Answers
Answer:
B.
[tex]{ \tt{f(x) = \sqrt[3]{x + 11} }}[/tex]
let the inverse of f(x) be m:
[tex]{ \tt{m = \sqrt[3]{x + 11} }} \\ { \tt{ {m}^{3} = x + 11}} \\ { \tt{ {m}^{3} - 11 = x}} \\ { \tt{ {f}^{ - 1}(x) = {m}^{3} - 11 }}[/tex]
substitute for x in place of m:
[tex]{ \bf{f {}^{ - 1}(x) = {x}^{3} - 11 }}[/tex]
Related Questions
I need help ASAP please
Answers
Answer:
yes how can I help you???
If f:X is 3x + b and ff(2) = 12, find the value of b
Answers
Answer:
[tex]b =6[/tex]
Step-by-step explanation:
Given
[tex]f(x) =3x + b[/tex]
[tex]f(2) = 12[/tex]
Required
Find b
[tex]f(2) = 12[/tex] implies that:
[tex]12 = 3 * 2 + b[/tex]
[tex]12 = 6 + b[/tex]
Collect like terms
[tex]b = 12 - 6[/tex]
[tex]b =6[/tex]
What is the sum (6x^3 – 5x^2 + 3x – 5) + (8x^4 + 3x^3 + 5x^2 + x + 4)?
A.9x^6 + 8x^4 + 4x^2 – 1
B.8x^4 + 9x^3 + 4x – 1
C.8x^4 + 3x^3 – 10x^2 + 4x – 1
D.8x^4 – 3x^3 + 10x^2 – 2x + 9
Answers
Answer:
8x^4+9x^3+4x-1
Step-by-step explanation:
(6x^3 – 5x^2 + 3x – 5) + (8x^4 + 3x^3 + 5x^2 + x + 4)
Group like terms
8x^4+6x^3+3x^3-5x^2+5x^2+3x+x-5+4
8x^4+9x^3+4x-1
Answer:
[tex]\left(6x^3-5x^2+3x-5\right)+\left(8x^4+3x^3+5x^2+x+4\right)[/tex]
Combine like terms
[tex]=8x^4+6x^3+3x^3-5x^2+5x^2+3x+x-5+4[/tex]
Add: -5x²+5x²=0
[tex]=8x^4+6x^3+3x^3+3x+x-5+4[/tex]
Now add 6x³+3x³=9x³
[tex]=8x^4+9x^3+3x+x-5+4[/tex]
Add like terms 3x +x=4x
[tex]=8x^4+9x^3+4x-5+4[/tex]
Now add -5+4=-1
[tex]=8x^4+9x^3+4x-1[/tex]
OAmalOHopeO
Step 3: Write the equation of the line that passes through the point (4,−1)
(
4
,
−
1
)
that is parallel to the line 2−3=9
Answers
Answer:
-
Step-by-step explanation:
-
Draw a frequency polygon for the following data:
Marks
0 - 10
10 - 20 20 - 30 30 - 40 40 - 5050 - 60
错误。
No. of Students
7
15
22
30
16
10
Answers
Answer:
See attachment
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Required
The frequency polygon
We have:
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
First, we calculate the midpoint of each class
[tex]\begin{array}{ccccccc}{Midpoint} & {(0+10)/2} & {(10+20)/2} & {(20+30)/2} & {(30+40)/2} & {(40+50)/2} & {(50+60)/2}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
[tex]\begin{array}{ccccccc}{Midpoint} & {5} & {15} & {25} & {35} & {45} & {55}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Lastly, we plot the midpoint against the frequency of students (see attachment)
Find f(-2) if f(x) =x^4 +2x^2-1
Answers
Answer:
Plug -2 in for x of f(x)
--> -2^4 + 2(-2)^2 - 1
---> 23
f(-2) = 23
Kira, Sam, and Josh sent a total of 85 text messages during the weekend. Sam sent 2 times as many messages as Josh. Kira sent 5 more messages than Josh.
How many messages did they each send?
Answers
Answer:
Josh: 20 messages
Kira: 25 messages
Sam: 40 messages
what represent the area of the rectangle in cm^2??
Answers
9514 1404 393
Answer:
d. 3x² +15x
Step-by-step explanation:
The area is the product of length and width.
