The table and the plotted data are in the attachment.
Answer and Step-by-step explanation: A line of best fit is the best approximation of the given data. It is used to show the relation of two variables and it can be determined, more accurately, by the Least Square Method.
To use the method, follow the steps:
1) Calculate the mean of the two variables:
[tex]X = \frac{\Sigma x_{i}}{n}[/tex]
[tex]Y=\frac{\Sigma y_{i}}{n}[/tex]
2) The Slope of the line is given by:
[tex]m=\frac{\Sigma (x_{i}-X)(y_{i}-Y)}{\Sigma (x_{i}-X)^{2}}[/tex]
3) The y-intercept is found by the formula:
[tex]b=Y-mX[/tex]
For the ripening of bananas, the least square method gives the line:
y = -0.142x + 5.56
The rate of change of a line equation is its slope, so
Rate of change = -0.14
The rate of change of ripening time with respect to exposure time is -0.14, which means the more expose the fruit is, the less time it needs to ripe.
For which system of inequalities is (3,-7) a solution?
A. x + y < -4
3x + 2y < -5
B. x + y ≤ -4
3x + 2y < -5
C. x + y < -4
3x + 2y ≤ -5
D. x + y ≤ -4
3x + 2y ≤ -5
Answer:
D) x + y ≤ -4
3x + 2y ≤ -5
Step-by-step explanation:
Step(i):-
we will choose the system of inequalities
x + y ≤ -4
3x + 2y ≤ -5
x + y = -4 ...(i)
3x + 2y = -5..(ii)
Multiply equation (i) with '3'
3x + 3y = -12
3x + 2 y = -5
- - +
0 + y = -7
Step(ii):-
Substitute y = -7 in equation (i)
x + y = -4
x - 7 = -4
x = -4 + 7
x = 3
The solution of the given inequalities is ( 3, -7)
If segment XY = 5 and segment YZ = 10, what is the length of XZ?
Answer:
The length of segment XZ is 15 units
Step-by-step explanation:
Given
[tex]XY = 5[/tex]
[tex]YZ = 10[/tex]
Required
Determine XZ
Assuming XY and YZ are on the same plane such that
[tex]XZ = XY + YZ[/tex]
Substitute values for XY and YZ
[tex]XZ = 5 + 10[/tex]
[tex]XZ = 15[/tex]
Hence, the length of segment XZ is 15 units
Troll Inc. has an outstanding issue of perpetual preferred stock with an annual dividend of $9.50 per share. If the required return on this preferred stock is 6.5%, at what price should the stock sell? * a) $104.27 b) $106.95 c) $109.69 d) $146.15 e) None of the above
Answer:
d) $146.15
Step-by-step explanation:
From the above Question, we are given the following values:
The annual dividend per share of a perpetual preferred stock = $9.50
The required return rate on this preferred stock = 6.5% = 0.06
The selling price of the stock = ??
The formula to calculate the Selling price of the stock =
Annual dividend per share / Required return rate
= $9.5/ 0.065
= $146.15384615
Approximately $146.15
Therefore, the price at which the stock should sell is $146.15.
According to Bureau of Labor Statistics, 22.1% of the total part-time workforce in the U.S. was between the ages of 25 and 34 during the 3 rd quarter of 2011. A random sample of 80 part-time employees was selected during this quarter. Using the normal approximation to the binomial distribution, what is the probability that fewer than 20 people from this sample were between the ages of 25 and 34?
