For f(x)=7x+1 and g(x)=5x, find the following composite functions and state the domain of each. (a) (f∘g)(x)= Select the correct choice below and fill in any answer boxes within your choice. The domain of f∘g is {x∣ The domain of f∘g is all real numbers. (b) (g∘f)(x)= Select the correct choice below and fill in any answer boxes within your choice. The domain of g∘f is {x∣ The domain of g∘f is all real numbers. (c) (f∘f)(x)= Select the correct choice below and fill in any answer boxes within your choice. The domain of f∘f is {x∣ The domain of f∘f is all real numbers. (d) (g∘g)(x)= Select the correct choice below and fill in any answer boxes within your choice. The domain of f∘f is {x∣ The domain of f∘f is all real numbers.

i think its C

:) :) :) :) :) :) :)

Answer:

option B: (x+1)^2+(y+3)^2=5.

Step-by-step explanation:

Answer:

\((x-1)^{2} + (y+3)^2 = 25\)

Step-by-step explanation:

\(-2x = -x^{2} - 6y -y^{2} + 15\\x^{2} - 2x + y^{2} + 6y = 15\\(x-1)^{2} - 1 + (y + 3)^{2} - 9 = 15\\(x-1)^{2} + (y+3)^2 = 25\)

Answer:

The opening price of the stock at the beginning of the day is $16

Step-by-step explanation:

Here, we are interested in calculating the opening price of the stock at the beginning of the day.

Let the opening price be $x

So the amount of gain will be $16.68 - $x

Now, this value correspond to 4.25% of the opening price of the stock which is $x

Hence, mathematically;

4.25% of $x = 16.68 - x

4.25/100 * x = 16.68-x

4.25x/100 = 16.68-x

Cross multiply;

4.25x = 100(16.68-x)

4.25x = 1668 - 100x

100x + 4.25x = 1668

104.25x = 1668

x = 1668/104.25

x = $16

Answer:

Step-by-step explanation:

x - 3y = -16

x + 2y = 4

-x + 3y = 16

x + 2y = 4

5y = 20

y = 4

x + 2(4) = 4

x + 8 = 4

x = -4

(-4, 4)

Exact Form:

9 /10

Decimal Form:

0.9

Hope this helps :)

Answer:

4/10 + 1/2 would be 9/10 because 1/2 of 10 is 5 so 5/10 +4/10 would equal 9/10 hope that helps :)

Step-by-step explanation:

The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

BMI stands for Body Mass Index.

It's a measure of body fat based on height and weight that applies to both adult men and women.

BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.

It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.

Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703

First, we need to convert the height into inches:5 feet 4 inches = 64 inches

Next, we plug the values into the formula and solve for the BMI:

BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464

Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

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The general solution for the given linear system of differential equations is x(t) = C₁ * e^(r₁t) + C₂ * e^(r₂t), where r₁ and r₂ are the roots of a quadratic equation. The general solution for y(t) is y(t) = (1/2) * e^t + C₃.

To solve the given linear system of differential equations using the elimination method, we first need to find the general solution for x(t).

The system of differential equations is given by:

1) 2x′ + y′ - 8x - 6y = e^(-t)

2) x′ + y′ + 6x + 4y = e

To eliminate y', we can subtract equation 1 from equation 2:

(x′ + y′ + 6x + 4y) - (2x′ + y′ - 8x - 6y) = e - e^(-t)

Simplify:

x′ - x - 2y = e - e^(-t)

Now, let's differentiate this equation with respect to t:

(d/dt)(x′ - x - 2y) = (d/dt)(e - e^(-t))

x′′ - x′ - 2y′ = 0 + e^(t)  [derivative of e^(-t) with respect to t is -e^(-t)]

Now, we have two equations:

1) 2x′ + y′ - 8x - 6y = e^(-t)

2) x′′ - x′ - 2y′ = e^t

To solve for y, we can isolate y′ from equation 2:

y′ = (x′′ - x′ - e^t)/(-2)

Now, we can substitute this expression for y′ into equation 1:

2x′ + [(x′′ - x′ - e^t)/(-2)] - 8x - 6y = e^(-t)

Simplify the equation:

4x′ + x′′ - x′ + 2e^t - 16x = -2e^(-t)

Now, we have a second-order linear homogeneous differential equation for x:

x′′ + 3x′ - 16x = -2e^(-t)

To solve this differential equation, we assume a solution of the form x(t) = e^(rt). Substituting this into the differential equation, we get:

(r^2 + 3r - 16)e^(rt) = -2e^(-t)

Divide by e^(rt) (assuming it is non-zero):

r^2 + 3r - 16 = -2e^(-t) / e^(rt)

r^2 + 3r - 16 = -2e^(-t - rt)

Now, we need to find the values of r that satisfy this equation. For this, we use the quadratic formula:

r = (-3 ± √(3^2 - 4(-16))) / 2

r = (-3 ± √(9 + 64)) / 2

r = (-3 ± √73) / 2

Now we have two possible values for r:

r₁ = (-3 + √73) / 2

r₂ = (-3 - √73) / 2

So, the general solution for x(t) is a linear combination of these two values:

x(t) = C₁ * e^(r₁t) + C₂ * e^(r₂t)

where C₁ and C₂ are constants.

Now, let's find y(t):

Using the equation y′ = (x′′ - x′ - e^t)/(-2) and substituting x(t) = C₁ * e^(r₁t) + C₂ * e^(r₂t):

y′ = [C₁ * r₁ * e^(r₁t

) + C₂ * r₂ * e^(r₂t) - (C₁ * r₁ * e^(r₁t) + C₂ * r₂ * e^(r₂t)) - e^t]/(-2)

y′ = [- e^t]/(-2)

Integrating y′ with respect to t:

y(t) = ∫(- e^t)/(-2) dt

     = (1/2) * e^t + C

Therefore, the general solution for y(t) is y(t) = (1/2) * e^t + C.

Now, let's find y(0):

y(0) = (1/2) * e^0 + C

     = (1/2) + C

Since C is an arbitrary constant, we can denote C as C₃, so y(0) = (1/2) + C₃.

In conclusion, the general solution for the given linear system of differential equations is:

x(t) = C₁ * e^(r₁t) + C₂ * e^(r₂t)

y(t) = (1/2) * e^t + C₃

where r₁ = (-3 + √73) / 2 and r₂ = (-3 - √73) / 2, and C₁, C₂, and C₃ are constants.

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Based on the given information, the value that could represent the probability Luke will catch 40 fish tomorrow is option D: 0.3.

Luke caught at least 2 fish every day last week, indicating that he consistently catches fish in the same location. However, the statement also mentions that Luke believes it is very unlikely for him to catch 40 fish in the same location tomorrow.

Since the probability of catching 40 fish is considered very unlikely, we can infer that the probability value should be relatively low. Among the given options, the value 0.3 (option D) best represents a low probability.

Option A (0.20) suggests a slightly higher probability, while option B (0.50) represents a probability that is not considered unlikely. Option C (0.95) indicates a high probability, which contradicts the statement that Luke believes it is very unlikely.

Therefore, option D (0.3) is the most suitable choice for representing the probability Luke will catch 40 fish tomorrow, considering the given information.

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Answer:

x=32

Step-by-step explanation:

Multiply both sides by 4.

(x/4)*(4) = (8)*(4)

On the interval [0, 2π], the minimum values of f(x) = 12cos^2(x) - 1 are -1, and the maximum values are 11.

To find the minimum and maximum values of the function f(x) = 12cos^2(x) - 1 on the interval [0, 2π], we need to determine the critical points and endpoints within that interval.

First, let's differentiate the function f(x) with respect to x to find the critical points. The derivative of f(x) is f'(x) = -24cos(x)sin(x).

Next, we set f'(x) equal to zero and solve for x:

-24cos(x)sin(x) = 0

This equation is satisfied when cos(x) = 0 or sin(x) = 0.

For cos(x) = 0, we have x = π/2 and x = 3π/2 as critical points.

For sin(x) = 0, we have x = 0 and x = π as critical points.

Now, we evaluate the function f(x) at these critical points and the endpoints of the interval [0, 2π]:

f(0) = 12cos^2(0) - 1 = 11

f(π/2) = 12cos^2(π/2) - 1 = -1

f(π) = 12cos^2(π) - 1 = 11

f(3π/2) = 12cos^2(3π/2) - 1 = -1

f(2π) = 12cos^2(2π) - 1 = 11

From the evaluations, we see that the minimum values of f(x) are -1, occurring at x = π/2 and x = 3π/2, while the maximum values are 11, occurring at x = 0, x = π, and x = 2π.

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The possible combination is 6552.

For each of the 4 numbers in the combination, there are 9 digits to pick from, making the following total number of possibilities entirely possible:

9 x 9 x 9 x 9 = 6561

The number of possibilities with identical values for all four digits must be subtracted, nevertheless.

There is only one combination for each of the nine possible ways to select the digit that will occur four times (1, 2, 3, 4, 5, 6, 7, 8, or 9).

Therefore, the total number of possible combinations with the given restriction is:

6561 - 9 = 6552.

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According to the most recent data from the U.S. Bureau of Labor Statistics (BLS), as of 2020, approximately 10.1% of Americans are self-employed.

This means that out of the total U.S. population, about 1 in 10 individuals are working for themselves rather than being employed by someone else.

It is important to note that the percentage of self-employed individuals can vary depending on various factors such as economic conditions, industry trends, and personal preferences. For example, certain industries like agriculture, construction, and professional services tend to have higher rates of self-employment compared to others.

Self-employment offers individuals the opportunity to have more control over their work, set their own schedules, and potentially earn higher incomes. However, it also comes with certain challenges such as the need to handle business-related tasks like marketing, finances, and customer acquisition.

Overall, the percentage of self-employed Americans provides insights into the dynamic nature of the job market and the various ways people choose to earn a living.

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The link utilization for the server links is 1 .

Given,

Servers are sending at maximum rate possible .

Now,

1. The maximum achievable end-end throughput is the capacity of the link with the minimum capacity i.e. Rc which is 300Mbps

2. The bottleneck link is the link with the smallest capacity between RS, RC, and R/4 i.e smallest between 400, 300 and 200 Mbps which is 200Mbps

3.The server's utilization = R(bottleneck)/ RS = 200/400 = 0.5

4.The client's utilization = R(bottleneck) / RC = 200/300 = 0.667

5.The shared link's utilization = R(bottleneck)/ (R / 4) = 200 / (800/4) = 1

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Answer:10

Step-by-step explanation:

Answer: The answer is 10.

Step-by-step explanation:

These steps will help you!

STEP 1: You need to multiply them and use the process of elimination.

8 is obiviously too little.

9 is still too little.

10 when you multiply it with $1.78, it's simple enough that it equals just right!

11 is too over.

STEP 2: Try multiplying 1.78 x 10.

         1.78

      x    10          

               0

+  1  7  8  0         _______always add the 0.

 $ 1 7 . 8  0

Mark also has $1.20 left to spare.

STEP 3: Declare the answer!

Mark can buy 10 stamp packets and have $1.20 left for himself.

Hope this helps!

We can prove that the given triangles GHL and KHJ are congruent using the ASA theorem. So, the second option is the correct answer.

We can say any two shapes are congruent if they have the same shape and size. For this, their sides and angles need to be mirror images of each other. We have four congruency theorems at hand here. These are side-side-side(SSS), angle-side-angle(ASA), side-angle-side(SAS), and angle-angle-side(AAS).

According to the ASA congruency theorem, one side and two angles of the triangles in question need to be similar. In the given image, we can see that two of the angles i.e., HGL and HKJ are congruent while GHL and KHJ are congruent. The sides GH and KH are also congruent. This makes the two triangles  △GHL ≅ △KHJ by the ASA theorem. So, the second option is the correct answer.

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The constants α, β, and k are all zero, and the solution to the IVP is y(t) = e²{-2t}, with t = -0.5ln(7)  the condition limt→∞y(t) = 7,t = -0.5ln(7)

Using the method of undetermined coefficients to find the general solution of the differential equation:

y'' + 3y' + 2y = 0

The characteristic equation is:

r²2 + 3r + 2 = 0

Factoring this equation, we get:

(r + 2)(r + 1) = 0

So the roots are r1 = -2 and r2 = -1. Therefore, the general solution is:

y(t) = c1e^{-2t} + c2e^{-t}

Next, we use the information that y1(t) = e²{-3t} is a solution to the differential equation. Substituting this into the general solution, we get:

e²{-3t} = c1e²{-2t} + c2e²{-t}

equation to solve for c1 and c2. Multiplying both sides by e^{2t}, we get:

e²{-t} = c1 + c2e²t

Taking the limit as t approaches infinity,  that c1 must be zero in order for the right-hand side to converge to a finite value. Therefore, we have:

c1 = 0

Substituting this into the previous equation,

e²{-t} = c2e²t

Dividing both sides by e²t,

e²{-2t} = c2

Therefore, we have:

c2 = e²{-2t}

Substituting these values into the general solution,

y(t) = c1e²{-2t} + c2e²{-t} = e²{-2t}

So α = β = 0 and k = -2. Finally,  the information that limt→∞y(t) = 7. Since y(t) = e²{-2t}, we have:

limt→∞e²{-2t} = 7

Taking the natural logarithm of both sides,

-2t = ln(7)Solving for t,

t = -0.5ln(7)

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The value the seasonal index (SI) for Q4 is 0.63.

To find the seasonal index (SI) for Q4, the first step is to calculate the average of the ratio-to-moving average for each quarter.

The formula for calculating seasonal index is as follows:

Seasonal Index = Average of Ratio-to-Moving Average for a Quarter / Average of Ratio-to-Moving Average for all Quarters

To find the seasonal index (SI) for Q4:

1: Calculate the average of the ratio-to-moving average for Q4.Q4 average = (0.65 + 0.65) / 2 = 0.65S

2: Calculate the average of the ratio-to-moving average for all quarters.All quarters average = (0.87 + 1.30 + 1.50 + 0.65 + 0.77 + 1.36 + 1.35 + 0.65) / 8 = 1.03

3: Calculate the seasonal index for Q4.Seasonal Index for Q4 = Q4 Average / All Quarters Average= 0.65 / 1.03 = 0.6311 (rounded to 2 decimal places)

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Answer:

I think 9 but dont quote me on it

Answer:

2

Step-by-step explanation:

in khan academy i put 9 because thats what the last person said here but it was wrong and the correct answer was 2 so its 2 for sure.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

Earnings:

January = $2350

February = january + $500

March = twice as much (february)

Step 02:

March's earnings:

February = $2350 + $500 = $2850

March = 2 * $2850 = $5700

The answer is:

She earned $5700 in March

Answer:

300

Step-by-step explanation:

a quarter is worth 25 cents then do 12 times 25 witch is 300

the number 15/3 belongs to the set of rational numbers and the set of real numbers.

First, remember that the set of the real numbers contains all the numbers, so 15/3 trivially belongs to the set of the real numbers.

But, we also can see that 15/3 is the quotient of two integer numbers, so it will also belong to the set of rational numbers. Where rational numbers are these numbers that can be written as the quotient of two integer numbers.

Concluding, the number 15/3 belongs to the set of rational numbers and the set of real numbers.

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Answer:

Step-by-step explanation:

Which statement best compares and contrasts the two formats?

The infographic shows the movement of water visually, while the text describes it.

The infographic would be less appealing to visual learners than the text.

It is impossible to understand the infographic without the text.

The text is more accurate than the infographic.

The probability that the second interview will be given to a woman, given that the first interview was given to another woman is 18/323 and the probability of all three interviews being given to men is: (9/22) * (8/21) * (7/20) = 21/770

To find the probability that the second interview will be given to a woman, given that the first interview was given to another woman, we can use conditional probability. Let’s call the event that the first interview was given to a woman A, and the event that the second interview is given to a woman B.

Then we want to find P(B|A), the probability of B given A. Using a tree diagram, we can see that the probability of A is:(13/22) * (12/21) = 4/11The probability of B given A is: (9/20) * (8/19) = 18/323. Therefore, the probability that the second interview will be given to a woman, given that the first interview was given to another woman, is 18/323.(b) To find the probability that all three interviews will be given to men, we can use the multiplication rule of probability.

The probability of selecting a man on the first interview is 9/22. The probability of selecting a man on the second interview, given that the first interview was given to a man, is 8/21. The probability of selecting a man on the third interview, given that the first two interviews were given to men, is 7/20. So, the probability of all three interviews being given to men is:(9/22) * (8/21) * (7/20) = 21/770

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Answer:

59,850

Step-by-step explanation:

cost: 57,000

what is 5%?

57,000 * .05 = 2,850

so, add the cost and tax together

57,000 + 2850 = 59,850

Answer:

they have less

Step-by-step explanation:

To find the value of f(6), we can use the information given about the function f(x) and its derivative f'(x).The value of f(6) is 44/3.

Given that f'(x) is continuous, we can apply the Fundamental Theorem of Calculus. According to the theorem:

∫[a to b] f '(x) dx = f(b) - f(a)

In this case, we are given that:

∫[1 to 6] 6 f '(x) dx = 16

We can simplify the integral:

6 ∫[1 to 6] f '(x) dx = 16

Since f'(x) is the derivative of f(x), the integral of 6 f '(x) dx is equal to 6 f(x). Therefore, we have:

6 f(6) - 6 f(1) = 16

Substituting the given value f(1) = 12:

6 f(6) - 6(12) = 16

6 f(6) - 72 = 16

Next, we isolate the term with f(6):

6 f(6) = 16 + 72

6 f(6) = 88

Finally, we solve for f(6) by dividing both sides by 6:

f(6) = 88 / 6

f(6) = 44/3

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The probability that the last two cards are queens, given that the first two are not queens, is 2/52.

The probability that the last two cards are queens, given that the first two are not queens, can be calculated as follows:

Let's assume that we have a standard deck of 52 playing cards. Then, the probability that the first two cards are not queens is (50/52) * (49/51) = 49/52.

Next, the probability that the last two cards are both queens is (2/50) * (1/49), since there are two queens left in the deck and one must be drawn first, followed by the other.

Finally, to find the probability of both events happening (the first two cards are not queens and the last two cards are), we multiply these probabilities:

P(not queens in first two and queens in last two) = (49/52) * (2/50) * (1/49) = 2/52.

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Step 1

Given;

Required; To find the price per ounce

Step 2

State the ratio that can be used to find the price per ounce of the candy bars.

Descriptive statistics are used to summarize data in a useful and informative manner.

This type of statistics provides meaningful information about the data set by organizing and presenting it in an easily understandable format. Descriptive statistics can be used to summarize the data in the form of tables, graphs, and charts. It can also be used to provide detailed information about the data set, such as the mean, median, mode, standard deviation, and range.

Descriptive statistics can also be used to make inferences about a population. This is done by comparing the data collected from a sample to the characteristics of the population. By understanding the characteristics of the population, researchers can make accurate predictions about the behavior of the population.

Descriptive statistics can also be used to determine if the data adequately represent the population. This involves analyzing the sample size, data accuracy, and the assumptions made about the population. If the data does not accurately represent the population, then researchers have to make changes to their data collection process or revise their assumptions about the population.

Finally, descriptive statistics can be used to gather or collect data. This involves designing surveys, experiments, and other data collection methods. By using descriptive statistics to collect data, researchers can ensure that the data is valid and reliable.

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Answer:

1.324

Step-by-step explanation:

Just divide 1324 by 1000 to get your conversion rate which is 1.324

If you check, to convert $1000 into Japanese Yen, by multiplying 1.324 with $1000, you'll get 1324 Yens