A company that manufactures and bottles apple juice uses a machine that automatically fills 32-ounce bottles. There is some variation, however, in the amount of liquid dispensed into the bottles. The amount dispensed has been observed to be approximately normally distributed with mean 32 ounces and standard deviation 1 ounce. Determine the proportion of bottles that will have more than 30 ounces dispensed into them. (Round your answer to four decimal places.)
Answer:
The proportion of bottles that will have more than 30 ounces dispensed into them is 0.9772 = 97.72%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
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. 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.
The amount dispensed has been observed to be approximately normally distributed with mean 32 ounces and standard deviation 1 ounce.
This means that [tex]\mu = 32, \sigma = 1[/tex]
Determine the proportion of bottles that will have more than 30 ounces dispensed into them.
This is 1 subtracted by the p-value of Z when X = 30, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 32}{1}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
1 - 0.0228 = 0.9772
The proportion of bottles that will have more than 30 ounces dispensed into them is 0.9772 = 97.72%.
Find the value of x and the value of y.
A. x = 4, y = 8
B.x=7, y=422
C. X= 4/3, y= 7.2
D. x= 73, y=412
Answer:
x = 7 and
y = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
as you can see from the image we need to draw a line and when we do so we get a special right triangle with angle measures 90-45-45 and side lengths represented by a-a-a[tex]\sqrt{2}[/tex]
since the line we drew is parallel to the rectangle's length it's = 4 and so the number represented with a is also = 4
from there on we see x = 7 and y = 4[tex]\sqrt{2}[/tex]
Answer:
I can confirm, it is B! x=7 and y=4sqrt2
Step-by-step explanation:
edge
Given h(x) = -x + 1, find h(0).
Answer:
Answer:
1
Step-by-step explanation:
Given,
h ( x ) = - x + 1
To find : h ( 0 ) = ?
h ( 0 )
= - ( 0 ) + 1
= 1
Answer: 1
Step-by-step explanation:
h(x) = -x + 1
To Find = h(0)
= -(0) + 1
= 1
Answered by GauthMath if you like pls heart it and comment thanks
I NEED HELP PLEASE ASAP!!
Answer:
Option B, 1
Step-by-step explanation:
tan 45° = 1/1 = 1
Two numbers total 31 and have a difference of 11. Find the two numbers
Answer:
let 2 no. be x and y
x+y=31 ..... (1)
x-y=11 .........(2)
from (1)
x=31-y ..........(3)
putting (3) in (2)
31-y-y=11
-2y=11-31
-2y=-20
2y=20
y=10
find the missing length indicated
Answer:
Step-by-step explanation:
192
Answer:
Step-by-step explanation:
For Coronado Industries, sales is $500000, variable expenses are $335000, and fixed expenses are $140000. Coronado’s contribution margin ratio is
a) 67%.
b) 33%.
c) 28%.
d) 5%.
Help! Please? Dont understand
A boat travels 400 kilometers in 9.6 hours (with a constant speed). How much time will it take to travel 138 kilometers? (round to the nearest tenth of an hour)
Step-by-step explanation:
here's the answer to your question
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
A. Combination.
B. 17020
Step-by-step explanation:
A. Determination whether it is permutation or combination.
From the question given above, we were told that the student body of 185 students wants to elect two (2) representatives.
This is clearly combination because it involves a selecting process (i.e selecting 2 out of 185).
NOTE: Combination involves selecting while permutation involves arranging.
B. Determination of the combination.
Total number of people (n) = 185
Number of chosen people (r) = 2
Number of combination (ₙCᵣ) =?
ₙCᵣ = n! / (n – r)! r !
₁₈₅C₂ = 185! / (185 – 2)! 2!
₁₈₅C₂ = 185! / 183! 2!
₁₈₅C₂ = 185 × 184 × 183! / 183! 2!
₁₈₅C₂ = 185 × 184 / 2!
₁₈₅C₂ = 185 × 184 / 2 × 1
₁₈₅C₂ = 34040 / 2
₁₈₅C₂ = 17020
Kesley works at a nursery she has 157 beads that she wants to share equally between 16 children for a necklace making activity.
How many beads will each child have and how many beads will be left over
Each child will get 9 pieces with 13 pieces left.
What is division?
'Division is a method of distributing a group of things into equal parts.'
According to the given problem,
Number of beads Kesley has = 157
Number of children to be shared between = 16
Number of beads in possession of each child = 157 ÷ 16
= 9
Number of beads divided equally = 144
Remaining beans = 157 - 144
= 13
Hence, we can conclude that out of 157 beans, 144 is divided equally among 16 children with each child getting 9 pieces.
Learn more about division here:
https://brainly.com/question/25502096
#SPJ2
Did any one know this?
Answer:
x sqrt(2)
Step-by-step explanation:
sqrt(a) / sqrt(b) = sqrt(a/b)
sqrt( 14 x^3) / sqrt(7x)
sqrt(14x^3/7x)
sqrt(2x^2)
sqrt(ab) = sqrt(a)sqrt(b)
sqrt(x^2) sqrt(2)
x sqrt(2)
Convert 653 in base 7 to base 10
A box of 8 marbles has 4 red, 2 green, and 2 blue marbles. If you select one marble, what is the probability that it is a red or blue marble.
Answer:
3/4
Step-by-step explanation:
add the no. of red marbles and blue marbles
2+4 = 6
Probability so divide 6/8 simplified to 3/4
A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 25 dieters, are chosen for the study.
Group A is required to follow a specific diet and exercise regimen, and also take a 500-mg supplement of calcium each day.
Group B is required to follow the same diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 12.7 pounds with a standard deviation of 2.2 pounds. The members of Group B had lost a mean of 10.8 pounds with a standard deviation 2.0 pounds during the same time period. Assume that the population variances are not the same.
Create and interpret a 95% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not.
Answer:
(0.7044 ; 3.0956)
Step-by-step explanation:
Given:
GROUP A:
n1 = 25
x1 = 12.7
s1 = 2.2
GROUP B :
n2 = 25
x2 = 10.8
s2= 2.0
The obtain the confidence interval assuming unequal population variance :
(x1 - x2) ± tα/2[√(s1²/n1 + s2²/n2)]
The degree of freedom :
df = (s1²/n1 + s2²/n2)² ÷ (s1²/n1)²/n1-1 + (s2²/n2)²/n2-1
The degree of freedom :
(2.2²/25 + 2²/25)² ÷ (2.2²/25)²/24 + (2²/25)²/24
df = 0.12503296 ÷ (0.0015617 + 0.0010666)
df = 47.57 ;
df = 48
Tcritical value ; α = 95% ; df = 48
Tcritical = 2.0106
C.I = (12.7 - 10.8) ± 2.0106[√(2.2²/25 + 2²/25)]
C.I = 1.9 ± (2.0106 * 0.5946427)
C.I = 1.9 ± 1.1955887
C. I = (0.7044 ; 3.0956)
What must be true about the discriminant of this quadratic equation for the mentioned values of k? Assume p>0.
value of the discriminant k > 0
Options:
B^2 - 4ac= 0
B^2 - 4ac is greater than 0
B^2 - 4ac is less than 0
Answer:
Step-by-step explanation:b
No real roots. Roots will have imaginary numbers. This means the quadratic is either always above the axis, or always below.
One real root. The graph touches the x -axis in one place. →
Two real roots. The graph crosses the x -axis twice.
I NEED HELP ASAP, I DON'T UNDERSTAND THIS PROBLEM!!!!!
Answer:
1
Step-by-step explanation:
Cosine is a trigonometric function that is represented by adjacent divided by the hypotenuse. The side adjacent to angle A is AC and the hypotenuse is AB, so we can say cos(A) = [tex]\frac{AC}{AB}[/tex]. We can do the same for angle B. The side adjacent to it is BC, and the hypotenuse is again AB. So, we can say
cos(B) = [tex]\frac{BC}{AB}[/tex]. We are solving for [tex]\frac{cosA}{cosB}[/tex], so we can substitute the value of those two and solve:
[tex]\frac{\frac{AC}{AB}}{\frac{BC}{AB} }[/tex]
[tex]\frac{AC}{AB} * \frac{AB}{BC} = \frac{AC}{BC}[/tex]
AC is given to be 3 and BC is also 3, so [tex]\frac{AC}{BC}[/tex] is [tex]\frac{3}{3}[/tex] which is just 1.
Calculate the next term in the geometric sequence that is calculated with a ratio of 19 if the current term is 38
Answer:
Step-by-step explanation:
The next term is going to be simply 38*19 = 722
The series is geometric which means that you multiply from one term to get to the next.
The ratio of 19, and the current term is 38. So to get to the next term, multiply 38 * 19
Find the length of the arc round your answer to the nearest 10th
Answer:
45
Step-by-step explanation:
The length of the arc is equal to the central angle it sees.
Determine whether the following events are mutually exclusive. Choosing a student who is a French major or a chemistry major from a nearby university to participate in a research study. (Assume that each student only has one major.)
A. Mutually Exclusive
B. Not Mutually Exclusive
Answer:
A. Mutually Exclusive
Step-by-step explanation:
Mutually exclusive events:
Two events are mutually exclusive if they cannot happen together, that is, supposing the events are A and B:
[tex]P(A \cap B) = 0[/tex]
Choosing a student who is a French major or a chemistry major
Since each student only has one major, the student cannot be both a French and a Chemistry major, that is, [tex]P(A \cap B) = 0[/tex], so they are mutually exclusive and the correct answer is given by option A.
A car travels 630 miles in 14 hours. At this rate, how far will it travel in 42 hours?
Assuming the car's speed [tex]\frac{630}{14}=45\mathrm{mph}[/tex] does not change, the car will travel [tex]45\cdot42=\boxed{1890}[/tex] miles.
Hope this helps :)
PLEASE HELPPPPP!!!! (answer in decimal)
Answer:
[tex]\approx 0.482659[/tex]
Step-by-step explanation:
The experimental probability is the chance of an event happening based on data, or rather the experiment results, and not on a theoretical calculation. In essence, a theoretical calculation can be described by the following formula:
[tex]\frac{desired}{total}[/tex]
However, the experimental probability can be described with the following formula:
[tex]\frac{number\ of\ desired\ outcomes}{number\ of \ trials}[/tex]
The number of trials is the sum of the number of outcomes. In this case, the desired outcome is tails. Therefore, the experimental probability can be described using the following formula:
[tex]\frac{tails}{total}[/tex]
One can also rewrite the formula as the following. This is because the total is the sum of the number of the two outcomes:
[tex]\frac{tails}{heads+tails}[/tex]
Substitute,
[tex]\frac{167}{167+179}[/tex]
Simplify,
[tex]\frac{167}{346}[/tex]
Rewrite as a decimal:
[tex]\approx 0.482659[/tex]
21. SCALE FACTOR A regular nonagon has an area of 90 square feet. A similar
nonagon has an area of 25 square feet. What is the ratio of the perimeters of
the first nonagon to the second?
Answer:
The ratio of the perimeters of the first nonagon to the second is 3.6 to 1.
Step-by-step explanation:
Given that a regular nonagon has an area of 90 square feet, and a similar nonagon has an area of 25 square feet, to determine what is the ratio of the perimeters of the first nonagon to the second, the following calculation must be performed:
25 = 1
90 = X
90/25 = X
3.6 = X
Therefore, the ratio of the perimeters of the first nonagon to the second is 3.6 to 1.
A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 83 months with a variance of 81. If the claim is true, what is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors? Round your answer to four decimal places.
Answer:
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
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 normal distributions can be solved using the z-score formula.
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. 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.
Central Limit Theorem
The Central Limit Theorem establishes 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.
The production manager claims they have a mean life of 83 months with a variance of 81.
This means that [tex]\mu = 83, \sigma = \sqrt{81} = 9[/tex]
Sample of 146:
This means that [tex]n = 146, s = \frac{9}{\sqrt{146}}[/tex]
What is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors?
