5. (10 points) The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 367 ml and a standard deviation of 3 ml. If all cans less than 358 or greater than 373 ml are scrapped, what proportion of cans is scrapped? Solution:
The proportion of cans that are scrapped is approximately 0.0241.
We know that the fill volume of cans follows a normal distribution with a mean of 367 ml and a standard deviation of 3 ml. Let's define X as the fill volume of a single can. Then we can write:
X ~ N(367, 3)
We want to find the proportion of cans that are scrapped, i.e., the proportion of cans with a fill volume less than 358 ml or greater than 373 ml. Let's call this proportion p:
p = P(X < 358 or X > 373)
To solve this problem, we can use the standard normal distribution and the z-score formula:
z = (X - μ) / σ
where μ is the mean and σ is the standard deviation of the distribution. We can standardize the values 358 and 373 using this formula:
z1 = (358 - 367) / 3 = -3
z2 = (373 - 367) / 3 = 2
Now we can find the probabilities of the two events separately using the standard normal distribution table or a calculator:
P(X < 358) = P(z < -3) ≈ 0.0013
P(X > 373) = P(z > 2) ≈ 0.0228
The probability of either event happening is the sum of the probabilities:
P(X < 358 or X > 373) = P(X < 358) + P(X > 373) ≈ 0.0241
To learn more about proportion here:
https://brainly.com/question/24261494
#SPJ1
The weatherman predicted that today's temperature would be 64°F. It was actually 38°F. What was the percent error of the weatherman's
prediction?
A 68.42%
B
40.63%
C 42.55%
D 64.82%
Answer:
Step-by-step explanation:
B. 40.63
Answer:
Step-by-step explanation:
B. 40.63
jackson well middle school find area.
multiply each shapes by length x width
Step-by-step explanation:
an example:
5x3 is 15
then do that for all of the shapes in this photo then add all of your answer together to get you're area
hope this helps
in the space below draw a triangle with angles 60° and 60° and an included length of 1 inch
The triangle presented in the diagram drawn is known as equilateral triangle.
What is triangle with angle 60?A triangle with angle 60 degrees is known as equilateral triangle because the sum of angles in a triangle is 180 degrees.
So if the total angles in a triangles is 180 degrees, and two known angles are 60 degrees, then the remaining side will be 60 degrees.
In an equilateral triangle, each of the interior angle measures 60 degrees.
Thus, the triangle presented in the diagram drawn is known as equilateral triangle.
Learn more about equilateral triangle here: https://brainly.com/question/17264112
#SPJ1
The Karns Recreation Hall needs to build a ramp. The height of the ramp must be 2 feet. The ramp will start 6 feet from the door. To the nearest tenth of a foot, how long will the ramp be?
Using the Pythagorean's theorem we can see that the length of the ramp is 6.32ft
How long the ramp will be?We know that the ramp is a right triangle whose legs are 2 ft and 6 ft. Remember that by Pythagorean's theorem we know that the square of the hypotenuse is equal to the sum of the squares of the legs.
Then the length of the ramp L will be:
L² = (2ft)² + (6ft)²
L = √((2ft)² + (6ft)²)
L = 6.32ft
LEarn more about right triangles at:
https://brainly.com/question/2217700
#SPJ1
Mariano has $3.55 in nickels and quarters. The total number of coins is 5 less than twice the number of nickels. Which system of equations can be used to determine q, the number of quarters, and n, the number of nickels, that Mariano has?
The system of equations that can be used to determine q and n is:
25q + 5n = 355
q = 2n - 5
We have,
Let's use q to represent the number of quarters and n to represent the number of nickels.
The value of q quarters is 25q cents, and the value of n nickels is 5n cents.
The total value of Mariano's coins is 3.55, or 355 cents.
We can write the first equation based on these values:
25q + 5n = 355
The second sentence tells us that the total number of coins is 5 less than twice the number of nickels.
Since each nickel is one coin, the number of quarters must be two less than the total number of coins.
We can write the second equation based on this information:
q = 2n - 5
Therefore,
The system of equations that can be used to determine q and n is:
25q + 5n = 355
q = 2n - 5
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
Please help.
Draw a sketch to show two
figures that have the same number of unit cubes
that look different from each other.
The two figures that have the same number of cubes are given.
We have,
The number of cubes in each figure drawn = 5 cubes
We can also find the area of each figure,
Consider each cube has a side of 2 cm
Figure 1:
Two rectangles.
