A train is moving at a rate of 65 miles/hour toward a railroad marker located 200 miles away. Which equation could be used to find the time it will take for the distance between the train and the railroad marker to be 4 miles apart, where h represents the time in hours?

The two solutions to the equation (2x - 3)(3x + 5) = 0 when solved are x = 3/2 and x = -5/3

Given that, we have the following equation

(2x - 3)(3x + 5) = 0

The above equation means that

2x - 3 = 0 and 3x + 5 = 0

When the equations are evaluated, the equations becoms

2x = 3 and 3x = -5

Lastly, we divide both sides of the equation by the coefficent of x i.e 2 and 3

So, we have

x = 3/2 and x = -5/3

So, the values of the solutions to the equation are x = 3/2 and x = -5/3

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If there are 243 students at the school, then there are 81 students at Rolling Hills Middle School who have pets.

If the ratio of the total number of students to the number of students with pets at Rolling Hills Middle School is 3 to 1, this means that for every 3 students at the school, there is 1 student with a pet.

Let's represent the total number of students at the school as "3x" (since the ratio is 3 to 1, we can use any multiple of 3 as a placeholder for the total number of students), and the number of students with pets as "x". Therefore, we can write the following equation:

3x : x = 3 : 1

To solve for x, we can cross-multiply:

3x * 1 = x * 3

3x = 3x

We can see that the equation is true for any value of x, which means that there are many possible solutions. However, since we know that the total number of students at the school is 243, we can use this information to solve for x:

3x = 243

x = 81

Therefore, there are 81 students at Rolling Hills Middle School who have pets.

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Answer: x= 71

Step-by-step explanation:

Since each triangle has a sun of all the angles to equal 180, we can figure what is X.

Answer:4x + 3x + 2x - 4 - 3

Step-by-step explanation:Hope this helps

If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.

Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.

Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800

Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.

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Answer:

Step-by-step explanation:

First, we need to calculate the annual interest rate from the given APR.

APR = 2.25%

Daily interest rate = 2.25% / 365 = 0.00616438

Now, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = time in years

In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.

A = 2000(1 + 0.00616438/365)^(365*4)

A = 2000(1.00616438)^1460

A = $2,388.34 (rounded to the nearest cent)

Therefore, the answer is option D) $2,388.34.

Answer:

To determine if Daniel should have filled out his W-4 form differently to receive a refund, we need to compare his tax liability with the total amount withheld from his paychecks for the year.

If Daniel's tax liability for the year is less than $3,900, he will receive a refund when he files his taxes. If his tax liability is more than $3,900, he will owe additional taxes when he files his taxes.

If Daniel's tax liability is exactly $3,900, he will neither owe additional taxes nor receive a refund when he files his taxes.

Therefore, to determine if Daniel should have filled out his W-4 form differently, we need to compare his tax liability with $3,900.

If Daniel's tax liability from part B, question 3, is less than $3,900, he will receive a refund when he files his taxes, as the total amount withheld from his paychecks is more than his tax liability. In this case, Daniel may want to consider filling out his W-4 form differently to reduce the amount withheld from his paychecks and increase his take-home pay.

On the other hand, if Daniel's tax liability from part B, question 3, is more than $3,900, he will owe additional taxes when he files his taxes, as the total amount withheld from his paychecks is less than his tax liability. In this case, Daniel may want to consider filling out his W-4 form differently to increase the amount withheld from his paychecks and reduce the amount he will owe when he files his taxes.

If Daniel's tax liability from part B, question 3, is exactly $3,900, he will neither owe additional taxes nor receive a refund when he files his taxes, and his W-4 form is correctly filled out for his tax situation.

In summary, whether or not Daniel should have filled out his W-4 form differently to receive a refund depends on his tax liability compared to the total amount withheld from his paychecks. If his tax liability is less than the total amount withheld, he may want to reduce the amount withheld to increase his take-home pay. If his tax liability is more than the total amount withheld, he may want to increase the amount withheld to reduce the amount he will owe when he files his taxes. If his tax liability is exactly equal to the total amount withheld, his W-4 form is correctly filled out for his tax situation.

The area of given polygon is 44 square units from the given graph.

What is Polygon ?

A polygon is a 2-dimensional geometric shape that is formed by joining a finite number of straight line segments to form a closed shape.

