Answers
Answers:
[tex]f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}[/tex]
===============================================
Work Shown:
[tex]f(x) = \sqrt[3]{x}\\\\\\f(g(x)) = \sqrt[3]{g(x)}\\\\\\f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\[/tex]
The idea is to replace every x with g(x). Then you'll plug in the definition of g(x).
---------------------------------
Similarly,
[tex]g(x) = \frac{x+1}{x^3}\\\\\\g(f(x)) = \frac{f(x)+1}{(f(x))^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{(\sqrt[3]{x})^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}\\\\\\[/tex]
Related Questions
Simplify the expression.
3p – 49 + 9 = 8p
Answers
Answer:
p=-5
Step-by-step explanation:
3p-49+9 -49+9=-40
3p-40=8p 3p-3p=0 8p-3p=5p
-40=5p p=5
(3g2−g)+(3g2−8g+4) find the sum
Answers
Answer: 6g2−9g+4
Step-by-step explanation: 3g2+−g+3g2+−8g+4
=(3g2+3g2)+(−g+−8g)+(4)
=6g2+−9g+4
Of the entering class at a college, % attended public high school, % attended private high school, and % were home schooled. Of those who attended public high school, % made the Dean's list, % of those who attended private high school made the Dean's list, and % of those who were home schooled made the Dean's list. A student is randomly chosen. a) Find the probability that the student made the Dean's list. b) Find the probability that the student , given that the student made the Dean's list. c) Find the probability that the student , given that the student did not make the Dean's list.
Answers
Answer:
(a) The probability that the student made the Dean's list is 0.1655.
(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.
(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.
Step-by-step explanation:
The complete question is:
Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.
a) Find the probability that the student made the Dean's list.
b) Find the probability that the student came from a private high school, given that the student made the Dean's list.
c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.
Solution:
Denote the events as follows:
A = a student attended public high school
B = a student attended private high school
C = a student was home schooled
D = a student made the Dean's list
The provided information is as follows:
P (A) = 0.71
P (B) = 0.21
P (C) = 0.08
P (D|A) = 0.16
P (D|B) = 0.19
P (D|C) = 0.15
(a)
The law of total probability states that:
[tex]P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})[/tex]
Compute the probability that the student made the Dean's list as follows:
[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)[/tex]
[tex]=(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655[/tex]
Thus, the probability that the student made the Dean's list is 0.1655.
(b)
Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:
[tex]P(B|D)=\frac{P(D|B)P(B)}{P(D)}[/tex]
[tex]=\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411[/tex]
Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.
(c)
Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:
[tex]P(C^{c}|D^{c})=1-P(C|D^{c})[/tex]
[tex]=1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185[/tex]
Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.
A wildlife biologist examines frogs for a genetic trait that is linked to sensitivity to an industrial toxin in the environment. Suppose exposure to the toxin tends to increase the prevalence of the genetic trait in the population of frogs. Previous research has established that this trait is usually found in about 2/10 of all frogs in a `clean' environment. Suppose a location is suspected of contamination. A sample of 10 frogs are collected, then examined for the genetic trait. We are asked to interpret the data collected and determine whether there is evidence suggesting contamination. What is the fewest number of frogs in the sample with the trait (number of successes) for which we can conclude the area is contaminated?
Answers
Answer:
3
Step-by-step explanation:
Usually, when there is contamination the smallest amount can have huge ramifications in the data collected. In this scenario, if in a "clean" environment the trait is found in 2/10 frogs then anything above this number should be considered contaminated. This is because data above this ratio would be considered uncommon or rare and this unique occurrence can be most likely tied to the only new factor which would be the contamination. Therefore the minimum number of frogs with this trait in the sample would be 3.
-2 = 3у – 18 — 5y
Solve for y
Answers
2y=-18+2
2y=-16
Y=-8
Find the reciprocal: 5/6
A. 1/6
B. 1/5
C. 5/6
D. 6/5
Answers
Answer:
D
Step-by-step explanation:
just flip the fraction
Answer:
D
Step-by-step explanation:
The reciprocal is just the fraction flipped.
if the school is havinng a pizza party they have 6,847 each kid will have 3 slices of the pizza how many slices of pizza the school need to order so each kid can have 3 slices help pls i got class at 8:30
Answers
what is the justification for Step 1 in the solution process?
