Chris and Jen decide to go apple picking at a local apple orchard. As the number of apples they pick increases the cost of the apples also increases. The function ff relates the varying cost of Chris and Jen's apples, cc , in terms of the varying number of pounds of apples that Chris and Jen pick, nn , where c=f(n)c=f(n) and ff is defined by f(n)=0.4n+6f(n)=0.4n+6.
Evaluate f−1(33) Note( this is F^-1)
Determine the rule for the function f^-1
Any relation that has an inverse is a function
The value of [tex]\mathbf{f^{-1}(33)}[/tex] is [tex]\mathbf{f^{-1}(33) = 67.5}[/tex]The rule of [tex]\mathbf{f^{-1}(n)}[/tex] is [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]The function is given as:
[tex]\mathbf{f(n) = 0.4n + 6}[/tex]
(a) Evaluate [tex]\mathbf{f^{-1}(33)}[/tex]
First, we calculate the inverse function
We have:
[tex]\mathbf{f(n) = 0.4n + 6}[/tex]
Rewrite as:
[tex]\mathbf{y = 0.4n + 6}[/tex]
Subtract 6 from both sides
[tex]\mathbf{y -6= 0.4n + 6 - 6}[/tex]
[tex]\mathbf{y -6= 0.4n}[/tex]
Divide both sides by 0.4
[tex]\mathbf{\frac{1}{0.4}(y -6)= \frac{0.4n}{0.4}}[/tex]
[tex]\mathbf{\frac{1}{0.4}(y -6)= n}[/tex]
[tex]\mathbf{2.5(y -6)= n}[/tex]
Make n the subject
[tex]\mathbf{n = 2.5(y -6)}[/tex]
Rewrite as:
[tex]\mathbf{n = 2.5(f(n) -6)}[/tex]
So, the inverse function is:
[tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]
Substitute 33 for n to calculate [tex]\mathbf{f^{-1}(33)}[/tex]
[tex]\mathbf{f^{-1}(33) = 2.5(33 -6)}[/tex]
[tex]\mathbf{f^{-1}(33) = 2.5(27)}[/tex]
[tex]\mathbf{f^{-1}(33) = 67.5}[/tex]
(b) The rule of [tex]\mathbf{f^{-1}(n)}[/tex]
In (a), we have: [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]
Hence, the rule of [tex]\mathbf{f^{-1}(n)}[/tex] is [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]
Read more about functions and inverses at:
https://brainly.com/question/10300045
PLEASE HELPPPP ASAP PLS WILL MARK BRAINLIEST
Answer:
5X+6+3X-2 =180
8X+4. =180
8X. =180-4
8X. =176
X=22
CBD=EBF=3x-2
=66-2
=64
CBD=64
A shipping carton is in the shape of a triangular prism. The base area of the triangle is 6 inches squared and the the height of the prism is 15 inches. how many cubic inches of space are in the carton?
51
Step-by-step explanation:
uajdnensjdkalsnnamakksls
c) Determine the location and values of the absolute maximum and absolute
minimum for the given function:
f(x) = (-x + 2)4, where 0 <x<3
Answer:
The absolute maximum on the interval 0 < x < 3 is at x = 2 and f(2) = 0. Since x = 2 can only give an absolute maximum, so there is no absolute minimum.
Step-by-step explanation:
f(x) = (-x + 2)⁴
to find the absolute maximum and minimum values, we differentiate f(x) with respect to x.
So df(x)/dx = f'(x) = 4(-x + 2)³
The maximum and minimum values are obtained when f'(x) = 0
So, 4(-x + 2)³ = 0
⇒ (-x + 2)³ = 0
⇒ -x + 2 = 0
-x = -2
x = 2
Now, f(2) = (-2 + 2)⁴ = 0⁴ = 0
So, the absolute maximum on the interval 0 < x < 3 is at x = 2 and f(2) = 0. Since x = 2 can only give an absolute maximum, so there is no absolute minimum.
I'm Stuck and need help please). The table shows the test scores and the sleep averages of several students. A) Write the least squares regression equation that models the data. Let x = the test score and y = average sleep. B) Use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night. Show Your Work. ( Will Mark Brainliest but no Links or nonsense answers please). Answer A and Answer B.
Answer:
a
you should take values of x and y that are similar or they are close to each other like 8 is close to 8.5
b
u will take the average of all the scores with 8hr sleep
PLSSSS HELP ASAP PLS !! will mark brainliest to whoever gets it right
Answer:
last option is correct
Step-by-step explanation:
angle 4 is 128 degree because it is corresponding with angle 3.
Corresponding angles are angles that are in the same position relative to lines intersected by a transversal. When a transversal intersects two lines, the two lines are parallel if and only if corresponding angles are congruent (equal in measure).