Answer:
The probability is [tex]P(X < 20 ) = 0.68807[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of total part-time workforce is [tex]\r p = 0.221[/tex]
The sample size is n = 80
Generally the mean is mathematically represented as
[tex]\mu = n* p[/tex]
[tex]\mu = 0.221 * 80[/tex]
[tex]\mu = 17.68[/tex]
The proportion of not part - time workforce
[tex]q = 1- p[/tex]
=> [tex]q = 1- 0.221[/tex]
=> [tex]q = 0.779[/tex]
The standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ 80 * 0.221 * 0.779 }[/tex]
[tex]\sigma = 3.711[/tex]
Now applying the normal approximation,
Then the probability that fewer than 20 people from this sample were between the ages of 25 and 34 is mathematically represented as
[tex]P(X < 20 ) = P( \frac{X - \mu }{ \sigma } < \frac{ 20 - 17.68 }{ 3.711} )[/tex]
Applying continuity correction
[tex]P(X < 20 ) = P( \frac{X - \mu }{ \sigma } < \frac{ (20-0.5 ) - 17.68 }{ 3.711} )[/tex]
[tex]P(X < 20 ) = P( \frac{X - \mu }{ \sigma } < \frac{ (20-0.5 ) - 17.68 }{ 3.711} )[/tex]
[tex]P(X < 20 ) = P( \frac{X - \mu }{ \sigma } < 0.4904 )[/tex]
Generally
[tex]\frac{X - \mu }{ \sigma } = Z ( The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X < 20 ) = P( Z< 0.4904 )[/tex]
From the z-table
[tex]P( Z< 0.4904 ) = 0.68807[/tex]
The probability is
[tex]P(X < 20 ) = 0.68807[/tex]
Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 100 subjects has a distribution that agrees with the distribution of state populations.
Answer:
Step-by-step explanation:
From the given information:
the null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathbf{H_o:}[/tex] The sample have a distribution that agrees with the distribution of state populations.
[tex]\mathbf{H_1:}[/tex] The sample have a distribution that does not agrees with the distribution of state populations.
The Chi-Square test statistics [tex]\mathbf{X^2 = \dfrac{(Observed \ value - Expected \ value )}{(Expected \ value ) ^2 }}[/tex]
Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana.
The observed and the expected value can be computed as follows:
States Observed Expected [tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
Washington 450 0.51 × 1000 = 510
Oregon 340 0.30 × 1000 = 300
Idaho 150 0.11 × 1000 = 110
Montana 60 0.08 × 1000 = 80
Total 1000 1000
For washington :
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(450 -510)^2}{510}[/tex]
[tex]X^2 = \dfrac{3600}{510}[/tex]
[tex]X^{2}=[/tex] 7.06
For Oregon
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(340- 300)^2}{300}[/tex]
[tex]X^2 = \dfrac{1600}{300}[/tex]
[tex]X^{2}=[/tex] 5.33
For Idaho
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(150- 110)^2}{110}[/tex]
[tex]X^2 = \dfrac{1600}{110}[/tex]
[tex]X^2 =14.55[/tex]
For Montana
[tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
[tex]X^2 = \dfrac{(60- 80)^2}{80}[/tex]
[tex]X^2 = \dfrac{400}{80}[/tex]
[tex]X^2 = 5[/tex].00
The Chi-square test statistics for the observed and the expected value can be computed as follows:
States Observed Expected [tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
Washington 450 0.51 × 1000 = 510 7.06
Oregon 340 0.30 × 1000 = 300 5.33
Idaho 150 0.11 × 1000 = 110 14.55
Montana 60 0.08 × 1000 = 80 5.00
Total 1000 1000 31.94
The Chi-square Statistics Test [tex]\mathbf{X^2 = 31.94}[/tex]
Degree of freedom = n - 1
Degree of freedom = 4 - 1
Degree of freedom = 3
At 0.05 level of significance, the critical value of :
[tex]X^2_{(df, \alpha) }=X^2_{(3, 0.05)[/tex] = 7.815
Decision Rule: To reject null hypothesis if the test statistics is greater than the critical value
Conclusion: We reject the null hypothesis since test statistics is greater than critical value, therefore, we conclude that there is sufficient information to say that the sample has a distribution that does not agrees with the distribution of state populations.
Find the missing side length using pythagorean theorem. simplify radicals if necessary* PLEASE HELP!!
Answer:
15
Step-by-step explanation:
a^2 + b^2 = c^2
9=a
12-b
Plug in the numbers
Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2), and is parallel to the graph of x + 3y = -5.
Answer:
2
Step-by-step explanation:
The parallel line will have the same coefficients, but a constant suited to the given point:
x + 3y = constant
That is, A=1, B=3, so B-A = 2.
___
The constant for the parallel line will be -1.
Can a vertical line be diagonal?
Answer:
No
Step-by-step explanation:
Assuming that the x- and y- axes are respectively horizontal and vertical, a vertical line has an undefined slope and cannot be diagonal.
Note that only a diagonal line can have a slope defined.
Solves the following equation for a. Show steps for full credit.
4a + 10 = 2a + 26
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{a = 8}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{4a + 10 = 2a + 26}[/tex]
Move 2a to left hand side and change it's sign
Similarly, move 10 to right hand side and change it's sign
⇒[tex] \sf{4a - 2a =26 - 10}[/tex]
Collect like terms
⇒[tex] \sf{2a = 26 - 10}[/tex]
Subtract 10 from 26
⇒[tex] \sf{2a = 16}[/tex]
Divide both sides of the equation by 2
⇒[tex] \sf{ \frac{2a}{2} = \frac{16}{2} }[/tex]
Calculate
⇒[tex] \sf{a = 8}[/tex]
Hope I helped!
Best regards!!
According to a poll taken last year, 45% of the cities' residents get most of their news from the Internet. To conduct a follow-up study that would provide 90% confidence that the point estimate is correct to within 0.04 of the population proportion, how large a sample size is required
Answer:
The sample size is [tex]n =419[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.45[/tex]
The margin of error is [tex]E = 0.04[/tex]
Given that the confidence level is 90%
Then the level of significance can be mathematically represented as
[tex]\alpha = 100 -90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the level of significance from the normal distribution table the value is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the sample size is mathematically represented as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * p(1- p )[/tex]
substituting values
[tex]n = [ \frac{1.645 }{0.04} ]^2 * 0.45(1- 0.45 )[/tex]
[tex]n =419[/tex]
Give an example of two 2×2 matrices A and B, neither of which is the zero matrix or the identity matrix, such that AB=BA.
Let
[tex]A=B=\begin{bmatrix}0&1\\1&0\end{bmatrix}[/tex]
Then
[tex]AB=BA=\begin{bmatrix}0&1\\1&0\end{bmatrix}^2=\begin{bmatrix}1&0\\0&1\end{bmatrix}[/tex]
HELP!! hOW DO YOU FIND FREQUENCY FROM CLASS LIMITS AND CLASS BOUNDARY???? I AM SO CONFUSED.
Data:
70 88 103 64 88 100 78 80 77 69
85 65 71 90 88 75 80 72 60 70
60 75 79
Class width: 7
Class limits
60-66
67-73
74-80
81-87
88-94
95-101
102-108
class boundaries
59.5-66.5
66.5- 73.5
73.5- 80.5
80.5- 87.5
87.5- 94.5
94.5-101.5
101.5-108.5
frequency
____
------
____
____
_____
___
_____
= Total frequency
Side Note: Format is off but it is three columns I need help figuring out this exact problem
JIM, Thank so you so much. How can I private message you?
The third column is optional/extra. It's to show which data values fit in what specific class limit interval.
===================================================
Explanation:
Imagine we had a bunch of cards. Each card will have a number that is from the data set {70, 88, 103, 64, ... etc}
The goal is to sort the cards into 7 boxes. The first box is labeled "60 through 66", the next is "67 through 73", etc.
The first box has 4 cards placed inside it because we have the values {64,65,60,60 } which fit the interval from 60 through 66. Therefore the frequency here is 4.
The next box has the cards labeled {70,69,71,72,70 } inside it. We have 5 cards here, so the frequency is 5.
This pattern is kept up until all of the cards have been sorted into the proper boxes.
What you'll end up with is what you see in the image below. It shows the table of class limits with their corresponding frequencies. I have added a third column to show which values go where, which is optional and likely something you wont put as your answer to the teacher. This third column is just something for you to help keep track of everything.
Jerry has reached 39% of his weekly exercise time goal so far this week if he has exercise for a total of 78 minutes this week. What is his weekly exercise time goal in minutes?
Answer:
his weekly exercise time goal in minutes = 200 minutes
Step-by-step explanation:
Jerry has reached 39% of his weekly exercise time goal.
so far this week ,he has exercise for a total of 78 minutes this week.
39% of total = 78 minutes
100%= x
X=100*78/39
X=100*2
X= 200 minutes
his weekly exercise time goal in minutes = 200 minutes
Solve the equation: x/4= 2
Answer:
[tex] \purple{ \boxed { \bold{\blue{x = 8}}}}[/tex]Step-by-step explanation:
[tex] \mathsf{ \frac{x}{4} = 2}[/tex]
Apply cross product property
[tex] \mathsf{x \times 1 = 2 \times 4}[/tex]
Calculate
[tex] \mathsf{x = 8}[/tex]
Hope I helped!
Best regards!
Answer:
[tex] \frac{x}{4} = 2[/tex]
X=2
Step-by-step explanation:
4•x/4=2•4
X=8
can you please help me?
Step-by-step explanation:
1.
Point M is the bisector of AB
AM = 13...(given)
Therefore, AB = 2AM = 2* 13 = 26
2.
Ray MC is the bisector of AB
AM = 8...(given)
Therefore, AB = 2AM = 2* 8 = 16
3.
Line l is the bisector of angle AB.
BM = 26...(given)
Therefore, AB = 2BM = 2* 26 = 52
x = 3 / 5 (cb+k)
Solve for b
Answer:
(5/3 x - k)/c =b
Step-by-step explanation:
x = 3 / 5 (cb+k)
Multiply each side by 5/3
5/3x =5/3* 3 / 5 (cb+k)
5/3x = (cb+k)
Subtract k
5/3 x - k = cb +k-k
5/3 x - k = cb
Divide by c
(5/3 x - k)/c = cb/c
(5/3 x - k)/c =b
find compound amount annually of p=4000,time=3/2 and rate =10% solve it step wise.
Step-by-step explanation:
Hey, there!!
Principal (p) = 4000
Time = 3/2= 1.5 yrs.
rate = 10%
Now, we have formula,
[tex]c.a = p \times {(1 + \frac{r}{100}) }^{t} [/tex]
Putting their values,
[tex]ca = 4000\times {(1 + \frac{10}{100} )}^{1.5} [/tex]
[tex]ca =4000 \times {(1 + 0.1)}^{1.5} [/tex]
[tex]ca = 4000 \times 1.153689[/tex]
Simplifying them we get,
C.A = 4614.75
Hope it helps...
The mean height of women in a country (ages 2029) is inches. A random sample of women in this age group is selected. What is the probability that the mean height for the sample is greater than inches? Assume . The probability that the mean height for the sample is greater than inches is nothing.
Complete Question
The mean height of women in a country (ages 20-29) is 64.4 inches. A random sample of 75 women in this age ground is selected. what is the probability that the mean height for the sample is greater than 65 inches? assume [tex]\sigma = 2.97[/tex]
Answer:
The value is [tex]P(X > 65) = 0.039715[/tex]
Step-by-step explanation:
From question we are told that
The mean is [tex]\mu = 64.4 \ inches[/tex]
The sample size is [tex]n = 75[/tex]
The probability that the mean height for the sample is greater than 65 inches is mathematically represented as
[tex]P(X > 65) = P[\frac{X - \mu }{ \sigma_{\= x} } > \frac{65 - 64.4 }{ \sigma_{\= x} } ][/tex]
Where [tex]\sigma _{\= x }[/tex] is the standard error of mean which is evaluated as
[tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x } = \frac{2.97}{\sqrt{75} }[/tex]
=> [tex]\sigma_{\= x } = 0.343[/tex]
Generally [tex]\frac{X - \mu }{ \sigma_{\= x } } = Z(The \ standardized \ value \ of \ X )[/tex]
[tex]P(X > 65) = P[Z> \frac{65 - 64.4 }{0.342 } ][/tex]
So
[tex]P(X > 65) = P[Z >1.754 ][/tex]
From the z-table the value of
[tex]P(X > 65) = P[Z >1.754 ] = 0.039715[/tex]
[tex]P(X > 65) = 0.039715[/tex]
what is the answer to 6y+21+7=4y−20+5y
Step-by-step explanation:
the answer for 6y+21+7=4y−20+5y is
y =16
What is the length ok a bus if the scale is 0.5 inches to 5 feet and the length of the bus is 4.5 inches
Answer:
4.5 divided by 0.5=9
9 times 5=45
45 feet
Step-by-step explanation:
Answer:
45 feet
Step-by-step explanation:
Set up a proportion:
[tex]\frac{0.5}{5}[/tex] = [tex]\frac{4.5}{x}[/tex]
Cross multiply:
0.5x = 22.5
x = 45
= 45 feet
what is the first operation used to evaluate 13-2x3+4 divided by 4+4
Answer:
multiplication
Step-by-step explanation:
The evaluation of ...
13 -2·3 +4/4 +4
starts with the multiplication, because there are no exponents or parentheses.
13 -6 +4/4 +4
Next is the division:
13 -6 +1 +4
Finally, the addition and subtraction:
7 +1 +4
8 +4
12
_____
We have assumed your x is not a variable, but is intended to indicate multiplication. We have also assumed that your "divided by" implies no particular grouping, so that the numerator is the first preceding number and only the first following number is in the denominator.
. A normal population has a mean of 80.0 and a standard deviation of 14.0. a. Compute the probability of a value between 75.0 and 90.0. b. Compute the probability of a value of 75.0 or less. c. Compute the probability of a value between 55.0 and 70.0. 19. Suppose the Internal Revenue Service reported that the mean
Answer:
a. 0.40198
b. 0.36049
c. 0.20046
Step-by-step explanation:
To solve for this we make use of the z score formula.
z-score formula is
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Compute the probability of a value between 75.0 and 90.0.
For x = 75
From the question, we know that
mean of 80.0 and a standard deviation of 14.0.
z = (x - μ)/σ
z = 75 - 80/ 14
z = -0.35714
Using the z score table to find the probability
P-value from Z-Table:
P(x = 75) = P(z = -0.35714)
= 0.36049
For x = 90
z = 90 - 80/14
z = 0.71429
Using the z score table to find the probability
P-value from Z-Table:
P(x = 90) = P(z = 0.71429)
= 0.76247
The probability of a value between 75.0 and 90.0 is:
75 < x < 90
= P( x = 90) - P(x = 75)
= 0.76247 - 0.36049
= 0.40198
Therefore, probability of a value between 75.0 and 90.0 is 0.40198
b. Compute the probability of a value of 75.0 or less.
For x = 75
From the question, we know that
mean of 80.0 and a standard deviation of 14.0.
z = (x - μ)/σ
z = 75 - 80/ 14
z = -0.35714
Using the z score table to find the probability
P-value from Z-Table:
P(x ≤ 75) = 0.36049
c. Compute the probability of a value between 55.0 and 70.0.
For x = 55
From the question, we know that
mean of 80.0 and a standard deviation of 14.0.
z = (x - μ)/σ
z = 55 - 80/ 14
z = -1.78571
Using the z score table to find the probability
P-value from Z-Table:
P(x = 55) = P(z = -1.78571)
= 0.037073
For x = 70
z = 70 - 80/14
z = -0.71429
Using the z score table to find the probability
P-value from Z-Table:
P(x = 70) = P(z = -0.71429)
= 0.23753
The probability of a value between 55.0 and 70.0 is:
55 < x < 70
= P( x = 70) - P(x = 55)
= 0.23753 - 0.037073
= 0.200457
Approximately to 4 decimal place = 0.20046
Expand and simplify the expression 6x-7(4 - 5) algabra btw
Answer:
[tex] \boxed{ \bold{ \red{6x + 7}}}[/tex]Step-by-step explanation:
[tex] \sf{6x - 7(4 - 5)}[/tex]
Distribute 7 through the parentheses
[tex] \sf{6x - 28 + 35}[/tex]
Calculate
[tex] \sf{6x + 7}[/tex]
Hope I helped!
Best regards!!
Name the figure. Select all answers that apply.
