Answers
Answer:
Option E. None of the above.
Step-by-step explanation:
From the question given above, the following data were obtained:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
Recall:
When a function f(x) is multiplied by it's inverse f¯¹(x), the result is equal to 1 i.e
f(x) × f¯¹(x) = 1
With the above information, we can determine the inverse of function given above as follow:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
f(x) × f¯¹(x) = 1
(x – 5)/(2x + 3) × f¯¹(x) = 1
f¯¹(x)(x – 5) / (2x + 3) = 1
Cross multiply
f¯¹(x)(x – 5) = (2x + 3)
Divide both side by (x – 5)
f¯¹(x) = (2x + 3) / (x – 5)
Thus, the inverse of the function is (2x + 3) / (x – 5).
Option E gives the correct answer to the question.
Related Questions
Data are drawn from a bell-shaped distribution with a mean of 25 and a standard deviation of 4. There are 1,000 observations in the data set.
a. Approximately what percentage of the observations are less than 33?
b. Approximately how many observations are less than 33?
Answers
Answer:
a. 97.72% of the observations are less than 33
b. Approximately 977 observations are less than 33.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 25 and a standard deviation of 4.
This means that [tex]\mu = 25, \sigma = 4[/tex]
a. Approximately what percentage of the observations are less than 33?
The proportion is the p-value of Z when X = 33. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33 - 25}{4}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
0.9772*100% = 97.72%
97.72% of the observations are less than 33.
b. Approximately how many observations are less than 33?
Out of 1000:
0.9772*1000 = 977.2
Approximately 977 observations are less than 33.
Solve for x round to the nearest tenth if necessary
Answers
Answer:
x = 2.8
Step-by-step explanation:
sin = opp/hyp
hyp = opp/sin
x = 2.4/sin60
x = 2.771281292110204
rounded
x = 2.8
Two towers A and B are 45m and 30m high. Tower A lies to the west and B to the east of a man 1.5m tall. From the mans eye level, the angle of elevation of the top of A and B are 66° and 28° respectively. Calculate correct to three signigicant fugures the distance between A and B.
Answers
Answer:
73.0m
Step-by-step explanation:
see the attachment. Hope it helps.
What is the standard form of y - 8 = 2(x + 3)
Answers
Answer:
y=2x+14
Step-by-step explanation:
y=2x+2.3+8=2x+14
Amanda, Bryan, and Carl are about to compete in 100
mixed IM swimming events. These are the only three
swimmers competing in this event. They are all working
hard to win first place.
How many different possible ways could the 3 swimmers
place?
2
Answers
9514 1404 393
Answer:
6
Step-by-step explanation:
Any of the three can be in first place.
Any of the remaining two can be in 2nd place.
The remaining swimmer will be in 3rd place.
There are 3 × 2 × 1 = 6 possible orderings of the swimmers.
Which inequality is graphed on the coordinate plane?
Answers
Answer:
A: y < -2x - 1
Step-by-step explanation:
First, to figure out which part of the graph to be looking at, you will look at the shaded region as the solution area.
So, the solution area is to the left of the line. Said line is a dotted line which means that the points on the line can not be a solution.
If the points on the line can not be a solution then it eliminates answer choices C and D because y can not equal the other side of the inequality.
Now, we will bring the shaded region back into focus to find out if y is greater than or less than the other side. The shaded area is "below" the line so it is less than -2x - 1.
To ensure this is correct, plug two points into the inequality we just chose, one from the shaded region and one not, just to make sure the answer is correct.
I picked (-3,4) to test. So plug them into the inequality to get:
4 < -2 (-3) - 1
So 4 < 6 - 1 which is correct.
Then from the other side of the line I picked (5,2)
2 < -2 (5) - 1
2 < -10 - 1
2 < -11 is not true so the inequality that we found was correct.
HELP!!!!! hurry pls
Answers
Answer:
100
Step-by-step explanation:
since its collinear it has to be 180 -80 which equals 100.
Let m Z1=(3x)º, m 22=(5x-7)", m 23=(4x+15), and m ZAFD=128º. Find m44 and m ZBFD.
Answers
Answer:
m<4 = 52°
m<BFD = 98°
Step-by-step explanation:
m<1 = (3x)°
m<2 = (5x - 7)°
m<3 = (4x + 15)°
m<AFD = 128°
✔️Find m<4:
m<4 = 180° - m<AFD (angles on a straight line)
Substitute
m<4 = 180° - 128°
m<4 = 52°
✔️m<BFD = m<2 + m<3
Substitute
m<BFD = (5x - 7)° + (4x + 15)°
We need to find the value of x.
