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3 years ago

Given that f(x) = 2x + 1 and g(x) = the quantity of 3x minus 1, divided by 2, solve for g(f(3)).

Mathematics

2 answers:

jarptica [38.1K]3 years ago

8 0

10 is the answer to your question.

kvv77 [185]3 years ago

4 0

In order to solve this problem you will have to find function notation.

Step 1: Find the function notation of f(3).
Make sure to sub everything that has a x in for 3. f(3)=2(3)+1

Step 2: Solve for this function notation.
f(3)=6+1
f(3)=7 *this is the function notation of f(3)

Step 3: Now you will need to sub in the answer for f(3) in for g(f(3)).
You'll have; g(7)

Step 4: Now you need to solve this function notation using 7 to sub in for anything that has a (x).
g(7)=(3x-1)÷2

Step 5: Now just the problem above.
*Make sure to follow rules of PEMDAS
g(7)=(3×7-1)÷2
g(7)=(21-1)÷2
g(7)=(20)÷2
g(7)=20÷2
g(7)= 10

Step 6: **REMEMBER TO PUT YOUR ANSWER BACK INTO THE FUNCTION NOTATION OF WHAT THEY ARE LOOKING FOR**
In this case we are looking for g(f(3))
So, g(f(3))= 10

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The mean is the average value of a given set of numbers, and the median is the number in the middle of a set of numbers arranged in increasing order

The correct values as response to the questions are;

The minimum possible top score is 21

The maximum possible top score is 32

The minimum of the possible standard deviation is approximately 1.26

The maximum of the possible standard deviation is approximately 11.7

The reason the above values are correct are as follows:

The given parameters are;

The number of students that take the test, n = 5

The amount of points for each problem = 1 point

The median score = 9

The mean Score = 10

Required:

The minimum possible score;

The maximum possible top score

The minimum of the possible standard deviations

The maximum of the possible standard deviations

Solution:

Given that there is a score (the median) which is 9, we have;

The scores obtainable in the test is Scores ≥ 9

Therefore, for a score of 10, we have;

The minimum total points obtainable = Mean × Number of students

Therefore;

Total minimum total points obtainable by the 5 students = 5 × 10 = 50

The minimum possible top score

By arrangement, with the median at the middle, the minimum possible top score is given as follows;

0, 0, 9, 20, 21

Therefore, the minimum possible top score is 21

The maximum possible top score

The maximum possible top score is similarly given by arrangement of the numbers as follows'

0, 0, 9, 9, 32

The maximum possible top score is 32

The minimum standard deviation

By arrangement and selection, the minimum standard deviation is given as follows;

The minimum of the possible standard deviations of (9, 9, 9, 11, 12) ≈ 1.26

The maximum of the possible standard deviation

The maximum of the possible standard deviation is given as follows;

The maximum of the possible standard deviation of (0, 0, 9, 9, 32) ≈ 11.7

Learn more about mean and median here:

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2 years ago

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TiliK225 [7]

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2 years ago

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a yard width is 2 less than it's length. If the perimeter of the yard is 20 feet determine the length and the width of the yard

Arte-miy333 [17]

Answer:

The length is 6 feet and the width is 4 feet

Step-by-step explanation:

Let x represent the length of the yard

The width can be represented by x - 2, since it is 2 less than the length.

Use the perimeter formula, P = 2l + 2w, where l is the length and w is width

Plug in the expressions and perimeter:

20 = 2x + 2(x - 2)

Solve for x:

20 = 2x + 2x - 4

20 = 4x - 4

24 = 4x

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So, the length is 6. Plug this into x - 2 to find the width

x - 2

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So, the length is 6 feet and the width is 4 feet

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2 years ago

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Anettt [7]

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4 0

3 years ago

HELPPPP- you just got your driver's license. Your parents buy you a car and agree to let you pay them back over a period of 70 m

Nitella [24]

Using the monthly payments formula, it is found that a car with a value of at most $25,293.

<h3>What is the monthly payment formula?</h3>

It is given by:

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

In which:

P is the initial amount.

r is the interest rate.

n is the number of payments.

In this problem, we have that the parameters are given as follows:

A = 400, n = 70, r = 0.035.

Hence:

r/12 = 0.035/12 = 0.002917.

Then we have to solve for P to find the maximum value of the car.

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

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$P = \frac{400[(1.002917)^{70}-1]}{0.002917(1.002917)^{70}}$

P = $25,293.

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1 year ago