Question 4 of 10 f(x) = x. What is g(x)? f(x)= x g(x) (2, 1) x

The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Check the picture below.

Their house will be worth approximately $240,154.57 in 8 years.

Non of the options is correct.

To determine how much their house will be worth in 8 years, we can substitute the value of t = 8 into the exponential equation:

y = 150,000(1.004)^(12t)

y = 150,000(1.004)^(12*8)

y = 150,000(1.004)^96

Using a calculator or computer software to evaluate the exponential expression, we find:

y ≈ 150,000 * 1.601030475

y ≈ 240,154.57

None of the provided answer choices match the calculated value. However, we can examine the available options and make an estimation:

A) $240,000: This option is very close to the calculated value of $240,154.57 and is a reasonable estimate.

B) $220,000: This option is significantly lower than the calculated value and is not a close estimate.

C) $1,258,884: This option is significantly higher than the calculated value and is not a close estimate.

D) $14,457,600: This option is extremely higher than the calculated value and is not a realistic estimate.

Based on the provided answer choices, option A) $240,000 is the closest estimate to the calculated value of $240,154.57. However, please note that the actual value may vary depending on the specific calculations and rounding methods used.

Non of the options is correct.

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Answer:

1 1/2 or 1.5

Step-by-step explanation:

If they split 1/2 of the bar with each other

3 bars x 1/2 split bar = 1.5 or 1 1/2 of the shared amount

3 *1/2=1.5 or 1 1/2

Answer:

\( \frac{9x { }^{2 } - 63x}{ 3x} \\ = \frac{3x(3x - 21)}{3x} \\ = 3x - 21 \)

hope it helps:)

Answer:3x-21

Step-by-step explanation:

\(\frac{9x^{2} - 63x }{3x}\) ⇒ \(\frac{3x * (3x - 21) }{3x}\) ⇒ cancel out 3x ⇒ 3x - 21

Answer: 12

Step-by-step explanation:

Step-by-step explanation:

first do parenthesis

2x3=6

then divide

-36 / 6 = -6

then add

5 + -6 = -1

The value of the variable "x" is 11.

We have a triangle. The vertices of the triangle are K, L, and M. The side KM is extended from point M to point N. The measures of the angles MKL, LMN, and KLM are (3x + 19)°, (7x + 5)°, and (2x + 8)°, respectively. We need to find out the value of the variable "x".

The angles LMK and LMN form a linear pair. It means they are supplementary angles. The sum of the angles is 180°.

∠LMK + ∠LMN = 180°

∠LMK + (7x + 5)° = 180°

∠LMK = 180° - (7x + 5)°

In the triangle KLM, we will use the angle sum property of a triangle. The sum of all the angles in a triangle is equal to 180°.

∠K + ∠L + ∠M = 180°

(3x +19)° + (2x + 8)° + [180° - (7x + 5)°] = 180°

3x +19 + 2x + 8 + 180 - 7x - 5 = 180

-2x + 22 = 0

2x = 22

x = 11

Hence, the value of the variable "x" is 11.

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An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

i feel you man

Step-by-step explanation:

thanks for helping me out even wharn i forgot how to multiply.

The capacity of this swimming pool is between B. 500 gallons to 1,000 gallons.

Capacity refers to the product of the length, width, and height of a three-dimensional object or space.

The capacity of an object means the same as its volume.

Olympic-size swimming pools have the following standard dimensions:

Length = 50 m

Width = 25 m

Height = 2 m

Capacity of an Olympic swimming pool = 2,500 m³ (50 x 25 x 2)

= 660,000 gallons (2,500 x 1,000 ÷ 3.785)

An interval estimate shows the lower and upper limits.

6 x 105 gallons = 630 gallons

Thus, the capacity of the swimming pool is Option B.

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A. 100 gallons to 500 gallons

B. 500 gallons to 1,000 gallons

C. 1,000 gallons to 1,500 gallons

D. 1,500 gallons to 2,000 gallons

The expression |-4| has a value of 4 when evaluated

From the question, we have the following parameters that can be used in our computation:

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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Answer:d

Step-by-step explanation:

All possible real zeros of the polynomial are values of x that would make the result 0. To find these values, we set the polynomial equal to 0 and solve for x. In this case, the real zeros are x=-2, 1.5, 1, and 2.5. In this case, we will use the Synthetic Division to evaluate f(x) when x=5.

Synthetic Division is a simplified way of dividing polynomials. It can be used to divide a polynomial of any degree by a linear factor to find the zeroes of a polynomial. It is a useful tool for quickly solving many problems without having to go through the lengthy process of long division.

To do this, we will create a synthetic division table with the coefficients of the polynomial. The first row of the table will be the coefficients of the polynomial, starting from the highest power: 3x⁴, -14x³ -10x², 25x, and 0. The second row will begin with the value of x, in this case 5, followed by the coefficients of the polynomial.

Starting from the left, we will divide the first coefficient, 3, by 5, then multiply the result by 5, and subtract the first row from the second row. This process is repeated for each coefficient, until the last coefficient is 0. The last number in the second row is the remainder when the polynomial is divided by (x-5). In this case, the remainder is -45.

The highest power is 4, so the graph will decrease to the left and increase to the right. The negative coefficient (-14x³) indicates that the graph will decrease more drastically to the left than to the right.

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Answer:

x>_-1

Step-by-step explanation:

x is such that x is greater or equal to -1

Answer: 0 is a imaginary number

Step-by-step explanation:

Answer:

0.168 ft aprox

Step-by-step explanation:

To solve this problem, we can use similar triangles and proportions. Let's denote the distance ahead of the car where the light beam hits the ground as "x" (in feet).

According to the given information, the light beam drops 2 inches for every 26 feet horizontally. We can set up the following proportion:

2 inches / 26 feet = x inches / x + 26 feet

To solve for x, we can cross-multiply and solve the resulting equation. Let's convert inches to feet to maintain consistent units:

2 inches = 2/12 feet = 1/6 feet

1/6 feet / 26 feet = x feet / x + 26 feet

1/6 * (x + 26) = 26 * x

x/6 + 26/6 = 26x

x + 26 = 156x

156x - x = 26

155x = 26

x = 26 / 155 ≈ 0.168 ft

Therefore, the headlights will hit the ground approximately 0.168 feet (or 2.016 inches) ahead of the car.

A) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%. b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

To solve this problem, we will use the properties of the normal distribution and z-scores. Given that the average completion time for the task is 10 minutes and the standard deviation is 3 minutes, we can proceed with the following calculations:

a) To find the percentage of nurses completing the task in less than 5 minutes, we need to calculate the z-score corresponding to a time of 5 minutes and then determine the area under the normal distribution curve to the left of that z-score.

The z-score formula is given by: z = (x - μ) / σ

where x is the time in question (5 minutes), μ is the mean (10 minutes), and σ is the standard deviation (3 minutes).

z = (5 - 10) / 3 = -5/3 ≈ -1.67

Using a standard normal distribution table or a calculator, we can find that the area to the left of -1.67 is approximately 0.0475 or 4.75%. Therefore, approximately 4.75% of nurses complete the task in less than 5 minutes.

b) To find the percentage of nurses requiring more than 10 minutes to complete the task, we calculate the z-score for a time of 10 minutes and find the area to the right of that z-score.

z = (10 - 10) / 3 = 0

The area to the right of z = 0 is 0.5 or 50%. Therefore, approximately 50% of nurses require more than 10 minutes to complete the task.

c) To find the probability that a nurse will take between 8 and 12 minutes to complete the task, we need to find the area under the curve between the z-scores for 8 and 12 minutes.

z1 = (8 - 10) / 3 = -2/3 ≈ -0.67

z2 = (12 - 10) / 3 = 2/3 ≈ 0.67

Using a standard normal distribution table or a calculator, we find the area to the left of z = -0.67 as approximately 0.2514, and the area to the left of z = 0.67 as approximately 0.7514. Therefore, the probability that a nurse will take between 8 and 12 minutes to complete the task is approximately 0.7514 - 0.2514 = 0.5 or 50%.

d) To find the task times that qualify staff nurses for additional training, we need to determine the z-score corresponding to the slowest 20% of completion times and then convert it back to the original time scale.

The z-score corresponding to the slowest 20% is found by locating the z-score that has an area of 0.2 to its left. Using a standard normal distribution table or a calculator, we find this z-score to be approximately -0.84.

Now, we can convert the z-score back to the original time scale:

z = (x - μ) / σ

-0.84 = (x - 10) / 3

Solving for x, we have:

-0.84 * 3 = x - 10

-2.52 = x - 10

x = 10 - 2.52

x ≈ 7.48

Therefore, the task times that qualify staff nurses for additional training are approximately greater than 7.48 minutes.

In summary:

a) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%.

b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

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Answer:

5

Step-by-step explanation:

Answer:

\( \frac{67}{30} \: \text{or} \:2 \frac{7}{30} \)

Step-by-step explanation:

5/6 ÷ 1/3 - 2/3 (2/5)

Hope it helps you! ＼(^ᴥ^)／

Answer:

There will be 132 seats in row 25

Step-by-step explanation:

1st term = 12

common difference = 5

f(x) = 12 + 5(x - 1)

f(25) = 12 + 5(25-1)

f(25) = 12 + 5(24)

f(25)= 12+120

f(25)=132

There will be 132 seats in row 25

The number of seats is 137 with the general equation \((12+5n)\) seats

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

Let the row number is \(n\)

The number of seats in the first row is 12

As per the plan, each row shall have 5 more seats.

So, in the first row seats=12

In the second row seats=\(12+5\)

In the third row seats=\(12+2\times5\)

\(n^{th}\)  row seats=\(12+5n\)

So, the number of seats in any row is \(12+5n\)

Where \(n\) is the row number

Now, for 25 rows, \(n=25\) then,

The number of seats is,

\(12+5\times25=137\)

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Answer:

A slope of the line over the interval of [-6, -1] is ⅕ as illustrated in the graph above

Problem 1

With simple interest, we take a percentage of the loan amount (or deposit depending how you frame things) to determine the interest paid or earned.

The simple interest formula is

i = P*r*t

Let's look at an example: You deposit $100 into an account earning 5% simple interest. You want to know how much interest you earn over 2 years.

i = P*r*t

i = 100*0.05*2

i = 10

You've earned $10 in simple interest. Notice how this is 10% of the original deposit ($100). You can think of the 5% interest rate doubling to 10% because we're working over a 2 year period.

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

Compound interest is where we can't take a simple percentage of the deposit. This is because we must use this formula

A = P*(1+r/n)^(n*t)

variables are:

An example: You deposit $100 at an interest rate of 5%. The interest is compounded quarterly (4 times a year). How much interest have you made in 2 years?

The input values will be

So,

A = P*(1+r/n)^(n*t)

A = 100*(1+0.05/4)^(4*2)

A = 110.448610118141

A = 110.45

i = interest

i = A - P

i = 110.45 - 100

i = 10.45

You've made $10.45 in interest over the two year period.

As you can see, we used an exponential function to determine compound interest. Whereas with simple interest, the function was linear. Exponential functions grow much faster compared to linear functions.

======================================================

Problem 2

Savings accounts offer higher interest rates, which encourages people to save their money (hence the name). Checking accounts on the other hand are used to write checks and are there for immediate withdrawals of cash. Checking accounts are also used for debit cards, such as for online shopping.

Both types of accounts are useful in their own different ways. Linking them together is handy to quickly move money without having to deal with tons of paperwork and/or lots of time spent.

======================================================

Problem 3

APR = annual percentage rate

APY = annual percentage yield

The APR value is often the stated item on a loan, since it is the smaller of the two values. When it comes to savings accounts in banks, they tend to state the APY value since it is larger.

Let's look at an example:

The APR is 5% and the money is compounded monthly (12 times a year). Compute the APY.

----------

Solution:

The formula we use is

y = (1+r/n)^n

where y is the APY and r is the APR

In this case we have

Giving us the following

y = (1+r/n)^n - 1

y = (1+0.05/12)^12 - 1

y = 1.05116189788173 - 1

y = 0.0512

Then multiply that by 100, aka move the decimal point two spots to the right, to arrive at an APY of approximately 5.12%

This example demonstrates how compound interest slightly bumps up the amount of return. We've gone from 5.00% to 5.12%

This slight increase is because the money is compounded 12 times a year. Each time we compound, we're adding to the pile ever so slightly. There's a limit to this process (see the continuous compounding interest formula); i.e. we can't grow the APY forever.

If we were using simple interest, then the APY formula shown above would not apply. For simple interest situations, the APY and APR are the same value.

Answer:

9

Step-by-step explanation:

5x-3= 2x+24

5x=2x+27

3x=27

X=9

Answer: A.  9

Step-by-step explanation:

The diagonal is bisected by the other diagonal.  So the 2 parts of the diagonal are equal

5x - 3 =  2x + 24                 >Bring like terms to 1 side

3x = 27                                >Divide both sides by 3

x = 9

Answer:

i can help with the problem