Create an equation to find x.
m<1 + m<2 + m<3 = m<AFD (angle addition postulate)
Substitute
3x + 5x - 7 + 4x + 15 = 128°
Add like terms and solve for x
12x + 8 = 128
12x + 8 - 8 = 128 - 8
12x = 120
12x/12 = 120/12
x = 10
m<BFD = (5x - 7)° + (4x + 15)°
Plug in the value of x
m<BFD = 5(10) - 7 + 4(10) + 15
m<BFD = 50 - 7 + 40 + 15
m<BFD = 98°
Ali wants to attend more group exercise classes at his gym. This week, he plans to attend 1 cardio class and 5 weightlifting classes, which will last a total of 237 minutes. Next week, he hopes to attend 5 cardio classes and 5 weightlifting classes, which will last a total of 465 minutes.
a) Write a system of equations that represents the above situation.
b) Use the elimination method to show the length of the cardio class and the length of the weightlifting class.
Answers
Answer:
x + 5y = 237
5x + 5y = 465
Step-by-step explanation:
Let
x = length of cardio class
y = length of weightlifting class
x + 5y = 237 (1)
5x + 5y = 465 (2)
Using elimination method
Subtract (1) from (2) to eliminate y
5x - x = 465 - 237
4x = 228
x = 228/4
x = 57 minutes
Substitute x = 57 into (1)
x + 5y = 237 (1)
57 + 5y = 237
5y = 237 - 57
5y = 180
y = 180/5
y = 36 minutes
x = length of cardio class = 57 minutes
y = length of weightlifting class = 36 minutes
Your job in a company is to fill quart sized bottles of oil from a full 50-gallon oil drum
Answers
Step-by-step explanation:
....
I Dont Known........
Answer:
16 full cases
Step-by-step explanation:
4 quarts to a gallon
50 gallons is 200 quarts (50 x 4)
200 quarts / 12 quarts per case = 16.66667 (.66667 isn't a full case)
so, it's 16
Stevens College plans to have 20 computers for every 100 students. How many computers are needed for 1,500 students?
Answers
Answer:
300 computers
Step-by-step explanation:
So I divided 1500 out of a 100 and got 15, then I multiply 15 to 20 and got 300.
(I am a high schooler so I hope this is 3rd grade math because I notice you are a college student and I hope this not some college tricky math, if you get this wrong I am truly sorry)
Ahmad made $114 for 12 hours of work. At the same rate, how many hours would he have to work to make $108?
Answers
Answer:6
Step-by-step explanation:
Answer: 6
Step-by-step explanation
using the digits 0-9 at most one time each fill in the boxes so that the fraction equals the decimal
Answers
Step-by-step explanation:
Z 00m
336"083"2553
(wZE2XQ) are
According to the National Beer Wholesalers Association, U.S. consumers 21 years and older consumed 26.9 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:
H, :μ< 26.9
Ha : μ> 26.9
a. Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?b. What is the Type I error in this situation? What are the consequences of making this error?c. What is the Type II error in this situation? What are the consequences of making this error?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
If the null is rejected, then we conclude that the average Consumption of beer and cider by customers who are 21 years and above is greater than 26.1
A type 1 error is committed if the null hypothesis is incorrectly rejected ; this means we will be concluding that customers who are 21 years and older have higher average Consumption when they actually do not. This may lead to a restriction on beer consumption in the city when there actually isn't a need for it.
For type 2 error, a false null is incorrectly accepted, in this scenario, we are saying that the consumption of beer and cider is not beyond the mean value when in actual sense it is.
Helen is taking part in a quiz on tv. The Probability she answers the questions correctly is 4/5. Helen is asked two questions. Calculate the probability she answered both questions correctly
Answers
Answer:
16/25
Step-by-step explanation:
To find the probability that she gets both questions right, multiply the probabilities together:
4/5 x 4/5
= 16/25
So, the probability that she answers both correctly is 16/25
What is the axis of symmetry for the function f(x)=7−4x+x2?
x = –3
x = –2
x = 2
x = 3
Answers
Answer:
x = 2
Step-by-step explanation:
[tex]y = {x}^{2} - 4x + 7 \\ y = (x - 2) {}^{2} - 4 + 7 \\ y = {(x - 2)}^{2} + 3[/tex]
Therefore, axis of symmetry is x = 2
The solution is: x=2, is the axis of symmetry for the function f(x)=7−4x+x2.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, we have,
f(x)=7−4x+x^2
Rewriting as
f(x) = x^2 -4x+7
a =1 b -4 c=7
The axis of symmetry is:
h = -b/2a
= -(-4)/ 2(1)
= 4/2(1)
= 4/2
=a
The axis of symmetry is x=2.
Hence, The solution is: x=2, is the axis of symmetry for the function f(x)=7−4x+x2.
To learn more on function click:
brainly.com/question/21145944
#SPJ7
Finding the Area of a Circle Given the Radius Th It The area in terms of pi isi mi? The approximated value for the area is A circle has a radius of 3 miles. Use the work shown below to identify the area in terms of pi and the approximate area of the circle. Use 3.14 for a and round the answer to the nearest tenth. A = 2 A= T(3 mi) A = 3.14(9 mi)
Answers
Answer:
I'd use A = πr^2
The area is 28.3 if we're using 3.14 as pi (rounded to the nearest tenth)
Question 1 of 10
Simplify this algebraic expression completely.
5y-3(y + 2)
Answers
Answer:
2y -6
Step-by-step explanation:
5y-3(y + 2)
Distribute
5y -3y - 6
Combine like terms
2y -6
If you help me I’ll mark brainliest
Answers
Answer:
∠2=92°
Step-by-step explanation:
Using an angle formula, -8x+144=2x+74
Simplification:
-8x+144=2x+74
-8x+70=2x
70=10x
x=7
Therefore, each angle is 88°
Now, because ∠2 is adjacent to one of 88°, they add up to 180°
Therefore,
180°=88°+∠2
∠2=92°
please solve asap thanks
Answers
10+ 16 = 26
15 x 4 = 60
25 + 15 = 40
158 cm is the answer
One day, a café sells 3 more than twice the number of cappuccinos as they do lattes. They sold a total of 33 cappuccinos and lattes together.
Which equation could be used to find the number of lattes, x, sold at café
Answers
Answer:
x=6
Step-by-step explanation:
calculate the value of A in the statement
Answers
please edit your question man
Given the set of vectors , decide which of the following statements is true:
A: Set is linearly independent and spans ℛ 3. Set is a basis for ℛ 3.
B: Set is linearly independent but does not span ℛ 3. Set is not a basis for ℛ 3.
C: Set spans ℛ 3 but is not linearly independent. Set is not a basis for ℛ 3.
D: Set is not linearly independent and does not span ℛ 3. Set is not a basis for ℛ 3.
(1,0,0),(0,1,2)
Answers
Average rate of the train
Answers
Answer:
Step-by-step explanation:
First of all, I'm having a bit of trouble seeing what the exponent on the leading term in the distance is, but I think its an x-squared so that's what I used to solve this. Keep in mind that you do NOT get a number answer here; you get another expression in terms of x for an "answer".
Let's simplify down the rate first by multiplying. What I did was put the denominator under each of the terms in the numerator and then simplified by dividing each term:
[tex]r=\frac{2x^2}{2x}-\frac{5x}{2x}-\frac{3}{2x}[/tex] which simplifies to
[tex]r=x-2.5-\frac{3}{2x}[/tex] Now let's get rid of that denominator there by multiplying everything by 2x to get
[tex]r=2x^2-5x-3[/tex] and we're ready to solve for time.
If d = rt, then
[tex]t=\frac{d}{r}[/tex] so filling in:
[tex]t=\frac{6x^2+3x}{2x^2-5x-3}[/tex] and we can divide this using the method of long division. It would be impossible to show you how to do that here in this forum, but when you divide, you get
[tex]t=3+\frac{18x+9}{2x^2-5x-3}[/tex] ...as crazy as that seems.
if y=8, evaluate the following expression: 40-5y
Answers
Explanation:
y = 8
40 - 5 x 8
40 - 40
= 0
Have a nice day
There are four white socks and six black socks in a drawer what is the probability of selecting a white sock not replacing it and then selecting another white sock
Answers
Answer:
Step-by-step explanation:
Add all the socks in the drawer to get a denominator
12
blue socks can be picked out of the
36
total socks, so
12
36
Then you take away one sock from the top and bottom, so you now have
11
35
Multiply the two numerators (
12
and
11
), then multiply the denominators (
36
and
35
), then divide the numerator by the denominator,
132
1260
, to get your answer.
Answer:
6/10
Step-by-step explanation:
1st step: 4+6=10
CAN YOU SOLVE THIS MATH PROBLEM 20 POINTS
Answers
Since the angles of a rectangle are right angles (90 degrees) you would set it up as 90=5x-20. Then combine like terms and solve the equation. (If you need me to show you how step by step tell me)
find the volume of pyrmaid
Answers
Answer:
37
Step-by-step explanation:
In the given figure the angles are vertically opposite angles so ;
4x + 2 = 150
or, 4x = 148
or, x = 37 ans .
solve for x round to the newest 10th i’d necessary
Answers
Answer:
x = 43.7°
Step-by-step explanation:
Reference angle (θ) = x°
Opposite side length = 43
Adjacent side length = 45
Apply the trigonometric function, TOA, which is:
Tan θ = Opp/Adj
Substitute
[tex] Tan(x) = \frac{43}{45} [/tex]
[tex] x = Tan^{-1}(\frac{43}{45}) [/tex]
x = 43.7° (nearesth tenth)
Hi if you have a 65% grade can a 80% bring it up to a C 70%
Answers
Answer:
Not a 70%, but a 72.5% (or a 73%)
Step-by-step explanation:
Assuming that the 65% is the first grade and the 80% is your second, adding both numbers and dividing by 2 will get you 72.5%.
The best possible grade you can get from that 65% is an 82.5%, or 83% if you round the grade up. 100+65=165÷2 will get you 82.5.