Answer:
x = [tex]10^{0}[/tex]
Step-by-step explanation:
From Δ MPL given that; <P = [tex]90^{0}[/tex], exterior angle to M = [tex]136^{0}[/tex] and <L = [tex](4x+6)^{0}[/tex].
In the triangle, the exterior angle is equal to the sum of the two adjacent interior angles. So that;
[tex]136^{0}[/tex] = [tex]90^{0}[/tex] + [tex](4x+6)^{0}[/tex]
= [tex]90^{0}[/tex] + 4[tex]x^{0}[/tex] + [tex]6^{0}[/tex]
[tex]136^{0}[/tex] = [tex]96^{0}[/tex] + [tex]x^{0}[/tex]
⇒ 4[tex]x^{0}[/tex] = [tex]136^{0}[/tex] - [tex]96^{0}[/tex]
4[tex]x^{0}[/tex] = [tex]40^{0}[/tex]
Divided both sides by 4 to have;
[tex]x^{0}[/tex] = [tex]10^{0}[/tex]
The value of x is [tex]10^{0}[/tex].
Answer:
The correct answer is in fact 10 degrees.
Step-by-step explanation:
I hope this helps!
Have a great day! :)
A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,722. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,870 and a standard deviation of $3900. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722? Test the relevant hypotheses using α = 0.05. State your conclusion.A. Reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.B. Do not reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.C. Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.D. Do not reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Answer:
Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Step-by-step explanation:
First of all let's define the hypothesis;
Null hypothesis;H0; μ = $48,722
Alternative hypothesis;Ha; μ > $48,722
Now, let's find the test statistic for the z-score. Formula is;
z = (x' - μ)/(σ/√n)
We are given;
x' = 48,722
μ = 49,870
σ = 3900
n = 50
Thus;
z = (49870- 48722)/(3900/√50)
z = 2.08
So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526
This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722
confidence interavls for a population proportion. suppose that a random sample of 1000 mortgage loans that were defaulted within the first year reveals 410 of these loans were approved on hte basis of falsified applications. what is point estiamte of and a 95% confidence interval for p, the proportion of all first year defaults that are approved on the basis of flsified application
Answer:
The 95% confidence interval is [tex]0.3795 < p < 0.4405[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 1000[/tex]
The number of approved loan is k = 410
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
substituting values
[tex]\r p = \frac{410}{1000}[/tex]
[tex]\r p = 0.41[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }= 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p(1- \r p)}{n} }[/tex]
substituting values
[tex]E = 1.96 * \sqrt{\frac{ 0.41(1- 0.41)}{1000} }[/tex]
[tex]E = 0.03048[/tex]
The 95% confidence interval for p is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
substituting values
[tex]0.41 - 0.03048 < p < 0.41 + 0.03048[/tex]
[tex]0.3795 < p < 0.4405[/tex]
Janine and Thor are both running for class president. Janine goes down a hallway in the school and puts a sticker on every fourth locker. Thor goes down the same hallway, putting one of his stickers on every fifth locker. If there are 130 lockers in the hallway, how many have both students' stickers?
Answer:
6 lockers have both students' stickers
Step-by-step explanation:
There are 130 lockers in the hallway
Janine goes down a hallway in the school and puts a sticker on every fourth locker.
Janine= 4th, 8th, 12th, 16th, 20th, 24th, 28th, 32nd, 36th, 40th, 44th, 48th, 52nd, 56th, 60th, 64th, 68th, 72nd, 76th, 80th, 84th, 88th, 92nd, 96th, 100th, 104th, 108th, 112th, 116th, 120th, 124th, 128th.
Thor goes down the same hallway, putting one of his stickers on every fifth locker
Thor= 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th, 45th, 50th, 55th, 60th, 65th, 70th, 75th, 80th, 85th, 90th, 95th, 100th, 105th, 110th, 115th, 120th, 125th, 130th.
Common multiples of Janine fourth locker and Thor fifth locker= 20, 40, 60, 80, 100, 120
Therefore,
6 lockers have both students' stickers
Can someone please help me?
Negative Integers are :
Less than zeroTo the left of zero on a number line.Given the diagram below, where and mDE = 105^ and mGE = 125^ Find m
a. 65
b. 62.5
c. 55
d. 52.5
*Complete Question:
Given the diagram below, where and mDE = 105^ and mGE = 125^ Find m<DEG
Answer:
m<DEG = 65°
Step-by-step explanation:
Angle DEG is an inscribed angle that intercepts the DG. Based on the theorem of inscribed angles, angle DEG = ½ of the measure of arc DG.
