Across a horizontal distance of 25 feet, a roller coaster has a steep drop. The height of the roller coaster at the bottom of the drop is -150 feet, compared to its height at the top of the drop. What is the average amount that the roller coaster's height changes over each horizontal foot?

Answer:

More than doubled

Step-by-step explanation:

The troop "strength" is basically just troop number. It went from about 200,000 to about 500,000.

US troop strength is more than doubled. The correct option is A.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

From the given data we can see that the troop "strength" is basically just troop number. It went from about 200,000 to about 500,000.

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Answer: 68.86 inches

Step-by-step explanation:

Given : In a survey of women in a certain country having

Mean : [tex]\mu=64.3\text{ inches}[/tex]

Standard deviation : [tex]\sigma=2.77\text{ inches}[/tex]

The z-value corresponds to 0.095 is 1.645.  [Using standard normal distribution table]

The height that represents the 95th percentile is given by :-

[tex]H=z\times\sigma+\mu\\\\=1.6449\times2.77+64.3=68.856373\approx68.86\text{ inches}[/tex]

Hence, the height represents the 95th ​percentile = 68.86 inches.

Answer:

95th ​percentile = 68.86 inches.

Step-by-step explanation:

Just took quiz :)

Answer:

Step-by-step explanation:

These are independent non-ordered events. The faculty members chosen don't affect the students and vice versa. There is no issue with replacement, and the only limitation is the number of people allowed to serve.

12C4*15C5

495*3003=1,486,485 ways

Answer:

about 75 percent of its force

Step-by-step explanation:

Answer:

That is known as a Vertex

A figure formed by two rays that share a common endpoint is known as an angle. The common endpoint is known as the vertex, while the rays are considered the sides of the angle.

In mathematics, a figure formed by two rays that share a common endpoint is known as an angle. The common endpoint is referred to as the vertex and the rays are referred to as the sides of the angle.

Rays in the context of angles means a straight line that starts from a point (vertex) and extends indefinitely in a particular direction. For example, in a page of a book when it is half open, the two visible pages represent the rays, and where the pages meet (the spine) represents the vertex.

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Answer:

  The supposition is incorrect.

Step-by-step explanation:

The growth rate of a child is not constant, so height versus time does not look like a straight line. Nothing is wrong with the prediction made using the false assumption. You can conclude anything you like when you start with a false premise.

Answer:

76800 cases

Step-by-step explanation:

The number of cases of new infectious diseases reported last year= 150 cases

Number of cases are going to be double every year

Number of the cases in next or first year=150+150=300

Number of the cases in next or second year=300+300=600

Number of the cases in next or third year=600+600=1200

Number of the cases in next or fourth year=1200+1200=2400

Number of the cases in next or fifth year=2400+2400=4800

Number of the cases in next or sixth year=4800+4800=9600

Number of the cases in next or seventh year=9600+9600=19200

Number of the cases in next or eight year=19200+19200=38400

Number of the cases in next or ninth year=38400+38400=76800

Hence , the total number of cases are 76800 cases

Answer:

38,400

Step-by-step explanation:

The answer above me is wrong

Got it right on the test

Answer:

8.

Step-by-step explanation:

It's none of those. It is 8, because 8 is a factor of 40 ( and of 8 of course).

Answer:

none of the above.

Step-by-step explanation:

when we talk about greatest common factor of  8 x  and 40 y

8 x = 2× 2× 2 × x........................................(1)

40 y = 2 × 2 × 2 × 5 × y..............................(2)

when we see both equation (1) and (2 )

then we can clearly see

that the greatest common are 2 × 2 × 2

so, the greatest common will be 2 × 2 × 2 = 8

hence , the correct answer will be none of the above.

Answer: 1.12

Step-by-step explanation:

The confidence interval for the mean [tex]\mu[/tex] and margin of error E is given by :-

[tex](\mu-E,\ \mu+E)[/tex]                                             --------------(1)

The given confidence interval : (0.21, 2.45)              -------------(2)

From (1) and (2), we  have

[tex]\mu-E=0.21-------(3)\\\\\mu+E=2.45--------(4)[/tex]

Subtract equation (3) from (4), we get

[tex]2E=2.45-0.21\\\\\Rightarrow\ 2E=2.24\\\\\Rightarrow\ E=\dfrac{2.24}{2}=1.12[/tex]

Hence, the margin of error is 1.12 .

The margin of error can be calculated as half the width of the confidence interval.

The margin of error can be calculated by finding half the width of the confidence interval. In this case, the confidence interval is (0.21, 2.45), so the width is 2.45 - 0.21 = 2.24. Therefore, the margin of error is half of this width, which is 2.24/2 =

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Answer:

  sin θ = 4/5

Step-by-step explanation:

The Pythagorean theorem tells you the distance (h) from the origin to the terminal point:

  h² = (-3)² +(4)² = 25

  h = 5 . . . . . . . . take the square root

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse

For angles other than 1st-quadrant angles, it can sometimes be difficult to identify the relevant sides of the relevant triangle. If the angle were a 1st-quadrant angle, it would be clear that the side opposite the angle is the y-coordinate of the point on the terminal side. That remains the case for all angles. The hypotenuse is always the positive distance from the origin to the terminal point.

So, you have

  sin θ = opposite/hypotenuse = 4/5

Answer:

  p² > 4/3(1 -p)

Step-by-step explanation:

Assuming candy selections are independent from one to the next, the probability of getting Coffee Toffee twice in a row will be p². The probability of getting some other selection than Coffee Toffee will be 1-p.

Lisa wants ...

  p² > (4/3)(1 -p)

_____

This has solution p > 2/3.

Answer:

Step-by-step explanation:

Answer:

The value of a is 10 and the value of b is 6

Step-by-step explanation:

* Lets revise how to solve the problem

- Remember in the number with exponent

-  a^n × a^m = a^(n + m)

- a^n ÷ a^m = a^(n - m)

Lets solve the problem

∵ [tex]\frac{7^{2}.7x^{8}}{7x^{4}}[/tex]

- Lets use the rule above

∵ [tex]7^{2}.7^{8}=7^{2+8}=7^{10}[/tex]

∴ [tex]\frac{7^{2}.7^{8}}{x^{4}}=\frac{7^{10}}{7^{4}}[/tex]

∵ [tex]\frac{7^{10}}{7^{4}}=\frac{7^{a}}{7^{4}}[/tex]

∴ a = 10

∵ [tex]\frac{7^{10}}{7^{4}}=7^{10-4}=7^{6}[/tex]

∵ [tex]7^{6}=7^{b}[/tex]

∴ b = 6

* The value of a is 10 and the value of b is 6

Answer: 10 and 6 for the next one its 2, 3, and 8

Step-by-step explanation: i hope this helps :)

Answer:

<1 = 100

<2 = 80

Step-by-step explanation:

Angle 1 and angle 2 are supplementary

Supplementary angles add to 180 degrees

<1 + <2 = 180

The angles are in a ratio of 5 to 4

Multiply by x to get the measure of each angle

<1 = 5x  <2 = 4x

5x+4x = 180

Combine like terms

9x = 180

Divide by 9

9x/9 =180/9

x =20

<1 = 5x = 5*20 = 100

<2 = 4x = 4*20 = 80

Answer:

he's right

Step-by-step explanation:

or she i dont discriminate

Answer:

x=15

Step-by-step explanation:

165+x=180

x=180-165

x=15

Answer:

15° = x

Step-by-step explanation:

By the Supplementary Angles Theorem, you add m<x by 165, and set that equal to 180°, or π. Of course you have to do the inverse of addition in order to get this, so deduct 165 from 180 to end up with 15.

Answer:

Step-by-step explanation:

1.  The calculation for the minimum payment is ...

  0.035 × $7600.97 = $266.03

__

2. The answer choices assume that Jorge makes a payment of $266.03 each month. After the first month, the minimum payment due is less than that amount. If Jorge only pays the minimum payment each month the balance will decrease by about 1.5% each month, and it will take about 31 years before the minimum payment is below $1.

The TVM Solver says it will be about 43 months for the card to be paid off if Jorge pays $266.03 each month.

Answer:

  7 +1.25m = 43.25

Step-by-step explanation:

Let m represent the number of minutes on the trampoline. Then the charge (in dollars) for minutes you're on it is 1.25m. The entrance fee is added to that to give the total charges:

  7 + 1.25m = 43.25

Answer:

He should prepare 260 pounds of first mixture and 0 pounds of second mixture

Step-by-step explanation:

Let x be the total quantity ( in pounds ) of cherries and mints in the first mixture and y be the total quantity in second mixture,

Since, first mixture will contain half cherries and half mints by weight,

That is, in first mixture,

Cherries = [tex]\frac{x}{2}[/tex]

Mints = [tex]\frac{x}{2}[/tex],

While, second mixture will contain one-third cherries and two-thirds mints by weight,

That is, in second mixture,

Cherries = [tex]\frac{y}{3}[/tex]

Mints = [tex]\frac{2y}{3}[/tex]

According to the question,

The manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock,

That is,

[tex]\frac{x}{2}+\frac{y}{3} \leq 130[/tex]

[tex]\frac{x}{2}+\frac{2y}{3}\leq 170[/tex]

Also, pounds can not be negative,

x ≥ 0, y ≥ 0,

Since, the first and second mixture must be sell at the rate of $2.00 per pound and $1.25 per pound respectively,

Hence, the total revenue,

Z = 2.00x + 1.25y

Which is the function that have to maximise,

By plotting the above inequalities,

Vertex of feasible regions are,

(0,255), (180, 120) and (260, 0),

Also, at (260, 0), Z is maximum,

Hence, he should prepare 260 pounds of first mixture and 0 pounds of second mixture in order to maximize his sales revenue.

To maximize sales revenue, the candy manufacturer should prepare one-third cherries and two-thirds mints mixture.

To maximize sales revenue, the candy manufacturer should prepare a mixture that contains one-third cherries and two-thirds mints by weight. Let's assume that he prepares x pounds of this mixture. To calculate the amount of the other mixture, we subtract x from the total weight of the ingredients in stock. So, the amount of the other mixture will be (130 + 170) - x pounds. The candy manufacturer should prepare x pounds of the one-third cherries and two-thirds mints mixture and (130 + 170) - x pounds of the other mixture to maximize his sales revenue.

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Answer:

1. 2.12 seconds

2. 10 feet

Step-by-step explanation:

1. "Pekka tosses a ball out of a window that is 40 feet in the air.  Its initial velocity is 15 feet per second.  The path of the ball is represented by:

h = -16t² + 15t + 40

How long does it take for the ball to hit the ground (in seconds) rounded to the nearest hundredth?"

When the ball hits the ground, its height is 0:

0 = -16t² + 15t + 40

0 = 16t² − 15t − 40

Solve with quadratic formula:

t = [ -b ± √(b² − 4ac) ] / 2a

t = [ 15 ± √(225 + 2560) ] / 32

t ≈ 2.12 or -1.18

t must be positive, so t = 2.12 seconds.

2. "Tricia bounces a ball in front of her feet.  The path of the ball from the time it hits the ground until it lands on the floor is represented by:

f(x) = -2(x − 3)² + 10

Assuming that Tricia's feet are located at the origin (0, 0), what is the maximum height of the ball (in feet)?"

The function is a parabola.  The vertex of this parabola is at (3, 10).  So the maximum height is 10 feet.

Answer:

A) 420 seconds = 7 minutes

B) 8 times

Step-by-step explanation:

A) After how many second would all three things happen together again?

Solution:

His clock ticked every 5 seconds , a tap was dripping every 7 seconds and     his pet dog snored every 12 seconds. It all happens simultaneously = 5*7*12=420 seconds

B) How many times would all three things happen together again between    midnight and one o'clock

Since all these events happen together after every 420 sec = 7 mins and there are 60 mins between midnight and 1 o'çlock , thus 60/7 = 8 times ....

Answer:

A.)  Slope of function B = 2 * the slope of Function A.

Step-by-step explanation:

The slope of Function A is 1  ( because of the x  ( = 1x) in the equation).

From the graph, the slope of Function B = 5 / 2.5 = 2.

Answer:

The correct option is A.

Step-by-step explanation:

The slope intercept form of a line is

[tex]y=mx+b[/tex]               .... (1)

where, m is slope and b is y-intercept.

The equation of Function A is

[tex]f(x)=x-9[/tex]      .... (2)

From (1) and (2) we get

[tex]m=1[/tex]

It means slope of Function A is 1.

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

From the given graph it is clear that the line passes through two points (0,-1) and (1,1).

[tex]m=\frac{1-(-1)}{1-0}=2[/tex]

The slope of Function B is 2.

We can say that

Slope of Function B = 2 x Slope of Function A

Therefore the correct option is A.

Answer:

  √3

Step-by-step explanation:

  cot²(θ) = csc²(θ) -1 . . . . . a relevant identity

  = 1/sin²(θ) -1

  = (1/(1/2))² -1 = 2² -1 = 3

Then ...

  cot(θ) = √3 . . . . . . . . take the square root

Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

It just is

Answer:

  1/2sin(6x) + 1/2sin(2x)

Step-by-step explanation:

You can look up the formulas for the product identities for sine and cosine, or you can guess and check using a graphing calculator. I did the calculator solution first (see the first attachment), then looked up the identities so I can tell you what they are (see the second attachment).

__

These identities are based on the sum and difference angle identities:

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

  = 2sin(α)cos(β)

Dividing by 2 gives the identity of interest in this problem:

  sin(4x)cos(2x) = (1/2)(sin(4x +2x) +sin(4x -2x))

  sin(4x)cos(2x) = (1/2)(sin(6x) +sin(2x))

Answer:   1/2sin(6x) + 1/2sin(2x)

Step-by-step explanation:

took the test and got a 100

Answer:

In vertex form it's [tex]y=(x+7)^2-9[/tex]

In standard form it's [tex]y=x^2+14x+40[/tex]

Step-by-step explanation:

We can use the vertex form to solve for a in

[tex]y=a(x-h)^2+k[/tex]

"a" is the number out front that dictates the steepness, or lack thereof, in a parabola.  That means that we need h and k (which we have in the vertex) and we need x and y (which we have in the form of one of the zeros).  Filling in using a vertex of (-7, -9) and a coordinate point (-7, 0):

[tex]0=a(-4-(-7))^2-9[/tex] simplifies a bit to

[tex]0=a(-4+7)^2-9[/tex] simplifies a bit more to

[tex]0=a(3)^2-9[/tex] and

[tex]0=a(9)-9[/tex] so

[tex]0=9a-9[/tex],

[tex]9=9a[/tex] and finally,

a = 1

Phew!  So there is the a value.  Now we can simply fill in the formula completely, using the vertex as our guide:

[tex]y=(x+7)^2-9[/tex]

In standard ofrm that is

[tex]y=x^2+14x+40[/tex]

We can check ourselves for accuracy by factoring that standard polynomial using whatever method of factoring you like for quadratics and get that the roots are in fact x = -10, -4

The only reason we needed the zeros is to use one of them as the x and y to solve for a.  

The dimensions that minimize the total cost of material for the shipping crate are:

- Length: 24 feet

- Width: 24 feet

- Height: 8 feet

To solve this problem, we can start by writing down the volume formula for a rectangular box with a square base:

Volume = Length × Width × Height

Given that the volume is 3072 ft³, we have:

3072 = L × W × H

We also know that the material for the top and sides costs $4 per square foot and the material for the bottom costs $2 per square foot. Let's denote the areas of the top, bottom, and sides as A_top, A_bottom, and A_sides, respectively.

A_top = L × W

A_bottom = L × W

A_sides = 2 × (L × H + W × H)

The total cost, C, can be expressed as:

C = 4 × (A_top + A_bottom) + 2 × A_sides

C = 4 × (L × W + L × W) + 2 × 2 × (L × H + W × H)

C = 8LW + 4LH + 4WH

We can substitute the volume equation into the cost equation to eliminate one variable. Let's express L in terms of W and H from the volume equation:

L = 3072 ÷ (W × H)

Now substitute L into the cost equation:

C = 8(3072 ÷ (WH))W + 4(3072 ÷ (WH))H + 4WH

C = 24576 ÷ H + 12288 ÷ W + 4WH

To minimize C, we take the derivative with respect to W and H, set them equal to zero, and solve for W and H:

∂C/∂W = -12288/W² + 4H = 0

∂C/∂H = -24576/H² + 4W = 0

Solving these equations gives us W = 24 and H = 8, which leads to L = 3072 ÷ (24 × 8) = 16.

So, the dimensions that minimize the total cost of material are Length: 24 feet, Width: 24 feet, and Height: 8 feet.

Complete Question:
A shipping company must design a closed rectangular shipping crate with a square base. The volume is 3072ft3. The material for the top and sides costs $4 per square foot and the material for the bottom costs $2 per square foot. Find the dimensions of the crate that will minimize the total cost of material.

Answer:

Choice A) [tex]F(x) = 3\sqrt{x + 1}[/tex].

Step-by-step explanation:

What are the changes that would bring [tex]G(x)[/tex] to [tex]F(x)[/tex]?

[tex]G(x) = \sqrt{x}[/tex]. The choices of [tex]F(x)[/tex] listed here are related to [tex]G(x)[/tex]:

The expression in the braces (for example [tex]x[/tex] as in [tex]G(x)[/tex]) is the independent variable.

To shift a function on a cartesian plane to the left by [tex]a[/tex] units, add [tex]a[/tex] to its independent variable. Think about how [tex](x-a)[/tex], which is to the left of [tex]x[/tex], will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by [tex]a[/tex] units, subtract [tex]a[/tex] from its independent variable.

For example, [tex]G(x+1)[/tex] is [tex]1[/tex] unit to the left of [tex]G(x)[/tex]. Conversely, [tex]G(x-1)[/tex] is [tex]1[/tex] unit to the right of [tex]G(x)[/tex]. The new function is to the left of [tex]G(x)[/tex]. Meaning that [tex]F(x)[/tex] should should add [tex]1[/tex] to (rather than subtract [tex]1[/tex] from) the independent variable of [tex]G(x)[/tex]. That rules out choice B) and D).

The graph of [tex]G(x)[/tex] is stretched vertically. However, similarly to the graph of this graph [tex]G(x)[/tex], the graph of [tex]F(x)[/tex] increases as [tex]x[/tex] increases. In other words, the graph of [tex]G(x)[/tex] isn't flipped about the [tex]x[/tex]-axis. [tex]G(x)[/tex] should have been multiplied by a number that is greater than one. That rules out choice C) and D).

Overall, only choice A) meets the requirements.

Since the plot in the question also came with a couple of gridlines, see if the points [tex](x, y)[/tex]'s that are on the graph of [tex]F(x)[/tex] fit into the expression [tex]y = F(x) = 3\sqrt{x - 1}[/tex].

Answer:

f(x) =3 sqrt(x+1)

Step-by-step explanation:

We notice two things about the graph, it has a shift to the left and is steeper

First the shift to the left

f(x) = g(x + C)  

C > 0 moves it left

C < 0 moves it right

g(x) is 0 at x=0   f(x) is 0 at  x=-1

We are moving it 1 unit to the left

This means our "c" is 1

f(x) = sqrt( x+1)

Now we need to deal with the graph getting steeper

f(x) = Cg(x)  

C > 1 stretches it in the y-direction

0 < C < 1 compresses it

Since it is getting taller, "c" must be greater than 1

Remember the - sign means it is a reflection across the x axis, which we do not have

f(x) =3 sqrt(x+1)

Explanation:

Step 1: find the mean of the data

Step 2: subtract the mean from every data value

Step 3: find the absolute values of the differences from Step 2

Step 4: find the mean of the absolute values from Step 3. This is the MAD.

_____

The mean and absolute value have their usual definitions.

The mean is the sum of a set of numbers, divided by the number of numbers in the set.

The absolute value is the numerical value of a number with its sign changed to positive, if it isn't already. For example, |-1| = 1 and |1| = 1. The vertical bars signify the absolute value of their contents.

Step-by-step explanation:

The only exception to that is that when you have a negative outside of the absolute value symbol, you will get a negative answer.

Ex: -|3| = -3

I am joyous to assist you anytime.

hihi! so the ratio 2:1:3 can be rewritten as 2/6 (red) 1/6 (blue) and 3/6 (yellow).

this is because you have 2 floz of red, 1 floz of blue, and 3 floz of yellow, which adds up to 6 floz of paint total in your ratio.

since you have 18 fl. oz. of paint, you multiply the ratio 3/6 by 18 to get 9 fl. oz. of yellow paint.

hope this helps!

There would be of 9 ounces yellow paint needed.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The total quantity of fluid of paint= 18 ounces,

And the ratio of red, blue and yellow paint = 2:1:3

Let the multiplying factor in ratio is x,

So, total paint will be 6x,

According to given condition,

6x = 18 ounces,

x = 3 ounces

Since yellow paint is 3x,

So 3x = 9 ounces

9 ounces yellow paint is required,

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Answer:

18 cubic units

Step-by-step explanation:

There are 18 cubic units in a box that is 3 units high.

3 x 3 = 6

6 x 2 = 18

The first step in simplifying a mathematical expression, especially those with parentheses, is to eliminate and simplify terms within the parentheses. This involves combining like terms or performing operations according to the order of operations. Subsequent steps may involve factoring and applying algebraic rules to further simplify.

The question is asking for the first step in simplifying a mathematical expression. To begin simplifying any expression, especially when involving parentheses, the first step typically involves eliminating terms within the parentheses wherever possible. This process often involves combining like terms or simplifying the algebraic expression by performing any operations inside the parentheses first, according to the order of operations (PEMDAS/BODMAS).

After simplifying the expression inside the parentheses, you can then apply other algebraic techniques, such as factoring, combining like terms outside the parentheses, and explicit multiplication of terms across the parentheses if needed. Always remember to check the answer to see if it is reasonable and to ensure that no simplification step has been missed.

If the expression involves complex denominators or numerators, applying algebraic rules such as the power rule or the chain rule can further simplify the expression. In cases involving equations, isolating the variable on one side can help in solving for the unknown value.

Answer:

A).  (7, 0) The time it takes to empty the water in the  pool.

Step-by-step explanation:

If we extend the values we see that they are

x f(x)

5 10

5 5

7 0

So at time 7 minutes the pool is empty.

Answer:

(7, 0); the time it takes to empty the water in the pool

Step-by-step explanation:

The following table shows the amount of water leaking from an inflatable pool as a function of time:

x (time in minutes)    f(x)

0                            35

1                            30

2                            25

3                            20

4                             15

f(x) represents the amount of water in the pool. x intercept is the point where f(x) is 0 .At x intercept the amount of water in the pool is 0.

WE need to find out the point where f(x) becomes 0

F(x) is decreasing by 5. LEts extend the table till we get f(x) becomes 0

Decrease f(x) by 5

x (time in minutes)    f(x)

3                            20

4                             15

5                                  15-5=10

6                                  10-5=5

7                                   5-5=0

When x=7, f(x)=0. (7,0) is the x intercept.

(7, 0); the time it takes to empty the water in the pool