Answer:
The simplified expression for f(g(x)) is x. The simplified expression for g(f(x)) is x. The functions are inverses of each other.Step-by-step explanation:
Given:
[tex]f(x)=\dfrac{1}{8}x^3\\\\g(x)=2x^{\frac{1}{3}}[/tex]
We find that ...
[tex]f(g(x))=\dfrac{1}{8}(2x^{\frac{1}{3}})^3=\dfrac{1}{8}(2^3)(x^{\frac{3}{3}})=\dfrac{8}{8}x\\\\\boxed{f(g(x))=x}\\\\g(f(x))=2\left(\dfrac{1}{8}x^3\right)^{\frac{1}{3}}=2\left(\dfrac{1}{8^{\frac{1}{3}}}\right)(x^{\frac{3}{3}})=\dfrac{2}{2}x\\\\\boxed{g(f(x))=x}[/tex]
__
So, the statements that apply are ...
The simplified expression for f(g(x)) is x. The simplified expression for g(f(x)) is x. The functions are inverses of each other.Answer:
A, D, E
The simplified expression for f(g(x)) is x.
The simplified expression for g(f(x)) is x.
The functions are inverses of each other.
Step-by-step explanation:
Got it right on edg :)
When a number x is multiplied by 6, the result is 3/8 What is the value of x?
Answer:
1/16.
Step-by-step explanation:
6x = 3/8
Divide both sides by 6:
6x / 6 = 3/8 / 6
x = 3/8 * 1/6
= 3/48
= 1/16.
Solve for g.
s=4g + 4u
Answer:
[tex]\frac{s-4u}{4}[/tex]
Step-by-step explanation:
[tex]s=4g+4u[/tex]
Switch sides:
[tex]4g+4u=s[/tex]
Subtract 4u from both sides:
[tex]4g+4u-4u=s-4u[/tex]
[tex]4g=s-4u[/tex]
Divide both sides by 4:
[tex]\frac{4g}{4}=\frac{s-4u}{4}[/tex]
[tex]g=\frac{s-4u}{4}[/tex]
Answer:
g= s/4-u
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
simplify to create an equivalent expression-4(z+3)-4(5-4z)
Answer:
12z−32
Step-by-step explanation:
Distribute:
=(−4)(z)+(−4)(3)+(−4)(5)+(−4)(−4z)
=−4z+−12+−20+16z
Combine Like Terms:
=−4z+−12+−20+16z
=(−4z+16z)+(−12+−20)
=12z+−32
Tim biked 40 miles in 2 hours. His Rate is
every hour.
This means Tim biked
miles for every hour ?
Answer:
20 miles/hour
Step-by-step explanation:
40 miles in 2 hours,
thus,
40/2 miles in 2/2 hours = 20 miles in 1 hour.
Therefore, Tim bikes 20 miles per hour.
Tell me the correct anser
Answer:
D is the correct answer
A rate of 5 yards per second is equal to how many yards per minute?
Answer:
300 yards per minute
Step-by-step explanation:
60 seconds in a minute 5 yards per second
5x60=300 yards per minute
what is the capital of poland?
Answer:
Warsaw is capital of poland
Answer:
Warszawa
Step-by-step explanation:
Which set of ordered pairs represents a function?
o {(5,-2), (-5,2), (-5, -4),(4, -5)}
{(9,6),(-1,7), (9,–7), (4,7)}
o {(-1,0),(-8, 9), (7,0), (1,3)}
{(8,6), (8, –4), (-7, -2),(-1, —8)}
Answer:
{(-1,0),(-8, 9), (7,0), (1,3)}
Step-by-step explanation:
number 3 is the only one with no colliding outputs.
Inez says you can plot 4/5 on a number line, but Jeremiah says you cannot. Who is correct?
Answer:
Inez is correct.
Step-by-step explanation:
You can plot any real number on a number line.
A rectangle with length of 9 centimeters and width of 5 centimeters. The perimeter of the rectangle is cm. If the rectangle is dilated by a scale factor of 6 to create a new rectangle, the new dimensions are . The perimeter of the new rectangle is ✔ 168 cm. When comparing the new perimeter to the original perimeter, the new perimeter is .
The perimeter of the new rectangle is 150 cm more than the original perimeter.
What is a rectangle?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.
A rectangle with a length of 9 centimeters and a width of 5 centimeters.
The perimeter of the rectangle will be
Perimeter = 2 (9 + 5)
Perimeter = 2(14)
Perimeter = 28
If the rectangle is dilated by a scale factor of 6 to create a new rectangle, the new dimensions will be
Length = 6 × 9 = 54 cm
Width = 6 × 5 = 30 cm
The perimeter of the new rectangle is 168 cm.
When comparing the new perimeter to the original perimeter, the new perimeter will be
→ New perimeter - original perimeter
→ 168 - 28
→ 150
The perimeter of the new rectangle is 150 cm more than the original perimeter.
More about the rectangle link is given below.
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Answer:
1. C
2. D
3. D
4. B
Step-by-step explanation:
I need help on fractions and decimal world problems
When Josh babysits, he chargers a flat fee of $14 plus an hourly rate of $9. How long would Josh need to babysit if he wants to earn $86 in one night?
Answer:
[tex]\frac{36}{7}[/tex]hours
Step-by-step explanation:
First let's get the flat fee of 14 out of the way, because he wants to earn 86 dollars and the 14 dollar fee is the y intercept.
[tex]86-14 = 72[/tex]
We would then divide 72 by the slope (14 per hour) to see how many hours he has to work:
[tex]72/14 \approx5.14285714286[/tex]
I would just simplify because this decimal isn't exact
[tex]72/14 = 36/7[/tex]
So 36/7 hours
2. Select all ratios that are equivalent to 3:18.
21:126
6:36
1:6
1:18
15
21
Answer:
21:126
6:36
1:6
Step-by-step explanation:
The robber stole only 25 pounds
Of quarters out of the coin machine. quarters are weighed in ounces. If there are 16 ounces in 1 pound how many ounces of quarters were stolen?
There are 75 students in a speech contest. Yesterday, 2/5 of them gave their speeches. Today, 1/3
of the remaining students gave their speeches. How many students still haven't given their speeches?
Work Shown:
2/5 of 75 = (2/5)*75 = 0.4*75 = 30
Yesterday 30 people gave speeches. There are 75-30 = 45 people left.
1/3 of 45 = (1/3)*45 = 15
Then another 15 people gave speeches today. So there are 45-15 = 30 people who haven't given their speeches yet.
HELP ME PLEASE WHAT IS THE ANSWER TO THESE QUESTIONS
Answer:
question 3.3 Answer: Angle 3
question 3.4 Answer: ABD and DBC are complementary angles
question 3.5 Answer: x is 7 degrees (first answer option)
Step-by-step explanation:
First question:
Recall that suplementary angles are those whose addition gives 180 degrees. Therefore the supplementary angle to angle 8 is angle 3.
Second question:
Recall that complementary angles are those angles which added give 90 degrees. Therefore, the only correct answer for this question is the third one: ABD and DBC are complementary angles.
Third question:
Notice that the two angles added should render 90 degrees, therefore, their expression should as well add to 90 degrees. Such can be written in equation form as:
( 6 x - 20 ) + (4 x + 40 ) = 90
combining like terms and later solving for x we get:
6 x + 4 x - 20 + 40 = 90
10 x + 20 = 90
10 x = 90 - 20
10 x = 70
x = 7
Therefore x is 7 degrees
How would you write an explanation for a, b, and c? Mississipi is the data point on the upper left that is an outlier
Step-by-step explanation:
a. Your answer is correct. The trend is that obesity rate increases with the number of fast food restaurants per capita. Since Mississippi has a high obesity rate and number of fast food restaurants per capita, it goes against the trend. It is an outlier in terms of the relationship.
b. The number of restaurants per capita is between 2 and 6 for most states. Mississippi's number of restaurants per capita is within this range, so it is not an outlier.
c. The obesity rate is between 22 and 38 for most states. Mississippi's obesity rate is within this range, so it is not an outlier.
Dan and David are marking exam papers. Each set takes Dan 37 minutes and David 1 hour.
Express the times Dan and David take as a ratio in its simplest form.
Answer:
37:60
Step-by-step explanation:
Change 1 hour into minutes= 60 minutes
37 minutes: 60 minutes
The ratio of times Dan and David take as a ratio in its simplest form is,
60 : 37.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, Dan and David are marking exam papers.
Each set takes Dan 37 minutes and David 1 hour or 60 minutes.
Therefore, The ratio of time taken by Dan and David is
60 : 37.
learn more about proportion here :
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(You will need a calculator.) Suppose you deposit $4800 into an account paying 3.2% simple annual interest and leave it there for six years.
Assuming that you make no other deposits or withdrawals, how much will the account hold at the end of that time?
Answer: $
(Round your answer to the nearest cent. Enter only the number without commas, not the dollar sign.)
Answer:
Step-by-step explanation:
principal (P) = $4800
Interest (I) = 3.2%
Time (T) = 6 years
Now
I = (P*T*R)/ 100 = (4800*3.2*6) / 100 = 921.6
Amount (A) = P + I = 4800 + 921.6 = $5721.6 = $5272
The volume of a cylinder is 675π cm3. The radius of the base of the cylinder is 5 cm. What is the height of the cylinder?
Answer: 27 cm
Step-by-step explanation:
We know that the volume of a cylinder is [tex]V=\pi r^2h[/tex]. Since we were given the volume and radius, we can plug them in and solve for height.
[tex]675\pi =\pi (5^2)h[/tex] [divide both sides by π]
[tex]675 = (5^2)h[/tex] [exponent]
[tex]675=25h[/tex] [divide both sides by 25]
[tex]h=27[/tex]
Now, we know that the height is 27 cm.
In an alloy of gold and silver the ratio of the amount of gold to the amount of silver is 2:5.
What is the weight of gold in the alloy, if there are 80g of silver?
Given :
The ratio of the amount of gold to the amount of silver is 2:5.
To Find :
The weight of gold in the alloy, if there are 80 g of silver.
Solution :
Let, amount of gold is x.
So, the ratio of amount of gold and silver is :
[tex]\dfrac{x}{80}=\dfrac{2}{5}\\\\x=32\ g[/tex]
Therefore, the weight of gold in the alloy is 32 g.
Hence, this is the required solution.
Answer:
32
Step-by-step explanation:
do 80÷5=16 to get unit. Then do 16*2=32
3,394 divided by 42
Answer:
80.80
Step-by-step explanation:
3394/42 simplified would be 1697/21
as a mixed form it would be 80 and 17/21
As a decimal, 80.809...
Hope this helps :)
Evaluate (-5z)^3 . Write your answer using only positive exponents. Evaluate any numerical powers.
Answer:
-125z³
Step-by-step explanation:
-5 times - 5 = 25 canceling negative
125 times -5 = -125
zXzXz = z to power of 3 =z³
help me please this is due today!!!!!!!!!!!!!!1111 :(
Answer:
Whatever y is you turn it to what x is plus a negative Ex: T(10, 9) U(0,9) V(0,0) W(10,0) Those are the answers.
Step-by-step explanation:
Did this help???
c. When the cost of flour was Rs 28 per kg, the weight of a bread was 496 gram.
What will be the weight of bread if the cost of flour increases to Rs 32 per kg?
Answer:
hope it helps
plz mark as brainliest
Answer:
when cost of flour was 28 then cost of bread is 496
so the coost of bread if flour cost 32 = 496*32/28=566.86
Step-by-step explanation:
ASAP
Sales tax is calculated as a percentage of the sales price. If sales tax is 6%, what is the sales tax on clot that cost 180
$6.00
O $9.80
$10.80
O $18.60
The equation of a parabola with a vertex as the origin is y2=−4px. If 4p=12, what is the equation of the directrix?
Answer:
-5
Step-by-step explanation:
When considering different sampling methods, cluster sampling includes the steps: _______.
a. use simple random sampling to select a set of groups; every individual in the chosen groups is included in the sample
b. list the members of the population; use simple random sampling to select a starting point in the population; let k = (number of individuals in the population)/(number of individuals needed in the sample); choose every kth individual in the list
c. starting with the one that was randomly selected
d. divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group
e. identify individuals of the population that are easily accessible; obtain data from these individuals
Answer:
d. divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group
Step-by-step explanation:
Remember, a cluster represents a selection out of a group belonging to a larger population. Thus, cluster sampling includes the steps;
divide the population into groups;use simple random sampling to identify a proportionate number of individuals from each group.For example, A bus company wants to survey all its customers for a particular day, using cluster sampling, they will randomly select 10 trips that day and survey some or all the passengers on those trips.
Answer:
B
Step-by-step explanation:
Combine like terms -2+5x-8x+4
Answer:
-3x+2
Step-by-step explanation:
5x-8x-2+4
= -3x+2
Answer:
-2+5x-8x+4
-3x+2
Step-by-step explanation:
4. Rewrite the expression using the distributive property.
(7•3) + (7•7)