Answers
9514 1404 393
Answer:
f⁻¹(x) = log(x)/log(16)
g⁻¹(x) = (2^x -1)/3
Step-by-step explanation:
In each case, you want to solve ...
x = f(y)
__
a. x = 4^(2y)
log(x) = 2y·log(4) . . . . . . . . take logs
y = log(x)/(2·log(4)) . . . . . . .divide by the coefficient of y
f⁻¹(x) = log(x)/log(16) . . . . simplify (4^2 = 16)
__
b. x = g(y)
x = log(3y +1)/log(2) . . . . use the change of base relation
x·log(2) = log(3y +1) . . . . multiply by log(2)
2^x = 3y +1 . . . . . . . . . . . take antilogs
2^x -1 = 3y . . . . . . . . . . . subtract 1
y = (2^x -1)/3 . . . . . . . . . . divide by the coefficient of y
g⁻¹(x) = (2^x -1)/3 . . . . . . . . note that "-1" is not part of the exponent of 2
Related Questions
The Statistical Abstract of the United States reported that the average cost per day of owning an automobile in the United states is $7.62. This includes the cost of the car, general maintenance, gasoline, and insurance. A researcher claims that college students' average daily ownership expenses are less than the national average. A random sample of 54 college students who own cars found the average cost per day to be $6.78 with standard deviation $1.77. Use a 5% level of significance to test the claim that a college student's average daily ownership expenses are less than the national average. State the Null and Alternate Hypotheses, calculate the test statistic, compute the P value for this test, state the alpha value, then state your conclusion. Is there enough evidence to support the claim?
Answers
Answer:
Step-by-step explanation:
The null and the alternative can be computed as:
[tex]H_o : \mu = 7.62[/tex]
[tex]H_1 : \mu < 7.62[/tex]
[tex]Claim: \mu < 7.62[/tex]
[tex]\alpha= 0.05[/tex]
The critical value for a left-tailed test at [tex]\alpha= 0.05[/tex] = -1.645
The test statistics can be computed as:
[tex]Z = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}} }[/tex]
[tex]Z = \dfrac{6.78 - 7.62}{\dfrac{1.77}{\sqrt{54}} }[/tex]
[tex]Z = -3.487[/tex]
The P-value = (Z< -3.487)
The P-value = 0.00024
Decision Rule: TO reject [tex]\mathbf{H_o}[/tex] at [tex]\alpha= 0.05[/tex], if test statistics is less than the critical value (left tailed)
Conclusion: We reject [tex]\mathbf{H_o}[/tex] at ∝ = 5%, thus there is enough evidence to support the claim that the college students average daily ownership expenses are less than the national average.
Evaluate -2x^2y, if x = -3 and y=-1.
-12
18
12
-18
Answers
Answer:
Option A is your answer
it cost 0.60 cents to run a fan for 4 hours how much does it cost to run the fan for 6 hours I need an answer asap
Answers
Answer:
$0.90
Step-by-step explanation:
So first you need to find the rate (showing how much money it costs to run for 1 hour) so you get 0.60 and divide it by 4 and its 0.15, then multiply 0.15 by 6 and get 0.90
5 cm
12 cm
What is the area
of this rectangle?
And why
Answers
Answer:
60cm^2
Step-by-step explanation:
5X12=60
subtract 10x^2-10x+2 from -8x^2+7x-7
Answers
Answer:
-18x^2+17x-9
Step-by-step explanation:
21< -4+5x Hurry I need it
Answers
uhhhhh because yea
A group decides to go white-water rafting on a river. The map they have of the river has the scale 3 inches:7 miles. On the map, the distance between the start point and the end point of their trip is 15 inches. What is the actual distance?
Answers
Students at Hampton Middle School sold T-shirts as a school fundraiser. Sylvie asked 12 random seventh-grade students how many T-shirts they sold for the fundraiser. The number of T-shirts each student sold is listed below.
3, 4, 8, 5, 2, 5, 0, 5, 3, 4, 3, 7
What is the mean of the data set rounded to the nearest tenth?
4.0 shirts
4.1 shirts
4.5 shirts
4.9 shirts
Answers
Answer:
4.1 shirts
Step-by-step explanation:
Mean can be found by adding all data points and dividing that by the total amount of data points.
There are 12 students selling shirt, which gives you 12 data points.
So (3+4+8+5+2+5+0+5+3+4+3+7)/12 = 4.083...
Which rounds to 4.1 shirts
Answer:
The correct answer is C: 4.1 shirts
Step-by-step explanation:
Did it on edge and got it correct
Hope This Helps!
Have a good day!
Help me out please I need you’re help with this question ✏️
Answers
the answer to your question might be (B).
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. x2 9y2
Answers
This question is incomplete, the complete question is;
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.
x² + 9y² = 9
(a) About
y = 3
(b) About
x = 3
Answer:
a) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
b) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
Step-by-step explanation:
a) the volume of solid of revolution
about y=3
Using SHELL METHOD;
Volume V = 2π . [tex]\int\limits^1_{y=-1} \,[/tex] (3-y) (2.3√(1-y²)) dy
= 12π . [tex]\int\limits^1_{y=-1} \,[/tex] (3-y) √(1-y²) dy
= 12π . [tex]\int\limits^1_{y=-1} \,[/tex] (( 3√(1-y²) - y(√(1-y²)) dy
= 12π[ [tex]\frac{3}{2}[/tex]π - 0 ]
= 18π² = 177.652879 ≈ 177.65288
Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
b)
the volume of solid of revolution
about x=3
Using SHELL METHOD;
Volume V = [tex]\frac{4}{3}[/tex]π . [tex]\int\limits^3_{y=-3} \,[/tex] (3-x) ([tex]2.\frac{1}{3}[/tex]√(9-x²)) dx
= [tex]\frac{4}{3}[/tex]π . [tex]\int\limits^3_{y=-3} \,[/tex] (3-x) √(9-x²) dx
= [tex]\frac{4}{3}[/tex]π . [tex]\int\limits^3_{y=-3} \,[/tex] (3√9-x² -x√(9-x²) dx
= [tex]\frac{4}{3}[/tex]π [ [tex]\frac{27}{2} \pi[/tex] - 0 ]
= 18π² = 177.652879 ≈ 177.65288
Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
Which expression shows another way to write 36+16?
4(9)+4
4(9+4)
6(6+8)
(6+4)(6+4)
Answers
Answer:
36+16= 52
4(9)+4= 40, which does not equal 52.
4(9+4) = 52.
6(6+8) = 84, which does not equal 52.
(6+4)(6+4) = 100, which does not equal 52.
So, 4(9+4) is correct.
Let me know if this helps!
You are given the following equation: (x+3)^2 + (y+9)^2 = 144 What is the
(h,k)
Answers
Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y -k)² = r²
(x+ 3)² + (y + 9)² = 144
(x+ 3)² + (y + 9)² = 12²
h = -3 ; k = -9
Mhanifa please help these 2 are confusing :( I will mark brainliest
Answers
Answer:
The key is to prove that the triangles are congruent, then their corresponding parts are congruent.
Step-by-step explanation:
#5)
It it given that:
Angle CBD is congruent to angle CDB.
Angle BAE is congruent to angle DEA.
Triangle CBD is isosceles because it's base angles are equal. Therefore, segment CB is congruent to segment CD.
Triangle CAE is isosceles because it's base angles are equal. Therefore, segment CA is congruent to segment CE.
CA-CB=BA
CE-CD=DE
segment BD is congruent to segment DB.
Angle ABD is supplementary to angle CBD (180-angle CBD= angle ABD).
Angle EDB is supplementary to angle CDB (1980-angle CDB=angle EDB).
therefore, angle ABD=angle EDB.
Triangles ABD and EDB are congruent because of the Side-angle-side theorem.
Triangles ABD and EDB are congruent, segment AD is congruent to segment EB because corresponding legs of congruent triangles are congruent.
#6)
It is given that:
Angle EBC is congruent to angle ECB
Segment AE is congruent to segment DE.
Triangle BEC is iscsceles because it's base angles are equal. Therefore, segment EB is congruent to segment EC.
AE+EC=AC
DE+EB=DB
segment BC is congruent to segment CB.
Triangle BAC is congruent to triangle CDB because of the side-angle-side theorem.
Segment AD is congruent to segment DC because corresponding legs of congruent triangles are congruent.
Answer:
Problem 5)
Step 1: < CBD = <CDB Reason: given
Step 2: BC = CD Reason: opposed sides in the isosceles triangle BCD
Step 3: < BAE = < DEA Reason: given
Step 4: AC = CE Reason: opposed sides in the isosceles triangle ACE
Step 5: triangle ACD = triangle BCE Reason: angle <C is common, and equal sides shown above so use SAS theorem.
Step 6: AD = BE Reason: third side in the equal triangles shown above.
Problem 6)
Step 1: < ECB = <EBC Reason: Given
Step 2> triangle BEC is isosceles Reason: has two equal angles
Step 3: BE = EC Reason: opposite sides in the isosceles triangle
Step 4: <DEC = < AED Reason: opposed by the vertex (vertical angles)
Step 5: AE = ED Reason: given
Step 6: triangle BAE = triangle EDC Reason SAS theorem
Step 7: side AB = side CD Reason: third side in the equal triangles
Lamar went to a baseball game. The game started at
11;50AM, and it was 3 hours 39minutes long. When did the game end?
Answers
11:50 + 3 hours = 2:50
2:50+ 39 mins = 3:29
Answer:
The game ends at 2:39
Step-by-step explanation:
11:50 + 3 hours (3:00) = 2:00
2:00+ 0:39 = 2:39
Jonny had ? cakes. He eats 1/2 of
his total amount of cakes. How much
cake does he have left?
Answers
Answer:
1/2 * (?)
