Question 2: The average price for a BMW 3 Series Coupe 335i is $39,368. Suppose these prices are also normally distributed with a standard deviation of $2,367. What percentage of BMW dealers are pricing the BMW 3 Series Coupe 335i at more than the average price ($44,520) for a Mercedes CLK350 Coupe? Round your answer to 3 decimal places.

Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's solve ~

Cost price for each Orange :

\(\qquad \tt \dashrightarrow \: \dfrac{60}{200} \)

\(\qquad \tt \dashrightarrow \:0.3 \: \: kobo\)

Now, Cost price for 8 oranges :

\(\qquad \tt \dashrightarrow \:0.3 \times 8\)

\(\qquad \tt \dashrightarrow \:2.4 \: \: kobo\)

And we have been given that selling price for 8 oranges is 12 kobo.

Therefore, the gain is :

\(\qquad \tt \dashrightarrow \:12 - 2.4\)

\(\qquad \tt \dashrightarrow \:9.6 \: \: kobo\)

Percentage gain is ~

\(\qquad \tt \dashrightarrow \: \dfrac{9.6}{2.4} \times 100\)

\(\qquad \tt \dashrightarrow \:4 \times 100\)

\(\qquad \tt \dashrightarrow \:400 \: \%\)

Answer: 2(x+3)(x+2)

Step-by-step explanation:

Answer:

p ( x > 2746 ) = p ( z > - 1.4552 )

                      = 1 - 0.072806

                      = 0.9272

This shows that there is > 92% of a republican candidate winning the election hence I will advice Gallup to declare the Republican candidate winner

Step-by-step explanation:

Given data:

51% of male voters preferred a Republican candidate

sample size = 5490

To win the vote one needs ≈ 2746 votes

In order to advice Gallup appropriately lets consider this as a binomial distribution

n = 5490

p = 0.51

q = 1 - 0.51 = 0.49

Hence \(n_{p}\) > 5  while \(n_{q}\)  < 5

we will consider it as a normal distribution

From the question :

number of male voters who prefer republican candidate  ( mean ) ( u )

= 0.51 * 5490 = 2799.9

std = \(\sqrt{npq}\) = \(\sqrt{5490 * 0.51 *0.49}\) = 37.0399  ---- ( 1 )

determine the Z-score = (x - u ) / std  ---- ( 2 )

x = 2746 , u = 2799.9 , std = 37.0399

hence Z - score = - 1.4552

hence

p ( x > 2746 ) = p ( z > - 1.4552 )

                      = 1 - 0.072806

                      = 0.9272

This shows that there is > 92% of a republican candidate winning the election hence I will advice Gallup to declare the Republican candidate winner

Answer: A, 4 inches.

Step-by-step explanation: 36 divided by 9 is 4.

The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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The constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

A proportional relationship is a mathematical equation that expresses two variables that are in proportion to one another. In this type of relationship, if one variable is multiplied by a certain constant factor, then the other variable will be multiplied by the same constant factor. For example, if the cost of 3 books is $15, then the cost of 6 books will be $30. In this case, the number of books and the cost of the books are in proportion to one another.

The constant of proportionality is the constant factor by which the two variables are multiplied to obtain each other. In other words, it is the ratio between the two variables that remain constant in a proportional relationship. It can be represented by the letter k, and is calculated by dividing one variable by the other.

To find the constant of proportionality from a graph, we need to look at the slope of the line. The slope is the ratio between the change in the y-values and the change in the x-values, which is also known as the rise over run. If the graph shows a proportional relationship, then the slope will remain constant throughout the graph.

For example, if the graph shows the relationship between the number of hours worked and the amount of money earned, and the slope is 10, then the constant of proportionality is 10. This means that for every hour worked, the person earns $10. The equation for this proportional relationship can be written as y = 10x, where y represents the amount of money earned and x represents the number of hours worked.

In conclusion, the constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

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Answer:

130

Step-by-step explanation:

let the inside value be,x

x+30°+20°=180°(Being sum of interior angle of triangle)

or,x+50°=180°

or,x=180°-50°

or,x=130°

Now,

let the exterior angle be,a

a=x(VOA)

a=130°

Therefore the value of a is 130°.

f (x) =x-6

or, f (5)= 5-6

= - 1

Answer:

2/1309

Step-by-step explanation:

\(\frac{1}{7} x\frac{4}{34} x\frac{1}{11}\)

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

Explanation:

There are 35 marbles and 7 colors. We have an equal amount of each color, so there are 35/7 = 5 marbles per color. We have 5 blue marbles to start.

We'll multiply out those fractions to get our final answer

(1/7)*(2/17)*(1/11) = (1*2*1)/(7*17*11) = 2/1309

Answer:

it would be 4,1

Step-by-step explanation:

because its the only one that startes with 4 and ends with 1

An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.

By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;

f(x) = |x|

y = A|x + B| + C

g(x) = -1/4|x + 1| - 2

In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.

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The probability that (50) dies within 10 years and dies after (40) is at least 0.02 but less than 0.04. So the answer is B. At least .02 but less than .04.

To calculate the probability that (50) dies within 10 years and dies after (40), we need to find the joint probability of the two events happening together.

Let X and Y be the future lifetimes of (40) and (50), respectively. We want to find P(Y≤10 and X<Y). Using the Law of Total Probability, we can write:

P(Y≤10 and X<Y) = ∫P(Y≤10 and X<Y|X=t) fX(t)dt

where fX(t) is the probability density function of X.

Since the force of mortality for (40) is constant, the probability density function for X is given by:

f X (t)=ue −ut

where u=0.05.

For (50), we have the survival function S(y) = 1 - y/10. So, the probability density function for Y is:

fY(y) = S'(y) = 1/10

Now, we can substitute these expressions into the integral and simplify:

P(Y≤10 and X<Y) = ∫P(Y≤10 and X<Y|X=t) fX(t)dt

= ∫∫P(Y≤10 and X<Y|X=t) fY(y)fX(t)dydt

= ∫∫P(Y≤10 and t<Y) (1/10)(0.05)e^(-0.05t)dydt

= (1/10)∫e^(-0.05t) ∫1≤y≤10 e^(0.1y) dydt

= (1/10)∫e^(-0.05t) (e - e^(-t/10)) dt

Evaluating this integral, we get:

P(Y≤10 and X<Y) ≈ 0.0286

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The perimeter of the figure is 4(π + 9)ft.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

Given is a 2 - D figure as shown in the figure attached.

We can write the perimeter as -

P = P{rectangle} + P{semicircle}

P = 2(10 + 8) + (4π)

P =  (4π) + (36)

P = 4(π + 9)

Therefore, the perimeter of the figure is 4(π + 9)ft.

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Answer:

Step-by-step explanation: 9091.6

Answer:

9091.6

Step-by-step explanation:

Answer:

To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.

First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.

Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.

Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.

However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

\(\dfrac{x}{3}+\dfrac{y}{4}=2\\\\\\\text{Multiply the whole equation by the LCM of 4 , 12 which is 12}\\\\ 12*\dfrac{x}{3}+12*\dfrac{y}{4}=12*2\\\\\\4x + 3y=24 \ -------------------(i)\)

\(\dfrac{2x}{3}+\dfrac{3y}{4}=5\\\\\\\text{Multiply the whole equation by 12}\\\\12*\dfrac{2x}{3}+12*\dfrac{3y}{4}=5*12\\\\\\\)

8x + 9y = 60 -------------------------(ii)

Multiply  equation (i) by (-2)

(i)*(-2)              -8x -6y = -48

(ii)                     8x +9y = 60   {Now add. x will be cancelled}

                                3y = 12    {Divide both sides by 3}

                                  y = 12/3

y = 4

Substitute y = 4 in equation (i)

4x + 3*4 = 24

4x + 12   = 24

         4x = 24 - 12

         4x = 12

           x = 12/4

x = 3

\(\boxed{x = 3 \ ; \ y = 4}\)

Answer: (-2,-3)

Step-by-step explanation:

5 years longer then Bill, 2x5=10.

10+2=12.

12-5=7

Hoang has be there for 12 years. Bill has for 7 years.

The rate of interest is given by the equation R = 3.5 %

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the rate of interest be represented as R

Now , the simple interest I = $ 175

The principal amount invested P = $ 2,500

The time period T = 2 years

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )

Substituting the values in the equation , we get

Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )

Rate of Interest R = 17500 / 5000

Rate of Interest R = 3.5 %

Hence , the interest rate is 3.5 %

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The equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

To determine the equation of a parabola that opens to the right, has a focus at (-1, -3), and a focal diameter of 8

we can use the standard form of the equation for a parabola with a horizontal axis:

(x - h)² = 4p(y - k)

Where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus.

Since the parabola opens to the right, the vertex will be to the left of the focus.

Therefore, the vertex will be at (-1 - p, -3).

The focal diameter is given as 8, which means the distance between the vertex and the focus is p = 8/2 = 4.

Plugging these values into the equation, we have:

(x - (-1 - 4))² = 4 × 4 × (y - (-3))

Simplifying:

(x + 5)² = 16(y + 3)

x² + 10x + 25 = 16y + 48

Rearranging to isolate y:

16y = x² + 10x + 25 - 48

16y = x² + 10x - 23

Dividing by 16:

y = (1/16)x² + (10/16)x - (23/16)

Therefore, the equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

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The area of the shaded region of a circle with a 100 degree angle and a radius of 3cm, using pi=3.14, is approximately 25.64 square centimeters.

To find the area of the shaded region of a circle, we need to subtract the area of the sector formed by the shaded region from the area of the whole circle.

The area of the whole circle is given by

A = πr²

where A is the area of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14 (as given in the question).

Substituting the given values, we get

A = π(3cm)²

A = 28.26 cm² (rounded to two decimal places)

Now, let's find the area of the sector formed by the shaded region.

The angle of the sector is given as 100 degrees. To find the area of the sector, we need to use the formula:

A = (θ/360)πr²

where θ is the angle in degrees, r is the radius of the circle, and π is again approximately equal to 3.14.

Substituting the given values, we get

A = (100/360)π(3cm)²

A = 2.62 cm² (rounded to two decimal places)

Finally, we can find the area of the shaded region by subtracting the area of the sector from the area of the whole circle

Shaded area = Area of circle - Area of sector

Shaded area = 28.26 cm² - 2.62 cm²

Shaded area = 25.64 cm² (rounded to two decimal places)

Therefore, the area of the shaded region of the circle is approximately 25.64 square centimeters.

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--The given question is incomplete, the complete question is given

" Find the area of a shaded region of circle and use 3.14 for pi "--