Answer:
The answer is Plane P
Step-by-step explanation:
The reason for the answer is because a closed, two-dimensional or flat figure is called a plane shape. Different plane shapes have different attributes, such as the numbers of sides or corners. A side is a straight line that makes part of the shape, and a corner is where two sides meet.
What is 4^6 times 2^3=??
Answer:
32,768
Step-by-step explanation:
Remember to follow PEMDAS.
First, solve for the exponents for both terms:
[tex]4^6 = 4 * 4 * 4 * 4 * 4 * 4 = 4096[/tex]
[tex]2^3 = 2 * 2 * 2 = 8[/tex]
Multiply the two terms together:
[tex]4096 * 8 = 32768[/tex]
32,768 is your answer.
~
You have a metal rod thats51/64 inch long, the rod beeds to be trimmed. You cut 1/64 inch long from one end and 1/32 from the other end. Next, you cut the rod into six equal pieces. What will be the final length of each piece?
Answer:
Length of each pieces= 1/8 inch
Step-by-step explanation:
Length of metal rod= 51/64 inch
1/64 was cut from one end and 1/32 was cut from the other end
Total cut out= 1/64 + 1/32
Total cut out= (1+2)/64
Total cut out= 3/64 inch
Length remaining= 51/64-3/64
Length remaining= 48/64 inch
So the remaining length was cut into six pieces.
Length of each pieces= (48/64) * 1/6
Length of each pieces= 8/64
Length of each pieces= 1/8 inch
Sheila_____ her case ,look(had pickrd, have, picked
Answer:
Had Picked
Step-by-step explanation:
Find the arc length of ABC .
Answer:
C.
Step-by-step explanation:
Since the radius of the circle is 12 units, we can calculate the circumference.
2 * pi * r = 2 * pi * 12 = 24 * pi = 24pi.
The arc angle is 240 degrees, and the whole circle would be 360 degrees. So, we can set up an equation.
[tex]\frac{24\pi }{360} =\frac{x}{240}[/tex]
[tex]\frac{24\pi }{6} =\frac{x}{4}[/tex]
[tex]\frac{4\pi }{1} =\frac{x}{4}[/tex]
1 * x = 4 * 4 * pi
x = 16pi
So, your answer is C.
Hope this helps!
Write the equation of the line that passes through the points (8,0)(8,0) and (-9,-9)(−9,−9). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
Hence, the equation of the line that passes through the points (8,0) and (-9,-9) is [tex]y =\frac{9x}{17} - \frac{72}{17}[/tex].
Step-by-step explanation:
We have to find the equation of the line that passes through the points (8,0) and (-9,-9).
Let the two points be ([tex]x_1,y_1[/tex]) = (8, 0) and ([tex]x_2, y_2[/tex]) = (-9, -9).
Now, we will find the two-point slope using the above two points, i.e;
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{-9-0}{-9-8}[/tex] = [tex]\frac{9}{17}[/tex]
Now, the equation of the line using one of the point, let's say ([tex]x_1,y_1[/tex]) = (8, 0) is given by;
[tex]y - y_1 = \text{Slope} \times (x - x_1)[/tex]
[tex]y - 0 =\frac{9}{17} \times (x - 8)[/tex]
[tex]y =\frac{9x}{17} - \frac{72}{17}[/tex]
Hence, the equation of the line that passes through the points (8,0) and (-9,-9) is [tex]y =\frac{9x}{17} - \frac{72}{17}[/tex].
Find the inverse of the radical function [tex]\sqrt[3]{x-2}[/tex]
Answer: y=x³+2 or f⁻¹(x)=x³+2
Step-by-step explanation:
To find the inverse of the radical function, we replace y with x and x with y. Then, you solve for y.
[tex]y=\sqrt[3]{x-2}[/tex] [replace y with x and x with y]
[tex]x=\sqrt[3]{y-2}[/tex] [cube both sides to cancel out the cubed root]
[tex]x^3=y-2[/tex] [add both sides by 2]
[tex]x^3+2=y[/tex]
Now that we have switched the variables and solved for y, we know that the inverse function is y=x³+2 or f⁻¹(x)=x³+2.
Answer:
f^-1(x)=x^3+2
Step-by-step explanation: