In physics, if a moving object has a starting position at s 0, an initial velocity of v 0, and a constant acceleration a, then the position S at any time t > 0 is given by:

S = at 2 + v 0 t + s 0.

Solve for the acceleration, a, in terms of the other variables. For this assessment item, you can use ^ to show exponents and type your answer in the answer box, or you may choose to write your answer on paper and upload it.

Answer:

[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]

The variable X represents the quantity.

Step-by-step explanation:

We are given that

The demand function for an auto parts manufacturing company is fiven by

f(x)=100000-25 x

Where x=Represents  price

f(x)= Represents quantity

We have to find inverse function [tex]f^{-1}(X)[/tex]

Let f(x)=X

[tex]X=100000-2500 x[/tex]

[tex]2500x=100000-X[/tex]

[tex]x=\frac{100000-X}{2500}[/tex]

Substituting the value of x then we get

[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]

Therefore, the inverse function

[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]

Where X= Represents the quantity

[tex]f^{-1}(X)[/tex]=Represents price

The length of the rectangular parking lot is  130 meters.

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

The perimeter of a rectangle is the sum of the lengths of all the sides.

Given, The length of a rectangular parking lot is 10 meters less than twice it's width.

Assuming the width of the rectangle is x meters, therefore length would be

(2x - 10) meters and the perimeter is 400 meters.

We know the perimeter of a rectangle is 2(length + width).

∴ 2( x + 2x - 10) = 400.

2(3x - 10) = 400.

6x - 20 = 400.

6x = 420.

x = 70 meters and length is (2.70 - 10) = 130 meters.

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Answer:

Option D. is the correct answer.

Step-by-step explanation:

In this graph, polygon PQRST has been dilated by a scale factor of 3 keeping origin as the center of dilation to form P'Q'R'S'T'.

We know when two polygons are similar, their angles will be same and their corresponding sides will be in the same ratio.

Therefore, option D.which clearly says that the ratio of side SR and S'R' is 1 : 3, will be the answer.

Answer:

The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.

Step-by-step explanation:

The average rate of a function f(x) on the interval [a,b] is defined as

[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]

The average rate of change from x = 2 to x = 3 is

[tex]m=\frac{f(3)-f(2)}{3-2}[/tex]             .... (1)

From the given graph it is clear that the value of the function is -3 at x=2 and -1 at x=3. It means f(2)=-3 and f(3)=-1.

Put  f(2)=-3 and f(3)=-1 in equation (1).

[tex]m=\frac{-1-(-3)}{3-2}[/tex]

[tex]m=\frac{-1+3}{1}[/tex]

[tex]m=\frac{2}{1}[/tex]

[tex]m=2[/tex]

The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.

Answer:

C. (4, 3, 2)

Step-by-step explanation:

Given : [tex]3x+2y+z=20[/tex]

            [tex]x-4y-z=-10[/tex]

            [tex]2x+y+2z=15[/tex]

To Find: Solution:

[tex]3x+2y+z=20[/tex]   -1

[tex]x-4y-z=-10[/tex]      --2

[tex]2x+y+2z=15[/tex]   --3

Substitute the value of z from 1 in 2 and 3

So in 2 , [tex]x-4y-(20-3x-2y)=-10[/tex]  

[tex]x-4y-20+3x+2y=-10[/tex]  

[tex]4x-2y=-10+20[/tex]  

[tex]4x-2y=10[/tex]  ---4

So, in 3 ,  [tex]2x+y+2(20-3x-2y)=15[/tex]

[tex]2x+y+40-6x-4y=15[/tex]

[tex]-4x-3y=15-40[/tex]

[tex]-4x-3y=-25[/tex]   -5

Now solve 4 and 5

Substitute the value of x from 4 in 5

[tex]-4(\frac{10+2y}{4})-3y=-25[/tex]

[tex]-1(10+2y)-3y=-25[/tex]

[tex]-10-2y-3y=-25[/tex]

[tex]-10-5y=-25[/tex]

[tex]-5y=-15[/tex]

[tex]y=3[/tex]

Now substitute the value of y in 4

[tex]4x-2(3)=10[/tex]

[tex]4x-6=10[/tex]

[tex]4x=10+6[/tex]

[tex]4x=16[/tex]

[tex]x=4[/tex]

Now substitute the value of x and y in 1 to get value of z

[tex]3(4)+2(3)+z=20[/tex]

[tex]12+6+z=20[/tex]

[tex]18+z=20[/tex]

[tex]z=20-18[/tex]

[tex]z=2[/tex]

Thus The solution is (4,3,2)

Hence Option c is correct.

Answer:

2143.6 in

Step-by-step explanation:

A +B = 181

A=181-B

4.70A+5.90B= 967.10

4.70(181-B) +5.90B =967.10

850.70-4.70B+5.90B=967.10

850.70+1.2B =967.10

1.2B=116.40

B =116.40/1.2 = 97

A=181-97 = 84 pounds of type A coffee

To estimate the average SAT score of first-year students at a college with a 95% confidence interval and a margin of error of 25 points, you would need to sample approximately 554 students.

This question involves using the concepts of mean, standard deviation, margin of error, and confidence intervals from probability and statistics. To determine the sample size needed to estimate the average SAT score with a certain margin of error, we'll use the formula for the sample size required for estimating a population mean in statistics:

n = (Z*σ/E)^2

Where:

Plugging the values into the formula, we get:

n = (1.96*300/25)^2 ≈ 553.47

As we cannot have a fraction of a student, we always round up to ensure our margin of error requirement is met. Therefore, you would need to sample approximately 554 students.