So,
Area = 6 x 2 + 4 x 2 = 12 + 8 = 20 square units
Figure 2:
Area = 10 x 2 = 20 square units.
Thus,
The two figures that have the same number of cubes are given.
Learn more about cubes here:
https://brainly.com/question/11168779
#SPJ1
distinguish the number of solutions . show your work. explain how you know the number of solutions. -6x-4y=-4, 3x +2y=6
The number of solutions to the system of equations is n = 0
Given data ,
Let the first equation be represented as A
-6x - 4y = -4 be equation (1)
Let the second equation be represented as B
3x + 2y = 6 be equation (2)
Now , on simplifying , we get
-6x - 4y = -4
Multiply by -1 on both sides , we get
6x + 4y = 4
Divide by 2 on both sides , we get
3x + 2y = 2 be equation (3)
Now , the equation (2) and ( 3) are similar but the constant term is different
The slope of the first equation is -3/2 and the slope of the second equation is also -3/2. Since the slopes are the same, the two lines are parallel to each other.
When two lines are parallel, they never intersect, which means there are no common solutions for the system of equations
Hence , the equations are solved
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
ou’re shopping for a jacket online and find one you like for €110.50 Euro, which is
equal to $125 U.S.
a. What is worth more, $1 U.S. or €1 Euro? Explain.
b. Fill in the blanks. Show how you arrive at your answers.
$1 U.S. ≈ €____________________ Euro €1 Euro ≈ $____________________ U.S.
c. You see the same jacket on another site for ₱ 2,000 Mexican Pesos. Use the fact that $1
U.S. is about ₱ 20.66 Mexican Pesos to determine whether this is cheaper than $125 U.S.
Show how you arrive at your answer.
7. The current average cost of gas in Italy is €1.726 Euro per liter. What is this cost in
U.S. Dollars per gallon? Use your answer to Problem #6b and the fact that there are
about 0.26 gallons in 1 liter.
75
Calculating Perpetuity Values
Curly’s Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $25,000 per year forever. A representative for the company tells you the policy costs $500,000. At what discount rate would this be a fair deal?
Provide the formula through excel
Answer:
a discount rate of 5%
Step-by-step explanation:
The formula to calculate the present value of a perpetuity is:
PV = PMT / r
Where PV is the present value, PMT is the constant payment, and r is the discount rate.
In this case, the PMT is $25,000 and the PV is -$500,000 (negative because it represents a cash outflow). So we can rearrange the formula to solve for r:
r = PMT / PV
r = $25,000 / -$500,000
r = -0.05 or -5%
Therefore, at a discount rate of 5%, the policy would be a fair deal.
To calculate this in Excel, you can use the following formula in a cell:
=r(-25000/500000)
This will give you a result of -0.05, or -5%, which represents the fair discount rate.
Hope this helps!
it’s geometry and i HATE geometry
Answer: <ABC = <GHI transitive property
Step-by-step explanation:
<ABC = <GHI transitive property
this is because if you have <B=<E and <H=<E then <B=<H
thisis a tranisitive property
Plsss help this is hard giving 20 pnts!!!
Answer:I need part A to answer
Step-by-step explanation:
Express the answers in simplest form. A list contains the names of six anthropology students, two sociology students, and four psychology professor's new study, find the probability that the chosen student (a) A psychology student (c) A psychology student or an anthropology (d) Not a sociology student.
a) P(psychology student) = 1/3. b) P(psychology or anthropology student) = 5/6. c) P(not sociology student)= 5/6
How to find the probability that the chosen student(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:
P(psychology student) = 4/(6+2+4) = 4/12 = 1/3
(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:
P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6
(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:
P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6
Learn more about probability at https://brainly.com/question/24756209
#SPJ1
what’s the value of x and y?
Answer:
the answer os 53
Step-by-step explanation:
calculate the lengths a, b, c, d, e, f, g and h
A.) The length of the missing part of the triangle would be given as follows;
a = 4
b = 3
How to calculate the length of the missing sides of the triangle?To calculate the missing part of the triangle, the sine formula should be used such as follows;
x /SinX = b/sinB
where;
x= 5
X = 90
b = ?
B = 37°
That is;
5/sin90 = b/sin37
make b the subject of formula;
b = 5× 0.601815023/1
= 3
a² = C²- b²
= 25-9
= 16
a = √16 = 4
Learn more about triangle here:
https://brainly.com/question/28470545
#SPJ1
7.54 Torque on a rusty bolt.
(a) Do you think it is reasonable to apply ANOVA in this case?
