Answer:
[tex]f^{-1}(x) = \sqrt[3]{\frac{x -4}{5}} +2[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5(x - 2)^3 + 4[/tex]
Required
Determine the inverse
[tex]f(x) = 5(x - 2)^3 + 4[/tex]
Replace f(x) with y
[tex]y = 5(x - 2)^3 + 4[/tex]
Swap the positions of x and y
[tex]x = 5(y - 2)^3 + 4[/tex]
Make y the subject
[tex]x -4= 5(y - 2)^3[/tex]
Divide by 5
[tex]\frac{x -4}{5}= (y - 2)^3[/tex]
Take cube roots of both sides
[tex]\sqrt[3]{\frac{x -4}{5}}= y - 2[/tex]
Add 2 to both sides
[tex]\sqrt[3]{\frac{x -4}{5}} +2 = y[/tex]
[tex]y = \sqrt[3]{\frac{x -4}{5}} +2[/tex]
Replace y with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = \sqrt[3]{\frac{x -4}{5}} +2[/tex]
Find the volume of each shape.
Answer:
Step-by-step explanation:
The probability distribution for a
random variable x is given in the table.
-3
-2
0
2
3
Probability
.17
.13
.33
.16
.11
.10
Find the probability that x < 0
Answer:
.21
Step-by-step explanation:
is
Answer: 0.79
Step-by-step explanation:
here's my work please help me
Answer: The answer is C
Step-by-step explanation:
Answer:
the answer is C.
find the area of the figure use 3.14
Answer:
466.08 m²
Step-by-step explanation:
The figure is composed of a triangle and a semicircle.
Therefore,
Area of the figure = area of the triangle + area of the semicircle
= ½*b*h + ½*πr²
Where,
b = 24 m
h = 20 m
π = 3.14
r = ½ of 24 m = 12 m
Substitute each value into the equation
Area of the figure = ½*24*20 + ½*3.14*12²
= 240 + 226.08
= 466.08 m²
Lesson 10 Problem Set 5•3
FONY OF UNITS
3. Darren bought some paint. He used 2 gallons painting his living room. After that, he had 3 - gallons left.
How much paint did he buy?
PLS HELP
Answer:
I think 5 gallon painting
Item 9
Find the surface area of the prism.
Answer: S = 2(lw + lh + wh)
Step-by-step explanation: Use this formula to find the total surface area of a prism.
Tonys birthday is 20 days befor anns anns birthday is 7 days after vics vics birthday is on the 20th when is tonnys birthday
Answer:
the 7th
Step-by-step explanation:
Answer:
the 27th
Step-by-step explanation:
Tonnys birthday is on the 27th
At a factory, two machines pack bottles into boxes for shipping. Machine A can pack 8 boxes per minute, and Machine B can pack 11 boxes per minute.
1. Before shipment, an inspector found that 7 of the boxes were defective and could not be shipped. At least 200 boxes were approved for shipment. Write and solve an inequality to find the amount of time Machine A spent packing the boxes that were approved for shipment.
Answer: 25 minutes
Step-by-step explanation:
A car is driving towards home at 0.5 miles per minute. If the car is 4 miles from home at t=0 , which of the following can represent the distance that the car has left to drive? Explain your reasoning.
A. 0.5t
B. 4+0.5t
C. 4-0.5t
D. 4(0.5t)
The distance that the car has left to drive can be represented as option (D) 4(0.5t) is the correct answer.
What is speed?
The speed is the rate of change of position of an object in any direction. Speed tells us how fast or slow an object travels and describes the distance traveled divided by the time taken to cover the distance.
For the given situation,
The speed of the car,S = 0.5 miles per minute
Let the time be t.
Let the distance be D.
The distance between the car and the home = 4 miles.
The formula that relates speed, distance and time is
[tex]Speed=\frac{Distance}{time}[/tex]
⇒ [tex]Distance=(Speed)(time)[/tex]
Here initially at t=0, the car is 4 miles apart from the home and it travels at 0.5 miles per minute, so the equation can be represented as
⇒ [tex]D=4(0.5t)[/tex]
Hence we can conclude that the distance that the car has left to drive can be represented as option (D) 4(0.5t) is the correct answer.
Learn more about speed, distance and time here
https://brainly.com/question/2004627
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The commutative property changes the _____ of two addends or factors.
A cube has an edge length of 12 meters. What is its volume, in cubic meters?
meters
3
Answer:
1728
Step-by-step explanation:
if its a cube then all sides are the same length. you need to times to base width and height. so it will be 12 times 12 times 12 which is 1728.
Come I need answers
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x^2 + 7x + 14), [−4, 1]
Find the stationary points of the function (where the derivative is zero):
f(x) = ln(x ² + 7x + 14)
→ f '(x) = (2x + 7) / (x ² + 7x + 14)
The denominator is always positive, since
x ² + 7x + 14 = (x + 7/2)² + 7/4 ≥ 7/4 > 0
so f '(x) = 0 when
2x + 7 = 0 → x = -7/2
at which point f (-7/2) = ln(203/4) ≈ 3.927.
Also check the endpoints of the given domain:
f (-4) = ln(2) ≈ 0.693
f (1) = ln(22) ≈ 3.091
Then on the interval [-4, 1], we have max(f ) = ln(203/4) and min(f ) = ln(2).
Solve similar triangles (advanced)
Solve for x
x=?
Answer:
x = 1.2
Step-by-step explanation:
AD/AB = DE/BC (Similarity Theorem)
AD = 6 + 4 = 10
AB = 6
DE = 2
BC = x
Plug in the values
10/6 = 2/x
Cross multiply
10*x = 2*6
10x = 12
Divide both sides by 10
x = 12/10
x = 1.2
PLS HELP I WILL REWARD BRAINIEST
Answer:
1/3 divided by 4
Step-by-step explanation:
Because you start off with 1/3 and then you split it into 4, 1/12's and 4*1/12 is equal to 1/3
So the answer is 1/3 divided by 4
please help NO LINKS I WILL REPORT YOU ( i will also mark brainliest)
Answer:
6.96 is the area of this triangle! So, option A is correct.
Hope this helps and please mark brainliest!
Help please! 50 points! Troll answers WILL be reported
Answer:
Think its B. but if not it should be E.
Step-by-step explanation:
FInd the area of the polygon
Answer:
A = 14 units ²
Step-by-step explanation:
Hello There!
The polygon shown is a triangle
The first step is to find the formula for area of a triangle
[tex]A=\frac{1}{2} bh[/tex]
where b = base and h = height
the following dimensions are given
base = 7 and 4 = height
so all we have to do is plug in the values into the formula
[tex]A=\frac{1}{2} 7*4\\7*4=28\\\frac{1}{2} 28=14\\A=14[/tex]
so we can conclude that the area of the polygon is 14 units ²
Answer:
area of polygon =area of TRIANGLE =
1/2 base×height =1/2×7×4=14 units²
please answer all the questions for 25 points and for brainliest if not answer correctly will report
Answer:
1) 56.52 in²
2) 565.2 ft²
3) 235.5yd²
4) 898.04 ft²
5) 942 yd²
6) 75.36 in²
Step-by-step explanation:
SA= πrS + πr²
1) (3.14)(2)(7) + (3.14)(2²) = 56.52 in²
2) (3.14)(9)(11) + (3.14)(9²) = 565.2 ft²
3) (3.14)(5)(10) + (3.14)(5²) = 235.5yd²
4) (3.14)(11)(15) + (3.14)(11²) = 898.04 ft²
5) (3.14)(10)(20) + (3.14)(10²) = 942 yd²
S =5 because 5² = 3² + 4²
6) (3.14)(3)(5) + (3.14)(3²) = 75.36 in²
1. The first bus stop on a bus route is 4 miles from school. How many yards is the first bus stop from school? A) 12 yards B) 1760 yards C) 5280 yards D) 7040
Answer:
D. 7040 yards
Step-by-step explanation:
2) If 3/5 of students carry an iPhone, what fraction of students is this using 75 as the denominator
Answer:
45/75
Step-by-step explanation:
75/5 = 15
15x3 = 45
PLEASE HELP ME, THIS MEANS EVERYTHING TO ME ITS APART OF MY FINALS.❗
The ages of students who play racquetball at a school are shown in the histogram below.
How many students play racquetball at the school?
A.
60
B.
51
C.
54
D.
57
Answer:
Uhhhh... 54?
Step-by-step explanation:
Just add them together.
“What is the gradient of the graph shown?”
someone please help I don’t understand how to do this.
Answer:
Step-by-step explanation:
It is easy to see that (-2, 0) and (0, -4) are points on the line.
gradient = (difference of y-coordinates)/(difference of x-coordinates) = (0-(-4))/(-2-0) = 4/(-2) = -2
expand and simplify (2x + 3) (3x - 1)
Answer:
6x^2+7x−3
Step-by-step explanation:
(2x+3)(3x−1)
Apply the distributive property by multiplying each term of 2x+3 by each term of 3x−1.
6x^2−2x+9x−3
Combine −2x and 9x to get 7x.
6x^2+7x−3
Graph if needed:
PLZ PLZ PLZ HELPPPP
Answer:
LCD is 6
first choice
Step-by-step explanation:
least common denominator of 2 and 3 is 6
The graph below shows the solution for a series of two equations. The first equation is y = -7x - 3. What is the other equation
shown on the graph?
it a tets please help it due today
Triangle DIG is reflected across the l-axis.
O (x, y) --> (-x, y)
O (x, y) --> (-X, -y)
(x, y) --> (y,x)
O (x,y) --> (x,-))
helpp its for a timed assignment
there is not such thing as an I axis, but I will show you what happens for both x and y axis so you can fill out the assignment with the correct information.
IF you meant flipping over the x axis, then the dot will go from top to bottom, bottom to up, the x position won't change only its height(y position)
This meant that for reflecting across the x axis, (x,y)->(x,-y)
For y axis its the opposite, just flipping to the side.
This meant that for reflecting across the y axis, (x,y)->(-x,y)
After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only three women among the last 21 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women. Help her address the charge of gender discrimination by finding the probability of getting three or fewer women when 21 people are hired, assuming that there is no discrimination based on gender.
Does the resulting probability really support such a charge?
Answer:
0.00071 = 0.71% probability of getting three or fewer women when 21 people are hired. This probability, which is very small, supports the charge of gender discrimination.
Step-by-step explanation:
For each employee hired, the are only two possible outcomes. Either it is a man, or it is a woman. The probability of a person hired being a man or a woman is independent of any other person. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
21 new employees.
This means that [tex]n = 21[/tex]
She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.
This means that [tex]p = 0.5[/tex]
Help her address the charge of gender discrimination by finding the probability of getting three or fewer women when 21 people are hired.
This is
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{21,0}.(0.5)^{0}.(0.5)^{21} \approx 0[/tex]
[tex]P(X = 1) = C_{21,1}.(0.5)^{1}.(0.5)^{20} = 0.00001[/tex]
[tex]P(X = 2) = C_{21,2}.(0.5)^{2}.(0.5)^{19} = 0.0001[/tex]
[tex]P(X = 3) = C_{21,3}.(0.5)^{3}.(0.5)^{18} = 0.0006[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.00001 + 0.0001 + 0.0006 = 0.00071[/tex]
0.00071 = 0.71% probability of getting three or fewer women when 21 people are hired. This probability, which is very small, supports the charge of gender discrimination.
In a class of 100 students 45 students read physics, 52 students read Chemistry and 15 students read both the subject. Find the number of people who student who study neither physics nor chemistry
Answer:
12
Step-by-step explanation:
First,
Add 45+52+15
Then the answer will be 112
Then -(minus) from 100
Answer:
18 students
Step-by-step explanation:
45 - 15 = 30 students only read physics
52 - 15 = 37 students only read chemistry
15 students read both
add all of them:
30 + 37 + 15 = 82
subtract the sum from 100
100 - 82 = 18
18 students doesn't study neither