Answer:
[tex]f^{-1}(x)=4x+48[/tex]
Step-by-step explanation:
To find the inverse, solve for y:
x = f(y)
x = (1/4)y -12
x +12 = (1/4)y . . . . add 12
4(x +12) = y . . . . . multiply by 4
y = 4x +48 . . . . . . simplify
The inverse function is ...
[tex]\boxed{f^{-1}(x)=4x+48}[/tex]
The accompanying data are the times to failure (in millions per cycle) of high-speed turbine engine bearings made out of two different compounds. These were taken from "Analysis of Single Classification Experiments Based on Censored Samples from the Two-parameter Weibull Distribution" by J.I. McCool (The Journal of Statistical Planning and Inference, 1979) Compound 1 3.03 5.53 5.60 9.30 9.92 12.51 12.95 15.21 16.04 16.84 Compound 2 3.19 4.26 4.47 4.53 4.67 4.69 5.78 6.79 9.37 12.75 (a) Find the 0.84 quantile of the Compound 1 failure times (b) Give the coordinates of the two lower-left points that would appear on a normal plot of the compound 1 data (c) Make back-to-back stem-and-leaf plots for comparing the life length properties of bearings made from Compounds 1 and 2 (d) Make (to scale) side-by-side boxplots for comparing the life lengths for the two compounds. Mark numbers on the plots indicating the locations of their main features (e) Compute the sample means and standard deviations of the two sets of lifetimes (f) Describe what your answers to parts (c), (d), and (e) above indicate about the life lengths of these turbine bearings.
Find the given attachments
What is the formula to find the area of parallelogram
Step-by-step explanation:
area of parallelogram= height * length of base
When estimating the minimum sample size for proportion, it is indicated to keep a 50/50 split between the probabilities of success (p) and failure (q), even if we know from previous studies where the split has been in the past.
a.True
b. False .
c. That's a tricky
Answer:
b) False
Explanation:
It is not needed to keep 50/50 split.
Express the function G in the form f∘g. (Enter your answers as a comma-separated list. Use non-identity functions for
f(x) and g(x).)
Answer:
i dont really know what it is
Here are three number cards.
The numbers are hidden.
?
?
?
The mode of the three numbers is 7.
The highest number is not 7.
The range is 4.
What are the three numbers? Write them in the boxes, from smallest to larges
O
INN
Answer:
7, 7, 11 are the three numbers.
Step-by-step explanation:
Given:
Mode of the three numbers = 7
Range of numbers i.e. difference between the smallest and the largest number is = 4
Value of highest number card [tex]\neq[/tex] 7
As per the definition of Mode:
Mode is the number that occurs the most number of times in the given set of numbers. In other words, mode is the number whose frequency is the highest in the given set of numbers.
Here, we have three numbers and mode is 7 that means 7 occurs at least two times in the three numbers.
Also, we are given that 7 is not highest number, plus 4 is the range that means 7 occurs exactly two times out of three numbers.
So, two numbers are 7 and 7.
7 is not highest and 4 is the range, so third number = 7+4 = 11
So, the numbers on the cards are 7, 7 and 11.
a business owes $8,000 on a loan. every month, the business pays half of the amount remaining on the loan. how much will the business pay in the six-month?
Answer:
$7875
Step-by-step explanation:
1 Month 4000 Paid
2 Months 2000 Paid
3 Months 1000 Paid
4 Months 500 Paid
5 Months 250 Paid
6 Months 125 paid
Total = $7875 Paid
Hope this helped ;)
Please answer this correctly I have to finish this today as this is my deadline
Answer:
r = 1.499619733762 m There is no such thing a quarter radius!
C = 9.4223886775301 m
A = 7.065 m^2
Step-by-step explanation:
Calculate r and C | Given A
Given the area of a circle calculate the radius and circumference
r = √(A / π)
C = 2πr
Agenda:
r = radius
C = circumference
A = area
π = pi = 3.1415926535898
√ = square root
simplify 3^5•3^4
a.) 3•20
b. 3^9
c.) 6^9
d.) 3^20
Answer:
But if we are doing 3^x we need to add both of them
This is a rule you should remember if you have both same base to x power when you are multiplying
5+4 = 9
answer is 3^9 or 19683
What is the value of X ?
A-12
B-17
C-23
D-25
Step-by-step explanation:
25 answer by considering
Please answer this correctly
Answer:
A =12.56 m^2
Step-by-step explanation:
Find the area of a circle with radius 4
A = pi r^2
A = 3.14 * 4^2
A =50.24
Since this is 1/4 of the circle, multiply by 1/4
A = 1/4 * 50.24
A =12.56 m^2
Answer:
12.56
Step-by-step explanation:
the formula for the area of a circle is the following:
[tex]\pi r^{2}[/tex]
so divide that formula by 4 to get a quarter and plug in the radius for r.
[tex](\pi )(4^2)/4= 12.56[/tex]
6x +7y=-46 3x-2y=32 solve this system of linear equations
Hello
We have two equations and need to find x and y
(1) 6x+7y=-46
(2) 3x-2y=32
multiply (2) by 2 it gives
(2') 6x-4y=64
(1) - (2') gives
6x+7y-6x+4y=-46-64 = -110
so 11y = -110
y = -10
replace in (2) it gives
3x+20=32
3x=12
x = 12/3 = 4
the solution is (4,-10)
do not hesitate if you need further explanation
if you like my answer, tag it as the brainliest :-)
Find the measure of angle x in the figure below: A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 56 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 51 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 72 degrees. The interior angle on the left is labeled as x.
Answer:
[tex]x=35^\circ[/tex]
Step-by-step explanation:
From the diagram which I have drawn and attached below:
[tex]56^\circ+y+51^\circ=180^\circ$ (Sum of Angles on a Straight Line)\\y=180^\circ-(56^\circ+51^\circ)\\y=73^\circ[/tex]
Next, in the triangle, the sum of the three interior angles:
[tex]y+x+72^\circ=180^\circ\\$Since y=73^\circ\\73^\circ+x+72^\circ=180^\circ\\x=180^\circ-(73^\circ+72^\circ)\\x=35^\circ[/tex]
The value of angle x is 35 degrees.
An unevenly heated plate has temperature T(x, y) in °C at the point (x, y). If T(2, 1) = 130, and Tx(2, 1) = 16, and Ty(2, 1) = −13, estimate the temperature at the point (2.03, 0.96). (Round your answer to 2 decimal places.)
Answer:
The estimated temperature at the point (2.03, 0.96) is 131
Step-by-step explanation:
In this question, we are to estimate the temperature at the given point using the temperature of the unevenly heated plate.
We proceed as follows;
In the question, we identify that the temperature at the point T(2,1) = 130 degrees celcius
Now, let’s look at how the temperature changes. There is a positive change of 16 units when we move across the x-axis and a negative decrease when we move up the y-axis to a tune of 16 units(negative)
Now, how does the problem wants us to move using the notation of change?
Look at the point (2.03, 0.96), since movement across the x-axis is positive, the motion here in terms of x i.e Δx is 0.03 while the corresponding motion in terms of y(albeit negative) is Δy = -0.04
Mathematically, the change in temperature is proportional to the distance traveled. What this means is that we need to multiply the changes in direction by the corresponding temperature. This is shown below;
ΔTx =Δx*Tx(2,1) => ΔTx = (0.03)*(16) = 0.48
ΔTy = Δy*Ty(2,1) => ΔTy = (-0.04)*(-13) = 0.52
We can now combine the equations above to form a single one as follows; which is an approximation;
ΔT = Δx*Tx(2,1) + Δy*Ty(2,1) => ΔT = (0.03)*(16) + (-0.04)*(-13) = 1
To arrive at the final answer, we add the change in temperature to the staring temperature which is ;
T(2.03,0.96) = T(2,1) + ΔT = 130 + 1= 131
Find the value of z
Answer:
87°
Step-by-step explanation:
In the given figure, a quadrilateral is inscribed in a circle. Therefore, it is a cyclic quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
[tex] \therefore \: z + 93 \degree = 180 \degree \\ \therefore \: z = 180 \degree - 93 \degree \\ \huge \red{ \boxed{\therefore \: z = 87 \degree}}[/tex]
Lindsay needs to make some house repairs in four years that will cost $8,000. She has some money in an account earning 8% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answer:
$5,882
Step-by-step explanation:
To calculate the money Lindsay needs today, you can use the following formula to calculate the present value:
PV=FV/(1+i)^n
PV= present value
FV= future value= $8,000
i= interest rate= 8%
n= number of periods= 4
PV= 8,000/(1+0.08)^4
PV=8,000/1.08^4
PV=8,000/1.36
PV= 5,882
According to this, Lindsay will need to have $5,882 in the account today so she will have enough to pay for the repairs in four years.
Dora likes to explore. Recently, she explored southeast Australia where she found some very large trees known as Eucalyptus regnans or Mountain Ash. She wondered if they were taller, on average, than the coastal Douglas Firs of her native state of Oregon in the United States, which have an average height of 250 feet in old growth areas. Dora measured the heights of 15 Mountain Ash trees in southeast Australia and found an average height of these trees of 293 feet. Suppose s 25 feet. Assume the heights of the 15 trees in Dora's sample are representative of the heights of all Mountain Ash trees in southeast Australia. The t-statistic for this problem is 6.661. Based on this t-statistic, which of the following is true? Choose the correct answer below.