To find the measure of angle DEG, find the measure of arc DG first.
Measure of arc DG = 360° - (105° + 125°) => a full circle measures 369°
Arc DG = 360° - 230 = 130°.
m<DEG = ½ of 130° = ½*130° = 65°
A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of seven marbles include at least one yellow one but no green ones
Answer: 8
Step-by-step explanation:
Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.
Total marbles other than green = 8
Total marbles other than green and yellow = 6
Then the number of sets of seven marbles include at least one yellow one but no green ones:-
[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]
Number of sets of seven marbles include at least one yellow one but no green ones = 8
You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.
Answer:
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Solution Set : { x = 123, y = 246, z = 11 }
Step-by-step explanation:
Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,
x + y + z = 380,
And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.
5x + 3y + 10z = 1460
The silly string tickets were sold for twice as much as the car wash tickets.
y = 2x
Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.
System of Equations :
[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,
[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three
And we can continue, canceling the leading co - efficient in each row until this matrix remains,
[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]
x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold
For
90° < 0 < 270°
, which of the primary trigonometric functions may have positive values?
Answer:
sine and tangent
will be positive.
Preeti and Shikha have bookshelves of the same size. Preeti’s shelf is 56 full of books and Shikha’s shelf is 35 full. Whose bookshelf is more full and by how much?
Answer:
Step-by-step explanation:
No of books in Preeti's shelf = 56
No of books in Shikha's shelf = 35
56 > 35
∴ Preeti's shelf is more full by 21 books
as 56 - 35 = 21
Hope this helps
plz mark as brainliest!!!
Yo help me real quick?
Answer:
1,2 and 6
Step-by-step explanation:
pie symbol
2/3
0.333333....
Officer Jacobi drove 180 miles in his patrol car during part of May. The distance represents 40% of May. How many miles did he drive all of May? a) 710 miles b) 420 miles c) 720 miles d) 450 miles Need Help on How to work this problem out, what formula would I use?
Answer:
D: 450 miles
Step-by-step explanation:
So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):
[tex]0.4D=180[/tex]
This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:
[tex]0.4D=180\\D=450[/tex]
So the answer is D or 450 miles.
Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.
For each ordered pair, determine whether it is a solution to y=-9.
Is it a solution?
Yes or No
(1, -9)
(7,3)
(-9,4)
(0, -9)
Answer:
(1, -9) yes
(7,3) no
(-9,4) no
(0, -9) yes
Step-by-step explanation:
The y value must be -9
The x value can be any value to satisfy the equation y = -9
A) Which of triangle A, B, C and D is congruent to triangle E.? B) Which other two triangles (from A, B, C and D) are congruent to each other? Please help!
Answer:
c is congruent to e congruent means to be the same
Step-by-step explanation:
8 less than one-fourteenth of some number, w
Answer:
The answer is 1/14w-8
Lori wants to buy a radio for 60 dollars.
She can pay $60 now, or she can pay $12
a month for 6 months. How much more will
she pay for the radio if she makes monthly
payments?
Answer:
Lori will pay $12 more if she makes monthly payments
Step-by-step explanation:
to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72
subtracting the amount she would pay as a down payment
$72 - $60 is $12
Lori will pay $12 more if she makes monthly payments
The graph of y = −4x2 + 13x + 12 is shown below. What are the zeros of the function (as exact values), the y-intercept, and the maximum or minimum value of the function?
Answer:
zeros: -3/4, 4y-intercept: 12maximum: 22 9/16Step-by-step explanation:
The graph tells you the zeros of the function are x=-3/4 and x=4.
The y-intercept is the constant in the function: 12.
The maximum is 22.5625 at x = 1.625.
Find the value of x.
A. 22
B. 7.3
C. 3.6
D. 5.5
Answer:
x= 5.5
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
x*4 = 11*2
4x = 22
Divide each side by 4
4x/4 = 22/4
x =5.5
Nan lives 13 miles from the airport. Felipe lives 6 miles from the airport.
How many more miles does Nan live from the airport than Felipe?
Answer:
7
Step-by-step explanation:
it's simply 13 - 6
7 it the answer, that was easy
Factor this trinomial completely. -6x^2 +26x+20
Answer:
Step-by-step explanation:
-6x²+26x+20
=-2(3x²-13x-10)
=-2(3x²-15x+2x-10)
=-2[3x(x-5)+2(x-5)]
=-2(x-5)(3x+2)
CD is the perpendicular bisector of XY Determine the value of x. Question 8 options: A) –2 B) –1∕2 C) 4 D) 1.25
Answer:
Step-by-step explanation:
12x - 9 = 8x + 7
4x - 9 = 7
4x = 16
x = 4
solution is C
The solution is Option C.
The value of x is given from the equation x = 4
What is perpendicular bisector?A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.
The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn
Given data ,
Let the first line be represented as CD
Let the second line be represented as XY
Now , CD is the perpendicular bisector of XY
So , the point F is the midpoint of the line segment XY
The measure of line segment XF = 12x - 9
The measure of line segment FY = 8x + 7
From the perpendicular bisector theorem ,
The measure of line segment XF = The measure of line segment FY
Substituting the values in the equation , we get
12x - 9 = 8x + 7
Subtracting 8x on both sides of the equation , we get
4x - 9 = 7
Adding 9 on both sides of the equation , we get
4x = 16
Divide by 4 on both sides of the equation , we get
x = 4
Therefore , the value of x = 4
Hence , the value of the equation is x = 4
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True or False. The statistician should use Printout C to perform a t-test on the GROUP variable in the regression model. g
Answer:
False
Step-by-step explanation:
Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.
(08.01 MC)
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet. What is the volume of the cube? (5 points)
Select one:
a. 3 cubic feet
b. 6 cubic feet
c. 18 cubic feet
d. 27 cubic feet
Answer:
d. 27 cubic feet
Step-by-step explanation:
volume of cube = s^3 = B * s
volume of pyramid = (1/3) * B * h
The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.
volume of pyramid = 9 cu ft
volume of cube = 3 * 9 cu ft = 27 cu ft
Answer: d. 27 cubic feet
Answer:
27 ft^3 (Answer d)
Step-by-step explanation:
Here the volume of the pyramid is (1/3) the volume of the cube:
Letting s represent the length of one side of the base,
(1/3)(s)^2(s) = 9 ft^3, equivalent to s^3 = 27.
Solving for s, we get s = 3 ft.
Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)
According to a Pew Research Center study, in May 2011, 40% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 341 community college students at random and finds that 147 of them have a smart phone. Then in testing the hypotheses:
H0: p = 0.4 versus
Ha: p > 0.4,
what is the test statistic?
z =________________. (Please round your answer to two decimal places.)
B.)
According to a Pew Research Center study, in May 2011, 33% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 349 community college students at random and finds that 138 of them have a smart phone. In testing the hypotheses:
H0: p = 0.33 versus
Ha: p > 0.33,
she calculates the test statistic as z = 2.5990.
Then the p‑value =________________ .
(Please round your answer to four decimal places.)
Answer:
z = 1.17
P - value = 0.0047
Step-by-step explanation:
A.
From the given information;
H0: p = 0.4 versus
Ha: p > 0.4,
Let's calculate the population proportion for the point estimate;
the population proportion [tex]\hat p[/tex] = 147/341
the population proportion [tex]\hat p[/tex] = 0.431085
However; the test statistics can therefore be determined by using the formula:
[tex]z = \dfrac{\hat p - p_o}{\sqrt{\dfrac{p_o(1-p_o)}{n}}}[/tex]
[tex]z = \dfrac{0.431085 - 0.40}{\sqrt{\dfrac{0.40(1-0.40)}{341}}}[/tex]
[tex]z = \dfrac{0.031085}{\sqrt{\dfrac{0.40(0.60)}{341}}}[/tex]
[tex]z = \dfrac{0.031085}{\sqrt{\dfrac{0.24}{341}}}[/tex]
[tex]z = \dfrac{0.031085}{\sqrt{7.03812317 \times 10^{-4}}}[/tex]
[tex]z = \dfrac{0.031085}{0.0265294613}[/tex]
z = 1.1717
z = 1.17 to two decimal places
B.)
The null and the alternative hypothesis is given as:
H0: p = 0.33 versus
Ha: p > 0.33,
The z = 2.5990.
The objective here is to determine the p-value from the z test statistics.
P - value = P(Z > 2.5990)
P- value = 1 - P(Z < 2.5990)
P - value = 1 - 0.9953
P - value = 0.0047
Mark has a collection of 80 coins. There are only nickels and dimes in the collection. The total value of the coins is $5.00. How many dimes does Mark have?
Answer:
number of nickel = 60
number of dimes = 20
Step-by-step explanation:
1 nickel = 5 cents
1 dimes = 10 cents
$1 = 100 cents
we will use these value to solve the questions
_______________________________
Total no of coins = 80
let the number of nickels be x
let the number of dimes be y
thus,
x+y = 80
y = 80-x equation 2
value of x nickels = 5x
value of y dimes = 10y
Total value of x nickels and y dimes = 5x+10y
The total value of the coins is $5.00
total value of the coins in cents = 5*100 = 500
thus
5x+10y = 500
using y = 80-x from equation 2
5x + 10(80 - x) = 500
5x + 800 - 10x = 500
-5x = 500 - 800 = -300
x = -300/-5 = 60
Thus,
number of nickel = 60
number of dimes = 80-60 = 20
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of business days, the mean closing price of a certain stock was $. Assume the population standard deviation is $. The 90% confidence interval is ( nothing, nothing). (Round to two decimal places as needed.) The 95% confidence interval is ( nothing, nothing). (Round to two decimal places as needed.) Which interval is wider? Choose the correct answer below
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 90% confidence interval is [tex][108.165 ,112.895][/tex]
The 95% confidence interval is [tex][107.7123 ,113.3477][/tex]
The correct option is D
Step-by-step explanation:
From the question we are told that
The sample size is n = 48
The sample mean is [tex]\= x = \$ 110.53[/tex]
The standard deviation is [tex]\sigma = \$ 9.96[/tex]
Considering first question
Given that the confidence level is 90% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 90)\%[/tex]
[tex]\alpha = 0.10[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = ZZ_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]
[tex]E = 1.645 * \frac{9.96}{ \sqrt{ 48} }[/tex]
[tex]E = 2.365[/tex]
The 90% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]110.53 - 2.365 < \mu < 110.53 + 2.365[/tex]
=> [tex]108.165 < \mu < 112.895[/tex]
Considering second question
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]
[tex]E = 1.96 * \frac{9.96}{ \sqrt{ 48} }[/tex]
[tex]E = 2.8177[/tex]
The 95% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]110.53 - 2.8177 < \mu < 110.53 + 2.8177[/tex]
=> [tex]107.7123 < \mu < 113.3477[/tex]
the city of James town is 2 meters below sea level. Takoradi, a city in western region, is 7 meters below sea level . How much higher is James town than Takoradi
Answer:
James town is 5 meters higher than Takoradi .
Step-by-step explanation:
Given:
Height of James town = 2 meters below sea level
Height of Takoradi town = 7 meters below sea level
To find:
How much higher is James town that Takoradi = ?
Solution:
As we can see the standard of height is how much the town is below the sea level.
So, the height of town having lesser value will be at a higher level.
Value of Height of James town is lesser than that of Takoradi town.
Therefore, James town is at a higher level.
Difference of height = 7 meters - 2 meters = 5 meters
So, the answer is:
James town is 5 meters higher than Takoradi.
Please answer fast! :)
Answer:
D
Step-by-step explanation:
The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.
When you plug 3 into equation D the entire right side it will become.
y-1=0
y=1, which is true.
When you plug 6 into that equation.
y-1=5
y=6 which is also true.
im sorry but the thing is i cant translate these words but the answer is D
What number is the opposite of -3?
Explain your reasoning
What is $121 divided into ratio of 7:4
Answer:
77:44
Step-by-step explanation:
Since 7:4 is equal to 11 and 121/11, each ratio can be multiplied by 11.
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). If q(t) = 4t³ – 1, what is p(t)?
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]
Cheers.
Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
What is composite functionThe composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.
In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.
Solving a composite function means finding the composition of two functions.
Function p(t)The expression of the composite function (q∘p)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:
s(t)= q[p(t)]
4t -21= 4[p(t)]³ – 1
Solving:
4t -21 +1= 4[p(t)]³
4t -20 = 4[p(t)]³
(4t -20)÷ 4 = [p(t)]³
4t÷4 -20÷ 4 = [p(t)]³
t -5 = [p(t)]³
[tex]\sqrt[3]{t-5}=p(t)[/tex]
Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
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