A = LW
A = (3x)(x+5) = 3x(x) +3x(5) . . . . use the distributive property
A = 3x² +15x
Answer: D) 3x^2 + 15
==========================================================
Explanation:
Draw a horizontal line to divide the rectangle into two parts (they don't necessarily have to be equal parts). Refer to the diagram below. The upper rectangle is x by 3x. So its area is length*width = x*3x = 3x^2
The lower rectangle is 5 by 3x, so its area is 5*3x = 15x
Combine those two sub-areas back together to get the overall area of 3x^2 + 15x
You could also use the distribution rule
3x*(x+5) = 3x*(x) + 3x*(5) = 3x^2 + 15x
You are enrolling swimmers in a study on lung capacity. You want 25% of your sample to be those who compete at 100m or less distances and 50% to be swimmers who compete at 100m-500m distances and 25% to be swimmers who compete at >500m distances. You begin enrolling for your study at 5am at the pool. By 9 AM you have all of your 100-500m swimmers enrolled, and all of your >500m swimmers enrolled. This is an example of what type of sampling method
Answers
Answer:
Stratified sampling
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
People divided by groups, for each group(<100, >100<500, >500), a number(not all) is selected, so stratified sampling.
A researcher utilizes a t-test to compare the average amount of beta-lactamase produced by two different types of bacteria. The Levene's test for equality of variances has a p value of 0.01. You know this means:
Answers
Answer:
The answer is "T-test results must not be presented if the same variations are expected".
Step-by-step explanation:
A t-test is used by a scientist to compare the average beta-lactamase of two distinct strains of bacteria. The Levene equality test does have a p-value of 0.01. Researchers know that all this means that research should report t-test findings with a failed assumption of identical variances because the Log-rank equality test has a p-value of 0.01 of less than 0.05 that shows different twp population variance.
How many ways can four marbles be chosen from a set of five marbles?
Answers
Answer:
120
Step-by-step explanation:
5x4x3x2x1=120
Which type of triangle will always have at least 1-fold reflectional symmetry?
right triangle
obtuse triangle
acute triangle
isosceles triangle
Answers
Answer:
D. isosceles triangle
Step-by-step explanation:
Ed22
A triangle with at least 1-fold reflectional symmetry is isosceles triangle, option D is correct.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
An isosceles triangle will always have at least 1-fold reflectional symmetry.
This is because an isosceles triangle has two congruent sides and two congruent angles.
If we draw a perpendicular bisector of the base (the side that is not congruent), it will bisect the base and the angle opposite to the base.
This means that the triangle is symmetric with respect to this line of reflection, which is the line of symmetry.
Therefore, the correct answer is isosceles triangle.
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As...
Which of the following geometric series diverges?
Answers
Answer:
II and II only.
Step-by-step explanation:
The first series converges because the common ratio r is 0.8 (<1).
II diverges as |r| > 1.
III is an alternating series with r = -4 - that is |r| = 4 so it diverges.
From the given-series, the series which diverges are : (ii) 4 + 8 + 16 + 32; and (iii) 2 - 8 + 32 - 128 + ..., So, correct option is (a) (ii) and (iii) only.
In option (ii), the series 4 + 8 + 16 + 32 is a geometric series with a common ratio of 2. We see that the "common-ratio" is greater than 1, this series diverges.
In option (iii), the series 2 - 8 + 32 - 128 is a geometric series with a common-ratio of |-4| = 4. We see that the "absolute-value" of the "common-ratio" is greater than 1, this series also diverges.
But, in option (i), the series -9.2 - 7.36 - 5.888 - 4.7104 is a geometric series with a common ratio of |-0.8| = 0.8. Since the "absolute-value" of the "common-ratio" is less than 1, this series converges.
Therefore, the correct answer is (a) (ii) and (iii) only.
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Write the expression as a trinomial: (y+7)(y-11). You want to make the expression into trynomial form, not simplified it
Answers
Answer:
y² - 4y - 77
Step-by-step explanation:
(y+7)(y-11)
y² - 11y + 7y - 77
y² - 4y - 77
graph a line with the slope of 1/4
Answers
Answer:
Used graphing calculator:
Slope .25
y-intercept: 0
x-intercept: 0
Step-by-step explanation:
The chi-square test statistic is χ2 = 18.68 and the P-value is between 0.0025 and 0.005. What conclusion should the researcher make? Use α = 0.05.
Answers
We don't know what the exact p-value is, but we are told that it's as large as 0.005 which is smaller than alpha = 0.05
Since the p-value is smaller than alpha, this means we reject the null hypothesis.
The way you can remember this is "if the p-value is low, then the null must go". By "low", I mean "smaller than alpha".
Recall that the p-value is the probability of observing that specific test statistic, or larger. So the chances of chi-squared being 18.68 or larger is a probability between 0.0025 and 0.005; there's a very small chance of this happening. The p-value is based entirely on the assumption that the null is correct. But if the null is correct, then the chances of landing on this are very small. We have a contradiction that basically leads to us concluding the null must not be the case. It's not 100% guaranteed of course, but it's fairly strong evidence.
In short, the p-value being smaller than alpha = 0.05 means we reject the null.
In order to accept the null, the p-value must be 0.05 or larger.
What is the remainder for the synthetic division problem below?
2/ 3 1 2 -7
A. 25
B. 17
C. -29
D. -39
Answers
Answer:
B.17
Step-by-step explanation:
B.17
B.17
B.17
B.17
An urn contains six red balls numbered 1, 2, 3, 4, 5, 6, two white balls numbered 7, 8, and two black balls numbered 9, 10. A ball is drawn from the urn. (Enter your probabilities as fractions.) (a) What is the probability that the ball is white
Answers
Answer:
2/10 = 1/5
Step-by-step explanation:
To figure out the probability of something, we can take
(number of outcomes of that something) / (number of total outcomes)
Here, we are trying to find the probability that the ball is white. The number of outcomes that are possible with the ball being white is 2, as there are two white balls and you can only pick one. You can pick either of the two white balls, but there is no way to pick one of them two times, pick two of them at once, or pick any other ball and have it be white.
The number of total outcomes is 10. There are 10 balls, and you can only pick one ball at a time. There are only 10 options to choose from.
Therefore, we can plug our numbers into the formula above and get 2/10 = 1/5 as our probability
Find the value of x.
X 9 9 7 x = [?]
Answers
What is the point slope equation of a line with slope -3 that contains points (-8,-4)
Answers
Answer:
y+4=-3(x+8)
Step-by-step explanation:
5 less than three times a number is 37 what is the number
Answers
Answer:
x = 14
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
3x - 5 = 37
Step 2: Solve for x
[Addition Property of Equality] Add 5 on both sides: 3x = 42[Division Property of Equality] Divide 3 on both sides: x = 14(1+y²)dx + (1+x²)dy = 0
Answers
This differential equation is separable:
(1 + y²) dx + (1 + x²) dy = 0
(1 + y²) dx = - (1 + x²) dy
dy/(1 + y²) = -dx/(1 + x²)
Integrating both sides gives
arctan(y) = -arctan(x) + C
and solving for y gives (over an appropriate domain)
y = tan(C - arctan(x))
(the domain being -1 ≤ y ≤ 1).
Most of the heat loss for outdoor swimming pools is due to surface
evaporation. So, the greater the area of the surface of the pool, the greater
the heat loss. For a given perimeter, which surface shape would be more
efficient at retaining heat: a circle or a rectangle? Justify your answer.
Answers
Answer:
rectangle
Step-by-step explanation:
Perimeter of 20 feet
rectangle (square is technically a rectangle):
sides 5 and 5
5*5 = 25ft²
Circle:
20/(2π) = 3.18309...
3.1809...²π = 31.831ft²
Max area of rectangle (i.e. square) has a smaller area than a circle.
Find the absolute maximum and absolute minimum for f (x )equals x cubed minus 2 x squared minus 4 x plus 2 on the interval 0 less or equal than x less or equal than 3.
Answers
9514 1404 393
Answer:
maximum: 2minimum: -6Step-by-step explanation:
The extrema will be at the ends of the interval or at a critical point within the interval.
The derivative of the function is ...
f'(x) = 3x² -4x -4 = (x -2)(3x +2)
It is zero at x=-2/3 and at x=2. Only the latter critical point is in the interval. Since the leading coefficient of this cubic is positive, the right-most critical point is a local minimum. The coordinates of interest in this interval are ...
f(0) = 2
f(2) = ((2 -2)(2) -4)(2) +2 = -8 +2 = -6
f(3) = ((3 -2)(3) -4)(3) +2 = -3 +2 = -1
The absolute maximum on the interval is f(0) = 2.
The absolute minimum on the interval is f(2) = -6.
An expression is shown below:
10n3 − 15n2 + 20xn2 − 30xn
Part A: Rewrite the expression so the GCF is factored completely. (4 points)
Part B: Rewrite the expression completely factored. Show the steps of your work.
Answers
Answer:
An expression is shown below:
10n³− 15n² + 20xn² − 30xn
Part A: Rewrite the expression so the GCF is factored completely. (4 points)
10n³− 15n² + 20xn² − 30xn
2*5*n*n*n-5*3*n*n+2*5*2*x*n*n-2*5*3*x*n
Greatest common factor=5*n=5n
Part B: Rewrite the expression completely factored. Show the steps of your work.
Solution given;
10n³− 15n² + 20xn² − 30xn
5n(2n²-3n+4xn-6x)
5n(2n²+4xn-3n-6x)
5n(2n(n+2x)-3(n+2x))
5n(n+2x)(2n-3)
Answer:
[tex]5n(2n-3)(n+2x)[/tex]
Step-by-step explanation:
Step 1: Rewrite the expression so the GCF is factored completely
[tex]10n^{3} - 15n^{2} + 20xn^{2} - 30xn[/tex]
The GCF is 5n so factor it out
[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]
Step 2: Rewrite the expression completely factored
[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]
[tex]5n(2n(n+2x)-3(n+2x))[/tex]
[tex]5n(2n-3)(n+2x)[/tex]
Answer: [tex]5n(2n-3)(n+2x)[/tex]
f(x) = x - 1. Find the inverse of f(x).
Answers
Answer:
f^-1 (x) = x+1
Step-by-step explanation:
f(x) = x-1
y = x-1
Exchange x and y
x = y-1
Solve for y
Add 1 to each side
x+1 = y-1+1
x+1 = y
The inverse is x+1
f^-1 (x) = x+1
A popular beach erodes 4 inches per year on average.
An eroding beach.
A. How many years will it take for the coastline to erode one foot?
Answers
Answer:
3 years
Step-by-step explanation:
4 inches per year on average
1 foot = 12 inches
12 divided by 4 equals 3
therefore it is 3 years
(b) Two isosceles triangles PQR and PQS are drawn on opposite sides.
of a common base PQ. If PQR = 66° and PSQ = 109°, calculate
the value of RQS.
Answers
9514 1404 393
Answer:
101.5°
Step-by-step explanation:
Angle PQS will be the complement of half of angle PSQ, so is ...
∠PQS = 90° -109/2° = 35.5°
Angle RQS is the sum of angles RQP and PQS:
∠RQS = 66° +35.5° = 101.5°
[tex]\sqrt{25}[/tex]=?
Answers
[tex]Hello[/tex] [tex]There[/tex]
The answer is...
[tex]5.[/tex]
[tex]HopeThisHelps!![/tex]
[tex]AnimeVines[/tex]
Hope it helps.
The speed of the light is approximately 3x10^14 centimeters per second.how much will it take light to Tavel 9x10^14 centimeters
Answers
Answer:
3 seconds
Step-by-step explanation:
First, let's calculate the approximate speed of light.
3 · 10^14 = 3 · 100,000,000,000,000
= 300,000,000,000,000
Approximately, light travels 300,000,000,000,000 centimeters per second.
Now, let's simplify 9x10^14.
9 · 10^14 = 9 · 100,000,000,000,000
= 900,000,000,000,000
To find out how many seconds light takes to travel 900,000,000,000,000 centimeters, we have to divide this number by 300,000,000,000,000, the approximate speed of light.
900,000,000,000,000/300,000,000,000,000 = 3
Therefore, it will take 3 seconds for light to travel 900,000,000,000,000 centimeters.
It will take 3 seconds to cover the distance of 9×10¹⁴ cm.
What is scientific notation?We use the scientific notation of numbers to write very large numbers in compact form.
In the scientific form, we write a number in the form of base×10ⁿ.
Where 0 ≤ base < 10 and n can be any rational number.
Given the speed of light s approximately 3×10¹⁴ cm/sec.
∴ It will take (9×10¹⁴/3×10¹⁴) = 3 seconds.
We know that exponents are added when the same base is multiplied and exponents are subtracted when the same base or integral multiple of the same base is divided.
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