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To limit the margin of error of your 95% confidence interval to 25 points, given the standard deviation is 300, use the formula for the margin of error for a confidence interval and solve for the sample size 'n'. Approximately 553 students should be sampled.

For this question, we can use the formula for the margin of error for a confidence interval which is calculated as: Margin of Error = z * (σ/√n). Here, 'z' represents the z-score, 'σ' is the standard deviation, and 'n' is the sample size.

In this case, we wish to have a 95% confidence level. From z-tables, we know that the z-value for a 95% confidence level is approximately 1.96. We want a margin of error of 25 points. The standard deviation (σ) for the dataset is said to be 300.

So, we can rearrange our formula to solve for 'n', giving us: n = (z * σ / Margin of Error)². Substituting in our numbers, we get n = (1.96 * 300 / 25)². So, to limit the margin of error on your 95% confidence interval to 25 points, you will need to sample approximately 553 students.

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Answer:  First Option is correct.

Step-by-step explanation:

Since we have given that

[tex](4x^3+2x^2-18x+38)\div(x+3)[/tex]

We will apply the "Remainder Theorem ":

So, first we take

[tex]g(x)=x+3=0\\\\g(x)=x=-3\\\\and\\\\f(x)=4x^3+2x^2-18x+38[/tex]

So, we will put x=-3 in f(x).

[tex]f(-3)=4\times (-3)^3+2\times (-3)^2-18\times (-3)+38\\\\f(-3)=-108+18+54+38\\\\f(-3)=2[/tex]

So, Remainder of this division is 2.

Hence, First Option is correct.

The remainder of the given expression is 2 and this can be determined by using the factorization method.

Given :

Expression  --  [tex]\rm \dfrac{4x^3+2x^2-18x+38}{x+3}[/tex]

The factorization method can be used in order to determine the remainder of the given expression.

The expression given is:

[tex]\rm =\dfrac{4x^3+2x^2-18x+38}{x+3}[/tex]

Try to factorize the numerator in the above expression.

[tex]\rm =\dfrac{4x^3+12x^2-10x^2-30x+12x+36+2}{x+3}[/tex]

[tex]\rm = \dfrac{4x^2(x+3)-10x(x+3)+12(x+3)+2}{(x+3)}[/tex]

Simplify the above expression.

[tex]\rm = (4x^2-10x+12) + \dfrac{2}{(x+3)}[/tex]

So, the remainder of the given expression is 2. Therefore, the correct option is A).

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The area of a rectangle can be directly calculated using the formula:

A = l * w

Where l is the length or the depth while w is the width

Therefore,

A = 50 feet * 100 feet

A = 5000 square feet

A) 2/5 = 0.4

B) 4% = 0.04

C) 0.29

D) 27/100 = 0.27

 least = 0.04, then 0.27, then 0.29, then 0.4

 so B, D, C A is the order

For a 30-60-90 triangle with a hypotenuse of length x, the perimeter would be defined by the formula x(3 + √3)/2.

In terms of mathematics, the question discusses a right triangle, specifically a 30-60-90 triangle. When it comes to a 30-60-90 triangle, certain ratios of sides exist. In this triangle, the ratio of the lengths of the sides opposite the 30°, 60° and 90° angles are 1:√3:2. Given that the length of the hypotenuse is x, the sides opposite the 30° and 60° angles would be x/2 and x√3/2, respectively. So, the perimeter of the triangle could be determined by adding up the lengths of all three sides i.e., x + x/2 + x√3/2. The simplified form of this equation indicates that the

perimeter

of the triangle = x(1 + 1/2 + √3/2), which can also be written as x(3 + √3)/2.

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Answer:

Step-by-step explanation:

BE is [tex]7.73[/tex]

What is Square?

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

What is equilateral triangle?

In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

According to question, The diagram below shows equilateral triangle ABC sharing a side with square ACDE.

We have to find BE.

Now, AB [tex]= 4[/tex] and AE [tex]= 4.[/tex]

The angle EAB is [tex]90+60 = 150[/tex]°

Using the law of the cosines, we get

[tex]BE^2 = AE^2 + AB^2 - 2(AB)(AE)cos(150)[/tex]

        [tex]=4^2 + 4^2 -[/tex][tex]2(4)(4)[/tex]×[tex]\frac{\sqrt{3} }{2}[/tex]

⇒[tex]BE=7.73[/tex]

Hence, we can conclude that BE is [tex]7.73[/tex]

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The equation to model the suspension cables of a bridge, where the lowest point of the cable is 40 feet above the bridge, and the towers are 100 feet tall and 200 feet from the center, is y = -0.0015x^2 + 60.

To find the equation that models the suspension cable of a bridge, we use the properties of a parabolic shape. Since the cable is attached to towers that are 100 feet tall and the lowest point of the cable is 40 feet above the bridge, we know the vertex of the parabola is 60 feet (100 - 40) below the top of the towers.

Let's define the coordinate system with the origin at the lowest point of the cable. Then the towers are at (-200, 60) and (200, 60) because the bridge is 400 feet long, so each tower is 200 feet horizontally from the center. The parabolic equation takes the general form y = ax^2 + bx + c. Because the vertex is at (0, 60), c = 60.

Using the points (-200, 60), we can substitute into the parabolic equation and write a system to solve for a and b. Since the parabola is symmetric, b = 0. The system becomes 60 = a(-200)^2 + 60, which simplifies to a = -60/40000.

Thus, the equation to model the cables is y = -60/40000x^2 + 60, or simplified, y = -0.0015x^2 + 60.