as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
\(\stackrel{f(x)}{y}~~ = ~~\cfrac{x+5}{x+7}\hspace{10em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{y+5}{y+7}} \\\\\\ xy+7x=y+5\implies xy-y+7x=5\implies xy-y=5-7x \\\\\\ \stackrel{\textit{common factoring}}{y(x-1)=5-7x}\implies y=\cfrac{5-7x}{x-1}=f^{-1}(x) \\\\[-0.35em] ~\dotfill\\\\ f^{-1}(-8)~~ = ~~\cfrac{5-7(-8)}{(-8)-1}\implies f^{-1}(-8)=\cfrac{61}{-9}\implies f^{-1}(-8)=-6\frac{7}{9}\)
Rename the fraction 1/4 using the least common denominator,12
Answer:
3/12
Step-by-step explanation:
to rename the fraction with the common denominator of 12, u have to multiply 1/4 by 3/3 to get 3/12. You can check ur answer by simplifying your answer. 3/12=1/4
Answer:
3/12
Step-by-step explanation:
12÷4=3 so I would be 3/12
Which number should replace the ç to make the subtraction problem correct?
9.866
- 7.97ç
1.889
Answer:
7
Step-by-step explanation:
for you to get the missing number just take the complete numbers and minus them then you'll get the incomplete digit needed good day.
Given the function, f(x)= Vx+1-6, choose the correct transformation.
o left 1, down 6
o left 1, up 6
O right 1, down 6
O right 1, up 6
What number is less than 6/9 of a dollar but greater than 0.45
Answer:
0.50
Step-by-step explanation:
to get both numbers in the same unit you have to change one, I'm changing 6/9
6 divided by 9 is ABOUT 0.6 so you can choose any numbr between 0.46 and 0.59
can you please help me
Answer:
what is the selection for the first one???
Step-by-step explanation:
A $320 suit is marked down by 10%. Find the sale price.
Please help
Answer: it costs $288, I hope this answers your question:)
Answer:
$288
Step-by-step explanation:
320 * 0.1 = 32
320-32= 288
reuben rented a truck for one day. There was a base fee of $19.95, and there was an additional charge of 83 cents for each mile driven. reuben had to pay $142.79 when he returned the truck. For how many miles did he drive the truck
Reuben drove the truck for 148 miles when he had to pay $142.79 when he returned the truck.
According to the question,
We have the following information:
Base fee of the truck = $19.95
Additional charge is of 83 cents.
The amount paid by Reuben when he returned the truck = $142.79
We know that 100 cents make 1 dollar.
So, we have to convert cents into dollars:
83 cents = 0.83 dollars
Let's take the distance travelled by the truck to be x miles.
Now, we have the following expression:
19.95+0.83x = 142.79
0.83x = 142.79-19.95
0.83x = 122.84
x = 122.84/0.83
x = 148 miles
Hence, Reuben drove the truck for 148 miles when he had to pay $142.79 when he returned the truck.
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Solve for x in the equation x + cube root of 3 is equals to 6/25
Hi!
The answer to the question: x+3^(3)=(6)/(25)
is x=-669/25
Work:
1)x+3^(3)=(6)/(25)
2)x+27=(6)/(25)
3)x=-669/25
Step 1: Write down the equation
Step 2: Solve the cube root of 3
Step 3: Subtract 27 from both sides.
I hope this helps have an amazing day/night!
God bless!
The scale on a map is 1 inch = 60 miles. If two cities are 2 3/4 inches apart on the map, how many miles are they apart?
Answer:
120.75 miles apart
Step-by-step explanation:
6 3/8 - 1 5/8 =
What is the answere?
I'll give brainest if right
The signed-rank test can be adapted for use in testing H0: μ = hypothesized value, where μ is the mean of a single population (see the last part of this section). Suppose that the time required to process a request at a bank’s automated teller machine is recorded for each of 10 randomly selected transactions, resulting in the following times (in minutes); 1.4, 2.1, 1.9, 1.7, 2.4, 2.9, 1.8, 1.9, 2.6, 2.2. Use the one-sample version of the signed-rank test and a .05 significance level to decide if the data indicate that the mean processing time exceeds 2 minutes.
Answer:
There is not enough evidence suggesting that the mean processing time exceeds 2 minutes.
Step-by-step explanation:
The hypothesis can be defined as follows:
H₀: The mean processing time is 2 minutes, i.e. μ = 2.
Hₐ: The mean processing time exceeds 2 minutes, i.e. μ > 2.
The significance level of the test is, α = 0.05.
