Which of the following functions are their own inverses? Select all that apply.
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
d. d(p) = 1/x^2
Answers
The appropriate choices are ...
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
Answer:
a,b and c.
Step-by-step explanation:
We have to find the the functions that are their own inverses.
a.t(p)=p
Then the inverse function of given function is
[tex]p=t^{-1}(p)[/tex]
Therefore, the given function is inverse function of itself.
Hence, option a is true.
b.y(j)=[tex]-\frac{1}{j}
Let y(j)=y then we get
[tex]y=-\frac{1}{j}[/tex]
[tex]j=-\frac{1}{y}[/tex]
[tex]j=-\frac{1}{y(j)}[/tex]
[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]
[tex]j=j[/tex]
Hence, the function is inverse of itself.Therefore, option b is true.
c.[tex]w(y)=-\frac{2}{y}[/tex]
Suppose that w(y)=w
Then [tex]w=-\frac{2}{y}[/tex]
[tex]y=-\frac{2}{w}[/tex]
[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]
[tex]w(y)=w[/tex]
[tex]w(y)=-\frac{2}{y}[/tex]
Hence, the function is inverse function of itself.Therefore, option c is true.
d.[tex]d(p)=\frac{1}{x^2}[/tex]
Let d(p)=d
If we replace [tex]\frac{1}{x^2}by p then we get
[tex]d=\frac{1}{x^2}[/tex]
[tex]x^2=\frac{1}{d}[/tex]
[tex]x=\sqrt{\frac{1}{d}}[/tex]
[tex]x=\sqrt{\frac{1}{d(p)}[/tex]
Hence, the function is not self inverse function.Therefore, option d is false.
Related Questions
A six-sided die is thrown 50 times. the numbers of occurrences of each face are shown below. face 1 2 3 4 5 6 count 12 5 9 11 6 7 can you conclude that the die is not fair?
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An executive invests $22,000, some at 8% and the rest at 6% annual interest. If he receives an annual return of $1,660, how much is invested at each rate?
Answers
0.08n + 0.06(22000-n) = 1660
Multiply both sides by 100:
8n + 132000-6n = 166000
Simplify:
2n + 132000 = 166000
Isolate n:
2n = 34000
n = 17000
8% invested: 17000
6% invested: 5000
The gpa at the super university has a normal distribution with a mean 2.29 and standard deviation 1.29 to be an honors student at this university your GPA has to be in the top 20% what is the smallest gpa you need to have to be an honors student?
Answers
[tex]\mathbb P(G\ge g)=0.20[/tex]
where [tex]G[/tex] is a random variable denoting GPA scores. Transform [tex]G[/tex] to the standard normal random variable [tex]Z[/tex] using
[tex]Z=\dfrac{G-\mu_G}{\sigma_G}\iff G=\mu_G+\sigma_GZ[/tex]
where [tex]\mu_G[/tex] and [tex]\sigma_G[/tex] are the mean and standard deviation of [tex]G[/tex], respectively. Now
[tex]\mathbb P(G\ge g)=\mathbb P\left(Z\ge\dfrac{g-2.29}{1.29}\right)=0.20[/tex]
Using the inverse CDF for the standard normal distribution, we find that the corresponding critical value is about 0.8416, which means
[tex]\implies\dfrac{g-2.29}{1.29}\approx0.8416\implies g\approx3.3757[/tex]
In a tournament team A won 7 less games than Team B, and Team B won exactly three times as many games as team C. If If Team C won g games, how many games did Team A win?
Answers
Team A won 3g - 7 games, where g is the number of games won by Team C. To determine the number of games Team A won, multiply the number of games Team C won by 3 and subtract 7.
Let's denote Team C's number of wins as g. According to the information provided, Team B won three times as many games as Team C, which can be expressed as 3g. It is also stated that Team A won 7 fewer games than Team B. So, if Team B won 3g games, then Team A won 3g - 7 games.
To find the number of games Team A won, simply multiply the number of games Team C won by 3 and subtract 7 from that total. This can be represented by the algebraic expression A = 3g - 7, where A represents the number of games won by Team A and g represents the number of games won by Team C.
Find the length of the arc shown in red. Leave your answer in terms of x.
Answers
S = r * theta
Where:
R: radius
Theta: central angle
For this case we have that the arc length is:
S = (30/180) * 9 * pi
S = (3/2) pi
Answer:
The length of the arc shown in red is:
S = (3/2) pi
do the scatter plot .........................
Answers
1 190
2 220
3 200
4 330
5 300
6 410
7 450
8 410
9 530
10 650
11 570
12 650
13 750
14 720
15 700
16 800
The scatter diagram shows that as the weeks increase, sales increase.
Answer:
See attached image.
what is the minimum value that the graph of y=sin x assumes?
Answers
Tripp and Rico are two dogs. Tripp weighs exactly 35 pounds more than Rico. Together, they weigh exactly 49 pounds. How much does each dog weigh? Please use Two-step equations!!!! plz, help!
Answers
We know that Tripp weights 35lbs more than Rico, or:
[tex]t=r+35[/tex]
We also know that the total weight of both dogs is 49lbs.:
[tex]t+r=49[/tex]
Now, by substitution:
[tex](r+35)+r=49[/tex]
[tex]2r+35=49[/tex]
[tex]2r+35-35=49-35[/tex]
[tex]2r=14[/tex]
[tex]r=\frac{14}{2}[/tex]
[tex]r=7[/tex]
Rico weighs 7lbs.
Then:
[tex]t=r+35[/tex]
[tex]t=7+35[/tex]
[tex]t=42[/tex]
Tripp weighs 42lbs.
To check our work:
[tex]t+r=49[/tex]
[tex]42+7=49[/tex]
[tex]49=49[/tex] CHECK!
Using a system of equations, it is found that Tripp weighs 42 pounds and Rico weighs 7 pounds.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Tripp's weight.Variable y: Rico's weight.Tripp weighs exactly 35 pounds more than Rico, hence:
x = 35 + y.
Together, they weigh exactly 49 pounds, hence:
x + y = 49
35 + y + y = 49
2y = 14 -> y = 7
x = 35 + y -> x = 42
Hence, Tripp weighs 42 pounds and Rico weighs 7 pounds.
To learn more about a system of equations, you can check https://brainly.com/question/24342899
9=7x-13x-21 show step by step
Answers
9 = 7x - 13x - 21 becomes 9 = - 6x - 21
Now add 21 to both sides to isolate our coefficient and variable.
- 6x -21 + 21 = 9 + 21
The 21s on the left cancel out.
- 6x = 30
Now divide both sides by - 6 to isolate the variable.
x = 30 / - 6
x = - 5
Instructions.find the volume and surface area of the rectangular prisms
Answers
SA = 2L + 2W + 2H
If the perimeter of a rectangle is 52 cm and the area is 165 square cm, then what are the dimensions of the rectangle?
Answers
Answer:
11 cm by 15 cm
Step-by-step explanation:
The perimeter is double the sum of length and width, so that sum is 26 cm. The area is the product of length and width, so you want to find two numbers whose product is 165 and whose sum is 26.
165 = 1·165 = 3·55 = 5·33 = 11·15
The numbers in the last factor pair total 26. These are the dimensions.
The dimensions are 11 cm by 15 cm.
Create a box and whisker plot for the average daily temperatures in Tucson, Arizona, in December: 67, 57, 52, 51, 64, 58, 67, 58, 55, 59, 66, 50, 57, 62, 58, 50, 58, 50, 60, 63
Answers
First, we'll arrange the number sequence from lowest to highest - 0,50,50,51,52,55,57,57,58,58,58,58,59,60,62,63,64,66,67,67.
Second, we'll find the median Q2 - (58+58) / 2 = 58
Third, we'll take the middle numbers before the median as our lower quartile Q1 - (52+55) / 2 = 53.5
Fourth, we'll take the middle numbers after the median as our upper quartile Q3 - (62+63) / 2 = 62.5
Then we graph (see attached picture)
Normal Distributions
I couldn't see the whole graph in the answer above, but using the quartiles, I chose graph A and that was right.
1. b. mean=75.8, median=76.5, mode=63
2. a. dots at 50, 53.5, 58, 62.5, and 67
3. c. 30th percentile=105, 90th percentile=176.
This is a controversial question because some of the numbers repeat, but as of 5/19, answer c is right.
4. d. mean=8, variance=18.3, standard deviation=4.3
5. a. 2
6. b. 22%
7. d. a^6-30d^5+375d^4-2,500d^3+9,375d^2-18,750d+15,625
8. a. 93%
9. b. 16%
10. c. 84%
The minimum value of a function is the smallest y-value of the function. A. True B. False
Answers
Cynthia invests some money in a bank which pays 5% compound interest per year. She wants it to be worth over £8000 after 3 years. What is the smallest amount, to the nearest pound, she can invest?
Simple steps please ?
Answers
A=p(1+r/100)^n
where:
A=future amount
p=principle
r=rate
n=time
From the question:
A=£8000, r=5%, n=3
thus plugging the values in the formula and solving for p we get:
8000=p(1+5/100)6n
8000=1.157625p
thus
p=6910.700
Hence the smallest amount is £6910.70~£6910
food costs are expected to rise 6% each month for the next year. Which series correctly depicts the cost (to the nearest cent) for the next three months if the current cost is $150 per month?
a. $150.00 + $159.00 + $168.00
b.$150.00 + $159.00 + $168.54
c.$159.00 + $168.00 + $177.00
d.$159.00 + $168.54 + $178.65
Answers
y = 150 * (1.06) ^ t
For the first month we have:
y = 150 * (1.06) ^ 1
y = 159 $
For the second month we have:
y = 150 * (1.06) ^ 2
y = 168.54 $
For the third month we have:
y = 150 * (1.06) ^ 1
y = 178.65 $
Answer:
d. $ 159.00 + $ 168.54 + $ 178.65
Answer:
the final answer is the last option, D
Step-by-step explanation:
Use forward or backward substitute to conjecture a closed formula which describes the nth term of the sequence an = an-1 – n, where a0 = 4.
Answers
an=a+d(n-1)
where
a=first term
d=common difference
n=number of terms
From the formula given:
a=4
d=n
thus the formula will be:
an=a+n(n-1)
an=4+n(n-1)
If (2 − 3i) + (x + yi) = 6, what is x + yi? 4 + 3i 4 − 3i -4 − 3i -4 + 3i 4x + 3i
Answers
(2 − 3i) + (x + yi) - (2 − 3i) = 6 -(2 − 3i)
(x + yi) = 6 - (2 - 3i)
Open the parenthesis taking care of the signs
(x + yi) = 6 - (2 - 3i)
= 6 - 2 + 3i
= 4 + 3i
Arthur took out a 20 year loan for $60,000 at an APR of 4.4% compounded monthly. Approximately how munch would save if he paid it off 3 years early Apex A. $4516.32,B. $1129.08,C. $376.36,D.$877.96
Answers
Answer:
D. $877.96
Step-by-step explanation:
You want the amount saved if a 20 year loan of $60,000 at 4.4% is paid off 3 years early.
PaymentThe monthly payment on the loan can be found from ...
[tex]A=\dfrac{Pr}{12(1-(1+r/12)^{-12t})}[/tex]
where P is the loan amount at rate r for t years.
For the 20 year loan of $60,000 at 4.4%, the payment is calculated as ...
[tex]A=\dfrac{60000(.044)}{12(1-(1+0.044/12)^{-12\cdot20})}=\dfrac{220}{0.584549}=376.3585[/tex]
Balance dueAfter 204 payments on the loan, the remaining balance due is ...
[tex]A=P\left(1-\dfrac{(1+r/12)^n-1}{(1+r/12)^{12t}-1}\right)\\\\\\A=60000\left(1-\dfrac{1.0036667^{204}-1}{1.0036667^{240}-1}\right)=12671.04[/tex]
SavingsThe remaining 36 payments on the loan come to about ...
36 × 376.3585 ≈ 13548.91
So, the savings from early payoff is about ...
13548.91 -12671.04 ≈ 877.86
Choice D, $877.96, is the best match for this value.
__
Additional comment
The actual savings will depend on the details of rounding of intermediate values in the calculation, and on the timing of the early payment. If the loan is amortized over 17 years, so more is paid each month, the savings can be more than $5000.
Here, we have calculated the savings on the assumption that payment number 204 includes the payoff amount.
Using the loan formula, monthly payments are $458.14. Remaining balance after 17 years is approximately $58,214.19. The savings would be approximately $1,785.81. The closest option to this calculation is C. $376.36
To calculate the amount saved by paying off the loan 3 years early, we need to find out the remaining balance of the loan after 17 years (20 years - 3 years). Then, we compare the remaining balance to the original balance to find the savings.
Let's break down the steps:
1. Find the monthly interest rate (r):
[tex]\[ r = \frac{4.4\%}{12} = \frac{0.044}{12} \][/tex]
2. Calculate the total number of payments (n):
[tex]\[ n = 20 \times 12 = 240 \text{ months} \][/tex]
3. Use the formula for the monthly payment (PMT) of a loan:
[tex]\[ PMT = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \][/tex]
where:
P = principal amount (loan amount)
r = monthly interest rate
n = total number of payments
We'll use PMT to find out the monthly payment Arthur has to make.
4. Use the monthly payment (PMT) to find the remaining balance after 17 years (204 months).
5. Finally, calculate the savings by comparing the remaining balance to the original loan amount.
Let's do the calculations:
1. Monthly interest rate:
[tex]\[ r = \frac{0.044}{12} = 0.00367 \][/tex]
2. Total number of payments:
[tex]\[ n = 20 \times 12 = 240 \text{ months} \][/tex]
3. Monthly payment (PMT):
[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot (1 + 0.00367)^{240}}{(1 + 0.00367)^{240} - 1} \][/tex]
[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot (1.00367)^{240}}{(1.00367)^{240} - 1} \][/tex]
[tex]\[ PMT = \frac{60000 \cdot 0.00367 \cdot 1.937}{1.937 - 1} \][/tex]
[tex]\[ PMT = \frac{429.33}{0.937} \][/tex]
[tex]\[ PMT= 458.14 \][/tex]
4. Remaining balance after 17 years (204 months):
[tex]\[ PV = \frac{PMT \cdot (1 - (1 + r)^{-n})}{r} \][/tex]
[tex]\[ PV = \frac{458.14 \cdot (1 - (1 + 0.00367)^{-204})}{0.00367} \][/tex]
[tex]\[ PV = \frac{458.14 \cdot (1 - 0.533)}{0.00367} \][/tex]
[tex]\[ PV = \frac{458.14 \cdot 0.467}{0.00367} \][/tex]
[tex]\[ PV = \frac{213.94}{0.00367} \][/tex]
[tex]\[ PV = 58214.19 \][/tex]
5. Savings:
Savings = 60000 - 58214.19
Savings ≈ 1785.81
So, Arthur would save approximately $1785.81 by paying off the loan 3 years early.
The closest option to this calculation is C. $376.36
I really really need help with this please.
Answers
= 1 + 3 + 3^2 + 3^3 + 3^4
= (3^5 - 1) / (3 - 1)
= 242 / 2
= 121
Since we included Tle-nle as the 1st generation, we will only compute up to the 4th power. If it is until the 6th generation, add 3^5 to the equation.
can someone help me 3y-20=8y
Answers
Step 1: Collect the y-terms.
To collect the y-terms, you'll need to subtract 3y from both sides.
3y - 20 - 3y = 8y - 3y
-20 = 5y
Step 2: Isolate y.
Now that there is only one variable term, you must isolate the variable by dividing the term by the coefficient of the variable.
-20 ÷ 5 = 5y ÷ 5
-4 = y
Answer:
y = -4
Sandra is traveling 19 mph on her bicycle. After 2 hours, how far will she have traveled?
Answers
to find total distance, multiply speed by time:
total distance = 19 mph x 2 hours = 38 total miles
How can 52/9 be expressed as a decimal?
Answers
For 52/9 to be expressed as a decimal, you need to divide the fraction.
52/9 = 5.78 (rounded by the 1hundreds in the decimals place).
what is the factored form of the expression? 4x^2-81y^2
Answers
[tex](2x)^2-(9y)^2 [/tex]
[tex](2x+9y)(2x-9y)[/tex]
[tex]4x {}^{2} - 81y {}^{2} [/tex]
Write the expressions 4 & 81 in exponential form with an exponent of 2.
[tex] = 2 {}^{2} x {}^{2} - 9 {}^{2} y {}^{2} [/tex]
Multiply the terms with equal exponents by multiplying their bases.
[tex] = (2x) {}^{2} - (9y) {}^{2} [/tex]
Using
[tex]a {}^{2} - b {}^{2} = (a - b)(a + b)[/tex]
Factor the expression.
[tex] = (2x - 9y) \times (2x + 9y)[/tex]
housing prices in a certain neighborhood average at 97.86 per square foot. If one house in this neighborhood is 1400 square feet, what should it be priced at?
Answers
(97.86/ft²)×(1400 ft²) = 97.86×1400 = 137,004
Jean gets an allowance of $15 each month plus an extra $2 for each chore she completes around the house. How much allowance will she earn if she does x chores in a month?
a. 15x + 2 dollars
b. 2x dollars
c. 2x + 15 dollars
d. 17x + 15 dollars
Answers
What is value of M in the figure below?
Answers
m/5 = (14 +5)/m
m^2 = 5*19 = 95
The best choice is ...
C. √95
Based on the right-angled triangle, the value of m is equal to: C. [tex]\sqrt{95}[/tex].
What is the geometric mean (leg) theorem?According to the geometric mean (leg) theorem, the length of the leg of a right-angled triangle is the geometric mean between its hypotenuse and the segment of the hypotenuse which is adjacent to that leg.
Mathematically, the geometric mean (leg) theorem can be modeled by the following formula;
Hypotenuse/leg = leg/part
where;
hypotenuse = 14 + 5 = 19
leg = m
part = 5
By applying geometric mean (leg) theorem, the length of the part (x) can be calculated as follows;
19/m = m/5
By cross-multiplying, we have the following:
[tex]m^2=19 \times 5\\\\m^2=95\\\\m=\sqrt{95}[/tex]
Read more on geometric mean here: brainly.com/question/26257841
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which picture justifies wheather -3x(5-4)+3(x-6) is equivalent to -12x-6
Answers
They are not equivalent because if you simplify the first equation you get:
- 3x(5 - 4) + 3(x - 6)
- 3x(1) + 3x - 18
- 3x + 3x - 18
0 - 18
-18
-18 ≠ - 12x - 6
Answer:
Your answer would be a. or the first problem.
Step-by-step explanation:
"a fair coin is tossed 5 times. what is the probability of exactly 4 heads?"
Answers
if a 9 inch pizza serves 4 people, how many people will a 12 inch pizza serve?
Answers
Identify the function in which Y varies directly with X