10. Find the slope of the line.

a) The linear function to find the annual excess fuel as a function of the number of years since 2000 is given as follows: y = 2.4x + 35.

b) The estimate for the consumption in 2011 is given as follows: 61.4 gallons.

The yearly increase in the consumption is constant, meaning that a linear function is used to model this situation.

The slope-intercept definition for the linear function is given as follows:

y = mx + b.

In which:

The consumption increases by about 2.4 gallons per person each year, hence the slope is of:

m = 2.4.

In 2005, which is five years after 2000, the excess consumption was of 47 gallons, hence the intercept b is calculated as follows:

47 = 2.4(5) + b

b = 47 - 2.4(5)

b = 35.

Meaning that the function is defined as follows:

y = 2.4x + 35.

2011 is 11 years after 2000, hence the estimate is obtained as follows:

y = 2.4(11) + 35

y = 61.4 gallons.

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The SAS (Side-Angle-Side) Congruence Rule states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

The SAS (Side-Angle-Side) congruence rule is a method used to determine if two triangles are congruent. This rule states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

To determine if two triangles are congruent using the SAS rule, we must first identify the two sides and the angle in one triangle that are congruent to the two sides and the angle in the other triangle. This means that they must have the same measures in terms of length and angle.

Once we have identified the corresponding sides and angles, we can use the SAS rule to determine if the two triangles are congruent. If the two sides and the angle of one triangle are congruent to the two sides and the angle of another triangle, then the two triangles are congruent.

However, if the two sides and the angle of one triangle are not congruent to the two sides and the angle of another triangle, then the two triangles are not congruent. The SAS rule is a simple and effective way to determine if two triangles are congruent.

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Answer: -2

Step-by-step

y = k*x

3 = k*-1

So k = -3

6 = -3 * x

6/-3 = -2

x = -2

Step-by-step explanation:

With bodmas rule

first should be solve divide

so 2^6/2^3=2^3

6^3*2^3=1728

The two types of figures are open and closed, geometric figures respectively. Figures that don't end where they begin are said to be open figures.

Closed geometric shapes are made up of points, line segments, circles, and curves. All around us, we can observe these types of shapes. Circle, rectangle, triangle, and other geometric shapes are a few examples. The triangle-shaped slices of a pizza are round.

Straight lines have been drawn on the floor, the door, the window, and the zebra crossing by the roadside in the classrooms. Even though angles are used in building construction, they also have connections to disciplines like physics and chemistry.

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Answer:103.83

Step-by-step explanation:

The line x= 5 is a vertical line that passes through the x-axis at the point

x = 5.

Option D is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The equation of a line is x = 5.

This means,

(0, 5)

This is a vertical line that passes through x = 5 on the x-axis.

Thus,

x = 5 is a vertical line.

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Answer:

16 gallons of gas are needed to travel 300 miles

Step-by-step explanation:

75x4=300

4x4=16

The possible arrangements would be:

Combination refers to the various ways that certain objects or numbers can be arranged. If the set already has an order, rearranging its elements, or placing its members in a linear or sequential order.

Given that solar panels use the sun's energy to generate power. A town wants to install 28 solar panels in an array.

The possible arrangements would be:-

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Answer: standard form: 2.3x 10⁴

               expanded form: 23.082

Everybody votes in a direct democracy to select a place for  the yearbook signing party.

Rules, institutions, and procedures known as "direct democracy" allow members of the public to vote directly on proposed constitutional amendments, laws, treaties, or policy decisions. Referendum and initiatives are the two most significant examples of direct democracy that are addressed in this primer.

Given:

It's the end of the school year, and your class of 250 students must decide the best place for the yearbook signing party.

To select the place:

They vote in direct democracy.

Because they have only 250 people.

And 250 people can have direct say.

Number of people is less.

So, selecting representatives would be not fair.

Therefore, everybody votes in a direct democracy.

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Answer:

what is it you need to solve for, y? x?

Answer:

Step-by-step explanation:

(i)2x+2y=4

We take value of y=[tex]\frac{4-2x}{2}[/tex]

2x+2([tex]\frac{4-2x}{2}[/tex])=4

2x + [tex]\frac{8-4x}{2}[/tex]=4

[tex]\frac{4x+8-4x}{2}[/tex] =4  (4x-4x=0)

[tex]\frac{8}{2}[/tex]=4 -> 4=4=0

2x+2y=4 is 0

(ii)3x+2y=7

y=[tex]\frac{7-3x}{2}[/tex]

3x+2([tex]\frac{7-3x}{2}[/tex])=7

[tex]\frac{6x+14-6x}{2}[/tex]=7

[tex]\frac{14}{2}[/tex]=7

7=7=0

The derivative of the function h(x) = 1 - x^2 sin^-1(x) -x^2-x is h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1.

What is derivative ?

The derivative of a function is a measure of how much the output of the function changes with respect to the change in its input. It is represented by the symbol "d/dx" or "∂/∂x" and it is a fundamental concept in calculus.

First, we will apply the chain rule to the term -x^2 sin^-1(x)

Let u = sin^-1(x)

du/dx = 1/(sqrt(1-x^2))

so, -x^2sin^-1(x) = -x^2u

then dh/du = -x^2

then dh/dx = -x^2 * (du/dx) = -x^2/(sqrt(1-x^2))

Next, we will differentiate the rest of the function ,

h(x) = 1 - x^2sin^-1(x) - x^2 - x

h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1

So, the derivative of the function h(x) = 1 - x^2 sin^-1(x) -x^2-x is h'(x) = - x^2/(sqrt(1-x^2)) - 2x - 1.

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The value of n in the vertical angles is 5 4 / 5.

Vertical angles are angles that are opposite of each other when two lines intersect each other.

Vertical angles share the same vertex. Vertically opposite angles are congruent to each other.

The measures of the two angles are 2n + 18 and 7n - 11. They are vertical angles.

Therefore, the two vertically opposite angles are congruent to each other. We will use the congruency to find the value of n in the equation.

2n + 18 = 7n - 11

2n - 7n = -11 - 18

-5n = -29

divide both sides by -5

n = -29 / -5

n = 29 / 5

Therefore,

n = 5 4 / 5

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The height of the cone is 16 feet.

A cone is a three-dimensional geometric shape.

The right cone has a slant height of 20 ft and the diameter of the base is 24 ft.

Therefore, the height of the cone can be found as follows:

Using Pythagoras's theorem,

c² = a² + b²

where

The slant height of the cone is the hypotenuse side of the detached right triangle. The radius and the height of the cone is the other legs of the detached right triangle.

Hence,

diameter = 24 ft

r = radius = 24 / 2  = 12 ft

Hence,

20² - 12² = h²

400 - 144 = h²

h = √256

h = 16 feet.

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The four statemen that describes the relationship of the model

A model refers to images, objects variables meant to depict a relation

In the model provided the relationship existing between the models is that the mass are equal hence there will be an equality sign to balance the relationship in the left and right hand side

examining the model shows that

3 cylinders = 1 cylinder + 1 cube

3 cylinders - 1 cylinder = 1 cube

2 cylinders = 1 cube

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The score 3 months ago is 2.31 If The team's engagement score was 4. 6 this month and The score has been improving at a rate of 11% per month.

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Have you ever borrowed money from your siblings when your pocket money is exhausted? Or lent him maybe? What happens when you borrow money? You use that money for the purpose you had borrowed it in the first place. After that, you return the money whenever you get the next month’s pocket money from your parents. This is how borrowing and lending work at home.

given,

employee engagement score this month= 4.6

rate of improvement = 1%

to find,

the employee engagement score 3 months ago

solution,

to find the employee engagement score 5 months ago, we can use the formula given below :

A= P [tex]( 1 + \frac{R}{100} ) ^{n}[/tex]

where:

A = current employee engagement score

P = initial employee engagement score

n = time period

4.6 = P [tex](1+\frac{11}{100} )^{3}[/tex]

4.6 = P [tex](\frac{111}{100} )^{3}[/tex]

P= 2.31

therefore, 3 months ago, the employee engagement score was 2.31.

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If the team's engagement score was 4. 6 this month, then with a improving rate of 11% per month, the score 3 months ago is approximately 3.46.

Therefore, the engagement score 3 months ago was approximately 3.46.

To find the engagement score 3 months ago, we need to first find the rate of improvement over 3 months. We can do this by multiplying the monthly rate of improvement by 3. So the rate of improvement over 3 months is

11% × 3 = 33%

If rate of improvement over 3 months is 33%, then

((current engagement score) - (score 3 months ago))/(score 3 months ago) × 100 = 33

that is

[tex]\frac{(current\ engagement\ score) - (score\ 3\ months\ ago)}{score\ 3\ months\ ago} \ 100 = 33[/tex]

Let score 3 months ago be a, then

(4.6 - a)/ a × 100 = 33, that is

[tex]\frac{4.6\ -\ a}{a} \ 100 = 33[/tex]

Multiplying by a and dividing by 100 on both sides

4.6 - a = 0.33a

Adding a on both sides

1.33a = 4.6

Dividing by 1.33

a = 4.6/ 1.33

a ≈ 3.46

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The interval for the proportion of 16- to 17- year old's who text while driving at 95% confidence (0.30717,0.37283).

a) The value of the point estimate is 0.34

b) The corresponding critical value [tex]$Z_{\alpha / 2}$[/tex] is 0.025

c) Margin of error is 0.016748134224444

d) The interval is (0.30717,0.37283)

As per the given data we have to obtain a 95% confidence interval for the proportion of 16- to 17- year olds who text while driving.

a)

[tex]\hat{p}=\frac{X}{N}=\frac{272}{800}[/tex]

= 0.34

b)

Calculate α:

α = 1 - Confidence Percentage

α = 1 - 0.95

α = 0.05

Find α spread range:

[tex]& \alpha=\frac{1}{2} (\alpha) \\[/tex]

[tex]& \alpha=\frac{1}{2} (0.05) \\[/tex]

α = 0.025

From the z-score table:

[tex]\text { z score }_{0.025}=1.96[/tex]

The z-score table is attached at the end of the solution.

c)

Calculate [tex]$\sigma_p$[/tex]

[tex]& \sigma_p=\frac{\sqrt{\hat{p}\left(1-\hat{p}\right)}}{\sqrt{N}} \\[/tex]

[tex]& \sigma_p=\frac{\sqrt{0.34(1-0.34)}}{\sqrt{800}} \\[/tex]

[tex]& \sigma_p=\frac{\sqrt{0.34(0.66)}}{\sqrt{800}} \\[/tex]

[tex]& \sigma_p=\frac{\sqrt{0.2244}}{\sqrt{800}} \\[/tex]

[tex]& \sigma_p =\sqrt{0.0002805} \\[/tex]

[tex]& \sigma_p[/tex] = 0.016748134224444

Calculate Margin of Error:

Margin of Error =[tex]\sigma_p[/tex] × z-Score

Margin of Error = 0.016748134224444 × 1.96

Margin of Error = 0.032826343079911

d)

Calculate high-end confidence interval total:

High End [tex]=\hat{p}+$ zscore $_a \times \sigma_p$[/tex]

High End = 0.34 + 1.96 × 0.016748134224444

High End = 0.34 + 0.032826343079911

High End =0.3728

Calculate low-end confidence interval total:

Low End [tex]=\hat{p}-$ Zscore $_{\mathrm{a}} \times \sigma_{\mathrm{p}}$[/tex]

Low End =0.34-1.96 × 0.016748134224444

Low End = 0.34 - 0.032826343079911

Low End =0.3072

Now we have everything, display our 95 % confidence interval:

0.3072 < p < 0.3728

This means that if we use the same sampling method to select different Samples and computed an interval estimate for each sample, our true population proportion (b) will fall between our confidence Interval (0.30717,0.37283) 95 % of the time.

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In the 2009 Parent-Teen Cell Phone Survey conducted by Princeton Survey Research Associates International, 800 randomly sampled 16- to 17- year olds living in the United States were asked whether they have ever used their cell phone to text while driving. Of the 800 teenagers surveyed, 272 indicated that they text while driving. Obtain a 95% confidence interval for the proportion of 16- to 17- year olds who text while driving.

A) Determine the point estimate: [tex]$\hat{p}=\frac{x}{n^{\prime}}$[/tex] and [tex]$\hat{q}=1-\hat{p}$[/tex]

B) Find the corresponding critical value [tex]$Z_{\alpha / 2}$[/tex]

Confidence Level            Critical Value([tex]$\mathbf{Z}_{\boldsymbol{\alpha} / \mathbf{2}}$ \\[/tex])

           90 %                                 1.645

           95 %                                 1.96

           98 %                                 2.33

           99 %                                 2.575

C) Determine the Error

[tex]$$E=Z_{a / 2} \sqrt{\frac{\hat{p} \hat{q}}{n}}$$[/tex]

D) Construct the interval

[tex]\hat{p}-E < p < \hat{p}+E[/tex]

Answer:

7+8=15 that's the total

7\15 or 8\15

Answer: that is it’s simplest form

Step-by-step explanation:

Answer:

3 1/3+2 3/4 = 73/12=6 1/12

Step-by-step explanation:

1.Conversion a mixed number 3  1/3 to a improper fraction: 3 1/3 = 3  1/3 = 3 · 3 + 1/3 = 9 + 1/3= 10

2.Conversion a mixed number 2  3/4 to a improper fraction: 2 3/4 = 2  3/4 = 2 · 4 + 3/4 = 8 + 3/4= 11

3.Add: 10/3 + 11/4 = 10 · 4/3 · 4 + 11 · 3/4 · 3 = 40/12 + 33/12 = 40 + 33/12 = 73/12

An equation that can you use to find h, the height of the window in meters is: A. 1/2(2h - 2)h = 42.

The height of the window in meters is equal to 7 meters.

Mathematically, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle = 1/2 × b × h

Where:

Since the window's base area is 2 meters shorter than twice the height, a mathematical expression which can be used to represent it is given by:

Base area, b = 2h - 2

Substituting the given parameters into the area of a triangle formula, we have the following;

Area of a triangle = 1/2 × b × h

42 = 1/2 × (2h - 2) × h

1/2(2h - 2)h = 42 [required equation].

Making the variable h the subject of formula, we have the following;

1/2(2h - 2)h = 42

Cross-multiplying, we have:

(2h - 2)h = 84

2h² - 2h = 84

2h² - 2h - 84 = 0

Dividing all through by 2, we have the following:

h² - h - 42 = 0

Next, we would solve the above quadratic function by using the factorization method;

h² - 7h + 6h - 42 = 0

h(h - 7) + 6(h - 7) = 0

(h + 6)(h - 7) = 0

h = -6 or 7 meters.

Therefore, the height of the window is 7 meters since it can't be negative.

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Since Elena's distances and times for a training run are given by the equation y = 8.5x, Tyler’s pace per minute is equal to 8.2 miles per minute.

In order to determine Tyler’s pace per minute, we would have to determine the rate of change (slope).

Mathematically, the rate of change is also referred to as slope and it can be calculated by using this formula;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change with respect to Tyler’s pace per minute, with the following data points (0, 0) and (1, 8.2):

Rate of change (slope), m = (0 - 8.2)/(0 - 1)

Rate of change (slope), m = -8.2/-1

Rate of change (slope), m = 8.2.

Therefore, Tyler’s pace per minute is 8.2 miles per minute.

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Complete Question:

Tyler and Elena are on the cross country team. Tyler’s distances and times for a training run are shown on the graph. Elena's distances and times for a training run are given by the equation y = 8.5x, calculate Tyler’s pace per minute.

The simplified form of the expression is ∛5/3x

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, [tex]\sqrt[3]{\frac{10x^{5} }{54x^{8} } }[/tex]

Simplifying, we get,

[tex]\sqrt[3]{\frac{10x^{5} }{54x^{8} } }\\= \sqrt[3]{\frac{10x^{3+2} }{2*27x^{3+3+2} } }\\= \frac{x}{3x^{2} } \sqrt[3]{\frac{10x^{2} }{2x^{2} } }\\= \frac{\sqrt[3]{5} }{3x}[/tex]

Hence, the expression is ∛5/3x

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Answer: 3 feet

It says the water is 3 feet deep, is it meant to say diver?

P(x)=ax⁵+bx⁴+cx³+12 is the polynomial which has 4 terms and vertical axis at y=12 and the degree is 5

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The standard form of a polynomial equation with a leading degree is 5 is expressed as P(x)=ax⁵+bx⁴+cx³+dx+e

Since the polynomial should have only 4 terms, the standard form of the equation will be P(x)=ax⁵+bx⁴+cx³+d

d is the constant

Since the graph of the Polynomial crosses the vertical axis at y = 12, hence the constant value "d" will be 12.

Substituting the constant value, the required equation of the polynomial will be expressed as P(x)=ax⁵+bx⁴+cx³+12

Hence, P(x)=ax⁵+bx⁴+cx³+12 is the polynomial which has 4 terms and vertical axis at y=12 and the degree is 5

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Answer: 42

Step-by-step explanation: you have to find the rule, which is 4, which means b X 4 = 168, and 168 divided by 4 = 42.

The missing value for the letter B is 42.

Given is that a teacher gives pens and pencils to elementary students at an equal rate.

Since the rate is equal, we can write -

(140 - 72)/(35 - 18) = (168 - 140)/(B - 35)

68/17 = 28/(B - 35)

68(B - 35) = 28 x 17

B - 35 = 7

B = 42

Therefore, the missing value for the letter B is 42.

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Bob's gift shop sold a total of 825 cards for Mother's Day.

To calculate the total number of cards sold for Mother's Day, we can use the following formula:

Total Cards Sold = (Number of Cards Sold by Salesman) / (Percent of Cards Sold by Salesman)

In this case, the total number of cards sold for Mother's Day would be calculated as:

Total Cards Sold = (33 cards) / (4%)

Using the above formula, the total number of cards sold for Mother's Day would be 825 cards.

To arrive at this answer, we first converted 4% to a decimal by dividing it by 100. This gave us 0.04. We then divided 33 cards by 0.04 to get 825 cards.

Therefore, Bob's gift shop sold a total of 825 cards for Mother's Day.

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The correlation coefficient is measured on a scale that varies from +1 ≤ 0 ≤ -1.

        [tex]${\displaystyle {\begin{aligned}r_{xy}&={\frac {\sum x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{ns'_{x}s'_{y}}}\\[5pt]&={\frac {n\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{{\sqrt {n\sum x_{i}^{2}-(\sum x_{i})^{2}}}~{\sqrt {n\sum y_{i}^{2}-(\sum y_{i})^{2}}}}}.\end{aligned}}}[/tex]

       where [tex]{\displaystyle s'_{x}}[/tex] and [tex]{\displaystyle s'_{y}}[/tex] are the uncorrected sample standard deviations of         X and Y.

Given is a term as correlation coefficient.

        [tex]$r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]

       where -

        [tex]r[/tex] = correlation coefficient

       [tex]x_{i}[/tex] = values of the x - variable in a sample

       [tex]\bar{x}[/tex] =  mean of the values of the x-variable

       [tex]y_{i}[/tex] = values of the y-variable in a sample

       [tex]\bar{y}[/tex] = mean of the values of the y-variable

Therefore, the correlation coefficient is measured on a scale that varies from +1 ≤ 0 ≤ -1.

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The total amount of cash = $247. The total deposit = $248.22.The dollars received in cash = $247. The cents received in coins = 22 cents.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

For the first check for $223.47, you will receive 2 ten-dollar bills, 2 one-dollar bills, and 47 cents in coins. The total amount in cash received for this check is $223.

For the second check for $24.75, you will receive 3 one-dollar bills, 10 quarters, and 10 dimes. The total amount in cash received for this check is $24.

The total amount of cash received for both checks is $223 + $24 = $247.

The total deposit for both checks is $223.47 + $24.75 = $248.22.

The dollars received in cash for both checks is $247.

The cents received in coins for both checks is 22 cents.

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Answer: What are the options??

Step-by-step explanation: