Answer:
16% of the apples have diameters that are less than 6.82cm
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 7.25cm
Standard deviation = 0.43cm
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Using the empirical rule, what percentage of the apples have diameters that are less than 6.82cm?
6.82 = 7.25 - 1*0.43
So 6.82 is one standard deviation below the mean.
Of the 50% of the diameters below the mean, 68% are within 1 standard deviation of the mean.
So 100-68 = 32% are not within 1 standard deviation of the mean.
0.5*0.32 = 0.16
16% of the apples have diameters that are less than 6.82cm
What is the volume of a square pyramid if the length of an edge of the base is 7 and the altitude
of the pyramid is 12?
(1) 28
(2) 56
(3) 196
(4) 588
We have been given that the length of an edge of a square pyramid is 7 and altitude of the pyramid is 12. We are asked to find the volume of the pyramid.
We will use volume of pyramid formula to solve our given problem.
[tex]V=\frac{1}{3}\cdot b\cdot h[/tex], where,
b = Area of base of pyramid,
h = Height of pyramid.
We know that area of a square is square of its side length, so area of the base of pyramid would be [tex]7^2=49[/tex].
The height of the pyramid will be equal to altitude.
[tex]V=\frac{1}{3}\cdot 49\cdot 12[/tex]
[tex]V=49\cdot 4[/tex]
[tex]V=196[/tex]
Therefore, the volume of the given pyramid would be 196 cubic units and 3rd option is the correct choice.
What is the solution to this system?
y= 4x + 3
2x - 3y = 21
Answer:
(-3,9)
Step-by-step explanation:
Use any of the method for solving systems of equations (substitution,elimination,equal to each other)
The solution to the system of equations y = 4x + 3 and 2x - 3y = 21 is x = -3 and y = -9, found by substitution.
The solution to the system of equations y = 4x + 3 and 2x - 3y = 21 is found by using the substitution or elimination methods.
To use substitution, we can first express y from the first equation and substitute it into the second equation. As an example, substituting y from y = 4x + 3 into the second equation yields:
2x - 3(4x + 3) = 21
2x - 12x - 9 = 21
-10x = 30
x = -3
Then, we substitute x back into the first equation to find y:
y = 4(-3) + 3
y = -12 + 3
y = -9
The solution to the system of equations is x = -3 and y = -9.
What is the hourly compensation per worker for a company with a unit labor cost of 0.9 and an hourly output per worker of $32.50? round your answer if necessary to the nearest whole number
Given Information:
Unit labor cost = 0.9
Hourly output per worker = $32.50
Required Information:
Hourly compensation per worker = ?
Answer:
Hourly compensation per worker = $36
Step-by-step explanation:
The unit labor cost is given by
[tex]U = \frac{O}{W}[/tex]
Where W is the hourly compensation per worker, O is the hourly output per worker and U is the unit labor cost.
Re-arranging for the hourly compensation yields,
[tex]U = \frac{O}{W}\\\\W =\frac{O}{U}\\ \\[/tex]
Now substitute the given values
[tex]W =\frac{32.50}{0.9}\\\\W = 36.11\\\\W = \$ 36[/tex]
Therefore, the hourly compensation per worker is $36.
Bonus:
Unit labor cost is the amount incurred with regard to labor expenses to produce one unit of a product. Calculating the unit labor cost helps in analyzing other aspects of the business such as product pricing, profit margin, sales etc.
5 95 8,994 + 11 11 9,010 =
Answer:
5,95,9005,11,9010
Step-by-step explanation:
Jayden’s lunch at the diner cost $17. He leaves a 18% tip for the server. How much money did Jayden leave the server for a tip?
Answer:
The tip is $3.06
Step-by-step explanation:
To find the tip, take the amount of the bill and multiply by 18%
17 * 18%
17 * .18
3.06
The tip is $3.06
The perimeter of a square is equal to the perimeter of an equilateral triangle. The length of a side of the square is given by x, and the length of a side of the equilateral triangle is given by x + 1. Which equation can be used to find the value of x?
Answer: The equation you could use is 4x = 3x + 3
Step-by-step explanation:
THE SQUARE
A square has sides with 4 equal sides. If one side is equal to x, then every other side is also x.
Add x + x + x + x to get the square’s perimeter.
The sqaure’s perimeter is 4x.
THE TRIANGLE
An equilateral triangle has equal sides too. If one side is x + 1, every other side is x + 1 too.
Add, (x + 1) + (x + 1) + (x + 1)
the triangles perimeter is 3x + 1
BOTH
The triangle and the square have the same perimeter. Therefore,
4x = 3x + 3. That is the equation.
( The solution would be x = 3, by the way)
Evaluate the expression 2x - 5 when x =3?
A) -4
B) 1
C) 6
D) 11
Answer:
Step-by-step explanation:
2x - 5
2(3) - 5
2 times 3 = 6
6-5=1
B) is the answer
I think the answer is B because you have to plug in 1 for the expression.
-Dhruva;)
Lindsey gets paid a base salary of $400 per week plus $0.15 commission on each sale she makes. Write a verbal model and a algebraic expression to represent Lindsay's total salary for the week if she makes d dollars during the week. Identify the unit for this expression???
Answer:
The verbal model and an algebraic expression representing Lindsay's total salary for the week is $400 + 0.15 d.
Step-by-step explanation:
The base salary of Lindsey is, B = $400.
The commission she earns on every sale made by her is, c = $0.15.
It is provided that Lindsey makes d dollars during the week.
The amount d dollars is the total commission earned by Lindsey in a week.
The formula to compute the commission earned will be represented by the expression:
C = c × $d
= 0.15 d
The expression represent Lindsay's total salary for the week is:
Total Salary = Base Salary + Total Commission
= B + C
= $400 + 0.15 d
Thus, the verbal model and an algebraic expression representing Lindsay's total salary for the week is $400 + 0.15 d.
6th grade math please help !
Answer:
okay my daughter is in 6th grade so the answer is c 45 dollars per 3 hours
Step-by-step explanation:
Mrs. Coloma-Flores walked Moana 30 minutes before school. She walked Moana for m more minutes after school. Enter an equation that represents that total number of minutes, t, that Mrs. Coloma walked Moana.\
Answer:
30 + m = t
Step-by-step explanation:
I think this is correct. I am so sorry if it is not.. Good luck! :)
To determine the total time Mrs. Coloma walked her dog Moana, we use the equation t = 30 + m, where t represents the total time in minutes and m represents the additional minutes walked after school.
Explanation:The question involves creating an equation that represents the total amount of time Mrs. Coloma spent walking her dog, Moana. The equation should include the time spent walking before and after school. We are given that the time spent walking before school was 30 minutes. Let m represent the additional minutes Mrs. Coloma walked Moana after school. The total time spent walking, represented by t, will be the sum of both these durations.
The equation representing the total time spent walking Moana is:
t = 30 + m
This equation can be used to calculate the total walking time once the value of m is known.
Inverse notation f^-1 used In a pure mathematics problem is not always used when finding inverses of applied problems. Rather, the Inverse of a function such as C= C(q) will be q= q(C). The following problem illustrates this idea.
The ideal body weight W for men (in kilograms) as a function of height h (m inches) is given by the following function.
W(h)= 49+2.2(h-60)
Required:
a. What is the ideal weight of a 6-foot male?
b. Express the height h as a function of weight W. Verify your answer by checking that W(h(W)) = W and h(W(h))h.
Answer:
a) 75.4 kg
b) [tex]h(W)=\frac{W+83}{2.2}[/tex]
Step-by-step explanation:
a) The ideal weight of a 6-foot (72 inches) male is given by simply applying h= 72 in to the expression:
[tex]W(72) = 49+2.2(72-60)\\W(72) =75.4\ kg[/tex]
b) Expressing height as a function of weight:
[tex]W(h)= 49+2.2(h-60)\\2.2h-132+49=W\\h(W)=\frac{W+83}{2.2}[/tex]
Verifying with W(h(W)):
[tex]W(h(W))= 49+2.2(\frac{W+83}{2.2} -60)\\W(h(W))= 49-132+W+83\\W(h(W))=W[/tex]
Verifying with h(W(h):
[tex]h(W(h))=\frac{(49+2.2(h-60))+83}{2.2}\\h(W(h))=\frac{(49+2.2h-132+83)}{2.2}\\h(W(h))=h[/tex]
Jasmine walked 15 blocks. She stopped at the store 3/5 of the way into her walk. How many blocks did she walk to the store?
Answer:
8
Step-by-step explanation:
Mrs. Duncan measured the lengths of a crayon and a pencil. The pencil is double the length of the crayon. The sum of their length is 24 centimeters. What are their lengths?
Answer: The length of pencil is 16 centimetres and length of crayons is 8 centimetres
Step-by-step explanation:
Let the length of crayon =[tex]x[/tex]
Length of a pencil =[tex]2x[/tex]
As according to question that the sum of their length is 24 centimetres
So we have
[tex]x+2x=24\\\\\Rightarrow 3x= 24 \\\\\Rightarrow x= \dfrac{24}{3} =8[/tex]
Therefore the length of crayon = 8 centimetres
Length of pencil= [tex]2x= 2\times x = 2\times 8 =16[/tex] centimetres
Hence, the length of pencil is 16 centimetres and length of crayons is 8 centimetres
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $21.1 for a random sample of 717 people. Assume the population standard deviation is known to be $12.6. Construct the 85% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Answer:
The 85% confidence interval for the mean per capita income in thousands of dollars is between $20.4 and $21.8.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.85}{2} = 0.075[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.075 = 0.925[/tex], so [tex]z = 1.44[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.44\frac{12.6}{\sqrt{717}} = 0.7[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 21.1 - 0.7 = $20.4.
The upper end of the interval is the sample mean added to M. So it is 21.1 + 0.7 = $21.8.
The 85% confidence interval for the mean per capita income in thousands of dollars is between $20.4 and $21.8.
A square has a perimeter of 44 yd. What is the length of each side?
Answer:
Each side has a length of 11yd
Step-by-step explanation:
To calculate the side of the square we have to apply the formula of the perimeter of a square and clear s
p = perimeter = 44yd
s = side
p = s * 4
p /4 = s
we replace with known values
44yd / 4 = s
11yd = s
Each side has a length of 11yd
Answer:
11
Step-by-step explanation:
The overall perimeter is all of the sides combined. If it is a square, then all of the sides are equal. 44 divided by 4 is 11.
What is the formula for the volume of a hemisphere?
Answer:
The formula to find the volume of a hemisphere is 2TTr3 / 3, where pi is 3.14, and the radius is half of the diameter.
Step-by-step explanation:
Answer:
hiii, the answer would be
b. 2/3 pi 3
hope this helps :)
Step-by-step explanation:
i just did the assignment
According to a 2014 research study of national student engagement in the U.S., the average college student spends 17 hours per week studying. A professor believes that students at her college study less than 17 hours per week. The professor distributes a survey to a random sample of 80 students enrolled at the college. From her survey data the professor calculates that the mean number of hours per week spent studying for her sample is 15.6 hours per week with a standard deviation of 4.5 hours per week. The professor chooses a 5% level of significance. What can she conclude from her data? Group of answer choices The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week. The professor cannot conclude that the average number of hours per week spent studying for students at her college is less than 17 hours per week. The sample mean of 15.6 is not significantly less than 17. Nothing. The conditions for use of a T-model are not met. The professor cannot trust that the p-value is accurate for this reason.
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 17
For the alternative hypothesis,
µ < 17
This is a left tailed test.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 80,
Degrees of freedom, df = n - 1 = 80 - 1 = 79
t = (x - µ)/(s/√n)
Where
x = sample mean = 15.6
µ = population mean = 17
s = samples standard deviation = 4.5
t = (15.6 - 17)/(4.5/√80) = - 2.78
We would determine the p value using the t test calculator. It becomes
p = 0.0034
Since alpha, 0.05 > than the p value, 0.0043, then we would reject the null hypothesis.
The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm3
What is the volume of the sphere?
Answer:
12 cm³
Step-by-step explanation:
Let's say the radius of the sphere and cylinder is r and the height is h. However, notice that the "height" of the sphere is the same thing as the diameter, which is 2r, so h = 2r.
The volume of a sphere is denoted by: [tex]V=\frac{4}{3} \pi r^3[/tex] , where r is the radius.
The volume of a cylinder is denoted by: [tex]V=\pi r^2h[/tex], where r is the radius and h is the height. Plug in 2r for h and 18 for V:
[tex]V=\pi r^2h[/tex]
[tex]18=\pi r^2*2r=2\pi r^3[/tex]
[tex]\pi r^3=18/2=9[/tex]
Now plug in 9 for πr³ in the volume formula for the sphere:
[tex]V=\frac{4}{3} \pi r^3[/tex]
[tex]V=\frac{4}{3} *9=12[/tex]
The volume of the sphere is 12 cm³.
MacGyver wants to estimate the width of a river so he can get to the other side to save the world. He makes the measurements pictured. How wide is the river? Will he be able to do it?
Answer:
Wideness ≈ 40 m
He will be able to do it .
Step-by-step explanation:
He wants to estimate the width of a river so he can get to the other side to save the world . The width of the river is the side AB. From the scale above 2 right angle triangle are formed . The smaller triangle is CDE and the larger triangle is CAB.
The angle ECD can be gotten below
tan C = opposite/adjacent
tan C = 8/6
tan C = 1.3333
C = tan⁻¹ 1.333
C = 53.1301022854
C = 53. 13°
∠ACB = ∠ECD (vertically opposite angles)
Using the angle to find the wideness of the river AB in triangle CAB.
tan C = opposite/adjacent
tan 53.13° = AB/30
AB = 30 tan 53.13
AB = 30 × 1.33332837108
AB = 39.9998511323
AB ≈ 40 m
He will be able to do it.
A coach of a baseball team orders hats for the 12 players on his team. Each hat costs $9.95. The shipping charge for the entire order is $5.00. There is no tax on the order. What is the total cost of the coach’s order ?
Answer:
124.4
Step-by-step explanation:
12 x 9.95 = 119.4 dollars
119.4+5.00=124.4
The total cost is $124.40.
Answer:
Step-by-step explanation:
Answer:
124.4
Step-by-step explanation:
12 x 9.95 = 119.4 dollars
119.4+5.00=124.4
The total cost is $124.40.
Translate this into an equation
Answer:
r + 6 = 90
Step-by-step explanation:
Answer:
90 = r6
Step-by-step explanation:
90 is the answer or product (multiplication) of Rita's age (r) and 6.
Meaning r times 6 = 90
Which rules give a repeating pattern that has a 7 as the 15th number? Select all that apply.
a) 1, 7
b) 1, 7, 9
c) 1, 9, 7
d) 1, 7, 7
e) 7, 1, 9
A food truck caters an event attended by 100 guests. Every guest orders one of two possible dishes: a salad or a turkey plate. The price of each meal decreases as more of that particular type are ordered. The price of a salad is $ 10.00 minus $ 0.04 for each salad ordered. The price of a turkey plate is $ 12.00 minus $ 0.02 multiplied by the square of the number of turkey plates ordered. Guests pay for their meal only after everyone has placed their order. Using differentiation, find the maximum revenue for the food truck. Remember that the number of meals is a positive integer. Round revenue to the nearest cent.
Answer:
Max revenue: R = $679.73
Step-by-step explanation:
total people = 100
each person orders 1 of 2 dishes
salad price = $10 - 0.04x
turkey price = $12 - 0.02*y^2
so x + y = 100
s = 10 - 0.04x
t = 12 - 0.02*y^2
Revenue = s*x + t*y
Revenue = (10 - 0.04x)*x + (12 - 0.02y^2)*y
y = 100 - x
so
Revenue = (10 - 0.04x)*x + (12 - 0.02*(100 - x)^2 )*(100 - x)
R =
R = (10 - 0.04x)*x + (12 - 0.02*(100 - x)^2 )*(100 - x)
R = 10x - 0.04x*x + (12 - 0.02*(10000 - 200x + xx) )*(100 - x)
R = 10x - 0.04x*x + (12 - 200 + 4x -0.02 xx )*(100 - x)
R = 10x - 0.04x*x + (-188 + 4x -0.02 xx )*(100 - x)
R = 10x - 0.04x*x + (-188 + 4x -0.02 xx )*100 -x (-188 + 4x -0.02 xx )
R = 10x - 0.04x*x + -18800 + 400x -2 xx -x (-188 + 4x -0.02 xx )
R = 10x - 0.04x*x + -18800 + 400x -2 xx + 188x - 4xx +0.02 xxx
R = 10x - 0.04x*x + -18800 + 588x -6 xx + 0.02 xxx
R = -18800 + 598x -6.04 xx + 0.02 xxx
dR/dx = 598 - 12.08x + 0.06 x^2
set = 0
598 - 12.08x + 0.06xx = 0
299 - 6.04x + 0.03xx = 0
x = -(-6.04)/(2*0.03) + root((-6.04)^2 - 4*0.03*299) / 2*0.03
x = 100.6667 - root(36.4816 - 35.88) / 0.06
x = 100.6667 - 12.927
x = 87.739
so that is where you get the maximum revenue, when you sell 87.7 salad plates and 12.2605 turkey dishes
Revenue = (10 - 0.04*87.739)*87.739 + (12 - 0.02(12.2605)^2)*12.2605
Revenue = 569.464715 + 110.266
R = $679.7307
R = $679.73
To find the maximum revenue, differentiate the revenue functions of salads and turkey plates with respect to the number of salads sold, considering a total of 100 guests, find critical points, and use the second derivative test or sign changes to identify the maximum revenue. Ensure that the number of meals are integers.
Explanation:To determine the maximum revenue for the food truck, we need to derive the revenue functions for salad and turkey plates and then find the total revenue function. Assuming s salads and t turkey plates are sold, the price functions are Ps(s) = 10 - 0.04s for salads and Pt(t) = 12 - 0.02t2 for turkey plates. The revenue functions would be Rs(s) = s × Ps(s) and Rt(t) = t × Pt(t). Because there are 100 guests, s + t = 100, hence t = 100 - s. We substitute t in Rt and add Rs and Rt for the total revenue R(s). To find the maximum revenue, we differentiate R(s) with respect to s, find critical points, and check these for the maximum value using the second derivative test or analyzing the sign changes of R'(s). Remember to check if the critical points result in s and t being positive integers, as per the conditions given.
Understand multiplying
Fill in the blanks to solve 2.000 x 9.
2,000 x 9
x 2 x 9
Step 1
Step 2
X 18
Step 3
Answer:
Step 1 : 1000 * 2 * 9
Step 2 : 1000 * 18
Step 3 : 18000
Step-by-step explanation:
Step 3
2000 * 9 = y ⇒ 18000
y = 18000
Step 1
Solving for this, we have:
Let a be the unknown variable
a * 2 * 9 = 18000
18a = 18000
a = 1000
Therefore, when we multiply 1000 by 2 & 9, we have 18000
Step 2
Solving for this, we have:
Let a be the unknown variable
a * 18 = 18000
18a = 18000
a = 1000
Therefore, when we multiply 1000 by 18, we have 18000
We therefore see that the value of the unknown variables (a, y) is shown above & the product of all the steps (step 1 - 3) is 18000
Which set of statements shows the correct steps to find 70 percent of 82? Write 70 percent as 7 ´ 1 percent. Write 1 percent as StartFraction 1 Over 100 EndFraction. Then, find StartFraction 1 Over 100 EndFraction of 82: 82 times StartFraction 1 Over 100 EndFraction = StartFraction 82 Over 100 EndFraction = 0.82. Multiply 0.82 by 7 to get 5.74. So, 70 percent of 82 is 5.74. Write 70 percent as StartFraction 1 Over 7 EndFraction. Then, find StartFraction 1 Over 7 EndFraction of 82: 82 times StartFraction 1 Over 7 EndFraction = StartFraction 82 Over 7 EndFraction = 11.71. So, 70 percent of 82 is 11.71. Write 70 percent as 7 ´ 10 percent. Write 10 percent as StartFraction 1 Over 10 EndFraction. Then, find StartFraction 1 Over 10 EndFraction of 82: 82 times StartFraction 1 Over 10 EndFraction = StartFraction 82 Over 10 EndFraction = 8.2. Multiply 8.2 by 7 to get 57.4. So, 70 percent of 82 is 57.4. Write 70 percent as StartFraction 1 Over 70 EndFraction. Then, find StartFraction 1 Over 70 EndFraction of 82: 82 times StartFraction 1 Over 70 EndFraction = StartFraction 82 Over 70 EndFraction = 1.17. So, 70 percent of 82 is 1.17.
Answer:
(C)
Step-by-step explanation:
To find 70 percent of 82
Write 70 percent as 7*10 percent.
Write 10 percent as [tex]\frac{10}{100}= \frac{1}{10}[/tex].
Then, find [tex]\frac{1}{10}$ of 82[/tex]
[tex]82 X\frac{1}{10}=8.2[/tex]
Multiply 8.2 by 7: 8.2 X 7 =57.4
Therefore, 70 percent of 82 is 57.4.
The steps in Option C are the correct steps.
Answer:
The answer to ur question is C
Step-by-step explanation:
samuel wants to buy a snake for 288 and the pet store owner wants hin to make 6 equal payments of 49 what error did the pet store owner make
Answer:
There is a multiplication error. The payment should be $48 per month.
Step-by-step explanation:
i took the assignment hopes this help can i get brainliest plzzzzz
The pet store owner made an error in his calculation. When you multiply the amount of each payment ($49) by the number of payments (6), the result is $294, not $288.
Explanation:The information provided in the question implies a situation that involves simple mathematics; specifically, multiplication and addition. To determine the total cost of the snake, it would be necessary to multiply the number of payments (6) by the individual amount of each payment ($49).
Here's how:
This means that
the pet store owner is asking for $294 in total
, not $288. Thus, the error that the pet store owner made was in the calculation of the total amount due for the snake.
Learn more about Math Error here:https://brainly.com/question/33345535
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Complete the following table for residuals for the exponential function: f(x) = 49.3(1.47)
Hours Retweets Predicted Value Residual
1 / 65 /
2/ 90 /
3/ 162 /
4/ 224 /
5/ 337 /
6/ 466 /
7/ 780 /
8/ 1087 /
Answer:
Predicted values:
[tex]\hat y_1 = 49.3 (1.47)^1 =72.471[/tex]
[tex]\hat y_2 = 49.3 (1.47)^2 =106.5324[/tex]
[tex]\hat y_3 = 49.3 (1.47)^3 =156.6026[/tex]
[tex]\hat y_4 = 49.3 (1.47)^4 =230.2058[/tex]
[tex]\hat y_5 = 49.3 (1.47)^5 =338.4025[/tex]
[tex]\hat y_6 = 49.3 (1.47)^6 =497.4517[/tex]
[tex]\hat y_7 = 49.3 (1.47)^7 =731.254[/tex]
[tex]\hat y_8 = 49.3 (1.47)^8 =1074.943[/tex]
Residuals:
[tex]e_1 = 65-72.471=-7.471[/tex]
[tex]e_2 = 90-106.5324=-16.5324[/tex]
[tex]e_3 = 162-156.6026 = 5.3974[/tex]
[tex]e_4 = 224-230.2058 = -6.2058[/tex]
[tex]e_5 = 337-338.4025 = -1.4025[/tex]
[tex]e_6 = 466-497.4617 = -31.4517[/tex]
[tex]e_7 = 780-731.254 = 48.7459[/tex]
[tex]e_8 = 1087-1074.493 = 12.0566[/tex]
Step-by-step explanation:
For this case we assume the following exponential function:
[tex]\hat y_i = 49.3 (1.47)^x [/tex]
Where x represent the hours and y the predicted values for each hour. We can find the estimated values like this:
[tex]\hat y_1 = 49.3 (1.47)^1 =72.471[/tex]
[tex]\hat y_2 = 49.3 (1.47)^2 =106.5324[/tex]
[tex]\hat y_3 = 49.3 (1.47)^3 =156.6026[/tex]
[tex]\hat y_4 = 49.3 (1.47)^4 =230.2058[/tex]
[tex]\hat y_5 = 49.3 (1.47)^5 =338.4025[/tex]
[tex]\hat y_6 = 49.3 (1.47)^6 =497.4517[/tex]
[tex]\hat y_7 = 49.3 (1.47)^7 =731.254[/tex]
[tex]\hat y_8 = 49.3 (1.47)^8 =1074.943[/tex]
Now we can find the residuals with this formula:
[tex] e_i = Y_i -\hat y_i [/tex]
And replacing we got:
[tex]e_1 = 65-72.471=-7.471[/tex]
[tex]e_2 = 90-106.5324=-16.5324[/tex]
[tex]e_3 = 162-156.6026 = 5.3974[/tex]
[tex]e_4 = 224-230.2058 = -6.2058[/tex]
[tex]e_5 = 337-338.4025 = -1.4025[/tex]
[tex]e_6 = 466-497.4617 = -31.4517[/tex]
[tex]e_7 = 780-731.254 = 48.7459[/tex]
[tex]e_8 = 1087-1074.493 = 12.0566[/tex]
[tex] \sqrt{2x + 3 } - \sqrt{x - 2} = 2 [/tex]
find x
Answer:
Step-by-step explanation:
hello : here is an solution
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A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 6262 minutes with a mean life of 606606 minutes. If the claim is true, in a sample of 9999 batteries, what is the probability that the mean battery life would be greater than 619619 minutes? Round your answer to four decimal places.
Answer:
0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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. 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 606, \sigma = 62, n = 99, s = \frac{62}{\sqrt{99}} = 6.23[/tex]
What is the probability that the mean battery life would be greater than 619 minutes?
This is 1 subtracted by the pvalue of Z when X = 619. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{619 - 606}{6.23}[/tex]
[tex]Z = 2.09[/tex]
[tex]Z = 2.09[/tex] has a pvalue of 0.9817
1 - 0.9817 = 0.0183
0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes