a rectangular box has a volume of 2860.what could be the dimension of its rectangular base if its height is 40cm?

The solution of the function is as follows:

f(3) = 16

h(0) = -4

h(g(x)) = 3x + 5

g(y) = y + 3

f(x) - h(x) =  x² - x + 5

A function relates input and output. In other words, a function is an expression that defines a relationship between one variable (the independent variable) and another variable(dependent variable).

Therefore, let's solve the function as follows:

f(x) = x² + 2x + 1

g(x) = x + 3

h(x) = 3x - 4

Therefore,

f(3) =  (3)² + 2(3) + 1 = 9 + 6 + 1 = 16

h(0) = 3(0) - 4 = -4

h(g(x)) = 3(x + 3) - 4 = 3x + 9 - 4 = 3x + 5

g(y) = y + 3

f(x) - h(x) =  x² + 2x + 1  - (3x - 4) =  x² + 2x + 1  - 3x + 4 = x² - x + 5

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9. The ball returns to 98.00% of its previous height after each bounce Option B

10. It will take 183 bounce until the ball bounces back to a height less than 3 inches.  Option B

To solve for k% of previous height after each bounce, we say

10×(k/100)⁵ = 9.04

k = [tex](9.04/10)^{1/5}[/tex]×100

k = 98.00

To find out how many bounces it takes for the ball to bounce back to a height less than 3 inches (or 0.25 feet), we use the inequality

10 × (0.961)ⁿ < 0.25

The logarithm of both sides gives

n × log(0.961) < log(0.025)

n > log(0.025) / log(0.961)

n > 182.593

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The first term of GP is  a₁ = -4.

Given that,

Sum of five terms of GP = s₅ = -16.3804

Common ratio = 9/10  which is less than 1

Number of terms = n = 5

We know that,

Sum of nth term of GP when common ration is less than 1,

s₅ = a₁(1-[tex]r^{n}[/tex])/(1-r)

Substituting the values,

⇒ -16.3804 = a₁(1-0.9⁵)/(1-0.9)

⇒             a₁ = -16.3804/4.0951

⇒             a₁ = -4

Hence, the value of  a₁ is -4.

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A type of transportation is LEAST likely to take more than 30 minutes include the following: d. train.

In order to determine the type of transportation that is least likely to take more than 30 minutes for Conrad to get to an appointment at the other end, we would have to compare the median minute for each data set (type of transportation) that is represented on the box-and-whisker plot shown above.

By critically observing the box-and-whisker plot, we can reasonably infer and logically deduce that a train is the type of transportation that is least likely to take more than 30 minutes because its median minute is the lowest compare to the other data set (type of transportation) that is represented on the box-and-whisker plot shown above.

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Answer:

C. Through a given point not on a given line, there is exactly one line parallel to the given line.

Step-by-step explanation:

hope i helped

Answer:

Look down

Step-by-step explanation:

Thanks for reaching out for assistance! Based on the context you provided, it seems like the correct answer is C. Playfair's axiom states that there is exactly one line parallel to a given line that can be drawn through a point not on it. I hope this helps! Let me know if there's anything else I can do for you.

Step-by-step explanation:

To find the slope of the line between two points, you can use the formula:

slope (m) = (y2 - y1) / (x2 - x1)

Plugging in the given coordinates, we have:

m = (-4 - (-2)) / (2 - (-2))

m = (-4 + 2) / (2 + 2)

m = (-2) / (4)

m = -1/2

The slope of the line through the points (-2, -2) and (2, -4) is -1/2.

Step-by-step explanation:

To determine the constant of proportionality (k) in a proportional relationship, we need to compare corresponding values of x and y and calculate the ratio between them.

Let's examine the given values:

2. UX: x 6 15 9 y 42 200

To find the constant of proportionality (k), we can take any pair of corresponding values and calculate their ratio. Let's choose the first pair: (6, 42).

k = y / x

k = 42 / 6

k = 7

So, the constant of proportionality (k) is 7.

Now, let's find the missing values for the second set of values:

d. X: 14 y: 21 6 15 3 7 8

Since we know the constant of proportionality is 7, we can calculate the missing values of y by multiplying each corresponding x value by 7.

Missing values for y:

- For x = 21, y = 21 * 7 = 147

- For x = 6, y = 6 * 7 = 42

- For x = 15, y = 15 * 7 = 105

- For x = 3, y = 3 * 7 = 21

- For x = 7, y = 7 * 7 = 49

- For x = 8, y = 8 * 7 = 56

Therefore, the missing values of y are: 147, 42, 105, 21, 49, and 56.

Answer: 8000

Step-by-step explanation:

Given that this is an isosceles triangle, then the lengths of the sides opposite the two 45º angles have to be the same length.

For this reason, x = 8.

And since x = 8 and there's only one answer with x=8, the first option must be the answer.

You can calculate the value of y using the Pythagorean Theorem.  

   [tex]y^2 = 8^2+8^2[/tex]
which will lead you to [tex]y=8\sqrt{2}[/tex].  

Answer:

$2.48 and $2.15, respectively

Step-by-step explanation:

2.30 * 1.08 = 2.48

1.99 * 1.08 = 2.15

Answer:

$223,787

Step-by-step explanation:

r = 0.02

C = 191,000

t = 8

S = 191,000 (1 + 0.02)⁸

Follow order of operations (PEMDAS).

S = 191,000 (1.02)⁸

S = 191,000 (1.171659381)

S = 223,786.9

(We want to round to the nearest dollar, which is the ones place, so ignore all digits after the tenths place.)

Rounding, S = 223,787

To solve for x in the equation −1.5x−2.7=20.1+4.5x, we need to isolate x on one side of the equation. We can do this by adding 1.5x to both sides of the equation and adding 2.7 to both sides of the equation, which gives us:

-1.5x - 2.7 + 1.5x = 20.1 + 4.5x + 1.5x

Simplifying the left side of the equation and combining like terms on the right side of the equation gives us:

-2.7 = 6x + 20.1

Subtracting 20.1 from both sides of the equation gives us:

-22.8 = 6x

Dividing both sides of the equation by 6 gives us:

x = -3.8

Therefore, the value of x that satisfies the equation is -3.8.

The number of terms n of the geometric progression is n = 12

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

10 + 30 + 90 + .... = 2657200

And , let the number of terms be n

common ratio r = 30 / 10 = 3

where sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

On simplifying , we get

2657200 = 10 ( 3ⁿ - 1 ) / ( 2 )

Divide by 5 on both sides , we get

3ⁿ - 1 = 5,31,440

Adding 1 on both sides , we get

3ⁿ = 5,31,441

Taking log on both sides , we get

n = 12

Hence , the number of terms of GP is n = 12

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Answer: 2/13.86

Step-by-step explanation:

A lines rate of change is equal to it's slope

Slope is rise over run (Y/X)

The point is up 2 on the Y axis and over 13.86 on the X axis

The slope is= 2/13.86

Answer:

8 am

Step-by-step explanation:

First train has a 50 m/hr x 3 hr = 150 mile head start

Second train is going 60 - 50 = 10 m/hr faster and will close this 150 mile distance

 in 15 hours to catch the first train

2pm + 3 hours + 15 hours = 8 am

Answer:

dwdaddaw

Step-by-step explanation:

ad plus devide

__________________________________

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The compound interest is solved and the amount in her account in 2047 is given by A = $ 1315.46

Given data ,

To determine how much money Carly has in her account after 37 years, we need to substitute the value of t as 37 into the equation:

P = 600(1.0375)^t

P = 600(1.0375)^37

P ≈ 600(1.0375)^37 ≈ 600(2.19243) ≈ $ 1315.46

Therefore , Carly has approximately $1315.46 in her account after 37 years.

To calculate the growth rate, we need to find the rate of change between the initial and final amounts over the given time period.

Regarding how long it takes for Carly's account to reach $750, we'll assume you mean when the account reaches or exceeds $750. Let's set up the equation and solve for t:

750 = 600(1.0375)^t

Dividing both sides by 600, we get:

1.25 = 1.0375^t

Taking the logarithm of both sides (base 1.0375):

log(1.25) = t * log(1.0375)

t ≈ log(1.25) / log(1.0375) ≈ 8.5 years

Hence , it takes approximately 8.5 years for Carly's account to reach or exceed $750

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Answer:14/165

Step-by-step explanation:

its a fraction i did the same qestion and got it right

The statement is examined using the equation to find that

1. False

2. False

3. True

4. False

The given equation is

f(x) = 32 / ( 1 + e⁰°⁵ˣ)

Evaluating the first statement by substituting

For x = 3, f(3 ) gives 5.84

For x = 6, f( 6) gives  1.52

5.82 - 1.52 is not equal to 9 ft hence the statement is False

Evaluating the second statement by substituting

when x = 0, the function gives 16 which is against 2 ft hence False

Evaluating the third statement by substituting

For x = 1, f(1) = 12.08 this is less than 16 ft hence a decline hence this is True

fourth statement

The trees maximum height, captured should be 16 ft not 35 ft hence False

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A higher credit score reduces your fixed costs because you will pay lower interest rates. That is option A.

A higher credit score is one of the factors that are being considered by banks or lenders before one is being viewed as being legible to borrow money.

This is soo because a higher credit score will reduce the lending interest rates of the individual because it shows such will pay back the borrowed money as soon as possible.

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"The correct option is (C) $25w < $168." This means that Joe needs to save for at least 7 weeks (since he can't save for a fraction of a week) to afford the hoverboard.

The hoverboard costs $168 and Joe earns $25 each week. To determine if Joe can afford the hoverboard, we need to determine how many weeks he needs to save to reach the cost of the hoverboard.

Let's represent the number of weeks Joe needs to save as "x". Each week, he earns $25, so the total amount he will have after "x" weeks is 25x. In order to buy the hoverboard, he needs to have saved $168. Thus, we can write the inequality:

25x ≥ 168

This inequality represents the fact that the amount of money Joe earns after "x" weeks must be greater than or equal to $168, the cost of the hoverboard, for him to be able to afford it. Simplifying this inequality, we get:

x ≥ 6.72.

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The Parallelogram area is 96 square meters.

We have,

The area of a parallelogram is given by the formula A = bh, where b is the length of the base and h is the height.

In this case,

The base of the parallelogram is the length of one of its parallel sides, which is 12 m.

The height of the parallelogram is given as 8 m.

Therefore, the area of the parallelogram is:

A = bh

A = 12 m x 8 m

A = 96 square meters

Thus,

The Parallelogram area is 96 square meters.

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The term (100 C 15) represents the number of ways to choose 15 defective screws out of 100 packs.

In a scenario where there are 2 defective screws out of 100 packs, each containing 500 screws, we can calculate the probability of obtaining 15 defective screws. Let's assume that each pack is independent of the others.

The probability of a single screw being defective is 2/500, as there are 2 defective screws out of 500 in each pack.

Conversely, the probability of a screw being non-defective is 498/500.

To find the probability of obtaining exactly 15 defective screws, we can use the binomial distribution formula. The probability (P) can be calculated as follows:

P = (100 C 15) * (2/500)^15 * (498/500)^85

The term (100 C 15) represents the number of ways to choose 15 defective screws out of 100 packs.

By plugging these values into the formula and performing the calculations, the probability of obtaining exactly 15 defective screws can be determined. However, I am unable to perform the calculation for you within the given word limit.

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The symmetric equations for the line are:

(36x + 40y - 28z - 100) / 0 = (x-5) / -6 = (y-8) / -5 = (z+2) / 7

To find the parametric equations for the line passing through A(5, 8, -2) and B(-1, 3, 5), we can use the vector equation:

r = A + t(B-A)

where r is the position vector of any point on the line, t is a scalar parameter, and A and B are the given points. Substituting the values, we get:

r = (5, 8, -2) + t((-1)-5, 3-8, 5-(-2))

r = (5, 8, -2) + t(-6, -5, 7)

The parametric equations for the line are:

x = 5 - 6t
y = 8 - 5t
z = -2 + 7t

To find the symmetric equations, we can use the fact that any point on the line is equidistant from points A and B. Thus, the distance from a point (x, y, z) to A must be the same as the distance from the same point to B. Using the distance formula, we get:

√[(x-5)² + (y-8)² + (z+2)²] = √[(x+1)² + (y-3)² + (z-5)²]

Squaring both sides and simplifying, we get:

36x + 40y - 28z - 100 = 0

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Answer: If the number is placed on the X as in (X,Y) the X value will rise but the Y value will stay the same, but if the number is played on the Y, the Y value will go up, and the X value will stay the same

Answer:

If it can be exactly 150, then 50.

there’s not exactly enough info for me to solve.