A. With a p-value of 0.999, there is sufficient evidence to accept the null hypothesis as true.
B. With a p-value less than 0.0001, there is not sufficient evidence to reject the null hypothesis and accept the alternative as true. y
C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.
D. With a p-value less than 0.0001, there is not sufficient evidence to accept the null hypothesis as true. 0 E. With a p-value of 0.999, there is not sufficient evidence to reject the null hypothesis and accept the alternative as true.
Answer:
C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.
Step-by-step explanation:
She performed an hypothesis test with the sample of size n=15 that she takes. The t-statistic has a value of 6.661.
The degrees of freedom for this sample size are:
[tex]df=n-1=15-1=14[/tex]
The P-value for a statistic t=6.661 and 14 degrees of freedom is:
[tex]\text{P-value}=P(t>6.661)=0.00001[/tex]
With these P-value we know that the effect is significant and the null hypothesis is rejected. There is enough evidence to support the claim that the mean height of Mountain Ash trees is greater than the coastal Douglas Firs.
The graph of g(x) = ax^2 opens downward and is narrower than the graph of f(x) = x^2. Which of the following could be the value of a?
The value of a should be less than -1.
Equation of parabola,The equation of a parabola is given by the following function,
[tex]y=f(x)=\pm a(x-h)^2+k[/tex]
where,
(h, k) denotes the coordinates of its vertex,
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given to us,[tex]f(x) = x^2[/tex]
[tex]g(x)=ax^2[/tex]
SolutionFor the parabola,g(x) to be narrower than the parabola f(x) the value of a should be less than 1. also for the parabola to open downward the value of a is needed to be negative.
Hence, the value of a should be less than -1.
Learn more about Equation of parabola:
https://brainly.com/question/4443998
Classify the following triangle. Check all that apply.
35°
10.1
7
102"
6
O A. Isosceles
O B. Equilateral
O c. Obtuse
O D. Right
O E. Scalene
F. Acute
Answer: obtuse and scalene
Step-by-step explanation:
Answer:
Obtuse And Scalene
Step-by-step explanation:
trust me!
In each of the following situations, data are obtained by conducting a research study. Classify each Experimental or Correlational.
Research Study
1. A researcher is interested in whether listening to different types of music or no music while taking a test affects test scores. Students are randomly assigned to one of three groups: The first group takes a test without listening to an iPod, the second group takes the same test while listening to classical music on an iPod, and the third group takes the test while listening to rock music on an iPod. The researcher compares the test scores across the three groups.
2. A psychologist is interested in gender and cognition. She collects data on a large sample of siblings, recording their gender, birth order, and IQ.
3. A professor of ophthalmology is interested in developmental precursors of vision disorders. He collects data from a sample of teenagers on right-eye vision, left-eye vision, and whether the bedroom light was kept off or on as they slept during the night as babies.
Answer:
1. Experimental
2. Correlational
3. Experimental.
Step-by-step explanation:
1. Experimental.
Researches are interested on finding the effects of music on a test.
2. Correlational
Researchers are interested on finding the correlation of the gender and cognition from different samples
3. Experimental
The Researcher wants to know the effects of bedroom light.
what is the value of x
14
15
16
17
Answer:
14
Step-by-step explanation:
Opposite angles in a rhombus are congruent. Even if you didn't know that, adding up the angles in this quadrilateral would tell you that ...
(5x)° = 70°
x = 70/5 = 14 . . . . . divide by 5
The value of x is 14.
Given the function g(x)=2∙3x+1, Find g−1 (x)
Answer:
[tex]g^{-1}(x)=\frac{x-1}{6}[/tex]
A researcher reports that the farther college students are from their parents, the more often they communicate with their parents (either by phone or by e-mail). Is this an example of a positive correlation or a negative correlation?
Answer:
Positive correlation
Step-by-step explanation:
A positive correlation exists between two variables, when both variables tend to move along the same direction. In order words, when one particular variable increases, there is also an increase in the other variable.
The case stated above is an example of positive correlation, because, the farther the students are from their parents, the more often they communicate with them. As distance increases, so does the number of, perhaps, phone calls increases as well.
Answer:
Positive correlation
Step-by-step explanation:
A positive correlation occurs whereby in a relationship between two variables, both variable move in the same direction meaning as one increases, the other also increases.
In this study, an increase in distance enforces an increase in communication with the parents.
Richard and Stephen win some money and share it in the ratio 6:1. Richard gets £60 more than Stephen. How much did they get altogether?
Answer:
They got £84 altogether.
Step-by-step explanation:
We can see that Richard get's 6 parts and Stephen gets 1 part. We can subtract these two to get 5 parts. We know that five parts equals £60, so we can divide by 5 to get 1 part equals £12. We are looking for the amount they got altogether, which is equal to 7 parts, 6 parts + 1 part. We multiply £12 by 7, leaving us with £84, which is our answer.
