Functions whose inverses are also functions.
What is inverse function?Inverse function is represented by [tex]f^{-1}[/tex] with regards to the original function and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.
If a horizontal line intersects the original function in a single region, the function is a one-to-one function and inverse is also a function.
Every function has an inverse, but not every inverse will be a function. The inverse may fail the vertical line test. If the original function is a one-to-one function, then its inverse will be a function. A one-to-one function not only passes the vertical line test, it also passes a horizontal line test.
Therefore, functions whose inverses are also functions.
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A car salesman is stringing banners from the top of the roof to a fence pole 20 feet away. The top of the roof is 29 feet from the ground. The fence pole is 8 feet high. How many feet of banner rope does he need to reach from the rooftop to the fence pole?
Answer:
29ft
Step-by-step explanation:
If some one makes and many slices of toast of toast as possible in 4 minutes and 40 seconds how many slices they can make?
Therefore , the solution of the given problem of expression comes out to be probably 4 slices.
Who or what is expression?In mathematics, it is possible can multiply, division, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression. Expressions and phrases can be contrasted.
Here,
you figure if a toaster takes about 1-2 minutes to toast a piece of bread and a toaster usually can fit 2 slices at a time i would say 4.
Preheat oven broil to high. Move oven rack to highest position.
Place sliced bread on an ungreased baking sheet. 4 slices of bread.
Broil bread for 1 minute, or until golden brown, then flip and broil for another 20-30 seconds. ...
Top with butter, jam, or any other favorite topping!
The temperature needed for the hot ambient air in a toaster, which makes the bread turn brown, is around 310°F (146°C). The heating element inside a toaster is a nickel-chromium alloy. The electrical current that runs through it heats it to make it red hot, with a temperature of 1,100°F to 1,200°F (519°C to 566°C).
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- Complete the function table for f(x) = 3x + 2.
groce
x
-2
-1
0
1
opies of graph pap
The value of the function f(x) at x = - 2, - 1, 0, 1 are - 4, - 1, 2, 5.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f(x) = 3x + 2.
Now,
At x = - 2, f(x) = 3(-2) + 2 ⇒ f(x) = - 4.
At x = - 1, f(x) = 3(-1) + 2 ⇒ f(x) = - 1.
At x = 0, f(x) = 3(0) + 2 ⇒ f(x) = 2.
At x = 1, f(x) = 3(1) + 2 ⇒ f(x) = 5.
This can also be written in the form of ordered pairs
(- 2, - 4), (- 1, - 1), (0, 2), (1, 5).
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A solid with volume 12 cubic units is dilated by a scale factor of 3. What is the new volume?
i will give Brainiest if you are right
Answer:
-4
Step-by-step explanation:
please mark brainliest
Answer:
-4
Step-by-step explanation:
So we can start with -2 + 3, (negatives mean -, and positives mean +)
= 1
Then, 1 - 4
= -3
-3 - 1
= -4
hope this helps :)
Please answer correctly with a fair explanation, I will give you brainliest.
Answer:
5 and 6
Step-by-step explanation:
We know that the square root of 36 is 6, so the square root of 35 must be between 5 and 6 as it is not a perfect square.
Mr. Wilson compares the quiz scores of her first-period math class and her second-period math class.
The third quartile of her second-period class is ______ more than the third quartile of her first-period class.
Answer:
and do you know the answer to this one
I really need this for a test
How do I get the width and area
Н
НОН
HHH
HHH
H
Но-н
нЩн
нон
HHH
HHH
HHH
What best describes these three molecules?
O They are not isomers.
O They are structural isomers.
O They are geometric isomers.
They are both structural and geometric isomers.
Answer:
Its B they are structural isomers
Step-by-step explanation:
Answer:
B) They are structural isomers.
Step-by-step explanation:
Got it right on Edge :D
Please help ASAP!!! Thank you!!
Answer:
-3/x-1
Step-by-step explanation:
Find the limit, if it exists.
lim (x - 3x2 + 3)
a.
8
C. -12
b. -1
d. None of these
Please select the best answer from the choices provided
Ο Α
B
Ο Ο Ο Ο
oo
Answer:
B. -1
Step-by-step explanation:
Edge 2021
In a chess club the probability that Shaun will beat Mike is 3/8 .
The probability that Shaun will beat Tim is 5/7 .
(Assume all the games are independent of one another)
If Shaun plays 1 game with Mike and then 1 game with Tim, what is the probability that Shaun loses both games?
Answer:
[tex]\frac{10}{56} = 0.1786[/tex] probability that Shaun loses both games
Step-by-step explanation:
Games are independent, so we find each separate probability, and multiply them.
In a chess club the probability that Shaun will beat Mike is 3/8.
So [tex]1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}[/tex] probability that Shaun loses.
The probability that Shaun will beat Tim is 5/7 .
So [tex]1 - \frac{5}{7} = \frac{2}{7}[/tex] probability that Shaun loses.
What is the probability that Shaun loses both games?
This is:
[tex]p = \frac{5}{8} \times \frac{2}{7} = \frac{5*2}{8*7} = \frac{10}{56} = 0.1786[/tex]
[tex]\frac{10}{56} = 0.1786[/tex] probability that Shaun loses both games
Consider these functions:
f(x) = x + 1
g(x)= 2/x
Answer:
its letter A.
[tex] \frac{2}{x + 1} [/tex]
Your driveway is rectangular in shape and measures 18 feet wide and 29 feet long. Calculate the area of your driveway.
a.
261 square feet
c.
250 square feet
b.
522 square feet
d.
500 square feet
Answer:
522 square feet
Step-by-step explanation:
Area is the term used to define the amount of space taken up by a 2D shape or surface. We measure area in square units : cm² or m². Area is calculated by multiplying the length of a shape by its width, so you mutiply 18 by 29 and got 522
Answer:
522
Step-by-step explanation:
Area of a rectangle = width times length
The length in this case is 29 feet, and the width is 18 feet.
29 times 18 = 522 square feet
a class is planning a field trip to the aquarium. The cost of a ticket is $25.95. With the cost of transportation, each student will pay $36.00 to go on the field trip. Jay wants to know how much he will pay for transportation. Which equation will help jay find the cost of transportation,t?
Answer:
25.95 + 36
Step-by-step explanation:
You don't have any options so the answer I would say is 25.95 + 36, or the other way around.
Hope this helped :]
2. What are the domain and range for the exponential parent function,
where b is a positive real number not equal to 1 and a > 0?
On solving the provided question, we can say that - the value of the given polynomials domain will be ( - infinity, 0)
what is domain?The range of values a function may accept is referred to as its domain. These numbers represent the x-values of a function like f. (x). The range of values that a function may operate on is referred to as its domain. The value that the function returns following the insertion of the x value is this set. A function containing the independent variable x and the dependent variable y is said to be y = f(x). A value of x is said to be in the domain of a function f if it can be used to successfully create a single value y utilizing the value of x for that purpose.
domain will be ( - infinity, 0)
range = (-infinity, +infinity)
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You may need to use the appropriate technology to answer this question. A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow. Hours of Sleep Age Group 39 or younger 40 or older Fewer than 6 36 34 6 to 6.9 60 57 7 to 7.9 79 77 8 or more 65 92 (a) Conduct a test of independence to determine whether hours of sleep are independent of age. State the null and alternative hypotheses. H0: Hours of sleep per night is independent of age. Ha: Hours of sleep per night is not independent of age. H0: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups. Ha: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups. H0: Hours of sleep per night is not independent of age. Ha: Hours of sleep per night is independent of age. H0: Hours of sleep per night is mutually exclusive from age. Ha: Hours of sleep per night is not mutually exclusive from age. Correct: Your answer is correct. Find the value of the test statistic. (Round your answer to three decimal places.) What is the p-value
Answer:
1) The null and alternative hypotheses.
H0: Hours of sleep per night is independent of age.
Ha: Hours of sleep per night is not independent of age.
Test Statistics χ²=4.009
The corresponding p-value for the test at χ²= 4.009 is 0.2604
Step-by-step explanation:
1) The null and alternative hypotheses.
H0: Hours of sleep per night is independent of age.
Ha: Hours of sleep per night is not independent of age.
2) The data is
≤ 39 ≥ 40 Total
6 hours 36 34 70
6.9-7 hours 60 57 117
7- 7.9 hours 79 77 156
8 hours or more 65 92 157
Total 240 260 500
3) The expected values are computed as follows
260×70/500=36.4
240×117/500 =56.16
260×117/500 =60.84
240×156/500 =74.88
260×156/500 =81.12
240×157/500=75.36
260×157/500 =81.64
4) The squared distances are calculated as
{(36 - 33.6)^2}/{ 33.6} = 0.171
{(34 - 36.4)^2}{ 36.4} = 0.158
{(60 - 56.16)^2}/{ 56.16} = 0.263
{(57 - 60.84)^2}/{ 60.84} = 0.242
{(79 - 74.88)^2}/{ 74.88} = 0.227
{(77 - 81.12)^2}/{ 81.12} = 0.209
{(65 - 75.36)^2}/{ 75.36} = 1.424
{(92 - 81.64)^2}{ 81.64} = 1.315
5) The significance level is set at α=0.05 for df = (4 - 1) (2 - 1) =3
degrees of freedom.
6) The critical region for this test is χ² = χ² >7.815
7) Test Statistics
χ²=i=∑(O ij −Eij )2/Eij
=0.171+0.263+0.227+1.424+0.158+0.242+0.209+1.315
= 4.009
8) Conclusion
As the calculated value χ² =4.009 does not lie in the critical region ≤χ² =7.815, null hypothesis is not rejected.
Therefore, we conclude that there is not enough evidence to accept the alternate hypothesis , at the α=0.05 significance level.
The p-value for the test at χ²= 4.009 is 0.2604
There are 90 new houses being built in a neighborhood last month 2/5
of them were sold this month 1/3 of the remaining houses were sold.How many houses are left to be sold?
The number of houses left to be sold is 12
How to calculate the number of houses left to be sold?There are 90 new houses built in the neighbourhood
2/5 were sold last month
2/5 × 90
= 18 × 2
= 36
1/3 of the remaining were sold this month
1/3 × 36
=12
Hence there are 12 houses left to be sold
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Glenn bought a $7 coffee and 10 granola bars at the airport. If he spent a total of $24, how much did each granola bar cost?
Answer:
1.7$
Step-by-step explanation:
To solve this, first subtract the coffee from the total cost, and then divide the cost by the amount of granola bars.
So first, subtract 7$ from 24(the coffee from the total cost):
24-7
=
17
Next divide the 17$ by the 10 granola bars:
17/10
=
1.7
So we know that the answer is each granola bar cost 1.7$
Hope this helps!
A bakery sells 5 apple muffins for every 2 bran muffins sold.Which table shows this ratio?
lex has $1,780.80 in his savings in his saving account that he opened 6 years ago his account has an annual interest rate of 6.8% compounded annually how much money did lex use to open his savings
Answer:
To find the principal, P we can use the same formula, A=P(1+rn)nt. We have the balance of the account, A, after 6 years, $1,780.80. The interest rate, r, is 6.8% (or 0.68 as a decimal) and is compounded annually, so n=1. The time, t, is 6, since we know he opened his account 6 years ago. Plug in the known values into the formula and solve for the missing variable, P.
Step-by-step explanation:
1,780.80 = P (1+0.0681 divided 1^(6)
1,780.80= 1.484P
1,200=P the principal amount Lex used to open his account 6 years ago
-2 3/4, -1 3/4, -3/5 < o > -2 3/4, -3/5, -1 3/4 cual es menor?
Therefore , the solution of the given question of fractions comes out to be 5th option -3/5.
What is fraction?An element of a fraction or ratio is a piece of a whole. The number of equally sized pieces into which the whole has been divided is represented by the denominator b, and the number of parts that are included is represented by the numerator a. The LCM of two fractions' denominators is the least common multiple (LCD) of those denominators.
Here,
Given:
2 [tex]\frac{3}{4}[/tex], -1 [tex]\frac{3}{4}[/tex], 3/5 , -2 [tex]\frac{3}{4}[/tex], -3/5, -1 , [tex]\frac{3}{4}[/tex],
Therefore , by seeing the above given numbers ,
We compare above number
and we get to know ,
The 5th number 3/5, comes out to be smallest number from the following given numbers.
Therefore , the solution of the given question of fractions comes out to be 5th option -3/5.
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What is the surface area of the rectangular prism?
Answer:
112 is your answer
Step-by-step explanation:
To calculate the surface area you have to count all of the squares. You can do this with these equations.
8 × 4 × 2 = 64
8 × 2 × 2 = 32
4 × 2 × 2 = 16
Next, add them up!
64 + 32 + 16 = 112
A Child wants to reach the cookies on the top shelf of the kitchen. The shelf is 1.5 m high. The cookie jar has a mass of 0.75 kg. what is the potential energy of the cookie jar before it is taken from the shelf?
Answer:
11.0325 J
Step-by-step explanation:
The formula for calculating Potential Energy is:
P.E. = mass * acceleration due to gravity * height
where mass is in kg
acceleration due to gravity is a constant at the surface of the earth = 9.8 m/sec^2
and height is in meters
Here:
P.E. = 0.75 kg * 9.8 meters/sec^2 * 1.5 meters
P.E. = 11.0325 kg*m^2/sec^2
Now kg*m^2/sec^2 = joules
so the answer is 11.0325 joules
The required potential energy of the jar is 11.0325 joules.
What is potential energy?Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases.
Given that,
The height of self h = 1.5 m.
The mass of cookie jar m = 0.75 kg.
To find the potential energy of jar,
Use formula of Potential Energy
Potential Energy = m × g × h
where m = mass is in kg
Ang g is gravity.
And the value of g at the surface of the earth = 9.8 m/sec²
and height is in meters
Substitute the values here,
Potential energy = 0.75 kg * 9.8 meters/sec² * 1.5 meters
Potential energy = 11.0325 kg x m²/sec²
Since, kg x m²/sec² = joules
Potential energy = 11.0325 joules.
Hence the required answer is 11.0325 joules.
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am is paying off his eight-year, $15,360 loan in semiannual installments. The loan has an interest rate of 9.58%, compounded semiannually, and a service charge of $1,294.64. Once the loan has been fully paid off, what percentage of the total finance charge will the service charge be? Round all dollar values to the nearest cent.
a.
5.48%
b.
8.43%
c.
18.55%
d.
15.65%
Please select the best answer from the choices provided
A
B
C
D
The percentage of the total finance charge on the loan that the service charge will be is about 15.65%. Option D is correct.
D. 15.56%
What is a loan?A loan is an item borrowed for a charged amount, such as an amount borrowed to be repaid with a specified interest fee.
The compound interest formula for the semiannual interest rate is presented as follows;
A = P·[1 + R/n]^(n·t)
Where;
P = The initial amount borrowed on loan = $15,360
t = The interest rate on the loan = 9.58% = 0.0958
n = The number of periods in a year = 2 for semiannual interest rate
t = The duration of the loan = 8 years
The equal semi annual installment (ESI) formula is presented as follows;
[tex]ESI = P\times \dfrac{\dfrac{r}{2} \times\left(1 + \dfrac{r}{2} \right)^n }{\left(1+\dfrac{r}{2} \right)^n-1}[/tex]
Therefore;
ESI = 15360 × ((0.0958/2)×(1 + 0.0958/2)¹⁶)/((1 + 0.0958/2)¹⁶-1) ≈ 1396.16
The total amount Sam pays = 16 × 1396.16 ≈ 22338.6
The finance charge ≈ 22338.6 - 15360 = 6978.6
The percentage of the finance charge represented the service charge is therefore;
(1294.64/(6978.6 + 1294.64))×100 ≈ 15.65%
The percentage of the total finance charge represented by the service charge is therefore about 15.65%
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In a bag of candy, Marsha found that there were 7 red, 8 blue, 5 yellow, and 9 greens pieces of candy. Marsha put all of the pieces of candy back in the bag, and drew one piece of candy out.
Part A:
Complete the following chart to determine the probability that Marsha drew each of the following pieces of candy.
Part B:
Marsha now wishes to determine compound probability. Complete the following chart to determine the probability that Marsha drew each of the following pieces of candy.
If you cannot see, zoom in. Don’t answer if you don’t know the answer. Whoever answers correctly will get Brainliest!
Answer:
Step-by-step explanation:
1) find the total candies
7 + 8 + 5 + 9 = 29
2) a probability can be expressed with a fraction whose denominator is the total candies, while the numerator represents the candies that we want to find
- red = 7/29
- blue = 8/29
- yellow = 5/29
- green = 9/29
3) compound probability
(red + blue)/29 = 15/29
(yellow + green)/29 = 14/29
(blue + yellow + green)/29 = 22/29
Find the measure of the missing angle
Help pls
Answer:
the answer is 51
Step-by-step explanation:
a triangle has 180 degree in total
180-124=56
73+56+x= 180
x= 51
Answer:
51
Step-by-step explanation:
Let the angle be xSum of two interior angles=exterior angle➝x+73=124
➝x=124-73
➝x=51
A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank. Write and solve a system of equations to find the family’s paddling speed in still water. Let s equal the families paddling speed and c represent the current
a.
s + c = 2.75
s - c = 1.5
2.125 mi/h
c.
s + c = 2.75
c - s = 1.5
.60 mi/h
b.
2.75s = c
1.5s = c
1.725 mi/h
d.
2.75c = s
1.5c = s
30 mi/h
On solving the provided question, we can say that In still water, a family must paddle at a speed of 2.125 miles per hour.
What is speed?Speed is the amount of distance traveled by an object in one unit of time when it is in motion.
Given that, a family is paddling a boat (with the current). Their average speed in relation to the riverbanks is 2.75 miles per hour. On the way back, they paddle upstream (against the current), moving toward the riverbank at an average speed of 1.5 miles per hour.
Here, Let the family's speed on still water be x and the current's speed be y. Upstream speed is calculated using the formula 1.5 = x - y - - - - (1)
2.75 downstream speed = x + y - - - - (1)
Equations 1 and 2 are solved as follows: 2x = 4.25 and x = 2.125 miles per hour In still water, a family must paddle at a speed of 2.125 miles per hour.
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Write the name of each of these polygons
Answer:
In geometry, a polygon can be defined as a flat or
plane, two-dimensional closed shape bounded with
straight sides. It does not have curved sides. The
sides of a polygon are also called its edges. The
points where two sides meet are the vertices (or
corners) of a polygon
1. polygon with four sides is called a Quadrilateral
2. polygon with six sides is called hexagon
3. polygon with five sides is called pentagon
Hope this helps?
What's the sum of 3 3/8 and 4 3/4? A.9 1/4 B. 8 3/4 C. 7 3/4 D. 8 1/8
Answer:
D
Step-by-step explanation:
3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{3}{4}[/tex] Use the common denominator of 8 Multiply [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{2}[/tex]
3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{6}{8}[/tex]
7[tex]\frac{9}{8}[/tex]
7 + [tex]\frac{8}{8}[/tex] + [tex]\frac{1}{8}[/tex] Another name for [tex]\frac{8}{8}[/tex] is 1
7 + 1 + [tex]\frac{1}{8}[/tex]
8[tex]\frac{1}{8}[/tex]