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The composition of the functions f(x) and g(x) gives the equation:

\(f(g(x)) = 4x^2 + 6x - 3\)

Here we want to get the composition of the two functions:

\(f(x) = x^2 + 3x - 3\\\\g(x) = 2x\)

f(x) is a quadratic and g(x) is a linear equation.

Now we want to get the composition:

\(f(g(x))\)

This means that we need to evaluate function f(x) in g(x), so we can replace all the "x" in the function f(x) by the notation "g(x)"

\(f(g(x)) = g(x)^2 + 3*g(x) - 3\)

Now we replace all the "g(x)" by the actual function g(x) = 2x, we wll get:

\(f(g(x)) = g(x)^2 + 3*g(x) - 3 = (2x)^2 + 3*(2x) - 3\)

finally, we can simplify this to get the composition, which is a quadratic function just like f(x).

\(f(g(x)) = 4x^2 + 6x - 3\)

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Answer:

B

Step-by-step explanation:

because 60÷3 is 20 which gives you your unit rate

Answer:

\(B . \: 20 \: per \: hour\)

Step-by-step explanation:

\(regards \\

♨Rage♨\)

Answer:

K = 75000 Joules

Step-by-step explanation:

K = 1/2mv^2

K = 1/2(1500)(10^2)

K = 1/2(150000)

K = 75000 Joules

Answer:

The total cost of adding wallpaper to the room is 487.20

Answer:

Step-by-step explanation:

Katie gets 32/8 = 4 lots of sweets

Pavel gets 4 lots x 3 = 12 sweets

The total volume of the composite figure is 123cm³

First let's do the prism, the volume is the product of the 3 dimensions, so we will get:

v = 12cm*1cm*5cm = 60cm³

Now let's do the cone, the formula for the volume is given, so we can just replace the numbers that we know, notice that the diameter is given and we need the radius which is half of that, so:

r = 6cm/2 = 3cm

Then the volume is:

V = 3*(3cm)²*7cm/3 = 63cm²

So the total volume is 63cm² + 60cm³ = 123cm³

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Answer:

45 is 100% of 45

Step-by-step explanation:

Answer: 45 is 100% of 45

Step-by-step explanation:

Answer:

250.50 - 35m = 300 - 45.25m

Step-by-step explanation:

Given :

International Business School :

Initial = 250.50

Spending per month = $35

Future Agricultural leaders club :

Initial = $300

Spending per month = 45.25

The number of months, m itvwi take for them to have the same amount of money :

Total spending after m months for both :

Initial - spending per month * number of months

International Business School :

250.50 - 35m - - - (1)

Future Agricultural Leaders Club :

300 - 45.25m - - - - - 2)

Equate both : (1) and (2)

250.50 - 35m = 300 - 45.25m

Answer:

250.50 - 35m = 300 - 45.25m

( option B )

O centroid

Step-by-step explanation:

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

To find the 3rd term of the sequence described by the expression 11 - n^2, we substitute n = 3 into the expression.

By replacing n with 3, we have: 11 - (3^2) = 11 - 9 = 2.

Thus, the 3rd term of the sequence is 2.

This means that when the sequence follows the pattern described by the given expression, the value of the 3rd term is 2.

The sequence itself is generated by substituting different values of n into the expression 11 - n^2. For example, if we were to find the 4th term, we would substitute n = 4 into the expression and evaluate it as 11 - (4^2) = 11 - 16 = -5.

In general, as we increase the value of n, the terms of the sequence decrease since the square of n becomes larger. The given expression provides a rule for generating the terms of the sequence based on the value of n.

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Answer:

it is a right angle triangle therefore

h²=b²+p²

8²=4²+p²

64-16=p²

48=p²

under root 48 =p

6.928

so 6.93 is the answer

Well the actual answer should be second one. the res don't add up to the right coordinates or are in the wrong order.

Answer:

Dena's answer

14ft^2

Step-by-step explanation:

Her answer is correct because area of triangle is base times height divided by two. Base is 7 and height is 4

From there, you can find the area which is 14.

hope this is correct

Answer:

r≈24.99

Step-by-step explanation:

Just use the equation and plug in the area and then divide by 4. and work backwordsfrom there.  

A=4πr^2

Step-by-step explanation:

theres your answer please mark s brainliest

Researchers try to gain insight into the characteristics of a sample population by examining a sample of the population.

A sample is a subset of individuals or units taken from a larger population. Researchers use sampling methods to select a representative group of individuals from the population they are interested in studying. By studying the sample, researchers can make inferences and draw conclusions about the characteristics, behaviors, or trends that may exist within the entire population.

The goal of sampling is to obtain a sample that accurately represents the population in terms of its relevant characteristics. Researchers carefully select their samples to ensure that they are representative and minimize bias. This allows them to generalize the findings from the sample to the larger population with a certain level of confidence.

By examining a sample, researchers can collect data, analyze patterns, and draw conclusions about the population as a whole. This approach is more feasible and practical than attempting to study the entire population, especially when the population is large or geographically dispersed.

Therefore, researchers use samples to gain insight into the characteristics of a population, making option d. "Sample" the correct answer.

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Answer:

36.

Step-by-step explanation:

Counting the squares, the length of the vertical side = 16.

The other 2 sides are of equal length and can be found by Pythagoras theorem:

The vertex of the triangle is 6 units from the longest side and the line of 6 units meets the longest side at its center ( 8 units from its ends),

so l^2 = 6^2 + 8^2

l^2 = 100

l = 10

So the perimeter is 16 + 10 + 10= 36.

By using the  unitary method in linear equation, the answer is 925.

We have a factory that makes 400 refrigerators every day and makes 125 more stoves per day than refrigerators is as follows:

Let's use the unitary method in linear equation to solve this problem. We can use the following equation to find x, the total number of refrigerators and stoves the factory makes in one day:

X = 400 (number of refrigerators) + (400 + 125) (number of stoves)

X = 400 + 525

X = 925

Therefore, the factory makes 925 refrigerators and stoves every day.

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Step-by-step explanation:

hope this will help you!

Answer:a=112°

b=112°

y=68°

x=78°

Step-by-step explanation:

Answer:

He ate 1 pound

Step-by-step explanation:

3 10/60. 6/60. then minus them so he ate one pound

6.5 x \(10^{11}\)

Answer:

6.5 × 10^-11

make sure its -11 because its a really small decimal. if it wasn't -11 i'd be huge.

Answer:

50.35

Step-by-step explanation:

Answer50.35

Step-by-step explanation:

i just copied other dude

ANSWER: the people residing locally that are attending collage is

70% and on the bottom it is 40% and the people entering the work force it is 30%

Step-by-step explanation:

GIVE BRAINLIEST

The percentage of all graduates who plan to enter the workforce and reside locally is 15%.

According to the tree diagram, we need to calculate the percentage of high school graduates who plan to enter the workforce and reside locally. To calculate this, we need to follow the branches in the tree diagram. Let's start from the top:

1. The first branch shows that 30% of high school graduates plan to enter the workforce.

2. From those 30%, 50% plan to reside locally.

3. To calculate the percentage of all graduates who plan to enter the workforce and reside locally, we need to multiply the percentages from steps 1 and 2 together: 30% * 50% = 0.30 * 0.50 = 0.15 or 15%.

Therefore, the percentage of all graduates who plan to enter the workforce and reside locally is 15%.

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Answer:

I have attached my answer below.

Step-by-step explanation:

Not sure if its correct or not. Hope this helps!!

Answer:

the slope of the line is

Answer:

1/4

Step-by-step explanation:

From 1 to 3 is two that is the ride of the slope and the run is from 1 to 9 witch is 8 and that means 2/8 but you can minimize the fraction to 1/4

Step-by-step explanation:

5x + 2y = 10

2x + y = 2, 4x + 2y = 4.

Therefore (5x + 2y) - (4x + 2y) = 10 - 4, x = 6.

=> 2(6) + y = 2, y = -10.

The solutions are x = 6 and y = -10.

Answer:

              There are three terms in the given expression.

Step-by-step explanation:

              First, a term is a single individual value on which mathematical operations occur in an algebraic expression. Essentially, terms are every part of an expression that is separated by any mathematical operation, such as PEMDAS. In the expression \(\frac{v}{3} -4*2\), \(\frac{v}{3}\), -4, and 2 are all terms. Therefore, there are three terms in the given equation.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

16C

Step-by-step explanation:

-4+16=12

-4+4=0 then u add 12 making it -4+16=12

The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.

The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.

Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.

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The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

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

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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