to arrive at the probability that the mean daily revenue for the upcoming 30 days will be between $7000 and $7500. This yields a result of 0.7333.

There is a 73.33% chance that the average daily income over the following 30 days will be less than $7000.

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Answer:

Step-by-step explanation:

the answer would be the second option

Answer:

35

Step-by-step explanation:

sum the parts of the ratio, 4 + 5 = 9 parts

divide 63 by 9 to find the value of 1 part of the ratio

63 ÷ 9 = 7 , then

4 parts = 4 × 7 = 28

5 parts = 5 × 7 = 35 ← larger share

The exponent of x in the expression (x¹⁰)³⁺⁵ is 6.

Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These rules can help simplify formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.

The mathematical process known as an exponent often indicates the power of a variable.

As of right now, we are aware that under the scenario of

[tex](x^{a})^{b} = x^{ab}[/tex]

Therefore, solve the power by multiplying 10 by 3/5, and we get

10 × (3/5)

=6

Thus, the expression simplified as

(x¹⁰)³⁺⁵ = x⁶

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Answer:

30 km/s

Explanation:

Formula for average speed = Total distance/total time

From the question,

Total distance = 600 km, Total time = 20 seconds

∴ Average speed = 600 km/20 seconds

Average speed = 30 km/s

2.69%, is the required maximum percent error among the predictions.

Given,

The predicted winning time in 200 meter sprint shows in the dot plot

The winner finished the race in 22.3 seconds

We have to find the greatest percent error among the predictions;

Here,

The actual time to complete is 22.3 seconds.

22.9 seconds is the prediction that is the most off.

The difference is, 22.9 - 22.3 = 0.6 seconds

To obtain a prediction, divide this by the actual time value.

= 0.6/22.3 = 0.0269 = 2.69

Therefore, 2.69%, is the required maximum percent error among the predictions.

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Answer:

1 x 10^16

Step-by-step explanation:

We are given a rectangle with the following dimensions;

Also, placed inside the large rectangle, is a smaller shaded rectangle which has the dimensions;

The ratio of both figures can be expressed as follows;

Substituting for the values of both figures, we now have;

We know that the length of a rectangle is twice its width. Then:

The area of a rectangle is the product of its width and length. Then:

Additionally, we know that the area is 162 in². Using the expression above we can obtain the value of x:

Finally, the perimeter (2P) is just twice the sum of the width and the length of the rectangle:

Given

Points (4,2) and (2,1)

Find

Slope of the line

Explanation

Slope of line is given by

so ,

Final Answer

Hence , the slope of line is m = 1/2

Answer:

Round 1350 to decimal form and your answer should be 1.35 kg.