Sonia works at a bakery. The function f(x) represents the amount of money Sonia earns per loaf, where x is the number of loaves she makes. The function g(x) represents the number of bread loaves Sonia bakes per hour, where x is the number of hours she works. Show all work to find f(g(x)), and explain what f(g(x)) represents.

f(x)=9x^2+1
g(x)=square root 2x^3

Answers

Answer 1

Answer:

18x^3+1

Step-by-step explanation:

since g(x)=√2x^3 and f(x)=9x^2+1 then

f(g(x))= 9(g(x))^2 +1 = 9(√2x^3)^2 +1 = 18x^3+1

this represents the amount of money Sonia earns baking loaves in x hours

Answer 2

The equation of f(g(x)) is [tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex], and it represents the amount of money Sonia makes when she bakes for x hours

The functions are given as:

[tex]f(x) = 9x^2 + 1[/tex]

[tex]g(x) = \sqrt{2x^3}[/tex]

Recall that:

[tex]f(x) = 9x^2 + 1[/tex]

Substitute g(x) for x

[tex]f(g(x)) = 9(g(x))^2 + 1[/tex]

Substitute [tex]g(x) = \sqrt{2x^3}[/tex]

[tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]

Hence, the equation of f(g(x)) is [tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]

Read more about composite functions at:

https://brainly.com/question/10687170


Related Questions

if V = 1/3 BH, what is h expressed in terms of B and V?
A) 1/3VB
B) V/3B
C) 3V/B
D) 3VB

Answers

V=(1/3)(B)(h)

multiply both sides by 3

3V=Bh

divide both sides by B

3V/B=h

Which proportion would you use to find what percent 6 is of 40?

Answers

Answer:

6/100 = x/40

Step-by-step explanation:

6% is represented by 6/100, x is the variable in the proportion, and 40 is the whole you are finding the percentage of

Can someone help me with this math homework please!

Answers

Answer:

3.5

Step-by-step explanation:

From the graph,

x1 = 0

x2 = 4

y1 = 0

y2 = 14

Formula : -

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

Slope

= ( 14 - 0 ) / ( 4 - 0 )

= 14 / 4

= 7 / 2

= 3.5

Answer:

7/2

Step-by-step explanation:

the slope of a line is the ratio of y/x.

it describes how many units y changes, when x changes a defined number of units.

an increase is indicated by "+", and a decrease by "-".

the point with full integer/natural numbers as coordinates is (4, 14).

that means that when coming from point 0 (0, 0) x increases by 4 units, and y increases by 14 units.

so, the slope of line is 14/4 = 7/2

two football tickets and one basketball ticket cost $126.77. one football ticket and 2 basketball tickets cost $128.86 find the cost of each ticket

Answers

Answer:

Cost of each football ticket=$41.56

Cost of each  basketball ticket=$43.56

Step-by-step explanation:

Let

Cost of each football ticket=x

Cost of each basket ball ticket=y

According to question

[tex]2x+y=126.77[/tex]...(1)

[tex]x+2y=128.86[/tex] ....(2)

We have to find  the cost of each ticket.

Equation (1) multiply by 2 then we get

[tex]4x+2y=253.54[/tex]  .....(3)

Now, subtract equation (2) from (3)

[tex]3x=124.68[/tex]

[tex]x=124.68/3[/tex]

[tex]x=41.56[/tex]

Now, using the value of x in equation (2)

[tex]41.56+2y=128.86[/tex]

[tex]2y=128.86-41.56[/tex]

[tex]2y=87.3[/tex]

[tex]y=87.3/2=43.65[/tex]

Hence, cost of each football ticket=$41.56

Cost of each  basketball ticket=$43.56

Can someone help me please hurry

Answers

9 tiles lay along each wall

please help with the fourth part ​

Answers

Answer:

ofc its p/q

Step-by-step explanation:

Find BD , given that line AB is the angle bisector of < CAD​

Answers

Answer:

23

Step-by-step explanation:

The answer is 23 by the definition of angle bisector.

0.5 + 1/9 show step by step and ill make you brainliest

Answers

Answer: 11/18          

1. Convert 0.5 to a fraction

5/10

5/10 simplifies to 1/2

2. Add 1/2 and 1/9 by finding a common denominator

Common deniminator is 18 (2*9=18, 9*2=18)

1/2=9/18

1/9=2/18

3. Add

9/18+2/18=11/18

4. The answer is 11/18

[tex]\displaystyle\ \Large \boldsymbol 0,5+\frac{1}{9} =\frac{1^{/9}}{2} +\frac{1^{/2}}{9}=\frac{9+2}{18} =\boxed{\frac{11}{18} }[/tex]

22. If y = 1/3(x - 2), express x in terms of y A. X = 3y - 2 B. x = 3y + 2 C. x=y D. x=-Y​

Answers

Answer:

B. x= 3y+2

Step-by-step explanation:

y=⅓x-⅔

⅔+y=⅓x

(⅔÷⅓)+(y÷⅓)=⅓x÷⅓

2+3y=x

someone please help me

Answers

Step-by-step explanation:

D) (A³/2)³ = A⁹/8

A³ whole to the power 3 is A⁹

2³ is 8

Moosonee: -1.5°C
Cold Lake: -4.5°C
Anchorage: -9.5°C and
Moscow: -1°C
Which city is warmer?

Answers

Answer:

Moscow

Step-by-step explanation:

In negatives the greater number is less. So -1 is the greatest, and thus, Moscow is the answer.

Moscow with a temperature of -1°C is warmer than Moosonee (-1.5°C), Cold Lake (-4.5°C), and Anchorage (-9.5°C).

The temperatures provided for the cities are as follows:

Moosonee: -1.5°C

Cold Lake: -4.5°C

Anchorage: -9.5°C

Moscow: -1°C

To determine which city is warmer, we compare the temperatures.

The higher the temperature, the warmer the city.

Moscow has the highest temperature of -1°C.

Therefore, Moscow is the warmest city compared to Moosonee, Cold Lake, and Anchorage, as it has a temperature that is closer to 0°C (warmer) compared to the other cities.

To learn more on Number system click:

https://brainly.com/question/1763119

#SPJ4

Which choice shows the coordinates of C' if the trapezoid is reflected across the y-axis?

Answers

Answer:

(-5, 3)

Step-by-step explanation:

angelA and angelB are complementary angles. If m angel = ( x-23)° and m angel B = (2x + 29°) then find the measure of angle B.​

Answers

Answer:

The measure of angle B is 29°.

Complete the sentence. The amount of time it takes to drive from your house to the library is most likely to be a function of the _____.

Answers

Answer:

D. distance

Step-by-step explanation:

really ? given the choices you needed help with that ?

only D makes sense. the rest is completely ridiculous and has nothing to do with driving from the house to the library.

Help me ASAP please people

Answers

Answer: 36

Step-by-step explanation= First let's calculate the area of the the inner rectangle so 6x4=24. Now let's add the area of the rectangle,(BY CUTTING IT INTO HALF) this part is hard but first lets add 3 cm then, 2 cm then lets add, 1 cm. So (3x2 is 6) now lets multiply that by 1, so you get 6. Multiply that by 4 it = 24 now let's add 24+24 which = 48. Hope it helps!!

Can someone help me with this math homework please!

Answers

Answer: f(t) = 1.5t + 5

What is the solution to this equation 1/2n^2+18=0

Answers

Answer:

n = ±6 .

Step-by-step explanation:

A quadratic equation is given to us and we need to find out the solution of the given equation . The given equation is ,

[tex]\rm\implies -\dfrac{1}{2}n^2+18=0 [/tex]

Subtracting 18 both sides ,

[tex]\rm\implies -\dfrac{1}{2}n^2 = -18 [/tex]

Multiplying both sides by -2 ,

[tex]\rm\implies -2\times\dfrac{1}{2}n^2 = -2\times -18 [/tex]

On simplyfing , we get ,

[tex]\rm\implies n^2= 36 [/tex]

Putting squareroot both sides ,

[tex]\rm\implies n= \sqrt{36} [/tex]

This equals to ,

[tex]\rm\implies \boxed{\quad\blue{\rm n =\pm 6 }} [/tex]

Hence the value of n is ±6 .

Add 1,249 and 594.
what is their sum rounded to the nearest hundred?

A. 700

B. 1,800

C. 1,900​

Answers

Answer:

1249+592=1843, rounding that you get B, 1,800

This will be C as it is rounded to the nearest 100 as 1,249 plus 594= 1833 we can infer the 1 is from the “thousands” column and the second one is “8” which is the hundreds column now if it’s 5 and above we round up if it’s below 5 we will round down therefore the answer is C-1900

I need help pleaseee

Answers

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, tangent.

Remember: SOH-CAH-TOA

From the angle, we know the opposite side and want to figure out the adjacent side. Therefore, we should use the tangent function.

tan(35) = 6/RS

RS = 6 / tan(35)

RS = 8.6

Hope this helps!

Find the area of the surface generated by revolving the curve xequals=StartFraction e Superscript y Baseline plus e Superscript negative y Over 2 EndFraction ey+e−y 2 in the interval 0 less than or equals y less than or equals ln 20≤y≤ln2 about the​ y-axis.

Answers

Solution :

[tex]$x=f(y) = \frac{e^y + e^{-y}}{2} , \ \ \ \ \ 0 \leq y \leq \ln 2$[/tex]

[tex]$\frac{dx}{dy} = \frac{e^y + e^{-y}}{2}$[/tex]

[tex]$\left(\frac{dx}{dy}\right)^2 = \frac{e^{2y} - 2 + e^{-2y}}{4}$[/tex]

[tex]$1+\left(\frac{dx}{dy}\right)^2 = 1+\frac{e^{2y} - 2 + e^{-2y}}{4} = \frac{e^{2y} + 2 + e^{-2y}}{4}$[/tex]

                  [tex]$ = \left(\frac{e^y + e^{-y}}{2}\right)^2$[/tex]

[tex]$\sqrt{1+\left(\frac{dx}{dy}\right)^2} = \sqrt{\left(\frac{e^y + e^{-y}}{2}\right)^2}=\frac{e^y + e^{-y}}{2}$[/tex]

[tex]$S = \int_{y=a}^b 2 \pix \sqrt{1+\left(\frac{dx}{dy}\right)^2 } \ dy$[/tex]

  [tex]$=\int_{0}^{\ln2} 2 \pi \left(\frac{e^y+e^{-y}}{2}\right) \left(\frac{e^y+e^{-y}}{2}\right) \ dy$[/tex]

  [tex]$=\frac{\pi}{2}\int_{0}^{\ln 2}(e^y+e^{-y})^2 \ dy = \frac{\pi}{2}\int_{0}^{\ln 2}(e^{2y}+e^{-2y}+2) \ dy $[/tex]

  [tex]$=\frac{\pi}{2} \left[ \frac{e^{2y}}{2} + \frac{e^{-2y}}{-2} + 2y \right]_2^{\ln 2}$[/tex]

  [tex]$=\frac{\pi}{2} \left[ \left(\frac{e^{2 \ln 2}}{2} + \frac{e^{-2\ln2}}{-2} + 2 \ln2 \right) - \left( \frac{e^0}{2} + \frac{e^0}{-2}+0\right) \right]$[/tex]

  [tex]$=\frac{\pi}{2}\left[ \frac{e^{\ln4}}{2} - \frac{e^{\ln(1/4)}}{2} + \ln 4 - \left( \frac{1}{2} - \frac{1}{2} + 0 \right) \right]$[/tex]

  [tex]$=\frac{\pi}{2} \left[\frac{4}{2} -\frac{1/4}{2} + \ln 4 \right]$[/tex]

  [tex]$=\frac{\pi}{2} \left[ 2-\frac{1}{8} + \ln 4 \right]$[/tex]

  [tex]$=\left( \frac{15}{8} + \ln 4 \right) \frac{\pi}{2}$[/tex]

Therefore, [tex]$S = \frac{15}{16} \pi + \pi \ln 2$[/tex]

 

Question 4 of 25
Suppose a normal distribution has a mean of 62 and a standard deviation of
4. What is the probability that a data value is between 58 and 64? Round your
answer to the nearest tenth of a percent.
A. 53.3%
B. 54.3%
C. 52.3%
D. 51.3%

Answers

Answer:

Step-by-step explanation:

We are looking for P(58 < x < 64). We need to find the percentage to the left of the z-scores for each of these numbers. To find the z scores, use the formula:

[tex]z=\frac{x_i-\bar{x}}{\sigma}[/tex]

[tex]z=\frac{58-62}{4}[/tex] which gives us a z-score of -1. The percentage of numbers to the left of a z-score of -1 is .1586553

Now for the other z-score:

[tex]z=\frac{64-64}{4}[/tex] which gives us a z-score of .5. The percentage of numbers to the left of a z-score of .5 is .69146246

The lower percentage subtracted from the higher gives the area in question:

.69146246 - .1586553 = .53280716, or as a percentage, 53.3%, choice A.

EASY BRAINLIEST ANSWER ASAP!!

Complete the ordered pairs, using the given equation:
4x + 3y = 12 (0, ) (-1, ) ( ,10 )

Answers

Answer:

(0, 4) (-1, 16/ 3) (-9/ 2, 10)

Step-by-step explanation:

In an ordered pair the term before the comma is the x variable and the term after the comma is the y variable.

1.

4x + 3y = 12 . . . . . .(0, _)

here were given the x variable

finding the other term

4× 0 + 3y = 12

3y = 12

y = 4

therefore the ordered pair is (0, 4)

2.

. . . . . . . (-1, _)

here were given the x variable

4 × -1 + 3y = 12

3y = 12 + 4

3y = 16

y = 16/ 3

ordered pair is (-1, 16/ 3)

3.

. . . . . . . . (_, 10)

here were given the y variable

finding the other term

4x + 3 × 10 = 12

4x + 30 = 12

4x = 12 - 30

4x = -18

dividing both sides by 2

2x = -9

x = -9/ 2

ordered pair is (-9/ 2, 10)

(x² - 3x)√(2x² - 3x - 2)≥0

Answers

Answer:

(-infinity, -1/2] and [3, infinity]  Let e know if anything didn't make sense.  

Step-by-step explanation:

A good way to think about it is a graph is either at 0, greater than 0 or less than 0.  If you can find all of the zeroes  then you can test each zero by checking points before and after.  the graph will either cross and change signs, or stay the same.

So we want to find the zeroes.

Much like the factored form of a quadratic (x - a)(x - b) this inequality has two expressions  being multiplied together, so if you can find when they are 0 you will have all the zeros.  We shoudl also check when they do not exist just to be safe.

(x^2 - 3x) itself is a quadratic.  so lets find its zeroes.

x^2 - 3x

x(x - 3)

So the zeroes are 0 and 3.  lets find the zeroes of the other expression before checking signs.

sqrt(2x^2-3x-2) will be at 0 when the quadratic inside is at 0, and will not exist if the quadrati is negative, so let's look for both.  first the 0s.  I am going to complete the square

2x^2 - 3x - 2 = 0

2(x^2 - (3/2)x - 1) = 0

2[(x - 3/4)^2 - 25/16] = 0

2(x - 3/4)^2 - 25/8 = 0

2(x - 3/4)^2 = 25/8

(x - 3/4)^2 = 25/16

x - 3/4 = +/- 5/4

x = +/-5/4 + 3/4

x = -2/4 or 8/4

x = -1/2 or 2

Let me know if you couldn't follow that.  Anyway, using those zeroes we can tell 2x^2 - 3x - 2 is negative  between the two zeroes, since it is a parabola that opens upwards and crosses the x axis at those zeroes.  this means sqrt(2x^2 - 3x - 2) does not exist from x=-1/2 and x=2.  This means for the other zero above at x=0, the iequality will not exist.  So now we have 3 points to look at.

-1/2 for its first 0 and where it then stops existing up to 2, which is also a 0.  Finally 3 is the last 0.

at x=-1/2 all values before it are positive

x=2 has values immediately after it negative

x=3 then it switches so all values after that are positive since it is the last 0

Now we know that (x^2 - 3x) * sqrt(2x^2 - 3x - 2)is positive or equal to 0 along the intervals, (-infinity, -1/2] and [3, infinity]

Anyone? Ive tried and its not clicking

Answers

Answer:

Hello Bro How Are You....?

here you go. is this correct?

One year josh had the lowest ERA​ (earned-run average, mean number of runs yielded per nine innings​ pitched) of any male pitcher at his​ school, with an ERA of 2.89. ​Also,alice had the lowest ERA of any female pitcher at the school with an ERA of 3.31 . For the​ males, the mean ERA was 5.083 and the standard deviation was 0.672. For the​ females, the mean ERA was 4.032 and the standard deviation was 0.649. Find their respective​ z-scores. Which player had the better year relative to their​ peers, josh or alice ​? ​(Note: In​ general, the lower the​ ERA, the better the​ pitcher.)

Answers

Answer:

Josh's ERA had a z-score of -3.26.

Alice's ERA had a z-score of -1.11.

Due to the lower z-score(ERA is a stat that the lower the better), Josh had a better year relative to his peers.

Step-by-step explanation:

Z-score:

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.

Josh:

ERA of 2.89, mean of 5.083, standard deviation of 0.672. So

[tex]X = 2.89, \mu = 5.083, \sigma = 0.672[/tex], and the z-score is:

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

[tex]Z = \frac{2.89 - 5.083}{0.672}[/tex]

[tex]Z =  -3.26[/tex]

Josh's ERA had a z-score of -3.26.

Alice:

ERA of 3.31, mean of 4.032, standard deviation of 0.649. So

[tex]X = 3.31, \mu = 4.032, \sigma = 0.649[/tex], and the z-score is:

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

[tex]Z = \frac{3.31 - 4.032}{0.649}[/tex]

[tex]Z =  -1.11[/tex]

Alice's ERA had a z-score of -1.11.

Which player had the better year relative to their​ peers, josh or alice ?

Due to the lower z-score(ERA is a stat that the lower the better), Josh had a better year relative to his peers.

SOMEONE HELP ME PLEASE

Answers

Answer:

y = 5/2

Step-by-step explanation:

An inverse variation is of the form

xy = k where k is a constant

From the first pair of point

2*5 = k

10 = k

xy = 10

Using the second pair of points

4y = 10

Divide by 5

4y/4 = 10/4

y = 5/2

Answer:

4,3

Step-by-step explanation:

it went up two so i guess the other has to go down two?

The number 55 is attached to a two-digit number on its left, and the formed 4-digit number is divisible by 24. What could be the two-digit number? List all options.

Answers

Answer:

the answer will be 44 I think I hoped I helped if not sorry.

Step-by-step explanation:

4|x+3|<8 i need help asap

Answers

Answer:

-5 <x<-1

Step-by-step explanation:

4|x+3|<8

Divide by 4

4|x+3| /4<8/4

|x+3|<2

There are two solutions one positive and one negative, remember to flip the inequality for the negative

x+3 <2    and x+3 >-2

Subtract 3 from each side

x+3-3 <2-3   and x+3-3 >-2-3

x<-1   and x>-5

-5 <x<-1

Solve for 2. Round to the nearest tenth of a degree, if necessary.
U
9.4

T
PLSSSS HELP

Answers

Step-by-step explanation:

sin x0= 7/9.4

sin x0= 0.745

x0 = sin^-1 0.745

x0= 48.2

Please help me❤️ I keep getting it wrong

Answers

Answer:

[tex] = { \tt{ \frac{30}{120} + \frac{40}{120} }} \\ = \frac{7}{12} [/tex]

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