The amount of energy associated with a production of bottled water is approximately Normal with a mean of 8.7 million Joules and a standard deviation 0.5 million Joules. How much energy should be required for the bottom 80% of bottled water?
Answers
Answer:
At most 9.12 joules should be required for the bottom 80% of bottled water
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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.
In this question, we have that:
\(\mu = 8.7, \sigma = 0.5\)
How much energy should be required for the bottom 80% of bottled water?
At most the 80th percentile.
The 80th percentile is X when Z has a pvalue of 0.8. So it is X when Z = 0.84.
\(Z = \frac{X - \mu}{\sigma}\)
\(0.84 = \frac{X - 8.7}{0.5}\)
\(X - 8.7 = 0.84*0.5\)
\(X = 9.12\)
At most 9.12 joules should be required for the bottom 80% of bottled water
Related Questions
let's see who can solve this. pleseeee
Answers
The correlation coefficient between X and Y is Corr(X, Y) = 0.
To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.
a. Marginal distribution of X:
To find the marginal distribution of X, we integrate the joint PDF over the range of Y:
∫[0, 1] J(x, y) dy
Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:
∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1
So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.
b. Expectation of X:
The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:
\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)
Therefore, the expectation of X is E(X) = 1/3.
c. Variance of X:
The variance of X can be calculated using the formula:
\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)
Therefore, the variance of X is Var(X) = 5/36.
d. Covariance of X and Y:
The covariance of X and Y can be calculated as:
Cov(X, Y) = E(XY) - E(X)E(Y)
Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:
\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)
\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)
Cov(X, Y) = 1/6 - (1/3)(1/6) = 0
Therefore, the covariance of X and Y is Cov(X, Y) = 0.
e. Correlation coefficient between X and Y:
The correlation coefficient can be calculated using the formula:
Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))
Since the covariance of X and Y is 0, the correlation coefficient will also be 0.
Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.
f. Conclusion based on the correlation coefficient:
The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the
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The total distance a ball rolls varies directly with the time in seconds. The ball rolls a total distance of 78 centimeters in 6 seconds.
What is the time in seconds the ball rolls when the total distance is 130 centimeters?
10 s
13 s
22 s
25 s
Answers
The time the balls roll when the total distance is 130 cm is 10 seconds.
let
d = total distance the ball rolls
t = time in seconds
The total distance is directly proportional to the time in seconds. Therefore,
d ∝ t
d = kt
where
∝ is the proportionality sign
k = constant of proportionality
when d = 78 cm, t = 6 seconds
Therefore, let's find the constant of proportionality.
k = d / t
k = 78 / 6
k = 13
The constanst of proportionality is known . Now let's find the time(seconds) when d = 130 cm .
d = kt
make t the subject of the formula
t = d / k
t = 130 / 13
t = 10 secs
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Which choice is equivalent to the quotient shown here for acceptable
values of X?
square root 30(x - 1)/square root15(x - 1)^2?
A. sr30(x - 1) - 5(x - 1)?
B. sr6(x - 1)
C. sr 6/(x - 1)
D. sr150(x - 1)^3
Answers
The curved surface area, A of a cone of height h and base radius r is π√h²+r².
Make h the subject of the formula.
Find the height of a cone of area 550 cm² and base radius 7 cm
Answers
The height of the cone is 580.36 cm.
The curved surface area of the cone is given by,
\(A = \pi \sqrt{h^{2} +r^{2} }\)
Squaring both sides, we get :
\(A^{2} =\pi ^{2} (h^{2} +r^{2} )\)
Now, it is given that the height of the cone is h,
The area of the cone = 550 \(cm^{2}\)
And the radius of the cone = 7cm,
Putting these values in the given formula, we get,
\(A^{2} =\pi ^{2} (h^{2} +r^{2} )\)
\(550^{2} = \pi ^{2} * ( h^{2} +7^{2} )\\\)
3,36,875 = \(h^{2}+49\)
\(h^{2}\) = 3,36,875 - 49 = 3,36,826
h = 580.36 cm
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the material for the base costs 29 cents/ft2, the material for the top costs 24 cents/ft2, and the material for the sides costs 10 cents/ft2. if x denotes the length of one side of the base (in feet), find a function in the variable x giving the total cost of materials used in constructing the box in cents. total cost, as a function of x
Answers
The total cost of materials used in constructing the box in cents can be given by the function \(C(x) = 29x^2 + 24x^2 + 10(4x) = 63x^2 + 40x\).
This formula can be derived by multiplying the cost per square foot of the base, top, and sides with their respective areas. The area of the base and top can both be expressed as \(x^2\), while the area of the four sides can be expressed as 4x. Thus, multiplying the cost per square foot of each material with its respective area, we obtain the total cost of materials used in constructing the box in terms of x, which is given by the expression \(C(x) = 63x^2 + 40x\).
For example, if x = 4, then the total cost of materials used in constructing the box in cents is \(C(4) = 63(4^2) + 40(4) = 1512 + 160 = 1672 cents\).
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I need help anyone please ?!!!!!!!
Answers
Answer:its a
Step-by-step explanation:you did it wrong
2. A standard package of pencils contains 24
pencils.
# of
packages
# of
pencils
127
?
1
?
3
?
4
?
6
1
2
?
Answers
Answer:
12, 24,72,96,156
Step-by-step explanation:
1/2 package would be 1/2 of 24 which is 12
21 x 24 = 24
3 x 24 = 72
4 x 24 = 72
We know that 3 packages is 72 so 6 packages is double that at 144. We also know that have a package is 12. so 144 + 12 = 156
Answer:
1/2 package = 1/2 of 24 = 12 pencils
1 package = 24 pencils
3 packages = 24*3 = 72 pencils
4 packages = 24*4 = 96 pencils
6 1/2 packages = 24*6.5 = 156
Step-by-step explanation:
1 package = 24 pencils
1/2 package = 1/2 of 24 = 12 pencils
1 package = 24 pencils
3 packages = 24*3 = 72 pencils
4 packages = 24*4 = 96 pencils
6 1/2 packages = 24*6.5 = 156
Mrs. Reynolds has $153. She buys a bicycle for $105.
Then, she finds $20 at the bottom of her purse.
How much money does she have now? Use the bar diagrams to help you.
Step 1:
Step 1: a bar diagram shows 105 and m, the money left after buying a bike. Together 105 and m are equal to 153.
Step 2:
Step 2: a bar diagram shows that 20 and m is equal to s, the money now.
Enter your answer in the box.
Mrs. Reynolds has $
now.
Answers
The total amounts of money which Mrs. Reynolds now has according to the descriptions in the task content is; $68.
How much does Mrs. Reynolds have now?It follows from the task content that;
Together 105 and m are equal to 153.20 and m is equal to s.On this note;
105 + m = 153m = 153 -105 = 48Hence, it follows that the amount of money, s she has now is;
s = 48 + 20 = $68Read more on addition and subtraction;
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A florist received a shipment of 16 dozen roses. The original order was for 20 dozen. What percent of the order did NOT arrive?
Answers
Answer:
20 percent
Step-by-step explanation:
Answer:
20%
Step-by-step explanation:
Hope this helps :)
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The proof of ΔRUV ≅ ΔSUT is shown below.
Given that:
RSTV is a rectangle and U is the midpoint of VT.
Here, We have to Prove:
⇒ ΔRUV ≅ ΔSUT
Now, We can prove as;
Statement Reason
1) RSTV is a rectangle Given
2) Angle V and T are Because every angle in a rectangle is 90
right triangle.
3) ∠V ≅ ∠T Because both are right angle.
4) U is the midpoint of VT. Given
5) VU = UT By midpoint theorem.
6) VR ≅ TS Opposite sides of rectangle.
7) ΔRUV ≅ ΔSUT By SAS congruency theorem.
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Find the number of 3-card hands that contain the cars specified. NO LINKS!! NOT MULTIPLE CHOICE!!!
5. 3 red cards
6. 3 aces
7. 3 face cards
8. 3 hearts
9. 3 of one kind
Answers
Answer:
Step-by-step explanation:
5.
26 red cards in a 52-card deck so 3 red cards combo = 26*25*24 = 15600
6.
4 aces in a deck so 3 aces = 4*3*2 = 24
7.
12 face cards in a deck so 3 face cards = 12*11*10 = 1320
8.
13 hearts in a deck so 3 hearts = 13*12*11 = 1716
9.
4 kinds in a deck: spade, heart, diamond and club so 3 of one kind = 4*1716
= 6864
Answer:
Step-by-step explanation:
5. half deck are red; 2nd card is 1 less n 3rd card 2 less: 26x25x24 = 15600
6. 4 aces total: 4x3x2 = 24
7. 3 face cards per suit; 12 total: 12*11*10 = 1320
8. 13 heart cards: 13x12x11 = 1716
9. 4 suits: 1716x4 = 6864
a + b=c make (a) the subject with working
Answers
Step-by-step explanation:
a= c-b pls let me know if it is correct or not
3. Write the inequality that best represents the relationship shown on this number line:
Answers
Is 12/19 rational or irrational?
Answers
Answer:
irrational
Step-by-step explanation:
The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answers
Answer:
Step-by-step explanation:
3.6*
It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2
For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.
We get
36 = s^2
Now, we need to get the square root of both sides, which gives us
s = √36 s = 6 cm
Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.
Therefore, the perimeter of the square is 24 cm.
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Identify which one of the following is a formula unit:NaCl,H2O,HCl,HNO3
Answers
Based on the definition of the formula unit, the only one that is an example of this concept is NaCl.
What is a formula unit?In chemistry, this concept refers to the representation of an ionic compound. This formula differs from others because it displays the lowest possible ratio in which the ions have the same charges and therefore the compound is neutral.
What is one example of this formula?A classical example of this concept is NaCl because this includes a cation (positively charged) and an anion (negatively charged). Moreover, in this formula, the compound shows the lowest possible ratio between the two elements.
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There are 20 pieces of fruit in a bowl and 5 of them are apples. What percent of the fruit are apples?
Answers
Answer: 25%
Step-by-step explanation:
Total pieces=20
apple pieces=5
=apple pieces/total pieces
= 5/20
for %age multipilying with 100
= 0.25×100
=25 percent
8. The area of a rectangle is 13x + 2 square units. The
width is 9. The length is x + 6. What is the length?
Answers
Answer:
L=19
Step-by-step explanation:
Since the formula to find the area of a rectangle is \(A= w(l)\) we must start by plugging the given data into this equation
\(13x+2=9(x+6)\)
Then solve!
\(13x+2=9(x+6)\\13x+2=9x+54\\4x+2=54\\4x=52\\x=13\)
Since we now know that x equals, we are able to find the length by plugging 13 into the given function for the length.
\(l=13+6=19\)
Make sure to check your work!
\(13(13)+2=9(13+6)\\169+2=9(19)\\171=171\)
joan’s finishing time for the bolder boulder 10k race was 1.81 standard deviations faster than the women’s average for her age group. there were 410 women who ran in her age group. assuming a normal distribution, how many women ran faster than joan? (round down your answer to the nearest whole number.)
Answers
Given that Joan's finishing time was 1.81 standard deviations faster than the women's average for her age group, we can use the properties of a normal distribution to find the corresponding percentage.
Since Joan is faster than the average, her finishing time would fall in the top portion of the distribution. Using a standard normal distribution table or a calculator, we can find the percentage of data below her finishing time. The Z-score associated with 1.81 standard deviations is approximately 0.9641, which corresponds to a percentage of 96.41%.
This means that approximately 96.41% of the women in her age group ran slower than Joan. To find the number of women who ran faster, we subtract this percentage from 100%: 100% - 96.41% = 3.59%.
To determine the number of women, we multiply the percentage by the total number of women in her age group: 3.59% * 410 = 14.709.
Rounding down to the nearest whole number, we can conclude that approximately 14 women ran faster than Joan.
Please help me outtttttttttttttttt
Answers
Answer: B
Step-by-step explanation: multiply 3/8 by 4 to get 3/2 then put 3/2 in decimal form to get 1.5
When using substitution to solve this system of equations, what is the result of the first step x=y+1 4=2x+3y
Answers
Please help !!! Ill give you brainliest!!!
Answers
Answer:
72
Step-by-step explanation:
s=9
t=8
therefore , st
9×8
= 72
Answer:
st
Putting the value of s and t in above equation
=> 9 × 8
=> 72
if x = -5 and y = -2 evaluate x2 - y3.
Answers
Answer: The answer is -4
Step-by-step explanation: The answer is -4 because you when you substitute x for -5(2) and y for -2(3). Which then equal -10 and the -6 turns into a positive 6 which then leads to -10+6 and equals -4!
Hope this Helps :D
20 Points for an answer! Please help! I have unlimited tries for the practice test, but I got this one wrong from an answer on here, Letter B doesn't work for the answer, I tried that already.
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?
Question options:
A.) If segment AC ≅ segment BC, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
B.) If segment AD ≅ segment CD, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
This one is incorrect according to my practice test I took.
C.) If segment AC ≅ segment BC, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
D.) If segment AD ≅ segment CD, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
Answers
Answer:
Well, according to the question, option D is the main answer
The figure is made up of a square and a rectangle. Find the area of the shaded region 16 by 3 by 7
Answers
Answer:
Go on Answers.com your welcome.
A florist sells flower bouquets. The table shows the prices for various amounts and kinds of bouquets.
Flower Bouquets
Tole Price
daisies
$23.90
tulips
$60.80
roses
?
A customer buys 3 bouquets of tulips and 2 bouquets of roses for $147.70. What is the price of a bouquet of roses?
$28.25
$29.54
$55.93
S86.90
Answers
Answer:
$28.25
Step-by-step explanation:
$28.25
& metalic discs of radius 0.75cm and thickness 0.2cm are
melted to obtain 508.68 cm² of metal. Find the number of
discs melted?
Answers
Answer:
Step-by-step explanation:
The total area of metal discs is given by:
total area = area of one disc * number of discs
The area of one disc is given by:
A = 2πrh + πr^2
where r is the radius and h is the thickness.
Substituting the given values, we get:
A = 2π(0.75 cm)(0.2 cm) + π(0.75 cm)^2
= 0.3π cm² + 0.5625π cm²
= 0.8625π cm²
The number of discs melted can be found by dividing the total area by the area of one disc:
number of discs = total area / area of one disc
number of discs = 508.68 cm² / 0.8625π cm²
number of discs ≈ 185.
Find the limit of the difference quotients for f(x) = x2+2x+1 if a= -1
Answers
The limit of the difference quotients for f(x) = x^2 + 2x + 1 as x approaches -1 is indeterminate.
To find the limit of the difference quotients for the function f(x) = x^2 + 2x + 1 as x approaches -1, we need to evaluate the following expression:
lim(x→-1) [f(x) - f(-1)] / (x - (-1))
First, let's substitute the values into the expression:
lim(x→-1) \([(x^2 + 2x + 1) - (-1^2 + 2(-1) + 1)] / (x + 1)\)
Simplifying further:
lim(x→-1) \([(x^2 + 2x + 1) - (1 - 2 + 1)] / (x + 1)\)
lim(x→-1)\([x^2 + 2x + 1 - 0] / (x + 1)\)
lim(x→-1) \((x^2 + 2x + 1) / (x + 1)\)
Now, we can directly substitute x = -1 into the expression:
\((-1^2 + 2(-1) + 1) / (-1 + 1)\)
(1 - 2 + 1) / (0)
0 / 0
We have obtained an indeterminate form of 0/0. This indicates that we need to further simplify the expression or use other techniques, such as L'Hôpital's rule, to evaluate the limit. However, without additional information or simplification, we cannot determine the precise value of the limit at x = -1.
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I just need help on 19r=-1, n=3, t=12, v=0 and w=-1/2
Answers
To evaluate the above expression, let's substitute the variables with their corresponding equivalent.
r = -1, n = 3, and t = 12
\(9(-1)^2+(3^2-1)(12_{})\)The first thing to do is to simplify/solve the numbers with the exponents.
\(9(1)+(9-1)(12)\)Next, eliminate the parenthesis by applying the operation connected to it.
\(\begin{gathered} 9+8(12) \\ 9+96 \\ 105 \end{gathered}\)Therefore, the answer to the above expression given the values of the variables is 105.
who ever answers ths is 52 minutes will get brainlyeiest
Which expression is equivalent to 8-(6r+2)?
-6r+6
2r+2
6r+10
-6r+10
Answers
Answer:
-6r+6
Step-by-step explanation:
Let us expand the expression:
8-(6r+2)=
8-6r-2=
6-6r
OR
-6r+6
I hope this helps! :)
Answer:
6r+6
Step-by-step explanation:
we dont know the variable's number value yet so you can't solve anything with the 6r. We use distribbutive property and solve 8-2 since the 8 is just subtracting everything in the parenthesis. 8-2=6 and you can't do anything with the 6r so the expression would end up as 6r+6.