If f(x)=3x^2 +2 and g(x)= x^2 + 2x, what is f(g(x)) when x=2?

Answer:

Step-by-step explanation:

The Pythagorean theorem states that the square of a right-angled triangle's hypotenuse is equal to the sum of the squares of its other two sides.

You can demonstrate the congruence of two right triangles using the Hypotenuse-Leg (HL) Triangle Congruence Theorem, which is a particular instance. A right triangle is congruent with another right triangle if its hypotenuse and one of its legs are congruent with its hypotenuse and one of its legs.

The hypotenuse (longest side) square in a right-angled triangle is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem (base and perpendicular).

The right triangles are said to be congruent if their respective hypotenuses and legs are congruent with one another, according to the hypotenuse-leg (HL) theorem. By the HL theorem, these triangles are congruent.

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Answer:

probably 30 degrees sorry if im wrong

The composite functions for this problem are given as follows:

a) (f ∘ g)(x) = 4x² + 24x + 32.

b) (g ∘ f)(x) = 2x² - 8x

The composite function of f(x) and g(x) is defined by the function presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the function for item a is given as follows:

(f ∘ g)(x) = f(2x + 8)

(f ∘ g)(x) = (2x + 8)² - 4(2x + 8)

(f ∘ g)(x) = 4x² + 32x + 64 - 8x - 32

(f ∘ g)(x) = 4x² + 24x + 32.

For item b, the function is given as follows:

(g ∘ f)(x) = g(x² - 4x)

(g ∘ f)(x) = 2(x² - 4x)

(g ∘ f)(x) = 2x² - 8x

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Answer: D. The distance from A to C

Step-by-step explanation:

This formula can be used to find the distance between two points on a three-dimensional coordinate system:

D(x, y, z) = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2} }\)

If you apply the formula for all options, you will find the distance from A to C is equal to \(\sqrt{5}\). The other distances are:

A. \(\sqrt{17}\)

B. \(\sqrt{45}\)

C. \(\sqrt{44}\)

So, the answer is D.

In this problem

we have that

sin(theta) is positive and cos(theta) is negative

That means

the angle theta lies on the II quadrant

Remember that

Find out the value of cos(theta)

substitute the given value

Find out the value of cot(theta)

substitute given values

simplify

Find out the angle theta

using a calculator

angle in II quadrant

The journal entry to record the replenishment of the petty cash fund shows a debit of $45 , $25 and $8 and a net credit of $78.

Replenishment of the Petty Cash Fund:

Petty cash refers to a small amount of fund that can be used for the day to day expenses for which disbursement of checks will not be suitable. As and when the petty cash balance is being used and reduced, the fund custodian requests and receives cash from the company's regular checking account, in order to maintain the same petty cash balance it initially had, which is nothing but the replenishment of the petty cash fund.

The journal entry to record the replenishment of the petty cash fund is made below:

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Complete question is given below :

On March 20, Harbor's petty cash fund of $100 is replenished when the fund contains $22 in cash and receipts for postage $45, supplies $25, and travel expense $8.

Prepare the journal entry to record the replenishment of the petty cash fund.

The Cash account is credited, Reflecting the decrease in the petty cash fund due to the various expenses incurred.

The expenses made from the Harbor's petty cash fund, we need to record the appropriate entries to reflect the decrease in cash for each expense category. Based on the given information, the expenses include $19 for postage, $40 for supplies, $26 for travel, and $15 for miscellaneous expenses.

1. Postage Expense:

To record the expense for postage, we will debit the Postage Expense account and credit the Cash account. Assuming the Postage Expense account has a normal debit balance:

  Postage Expense   $19

     Cash                         $19

2. Supplies Expense:

For supplies expenses, we will debit the Supplies Expense account and credit the Cash account:

  Supplies Expense   $40

     Cash                       $40

3. Travel Expense:

To account for the travel expenses, we will debit the Travel Expense account and credit the Cash account:

  Travel Expense   $26

     Cash                     $26

4. Miscellaneous Expense:

Lastly, for the miscellaneous expenses, we will debit the Miscellaneous Expense account and credit the Cash account:

  Miscellaneous Expense   $15

     Cash                                  $15

After recording these entries, the petty cash fund will have been reduced by the total expenses. It's important to note that the remaining balance of the petty cash fund should be adjusted accordingly.

the journal entries to account for the expenses from the Harbor's petty cash fund are as follows:

Postage Expense   $19

  Cash                         $19

Supplies Expense   $40

  Cash                       $40

Travel Expense   $26

  Cash                     $26

Miscellaneous Expense   $15

  Cash                                  $15

These entries ensure that the appropriate expense accounts are debited and the Cash account is credited, reflecting the decrease in the petty cash fund due to the various expenses incurred.

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Answer:

(x +5)/-16=-1 this is the answer

Answer:

\(\\(x- -1)^{2} + (y- -1)^{2} = 13\)

so, -1, -1 and 13

The probability that either event will occur is 0.33

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

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 8 + 7 + 30

Evaluate

Total = 45

So, we have

P(A) = 8/45

P(B) = 7/45

For either events, we have

P(A or B) = 8/45 + 7/45

P(A or B) = 15/45

Evaluate

P(A or B) = 0.33

Hence, the probability that either event will occur is 0.33

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Answer:

A

Step-by-step explanation:

For a right triangle

\(A=\frac{ab}{2} \\\frac{(10.4)(15.3)}{2} =79.56\)

This is the same as the other triangle because they are the same size because of congruency

Area of the rectangle

\(a^2+b^2=c^2\\\)

\(\sqrt{(10.4^2+15.3^2} =c\)

\(c= 18.5\)

18.5 x 7 = 129.5

Add them all up

129.5+79.56+79.56= 288.62

Answer:

I think it's figure b

Step-by-step explanation:

Answer:

Figure B

Step-by-step explanation:

The rest of the shapes are either reflected or rotated but, Figure B maintains the same direction that its facing as Figure 1.

Answer:

182 gallons of water

Answer:

X=58

Y=32

Step-by-step explanation:

Right angle is 90°

90-58=32

The one thats 58° is opposite on x so they are th same what means y is 32°

When writing a proof , by copying the “given” statement(s) from the original problem

Given data ,

A true assertion that is provided in the problem or is known to be true should be the first statement in a proof. The subsequent logical argument has this as its foundation.

We can provide the groundwork for the proof and proceed to the desired conclusion by duplicating the "given" statement(s) from the original problem.

Once the first statement is established, we can move on to writing additional statements that are each logically supported by the first statement.

The logical evolution of the preceding assertions demonstrates that the last statement should be the intended conclusion.

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Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.

Given that,

The equation f(x)=1.9(0.41)ˣ.

We have to state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x.

We know that,

In order to translate their graphs over the 2D coordinate plane, I will offer the vertex form of an exponential equation for both the growth and decay functions.

In the case of growth, f(x) = a(1+r\()^{x-h}\)+k, where b = 1+r

Decay is defined as f(x)=a(1-r)(x-h\()^{x-h}\)+k, where b=1-r.

Consider the function  f(x)=1.9(0.41)ˣ.

We write as

f(x)=1.9(1-0.59)ˣ

So, initial value C is 1.9

Decay factor =0.41

Growth factor = 0.59

Therefore, Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.

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Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).

Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

Null hypothesis:\(\mu \leq 6\)      

Alternative hypothesis:\(\mu > 6\)      

The statistic is given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)      

Replacing the info we got:

\(t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335\)

\(p_v =P(t_{25}>1.335)=0.097\)  

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes

Step-by-step explanation:

Information given

\(\bar X=370.69/60 =6.178\) represent the sample mean

\(s=24.36/36=0.68\) represent the standard deviation for the sample    

\(n=26\) sample size      

\(\mu_o =6\) represent the value to verify

\(\alpha=0.05\) represent the significance level

t would represent the statistic

\(p_v\) represent the p value

System of hypothesis

We want to test if the true mean is at least 6 minutes, the system of hypothesis would be:      

Null hypothesis:\(\mu \leq 6\)      

Alternative hypothesis:\(\mu > 6\)      

The statistic is given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)      

Replacing the info we got:

\(t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335\)      

The degrees of freedom are:

\(df=n-1=26-1=25\)  

The p value would be given by:

\(p_v =P(t_{25}>1.335)=0.097\)  

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes.

Answer:

120

Step-by-step explanation:

Answer:

1:4

Step-by-step explanation:

Answer:

1:4

Step-by-step explanation:

15 is the common factor so divide both numbers by 15 and that's what you get

Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

Answer:

12 numbers away

(sorry if I write this but the answer requires 20 characters)

Answer:

18

Step-by-step explanation:

In the linear regression equation y=a+bx, slope coefficient b represents average unit increases in y variable due to unit increase in x variable.

In the given equation ŷ = 84 + 18x, b=18 represents average unit increases in gas used due to unit increase in degree day.

Hence,on average,  gas used increase by 18 for each additional degree-day.

if we will divide 137 with 100 and then multiply it with 680 you will gett your answer

the answer is 931.6

Answer:

931.6

Step-by-step explanation:

We need to change the percent to decimal form.

137%  = 1.37

Multiply this by 680.

1.37 * 680

931.6

Answer:

1. 2 x 2 x 2=8

2.3x3=9

3. I'm uncertain about this one but i think maybe 12x2=24 please recheck it

Step-by-step explanation:

considering u call it easy imma assume u know how to do it

The marked price of the ring given the cost as 8740 inclusive of 15% tax and discount of 5% is $7,283.3.

8740 = x + (15% of x) + (5% of x)

8740 = x + (0.15x) + (0.05x)

8740 = x + 0.15x + 0.05x

8740 = 1.20x

x = 8740 / 1.20

x = 7283.33333333333

Approximately,

x = $7,283.3

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