the amusement park built a new roller coaster.When the train exits the gate, it climbs 170 feet up the first hill before dropping 164 feet down. write an solve an equation to represent the change in elevation

Answer:

16

Step-by-step explanation:

there are four of them and four spaces, so you would do 4x4. 4x4= 16

The required length of one of the longest sides is 29 in the given pentagon.

The pentagon has 3 sides of length (2x - 1) and 2 sides of length (x + 5) and the perimeter of the pentagon is 127.

We know that the perimeter of the pentagon is the total length of all its sides, so we can set up the following equation:

3(2x - 1) + 2(x + 5) = 127

Apply the distributive property of multiplication,

6x - 3 + 2x + 10 = 127

Combine the likewise terms of the equation,

8x + 7 = 127

Finally, we can solve the equation by subtracting 7 from both sides and dividing both sides by 8:

8x = 120

x = 15

Therefore, the length of one of the longest sides is (2 × 15 - 1) = 29.

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It would cost $1804.86 to buy concrete for repavement of the driveway if 1 cubic yard of concrete costs $130 .

Given,

Width of driveway = 30 ft = [tex]\frac{30}{3}[/tex] = 10 yard

Length of driveway  = 50ft = [tex]\frac{50}{3}[/tex] = 16.667 yard

As the driveway is repaved by pouring concrete then it's height will increase

Height of driveway = 3 inch = [tex]\frac{3}{36}[/tex] = 0.0833 yard

Volume of driveway = length x breadth x height

Volume of driveway = 10 x 16.667 x 0.0833

Volume of driveway = 13.8836 cubic yard

Cost of 1 cubic yard of concrete = $130.00

then cost of 13.8836 cubic yards of concrete  will be

130.00 x 13.8836 = $1804.86

Thus, the cost of concrete will be $1804.86.

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a) The average cost of the promotion is $0.01 per tire.

b) The probability that Greer will refund more than $25 for a tire is 0.9

According to the Question:

Greer Tire Company has:

Lifetime mileage = 33500

Standard Deviation = 3500 miles

a)

Meal lifetime mileage : $33,500

Standard deviation of mileage $3,500

Observed miles 30,000 miles

100 miles failed $1.00

Hence :

The average cost of the promotion:

= (33,500 – 30,000) / 3500

= 3500 /3500

= 1

Therefore,

Cost of production

100 miles = $1.00

= 1 * 1 / 100

= $0.01 per tire

b)

 P (z < 25000 -33500/ 3500

= P (z < -8500/ 3500)

= z < -2.4

Hence:

= 1 - 0.1

= 0.9

Therefore, the Probability that gear will refund more than $25.00 per tire is: 0.9

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Answer: To solve for an area of something, we must first multiply the length by the width, something that is 5 inches long and 2 inches wide has an area of 10 square inches. It's basically multiplying the numbers together in order to find the amount of area it has.

Step-by-step explanation:

The probability that the coin will land heads up on the first flip, tails up on the second flip, and tails up on the third flip is (1/8).

If we toss a coin, we have two possible outcomes: head or tail. Now:

P(E) = Favourable outcomes / Total outcomes

      = 1/2

As per the question, we need heads on the first throw and tails on the next two throws. We know that for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

Let A be the event of getting head on the first throw and B and C be events of getting tails on the second and third throws of dice respectively.

P(A) = P(B) = P(C) = 1/2

So, P(A∩B∩C) = (1/2)*(1/2)*(1/2) = 1/8

So, the Required probability is (1/8)

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⇒The first step let us find the lowest common denominator to get r of the fraction.

⇒In this case the lowest denominator is 3,meaning3 will multiply all the terms in the equation

⇒[tex]-14(3)=-\frac{4}{3} a(3)\\-42=-4a[/tex]

⇒ Divide all the terms of the equation with the coefficient of the unknown variable to leave it independent.

⇒We are going to divide all the terms of the equation on this case by -4 since it tis the coefficient of the unknown variable

[tex]-\frac{42}{-4} =-\frac{4a}{-4} \\a=10.5[/tex]

∴a=10.5

The pre-image and image have the same shape after dilatation, but they are not the same size.

In the given question, we have to explain what is true about an image after a dilation.

The pre-image and image have the same shape after dilatation, but they are not the same size.

The figure is the same from every perspective. The midpoints of the figure's sides and the dilated shape's midpoint are both unchanged. Lines that are parallel and perpendicular to one another in the figure are identical to those in the dilated figure. The pictures stay the same.

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The function that represents the graph will be y = 1 - 2x in interval (∞, 2], y = -3 in interval [2, 3), y = -2 at x = 3, and y = 2(x - 4)² - 2 in interval (3, ∞).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

From the graph, the equation of the line that passes through (0, 1) and (2, -3) is given as,

(y - 1) = [(1 + 3) / (0 - 2)](x - 0)

y - 1 = -2x

y = 1 - 2x, (∞, 2]

In intervals [2, 3), the equation is

y = - 3

At x = 3, the value of y is -1.

