Find a formula for the linear function depicted in the following graph.

The height of the tree is equal to 210 ft to the nearest foot using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

angle opposite of the tree = 56 - 26 = 30

angle opposite of the shadow = 180 - 90 - 56= 34

by application of sine rule:

sin 30/h = sin 34/235

h = (235 × sin 30)/sin 34 {cross multiplication}

h = 117.5/0.5592

h = 210.1216 ft.

Therefore, the height of the tree is equal to 210 ft to the nearest foot using the sine rule.

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Jane sold 27 boxes of cookies last year if Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Given ,

Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.

Let's assume the number of boxes Jane sold last year as x.

As per the given condition, 50 = 2x - 4

Adding 4 on both sides, we get:

50 + 4 = 2x - 4 + 4

54 = 2x

Dividing by 2 on both sides, we get:

x = 27

Therefore, Jane sold 27 boxes of cookies last year.

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The conclusion is that if A is true, B is true, then C must be true as well.

What is statement ?

In logic and mathematics, a statement is a declarative sentence that is either true or false. It is an assertion about a fact or a relationship between facts. A statement can be a simple sentence, such as "The sun is shining," or a complex one, such as "If it rains tomorrow, I will stay indoors."

If the statement "If A AND B, then C" is true, and if its reverse statement is also true, then the converse of the statement is "If C, then A AND B."

If A is true and B is true, then A AND B is also true. Therefore, by the original statement, C must also be true.

Therefore, the conclusion is that if A is true, B is true, then C must be true as well.

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The values of h1 and h2 for which v3 is a linear combination of v1 and v2 is given as follows:

Vector v3 being a linear combination of v1 and v2 means that the following system of equations is used to relate the three vectors:

xv1 + yv2 = v3.

From each line of each vector, the system of equations relating these amounts is given as follows:

From the second equation, considering h1 = 1, the value of y is given as follows:

1 = -y

y = -1.

Hence, from the third equation, the value of h2 is obtained as follows:

-1 + 3(-1) = h2

-1 - 3 = h2

h2 = -4.

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If we take the values are h₁ = -1,  h₂ = 2, then the last vector is a linaer combination of the first two.

Here we want to find the values of h₂ and h₃ such that the last vector is a linear combination of the first one, that means that we can write:

a*v₁ + b*v₂ = v₃

For each of the components we can write:

a*1 + b*0 = 1

a*0 + b*-1 = h₁

a*-1 + b*3 = h₂

With the first equation we conclude that a = 1, then:

1*0 + b*-1 = h₁

1*-1 + b*3 = h₂

If we also take b = 1 we will get:

0 - 1= h₂

-1 + 3 = h₃

Then the values are h₁= -1,  h₂ = 2.

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Answer:

Translation of three units to the right (on the x-axis) and one unit down (on the y-axis).

If you want, this can be represented in vector form (3 1).

Step-by-step explanation:

This was done by translating the shape three units to the right and one unit down

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The difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is $83,421.

What is the interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

First, we need to calculate the monthly payment at a 10% interest rate for 25 years:

PV = 90,000

i = 0.10/12

n = 25*12 = 300

Using the formula for the monthly payment of a mortgage loan, we get:

[tex]P = i PV / (1 - (1 + i)^{(-n)})[/tex]

= 805.23

So, if Jackie paid the minimum monthly payment, she would pay $805.23 per month. The total amount paid over the lifetime of the loan would be:

Total amount paid = P * n = 805.23 * 300 = $241,569

The amount of interest paid would be:

Interest paid = Total amount paid - PV = 241,569 - 90,000 = $151,569

If Jackie had made payments of $527.16 per month, the total amount paid over the lifetime of the loan would be:

Total amount paid = 527.16 * 300 = $158,148

The amount of interest paid would be:

Interest paid = Total amount paid - PV = 158,148 - 90,000 = $68,148

Therefore, the difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is: $151,569 - $68,148 = $83,421

hence, the answer is not one of the choices provided.

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Here the option is (D): Sum of Cubes.

The Given expression can be written as:

a³ + b³ = (a + b)(a² - ab + b²)

we can write 8x³ as (2x)³ and 243 as 3³.

we have,

8x³ + 243 = (2x)³ + 3³

we can rewrite the above equation

(2x + 3)(4x² - 6x + 9)

Therefore, the identity that can be used to rewrite the given expression is an option (D): Sum of Cubes

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Answer: -5/6

Step-by-step explanation:

Hopefully this helps, my friend, best of luck to you :)

b) The mean and standard deviatiοn οf the data is 8.022 and 0.335 respectively.

In statistics, mean is measure οf central tendency that represents average value οf set οf numbers. It is calculated by adding up all  values in  set and dividing  sum by the tοtal number οf values in  set.

b) Tο determine the mean and standard deviatiοn οf the data, we can input the given values intο a calculatοr οr a spreadsheet prοgram and use the apprοpriate fοrmulas. Here are the calculatiοns:

Mean = (7.96 + 8.54 + 7.92 + 8.40 + 8.02 + 7.91 + 8.12 + 7.85 + 8.27 + 7.67) / 10

= 8.022

Standard deviatiοn = sqrt([(7.96 - 8.022)² + (8.54 - 8.022)² + ... + (7.67 - 8.022)²] / 9)

= 0.335 (rοunded tο 3 decimal places)

Therefοre, the mean petrοl price is 8.022 and the standard deviatiοn is 0.335.

c) The histοgram appears tο be slightly skewed tο the right, as the tail οf the histοgram extends further tο the right than tο the left.

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Answer:71

Step-by-step explanation:

-3-(-10)-(-64)=-3+10+64=71

For the graph of the rational function the as x → −∞​, f(x) → −∞​.

A rational function is the ratio of two polynomial functions with a non-zero denominator polynomial. R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, is the standard representation of this relationship. We studied the rational number idea in previous grades. When the denominator is not equal to zero, it is the quotient or ratio of two integers. Rational, then, is a name that comes from the term ratio.

From the given graph we observe that as the value of x tends to - ∞, the value of f(x), that is, the value of y constantly goes upwards and leftwards.

Thus,

As x → −∞​, f(x) → −∞​.

Hence, for the graph of the rational function the as x → −∞​, f(x) → −∞​.

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Answer: 19

Step-by-step explanation:

(5x + 30) = 125   (opposite angles are equal)

5x = 95

x = 19

Answer:

0.19^9

0.19 to the 9th power

Step-by-step explanation:

Use Exponent Rules:

If you are multiplying terms with the same base, then ADD the exponents.

see image

Answer:

The correct answer is: slope= -1;  y-intercept (0,2)

Step-by-step explanation:

The given equation is:   [tex]q=2-r[/tex]

Assuming [tex]q[/tex] and [tex]r[/tex] as [tex]y[/tex] and [tex]x[/tex] respectively, the equation becomes:  [tex]y=2-x[/tex]

Rearranging the terms in right side:  [tex]y=-x+2[/tex]

Comparing this above equation with the slope-intercept form [tex]y=mx+b[/tex], we will get.....

[tex]mx=-x[/tex] ⇒ [tex]m=\frac{-x}{x} =-1[/tex]

[tex]and[/tex]

[tex]b=2[/tex]

So, the slope is -1 and y-intercept is (0, 2)

Answer:

[tex]\mathrm{y\:=\:\frac{3}{2}x\:+\:7}[/tex]

Step-by-step explanation:

To find the equation of a line parallel to -4y = 32 - 6x, we first need to rewrite this equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

-4y = 32 - 6x

Divide both sides by -4:

y = -8 + (3/2)x

So the slope of this line is 3/2. Since we want a line parallel to this one, it will have the same slope of 3/2.

Now we can use the point-slope form of a linear equation to find the equation of the line that passes through (0,7) with a slope of 3/2:

y - y1 = m(x - x1)

where m = 3/2 and (x1,y1) = (0,7)

y - 7 = (3/2)(x - 0)

Simplifying:

y - 7 = (3/2)x

y = (3/2)x + 7

So the equation of the line parallel to -4y = 32 - 6x that passes through the point (0,7) is y = (3/2)x + 7.

Answer:

7/8 - 5/7 =

49-40/56 =

9/56

Answer:

To estimate the dealership's cost for the car, we need to first calculate the dealership's selling price. We know that the car has an MSRP of $34,995.99, and we know that dealerships typically have a 20% markup on selling price.

So, to find the dealership's selling price, we can use the formula:

Selling price = MSRP + (Markup percentage * MSRP)

Substituting the values we have:

Selling price = $34,995.99 + (20% * $34,995.99)

Selling price = $34,995.99 + $6,999.20

Selling price = $41,995.19

Therefore, we estimate that the dealership paid $41,995.19 - the 20% markup - for the car.

To check this estimate, we can calculate the dealership's cost using the formula:

Cost = Selling price - Markup

Substituting the values we have:

Cost = $41,995.19 - (20% * $41,995.19)

Cost = $41,995.19 - $8,399.04

Cost = $33,596.15

This is very close to the MSRP of $34,995.99, which suggests that our estimate is reasonable.

The solutions to the indicated quantities are x = 25, MIK = 25 and KIE = 50 degrees

The value of x

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

Angle MIE = 75

Using the above as a guide, we have the following:

x + 2x = 75

Evaluate

3x = 75

So, we have

x = 25

The angle MIK

From the figure, we have

MIK = x

So, we have

MIK = 1 * 25

MIK = 25

The angle KIE

From the figure, we have

KIE = 2x

So, we have

KIE = 2 * 25

KIE = 50

Hence, the measure of angle KIE is 50 degrees

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The first step in developing a strategy for investing in two different stocks is to perform research on the stocks and their respective industries.

Stock is a type of security that signifies ownership in a company and represents a claim on part of the company's assets and earnings. It is a share of ownership in a company. It is bought and sold on a stock exchange, and the price of the stock is determined by the supply and demand of the stock.

This can be done by looking at the company’s financials, track record, industry trends, and more. This research can help you to determine which stock is more likely to perform better in any given economic condition. By doing this, you can maximize your return while also minimizing your risk. This can be done by using a risk-adjusted return metric such as the Sharpe Ratio.

Finally, you must decide how to allocate funds across the two stocks. This will depend on your risk tolerance and investment goals. For example, if you are a conservative investor, you may want to allocate more funds to the stock with the highest expected return under all economic conditions. On the other hand, if you are a more aggressive investor, you may want to allocate more funds to the stock with the highest expected return under one or two of the economic conditions.

Overall, developing a strategy for investing in two different stocks takes into account several factors, including research, expected returns, and risk tolerance. By doing this, you can maximize your return while also minimizing your risk.

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Therefore , the solution of the given problem of expressions comes out to be b + 8 when 8a-2b+8 and -2a+6b are added together.

There is a need for calculations like joining, random variable division, variable multiplication, and removal. If they were united, the following would happen: A mathematical equation, some data, and a formula. A statement of truth is composed of numerical data, formulae, components, and mathematical operations like additions, subtractions, errors, and segmentations. One can assess and analyse words and sentences.

Here,

The formula is as follows:

=> 8a - 2b + 8 - 2a + 6b - (5b - 6a)

By combining similar words to make the expression shorter, we get:

=> (0a - b + 8 = -b + 8)

=>  (8a - 2a - 6a) + (-2b + 6b - 5b)

Therefore, the answer is b + 8 when 8a-2b+8 and -2a+6b are added together.

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Answer:

Step-by-step explanation:

Farmer Ed has 1,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

Hello and Regards zoecenters91522.

Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.

The distance between two points is the measure of the length of the straight line that joins them. On a Cartesian plane, the distance between two points is calculated using the Euclidean distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is equal to the square root of the sum of the squares of the differences of their coordinates:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

This formula can be used to calculate the distance between two points on any plane, such as a three-dimensional plane or Euclidean space of any dimension.

Now we locate the points of x and y.

We substitute the points in the formula and solve:

[tex]\huge \boxed{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]

[tex]\huge \boxed{d=\sqrt{(-10-15)^2+(-17-(-17))^2 } }[/tex]

[tex]\huge \boxed{d=\sqrt{(-25)^2+0^2}=\sqrt{625+0} }[/tex]

[tex]\huge \boxed{d=\sqrt{625}=25 \ units }[/tex]

Therefore, the distance between the points (15,-17) and (-10,-17) is 25 units.

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Answer:

5 < x < 21

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

13 - 8 < x < 13 + 8 , then

5 < x < 21

Answer:

The best option that describes a sample that enables you to draw accurate inferences from the sample is option C: "The sample is random and representative, but not biased."

A random sample is one in which every member of the population has an equal chance of being selected. This helps to ensure that the sample is not influenced by any outside factors that could skew the results.

A representative sample is one that accurately reflects the characteristics of the population it is drawn from. This ensures that the results obtained from the sample can be generalized to the larger population.

However, if the sample is biased, it may not accurately represent the population. This could lead to inaccurate inferences and conclusions.

Therefore, a random and representative sample that is not biased is the best option for drawing accurate inferences from the sample.

Step-by-step explanation:

Answer:

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After reflection and shifts, all three transformations gives us the final function: y = -√(x+9) + 9. This function starts at the point (-9,9) and decreases as x increases. The graph of this function is a reflection of the original graph of y = √x about the x-axis, shifted up by 9 units, and shifted left by 9 units.

This function starts at the origin (0,0) and increases as x increases.

1. Reflect about the x axis:

A reflection about the x-axis takes every point on the graph of y = √x and maps it to a new point with the same x-coordinate, but the opposite y-coordinate. For example, the point (1,1) on the graph of y = √x would be reflected to the point (1,-1) on the new graph. This transformation effectively flips the graph upside down.

2. Shift up 9 units:

This transformation moves the entire graph up by 9 units. Every point on the graph is shifted vertically by 9 units. For example, the point (1,-1) on the reflected graph would be shifted up to the point (1,8) on the new graph.

3. Shift left 9 units:

This transformation moves the entire graph to the left by 9 units. Every point on the graph is shifted horizontally by 9 units. For example, the point (1,8) on the shifted graph would be shifted left to the point (-8,8) on the final graph.

Combining all three transformations gives us the final function: y = -√(x+9) + 9.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

A. The intercept does not have a practical interpretation and is not statistically meaningful.

What is line regression?

Linear regression is a statistical method used to model the relationship between a dependent variable (also called the response or target variable) and one or more independent variables (also called predictors or explanatory variables) in a linear fashion.

B. The intercept is 4.62 mpg.

C. The value of the intercept represents the predicted city mileage for Highway gas mileage of 0 mpg. However, such a car does not exist, so the intercept is not statistically meaningful.

The intercept represents the value of the dependent variable (highway gas mileage) when the independent variable (city gas mileage) is equal to 0. However, in this case, it is not possible for a car to have 0 city gas mileage and still be in operation.

Therefore, The intercept does not have a practical interpretation and is not statistically meaningful.

In fact, the intercept can be considered as a theoretical value that is not meaningful in the context of the data.

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There are 20 different election outcomes are possible.

An outcome is a possible result of a random experiment or event. It is a specific occurrence that may or may not happen, but that could happen under certain conditions. Outcomes are often associated with probabilities, which are measures of the likelihood that a particular outcome will occur.

This is a problem of counting the number of ways to choose 3 people out of 6 for 3 distinct positions. We can solve this using the combination formula:

ⁿCr = C(n, r) = n! / (r! * (n-r)!)

C(6, 3) = 6! / (3! * (6-3)!) = 20

Therefore, there are 20 different election outcomes possible for the president, secretary, and treasurer positions among a group of 6 people.

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