Recorded Time (x) (x - μ) + Ranks -Ranks
1.4 -0.6 8
2.1 0.1 1
1.9 -0.1 1
1.7 -0.3 6
2.4 0.4 7
2.9 0.9 10
1.8 -0.2 4
1.9 -0.1 1
2.6 0.6 8
2.2 0.2 4
TOTAL 30 20
Sum of +Ranks = 30
Sum of -Ranks = 20
Test statistic = Min (∑+Ranks, ∑-Ranks)
= Min (30, 20)
= 20
Compute the critical value using the Wilcoxon Signed-rank test table.
Critical value = 11
As the test statistic value is more than the critical value, the null hypothesis was failed to be rejected.
Thus, there is not enough evidence suggesting that the mean processing time exceeds 2 minutes.
Use the shapes to answer the questions that follow:
Answer:
50%
Step-by-step explanation:
Theres 10 shapes and 5 of them are yellow. So that is 5/10 which equals 50%
hope this helps <3
Answer:
50%
Step-by-step explanation:
5/10 are yellow so 5% I think
੧. ਸ਼ੋਰ ਨੂੰ ਮਾਪਣ ਵਾਲੀ ਇਕਾਈ ਕਿਹੜੀ ਹੈ ?
Answer:
Once the mother of a Delhi gangrape victim was giving her views at a seminar on crimes against women when one of the listeners asked why Jyoti was going to see a movie with her friend at nine o'clock.
That is what it means
Answer: We measure sound intensity (also referred to as sound power or sound pressure) in units called decibels. Decibels (dB) are named in honor of Alexander Graham Bell, the inventor of both the telephone and the audiometer.
Step-by-step explanation:
please help me with theses!! need to get it done asap.
Answer:
Question 1 : Pierre is right
Question 2 : 0.85 (because 1 - 0.15 = 0.85)
Question 3 : Less than 1
Step-by-step explanation:
The distance between (-1,2) and (-2,1)
Answer:
About 10 i think
Step-by-step explanation:
idk
Please help........................
Answer:
I think it is 2 one
Step-by-step explanation:
This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =\($36.34 + $26.03\)
= \($62.37\)
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = \($36.34 + $26.03\)
= \($62.37\)
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
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Please I need some answers just a few are fine
Answer:
a) 16
b) 36
c) 4
d) 81
Explanation:
Finding the square root of a number is the inverse operation of squaring that number. Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers. The square root of a number, n, written below is the number that gives n when multiplied by itself.
simpify | 17 - (-30) 1+1 - 71 =
ANO ANS
Answer:
-23
Step-by-step explanation:
Any number multiplied by 1 is the same
*17-(-30)x1+1-71
=17+30+1-71
=47+1-71
=48-71
=-23
Step-by-step explanation:
17-(-13)1+1-71=
17+13×1+1-71=
17+13+1-71=
30+1-71=
31-71=
=-40
Select the correct answer.
Answer:it might be A
Jon had $83.50 in his checking account on Monday. On Friday, his balance was
$325.75 after depositing his paycheck. If Jon gets paid $14.25 per hour, how
many hours did he work this week?*
Your answer
Answer:
about 20.5 hours
Step-by-step explanation:
first find out how much money he earned during the week by subtracting the friday balance and the monday balance
375.75 - 83.50 = $292.25 was the amount earned during the week
divide the amount earned by the amount earned per hour
292.25 / 14.25 ≈ 20.5 hours worked that week
hope this helps <3
30 POINTS!!! Louie is trying to find a rectangular canvas for his art project. Its diagonal must measure 23.3 inches and form a 31° angle with the bottom of the canvas. What is the height of the canvas? Round your answer to the nearest inch. 12 inches 14 inches 24 inches 27 inches
Answer:
12 inches
Step-by-step explanation:
Given
\(\theta = 31^{\circ}\)
\(diagonal = 23.3\ in\)
Required
Determine the height of the canvas
The question is illustrated using the attached image.
Using the attachment as a point of reference, the height is calculated from
\(sin \theta = \frac{opp}{hyp}\)
This gives:
\(sin 31^{\circ}= \frac{h}{23.3}\)
Make h the subject
\(h = 23.3 * sin(31^{\circ)\)
\(h = 23.3 * 0.5150\\\)
\(h = 11.9995\)
\(h = 12\ inches\)
A rectangle has right angles as its interior angles. Secondly, when you draw a diagonal and has its angle with bottom, then you get a right angled triangle with known angle.
The height of the rectangle is given by:
Option D: 12 inches
Given that:There is a rectangular canvas.The angle that the diagonal of the rectangle makes with bottom is 31° The length of diagonal = 23.3 inchesTo find:The height of that rectangular canvas.
Using the right angle triangle and sine ratio to find height of canvas:I have attached a figure below which you can refer.