Step-by-step explanation:
Divide (?) Cakes in half
Answer:
How many cakess did he have? impossible to answer otherwise
Step-by-step explanation:
Can you look at the photo and help please.?
Answers
Answer:
sorry it aint werking for meeee
Step-by-step explanation:
60÷(63÷7)=
I don't understand plz help
Answers
Answer:
answer is simple
first we will solve the bracket
(63÷7)
it is 9
and then 60÷ 9
which gives 6.67
An exponential function has an initial value of 500 and a decay rate of 15%. Compare the average rate of change for the interval 0 < x < 4 to the average rate for the interval 4 < x < 8 What do you think will happen to the average rate of change for intervals beyond x = 8 ? Explain.
Answers
For 0<x<4, the average rate of change will be -60
For 4<x<8 the the average rate of change will be -31
And for the sentence (on savass in order is)
Stay negative, -31, decrease but at a slower rate
In this exercise we have to use the knowledge of functions to describe the average rates of each one of them, so:
For 0<x<4 will be -60
For 4<x<8 will be -31
First, we have to remember what an average rate means, like:
It is a measure of in what way or manner much the function altered for one, approximately, over that pause. It happen derived from the slope of the direct route joining the break's endpoints in contact the function's diagram.So we can say that:
[tex]0
See more about functions at brainly.com/question/5245372
Help me pls pls pls
Answers
Answer:
1.61
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.61
work out yhe value of 6.105×10^8/3.7×10^3 give your answer in standard form
Answers
Hope this helps
Jennifer has a hair ribbon that is 12 centimeters long. What is the length of the ribbon in millimeters? will mark brainliest
Answers
Answer:
120 mm
Step-by-step explanation:
Change x+2y=-6 into y=mx+b form
Answers
Answer:
y = -3 - x/2
Step-by-step explanation:
x + 2y = -6
You have to isolate y by minusing x on both sides
2y = -6 - x
Then you will isolate y by dividing both sides by 2
y = -3 - x/2
How do you know 31/40 is greater than 3/4, but less than 4/5
Answers
Step-by-step explanation:
So you have 31/40
3/4=30/40 (multiply by 10/10)
4/5=32/40 (multiply by 8/8)
So, there you have it, 31/40 is right in between those two.
turn it into decimal format. just do the division,. 31 divided by 40 = .775 and 3 divided by 4 = .75 and 4 divided by 5 = .8. all you have to do is the division and once it is in decimal format you can tell which is greater. hope this helps
9514 1404 393
Answer:
30/40 < 31/40 < 32/40
Step-by-step explanation:
The fractions are easiest to compare when they have a common denominator. A denominator of 40 will serve.
3/4 = 30/40
4/5 = 32/40
Then the relation between the fractions is ...
30/40 < 31/40 < 32/40
3/4 < 31/40 < 4/5 . . . . 31/40 is greater than 3/4 and less than 4/5
_____
You can also compare the numbers as decimals.
3/4 = 0.750
31/40 = 0.775 . . . . greater than 3/4
4/5 = 0.800 . . . . greater than 31/40
Find cosX and cosZ. Write each answer as a fraction and as a decimal. Round to four decimals places, if necessary. Fractions to reduce and use /.
Answers
Answer/Step-by-step explanation:
Recall the acronym, SOHCAHTOA.
✔️Cos X = adj/hyp (CAH)
Adj = 10
Hyp = 26
Cos X = 10/26
Simplify
Cos X = 5/13 (as a fraction)
Cos X = 0.3846 (as a decimal to 4 d.p)
✔️Cos Z = adj/hyp (CAH)
Adj = 24
Hyp = 26
Cos Z = 24/26
Cos Z = 12/13 (as a fraction)
Cos Z = 0.9231 (as a decimal to 4 d.p)
the length of a rectangle garden is 5 m the area is 176 m2 what is the width of the garden
Answers
Answer:
Step-by-step explanation:
L = 5 m
area = L×W = 176 m²
5W = 176
W = 176/5 = 35.2 m
Are they Equivalent why or why not?
Answers
Answer:
They are equivalent because when you distribute the -0.5 into 3x+5 you get the expression -1.5x+2.5
please help giving lot of points
Answers
Answer:
They would need to sell 32 calendars to EXCEED their goal.
Explanation:
8 x 32= 256, which is more than the $250 needed!
Step-by-step explanation:
Help me out please mathematic ✏️
Answers
To solve this you need to take the two degree values you already have, 90 degrees and 25 degrees. From there you can subtract 90 from 25.
Which is the slowest reading rate?
A. 3 pages in 9 minutes
B. 4 pages in 10 minutes
C. 5 pages in 13 minutes
D. 7 pages in 20 minutes
Answers
Answer:
A. 3 pages in 9 minutes
Step-by-step explanation:
3 & 9 are all the lowest out of those options.
So far, Monica has read ã of a book. She
has read the same number of pages each
day for 5 days. What fraction of the book
does Monica read each day?