The area of each triangle can be found by using the formula:

Area = (base * height)/2

Triangle 1: Base = 4 units, Height = 5 units

Area of Triangle 1 = (4*5)/2 = 10 square units

Triangle 2: Base = 8 units, Height = 3 units

Area of Triangle 2 = (8*3)/2 = 12 square units

The area of the trapezoid can be found by using the formula:

Area = (Sum of parallel sides * Height)/2

Trapezoid: Height = 4 units, Parallel side 1 = 3 units, Parallel side 2 = 7 units

Area of Trapezoid = ((3+7)*4)/2 = 20 square units

Therefore, the total area of the polygon is:

Total Area = Area of Triangle 1 + Area of Triangle 2 + Area of Trapezoid

Total Area = 10 + 14 + 20 = 44 square units

Hence, The area of given polygon is 44 square units from the given graph.

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three and seven tenths times five

After solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, the cost of each blouse and skirt:

x be the price of one blouse and y is the price of one skirt.

For a total of $215, Carol purchased 3 skirts and 5 blouses.

5x + 3y = 215

For a total of $135, Ellen purchased 2 skirts and 3 blouses.

3x + 2y = 135

By resolving the equations in the system:

5x + 3y = 215

3x + 2y = 135

We will obtain:
x = $25

y = $30

Therefore, after solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.

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Correct question:

Carol bought 5 blouses and 3 skirts for a total of $215. At the same time, her sister Ellen bought 3 blouses and 2 skirts for a total of $135. What was the price of each blouse and each skirt?

One figure should be rotated to match the other's alignment. Expand one figure till it is the same size as another.

A figure or object in a coordinate plane can be transformed to create a new figure or object that has been relocated, flipped, or altered in some other way. Translations, rotations, and reflections are the three primary forms of transformations. Moving a figure horizontally or vertically without altering its size or shape is known as translation. Rotation entails angling a figure around a fixed point, often known as the rotational center.

given

The subsequent transformations must be used in order to demonstrate similarity between two figures:

Translation (moving the figures to the same spot) (moving the figures to the same position)

Rotation (rotation one figure to fit the other) (rotating one figure to match the other)

Dilation (resizing the figures such that they have the same shape, but maybe different sizes) (resizing the figures so that they have the same shape, but possibly different sizes)

Consequently, the following set of transformations should be used to demonstrate that the figures abc and def are similar.

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Answer:

11

Step-by-step explanation:

15 - (p + 1)

Let p=3

15 - (3 + 1)

Parentheses first

15 - (4)

11

Answer:

11

Step-by-step explanation:

Given that,

p = 3

So, to find the value of the expression you have to solve it by replacing p with 3.

15 - ( p + 1 )

15 - ( 3 + 1 )

15 - 4

11

Answer: slope=4

Step-by-step explanation:

[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]

[tex]Slope=\frac{4- - 4}{3-2}[/tex]

[tex]Slope=\frac{4+4}{3-2}[/tex]

[tex]Slope=4[/tex]

The value of f(4) using recursive formula f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2  is 22

Given that f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2.

To find the value of f(4), we can use the recursive formula to work our way up from f(1) to f(4):

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

f(2) = f(1) + 4 = 10 + 4 = 14

Next, we have

f(3) = f(2) + 4 = 14 + 4 = 18

Next, we have

f(4) = f(3) + 4 = 18 + 4 = 22

Therefore, the value of f(4) is 22.

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Answer:

Data Visualization Tools

Step-by-step explanation:

2x + y = -7

y= -7-2x

put this value in 2nd equation

3x=6+4(-7-2x)

3x=6-28-8x

11x= -22

x= -2

y= -7-2(-2)

y= -7+4

y= -3

A tangent line is a straight line that intersects a circle at only one point, and it is perpendicular to the radius that goes through that point.

Tangent lines are important because they help us determine the relationship between circles and other geometric shapes.
To find the tangent line to a circle, we need to first identify the point of intersection between the circle and the line.
A tangent line to a circle is a line that intersects the circle at exactly one point, called the point of tangency. The tangent line is perpendicular to the radius that intersects the point of tangency.

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

where m is the slope of the tangent line, and r is the radius of the circle.

The equation of a tangent line to a circle can be found using the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1, y1) is the point of tangency and m is the slope of the tangent line.

The length of the tangent segment from the point of tangency to the point of intersection with a secant line can be found using the formula:

[tex]t^2[/tex] = s1 * s2

where t is the length of the tangent segment, and s1 and s2 are the lengths of the two segments of the secant line that intersect the circle.
In terms of calculating the tangent line, we can use the point-slope formula.

Let's say we have a circle with equation [tex]x^2[/tex] + [tex]y^2[/tex] = [tex]r^2[/tex] and we want to find the tangent line at the point (a,b).

We can start by taking the derivative of the equation with respect to x, which gives us 2x + 2yy' = 0.

Solving for y', we get y' = -x/y.

Then, we substitute the values of x and y at the point of intersection (a,b) to get the slope of the radius at that point.

Finally, we take the negative reciprocal of that slope to get the slope of the tangent line, and use the point-slope formula to find the equation of the tangent line.
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Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.

To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.

In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:

P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)

Using a calculator or statistical software, we can evaluate this expression to find:

P(X = 7) ≈ 0.170

This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.

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Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

The number of feet away is the base of the ladder from the end of the slide, g, as shown is 3 ft.

The base of the ladder from the end of the slide forms a right triangle.

Hypotenuse² = opposite² + adjacent²

Hypotenuse = 5 ft

Opposite = 4 ft

Adjacent = g

So,

Hypotenuse² = opposite² + adjacent²

5² = 4² + g²

25 = 16 + g²

subtract 16 from both sides

25 - 16 = g²

9 = g²

find the square root of both sides

√9 = g

g = 3 ft

In conclusion, the base of the ladder is 3 ft away from the end of the slide.

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The adaptive-response-rate single exponential smoothing model is best applied to time series data that are non stationary and seasonal which means option D is the right answer.

The adaptive response rate single exponential smoothing model is used to demonstrate the changes in the forecasting data and the fluctuation in data values with respect to time which are smoothened by a coefficient. The larger the coefficient, the greater the smoothing effect.

This kind of model is ineffective for stationary time series as it takes into account the smoothing of the information. Adaptive smoothing is computationally difficult. Exponential smoothing produces accurate forecasts. The forecast shows projected demand and actual demand.

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Check the picture below.

[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]

The value of x is 4.5 rounded to the nearest tenth.

Tangent of a circle is defined as the line which passes through exactly one point on the circle.

Secant of a circle is the line which passes through two points on the circle.

Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.

Using the theorem, we can say here that,

(8 + 2) 2 = x²

x² = 10 × 2

x² = 20

x = √20

x = 4.472 ≈ 4.5

Hence the value of x is 4.5.

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Using graphs,

The ordered pair, (6,15) represents here the cost of 6 pounds of noodles that is $15.

A structured representation of the data is all that the graph is. It assists us in comprehending the info. Data are the numerical details gathered by observation. Data is a derivative of the Latin term datum, which means "something provided."

Data is continuously gathered through observation once a research question has been formulated. After that, it is arranged, condensed, and categorised before being graphically portrayed.

Here in the question,

As we can see that the graph is a relation between the number of noodles in pounds and the cost of noodles in dollars has been given and compared.

So, as per the question,

The ordered pair that represents here the cost of 6 pounds of noodles is (6,15).

As, from the graph:

When noodles in pounds is 6, cost in dollars is 15.

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The complete question is:

the points on the graph show how much chee pays for different amounts of noodles, complete the statement about the graph

Answer:

They're not promise

Step-by-step explanation:

I did it on the calculator

I hope this helps youuu

Have a good day <3

The values for the variables x and y in the parallelogram are equal to 10 and 17 respectively.

The parallelogram OPSR have two pairs of parallel sides hence OP = RS and PS = OR.

We shall evaluate for variables x and y as follows:

2x - 1 = x + 9

2x - x = 9 + 1 {collect like terms}

x = 10

y = x + 7

y = 10 + 7 {substituting 10 for x}

y = 17

Therefore, the values for the variable x and y in the parallelogram are equal to 10 and 17 respectively.

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The expression 3x-(4-x) is equivalent to 4x-4

The distributive property is a mathematical property that describes the relationship between multiplication and addition or subtraction. It states that when a number is multiplied by a sum or difference of two or more numbers, the result is the same as if we multiplied the number by each of the individual terms inside the parentheses and then added or subtracted the products.

To simplify the expression 3x-(4-x), we can distribute the negative sign to the second term inside the parentheses, which gives:

3x - (4 - x) = 3x - 4 + x

Now we can combine the like terms (3x and x) to get:

3x - 4 + x = 4x - 4

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The given question is incomplete, the complete question is:

Which expression is equivalent to 3x-(4-x)?

Answer:

If you add two positive numbers together you will get a positive.

Step-by-step explanation: