Using composition of functions, determine if the two functions are inverses
of each other.
F(x)=√x-6
G(x) = (x+6)²
OA. Yes, but only within the domain x ≥ 0.
OB. No, because the composition does not result in an answer of x.
OC. Yes, because F(x) is equal to - G(x).
OD. No, because the functions contain different operations.

Answer:

33 , 39

Step-by-step explanation:

given

9 , 15 , 21 , 27

there is a common difference between consecutive terms, that is

15 - 9 = 21 - 15 = 27 - 21 = 6

to obtain terms in the sequence add 6 to the preceding term

27 + 6 = 33

33 + 6 = 39

the next two terms are 33 and 39

Answer:

242 days

Step-by-step explanation:

1081-597=484

it is increasing by 2wins every day so 484/2=242 days

Answer:

103

Step-by-step explanation:

14 x 8 =112 - 9 =103

Answer:

The Correct Answer is 103 slices.

Step-by-step explanation:

14 x 8 = 112

112 - 9 = 103

i dont know how he could eat 9 slices at once, but so be it :shrug: lol

Hope This Helps!

The greatest weight that can be loaded into the container is 24000 kilograms.

Let y be the weight of the container

Already loaded 11600 Kg in the container.

It can be loaded with several 50kg crates.

The equation to find the x number of 50 kg crates is

Hence the number of 50-

it would still be 75, because translations preserve angle measures

Answer$ 2.73 per gallon

Step-by-step explanation:

Answer:7 quarters and 6 dimes

Step-by-step explanation:

The answer is the A because they are similar and congruent

Answer:

A

Step-by-step explanation:

Answer:

-5/4

Step-by-step explanation:

Let \((x_1,y_1)=(-4,4)\) and \((x_2,y_2)=(0,-1)\). The slope of the line would be:

\(\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}\)

Answer: -5/4

Step-by-step explanation:

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

Slope = (y2 - y1)/(x2 - x1)

Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:

slope = (4 - (-1))/(-4 - 0)

slope = (4 + 1)/(-4)

slope = 5/-4

Therefore, the slope between the two points is -5/4.

The equation of the normal plane is 4y = 4π, or equivalently, y = π.

The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.

To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:

Step 1: Find the first and second derivatives of the curve with respect to t.

x' = 2cos2t

y' = 1

z' = -2sin2t

x'' = -4sin2t

y'' = 0

z'' = -4cos2t

Step 2: Evaluate the derivatives at t = π.

x'(π) = 2cos2π = 2

y'(π) = 1

z'(π) = -2sin2π = 0

x''(π) = -4sin2π = 0

y''(π) = 0

z''(π) = -4cos2π = -4

So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.

Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.

The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:

n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩

Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.

The equation of the osculating plane is given by:

4(x - 0) + 0(y - π) + 0(z - 1) = 0

Simplifying, we get:

4x - 4 = 0

So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.

Step 5: Use the curvature vector to find the normal vector of the normal plane.

The normal vector of the normal plane is given by the curvature vector:

n' = κv = ⟨0, 4, 0⟩

Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.

The equation of the normal plane is given by:

0(x - 0) + 4(y - π) + 0(z - 1) = 0

Simplifying, we get:

4y - 4π = 0

So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.

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Answer:

64

Step-by-step explanation:

Multiplication

8 * 4 = 32

32* 2 = 64

Answer:

OB. g(x) = 31x1

C. g(x) = 13x1

Step-by-step explanation:

Answer:

Kitchen

25.2

17.4

22.8

21.9

19.7

​

amp;Master Bedroom

amp;18

amp;22.9

amp;26.4

amp;24.8

amp;26.9

​

amp;Kitchen

amp;23

amp;19.7

amp;16.9

amp;21.8

amp;23.6

​

amp;Master Bedroom

amp;17.8

amp;24.6

amp;21

​

Step-by-step explanation:

Step 1: Write out the formula for finding the area of traingle given the three coordinates

Step 2: Write out the given parameters

Step 3: Substitute the parameters into the formula

Hence, the area is 14square unit

Answer: Just look it up on goo gle

Step-by-step explanation:

The rate per annum compound interest is approximately 11.5%.

To find the rate per annum compound interest, we can use the formula for compound interest:

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

Where:

A = the final amount (N5353 in this case)

P = the principal amount (N4000 in this case)

r = the annual interest rate (what we want to find)

n = the number of times interest is compounded per year (assuming once per year)

t = the number of years (5 years in this case)

Now, we can plug in the values:

\(N5353 = N4000(1 + r/1)^{1*5}\)

Divide both sides by N4000:

\(1.33825 = (1 + r)^5\)

Now, isolate (1 + r) by taking the fifth root of both sides:

\(1 + r = (1.33825)^{1/3}\\1 + r \approx 1.115\)

Now, subtract 1 from both sides to find the interest rate (r):

r ≈ 1.115 - 1

r ≈ 0.115

Finally, convert the interest rate to a percentage:

r ≈ 0.115 * 100

r ≈ 11.5%

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Answer: 207

Step-by-step explanation:

Let's start by converting 4 3/5 to an improper fraction. We do this by multiplying 4 * 5 and adding it to 3. This full equation is (4 * 5) + 3 = 23. We then have 23/5. We multiplying this by 45 to get our answer. This is done by multiplying 23 * 45 and then dividing that by 5. This full equation is (23 * 45) / 5 = 207. Therefore, our answer is 207.

The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

\(y = 20000(0.95)^5\)

Calculating the expression, we find:

\(y ≈ 20000(0.774)\)

Simplifying further, we get:

\(y ≈ 15480\)

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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In hypothesis testing, null hypothesis (H0) is a claim that the person conducting the research wants to test while an alternative hypothesis (H1) is a contradiction of the null hypothesis.

There are two types of tests in hypothesis testing is known.

One tailed test: In first tailed test, a claim that a parameter is greater than/ less than a value is being tested.

mean > value or mean < value.

Second tailed test: In a two tailed test, a claim that a value is equal to a value is tested,

mean = value.

Since we can see that Colleen is testing the claim that the average score of her class is the same as others against that it is different from others.

Hence, the null hypothesis is H0: mean = 514

and the alternative hypothesis is H1: mean ≠ 514

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The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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The number of pork sliders sold is given as follows:

24 pork sliders.

The number of pork sliders sold is obtained applying the proportions in the context of the problem.

The total number of pork sliders is given as follows:

120 pork sliders.

The percentage of pork sliders sold is given as follows:

20%. (proportion of 0.2).

Hence the amount sold is given as follows:

0.2 x 120 = 24 pork sliders.

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Answer:

2000

Step-by-step explanation:

1 dm =1000

2dm =?

2dm x 1000

1dm

2000

Answer:

1)   A - B = {2, 4, 6}

2)   B - A = {9}

3)   (A ∪ B) - C​ = {1, 3, 5, 7, 9}

Step-by-step explanation:

Set Notation

\(\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}\)

Given sets:

Question 1

\(\begin{aligned}\sf A-B & =\sf \{ 1, 2, 3, 4, 5, 6, 7 \} - \{1, 3, 5, 7, 9 \}\\& =\sf \{ 2, 4, 6 \}\end{aligned}\)

Question 2

\(\begin{aligned}\sf B-A & =\sf \{1, 3, 5, 7, 9 \} - \{ 1, 2, 3, 4, 5, 6, 7 \}\\& =\sf \{9 \}\end{aligned}\)

Question 3

\(\begin{aligned}\sf (A \cup B)-C & =\sf \left(\{ 1, 2, 3, 4, 5, 6, 7 \} \cup \{1, 3, 5, 7, 9 \} \right) - \{0, 2, 4, 6, 10 \}\\& =\sf \{ 1, 2, 3, 4, 5, 6, 7, 9 \} - \{0, 2, 4, 6, 10 \}\\& = \sf \{ 1, 3, 5, 7, 9 \}\end{aligned}\)

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Answer:

Step-by-step explanation:

Given that;

the following procedure for accomplishing our task are:

1. Flip the coin.

2. Flip the coin again.

From here will know that the coin is first flipped twice

3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails

But if the outcomes of the two flip are different i.e they did not land on both heads or both did not land on tails , then we will consider such an outcome.

Let the probability of head = p

so P(head) = p

the probability of tail be = (1 - p)

This kind of probability follows a conditional distribution and the probability  of getting heads is :

\(P( \{Tails, Heads\})|\{Tails, Heads,( Heads ,Tails)\})\)

\(= \dfrac{P( \{Tails, Heads\}) \cap \{Tails, Heads,( Heads ,Tails)\})}{ {P( \{Tails, Heads,( Heads ,Tails)\}}}\)

\(= \dfrac{P( \{Tails, Heads\}) }{ {P( \{Tails, Heads,( Heads ,Tails)\}}}\)

\(= \dfrac{P( \{Tails, Heads\}) } { {P( Tails, Heads) +P( Heads ,Tails)}}\)

\(=\dfrac{(1-p)*p}{(1-p)*p+p*(1-p)}\)

\(=\dfrac{(1-p)*p}{2(1-p)*p}\)

\(=\dfrac{1}{2}\)

Thus; the probability of getting heads is \(\dfrac{1}{2}\) which typically implies that the coin is fair

(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?

For a fair coin (0<p<1) , it's certain that both heads and tails at the end of the flip.

The procedure that is talked about in (b) illustrates that the procedure gives head if and only if the first flip comes out tail with probability 1 - p.

Likewise , the procedure gives tail if and and only if the first flip comes out head with probability of  p.

In essence, NO, procedure (b) does not give a fair coin flip outcome.

Answer:

The answer is 2

Step-by-step explanation:

You need to find out what is 56 divided by 6 which is 9. Then subtract, 9-7 which equals 2. So the answer is 2.

Using the vertex, it is found that the maximum height of the punt is of 27.7 feet.

The height of the punt, after x seconds, is given by:

\(f(x) = -0.0152x^2 + 1.25x + 2\)

It is a quadratic equation with coefficients \(a = -0.0152, b = 1.25, c = 2\).

The maximum value is the value of the function at the vertex, hence:

\(f_V = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}\)

Applying the coefficients:

\(f_V = -\frac{b^2 - 4ac}{4a} = -\frac{(1.25)^2 - 4(-0.0152)(2)}{4(-0.0152)} = 27.7\)

The maximum height of the punt is of 27.7 feet.

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Answer:

2.56

Step-by-step explanation:

8% of 32 is 2.56

Answer:

12.5 %

Step-by-step explanation:

There are 8 total sections, and only one of them is yellow. So if we spun it eight times, the possibility of getting yellow is one time. As a result, 1/8 is 12.5%