Answers
Answer:
mulitply
Step-by-step explanation:
PEMDAS
mutiply
divide
add
and subtract
What is the correct order of the numbers from least to greatest. 0, -3/2, 7/3, 2.1, -2
Answers
Answer:
-3/2, -2, 0, 2.1, 7/3
Step-by-step explanation:
Please correct me if I am wrong. Thank you.
Which interval notation represents the set of all numbers greater than 0 and less than or equal to 3?
Answers
Answer:
(0,3)
Step-by-step explanation [0,3] indicates that the numbers are greater or equals to 0 and less than or equals to 3; while (0,3) leaves out the equal sign
How to Solve this??! 6x-2=x+13
Answers
Answer:
x=3
Step-by-step explanation:
We are given the equation, 6x-2=x+13.
1. 6x=x+15
2. 5x=15
3. x=3
Hope this helps! Good luck on your assignment!
Answer: x=3
Step-by-step explanation:
6x-2=x+13
First get both x’s on one side
We are going to subtract x from both sides
5x-2=13
Now we want to get 5x alone
We are going to add 2 to both sides
5x=15
Now we want to get x alone
We are going to divide by 5
x=3
From house to his job as a janitor, you can walk in a straight line. In the afternoon he has to stop twice on his way home. His first stop is at the bodega to get something to eat. The bodega is exactly halfway between his house and the school. The second stop will be at OWL Barbershop for his haircut. The OWL Barbershop location partitions the way from Wilfred’s house and job in the ratio 3:1. The coordinates of his house are H (-3, -4) and his job coordinates are J(5, 0). Please use B to represent the Bodega and O to represent OWL Barbershop.
Answers
Answer:
The coordinates of Bodega is B(1,-2)
The coordinates of OWL Barbershop is O(3,-1)
Step-by-step explanation:
Coordinates of House H = (-3,-4)
Coordinates of Job J= (5,0)
His first stop is at the bodega to get something to eat. The bodega is exactly halfway between his house and the school.
Let B to represent the Bodega
Now to find coordinates of Bodega we will use use mid point formula since bodega is exactly halfway between his house and the school.
[tex]x=\frac{x_1+x_2}{2} , y = \frac{y_1+y_2}{2}\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\x=\frac{-3+5}{2} , y = \frac{-4+0}{2}\\x=1, y = -2[/tex]
So, The coordinates of Bodega is B(1,-2)
Now we are given that The OWL Barbershop location partitions the way from Wilfred’s house and job in the ratio 3:1.
Le O to represent OWL Barbershop.
We will use section formula
[tex]x=\frac{mx_2+nx_1}{m+n} , y =\frac{my_2+ny_1}{m+n}\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\m:n=3:1\\x=\frac{3(5)+1(-3)}{3+1} , y =\frac{3(0)+1(-4)}{3+1}\\x=3,y=-1[/tex]
So, The coordinates of OWL Barbershop is O(3,-1)
5. If mZWXZ = (5x + 3)", mZZXY = (8x - 4)", and
ZWXY is a right angle, find each measure.
W
Х
z
Y
mZWXZ =
mZZXY =
Answers
Answer:
m∠WXZ = 38°
m∠ZXY = 52°
Step-by-step explanation:
In the question
∠WXZ and ∠ZXY are two adjacent angles and formed together ∠WXYThat means the measure of ∠WXY equal the sum of measures of ∠WXZ and ∠ZXY∵ ∠WXY is a right angle
→ That means its measure is 90°
∴ m∠WXY = 90°
∵ m∠WXZ + m∠ZXY = m∠WXY
∵ m∠WXZ = (5x + 3)°
∵ m∠ZXY = (8x - 4)°
∵ m∠WXY = 90°
→ Substitute their values in the equation above
∴ (5x + 3) + (8x - 4) = 90
→ Add the like terms in the left side
∵ (5x + 8x) + (3 - 4) = 90
∴ 13x + (-1) = 90
∴ 13x - 1 = 90
→ Add 1 to both sides
∴ 13x - 1 + 1 = 90 + 1
∴ 13x = 91
→ Divide both sides by 13
∴ [tex]\frac{13x}{13}=\frac{91}{13}[/tex]
∴ x = 7
→ To find the measure of each angle substitute x by 7 in their measures
∵ m∠WXZ = 5x + 3
∴ m∠WXZ = 5(7) + 3
∴ m∠WXZ = 35 + 3
∴ m∠WXZ = 38°
∵ m∠ZXY = 8x - 4
∴ m∠ZXY = 8(7) - 4
∴ m∠ZXY = 56 - 4
∴ m∠ZXY = 52°
What is the equation of the line that passes through the point (-8,5) and has a slope
of o?
Answers
Answer: y = 5
Step-by-step explanation:
If the slope is 0, the graph of the line is a horizontal line (parallel to the x-axis). 0 slope means it is flat.
Here it passes through the y-axis at +5 and passes through every value of x.
A rectangle has a side length of 2 5/8 feet and 3 1/5 feet. Find the perimeter of the rectangle.
Answers
Answer: 2
Step-by-step explanation: ( l + w )
plz help me with this problem I'm pretty confused.
Answers
Answer:
m∠1 = 40°
Step-by-step explanation:
Measures of angle 1 and angle 2 are examples alternate exterior angles. Alternate exterior angles are basically a pair of angles that are outside the parallel lines and are on opposite sides of the transversal. In other words, alternate exterior angles are congruent to each other.
Since we are given that measure of angle 2 is 40°. Measure of angle 1 has to be 40° because both angle 1 and angle 2 are alternate exterior angles.
Michelle has some dimes and quarters. If she has 22 coins worth a total of $2.80, how many of each type of coin does she have?
Answers
Answer:
she has 4 quarters and 18 dimes
Answer:
16 dimes and 8 quarters
Step-by-step explanation:
.25x8=2
.05x16=.8
$2+$.8=$2.80
What is the most simplified expression for 4 c squared d + 3 d c minus 2 (d c squared + c d) + 6 c squared d squared?
A. 2 c squared d + d c + 6 c squared d squared
B. 2 c squared d + 5 d c + 6 c squared d squared
C. 3 c squared d + 3 d c + 6 c squared d squared + c d
D. 3 c squared d + 2 d c + 6 c squared d squared minus 2 cd
Answers
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Consider the enlargement of the parallelogram. A smaller parallelogram with side lengths of one-third foot and x feet. A larger parallelogram with side lengths 8 feet and 6 feet. Set up a proportion to solve for the missing measure of the original parallelogram. Which side of the original parallelogram corresponds to the 6 ft side of the enlarged parallelogram? What is the second step in solving the proportion? What is the value of the missing measure?
Answers
Answer:
Enlargement rate is 24
Step-by-step explanation:
Divide 8 by one third to get the enlargement rate. I hope this helps:)
Answer:
Which side of the original parallelogram corresponds to the 6 ft side of the enlarged parallelogram? ITS IS x ft
What is the second step in solving the proportion? IT IS cross multiply
What is the value of the missing measure? IT IS 1/4
Step-by-step explanation:
i got this right
What is the largest three-digit number divisible by 24 and 54?
Answers
Answer:
The largest three-digit number divisible by 24 and 54 is:
864Step-by-step explanation:
To identify the largest number what I did was dividing 999 (the largest whole three-digit number of all) in the first number given (24):
[tex]\frac{999}{24}=41.625[/tex]With this number, you know that you must multiply 24 by a number like 41 or less until you find a number that can be divisible by 54 and obtain a whole number, so:
24*41= 984/54= 18.22 (how the number obtained is not a whole number, this is not the correct).24*40= 960/54= 17.77 (this is not).24*39= 936/54= 17.33 (this is not).24*38= 912/54= 16.88 (this is not).24*37=888/54= 16.44 (this is not).24*36= 864/54= 16 (This is the correct).Now, you have identified that the number 864, you can prove it by dividing this in 24 and 54:
[tex]\frac{864}{24}=36[/tex][tex]\frac{864}{54}= 16[/tex]
select the answers below that are equivalent to 18/30
A.15/25
B.6/11
C.3/4
D.3/5
E. 9/15
Answers
Answer:
A, D ,E
Step-by-step explanation:
18/30
Divide the top and bottom by 6
3/5
A.15/25 Divide top and bottom by 5 = 3/5
B.6/11 cannot be simplified
C.3/4 cannot be simplified
D.3/5 cannot be simplified
E. 9/15 divide top and bottom by 3 = 3/5
3. A savings account is started with an initial deposit of $3000. The account earns 9% interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach 1 million. Show your work.
Note: 1 million is a 1 with 6 zeros. Note2: you must use log functions to solve.
Answers
Answer:
See below
Step-by-step explanation:
GivenDeposit = $3000Interest rate = 9% compoundedNumber of years = tNumber of compounds = 1 per year Solution(a) the equation
f(t) = 3000*(1.09)^t(b) If f(t) = 1000000
1000000 = 3000*(1.09)^t(1.09)^t = 1000000/3000(1.09)^t = 333.3333log (1.09)^t = log 333.3333t log 1.09 = 2.52290.03742t = 2.5229t = 2.5229/0.03742t = 67.4 ≈ 68 yearsI REALLY NEED HELP IF NOT I'M GOING TO FAIL
Answers
Answer:
1. x > 9
2. n < 5
3. b > 2
4. p < 4
5. p < -2
6. m > 0
Step-by-step explanation:
1.
x - 2 - 2 > 5
x - 4 > 5
x > 5 + 4
x > 9
2.
5 + n < 2 x 5
n < 10 - 5
n < 5
3.
50b > 100
b > 100 : 50
b > 2
4.
-5 + p + 2 < 1
p < 1 + 3
p < 4
5.
p + 6 + 8 < 12
p + 14 < 12
p < 12 - 14
p < -2
6.
80m - 64 - 2 > -66
80m > -66 + 66
m > 0:80
m > 0
What do you know about distance? math
Answers
Answer: Mathematical distance is defined as the amount of space between two points. This distance can be calculated using the distance formula, which is just a derivation of the Pythagorean theorem, which is used to find the length of any one side of a right triangle when you know the other two sides
Step-by-step explanation:
Can someone please help, ty!!
Answers
Answer:
(-1,0)
Step-by-step explanation:
Answer:
(-1, 0)
Step-by-step explanation:
The x-axis is the horizontal line in bold. It's basically asking what points in the form (x,y) are touching said line.
So we use our eyes and determine that the line intercepts the x-axis at -1 because that vertical bold line is the y-axis and it determines that the left side of the graph is negative and the right side is positive.
Since it is an x-intercpet, when the y-value is 0 the y-term in
(x,y) is 0
and the x-term would be the -1
Can you help me fill the graph please?
Answers
Answer:
8=6 2/5
50=40
100=80
Step-by-step explanation:
8x4/5=6 2/5
4x10=40 so 5x10=50 (I got this from the second row)
5x20=100 so 4x20=80 (also from second row)
What is the solution to the system of equations?
6x – 9y = 16
2x – 3y = 7
A) (5, 1)
B) (2, -1)
C) (3,
2
9
)
D) no solution
Answers
Answer:
no solution
Step-by-step explanation:
[1] 6x - 9y = 16
[2] 2x - 3y = 7
// Solve equation [2] for the variable x
[2] 2x = 3y + 7
[2] x = 3y/2 + 7/2
// Plug this in for variable x in equation [1]
[1] 6•(3y/2+7/2) - 9y = 16
[1] 0 = -5 => NO solution
No solution
xanthe ran one quarter of a kilometer. She took a 5 minute rets, then ran another ten eighths of a kilometer. How many kilometers did she run in total.
Answers
Answer:
1 1/2 kilometers
Step-by-step explanation:
She ran 1/4 of a kilometer and then ran another 10/8 kilometer.
The 5 minute rest is to throw people off, so ignore it.
10/8 can simplify to 5/4 kilometers, so you can add that to the first quarter of a kilometer she already traveled.
5/4 plus 1/4 equals 6/4.
6/4 can be simplified to 3/2 which is equal to one and one half.
1 1/2
Hope this helps!
On Monday, Allison’s bank account showed $0. She made 5 transactions that were all the same amount between Monday and Friday. If her bank account showed -$120 on Friday, what was the amount of each transaction?
Answers
Answer: $24
Step-by-step explanation: if you divide $120 by 5 then you get $24
Can you help me solve this
Answers
Step-by-step explanation: