The probability that the mean of a sample of 45 boards will be between 94.5 inches and 95.1 inches, given that the length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches, can be calculated using the Central Limit Theorem. The theorem states that the distribution of sample means will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, the population mean (μ) is 95 inches, the population standard deviation (σ) is 0.52 inches, and the sample size (n) is 45. The standard deviation of the sample mean is σ/√n = 0.52/√45 ≈ 0.0775.
To find the probability, we can use the Z-score formula:
Z = (X - μ) / (σ/√n)
For the lower limit of 94.5 inches, the Z-score is:
Z1 = (94.5 - 95) / 0.0775 ≈ -6.45
For the upper limit of 95.1 inches, the Z-score is:
Z2 = (95.1 - 95) / 0.0775 ≈ 1.29
Now, using a Z-table or calculator, find the probability for each Z-score:
P(Z1) ≈ 0 (since it is a very low Z-score)
P(Z2) ≈ 0.9015
The probability that the mean of the sample will be between 94.5 inches and 95.1 inches is the difference between these probabilities:
P(94.5 < X < 95.1) = P(Z2) - P(Z1) = 0.9015 - 0 ≈ 0.9015, or approximately 90.15%.
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One pint of paint covers 100 square feet. What is the least amount of pints of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 16 feet, a width of 14 feet, and a height of 11 feet?
To find the surface area of the rectangular prism, we need to calculate the area of each of the six sides and then add them together. The area of each of the four walls is the product of the length and height, which gives us:
16 feet × 11 feet = 176 square feet (for the two longest walls)
14 feet × 11 feet = 154 square feet (for the two shorter walls)
The area of the ceiling and floor is the product of the length and width, which gives us:
16 feet × 14 feet = 224 square feet (for the ceiling)
16 feet × 14 feet = 224 square feet (for the floor)
To find the total surface area, we add up the areas of all six sides:
176 + 176 + 154 + 154 + 224 + 224 = 1104 square feet
Therefore, we need at least 1104/100 = 11.04 pints of paint to cover the walls of the room. Rounding up to the nearest whole pint, we need 12 pints of paint.
What number solves this equation? × (3 + 8) = 55
To solve the equation × (3 + 8) = 55, we need to simplify the expression inside the parentheses first, which gives us:
× (3 + 8) = × 11
Now we substitute × 11 back into the original equation:
× 11 = 55
To solve for ×, we divide both sides by 11:
× = 5
Therefore, the number that solves the equation × (3 + 8) = 55 is 5.
The data given represents the height of basketball players, in inches, on two different girls' teams.
Allstars
73 62 60
63 72 65
69 68 71
66 70 67
60 70 71
Champs
62 69 65
68 60 70
70 58 67
66 75 70
69 67 60
Compare the data and use the correct measure of center to determine which team typically has the tallest players. Explain your answer.
The Allstars, with a mean of about 67.1 inches
The Champs, with a mean of about 66.4 inches
The Allstars, with a median of about 68 inches
The Champs, with a median of about 67 inches
To determine which team typically has the tallest players, we need to compare the measures of center for each team. Since the data sets have outliers, it's better to use the median as a measure of center.
Calculating the median for each team:
Allstars: arrange the heights in order from smallest to largest: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73. The median is the middle value, which is 68 inches.
Champs: arrange the heights in order from smallest to largest: 58, 60, 60, 65, 67, 67, 68, 69, 70, 70, 75. The median is the middle value, which is also 68 inches.
Since both teams have the same median height of 68 inches, we can't say that one team typically has taller players than the other based on this measure alone. Therefore, neither option (C) nor (D) is correct. Instead, we need to choose between options (A) and (B) based on the mean height for each team.
Calculating the mean for each team:
Allstars: add up all the heights and divide by the total number of players: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 1006/15 ≈ 67.1 inches.
Champs: add up all the heights and divide by the total number of players: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 996/15 ≈ 66.4 inches.
Thus, the team with the higher mean height is the Allstars, so the correct answer is option (A): "The Allstars, with a mean of about 67.1 inches."
Brenda went to the store with her dad toy buy snacks. They bought a box of 16 snack-size bangs of chips for $7.84 and a box of 24 snack-size of pretzels for $12.48.How much more do pretzels cost pero bag than chips?
Answer:
$0.03 pretzels cost more than cost of bag of chips.
Step-by-step explanation:
price of 16 snack- size bags of chips = 7.84
Cost of 1 bag of chip = 7.84 /16 = $0.49
Price of 24 snack-size bags of pretzels = 12.48
Cost of 1 snack-size bags of pretzels = 12.48 / 24 = 0.52
$0.03 pretzels cost more than cost of bag of chips.
A tiger in a zoo is 8 feet long. A scale model of the tiger is 4 inches long. What is the scale factor?
Answer:
1/24
Step-by-step explanation:
1 ft = 12 in
8 X 12 = 96
96/4 = 24
1/24 is the scale factor
Answer: 24:1 (The tiger : The tiger model)
Step-by-step explanation:
1 feet =12 inch
so 8 feet=96 inch
The tiger : The tiger model= 96:4= 24:1
help asap assignment closes soon!
The approximate surface area of the cone is equal to 35 ft²
How to calculate surface area of a cone?In Mathematics, the surface area (SA) of a cone can be calculated by using this mathematical expression:
Surface area (SA) of a cone = πr(l + r)
Where:
l represents the slant height of the cone.r represents the radius of the cone.Note: Radius = diameter/2 = 2/2 = 1 feet.
By substituting the given parameters into the formula for the surface area (SA) of a cone, we have the following;
Surface area (SA) of a cone = 3.14 × (1 + 10)
Surface area (SA) of a cone = 3.14 × (11)
Surface area (SA) of a cone = 34.54 ≈ 35 ft²
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Simplify the expression using basic identities Cosu - cosu sin^2u
Cos u - cos u sin²u simplifies to cos³(u). We can solve it in the following manner.
Starting with the expression Cos u - cos u sin²u, we can factor out cos(u) to get:
Cos u - cos u sin²u = cos(u) (1 - sin²(u))
Using the identity sin²(u) + cos²(u) = 1, we can substitute cos²(u) for 1 - sin²(u):
cos(u) (1 - sin²(u)) = cos(u) cos²(u) = cos³(u)
Therefore, Cos u - cos u sin²u simplifies to cos³(u).
In mathematics, a factor refers to a number, algebraic expression, or function that divides or multiplies with another number, algebraic expression, or function without leaving a remainder. For example, in the expression 12x, 12 is a factor of the expression because it can be divided evenly by 12.
In algebra, factoring is the process of finding the factors of an algebraic expression, which means breaking it down into simpler parts that can be multiplied together to get the original expression. Factoring is an important skill in algebra, as it allows us to simplify and solve equations, identify common factors, and manipulate expressions more easily.
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suppose we want to test whether there is a difference between the room rates of luxury hotels in new york versus los angeles. we collect data from 20 random luxury hotels in new york and 30 random luxury hotels in l.a. what are the degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval? type your answer here
The degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval in the given case would be 48.
When a pooled-variance two-sample t-test or confidence interval is to be conducted on two groups, the degrees of freedom is calculated using the following formula: df = n1 + n2 - 2, where n1 and n2 are the sample sizes of the two groups being compared.
In the given scenario, data is collected from 20 random luxury hotels in New York and 30 random luxury hotels in Los Angeles. Therefore, the degrees of freedom for a pooled-variance two-sample t-test or confidence interval would be:df = 20 + 30 - 2df = 48. Hence, the degrees of freedom associated with a pooled-variance two-sample t-test or confidence interval are 48.
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what does 56 3/4 ( 1 3/8 + 1 1/5) equal
Answer:
23,381/160 or 146 21/160
Step-by-step explanation:
56 3/4 = 227/4
1 3/8 = 11/8
1 1/5 = 6/5
227/4( 11/8 + 6/5)
227/4(55/40 + 48/40)
227/4( 103/40) = 23,381/160 or 146 21/160
Keeshawn measured the box show below. What is the surface area of the box
help???? thanks! i do not get this at all!!
Answer:
S = [tex]\sqrt{3}[/tex]
H = 2
It's D
Step-by-step explanation:
Considering the attached picture
h = 1 x 2 = 2
s = 1 x [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex]
Cool-Down The background of this graph is the same coordinate grid from the previous screen. Both the x- and y-axes run from negative 8 to 8.Line "g" is graphed. Line "g" goes through the points ( negative 4 , 4 ) and ( 4 , negative 2 ). Here is a line on a coordinate grid. Write an equation for the line.
The equation of line "g" is y = (-3/4)x + 1. To find the equation of line "g" that goes through the points (-4, 4) and (4, -2), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we can find the slope of the line by using the slope formula, which is:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the two points given, we have:
m = (-2 - 4) / (4 - (-4)) = -6 / 8 = -3 / 4
Next, we can use the slope-intercept form and one of the two points to find the y-intercept, b. Using the point (-4, 4), we have:
4 = (-3/4)(-4) + b
4 = 3 + b
b = 1
Finally, we can substitute the values of m and b into the slope-intercept form to get the equation of line "g":
y = (-3/4)x + 1
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f(x) = 1 + 4x 1
Find the value of x when f(x) = 15.
Answer:
the value of x when f(x) = 15 is 3.5.
Step-by-step explanation:
We are given that:
f(x) = 1 + 4x
We need to find the value of x when f(x) = 15.
So we can set up the equation:
1 + 4x = 15
Subtracting 1 from both sides, we get:
4x = 14
Dividing both sides by 4, we get:
x = 14/4
Simplifying, we get:
x = 3.5
Therefore, the value of x when f(x) = 15 is 3.5.
why does the vertical line test tell us whether the graph of a relation represents a function? when a vertical line intersects the graph of a relation more than once, it indicates that for that input there is more than one output, which means the relation is not a function. when a vertical line intersects the graph of a function more than once, it indicates that for that output there is more than one input, which means the function is not a relation. when a vertical line intersects the graph of a function more than once, it indicates that for that input there is more than one output, which means the function is not a relation. when a vertical line intersects the graph of a relation more than once, it indicates that for that output there is more than one input, which means the relation is not a function.
When a vertical line intersects the graph of a function more than once, it indicates that for that output there is more than one input, which means the function is not a relation. (option b).
In mathematics, functions are an essential concept used to describe relationships between sets of numbers. A function is a set of ordered pairs, where each input corresponds to exactly one output.
Conversely, if every vertical line intersects the graph at most once, then the graph represents a function. This is because there is only one output for each input, satisfying the definition of a function.
It's important to note that not all relations are functions. A relation is a set of ordered pairs, while a function is a relation where each input corresponds to exactly one output.
Therefore, if a vertical line intersects a graph more than once, it indicates that there is more than one output for that particular input, and the relationship is not a function.
Hence the option (b) is correct.
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Three security guards: A, B and C, who guard a jewellery shop, work under the following conditions:
None of the guards is called to work for three consecutive days.
Guard A does not work on Tuesday, Thursday and Sunday.
Guard B does not work on Monday, Wednesday and Saturday.
Guard C does not work on Tuesday, Thursday and Sunday.
On which day of the week are all of them present for work?
Can somebody please help me with this Geometry asap. In advance, thank you so much.
6.61 is the value of x in the circle.
What does the circle's tangent look like?
A line that only has one point of intersection with a circle is said to be tangent to the circle. Point of contact is the term used to describe the location where the circle and the tangent meet. A straight line that touches a circle at point P is said to be tangent to the circle at P. As the radius connects the circle's centre to point P, the tangent is perpendicular to that radius.
(39x - 4) = 254
39x = 254 + 4
39x = 258
x = 258/39
x = 6.61
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according to a study published by a group of university of massachusetts sociologists, approximately 60% of the valium users in the state of massachusetts first took valium for psychological problems. find the probability that among the next 8 users from this state who are interviewed
the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is 60% is 0.03456.
As per the given information, 60% of the valium users in Massachusetts first took it for psychological problems. Now, we are supposed to find the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is: 60%.
What is Valium?
Valium is a prescription medicine that is used to treat the symptoms of anxiety, alcohol withdrawal, and muscle spasm. The use of Valium can lead to addiction, especially if it is not taken as prescribed by the doctor.The probability of the first 6 users first took it for psychological problems is 60%. Hence, the probability that the first user did not take it for psychological problems is: 40%.
Probability of first user did not take Valium for psychological problems = P(A) = 0.40
Probability of first user took Valium for psychological problems = P(B) = 0.60
Now, we are supposed to find the probability that among the next 8 users from this state who are interviewed, the first 6 users first took it for psychological problems is: 60%.Probability of the first 6 users first took it for psychological problems is:
Probability of the next 5 users took it for psychological problems = P(B) × P(B) × P(B) × P(B) × P(B) = (0.60)⁵
Probability of the next 2 users did not take it for psychological problems = P(A) × P(A) = (0.40)²
Thus, the probability that among the next 8 users from this state who are interviewed, the probability of the first 6 users first took it for psychological problems is 60%, is:(0.60)⁵ × (0.40)²= 0.03456 (rounded to five decimal places)
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when the sum of the first ten terms of an arithmetic progression is four times the sum of the first five terms, the ratio of the first term to the common difference is:
The ratio of the first term to the common difference is 1 is to 1 (1:1).
Let's say the first term of the arithmetic progression is 'a' and the common difference is 'd'.
Then the sum of the first five terms will be,
S5 = a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 5a + 10d
And the sum of the first ten terms will be,
S10 = a + (a + d) + (a + 2d)+ ... + (a + 9d)
=10a + 45d
We have been given that sum of the first 10 terms is equal to four times the sum of the first 5 terms, i.e
S10 = 4S5
Substituting the expressions for S5 and S10 in terms of a and d, we get,
10a + 45d = 4(5a + 10d)
Simplifying this equation, we get,
10a + 45d = 20a + 40d
10d = 10a
d = a
So the ratio of the first term to the common difference is 1:1 or 1/1.
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Can u do step by step on how u got it I have to show my work
Write the name of the quartite which divides Continuous data he low 25%
Answer:
The first quartile ([tex]Q_{1}[/tex]) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower or 25th empirical quartile, as 25% of the data is below this point.
Answer:
The first quartile (Q1) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower or 25th empirical quartile, as 25% of the data is below this point.
Step-by-step explanation:
PLEASE HELP ASAP!!!!!!!
REASONING Meghana is making a kite out of nylon. The material is sold for $5.99 per square yard. She needs enough material to cover her kite on both sides.
a. What is the area of Meghana’s kite?
b. How many yards of material will Meghana need to cover both sides of her kite?
c. How much will the material cost before taxes?
Answer: The material will cost Meghana $95.84 before taxes.
Step-by-step explanation:
a. To find the area of Meghana's kite, we first need to convert the dimensions from feet to yards since the material is sold per square yard:
Length = 18 ft = 6 yards (since 1 yard = 3 feet)
Width = 4 ft = 4/3 yards (since 1 yard = 3 feet)
The area of the kite is the product of its length and width:
Area = Length x Width = 6 x 4/3 = 8 square yards
b. Meghana needs enough material to cover both sides of her kite, so she needs twice the area of the kite:
Area of both sides = 2 x Area of one side = 2 x 8 = 16 square yards
Therefore, Meghana needs 16 square yards of nylon material.
c. The material is sold for $5.99 per square yard, so the total cost of the material before taxes is:
Total cost = Cost per square yard x Number of square yards
Total cost = $5.99 x 16 = $95.84
Therefore, the material will cost Meghana $95.84 before taxes.
how do you solve for x when the equation is 3x+15=45
Answer:
x = 10
Step-by-step explanation:
To solve for x, we need to get x by itself.
Whatever we do to one side, we do it to the other side to keep it balanced.
3x + 15 = 45
- 15 = -15 (Subtract 15 from both sides)
3x = 30 (Divide both sides by 3)
3 = 3
x = 10
the number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is:
Thus, the number of 6-digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is 20.
What is the number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated?There are 1200 6-digit numbers that can be formed using the digits 0, 1, 2, 5, 7, and 9.Using the formula for a 2-digit number, namely A and B, the number must satisfy A - B = 0,11 or -11.
There is a pattern, therefore, there are 100 numbers that satisfy each. It's because the numbers 0, 1, 2, 5, 7, and 9 are such that the sum of the odd digits minus the sum of the even digits is always either 0, 11, or -11. This is only possible if there is an even number of odd digits or an even number of even digits.
There are 6C3 ways to pick 3 odd digits from {1,5,7,9} and 3C3 ways to pick 3 even digits from {0,2}. By taking the product of these values, we can find the total number of possibilities:[tex]6C3 × 3C3 = 20 × 1 = 20[/tex]
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Mr. Smith keeps track of his students' homework completion. He keeps track of how many boys and
girls do not complete their homework. He puts students who don't complete their homework into two categories: first-time offenders and repeat offenders. He uses a table to keep track of the results.
Boys-Girls-Total-First-Time Offenders & Repeat Offenders
a. In one month 36 girls and 12 boys did not do their homework for the first time. 12 girls and 30
boys did not do their homework again. Put these figures in your table.
b.How many students did not complete all of their homework assignments this month?
c. What percentage of the students who did not complete their homework were boys who were
First-Time Offenders?
d. Are boys or girls more likely to not complete their homework? Explain your reasoning.
Answer:
The question seems to be incomplete. It mentions that Mr. Smith keeps track of his students' homework completion and how many boys and girls do not complete their homework. It also mentions that he puts students who don't complete their homework into two categories: first-time offenders and repeat offenders, and uses a table to keep track of the results[1][2]. However, it does not provide enough information to answer a specific question.
If you have a specific question related to this topic, please provide more details so that I can assist you better.
7. Groceries Galore sells bags of chips from two different companies., The mean absolute deviation of the number of chips in each bag from Company A is higher than the mean absolute deviation of the number of chips in each bag from Company B. Heather believes this means that Company A tends to sell more chips in each bag. Do you agree? Explain why or why not. CHIPS
Answer:
Always need to do research to improve your studies
i need help with an ixl. i dont understand it at all. please help !!
The value of m∠U in the circle is 168 degrees
How to find the tangent of a circle?The tangent of a circle is the line that touches the circle at only one point.
The tangent to a circle is always perpendicular to the radius. Therefore, it forms a right angle.
Therefore, let's use the theorem to find the angle m∠U
Hence,
m∠STU = 90 degrees
m∠UTV = 90 - 84 = 6 degrees
Therefore, the triangle STV is an isosceles triangle. This means the base angle is congruent .
Hence,
m∠SVT = 84 degrees
Therefore,
m∠U = 180 - 6 - 6
m∠U = 180 - 12
m∠U = 168 degrees
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What happens when you use each of the following on a inequality number line?
Answer: If you add the same number to both sides of an inequality, the inequality remains true. If you subtract the same number from both sides of the inequality, the inequality remains true. If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true.
Mrs. Myrtle wants to buy this plastic toy for Willow. How much plastic would it take to construct the following toy? [Assume toy is solid plastic]
9m
13 m
Radius: type your answer...
type your answer...
Height of the Cone: type your answer....
; Total: type your answer...
Cone: type your answer...
; Hemisphere:
Answer:
Step-by-step explanation:
6
Points-
Pls answer this correctly!
After 60 minutes in the refrigeration, the can of soda will be approximately 42°F.
What is refrigeration?
We are given the following information:
[tex]T_{a}[/tex] = 35°F (temperature of the refrigerator)
To = 73°F (initial temperature of the can of soda)
T = 58°F (temperature of the can of soda after 10 minutes)
We can use these values to find the decay constant k:
T = [tex]T_{a}[/tex] + (To - [tex]T_{a}[/tex])[tex]e^{-kt}[/tex]
58 = 35 + (73 - 35)[tex]e^{-10k}[/tex]
23 = 38[tex]e^{(-10k)}[/tex]
ln(23/38) = -10k
k ≈ 0.0725 (rounded to the nearest thousandth)
Now we can use this value of k to find the temperature of the can of soda after 60 minutes:
T = [tex]T_{a}[/tex] + (To - [tex]T_{a}[/tex])[tex]e^{-kt}[/tex]
T = 35 + (73 - 35)[tex]e^{(-0.0725*60x^{2} )}[/tex]
T ≈ 42°F (rounded to the nearest degree)
Therefore, after 60 minutes in the refrigerator, the can of soda will be approximately 42°F.
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Please help me!!!!!!
The rotation that we need to apply to CD is of 270° clockwise.
Which should be the angle of rotation?We want a clockwise rotation that maps CD in E'F'.
Remember that a rotation of 90° will move the figure from one quadrant to the previous one. We can see that E'F' is on the third quadrant. while CD is on the second qudrant, then we need to go from.
Second to first quadrant ---> 90°
First to fourth quadrant ---> 90°
Fourth to third quadrant ---> 90°
Adding these 3 we get.
90° + 90° + 90° = 270°
So we need to applly a rotation of 270° clockwise to CD.
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