Data about the outside temperature and gas used for heating a building are given in the table.

Use a graphing calculator to create the line of best fit for the data.
temperature
(deg F) gas usage
(therms)
58 5,686
62 7,373
64 5,805
67 5,636
70 3,782
73 3,976
74 3,351
74 3,396
75 2,936
73 3,078
65 4,549
59 7,022
58 6,106
62 4,566
64 4,608
67 5,790
70 6,501
73 3,843
What is the equation of the line of best fit for this data? Round numbers to the nearest whole number.
What is the slope of the line of best fit? What does it mean in this situation?
What does the line of best fit estimate for gas usage when the outside temperature is 59 degrees Fahrenheit?
How does the actual gas usage compare to the estimated gas usage when the outside temperature is 59 degrees Fahrenheit?

a) The perimeter of the cross is: P = 4a = 4(c - b) = 4c - 4b

b) The area of the cross is:[tex]A= 2cb - 2b^2 \ cm^2[/tex]

c) b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]

What is area and perimeter?

The perimeter of a shape is the distance around its outside. The space inside a shape is measured by area.

a) The perimeter, P, of the cross is equal to the sum of the lengths of its four arms.

The length of one arm of the cross can be found by subtracting the length of one rectangle from the length of the other rectangle. Since each rectangle has dimensions c cm × b cm, the length of one arm is:

a = c - b

Therefore, the perimeter of the cross is:

P = 4a = 4(c - b) = 4c - 4b

b) The area, A, of the cross is equal to the area of the two rectangles minus the area of the four triangles formed by the arms of the cross.

The area of each rectangle is:

[tex]Area_{rect} = c * b[/tex]

The area of each triangle is:

[tex]Area_{tri} = (a * b) / 2 \\\\= \frac{[(c - b) * b]}{2} \\\\= \frac{ (c * b - b^{2} )}{2}[/tex]

Since there are four triangles, the total area of the triangles is:

[tex]4A_{tri} = 2cb - 2b^2\ cm^2[/tex]

Therefore, the area of the cross is:

[tex]A = 2A_{rect} - 4A_{rect} \\\\ = 2cb - 2b^2[/tex]

c) c) To find b in terms of A and C, we can use the formula for the area of the cross that we found in part b:

[tex]A = 2cb - 2b^2[/tex]

We can rearrange this equation to put it in the form of a quadratic equation:

[tex]2b^2 - 2cb + A = 0[/tex]

This is a quadratic equation in standard form, with a = 2, b = -2c, and c = A. We can use the quadratic formula to solve for b:

b = (-b ± sqrt(b^2 - 4ac)) / 2a

b = (2c ± sqrt((2c)^2 - 4(2)(A))) / (2 × 2)

[tex]b=\frac{-b ± \sqrt{(b^2 - 4ac)} }{2a} \\\\b= \frac{2c ± \sqrt{(2c^2 - 4(2)c)}}{4} \\\\b= \frac{2c ± \sqrt{(4c^2 - 16A)}}{4} \\\\b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]

Therefore, b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]

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Step-by-step explanation:

x = number of quarters

y = number of dimes

x + y = 34

therefore, we can say right away

y = 34 - x

0.25x + 0.1y = 4

because a quarter is worth $0.25, and a dime is worth $0.10.

now we are using the first equation in the second :

0.25x + 0.1(34 - x) = 4

0.25x + 3.4 - 0.1x = 4

0.15x + 3.4 = 4

0.15x = 0.6

x = 0.6/0.15 = 4

y = 34 - x = 34 - 4 = 30

the solution is therefore (4, 30).

she has 4 quarters and 30 dimes.

Peng has 4 quarters and 30 dimes.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, Peng has $4 in quarters and dimes. She has 34 coins.

we need to find the number of quarters and dimes, does Peng have,

Let x = number of quarters and y = number of dimes

Therefore, establishing the equations :-

x + y = 34

y = 34 - x...(i)

Since, a quarter is worth $0.25, and a dime is worth $0.10.

Therefore,

0.25x + 0.1y = 4.....(ii)

Therefore,

0.25x + 0.1(34 - x) = 4

0.25x + 3.4 - 0.1x = 4

0.15x + 3.4 = 4

0.15x = 0.6

x = 0.6/0.15

x = 4

Put x = 4 in the eq(i)

y = 34 - x = 34 - 4 = 30

y = 30

Hence, she has 4 quarters and 30 dimes.

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0.75 times the amount of miles+the base fee

Answer:

Y=0.75X+3

Yes, I can help them determine how they did within their respective groups. A higher Z-score indicates a faster time compared to the average for their group, while a lower Z-score indicates a slower time.

To do this, we will calculate the standard score or Z-score for each of them, which measures how many standard deviations above or below the mean their finishing time was. Calculation is as follows:

For Leo:

Z = (4948 - 4313) / 583 = 1.01

For Mary:

Z = (5513 - 5261) / 807 = 0.33

So, Leo finished 1.01 standard deviations above the mean for the Men, Ages 30 - 34 group, while Mary finished 0.33 standard deviations below the mean for the Women, Ages 25 - 29 group.

As for your second question, if the distributions of finishing times were not nearly normal, then the values of the standard score would change. This is because the standard score is calculated using the mean and standard deviation, which are important parameters of a normal distribution, these parameters may not accurately represent the data, and therefore the standard score would not be an accurate measure of relative performance.

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Answer:

Step-by-step explanation:330.693 lbs

The equation to find the height of the water after x minutes is height = = 3 x + 50.

The height of the water after 10 minutes would be 80 centimeters.

To find the height of the water, the formula that can be used is :
= rate of change x number of minutes + starting height

Rate of change :
= Change in height / Change in minutes

= ( 53 - 50 ) / ( 1 - 0 )

= 3 / 1

= 3

The equation is therefore:

= 3 x + 50 ( this is the height at 0 minutes)

At 10 minutes, the height would be:

= 3 ( 10 ) + 50

= 30 + 50

= 80 minutes

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1.
a) Length = 6 inches
   Width = 2 inches
   Height = 7 inches
   Base Area = 6 x 2 = 12 inches

b) V = l x w x h = 6 x 2 x 7
   

c)  V = B x h = 12 x 7

d) V = 84 inches cubed

Answer: explained below (answers you need to fill in are in bold)

Step-by-step explanation:

1.

a. the dimensions of the box are

l = 6

w = 2

h = 7

B = 12 ... B means base. When finding base, you simply just multiply L x W. In this case, you do 6 x 2 = 12 which will be your base

b.

V = l x w x h = 6 x 2 x 7

c.

V = B x h = 12 x 7

d.

V = 84 ... ( 12 x 7 = 84)

8/19 or 42.1%

add all values up to a total, then find the percentage from that total.

8 + 2 + 1 + 3 + 5 = 19 balls total

8 tennis valls to 19 total.

8/19 or 42.1%

The y- coordinate for the solution to the system of equations is 4

From the question, we have the following parameters that can be used in our computation:

8x−4y=−32,

2x+2y=4

Multiply the second equation by 4

So, we have the following representation

8x − 4y = −32

8x + 8y = 16

Subtract the equations

So, we have the following representation

12y = 48

Divide by 12

y = 4

Hence, the solution is y = 4

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The y-coordinate for the solution to the system of equations is equal to 4.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (-2, 4).

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The value that represents the number of ways in which the expected classes are free to vary in the chi-square goodness-of-fit test is called the degrees of freedom (df).

It is equal to the number of categories minus one. The degrees of freedom provide a measure of the amount of information available in the sample to estimate the parameters of the distribution.

In a goodness-of-fit test, the degrees of freedom are calculated as the number of categories minus one, which represents the number of ways in which the expected classes are free to vary.

For example, if you are conducting a chi-square goodness-of-fit test to compare the distribution of a categorical variable with expected frequencies, you would have one degree of freedom for each category or class, with the exception of the last category.

The last category's frequency is determined by subtracting the sum of the observed frequencies for all other categories from the total sample size. This means that the last category is not free to vary independently, so it is not counted in the degrees of freedom calculation.

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According to the California Board of Accountancy's requirements for CPA license renewal, if the highest level of service provided during the two years prior to the renewal date was a compilation engagement, the CPA must complete 24 hours of continuing education in accounting and auditing subjects.

Here is the breakdown of the requirements for the Accounting and Auditing Education Requirement:

- If the highest level of service provided was an audit, review, or attestation engagement, the CPA must complete 40 hours of continuing education in accounting and auditing subjects.

- If the highest level of service provided was a compilation engagement, the CPA must complete 24 hours of continuing education in accounting and auditing subjects.

- If the highest level of service provided was preparation of financial statements, the CPA must complete 8 hours of continuing education in accounting and auditing subjects.

- If the CPA did not provide any of the above services, they are not required to complete any continuing education in accounting and auditing subjects.

In Brandon's case, since his highest level of service provided was a compilation engagement, he must complete 24 hours of continuing education in accounting and auditing subjects out of the total of 80 continuing education hours required.

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Answer:

10 miles; it represents the original distance of the bird from its nes

Step-by-step explanation:

Answer:

B. 8*1/3

Step-by-step explanation:

The probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John is 0.60 or 60%

We can find the probability that a person does not believe Marilyn Monroe had an affair with John F Kennedy by dividing the number of people who responded "no" by the total number of people who responded to the survey:

Probability of "no" = Number of "no" responses / Total number of responses

Total number of responses = Number of "yes" responses + Number of "no" responses

Total number of responses = 110 + 163 = 273

Probability of "no" = 163 / 273

Simplifying the fraction, we get:

Probability of "no" = 0.5967 or approximately 0.60

So, the probability that if a person is chosen at random, he does not believe Marilyn Monroe had an affair with John F Kennedy is approximately 0.60, or 60%.

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The mean absolute deviation from the given data set is 1.6

The mean absolute deviation measures how far the data points are on average from a center point. Mean, median, mode, or any other random figure can serve as the center point.

The mean is frequently used as the center point, In this situation,  The method for computing mean absolute deviation (MAD) is helpful, which represents the average of the absolute departure of the data points from the mean of the data set.

Mean = (1+5+5+6+8)/5

Mean = 25/5

Mean = 5

The distance of each value from the mean is as follows:

Value     distance from the mean 5

1               4

5              0

5              0

6              1

8              3

MAD = (4 + 0 + 0 + 1 + 3)/5

MAD = 8/5

MAD = 1.6

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The required inequality, which represents the possible values for the number of apples and bananas purchased is 2a + 0.6b ≤10.

What is inequality?

Inequality can be defined as the relation of the expression containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

Let, the number of apples purchased, a, and the number of bananas purchased, b.

According to the question, Each apple costs $1.25 and each banana costs $0.60. London has a total of $10 to spend on apples and bananas.

So,

1.25a + 0.6b ≤10

Thus, the required inequality, that represents the possible values for the number of apples and bananas purchased is 1.25a + 0.6b ≤20.

The answer would be figure B. (pentagon)

The simplified form of subtraction is 3/2.

The simplified form of x+7/2 subtracted by x+4/2 is 3/2.

1. Start with the original expression: x+7/2 - (x+4/2)

2. Distribute the negative sign: x+7/2 - x - 4/2

3. Combine like terms: 7/2 - 4/2

4. Simplify by subtracting: 3/2

So the simplified form is 3/2.

Subtraction is an arithmetic operation tat represents the operation of removing an object from a collection. Subtraction is indicated by a minus sign, −. For example, in the image next to it, 5 − 2 peaches—meaning 5 peaches with 2 picked for a total of 3 peaches.

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Answer:
We know it's 1 P.M., and he's traveled 114 miles by now, he needs to go 86 more miles before he reaches his destination. He would need to travel 43 mph to reach his destination by 3.

Step-by-step explanation:

At 1, he has two more hours, and he has 86 more miles to go, so four times two is 8, and 3 times two is 6, so 46. There's probably a proper way to do this but yup 43 mph I hope I'm right and I helped you out :')

Answer:

Oliver would need to travel 43 mph for the remainder of his journey.

Step-by-step explanation:

First, we need to find out how many miles Oliver traveled for those 3 hours.

3 speed × 38 mph = 114 mph in total.

Now we need to know how many remaining miles Oliver needs to travel.

200-mile trip - 114 miles driven = 86 miles left.

Next, We need to know what time Oliver is currently at to know how many hours he needs to travel until it's 3 pm.

10 am + 3 hours = 1 pm

So, we have 2 hours left until it's 3 pm. Oliver needs to go 86 miles in 2 hours to arrive at his destination. So then divide the 86 miles by those 2 hours.

86 miles left ÷ 2 hours = 43 mph

Answer: 16

Step-by-step explanation:

6 ÷ 3 = 2

[tex]2^{3}[/tex] = 2 x 2 x 2

2 x 2 x 2 = 8

2 x 8 = 16

The basic portrait packages costs $70 and deluxe portrait packages costs $97.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the basic portrait packages costs $x.

and, the deluxe portrait packages costs $y.

So, the system of Equation

50x + 52y = 8544..............(1)

93x + 73y = 13591.............(2)

Solving above two equation we get

x=70 and y= 97.

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Each points in the graph is satisfying the equation c = 25j, that means the equation is linear.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given that, Casey claims the linear equation for the relationship shown by the graph is c=25j.

We have points on it,

(1, 25), (3, 75), (5, 125) and (7, 175)

Put each point in the equation,

c = 25j

Put j = 1, 3, 5, and 7

We get the corresponding value, 25, 75, 125, 175

That means, the points are satisfying the equation,

Hence, Each points in the graph is satisfying the equation c = 25j, that means the equation is linear.

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The given graph is :-

PPM stands for "parts per million" and is a way of expressing small concentrations of substances in a larger mixture. To calculate PPM, divide the mass or volume of the substance by the total mass or volume of the mixture and multiply by one million.

To calculate PPM, you need to know the mass of the substance in question and the total mass of the mixture. Here are the steps to calculate PPM:

1. Determine the mass of the substance in question. For example, let's say you have a mixture that contains 0.5 grams of salt.

2. Determine the total mass of the mixture. For example, let's say the total mass of the mixture is 1000 grams.

3. Divide the mass of the substance by the total mass of the mixture. In this example, 0.5 grams / 1000 grams = 0.0005.

4. Multiply the result by 1,000,000 to get the PPM. In this example, 0.0005 x 1,000,000 = 500 PPM.

So, the concentration of salt in the mixture is 500 PPM. Remember to always use the same units of measurement for both the substance and the mixture when calculating PPM.

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Answer:

14 oz of flour.     2 oz yeast.

Step-by-step explanation:

If you're making 40 servings of bread and using 0.35 oz of yeast, you need:

0.35 oz yeast / 1 yeast : 200 flour = 0.35 oz yeast / 1 : 200 flour = 0.00175 oz yeast/flour

So, you need 0.00175 oz yeast/flour * 40 servings * 200 flour/serving = 14 oz of flour.

If you're making 90 servings of bread and using 360 oz of flour, you need:

1 yeast : 180 flour = 360 oz flour / 90 servings / 180 flour/serving = 2 oz yeast.

Answer:

Step-by-step explanation:

n

The equation AB=BC for [tex]A=BCB^{-1}[/tex].

The solution of AB = BC  for A, assuming that A,B and C are square matrices and B is invertible is

We have to solve the equation

AB = BC given that these all are square matrices and B is invertible.

Write the required Equation:

Multiply both sides by inverse of B

The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.

⇒[tex]ABB^{-1} =BCB^{-1}[/tex]

⇒[tex]AI=BCB^{-1}[/tex]

⇒[tex]A=BCB^{-1}[/tex]

Therefore, the solution of AB = BC is [tex]A=BCB^{-1}[/tex].

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The equation of the line that is perpendicular to this line and passes through the point (5, −1) is y = (9/4)x - (49/4) and the equation of the line that is parallel to this line and passes through the point (5,−1) is y = (-4/9)x + (11/9).

An equation of a line is provided: -4x - 9y = 2

                                       -9y = 4x + 2

                                    y = (-4/9)x - 2/9

The slope-intercept form of the line is y = mx + c

So, the Slope of the line is -4/9

The slope of the perpendicular line is -1/(-4/9) = 9/4

Equation of line with slope 9/4 and containing the point (5, -1):

                                  y - (-1) = (9/4)(x - 5)

                                          y = (9/4)x - (49/4)

Parallel lines have the same slope, so the equation of the line with slope -4/9 and which contains the point (5, -1) is:

                              y - (-1) = (-4/9)(x - 5)

                               y = (-4/9)x + (11/9)

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The 10,000 seconds can be stated as 166.6777 minutes and 2.7778 hour.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

We have 10,000 sec

As, 1 minute= 60 seconds

So, In minutes

= 10000/60

= 1000/6

= 166.6667 minutes

Now, 1 hour= 60 minutes

So, In hour

= 10000/ 60 x 60

= 10000/3600

= 2.7778 hour

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The equation of hyperboloid of one sheet: [tex]\frac{x^{2} }{A^{2} } +\frac{y^{2} }{B^{2} } -\frac{z^{2} }{C^{2} } =1[/tex] which is used to calculate hyperboloid.

The most challenging quadric surface is probably the hyperboloid of a single sheet. For starters, it is puzzling since its equation is quite similar to that of a hyperboloid with two sheets. For information on how to tell them apart, see to the section on the two-sheeted hyperboloid. Its cross portions are also highly intricate equation.

Having said all of that, everyone who has watched The Simpsons, even for the first time, will recognize this form. One-sheet hyperboloids have a striking resemblance to Springfield Nuclear Power Plant cooling towers.

The cross sections of a straightforward one-sheeted hyperboloid with A = B = C = 1.

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Answer:2

Step-by-step explanation:

y = -3x.

Substitute this value in the second equation for y.

=> 2x-3(-3x)=22

=> 2x+9x=22

11x =22

Therefore, x=2.

Hope this helps :)