beer Bottles are filled so that they contain an average of 475 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 8 ml.
Answers
We use the normal distribution density function f(z) to find the probability of a specific range of values.
Z= ((X-μ)/σ)
μ = 475
σ = 8
a) X< 470 ml
P[X<470] = P[Z<(470-475)/8] = P[Z<(470-475)/8] = P[Z<-0.625] = 0.2659
b) 6 pack with a mean of less than 470ml
Z = ((X-μ)/(σ/√n))
Z = (470-475)/(8/√6)
P [Z<-1.53] = 0.063
c) 12 pack with a mean of less than 470ml
Z = ((X-μ)/(σ/√n))
Z = (470-475)/(8/√12)
P [Z<-2.165] = 0.0152
Final answer:
The question is related to the mathematics subject area and addresses the high school grade level. It involves understanding the normal distribution, mean, standard deviation, and the application of these concepts in quality control and filling volumes for beverage containers.
Explanation:
The subject of the question relates to the concept of normal distribution, which is a fundamental concept in statistics, a branch of mathematics. The student is provided with the information that beer bottles are filled so that they contain an average of 475 ml of beer, with the amount of beer being normally distributed and having a standard deviation of 8 ml. This scenario involves understanding concepts like mean, standard deviation, and the properties of a normal distribution.
To visualize similar quantities, consider that an eyedropper holds about 1 milliliter, a juice box holds about 25 centiliters (or 250 milliliters), and a soda bottle holds about 1 liter. The provided beer bottle contains roughly half the amount of a typical soda bottle. Knowledge of standard units such as liters and milliliters is essential in this context.
Furthermore, the question can be connected with practical scenarios such as the filling volumes for beverage containers, where manufacturers need to ensure that the bottles and cans contain the labeled amount of liquid. Quality control relies on statistics to test whether the actual amounts meet the desired standards, factoring in variations from measurement processes or filling mechanisms.
Related Questions
A square has an area of x^2+4x+4 square meters. Write an expression that best represents the length of one side of the square.
Answers
1) Rewrite x^2+4x+4 as the square of a binomial:
(x+2)^2
2) So now you know that (x+2)(x+2)=x^2+4x+4 (the area)
3) The length is x+2
The expression that represents the length of one side of the square is (x+2)
What is Polynomial?In mathematics, a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface.
Given,
Area of the square = [tex]x^{2} +4x+4[/tex]
Area of the square = l × l
were l is the length
Then,
[tex]x^{2} +4x+4=(x+2)(x+2)[/tex]
Hence, The expression that represents the length of one side of the square is (x+2)
Learn more about polynomial and area here
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8.73e16 in standard form
Answers
Here is your answer:
The proper answer to this question is 87300000000000000.
Here is how:
8.73e16=87300000000000000.
Your answer is 87300000000000000.
If you need anymore help feel free to ask me!
Hope this helps!
(P.S. REMEMBER E IS EXPONET OR ^)
Answer:
The standard form of the given number is [tex]8.73\times 10^{16}[/tex].
Step-by-step explanation:
Standard form of a number is a easy ways to write very small numbers and very large numbers.
In the standard form the number is written as the number lies between 1 to 10 and multiple of power of 10.
The given number is
[tex]8.73e16[/tex]
It can be written as
[tex]8.73e16=87300000000000000[/tex]
[tex]8.73e16=8.73\times 10^{16}[/tex]
Therefore the standard form of the given number is [tex]8.73\times 10^{16}[/tex].
A tree cast a shadow 21 feet long , while Enzo, who is 5 feet tall , cast a shadow 6 feet long
Answers
Can someone help me please answer this question
Answers
Which point is a reflection of point R (-2, 9) first across the y-axis and then across the x-axis?
A : (-9, -2)
B: (-2,-9,)
C: (2, -9)
D: (9, -2)
Answers
Final answer:
Explaining how to find the reflection of a point across the y-axis and then the x-axis that is option C is correct.
Explanation:
To find the reflection of point R(-2, 9) first across the y-axis and then across the x-axis, we apply the transformations for each axis separately. When reflecting across the y-axis, the x-coordinate changes sign, making it (-2, -9). Then, reflecting across the x-axis changes the sign of the y-coordinate, resulting in the final reflection at point (2, -9).
During a sale, all video games $10 off. Rebecca used a coupon to get an additional $15 off her purchase. If the original price of a video game was $60, how much did Rebecca pay?
