Function Composition:
Let the function [tex]f(x)= 3x + 2[/tex] and [tex]g(x) = \frac{x+3}{2x-10}[/tex] , determine:

Function Composition:Let The Function [tex]f(x)= 3x + 2[/tex] And [tex]g(x) = \frac{x+3}{2x-10}[/tex]

Answers

Answer 1

Answer:

Given

f(x) = 3x + 2g(x) = (x + 3) / (2x - 10)

#1

g · f(x) = g(f(x)) = (3x + 2 + 3)/ (2(3x + 2) - 10) = (3x + 5) / (6x - 6)

#2

f · g(x) = f(g(x)) = 3[(3x + 2) / (2x - 10)] + 2 = (9x + 6) / (2x - 10) + 2 = (9x + 6 + 4x - 20)/ (2x - 10) = (13x - 14) / (2x - 10)


Related Questions

2.247 divided into 7 equals what​

Answers

I think it’s 200.000

If a price decreases by 20%, I can calculate 20% of the price and subtract it
from the original price.
Or I can calculate in one step if I find ____ % of the original price

Answers

Answer:

To subtract any percentage from a number, simply multiply that number by the percentage you want to remain. In other words, multiply by 100 percent minus the percentage you want to subtract, in decimal form. To subtract 20 percent, multiply by 80 percent (0.8)

Step-by-step explanation:

In a certain section of Southern California, the distribution of monthly rent for a one-bedroom apartment has a mean of $2,275 and a standard deviation of $290. The distribution of the monthly rent does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month

Answers

Answer:

100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of $2,275 and a standard deviation of $290.

This means that [tex]\mu = 2275, \sigma = 290[/tex]

Sample of 65:

This means that [tex]n = 65, s = \frac{290}{\sqrt{65}}[/tex]

Finding the mean to be at least $2,095 per month

This is 1 subtracted by the p-value of Z when X = 2095. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2095 - 2275}{\frac{290}{\sqrt{65}}}[/tex]

[tex]Z = -5[/tex]

[tex]Z = -5[/tex] has a p-value of 0.

1 - 0 = 1

100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month

Solve for x . Round to the nearest tenth, if necessary.
D
x
C
1
B
30

Answers

Answer: 0.6

Step-by-step explanation:

Write the expression as a product of expressions.

(Factor this expression.)
`a^{3}b^{3}-a^{2}b^{2}-a^{2}c^{2}`

PLEASE HELP THIS IS URGENT

Answers

Answer:

[tex]a^2(ab^{3}-b^{2}-c^{2})[/tex]

Step-by-step explanation:

Given

[tex]a^{3}b^{3}-a^{2}b^{2}-a^{2}c^{2}[/tex]

Required

Factor

[tex]a^{3}b^{3}-a^{2}b^{2}-a^{2}c^{2}[/tex]

Factor out [tex]a^2[/tex]

[tex]a^2(ab^{3}-b^{2}-c^{2})[/tex]

The expression cannot be further factored


What is the solution set of the system of equations
x+y = 5 and y=x^2- 25?
1) {(0.5) (11,-6)}
2) {(5,0).(-6,11)
3) {(-5,0),(6,11)
4) {(-5,10).(6.-1)

Answers

You can basically just plug in the values. “2) {(5,0).(-6,11)}” is correct.

the minute hans on the clock shown below has a length of 7.5 cm. which of the following is closest to the distance that the tip of the hand travels as it moves from 12 to 4

Answers

Answer:

16

Step-by-step explanation:

The  following is closest to the distance that the tip of the hand travels as it moves from 12 to 4 should be considered as the 16 cm.

Calculation of the distance:

Since the minute hans on the clock shown below has a length of 7.5 cm

And, the tip of the hand travels as it moves from 12 to 4

So,

For full rotation it should be like [tex]2\pi[/tex] radians

Since angle turned by minute hand in 5 minutes so it should be like [tex]= 2\pi \div 12[/tex] radians

So

[tex]= 7.5 \times 2.094[/tex]

= 15.7 cm

Learn more about distance here: https://brainly.com/question/13448007

Help please!!!! will Brainly!!!

Answers

Answer:

true

Step-by-step explanation:

.................

True :) have a nice day! :) can u make me brainliest? Pls :)? Ty ✨

What is the value of the expression below?
16.86 x 103

Answers

Answer:

1736.58

Step-by-step explanation:

16.86 x 103 = 1736.58

Answer:

1736.58

Step-by-step explanation:

HELP ME PLEASEEEEEEEEEEEEEEEEEEE

Answers

True.


Hope it helps..............!

HELP 10 POINTS!!!
[ I will report any links or ridiculous answers ]

Answers

Im sorry i dont know the answer, but some good other apps to try are photo math and camera math. Sorry if this was not helpful

Interest charged when you miss a payment is called _____. A. accrued interest B. late interest C. past due interest D. late payment interest

Answers

Answer:

A

Step-by-step explanation:

Answer:

its d , Late payment interest

Step-by-step explanation:

AB has points A at (2,−5) and B at (5,−3).

AB iis reflected across the y-axis and then translated 3 units right. What are the coordinates of the endpoints of the image A′B'?

Answers

9514 1404 393

Answer:

A'(1, -5)B'(-2, -3)

Step-by-step explanation:

Reflection over the y-axis and translation 3 right is modeled by the transformation ...

  (x, y) ⇒ (-x +3, y)

Then the image end points are ...

  A(2, -5) ⇒ A'(-2+3, -5) = A'(1, -5)

  B(5, -3) ⇒ B'(-5+3, -3) = B'(-2, -3)

_____

In the attached figure, the reflection is shown as A'B' in light purple. The line after the final translation is shown as A"B" in blue.

When a water-cooled nuclear power plant is in operation, oxygen in the water is transmuted to nitrogen-17. After the reactor is shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level. Required:
a. Write a differential equation that expresses the rate of change in the radiation level in terms of the radiation level.
b. Suppose that when the reactor is first shut down, the radiation level is 3 × 1017 units. After 60 s the level has dropped to 5.6 × 1013 units. Write the particular equation.
c. Sketch the graph of radiation level versus time.
d. It is safe to enter the reactor compartment
when the radiation level has dropped to
7 × 10–3 units. Will it be safe to enter the reactor compartment 5 min after the reactor has been shut down? Justify your answer.

Answers

Answer:

hold on ill edit this once i get answer!! <3

Step-by-step explanation:

I do need to know NOTHING.

Answers

Answer:

Thats cool man.

Step-by-step explanation:

round 98,376 to the nearest thousand

Answers

Answer:

98000

Step-by-step explanation:

The sidewalk is 5 feet wide and the garden measures 20 feet across. Which measurement is closest to the area of the outer edge of the sidewalk?
A.
200 ft2

B.
400 ft2

C.
700 ft2

D.
1,000 ft2

Answers

Answer:

A (obviously)

Step-by-step explanation:

Info Given

Sidewalk is 5 ft. wideGarden is 20 ft. across

Pleaseeee helpppppppp!!!

Answers

Answer:

x = 46°

Step-by-step explanation:

Appling the principle of supplementary angle in Geomentry.

Supplementary angle: These are angles that sum up to 180°

From the diagram above, x and 134° are supplementry because they sum up to 180°.

Therefore,

134+x = 180 (Supplementary angle)

Solve for x

x = 180-134

x = 46°

Therefore, the value of the missing angle is 46°

Plz help find the rule 50 points

Answers

Answer:

1², 2²,3², 4², 5², 6², 7², 8², 9², 10², 11², 12², 13², 14², 15², 16², 17², 18², 19², 20²,........

Each number is multiplied by itself.

Degree and Radian Measures

Convert the given radian measure to a degree measure.
1.2 /pi (π)

a. -216°
b. 108°
c. 216°
d. -108°

Please select from the best choices provided

Answers

Answer:

C. 216°

Step-by-step explanation:

I calculated it logically

All of the following are equivalent except _____.
7.5:4.5
5 is to 3
15/5
45/27

Answers

Answer:

15/5

Step-by-step explanation:

because 7.5 ÷ 4.5 = 1.66667

5 ÷ 3 = 1.66667

and 45 ÷ 27 = 1.66667

but 15 ÷ 5 = 3 therefore it's the off one out.


Find the distance between A (-1, 9) and B (-4, 1). Leave your answer in exact radical form.

Answers

The distance between two points is given by the expression,

[tex]d = \sqrt{ {(y2 - y1)}^{2} + {(x2 - x1)}^{2} } [/tex]

Plugging in our values,

[tex]d \: = \sqrt{ {(1 - 9)}^{2} + {( - 4 - - 1)}^{2} } \\ d \: = \sqrt{ {( - 8)}^{2} + {( - 3)}^{2} } \\ d \: = \sqrt{64 + 9} \\ d = \sqrt{73} [/tex]

So, the distance between the points in it's exact radical form is

[tex] \sqrt{73} \: units[/tex]

Write an equation of a line with slope -4 and y- intercept of 0

Answers

Answer:

y=-4x

Step-by-step explanation:

For the following scenarios, determine whether or not they represent paired samples.
a. Test scores for students in a biology class taught by Professor Quick are being compared to test scores in a different section of the biology class taught by Professor Quack
b. Pulse rates for students at the beginning of class are being compared to pulse rates for the same students at the end of class.
c. The weights of 10-year-olds in 2009 are being compared to the weights of 10- year-olds in 1994.

Answers

Answer:

A = Not a paired sample

B = paired sample

C = Not a paired sample

Step-by-step explanation:

Paired samples also commonly referred to as dependent samples are often characterized by having to different data points which are taken at different times, location and so on. Such that each pair of data points or observation can be matched based on the basis of the subject or sample name usually for the sake of analysing if any statistical difference exists between the occurrence of each observation.

For the instances given above ;

a.) this isn't a paired sample, because Professor Quick and Professor Quacks students are different, hence each student has only one reading and as such a match of the two test scores cannot be made on the basis of student name or identity. Hence, it is not a paired sample

B.) This is a paired sample, two different readings are available for each students ; one at the beginning, the other at the end. Hence, it is a paired sample

C.) This is not a paired sample, because the subjects used to obtain the weight of 10 year old in 1994 aren't the same samples used in 2009

It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 45 people in the first group and this group will be administered the new drug. There are 75 people in the second group and this group will be administered a placebo. After one year, 12% of the first group has a second episode and 14% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is less than the true percentage of those in the second group who suffer a second episode.
A. [ z < -1.65, RHo].
B. [ z < -1.65 and z > 1.65, FRHo].
C. [z > 1.65, FRHo].
D. [z < -1.65 and z > 1.65, FRHo].
E. [z > -1.65 and z < 1.65, RHo].
F. None of the above.

Answers

Answer:

F. None of the above.

Step-by-step explanation:

Let the null and alternate hypothesis be

H0: p1 ≥ p2 against the claim Ha: p1 < p2

the significance level is 0.1

The critical region is z < z∝= 1.28

The test statistic is

Z= ( p^1-p^2)- (p1-p2)/√p1^q1^/n1 + p2^q2^/n2

Here n1= 45 ,   n2= 75

         p1= 0.12         p2= 0.14

         q1= 0.88        q2= 0.86

z= 0.12- 0.14/√0.12*0.88/45 +0.14*0.86/75

Z=  0.02/ √0.00235 + 0.00161

Z=  0.02/0.062891

z= 0.318

The calculated value of z= 0.318  lies in the critical region z < 1.28

therefore accept Ha.

All of the options are incorrect as the critical value for one tailed test for 0.1 is 1.28 .

What is the volume of this shape to the nearest tenth

Answers

The answer is 75.39822 or 75.4 rounding to the nearest tenth.

A family eats at a restaurant and leaves a tip that
increases the cost of the meal by 20%. The cost of the
meal before the tip is $41.27. How much is the cost of the
meal with the tip included?

Answers

Answer:

49.52

Step-by-step explanation:

Answer:

49.52 !!

Step-by-step explanation:

They’re correct ⬆️

twice y is at most 29

Answers

Answer:

2t=29

Step-by-step explanation:

the phrase is at most means we set the constant 29 less than or equal to the term 2t using the (<=) operator

Find the slope and the y-intercept of the line. 6x + 3y = -3 Write your answers in simplest form​

Answers

Answer:

[m] slope = -2

[b] y-intercept = -1 ; (0, -1)

[y = mx + b] slope-intercept = -2x – 1

Step-by-step explanation:

Given the algebraic equation 6x + 3y = -3 currently in standard form:

Ax + By = C →

By = C – Ax →

By = -Ax + C →

y = -Ax / B + C / B →

y = (-A / B)x + (C / B) →

y = mx + b →

m = -A / B. b = C / B.

6x + 3y = -3

↓ ↓ ↓

A = 6. B = 3. C = -3.

[Substitute]

m = -A / B. b = C / B

m = -(6) / (3). b = (-3) / (3)

↓ ↓

m = -2. b = -1.

↓. ↓

Slope = -2. y-intercept = -1.

_______________________

Slope is ∆y/∆x [change in y over the change in x] = y2 – y1 / x2 – x1.

The y-intercept is the point where x is 0.

The easiest way to determine this is to substitute 0 in for x in an equation and solve for y.

This means that the y intercept in coordinate form is (0, b).

Suppose that two investors A and B have exhibited the indifference probabilities as shown in table below. Indifference probability Investor A Investor B Net return (RM) -2000 0 0 - 1000 0.70 0.10 0 0.80 0.20 1000 0.85 0.30 2000 0.90 0.50 3000 0.95 0.60 4000 1.00 1.00 a) Determine the utility value (for each monetary value) for each investor and fill it in table above. b) Graph the utility functions for both investors and categorize each investor as either a risk- averse person or a risk seeker. c) Suppose that investor A has the chance to invest in one of two ventures. Venture I can produce a net return of RM3000 with probability 0.40 or a net loss of RM1000 with probability 0.60. Venture II can produce a net return of RM2000 with probability 0.60 and no return with probability 0.40. Based on utility function in (b), use the expected utility criterion to determine the venture investor A should select. What is the expected monetary value associated with the selected venture?

Answers

Answer:

Da Answer is Suppose that two investors A and B have exhibited the indifference probabilities as shown in table below. Indifference probability Investor A Investor B Net return (RM) -2000 0 0 - 1000 0.70 0.10 0 0.80 0.20 1000 0.85 0.30 2000 0.90 0.50 3000 0.95 0.60 4000 1.00 1.00 a) Determine the utility value (for each monetary value) for each investor and fill it in table above. b) Graph the utility functions for both investors and categorize each investor as either a risk- averse person or a risk seeker. c) Suppose that investor A has the chance to invest in one of two ventures. Venture I can produce a net return of RM3000 with probability 0.40 or a net loss of RM1000 with probability 0.60. Venture II can produce a net return of RM2000 with probability 0.60 and no return with probability 0.40. Based on utility function in (b), use the expected utility criterion to determine the venture investor A should select. What is the expected monetary value associated with the selected venture?

Step-by-step explanation:

LESSSSSSS GOOOOOOOOOO

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