6(x/2 + 4) greater than or equal to 9
Answer:
Greater than 9.
Step-by-step explanation:
[tex]6(x/2 + 4)[/tex]
[tex]3x+24[/tex]
I will mark you as BRANLIEST and I will give you 55 points if you answer correctly.
~Solve each system of equations using elimination. SHOW YOUR WORK
1) -4x+3y=-5
4x-5y=3
2) 2x+3y=36
10x-6y=12
Answer:
1. x = 2 y = 1
2. x = 17 y = 29/3
Step-by-step explanation:
1. Use elimination
-4x+3y=-5
4x-5y=3
x's cancel, so add them
-2y = -2
y = 1
substitute
4x -5(1) = 3
4x - 5 = 3
4x = 8
x = 2
2. Use elimination
2x+3y=36
10x-6y=12
Multiply top equasion by 5
10x+30y = 360
10x-6y = 12
x's cancel so subract
36y = 348
y = 29/3
Substitute
2x+3(2/3)=36
2x+2 = 36
2x = 34
x = 17
Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?
If the variable n represents the number of nickels, then which of the following expressions represents the number of quarters?
Answer:
2 nickels8 quartersStep-by-step explanation:
If n represents the number of nickels, and the number of quarters is 4 times the number of nickels, then the number of quarters is represented by 4n.
The total value of the coins in cents is ...
5(n) +25(4n) = 210
105n = 210 . . . . . . . . collect terms
n = 210/105 = 2 . . . . number of nickels
4n = 4(2) = 8 . . . . . . number of quarters
Peggy has 2 nickels and 8 quarters.
If your answer is in decimal form, round to 2 decimal places. For example, if your answer is .412, enter it into the fill-in-the-blank as .41, or if your answer is 1.415, enter it into the fill-in-the-blank as 1.42. If there are no decimals in your answer, you will simply enter the number; so if your answer is 2, enter 2 with no decimals. Do not enter any extra spaces, do not enter commas or $ or % symbols.
Answer:
If there is no decimal just put number and if the number is higher than 5 you round up example 1.46 you would put 1.5
Step-by-step explanation:
HOPE IT HELPS
Suppose you have a job teaching swimming lesson and get paid $6 an hour you also have a job as a chasier and get pay $8 and hour if you cannot work more than 15 hours a week what are the number you f hours you can work at each job and still make at least $100
Answer:
You can work no more than 10 hours teaching, and must work at least 5 hours cashiering. The remaining hours can be worked at the other job until the goal is reached.
Step-by-step explanation:
The restrictions give rise to two inequalities. If we ...
let x represent teaching hours
let y represent cashiering hours
then the restrictions are ...
x + y ≤ 15 . . . . total hours cannot exceed 15
6x +8y ≥ 100 . . . . you want to earn at least $100
The solution set for these inequalities is a triangular area on a graph with vertices at ...
(x, y) = (10, 5), (0, 12.5), (0, 15)
You must work at least 5 hours cashiering, and the remainder of necessary time at teaching.
Given that f(x)=x^2+4x-32f(x)=x
2 +4x−32 and g(x)=x-4g(x)=x−4, find (f+g)(x)(f+g)(x) and express the result in standard form.
Answer:
So your question was not very clear but with (f+g) im guessing thats f(x)+g(x)
So first we add them x^2+4x-32 + x-4 then we will get x^2 + 5x - 36
Then we need to multiply both
(x^2+5x-36)(x^2+5x-36)
=
(x^2+5x-36)^2
The only reason im not solving it out is because it yields large numbers and you might not understand.
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to move forward with a purchase agreement unless it can be demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 lightbulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using computer software, which gave the following results.
Variable N Mean St Dev SEMean Z P-Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
1. What conclusion would be appropriate for a significance level of.05?
2. What significance level would you recommend?
Answer:
a) For this case since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 750 hours
b) We can use a significance level minimum of 2% in order to ensure the conditions in favor to the alternative hypothesis and then the potential customer will decide to move forward with a purchase witht his condition.
Step-by-step explanation:
For this case we have the following info given after conduct the following system of hypothesis:
Null hypothesis: [tex]\mu \geq 750[/tex]
Alternative hypothesis: [tex]\mu< 750[/tex]
The output is:
Variable N Mean St Dev SEMean Z P-Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
For this case the statistic calculated was:
[tex] z = -2.14[/tex]
And the p value calculated is:
[tex] p_v =p(z<-2.14) = 0.016[/tex]
Part a
For this case since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 750 hours
Part b
We can use a significance level minimum of 2% in order to ensure the conditions in favor to the alternative hypothesis and then the potential customer will decide to move forward with a purchase witht his condition.
