Help me please!
Consider the function f(x) = V2x – 4. Iff-'(x) is the inverse function of f(x), find
f-16)
Answers
Answer:
[tex]f^{-1}(6) = 50[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \sqrt{2x} - 4[/tex]
Required
Find [tex]f^{-1}(6)[/tex]
First, we calculate the inverse function
[tex]f(x) = \sqrt{2x} - 4[/tex]
Express f(x) as y
[tex]y = \sqrt{2x} - 4[/tex]
Swap the positions of x and y
[tex]x = \sqrt{2y} - 4[/tex]
Solve for y: Add 4 to both sides
[tex]4 + x = \sqrt{2y} - 4+4[/tex]
[tex]4 + x = \sqrt{2y}[/tex]
Square both sides
[tex](4 + x)^2 = 2y[/tex]
Divide both sides by 2
[tex]y = \frac{(4 + x)^2}{2}[/tex]
Express y as an inverse function
[tex]f^{-1}(x) = \frac{(4 + x)^2}{2}[/tex]
Next, solve for: [tex]f^{-1}(6)[/tex]
Substitute 6 for x
[tex]f^{-1}(6) = \frac{(4 + 6)^2}{2}[/tex]
[tex]f^{-1}(6) = \frac{(10)^2}{2}[/tex]
[tex]f^{-1}(6) = \frac{100}{2}[/tex]
[tex]f^{-1}(6) = 50[/tex]
Related Questions
You withdrew $36.25 from your checking account. Now your balance is −$14.75. Write and solve an equation to find the amount of money in your account before you withdrew the money?
Answers
Answer:
SIMPLE, −$14.75 + $36.25 = $21.50
Step-by-step explanation:
TO CHECK OURSELVES:
21.50 - 36.25 = -14.75
YOUR WELCOME
A marine biologist wants to test the effect of water temperature on the length of time sea otters can remain under water during a dive. He gathers data on randomly selected dives by 7 different otters, recording dive duration (in seconds) and water temperature (in degrees Celsius). A computer regression analysis of his data is given below. Assume all conditions for inference for slope have been met.
Predictor Coef SE coef T P
Constant 52.789 5.257 10.04 0.000
Water temp 3.3684 0.4216 7.990 0.002
S= 5.557 R- Sq= 92.7% R-Sq(adj)= 91.3%
Required:
What is the estimate of the standard deviation of the sampling distribution of b, the slope of the sample regression line for this relationship?
Answers
Answer:
0.4216
Step-by-step explanation:
from the data given The estimate of the standard deviation of the sampling distribution of b,
( The slope of the sample regression line for the relationship )
= 0.4216 ( i.e. intersection of SE coef and water temperature )
Testing the effect of water temperature on the length of time sea otters can remain
Someone pls help me out thanks
Answers
Answer:
C(7,-8)
R= 8
The general formula of a circle = (x-a)+(y-b)=r²
You need to establish _____ for how to judge a concept.
Answers
Questions
Points
Criteria
Answers
Answer:
Criteria.
Step-by-step explanation:
A series of criteria is a set of parameters established by whoever seeks to interpret a certain information or quantity of concepts, by means of which a set of interpretive rules is established that should be equal to all the concepts to be analyzed. Thus, the criteria allow a set of data to be analyzed under the same parameters or information processing requirements.
Find the value of x in the triangle shown below.
a. x=80
b. x=48
c. x= 32
d. x=12
Answers
h.c gjsussisuse udrih eieeiee Getty e
13.) In 1990, a radio costs $25. Now,
the radio costs $5. What is the
percent of change?
Answers
Answer:
Step-by-step explanation:
80% of 25 = 5
because 10% of 25 = 2.5
and then 10 x 8 = 80
so 2.5 x 8 = 20
25 - 20 = 5
therefore, the percentage change is 80%
GIVE BRAINLIEST
hope this helped,
-cheesetoasty
Please quickly help me with this question please please please please please I’m beggig
Answers
Answer:
D: Point A is 1 unit to the right of the origin and point B is 3 units to the right of the origin.
Step-by-step explanation:
The coordinate (1, 3) is in quadrant 1 with a positive y, moving the point up, and a positive x, moving the point right. Because the x is 1, the point moves 1 unit right from the origin.
The coordinate (3, 1) is also in quadrant 1 with a positive y and x, but this time the x is 3, moving the point 3 units right from the origin.
1-4: Find the measures of central tendency, then determine the range of the data.
Daily High Temperatures (°F) for a week: 68 70 67 68 75 75 74 (1 pt each)
1. Mean:
2. Median:
3. Mode(s):
4. Range:
Answers
Answer:
Step-by-step explanation:
1=71
2=70
3= 68 and 75, they both appear twice
4= 8
Find the value of x in the triangle shown below
a.x=28
b.x=56
c.x=28
d.x=20
Answers
Answer:
D.
Step-by-step explanation:
Answer:
[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ [/tex]
by using Pythagoras law:
h²=p²+b²
x²=16²+12²
x=√400
x=20 units.
How much water will be needed to completely fill a rectangular tank that has a length of 3 meters a width of 3 meters
and a height of 18 meters?
(A) 162 cubic meters
(B) 24 cubic meters
(C) 324 cubic meters
(D) 108 cubic meters
Answers
Answer:
A
Step-by-step explanation:
because when you multiply 3x3 (the base) times 18(the height) you get= 162
Find the length of the cable in the diagram below.
Answers
Answer:
13.4
Step-by-step explanation:
it is A square +b square =c square which is just 12×12=144 + 6×6=36 and then add them together which is 180, then just square root 180 can do it for every type of question like that and always remember the longest side is c, and the other two it doesn't matter which is A or B.
1. What is the difference in the ranges?
A 5 points
C 20 points
B 10 points
D 35 points
2. Which test has a greater median?
A Test 1
B Test 2
C They have the same median.
D You cannot tell from the dot plots.
Answers
What is the volume of a rectangular prism with length equal to 13,width equal to 6 and height equal to 4
Answers
Given:
Length of the rectangular prism = 13 units.
Width of the rectangular prism = 6 units.
Height of the rectangular prism = 4 units.
To find:
The volume of the rectangular prism.
Solution:
We know that the volume of the rectangular prism is:
[tex]V=l\times b\times h[/tex]
Where, l is length, b is breadth or width and h is the height of the rectangular prism.
Putting [tex]l=13,b=6,h=4[/tex] in the above formula, we get
[tex]V=13\times 6\times 4[/tex]
[tex]V=312[/tex]
Therefore, the volume of the given rectangular prism is 312 cubic units.
The scatter plot shows the number of hours worked and money spent on entertainment by each of 24 students. Also shown is the line of best fit for the data. Fill in the blanks below.
Answers
The given scatter plot has a positive correlation.
Given that, the scatter plot shows the number of hours worked and money spent on entertainment by every 24 students.
What are scatter plots?A scatter plot is a means to represent data in a graphical format. A simple scatter plot makes use of the coordinate axes to plot the points, based on their values. The following scatter plot excel data for age (of the child in years) and height (of the child in feet) can be represented as a scatter plot.
A positive correlation—when the correlation coefficient is greater than 0 signifies that both variables move in the same direction.
The blanks for the given questions are filled below:
a) increase
b) strong positive
c) $22.50
Therefore, the given scatter plot has a positive correlation.
To learn more about the scatter plot visit:
https://brainly.com/question/13984412.
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Which phrase describes the shape of the data?
.
.
.
12
13
14
15
10
17
18
A. Symmetric, not bell-shaped
B. Not symmetric, bell-shaped
C. Not symmetric, not bell-shaped
D. Symmetric bell-shaped
Answers
Answer:
C. Not symmetric; not bell-shaped.
Step-by-step explanation:
In a symmetric data distribution, the shape on the left side is almost the same as the shape on the right side of the middle. In this type of data distribution, if different measure of centers are calculated (mean, median, and mode), they will have a similar figures that are close together. Symmetric distributions are bell-shaped.
On the other hand, if the data distribution is not symetric, it means the left and the right side of the distribution are not equal and do not have the same shape.
The data in the dot plot above is considered as NOT SYMMETRIC. Also, it is not bell-shaped.
Answer:
c
Step-by-step explanation:
She has 12 watermelons, 30 pears, and 42 apples
For each basket Kerra makes they must have the same number of fruit.
She must use all the fruit.
What is the greatest number of baskets that Kerra can make?
Answers
12/6=2
30/6=5
42/6=7
A cube with sides that are 2 cm has a mass of 48 g and its density would be
___________ g/cm3.
Answers
Answer:
6g/cm^3
Step-by-step explanation:
The density of the cube would be 6 grams/cm^3. I got this answer by first finding the volume of the cube, 2^3 which gives me 8 cm as the initial volume of the cube. Then, the 48 grams of mass the cube has allows me to divide 48 / 8 which gave me 6. And 6 would be the density of the cube in grams.
Answer: 6g/cm^3
Hope this helps!
Answer:
p = 6 g/cm³
Step-by-step explanation:
Given: cube sides= 2 cm and 48 g
To find: The cube's density
Formula: [tex]{p} \frac{m}{V}[/tex]
Solution: Measure the height, width, and depth of the shipment in inches.
Multiply the three measurements (height x width x depth).
Divide the total cubic inches by 1,728 (the number of cubic inches in a cubic foot).
Divide the weight (in pounds) of the shipment by the total cubic feet.
p = density
m = mass
V = volume
You own a truck that has a trailer in the shape of a rectangular prism. It has a height of 15 m and a length of 40m, and a width of 10 m. If you wish to fill this trailer with 5m x 5m x 5m cubic boxes, how many boxes will fit into
the trailer
Answers
Answer:
48 boxes
Explanation:
First, find the volume of the rectangular prism (l*w*h) to find out how much it can hold.
15*40*10= 6,000
Then, find the volume of the cubic boxes (l*w*h) to find how much space each of them take up.
5*5*5= 125
Finally, divide the rectangular prism's volume by the boxes' to find out how many can fit inside.
6,000/125= 48 boxes
Find the distance between the two points. (2, 4), (7, 2)
Answers
Answer:
5.38516480 or √ 29
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
5.385165 or sqrt 29
Step-by-step explanation:
d = distance
d= sqrt (7-2)^2+(2-4)^2
and when simplified fully you get
sqrt or 5.385165
The authors of a paper studied a random sample of 350 Twitter users. For each Twitter user in the sample, the "tweets" sent during a particular time period were analyzed and the Twitter user was classified into one of the following categories based on the type of messages they usually sent.
Category Description
IS Information sharing
OC Opinions and complaints
RT Random thoughts
ME Me now (what I am doing now)
O Other
The accompanying table gives the observed counts for the five categories (approximate values read from a graph in the paper).
Twitter Type IS OC RT ME O
Observed count 50 61 64 102 73
Required:
Carry out a hypothesis test to determine if there is convincing evidence that the proportions of Twitter users falling into each of the five categories are not all the same. Use a significance level of 0.05.
Answers
Answer:
The null hypothesis is rejected.
Step-by-step explanation:
Assuming the proportions in each of the categories is the same which is 1/5 = 0.20.
H0: p1 = p2 = p3 = p4 = p5 = 0.2
Ha: H0 is not true.
The table is as below:
Twitter Type: Observed Count p E=350*p (O-E)^2/E
IS 50 0.2 70 5.7143
OC 61 0.2 70 1.1571
RT 64 0.2 70 0.5143
ME 102 0.2 70 14.6285
O 73 0.2 70 0.1286
-----------------------------------------------------------------------------------------------
Total 22.1428
The test statistic [tex]\chi^2[/tex] is 22.1421
The degree of freedom d is n-1=5-1 =4
The corresponding p-value from the chi-squared table is .000188.
As this value is less than the p-value for the H0 thus we reject the null hypothesis.
Please help, I will give brainliest!!!
The table models the flight of the projectile from Part A
Which of these statements is true?
A) h(4) < h(20)
B) The flight is symmetric about the line t=10
C) The projectile will hit the ground at some value of t less than 24.
D) If 0<a<12, then h(12-a) = h(12+a).
Answers
If 0 < a < 12, then h(12 – a) = h(12 + a) is true. Then the correct option is D.
What is a projectile motion?When a body is thrown in the air at an angle, then the term is known as projectile motion.
The table is given in the question.
A) h(4) < h(20), this statement is incorrect, because the h(4) = h(20).
B) The flight is symmetric about the line t = 10, this statement is incorrect, because symmetric about t = 12.
C) The projectile will hit the ground at some value of t less than 24. This is incorrect, because t > 24.
D) If 0 < a < 12, then h(12 - a) = h(12 + a). This statement is correct.
Then the correct option is D.
More about the projectile motion link is given below.
https://brainly.com/question/11049671
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The distance by road from town A to town B is 242km.
What is 50% of that distance? A484 b 121 c 242 d
13
Answers
Answer: Option b 121km
50% means half, so the half of 242km is 121km, so option B 121 is correct.
Step-by-step explanation:
242/2=121
Have a nice day!
and can I maybe have brainliest? Thanks!
Answer:
Step-by-step explanation:
36 - 4
Step-by-step explanation:
(6x - 2)(6x + 2)
= (6x)(6x) + (6x)(-2) + (2)(6x) + (-2)(2)
= 36 - 12x + 12x - 4
= 36 - 4
if 16c 1 gal then 1 1/4 gal __= c
Answers
Answer:
20 cups
Step-by-step explanation:
16 x 1.25 = 20
Answer:
11/4 c = 44 gal
I hope it's helps you
What is the area, in square centimeters, of the shaded part of the rectangle shown below
Answers
Answer:
Step-by-step explanation:
i think you forgot to link or import the question
Please help. I NEED GOOD GRADES
Answers
Answer:
The circle should be open and the arrow should go the other way.
the area of the trangle is......
Answers
Answer:
30 cm²
Step-by-step explanation:
To find the area of a triangle, multiply the base and the height, then, divide the product by 2.
In this case, the base is 6 and the height is 10.
6 x 10 = 60
The product is 60.
60 / 2 = 30
Therefore, the area of this triangle is 30 cm².
Answer:
30
Step-by-step explanation:
Formula for area of a triangle: [tex]A=\frac{bh}{2}[/tex]
where b = base length and h = height
The triangle shown has a base length of 6 cm and a height of 10 cm
Using this information we plug in the values into the formula
So...
[tex]A=\frac{10*6}{2} \\10*6=60 \\\frac{60}{2} =30[/tex]
Hence, the area of the triangle is 30 square centimeters.
hey guys i'm having a rough night and i can't figure out my homework rn i'm just too stress please help
Answers
Answer:
3a) 54/99
3b) 257/999
Hope this'll help you!
What is the value of 12(x + 5)?
Answers
Answer:
12(x+5)=
12x+60=
12x÷12 & 60÷12
x=5
What is cot(A)?
A. -3 sqrt 7/7 correct
Answers
Step-by-step explanation:
[tex]to \: help \: you \\ \cot(A) = { (\tan(A)) }^{ - 1} = \frac{ \cos(A) }{ \sin(A) } \\ or : \\ \cot(A) = \sqrt{(1 + {( \tan(A) )}^{2} } [/tex]
Answer:
A is correct :)
Step-by-step explanation:
edge 2021
thank you! have a great day
a triangle has two sides of lengths 5 and 12, what value could the length of the third side be? check all that apply
Answers
Answer:
11 and 9
Step-by-step explanation:
The inequality is 12-5<x<12+5, which simplifies to 7<x<17, so the length of the third side can be any number between 7 and 17, but not including those numbers.
The answer is 11 and 9