The vertex of the parabola is at (4, -2). Then the parabolic function is given as,

y = a(x - 4)² - 2

The equation is passing through (0, 5), then we have

0 = a(5 - 4)² - 2

2 = a

The function is y = 1 - 2x in interval (∞, 2], y = -3 in interval [2, 3), y = -2 at x = 3, and y = 2(x - 4)² - 2 in interval (3, ∞).

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the probability is 68‰

For the normal distribution,

The scores on standardized admissions tests are normally distributed with a mean of 500

Mean (μ)=500

standard deviation(σ)=100

The probability that scores lies between 400 and 600  i.e, P(400

For the standard normal distribution curve

Z=(x-μ)/σ

(400-500)/100<(x-μ)/σ<(600-500)/100

-1

For standard normal distribution mean shifted to zero,  P(x)dx=1/(sqrt(2pi))e^(-z^2/2)dz.

so the probability would be 68‰

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Answer: the first one

Step-by-step explanation:

Answer: should be this V≈549.78

Step-by-step explanation:

Answer: 4 whole laps plus 1/2 of a lap

Step-by-step explanation:

let x = number of laps

2/3x=3

x=9/2

x=4 1/2

4 whole laps plus 1/2 of a lap

The committee can be chosen in 99.98.97.96.95 different ways.

What is a combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Here, we have

Given

The 5 equal members of the terraforming committee of the united martian colonies are randomly chosen from the council of 99 leaders.

We have to find out how many different ways can this committee be chosen.

For this, we concluded that the committee can be chosen in 99.98.97.96.95 different ways.

Hence,  the committee can be chosen in 99.98.97.96.95 different ways.

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No, they cannot form the vertices of a right triangle. The points must be three distinct points and all three must be located in different quadrants.

No, they cannot form the vertices of a right triangle. A right triangle is a three-sided polygon with one 90 degree angle. To form a right triangle, the three points must be three distinct points in different quadrants. In this case, the points (-4 3) and (-1 1) are both in the same quadrant. Additionally, 1/3 is not a point, but a fraction.

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Answer:

Step-by-step explanation:

Step 1: You have the slope so its already y=-4x+b. So you need to find the y intercept.

To find the y intercept, you need to plug the coordinates in. So 2=-4(-3)+b. Then you solve the equation from there.  

Hope this helps!

Answer: y=833.333⇒

Step-by-step explanation:

y=[tex]\frac{3250*40} {40}[/tex]=833.333>

The correct option is a survey based on multidimensional scaling”.

What is multidimensional scaling?

Using multidimensional scaling (MDS), it is possible to see how similar the individual examples in a dataset are to one another. The pairwise "distances" between a group of items or people are translated using MDS into a configuration of points that are mapped onto an abstract Cartesian space.

Companies utilize multidimensional scaling (MDS) as a technique to visualize the degree of similarity between diverse goods or datasets.

Since the study asks participants to rate how similar two brands are. Consequently, it is regarded as multidimensional scaling (MDS).

Hence the correct option is a survey based on multidimensional scaling”.

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Complete Question
You are a customer taking a survey. It lists two brands and asks you to rate how similar they are. What type of survey are you taking?

A. a focus group application survey
B. a survey based on multidimensional scaling
C. a survey based on attributes
D. a conjoint analysis survey.

The linear function that represents the graph of that has the points on the table is: A. .f(x) = 32(3x - 1).

If a point is on a graph of a linear function, its coordinates will make the equation of the linear function true, if plugged into the equation.

Given the table that represents some of the points that are on a linear function graph, use one point, (1, 64), to check which of the functions represents the table.

Substitute x = 1 and .f(x) = 64 into each of the functions given to see which is true:

.f(x) = 32(3x - 1)

64 = 32(3(1) - 1)

64 = 32(3 - 1)

64 = 32(2)

64 = 64 [true]

.f(x) = -32(x - 3)

64 = -32(1 - 3)

64 = 64 [true], however, if we use another set of values, say (5, 448), this function will not be true.

.f(x) = -2(32x - 3)

6 = -2(32(1) - 3)

6 = -2(29)

64 = -58 [not true]

.f(x) = 16(2x - 1)

64 = 16(2(1) - 1)

64 = 16(1)

64 = 16 [not true]

Therefore, the function that represents the table is: A. .f(x) = 32(3x - 1).

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The approximate percentage of daily phone calls numbering between 37 and 47 is of:

68%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

The mean and the standard deviation in this problem are given as follows:

Hence the percentage is of 68%, as these measures are within one standard deviation of the mean.

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Answer: -1

Step-by-step explanation: Plug 1 in as x. You get h(1)=-3(1)+2. If you solve this, it is h(1)=-3+2, or h(1)=-1

Answer:

[tex] \sf \: h(1) = - 1[/tex]

Step-by-step explanation:

Given equation,

→ h(x) = -3x + 2

Now the value of h(1) will be,

→ h(x) = -3x + 2

→ h(1) = -3(1) + 2

→ h(1) = -3 + 2

→ [ h(1) = -1 ]

Hence, the value of h(1) is -1.

1.46% probability that fewer than 700 children received their vaccine.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

95% of children have received their DTaP vaccine p = 0.95

Sample of 750, n = 750

For the approximation, the mean and the standard deviation are given by:

u = np = 750×0.95 = 712.5

σ = [tex]\sqrt{np(1-p)}[/tex]

σ = [tex]\sqrt{750(0.95)(0.05)}[/tex]

σ = 5.97

Using continuity correction, the probability that fewer than 700 children received their vaccine is P(X < 700 - 0.5) = P(X < 699.5), which is the p-value of Z when X = 669.5.

Z = X-u/σ

Z = 669.5 - 712.5/5.97

Z = - 2.18

The p-value of Z = - 2.18 is 0.0146.

Hence, 1.46% probability that fewer than 700 children received their vaccine.

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After solving the system of equation we will get

x = 5y/2 +1  

y = 2/5- 2x/5

First equation is written

−2x+5y=−2

Subtract 5y from both sides.

−2x =−2−5y

The equation is in standard form.

−2x=−5y−2

Divide both sides by −2.

-2x/-2 = -5y-2/ -2

Dividing by −2 undoes the multiplication by −2.

x= −5y-2/-2

​Divide  −2−5y  by −2.

so

x= 5y/2 + 1

Now the second equation is

4x−10y=4

Add 4x to both sides

-10y = 4-4x

The equation is in standard form.

Divide both sides by 10

-10y/10= 4-4x/10

Dividing by 10 undoes the multiplication by 10.

y= 4-4x/10

Divide 4-4x by 10.

so

y= 2/5- 2x/5

​

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Answer:

1 and 5

Step-by-step explanation:

first category and fifth one up

Answer:$ 16.50

Step-by-step explanation:If you are adding, you do

$8.50+

8.00

------------

16.50

0 plus 0 is nothing.

5 plus 0 is 5.

8 plus 8 is 16.

Your answer is now "16.50" .

The estimated population is 114.74 microorganisms after three hours.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases with time.

a type of growth when the values' logarithms rise linearly with time. This indicates that the value increases faster than it would with linear development. A population that increases by 10% of its value each unit of time would be an example of exponential growth.

let A(f) = number of bacterial 'I' now. in

A(t) = Ao × e^kt

= 71 × e^(0.16XA)

For t = 3 hours

A(t) = 71 × e^(0.16×3)

= 114.74 bacteria

Complete question:

The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 16% per hour. Suppose that a sample culture has an initial population of 71 bacteria. Find the predicted population after three hours Do not round any intermediate computations, and round your answer to the nearest tenth bacteria

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The standard deviation of the quantitative variable of interest in the population is called the. Population Standard Deviation.

"Information available from the question"

In the question:

The mean of the quantitative variable of interest in the population is called the

Now, According to the question:

Let's know:

Sample Mean:

A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set. The sample mean can be applied to a variety of uses, including calculating population averages.

The mean of the quantitative variable of interest in the sample is called the. Sample Mean. The standard deviation of the quantitative variable of interest in the population is called the. Population Standard Deviation.

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Answer:

Below

Step-by-step explanation:

4 minutes = 4  x 60 = 240 seconds

240 seconds / 15 q   = 16 s/q

Answer:

? = 5

Step-by-step explanation:

There are no like terms to 5, so it stays the same

Its means that the addition of natural numbers obeys the closure property.

In mathematics, the closure property is a property that states that if a set is combined with all its limit points, then the combined set is also a limit point. The closure property applies to sets of real numbers, vectors, and matrices. It states that the closure of a set is itself, i.e., the set is closed under the given operation. The phrase "closed under addition" means that when two natural numbers are added together, the result is also a natural number. In other words, natural numbers are part of a closed system concerning addition; the addition operation always produces another natural number.

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y = -5x – 13 equation is the equation of a line that passes through (- 10 3 and is perpendicular to Y 5x 7 with slope

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. To find the equation of a line that passes through (-10, 3) and is perpendicular to y = 5x + 7, we need to find m, the slope of the line.

We can find the slope of the line by using the point-slope form of a line, which is y - y1 = m(x - x1). In this equation, m is the slope, (x1, y1) is a given point on the line, and (x, y) are the coordinates of any point on the line.

Plugging in the given point of (-10, 3) and the line y = 5x + 7 into this equation, we get:

3 - 3 = m(-10 - -10)

The left side of this equation is 0, so the right side must also be 0. That means that m = 0.

Now that we have the slope of the line, we can plug it into the equation of a line, y = mx + b, to get the equation of the line:

y = 0x + b

Next, we need to find the y-intercept, b. To do this, we can use the given point (-10, 3). Plugging this in to the equation above, we get:

3 = 0x + b

Simplifying, we get:

b = 3

Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form:

y = 0x + 3

Finally, we can simplify this equation to get the final answer:

y = -5x – 13

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