Answers
8x-5y=11 4x-3y=5 solve using elimination method
Answers
Answer:
8x - 5y = 11---->8x - 5y = 11
4x - 3y = 5---->-8x + 6y = -10
-------------------
y = 1, x = 2
{(2, 1)}
What plus what equals 24
Answers
Final answer:
Different pairs of numbers can add up to 24.
Explanation:
The sum of two numbers that equals 24 depends on the specific values of the two numbers. However, here are a few examples:
12 + 12 = 24
20 + 4 = 24
15 + 9 = 24
These examples show that different pairs of numbers can add up to 24. The sum can be found by adding the two numbers together.
kim has a scale drawing of a car with a scale of 1 in : 3 ft. what is the scale factor
Answers
Final answer:
The scale factor for the scale drawing of a car with a scale of 1 inch : 3 feet is 1:36, or the fraction 1/36.
Explanation:
The student has a scale drawing of a car with a scale of 1 inch : 3 feet. To find the scale factor for this drawing, you need to convert feet into inches since the scale is given in inches to feet. There are 12 inches in a foot, so 3 feet is the same as 36 inches. Therefore, the scale for the car drawing is 1 inch on the drawing for every 36 inches of the actual car.
The scale factor is the ratio of the dimension in the drawing to the actual dimension of the object. In this case, the scale factor is 1:36, which can be written as the fraction 1/36. This means that every inch on the scale drawing represents 36 inches on the actual car.
PLEASE HURRY
This function models the relationship between the hours worked, x, and the amount of money earned, f(x).
f(x)=10.25x
Which choices could be elements of the domain of the function? Check all that apply.
A) 5
B) 200
C) 25.5
D)14/3
E) 77 1/2
F) –10
G) –43.5
H) –113 4/5
Answers
Answer:
A) 5
B) 200
C) 25.5
D) 14/3
E) 77 1/2
Step-by-step explanation:
We have been given a function [tex]f(x)=10.25x[/tex], where, [tex]f(x)[/tex] represents the amount of money earned after x hours.
We are asked to choose the elements of the domain of the function.
Since the x represents time in hours, so negative numbers wouldn't be domain of the given function. as times cannot be negative.
Therefore, options A, B, C ,D and E are correct choices.
Answer:
The first 5 is the right answer
Step-by-step explanation:
Laticia randomly selected 25% of the seventh grade students in her school and asked them their favorite season. Of the students surveyed, 51 chose summer as their favorite season. Based on the data, what is the most reasonable prediction of the number of seventh grade students in her school who would choose summer as their favorite season?
A) 15
B) 75
C) 150
D) 200
Answers
The most reasonable prediction of the number of seventh grade students in her school who would choose summer as their favorite season is 75.
To predict the number of seventh-grade students in Laticia's school who would choose summer as their favorite season, we can use the fact that she surveyed 25% of the seventh-grade students and found that 51 of them chose summer.
First, we need to find out how many seventh-grade students there are in total. Since Laticia surveyed 25%, we can set up a proportion:
[tex]\[\frac{51}{25\%} = \frac{x}{100\%}\][/tex]
Solving for x, the total number of seventh-grade students, we get:
[tex]\[x = \frac{51 \times 100\%}{25\%} = 204\][/tex]
Now, since 51 students chose summer as their favorite season out of 204 seventh-grade students, to find out how many students might choose summer if all seventh-grade students were surveyed, we can set up another proportion:
[tex]\[\frac{51}{204} = \frac{y}{100\%}\][/tex]
Solving for y, the number of students who might choose summer if all seventh-grade students were surveyed:
[tex]\[y = \frac{51 \times 100\%}{204} = 25\%\][/tex]
This comes out to (y = 51), which means if all seventh-grade students were surveyed, we could reasonably predict that 51 of them would choose summer as their favorite season. Therefore, option B) 75 is the most reasonable prediction.
During a sale, a store manager reduces a sweater's price by 30%. After the sale, the manager increases the price by 30%. Are the prices before and after the sale equal?
Answers
sweater initially = $10
decrease by 30% = $7
increase $7 by 30% = $9.10
No, they are not equal.
sweater cost $20.00 - 30% = $14.00
$14.00 + 30% = $4.2 total of 18.20
no cause the sale price was lower when adding on 30%
I need to increase my sales by 35% this month I’m currently at 45 sales how many sales do I need to meet my goal ?
Answers
You can create a ratio to help you solve for x
45 = 100%
x = 35 %
Which is equal to this fraction: (45/x) = (100/35)
Solving for X by cross multiplying and dividing by 100:
[(45)(35)] / 100 = X = 15.75 = 16 sales (rounded up)
You would need at least 16 sales to increase sales total by 35%
Answer:
61 sales.
Step-by-step explanation:
Let x represent present sales.
We have been given that you need to increase your sales by 35% this month. You are currently at 45 sales.
To find the number of sales to meet the goal, we will find 35% of 45 and add to 45 as:
[tex]\text{The number of sales to meet the goal}=45+\frac{35}{100}*45[/tex]
[tex]\text{The number of sales to meet the goal}=45+0.35*45[/tex]
[tex]\text{The number of sales to meet the goal}=45+15.75[/tex]
[tex]\text{The number of sales to meet the goal}=60.75[/tex]
[tex]\text{The number of sales to meet the goal}\approx 61[/tex]
Therefore, you need to make 61 sales to meet you goal.
Please help! Im bad at math!!!!
Answers
_____
Of course, you do need to know how to set your calculator to the proper mode for scientific notation display.
The 1st selection is appropriate.
By what factor is the volume of a right square pyramid multiplied if its height is multiplied by 8 but the dimensions of its base are unchanged?
A. 1/16
B. 1/8
C. 4
D. 8
Answers
the volume of a right square pyramid ---------- > (1/3)b²h
Let
V1------------ > initial volume
V1=(1/3)b²h
if its height is multiplied by 8
V2=(1/3)b²(8h)-------------- > V2=V1*8
therefore
the answer is the option D
the factor is is 8
What are the solutions of the system? y=6x+6y=−x2+5x+6
Answers
Answer:
Given the system of equations:
[tex]y = 6x+6[/tex] .....[1]
[tex]y = -x^2+5x+6[/tex] .....[2]
Equate these two equations we have;
[tex]-x^2+5x+6 = 6x+6[/tex]
Subtract 6 from both sides we have;
[tex]-x^2+5x= 6x[/tex]
Subtract 6x from both sides we have;
[tex]-x^2-x= 0[/tex]
⇒[tex]-x(x+1) = 0[/tex]
By zero product property we have;
⇒x = 0 and x+1= 0
⇒x = 0 and x=-1
Substitute these values in [1] we have;
For x = 0
y = 6(0)+6 = 6
for x = -1
y =6(-1)+6 = -6+6= 0
Therefore, the solutions of the given systems are, (0, 6) and (-1, 0)
A cone-shaped container has a height of 9 inches and diameter of 2 inches. It is filled with a liquid that is worth $2 per cubic inch.
What is the total value of the liquid in the container?
Use 3.14 for π .
Enter your answer in the box.
Answers
A cone:
a radius (r)...1 in.
a diameter... 2 in.
a height (h) ... 9 in.
....3.14
cone volume formula:
v=1/3*3.14*1^2*9=1/3*3.14*1*9
c=9.42 cubic inches
$2...1 cubic inch
$x = ?... 9.42
x=$18.84
the correct result $18.84.
have a nice day!!!
Answer:$18.84. I hope this helps. Have a great day!♡
Step-by-step explanation:
Combine like terms to simplify.
2. 3v + w +8 - 2n
Answers
Simplifying 3v + w + 8 + -2n
Reorder the terms: 8 + -2n + 3v + w
Hopes it helped!
Kendrick’s math quiz grades are 90, 100, 48, 88, 100, and 96. Find the MEAN of Kendrick’s scores. A) 48 B) 52 C) 87 D) 93
Answers
so first you need to add all the numbers together. then divide by 6 because you added 6 different numbers together. then you should get 87
90+100+48+88+100+96=522
522÷6=87
Therefore, the answer is C
Sarah spends 1/6 hour vacuuming her mom's car. She spends 4 times as long washing the car. Then she spends twice as long waxing the car as she does washing the car. What is the total amount of time Sarah spends vacuuming, washing, and waxing her mom's car?
Answers
your answer will be 2 hours and 10 minutes
mark brainliest
Answer:
2 10
Step-by-step explanation:
210
If were to walk 15 miles today and stoped every 0.5 how many stops will I stop and rest?
Answers
15 x 2 because in one mile there would be 2 stops equals 30
=15 ÷ 0.5
=30 stops
ANSWER: 30 stops
Hope this helps! :)
If i= √-1 what is the value of i^3
Answers
i = sqrt(-1)
i^2 = [ sqrt(-1) ]^2
i^2 = -1
Now multiply both sides by i
i^2 = -1
i*i^2 = i(-1)
i^3 = -i
Final Answer: -i
(this is negative i)
Final answer:
To calculate i^3, we use the powers of i, where i = √-1. We find that i² = -1, and thus i³ = i² × i = -1 × i = -i.
Explanation:
The value of i to the power of 3, denoted as i3, can be determined by understanding the fundamental properties of the imaginary unit i, where i is defined as i = √-1. To find i3, we start by considering the powers of i:
i1 = i,
i2 = -1,
i3 = i2 × i = -1 × i = -i,
i4 = (i2)2 = (-1)2 = 1.
Therefore, the value of i3 is -i.
Which of the following is a rational number?
Square root of 22
Square root of 23
Square root of 24
Square root of 25
Answers
Answer:
√25
Step-by-step explanation:
√25 = √(5²) = 5 . . . . a rational number
The other roots are not the roots of perfect squares, so are irrational.
(06.02)A six-sided number cube labeled 1 through 6 is rolled 500 times. An odd number is rolled 325 times. Compare the experimental probability of rolling an odd number with the theoretical probability of rolling an odd number and select one of the statements below that best describes the situation.
The experimental probability and theoretical probability are the same.
The experimental probability is larger than the theoretical probability.
The experimental probability is smaller than the theoretical probability.
There is not enough information to determine the relative frequency.
Answers
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
Number of times a die rolled = 500
Number of times an odd number occurs =325
so, the experimental probability would be
[tex]\dfrac{325}{500}\\\\=0.65[/tex]
And we know that
Number of outcomes in a die = 3
Number of total outcomes = 6
So, The theoretical probability would be
[tex]\dfrac{3}{6}=\dfrac{1}{2}=0.5[/tex]
So, The experimental probability is larger than the theoretical probability.
Hence, Second option is correct.
Which best describes the meaning of the term theorem ?
Answers
13,006,017 in word form
Answers
find the unknown side length. simplify answers that are radicals . tell whether the side lengths form a Pythagorean triple
Answers
a²+b²=c²
In our case,
[tex](\sqrt{7})^2+b^2=(\sqrt{19})^2[/tex]
[tex]7+b^2=19[/tex]
Subtract 7 from each side:
[tex]7+b^2-7=19-7 \\b^2=12[/tex]
Take the square root of both sides:
[tex]\sqrt{b^2}=\sqrt{12}=\sqrt{4*3}=2\sqrt{3}[/tex]
Although these numbers work in the Pythagorean theorem, they are not Pythagorean triples, as they are not integers.
If there are 52 cards in a deck what is the probability of drawing two cards, and getting a king both times?
Answers
There are two cases here:
Case 1: First card chosen is a queen
452∗351=1221452∗351=1221Case 2: First card chosen is not a queen.
4852∗451=162214852∗451=16221Adding both the cases, we get 1722117221 = 452452 = 113113
In a simpler case: Think about it this way: Shuffle a deck of cards randomly. The probability of drawing a queen as your second card is the same as the probability that the second card in the deck is a queen, which is clearly 4/52.
Complete the coordinate table for the given equation.
Answers
y=1,2,4,-4,-2,-1
Which of the following statements is true? A 15 kg box has more inertia than a 10 kg box. Forces occur in equal and opposite force pairs. Objects in motion will keep moving at the same velocity unless acted upon by an outside force. All of the above.
Answers
Answer:
All of the above
Step-by-step explanation:
A 15 kg box has more inertia than a 10 kg box. --TRUE
Inertia is a property of matter related to its mass. The more mass an object has, the greater its inertia. S o the statement is correct since 15 kg is greater in mass than 10 kg therefore it has more inertia.
Forces occur in equal and opposite force pairs. -- TRUE
This statement is correct and is known as Newton's third law. Which tells us that for every force of action there is a reaction force that is equal in magnitude but opposite in direction.
Objects in motion will keep moving at the same velocity unless acted upon by an outside force. -- TRUE
This is Newton's first law of motion, it tells us that an object will retain its state of rest or movement as long as there is no resulting force or external force acting on it.