(b) Regardless of your answer in part (a), describe hypotheses for ANOVA in this context, and use the table below to carry out the test. Give your conclusion in the context of the data.
(c) The table below are p-values for pairwise t-tests comparing each of the different groups. These p-values have not been corrected for multiple comparisons. Which pair of groups appears most likely to represent a difference?
(d) There are 28 p-values shown in the table in part (c). Determine if any of them are statistically significant after correcting for multiple comparisons. If so, which one(s)? Explain your answer.
Answer:
Answer is obstacle by giving up yours
Write an equation to represent the function: reflected over the x-axis, then translated 6 units left
The equation of the transformed function is y = -f(x + 6)
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x
On simplifying , we get
Reflecting over the x-axis: To reflect a function over the x-axis, we multiply the function by -1. This changes the sign of the y-coordinate of each point on the graph of the function. So, the function after reflection over the x-axis would be y = -f(x).
Translating 6 units left: To translate a function 6 units to the left, we replace x with (x + 6). This shifts the graph of the function horizontally to the left by 6 units. So, the function after translation 6 units left would be y = -f(x + 6)
Hence , the function is y = -f(x + 6)
To learn more about transformation of functions click :
https://brainly.com/question/26896273
#SPJ1
You are biking to the library. When you are 75% of the way there, you realize you forgot a book. So you turn around and head back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library. How far do you live from the library
The distance you live from the library, would be 6. 4 miles.
How to find the distance ?Assigning the distance between your house and where you can find books as x miles, we could approximate that initially you cycled 0.75x miles before retracing your route back a third of what had already been travelled; converting to 0.25x mile. Thus, at this stage, you will have covered an accumulated distance of 0.5x - taking into account earlier computations.
Realizing that borrowing such book would be unnecessary, you rode back to the library from whence you started- making it 3.2 miles. As you have advanced some length by travelling a cumulative distance of 0.5x from your private residence on previous trial, only another 0.5x miles stands between you and the target place after spinning around anew.
The equation is:
0. 5 x = 3. 2
x = 3. 2 / 0. 5
x = 6. 4 miles
Find out more on distance at https://brainly.com/question/24883865
#SPJ1
A rectangle has sides measuring (2x + 7) units and (5x + 9) units.
Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Answer:
A: (2x + 7)(5x + 9) = 10x^2 + 53x + 63
B: second-degree (quadratic) polynomial
C: The product of two polynomials is a polynomial.
Part A: we simply need to multiply this out using the distributive property:
Area = 2x5x + 2x9 + 75x + 79
= 10x² + 18x + 35x + 63
= 10x² + 53x + 63 (4 points)
Part B:A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)
Part C:In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)
Part A:
The area of a rectangle is given by the product of its length and width. Therefore, for a rectangle with sides measuring (2x + 7) units and (5x + 9) units, the area can be represented as:
Area = (2x + 7)(5x + 9)
Now, we simply need to multiply this out using the distributive property:
Area = 2x5x + 2x9 + 75x + 79
= 10x² + 18x + 35x + 63
= 10x² + 53x + 63 (4 points)
Part B:
The degree of a polynomial is the highest power of x in the polynomial. Here, the highest power of x is 2 (in the term 10x²), so the degree of this polynomial is 2.
A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)
Part C:
The closure property of an operation (like addition, multiplication, etc.) on a set says that applying the operation to any elements in the set always results in an element that is also in the set.
In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)
Learn more about distributive property here :
brainly.com/question/843621
#SPJ2
1. Order the following rational numbers from least to greatest: -5/6, -0.2001, 20%, -78
Answer:
-78, -5/6, -0.2001, 20%
Step-by-step explanation:
The first step is to convert all of the numbers into the same form. In this case, it is easiest to use decimal form.
-5/6 = -0.8333...
-0.2001
20% = 0.2
-78
-78 is the smallest by far
-0.8333... is the next smallest
-0.2 is next
and 0.2 is the largest
You have a credit card with a current balance of $1500. The interest rate is 15.99%. If your minimum payment is 15% of your new balance, what is the balance of your card month 24? If your minimum payment is $75, what is the balance of your card month 24?
a) If the minimum payment is 15% on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,291.99.
b) If the minimum payment is $75 on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,293.99.
What is the credit card balance?The credit card balance refers to the difference between the beginning balance, payments, and interests.
a) Current balance on a credit card = $1,500
Interest rate = 15.99%
Minimum payment = 15%
= $225 ($1,500 x 15%)
Interest = $16.99 ($1,500 - $225 x 15.99% x 1/12)
Ending Balance = $1,291.99 ($1,500 +$16.99 - $225)
b) Current balance on a credit card = $1,500
Interest rate = 15.99%
Minimum payment = $75
Interest = $18.99 ($1,500 - $75 x 15.99% x 1/12)
Ending Balance = $1,293.99 ($1,500 +$18.99 - $225)
Learn more about credit card minimum payments at https://brainly.com/question/21208856.
#SPJ1
Michael has an average daily balance on his credit card of $327.50. His credit card charges 11.99% annual interest. What will his monthly finance charge be?
Answer:
First, we need to calculate Michael's daily interest rate:
0.1199 / 365 = 0.0003282
Then, we can calculate his daily finance charge:
327.50 x 0.0003282 = 0.1075
To find his monthly finance charge, we multiply his daily finance charge by the number of days in a month:
0.1075 x 30 = 3.225
So Michael's monthly finance charge will be $3.23 (rounded to the nearest cent).
PLEASE HELP ME PLEASE LOOK AT THE PICTURE BELOW
Answer:
162 square units
Step-by-step explanation:
You want the surface area of the trapezoidal prism.
Base areaThe triangle at the top of each base is a right triangle with leg 3 units and hypotenuse 5 units. This tells you it is a 3-4-5 right triangle and the width of the prism is 4 units.
The area of each trapezoidal base is ...
A = 1/2(b1 +b2)h = 1/2(3 +6)(4) = 18 . . . . . square units
Lateral areaThe lateral area is the product of the height of the prism (7) and the perimeter of the base. The vertical edges of the base are 3 and 6, the horizontal edge is 4 (see above), and the slant edge is shown as 5. This means the perimeter is 3+6+4+5 = 18 units.
The lateral area of the prism is ...
LA = Ph = (18)(7) = 126 . . . . . square units
Total surface areaThe total surface area of the prism is the sum of the areas of the two bases and the lateral area:
2(18) +126 = 162 . . . . . . square units
The surface area of the composite solid is 162 square units.
__
Additional comment
If you have forgotten about the 3-4-5 right triangle, you can find the missing side length using the Pythagorean theorem.
a² +b² = c²
3² +b² = 5²
b² = 25 -9 = 16
b = √16 = 4 . . . . . . the missing triangle side is 4 units long
<95141404393>
999.989959+9999999999.584775748845747887=
If 30% of (B-A)= 18% of (A+B), then the ratio A:B will be
Answer:
1:4
Step-by-step explanation:
30% of (B - A) = 18% of (A + B)
0.3(B - A) = 0.18(A + B) (converting percentages to decimals)
0.3B - 0.3A = 0.18A + 0.18B (distributing on both sides)
0.3B - 0.18B = 0.18A + 0.3A (grouping like terms)
0.12B = 0.48A
Simplifying further gives:
B/A = 0.48/0.12 = 4/1
Therefore, the ratio of A:B is 1:4.
Let's start by simplifying the given equation:
30% of (B-A) = 18% of (A+B)
0.3(B-A) = 0.18(A+B)
0.3B - 0.3A = 0.18A + 0.18B
0.12B = 0.48A
B = 4A
Now we know that B is 4 times A.
To find the ratio A:B, we can express B in terms of A:
B = 4A
A:B = A/4A = 1/4
Therefore, the ratio A:B is 1:4.
school administrator believes that the mean class GPAs for a given course are higher than the preferred mean of 2.75 at a significance level of 0.05, and checks a randomly chosen sample of 50 classes. Create a histogram, and calculate x, the t-statistic, and the p-value.
3.09
2.73
2.58
2.68
2.84
2.68
2.64
2.62
2.35
2.72
2.63
2.77
2.72
3.03
2.71
2.96
2.74
3.01
2.88
2.68
2.83
3.02
2.83
2.71
2.67
2.79
2.65
2.56
2.78
2.89
2.40
2.38
2.41
2.83
2.86
3.01
2.80
2.84
2.95
2.75
2.93
2.48
2.34
2.97
2.85
2.74
2.84
3.10
2.62
2.77
It can be concluded that there exists ‘insufficient evidence’ depicting that the ‘new mean GPA is more than 2.75’.
Therefore, X= 2.7532; T = 0.1203; P = 0.4524.
How to solveH0: ‘The mean class GPAs for a given course’ is equal to 2.75.
H1: ‘The mean class GPAs for a given course’ exceeds 2.75.
Our 'sample size' n = 50 and we calculate the ‘sample mean and sd’ with 'Excel', through its respective code ‘AVERAGE()’.
The resultant ‘sample mean’ xbar equals to 2.7532, while implementing the code ‘STDEV.S()’ gives us the ‘sample sd’ s being 0.188164.
The ‘hypothesized mean’ μ0 is again fixed at 2.75. Given that the ‘population sd is unknown’, we are obliged to perform a ‘t-test’ in order to receive our data.
Evaluating this test statistic provides us with-
T = (xbar-μ0)/(s/√n)
= (2.7532-2.75)/(0.188164/√50)
= 0.0032/0.0266
= 0.1203
Also, taking into account the 'degrees of freedom', which is (n-1), we figure out that it sums up to 49.
After conjuring a 'students t distribution', we get a P-value of 0.4524. Hereby, as the ‘P-value surpasses the significant level of 0.05’, the ‘null hypothesis fails to be dismissed’.
Consequently, it can be concluded that there exists ‘insufficient evidence’ depicting that the ‘new mean GPA is more than 2.75’.
Therefore, X= 2.7532; T = 0.1203; P = 0.4524.
Read more about t-statistic here:
https://brainly.com/question/29236955
#SPJ1
Victoria bought a box of raisins and gave of the raisins to her younger brother.
About what percent of the raisins did she keep for herself?
F 30%
G 33%
H 66%
J 70%
The percent of the raisins that Victoria she keep for herself is 70%
How to calculate the percentageBased on the information, a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100.
Since Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother. The percent of the raisins she keep for herself will be:
= (1 - 3/10) × 100
= 70%
Therefore, the percent of the raisins that Victoria she keep for herself is J 70%
Learn more about percentages on
https://brainly.com/question/24877689
#SPJ1
Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother.
About what percent of the raisins did she keep for herself?
F 30%
G 33%
H 66%
J 70%
Mrs. Thomas made 31⁄2 gallons of tea for the family reunion. She estimates that each of the 17 family members will drink about 3 cups of tea that day. Did she prepare enough?
5. Let U = (x/x is less than 20, x €
N] and let A = (x/3 < x < 15), B =
(x/1 < x < 15) and C (x/x is an odd
number, x € Llj Carry out the
following operations and make
the Venn diagram
(a) AnB'
(B C'UA
(the bac
[d) (A'nc')
Okay, let's break this down step-by-step:
U = {x | x < 20, x is a natural number}
A = {x | 3 < x < 15}
B = {x | 1 < x < 15}
C = {x | x is an odd number, x is a natural number}
(a) A n B' (using De Morgan's law: A n B' = A' U B')
= {x | x ≥ 15 or x ≥ 3}
= {16, 17, 18, 19}
(b) B C' U A
= B U (C' U A)
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} U {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 14}
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
(c) (A' n C ')
= (A' C') (by De Morgan's law)
= {x | x > 15 and x is even, x is a natural number}
= {16, 18}
The Venn diagram would be:
U A B C
_____|_____|_____|_____
| | | |
| | | |
| | ___|_____|___
| | | |
| | | 16, 17, 18, 19
| | | |
| | |_____|_____|___
| | | | |
| | | ___|_____|___
| | | | 16, 18
| | | |_____|_____|___
Does this make sense? Let me know if you have any other questions!
Lily took a survey of 80 students on 7th grade and 150 students in 8th grade she found that 80% of the 7th graders like country music while only 60% of the 8th graders like it. Which statement is true
If Lily took a survey of 80 students of 7th grade and 150 students of 8th grade, then there are 64 "7th" grade students, and 90 "8th" grade students who like music.
First we find the the number of students who like music in "7th-grade".
Number of 7th grader students that are being surveyed = 80,
Percent of 7th graders who like country music = 80%,
So, Number of 7th graders who like country music are
⇒ 80% of 80 = 0.8 × 80 = 64
So, 64 out of the 80 students in 7th grade like country music.
For 8th graders;
Number of "8th-grader" students that are being surveyed = 150,
Percent of 8th graders who like country-music = 60%,
So, Number of 8th graders who like country music
⇒ 60% of 150 = 0.6 × 150 = 90,
Therefore, 90 out of the 150 students in 8th grade like country music.
Learn more about Percent here
https://brainly.com/question/13744961
#SPJ1
The given question is incomplete, the complete question is
Lily took a survey of 80 students on 7th grade and 150 students in 8th grade she found that 80% of the 7th graders like country music while only 60% of the 8th graders like it. Find the number of students from each grade who like music.