Answer:
128 because it is corresponding with 3
Sara has 5 blue bows and 7 white bows in a bag for her fellow cheerleaders to wear in their hair for each game. The bows are
pulled out randomly by the team. Determine if the following is an
Independent or a Dependent event. Then find the probability.
1.) Sara pulls out a blue bow and her teammate pulls out a white bow.
Answer: The events are dependent
The probability is 35/132
==============================================================
Explanation:
If the first bow Sara pulls out isn't put back, then the two events are dependent. This is because the probability of pulling a white bow changes depending on what Sara pulls out.
If Sara pulls out a blue bow, then the teammate's chances of pulling a white bow are 7/11 because there are 7 white bows out of 4+7 = 11 left over (or you could compute 5+7-1 = 11).Or if Sara pulls out a white bow, then the chances of a teammate pulling out another white bow is 6/11 instead of 7/11. The probability has changed.So again, it all depends on what Sara does because she goes first. This is of course not the case if Sara puts the bow back. If she put it back, then the chances of the teammate pulling the white bow is 7/12
---------
To find the overall probability of Sara selecting a blue bow and not putting it back, followed by a teammate getting a white bow, we multiply the fractions 5/12 and 7/11 to get (5/12)*(7/11) = 35/132
For more info, search out conditional probability.
Write the equation of a line with a slope of −2 and a y-intercept of 5.
9514 1404 393
Answer:
y = -2x +5
Step-by-step explanation:
The slope-intercept form of the equation for a line is ...
y = mx + b . . . . . . . . . line with slope m and y-intercept b
You want a line with slope -2 and y-intercept 5, so your equation is ...
y = -2x + 5
Drew hiked two trails Rocky Hill is 7 /8 miles long battle in Brook Trail is 4/5 mile long how much further did Drew hike on Rocky Hill Trail then I'll babbling Brook Trail write an equation
PLEASE HELP !! suppose that F(x)=x^2 and G(x)=3x^2+8.which statement best compares the graph of G(x) with the graph of F(x)
Answer:
The graph of g(x) is the graph of f(x) stretched by 3 and shifted 8 units up
Step-by-step explanation:
Given
[tex]f(x)=x^2[/tex]
[tex]g(x) =3x^2 + 8[/tex]
Required
Compare g(x) and f(x)
We have:
[tex]g(x) =3x^2 + 8[/tex]
Rewrite as:
[tex]g(x) =3[x^2] + 8[/tex]
Substitute:[tex]f(x)=x^2[/tex]
[tex]g(x) =3f(x) + 8[/tex]
This means that:
3f(x)
f(x) is stretched vertically by a factor of 3
+8
Then shifted upwards by 8 units to give g(x)
58. Consider the graph of the line below. a State the slope of the line. b. State the x-intercept as an ordered pair. c. State the y-intercept as an ordered pair. d. Write the equation of the line in the form y = mx + b.
Answer:
No solution is possible
Step-by-step explanation:
You failed to include the graph.
The college Physical Education Department offered an Advanced First Aid course last summer. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below.
Robert, 1.11 Juan, 1.66 Susan, –1.9 Joel, 0.00 Jan, –0.65 Linda, 1.46
(a) Which of these students scored above the mean?
a. Jan
b. Joel
c. Juan
d. Linda
e. Robert
f. Susan
(b) Which of these students scored on the mean?
a. Jan
b. Joel
c. Juan
d. Linda
e. Robert
f. Susan
(c) Which of these students scored below the mean?
a. Jan
b. Joel
c. Juan
d. Linda
e. Robert
f. Susan
(d) If the mean score was ? = 156 with standard deviation ? = 24, what was the final exam score for each student? (Round your answers to the nearest whole number.)
a. Janb. Joelc. Juand. Lindae. Robertf. Susan
Answer:
a)
b. Joel
c. Juan
d. Linda
b)
b. Joel
c)
a. Jan
f.Susan
d)
a. Jan: 140
b. Joel: 156
c. Juan: 196
d. Linda: 191
e. Robert: 183
f. Susan: 110
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean, positive z-scores are above the mean, negative are below the mean and 0 is the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Question a:
Robert, Juan and Linda had positive z-scores, so they scored above the mean, and the correct options are c,d,e.
(b) Which of these students scored on the mean?
Joel, which had a z-score of 0, so the correct option is b.
(c) Which of these students scored below the mean?
Jan and Susan had negative z-scores, so them, options a and f.
Question d:
We have that [tex]\mu = 156, \sigma = 24[/tex], so we have to find X for each student.
Jan:
Z = -0.65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.65 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = -0.65*24[/tex]
[tex]X = 140[/tex]
b. Joel
Z = 0, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 0*24[/tex]
[tex]X = 156[/tex]
c. Juan
Z = 1.66, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.66 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 1.66*24[/tex]
[tex]X = 196[/tex]
d. Linda
Z = 1.46. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.46 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 1.46*24[/tex]
[tex]X = 191[/tex]
e. Robert
Z = 1.11. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.11 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 1.11*24[/tex]
[tex]X = 183[/tex]
f. Susan
Z = -1.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.9 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = -1.9*24[/tex]
[tex]X = 110[/tex]
A new car's original price is $13,999. If it's on sale
for 10% off, what's the new price?
Divide Rs. 1800 among Marmik, Sujata and Kapil in the ratio of 1/3:1/4:1/6
Answer:
Marmik = 800; Sujata = 600; Kapil = 400
Step-by-step explanation:
Given
Let
[tex]M \to Marmik[/tex]
[tex]S \to Sujata[/tex]
[tex]K \to Kapil[/tex]
Given
[tex]M:S:K = \frac{1}{3}:\frac{1}{4}:\frac{1}{6}[/tex]
[tex]Amount = 1800[/tex]
Required
Divide
We have:
[tex]M:S:K = \frac{1}{3}:\frac{1}{4}:\frac{1}{6}[/tex]
Multiply the ratio by 12 (to convert them to whole numbers)
[tex]M:S:K = 12 *\frac{1}{3}:12*\frac{1}{4}:12*\frac{1}{6}[/tex]
[tex]M:S:K = 4 : 3 : 2[/tex]
The total ratio is:
[tex]Total = 4 + 3 + 2 = 9[/tex]
So, the amount each collected is:
[tex]Marmik = \frac{M}{Total} * Amount[/tex]
[tex]Marmik = \frac{4}{9} *1800 = 800[/tex]
Using the same formula for others, we have:
[tex]Sujata = \frac{3}{9} *1800 = 600[/tex]
[tex]Kapil = \frac{2}{9} *1800 = 400[/tex]
Please help!! Will mark brainilest, thank you in advance. :))
Answer:
See image below:) :)
Step-by-step explanation:
Workplace accidents are categorized in three groups: minor, moderate, and severe. The probability that a given accident is minor is 0.5, that it is moderate is 0.4, and that it is severe is 0.1. Two accidents occur independently in one month. Calculate the probability that neither accident is severe and at most one is moderate.
Answer: The probability when neither of the accidents is severe and at most one is moderate is 0.65
Step-by-step explanation:
Given values:
Probability when the accident is minor = 0.5
Probability when the accident is moderate = 0.4
Probability when the accident is severe = 0.1
As two accidents are occurring independently and we need to calculate the probability of an event that neither accident is severe and at most one is moderate.
So, the equation for the probability becomes:
[tex]=\text{P[moderate, minor]}+\text{P[minor, moderate]}+\text{P[minor, minor]}\\\\= (\text{P[moderate]}\times \text{P[minor]}) + (\text{P[minor]}\times \text{P[moderate]}) + (\text{P[minor]}\times \text{P[minor]})[/tex]
Putting values in above equation, we get:
[tex]=[(0.40)\times (0.5)] + [(0.5)\times (0.4)] +[((0.5)\times (0.5)]\\\\= 0.65[/tex]
Hence, the probability when neither of the accidents is severe and at most one is moderate is 0.65
Select all the numbers that show 4% as an equivalent fraction, decimal, or percent.
[] 0.04
[] 40%
[] 10
[] 4
[] 100
[] 0.4
How many beans stacked on top of each other would it take to reach the moon. And we're talking Lima beans here.
Answer:
I would say more than 4 billion...
Step-by-step explanation:
let abc is a right angle triangle at b. if ac=10cm and ab=8cm the what is the lenght of bc is
Answer:
using Pythagoras theorem
bc²=ac²-ab²
bc²=100-64
bc=√36
bc =6
A hemispherical tank is filled with water and has a diameter of 22 feet. If water
weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank,
to the nearest pounds
Answer:
173 949 pounds
Step-by-step explanation:
radius of the hemisphere = diameter / 2 = 11 feet
Volume of the hemisphere = (2/3 * radius^3 * pi) = = (2/3 * 11^3 * pi) = 2.787,639881 ft^3
Total weight = volume of the hemisphere * 62.4 = 173,948.728592
Please help me figure out which is the correct answer, i have attached the picture for you to look at. Thanks so much!
Answer:
The answer is B ;)
Step-by-step explanation:
4x+5 is greater than or equal to 13
subtract 5 from each side to get 4x is greater than or equal to 8
then divide both sides by 2 to get
x is greater than or equal to 2
Write the product in its simplest form : 6c • (-7c^6)
Answer:
Step-by-step explanation:
(-7*6)(c*c^6) = -42c^7
The function f is defined by f(x)=x^2+3x-10
Answer:
hope it is helpful to you
Find the slope and the y-intercerpt f(x) = 8 -7/8x
Answer:
slope = -7/8
y-intercept = 8
Step-by-step explanation:
slope intercept form is
y = mx + b
m is slope
b is y-intercept
------------------------
f(x) = 8 - 7/8x
Rearrange into slope intercept form
f(x) = -7/8x + 8
slope = -7/8
y-intercept = 8
Answer:
Slope = -7/8
Y-intercept = 8
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
f(x) = 8-7/8x
Given the above, rearrange it in slope-intercept form to help us find the slope and y-intercept:
f(x) = -7/8x+8
Now, we can see clearly that -7/8 is in place of m and 8 is in place of b. This means that -7/8 is the slope of the line and 8 is the y-intercept.
I hope this helps!
[100 point question answer asap]find the areas of the trapezoids
Answer:
7.5
Step-by-step explanation:
You have two triangles with areas of 1.5 and 3 as well as a rectangle with an area of 3
Answer:
Area = 7.5
Step-by-step explanation:
Use this formula to find the area of a trapezoid A = [tex]\frac{a + b}{2} h[/tex]
Plug numbers in[tex]\frac{1 + 4}{2}*3[/tex]Area is = to 7.5
Area of circle with a diameter of 8ft?
Answer:
it is 50.27
Step-by-step explanation:
the formula for finding the area it
A= pi r^2
pi=3.14
so that being said you want to:
you want to divide the diameter by 2 to get 4,then you want to do 4^2 to get 16. then multiply 16 by 3.14 to get 50.265 then you want to round up to 50.27
Canterbury Cycles sells Harleys and pays each salesperson a commission of $800 for each cycle sold. During the month of December, a salesperson sold 3 cycles. The company pays commissions on the 5th day of the month following the sale. Which of the following statements is true?a. The salesperson will recognize commission revenue earned in the amount of 2400 in Decemberb. The company will recognize commission expense in the amount of $2,400 in December.c. The salesperson will recognize commission expense in the amount of $2,400 in January.d. The salesperson will recognize revenue in the same month that the cycle dealer recognizes expense.
Answer: The company will recognize commission expense in the amount of $2,400 in December
Step-by-step explanation:
Based on the information given in the question, the company will recognize commission expense in the amount of $2,400 in December.
A commission is regarded as a fee which is paid to a salesperson by a company in exchange for completing a sale.
It should be noted that in the accrual basis of accounting, commission should be recorded in the same period as when the sale generated was generated.
Answer:
b. The company will recognize commission expense in the amount of $2,400 in December.
Step-by-step explanation:
Based on the information given the statements that is true will be: THE COMPANY WILL RECOGNIZE COMMISSION EXPENSE IN THE AMOUNT OF $2,400 IN DECEMBER reason been that each salesperson were paid a commission in the amount of $800 for each cycle sold, which is 3 cycles during the month of December.
Calculation to determine the Commission Expense
Commission Expense=$800*3 cycles
Commission Expense=$2,400
Therefore The company will recognize commission expense in the amount of $2,400 in December.
Given a circle with a radius of 22 inches, what is the circumference in terms of π?
Answer:
[tex]circumference = 2\pi \: r \\ = 2 \times \pi \times 22 \\ = 44\pi \: inches[/tex]
Answer:
The circumference is 44 pi.
Step-by-step explanation:
You have to use the formula, C=2 Pi R but since it's in terms of pi, we can not include pi in the equation. 2 times r (radius) is 44, therefor the answer is 44 pi.
Find the area of the circle the area is ? m2
Answer:
roughly 12.57
Step-by-step explanation:
pi times [tex]r^{2}[/tex]
Answer:
4π
Step-by-step explanation:
Hello!
The area of a circle is calculated using the formula [tex]A = \pi r^2[/tex].
A = areaπ = pir = radiusTo solve for the area, we plug in the value for the radius.
Find the Area[tex]A = \pi r^2[/tex][tex]A = \pi (2)^2[/tex][tex]A = 4\pi[/tex]Usually we round Pi to 3.14 and multiply, but since it's asking for the exact value, we can just leave it as is.
The area in terms of Pi is 4π.
Mr Zuro finds the mean height of all 13 students in his statistics class to be 68.0inches. Danielle walks in late. Danielle is 72.2 inches tall. What is the mean height of the 14 students in the class
Answer:
68.3 inches
Step-by-step explanation:
Let the sum of the original 13 students heights be S, so the average of their heights are S/13.
We are given that average height of the original 13 students heights is 68 inches, so S/13 = 68 -> S = 68*13 = 884 inches.
The average of the heights of all 14 students is the sum of all 14 students (S + Danielle’s height) divided by 14. We are given that Danielle’s height is 72.2 inches, so the mean height of all 14 students is:
(S+72.2)/14 = (884+72.2)/14 = 68.3 inches
I hope this helps! :)