This is 1 subtracted by the p-value of Z when X = 81.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{81.2 - 83}{\frac{9}{\sqrt{146}}}[/tex]
[tex]Z = -2.42[/tex]
[tex]Z = -2.42[/tex] has a p-value of 0.0078.
1 - 0.0078 = 0.9922.
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
1) A book contains 192 pages. A boy reads x complete pages everyday.if he has not finished the book after 10days, find the highest possible value of x
9514 1404 393
Answer:
19
Step-by-step explanation:
After x days, the boy will have read 10x. If this is less than 192, we have ...
10x < 192
x < 192/10
x < 19.2
If x is an integer, the largest possible value x could have is 19.
How many centilitres are in 156000m^3
9514 1404 393
Answer:
1.56×10^10 cL
Step-by-step explanation:
There are 1000 liters in a cubic meter, so 10^5 centiliters in a cubic meter. The 1.56×10^5 cubic meters will then have ...
(1.56×10^5 m^3)×(10^5 cL/m^3) = 1.56×10^10 cL
_____
That's 15,600,000,000 cL.
"Centi-" is a prefix meaning 1/100.
How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol. Write as an expression.
Answer:
13/9l or 1 4/9 l
Step-by-step explanation:
Answer:
quantity of alcohol = l liters
we need to make a solution of having 45% alcohol by adding water.
45% alcohol means whatever id the total quantity of solution there is 45% alcohol.
Let the total quantity of solution be x.(
then
quantity of alcohol in terms of x = 45% of x = 45/100 x
but we know that quantity of alcohol = l liters
45/100 x = l
x = 100/45 l
Thus, total quantity of solution is 100/45 l,
but in it, there are l liters of alcohol.
to find the quantity of water we need to subtract the quantity of alcohol from the total quantity of solution
quantity of water in the solution = 100l/45 - l = (100l - 45l)/45 = 65l/45
quantity of water in the solution = 13/9l = 1 4/9 l -------->answer.
Thus, 1 4/9 liters of water needs to be added to l liters of alcohol to make a solution of 45% alcohol.
PLEASE MARK THIS AS BRAINLIST
which of the rolling equations have exactly one solutions ?
ps: (click the picture to see answer choices)
Answer:
All have exactly one solution
Step-by-step explanation:
a) -13x + 12 = 13x - 13
+13x +13x
-------------------------------
12 = 26x - 13
+13 +13
-------------------
25 = 26x
----- ------
26 26
25/26 = x
b) 12x + 12 = 13x - 12
-12x -12x
-----------------------
12 = x - 12
+12 +12
-----------------
24 = x
c) 12x + 12 = 13x + 12
-12x -12x
-----------------------------
12 = x + 12
0 = x
d) -13x + 12 = 13x + 13
+13x +13x
-----------------------------
12 = 26x + 13
-13 -13
-----------------------
-1 = 26x
--- -----
26 26
-1/26 = x
The length of a rectangle is 10 yd less than three times the width, and the area of the rectangle is 77 yd^2. Find the dimensions of the rectangle.
Answer:
W=7 and L=11
Step-by-step explanation:
We have two unknowns so we must create two equations.
First the problem states that length of a rectangle is 10 yd less than three times the width so: L= 3w-10
Next we are given the area so: L X W = 77
Then solve for the variable algebraically. It is just a system of equations.
3W^2 - 10W - 77 = 0
(3W + 11)(W - 7) = 0
W = -11/3 and/or W=7
Discard the negative solution as the width of the rectangle cannot be less then 0.
So W=7
Plug that into the first equation.
3(7)-10= 11 so L=11
A pool can be filled with water by a large pipe within six hours .A smaller pipe will take 9 hours to fill the pool.How long will it take to fill the pool if the two pipes operate together
Answer:
3.6 hours
Step-by-step explanation:
The formula is
1/a+1/b = 1/c where a and b are the times working along and c is the time working together
1/6 + 1/9 = 1/c
Multiply by 36c to clear the fractions
36c (1/6 + 1/9 = 1/c)
6c +4c = 36
10c = 36
Divide by 10
10c/10 = 36/10
c = 3.6 hours working together