The triangle ABC is right angled triangle. Using the sine ratio from angle A's viewpoint:
\(sin(A) = \dfrac{BC}{AC}\\\\ sin(31^\circ) = \dfrac{h}{23.3}\\\\ h \approx 0.515 \times 23.3\\ h \approx 12 \: \rm inches\)
Thus, the height of the specified canvas is 12 inches.
Thus, Option D: 12 inches is correct.
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Show that the partition of G into left cosets of H is different from its partition into right cosets?
It is shown below that the partition of G into left cosets of H is different from its partition into right cosets when n ≥ 3.
How to prove right cosets?Let us first find the left cosets of H in G:
H = {1, s₀}
s₁H = {s₁, s₁s₀}
s₂H = {s₂, s₂s₀}
s₃H = {s₃, s₃s₀, s₂s₁, s₂s₁s₀}...
Now, find the right cosets of H in G:
H = {1, s₀}
Hs₁ = {s₁, s₀s₁}
Hs₂ = {s₂, s₀s₂}
Hs₃ = {s₃, s₀s₃, s₁s₂, s₀s₁s₂}...
Observe that the left cosets of H in G and the right cosets of H in G are not the same when n≥3. This is because s₁s₀ is not in H, but s₀s₁ is in H.
Therefore, the left coset s₁H is not the same as the right coset Hs₁. Similarly, s₂s₁s₀ is not in H, but s₀s₁s₂ is in H, so the left coset s₃H is not the same as the right coset Hs₃.
Thus, it is shown that the partition of G into left cosets of H is different from its partition into right cosets when n≥3.
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the following set of data represents the top managers' bonuses (in thousands), find the sample variance: 10, 3, 6, 3, 8 round your answer to one decimal place.
The sample variance is 9.5.
The formula for the sample variance of a set of data is:
s^2 = (1/(n-1)) * sum((x_i - x_mean)^2)where x_i is each data point, x_mean is the sample mean, and n is the sample size.
First, we need to find the sample mean:
x_mean = (10 + 3 + 6 + 3 + 8) / 5 = 6Next, we calculate the sum of squared deviations:
(10 - 6)^2 + (3 - 6)^2 + (6 - 6)^2 + (3 - 6)^2 + (8 - 6)^2 = 16 + 9 + 0 + 9 + 4 = 38Finally, we calculate the sample variance:
s^2 = (1/(n-1)) * 38 = (1/(5-1)) * 38 = (1/4) * 38 = 9.5Rounding to one decimal place, the sample variance is 9.5.
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! TRIG RATIOS!!!!!!!!!!!!
Answer:
cos Z = 7/25, ∠Z ≈ 73.74°
Step-by-step explanation:
SOH CAH TOA
↑ adjacent/hypotenuse
cos Z = 7/25
=> Z = cos^-1 (7/25)
=> Z ≈ 73.74°
20points. Find an equation for the linear graph.
Use the two endpoints to find the slope:
(0,2) and ( 5,5.5)
Slope = change in y over change in x:
Slope = (5.5-2)/(5-0) = 3.5/5 = 0.7
The y intercept is the y value when x is 0, which is 2
Equation: c = 0.7x + 2
i need the answer of this 9th grade question
The amount of fabric used to make the number cube is given as follows:
C. 294 cm².
How to obtain the amount of fabric?The amount of fabric used to make the number cube is represented by the surface area of the number cube.
The surface area of a cube of side length a is given by the equation presented as follows:
S = 6a².
The side length for this problem is given as follows:
a = 7 cm.
Hence the surface area of the cube is calculated as follows:
S = 6 x 7²
S = 294 cm².
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c) You have a magical room filled with puppies
and kittens where you go to relax. There are 7
puppies for every 5 kittens.
If the room contains 156 animals, how many of
them are puppies?
Answer:
78
Step-by-step explanation:
Bob wants to paint a rectangular wall that measures 16•9 ft. the wall fountains a window with the dimensions shown. if bob does not want to paint the window, what is the total shaded area he would paint
SOLUTION
Total shaded Area = ( L X B ) - ( l x b)
= ( 16 x 9 ) - ( 8 x 5 )
= 144 - 40
= 104 feet^2
On a test that has a normal distribution, a score of 29 falls three standard deviations above the mean, and a score of 23 falls one standard deviation above the mean. Determine the mean of this test.
The mean of the test is 20.
To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.
Let's denote the mean of the test as μ, and the standard deviation as σ.
We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:
29 = μ + 3σ
Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:
23 = μ + σ
Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.
From the second equation, we can isolate μ:
μ = 23 - σ
Substituting this value into the first equation, we have:
29 = (23 - σ) + 3σ
Simplifying the equation, we get:
29 = 23 + 2σ
2σ = 29 - 23
2σ = 6
σ = 3
Substituting the value of σ back into the second equation, we find:
μ = 23 - 3
μ = 20
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