The difference in percentage of youngest and oldest age groups is 15.4%
The percentage from 11 to 20Start by calculating the total number of people, as follows
People = 102 + 36 + 66 + 150 + 78 + 60 + 90 + 11 + 9
Evaluate
People = 602
The number of people in the age group 11 to 20 is:
Group = 36
So, the percentage is
Percentage = 36/602
Percentage = 6.0%
Hence, the percentage from 11 to 20 is 6.0%
The percentage from 31 to 40The number of people in the age group 31 to 40 is:
Group = 150
So, the percentage is
Percentage = 150/602
Percentage = 24.9%
Hence, the percentage from 31 to 40 is 24.9%
The percentage from 71 to 80The number of people in the age group 71 to 80 is:
Group = 11
So, the percentage is
Percentage = 11/602
Percentage = 1.8%
Hence, the percentage from 71 to 80 is 1.8%
The lowest percentageThis is the percentage of age group 81 to 90
And, the percentage is
Percentage = 9/602
Percentage = 1.5%
Hence, the lowest percentage on the chart is 5%
The percentage from 51 to 60 and 61 - 70 combinedThe number of people in the age group 31 to 70 is:
Group = 60 + 90 = 15-
So, the percentage is
Percentage = 150/602
Percentage = 24.9%
Hence, the percentage from 51 to 60 and 61 - 70 combined is 24.9%
The difference in percentage of youngest and oldestThe youngest is 0 to 10 and the oldest is 81 to 90.
The number of people in these age groups are:
Youngest = 102
Oldest = 9
The difference is
Difference = 102 - 9
Difference = 93
So, the percentage is
Percentage = 93/602
Percentage = 15.4%
Hence, the difference in percentage of youngest and oldest is 15.4%
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Noah was at home. He got on his bike and rode to his friends
Answer:
what's your exact question
Answer:
can u pls type the full question
I need help with number 5, find the area, thank you
Answer:
96
Step-by-step explanation:
So for number 5 your going to multiply 8 and 12
8 x 12 = 96
So the answer for 5 is
Answer: 96
the cost of the two chairs is $1,800. After a month, cost of each chair and each table increased by 20%. The office again bought 6 chairs and 2 tables at $4,800 Calculate the new cost of a chair and a table
Given statement solution is :- The new cost of a table is:
New cost of a table = T + (T * 20%)
New cost of a table = T + (T * 0.2)
New cost of a table = 1.2T
The new cost of a chair is:
A new chair would cost $900 plus ($900 * 20%)
A chair would cost $900 new plus ($900 * 0.2)
A new chair would cost $900 plus $180.
New cost of a chair = $1,080
Let's assume that a chair originally cost C and a table originally cost T.
The price of two chairs, based on the information provided, is $1,800. So we can set up the following equation:
2C = $1,800
When we multiply the two sides of the equation by 2, we get:
C = $1,800 / 2
C = $900
This indicates that a chair once cost $900.
After a month, the price of every chair and every table has now gone up by 20%. This means the new cost of a chair is 120% of the original cost, and the new cost of a table is also 120% of the original cost.
The new cost of a chair is:
A new chair would cost $900 plus ($900 * 20%)
A chair would cost $900 new plus ($900 * 0.2)
A new chair would cost $900 plus $180.
New cost of a chair = $1,080
Similarly, the new cost of a table is:
New cost of a table = T + (T * 20%)
New cost of a table = T + (T * 0.2)
New cost of a table = 1.2T
According to the given information, the office bought 6 chairs and 2 tables at $4,800. Using the updated costs, we can construct the following equation:
(6 * $1,080) + (2 * 1.2T) = $4,800
Simplifying the equation, we have:
6,480 + 2.4T = 4,800
Subtracting 2.4T from both sides, we get:
6,480 = 4,800 - 2.4T
Subtracting 4,800 from both sides, we have:
1,680 = -2.4T
Dividing both sides by -2.4, we find:
T = 1,680 / -2.4
T ≈ -$700
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Will Mark Brainlest Help Please ,,,,
Step-by-step explanation:
from the second:
A=[3 -1]. -2B
[-5 0]
input this into 1
2([3 -1]) -(2B) -B =[1 3]
([-5 0]). [0 5]
[6 -2] -4B-B=[1 3]
[-10 0]. [0 5]
-5B=[1 3] -[3 -1]
[0 5]. [-5 0]
-5B= [1-3 3+1]
[0+5 5+0]
B= [-2/5 4/5]
[1 1]
A=[(19/5) (3/5)]
[-3. 2]
using the formula I derived
that's how I got A
I wish someone could love me just like how someone use to
Answer:
me too bro me too........
Find an expression which represents the sum of (3x+9y)(3x+9y) and (5x+7y)(5x+7y) in simplest terms.
The expressions (7x - 6y) and (3x - 5y) added together result in 10x - 11y.
What is unitary method?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Consider your square as being composed of smaller unit squares.
The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.
Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.
According to our question-
(7x – 6y) and (3x – 5y
Then the sum of the expressions will be
(7x – 6y) + (3x – 5y)
7x – 6y + 3x – 5y
10x – 11y
Hence, The expressions (7x - 6y) and (3x - 5y) added together result in 10x - 11y.
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Let X1, X2, X3 be independent normal random variables withcommon mean μ1 =60 and comman variance σ1^2 = 12. Alsolet Y1, Y2, Y3 be independent normal random variables with commonmean μ2 = 65 and common variance σ2^2 = 15.
(a) Specify the distribution of X1 +X2+X3.
(b) Find P(X1 +X2 +X3 > 185).
(c) Specify the distribution ofand
(d) Find P (Y- X > 8)
a)The distribution of \(X_{1} +X_{2}+X_{3}\) is a normal distribution with mean μ = 180 and variance σ² = 36.(b)P( \(X_{1} +X_{2}+X_{3}\) > 185) ≈ P(Z > 5/6).(c) The distribution of Y - X is a normal distribution with mean μ = 5 and variance σ² = 27.(d)P(Y - X > 8) ≈ P(Z > 1.732)
(a) The sum of independent normal random variables follows a normal distribution. In this case, X1, X2, and X3 are independent normal random variables with a common mean μ1 = 60 and a common variance σ1² = 12. Therefore, the distribution of \(X_{1} +X_{2}+X_{3}\) is also a normal distribution with the following parameters:
Mean: μ = μ1 + μ1 + μ1 = 60 + 60 + 60 = 180
Variance: σ² = σ1² + σ1² + σ1² = 12 + 12 + 12 = 36
So, the distribution of \(X_{1} +X_{2}+X_{3}\) is a normal distribution with mean μ = 180 and variance σ² = 36.
(b) To find P(\(X_{1} +X_{2}+X_{3}\) > 185), we need to calculate the probability that the sum of X1, X2, and X3 exceeds 185. Since X1, X2, and X3 are normally distributed with a mean of 180 and a variance of 36, we can standardize the variable using the Z-score formula.
Z = (X - μ) / σ
Z = (185 - 180) / √36 = 5 / 6
Now, we need to find the probability that Z is greater than 5/6. We can look up this probability in the standard normal distribution table or use statistical software to find the corresponding value.
P(\(X_{1} +X_{2}+X_{3}\) > 185) ≈ P(Z > 5/6)
(c) The difference of independent normal random variables follows a normal distribution. In this case, Y - X is the difference between Y (with mean μ2 = 65 and variance σ2² = 15) and X (with mean μ1 = 60 and variance σ1² = 12).
The mean of Y - X is μ2 - μ1 = 65 - 60 = 5.
The variance of Y - X is σ2² + σ1² = 15 + 12 = 27.
Therefore, the distribution of Y - X is a normal distribution with mean μ = 5 and variance σ² = 27.
(d) To find P(Y - X > 8), we need to calculate the probability that the difference between Y and X exceeds 8. Since Y - X is normally distributed with a mean of 5 and a variance of 27, we can standardize the variable using the Z-score formula.
Z = (Y - X - μ) / σ
Z = (8 - 5) / √27 ≈ 1.732
Now, we need to find the probability that Z is greater than 1.732. We can look up this probability in the standard normal distribution table or use statistical software to find the corresponding value.
P(Y - X > 8) ≈ P(Z > 1.732)
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30 members of a local gym were randomly selected to answer a survey. The selected gym members were between the ages of 50 and 65. Does that mean that all of the gym members are between the ages of 50 and 65?
Answer:
no
Step-by-step explanation:
no, only the selected were from that ages that doesnt mean they are ALL in that age range
Not all the members who are randomly selected, are between the ages of 50 and 65.
What is the procedure of random selection?"Random Selection is a procedure of collecting a sample for a particular experiment in a truly random way."
30 members of a local gym were randomly selected to answer a survey.
The selected gym members were between the ages of 50 and 65.
Therefore, not all the members are between the ages of 50 and 65.
Only those 30 members who are selected randomly, fall in the age group of 50 and 65.
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-2 ≤2x-4 <4 solve inequality
-8 < 4
hope it helps
Answer: -2≤-8<4
Step-by-step explanation:
A landscaping company uses a mixture of 20 pounds of grass seed and 356 pounds of fertilizer when reseeding a customer's lawn.
How many pounds of fertilizer will the company need for each pound of grass seed?
O A. 20
O B. 5. 6
O C. 16. 0
D. 17. 8
Answer:
D
Step-by-step explanation:
for 20 pounds of grass seed, we need 356 pounds of fertilizer
20 pounds of grass seed : 356 pounds of fertilizer
divide both sides by 20 to get 1 pound of grass seed on one side, as we want to figure out the corresponding amount of fertilizer for 1 pound of grass seed
20 pounds of grass seed/20 : 356 pounds of fertilizer/20
1 pound of grass seed: 17.8 pounds of fertilizer
How much time will Alex need to walk to his school, which is 2 1/4 miles away from his house, if he would walk with the speed of
4 1/2 mph
a piggy bank contains d dimes n nickels and p pennies. write an expression for the total amount of money in the bank
This is the total value of the coins in cents
To convert this to dollars, divide by 100. So the total value in dollars is (10d+5n+p)/100.
The three terms are
10d = value of all the dimes only5n = value of all the nickels onlyp = value of all the pennies only------------
Let's look at an example with actual numbers.
d = 9 dimesn = 3 nickelsp = 5 penniesI picked three whole numbers at random.
So,
10d = 10*9 = 90 cents comes from the dimes only5n = 5*3 = 15 cents comes from the nickels onlyp = 5 cents comes from the pennies onlyThe total value is 10d+5n+p = 90+15+5 = 110 cents aka 110/100 = 1.10 dollars.
What is the slope of a line that is parallel to the line y = 3/4x + 2?
Answer:
in this form the first one next to the x is the slope and the added value is the y intercept
if something is parrell that means the same slop so
3/4
Hope This Helps!!!
Shawrya Singh moved from India to Australia on 1 December 201W on a permanent residency visa to work for an Australian auditing firm. He is also a shareholder in a number of Australian companies, none of which is a base rate entity.
During the 201W/1X year he received the following distributions:
01/10/201W
70% franked distribution from CSL
$2,000
01/03/201X
60% franked distribution from BHP
$4,000
13/04/201X
Fully franked distribution from NAB
$3,200
15/06/201X
Unfranked distribution from ANZ
$4,500
Shawrya also received a salary of $57,000 paid by his Australian employer in the 201X/1W year.
Required
Assuming Shawrya does not have any allowable deductions in the current year, calculate his taxable income and tax liability for the year ending 30 June 201X, stating relevant legislation to support your answer.
The taxable income of Shawrya Singh for the year ending 30 June 201X is $18,871.43, and the tax liability is $6,039.98.
Calculation of Shawrya Singh's taxable income and tax liability for the year ending 30 June 201X:
The following distributions were received by Shawrya Singh during the year 201W/1X:01/10/201W: 70%
franked distribution from CSL: $2,000
Franking Credit = 2,000 * 0.7 = $1,400
Grossed-up dividend = $2,000 + $1,400 = $3,40001/03/201X: 60%
franked distribution from BHP: $4,000 13/04/201X
Credit = 4,000 * 0.6 = $2,400
Grossed-up dividend = $4,000 + $2,400 = $6,400
13/04/201X: Fully franked distribution from NAB: $3,200
Franking Credit = 3,200
Grossed-up dividend = $3,200 / (1 - 0.3) = $4,571.43* 15/06/201X: Unfranked distribution from ANZ: $4,500
Grossed-up dividend = $4,500 / (1 - 0) = $4,500
Total Grossed-up Dividend = $3,400 + $6,400 + $4,571.43 + $4,500 = $18,871.43*
The franking rate is assumed to be 30% because Shawrya is not a base rate entity. Deducting the Deductions: No deductions are allowable; thus, the taxable income is equivalent to the grossed-up dividend of $18,871.43.
Tax Payable = $18,871.43 * 0.32 = $6,039.98 (Marginal tax rate is 32%)
Therefore, the taxable income of Shawrya Singh for the year ending 30 June 201X is $18,871.43, and the tax liability is $6,039.98. Relevant legislation to support the answer is available in the Income Tax Assessment Act 1997.
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A formula is an equation stating that a single variable is equal to an expression. Distance traveled (\(d\)) is related to rate (\(r\)) and time (\(t\)) using the formula \(d\)=\(rt\). Use this formula to answer the following:
a. You traveled 3 hours at 55 mph. \(d\)= ____
b. You traveled \(x\) hours at 55 mph. \(d\)= ____
The value of the distance is 165 m and the value of the distance is 55x
How to determine the values of the variables?The formula is given as:
d =rt
a. You traveled 3 hours at 55 mph
This means that
r = 55 and t = 3
So, we have:
d = rt
This gives
d = 55 * 3
Evaluate
d = 165
Hence, the value of the distance is 165 m
b. You traveled x hours at 55 mph. = ____This means that
r = 55 and t = x
So, we have:
d = rt
This gives
d = 55 * x
Evaluate
d = 55x
Hence, the value of the distance is 55x
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Please help!!! Much appreciated!!
Answer:
C
Step-by-step explanation:
As n → ∞
\(\frac{85}{n}\) , \(\frac{75}{2n}\) , \(\frac{15}{2n^2}\) → 0
Then
15 - 35 - 0 + 55 + 0 + 0
= - 20 + 55
= 35 → C
The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.6 years, with a standard deviation of 3.5 years. The winner in one recent year was 30 years old. (a) Transform the age to a z-score. (b) Interpret the results.
(a) The z-score for an age of 30 years is approximately 0.6857.
(b) The winner's age of 30 years is roughly 0.6857 standard deviations above the mean age of the winners (27.6 years), indicating they were slightly older than the average age.
(a) To transform the age of 30 years to a z-score, we use the formula:
z = (x - μ) / σ
where:
x = individual value (age of the winner) = 30 years
μ = mean age = 27.6 years
σ = standard deviation = 3.5 years
Plugging in the values, we get:
z = (30 - 27.6) / 3.5
Calculating this expression, we find:
z ≈ 0.6857
Therefore, the z-score for an age of 30 years is approximately 0.6857.
(b) Interpretation of the results:
The z-score indicates the number of standard deviations an individual value (in this case, the age of the winner) deviates from the mean. A positive z-score suggests that the individual value is above the mean.
In this context, the z-score of approximately 0.6857 means that the age of the winner (30 years) is roughly 0.6857 standard deviations above the mean age of the winners (27.6 years). This suggests that the winner in that recent year was slightly older than the average age of the tournament winners.
By using z-scores, we can compare and interpret individual values within the context of a distribution, such as the bell-shaped distribution of ages in the cycling tournament winners.
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A twelve pack of Orange Crush is priced at $3.00. What is the unit rate or the price per soda?
Divide price by quantity:
3.00 / 12 = $0.25 per can.
The area of the regular pentagonal base of this prism is 43.06 square units. What is the volume of this prism?
125.00 cubic units
17.25 cubic units
431.25 cubic units
148.35 cubic units
The Volume of this prism is 148.35 cu.units, Option D is the right answer.
What is Volume ?The space occupied by a three dimensional object is called Volume.
Area of the base of the prism is the area of the pentagon
Area of the pentagon is given by
\(\rm A = \dfrac{1}{4} \sqrt{5(5+2\sqrt{5})} a^2\)
The area is given as 43.06 sq. units
On solving the side of pentagon is 5 units
The volume of the pentagonal prism is given by
V = (5/2)abh
where a is the length of apothem , b is the base length and h is the height
V = (5/2) * 3.44 * 5* 3.45
V = 148.35 cu.units
Therefore the Volume of this prism is 148.35 cu.units , Option D is the right answer.
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Answer:
148.35 cubic units!
Step-by-step explanation:
Approximate f(x)=xsinx by a Taylor polynomial with degree 4 at the number a=0. b) Use Jaylor's Inequality to estimate the accuracy of the approximation f(x)≈T4(x) when x lies in the interval −1≤x≤1
The degree 4 Taylor polynomial for f(x) = x sin(x) at a = 0 is: T4(x) = x²/2 − x⁴/24 and the maximum error is approximately 0.002.
a) Approximate f(x) = x sin x by a Taylor polynomial with degree 4 at the number a = 0. In order to find the degree 4 Taylor polynomial for f(x) = x sin(x) at a = 0, we need to find its derivatives up to the fourth degree. Here are the first five derivatives:
f(x) = x sin(x)f'(x) = sin(x) + x cos(x)
f''(x) = 2 cos(x) − x sin(x)
f'''(x) = −3 sin(x) − x cos(x)
f''''(x) = −4 cos(x) + x sin(x)
Now, we evaluate each derivative at x = 0:
f(0) = 0
f'(0) = sin(0) + 0 cos(0) = 0
f''(0) = 2 cos(0) − 0 sin(0) = 2
f'''(0) = −3 sin(0) − 0 cos(0) = 0
f''''(0) = −4 cos(0) + 0 sin(0) = −4
Therefore, the degree 4 Taylor polynomial for f(x) = x sin(x) at a = 0 is:T4(x) = f(0) + f'(0)x + (f''(0)/2!) x² + (f'''(0)/3!) x³ + (f''''(0)/4!) x⁴T4(x) = 0 + 0x + 2/2! x² + 0x³ − 4/4! x⁴T4(x) = x²/2 − x⁴/24
Therefore, the degree 4 Taylor polynomial for f(x) = x sin(x) at a = 0 is: T4(x) = x²/2 − x⁴/24
b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x)≈T4(x) when x lies in the interval −1≤x≤1. Taylor's Inequality states that the error between the actual value of a function and its Taylor polynomial approximation can be bounded by the following formula: |f(x) − Tn(x)| ≤ M(x − a)^{n+1}/(n+1)!
where M is an upper bound for |f^{(n+1)}(t)| for some t between a and x.
In our case, n = 4, a = 0, and we want to estimate the error for −1 ≤ x ≤ 1. Thus, we need to find an upper bound for |f^{(5)}(t)| for some t between 0 and 1. The fifth derivative of f(x) = x sin(x) is: f^{(5)}(x) = −5 cos(x) + x sin(x)
Thus, an upper bound for |f^{(5)}(t)| when −1 ≤ t ≤ 1 is 6. Therefore, the error between f(x) and T4(x) is bounded by: |f(x) − T4(x)| ≤ 6|x|⁵/5!when −1 ≤ x ≤ 1. Plugging in x = 1, we get: |f(1) − T4(1)| ≤ 6/5!
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How much force is needed to push a car with 1,300 kg of mass at an acceleration of 1.5 m/s2?
C)16,562 N
A)8,493 N
B)1,950 N
Answer:
I think its C
hope this helps you
Suppose X and Y are continuous random variables with joint pdf given by f(x, y) = 24xy if 0 < x, 0 < y, x + y < 1, and zero otherwise.
(a) Are X and Y independent? Why or why not?
(b) Find P(Y > 2X).
(c) Find the marginal pdf of X.
X and Y are not independent.
P(Y > 2X) = 3/16.
Marginal pdf of X = 12x(1-x)² for 0 < x < 1
Briefly explain about what method is used to answer each part of the question?(a) To determine if X and Y are independent, we need to check if the joint pdf can be factored into the product of the marginal pdfs:
f(x,y) = 24xy if 0 < x, 0 < y, x + y < 1, and zero otherwise.
Marginal pdf of X can be calculated by integrating the joint pdf over the all possible values of y:
f(x) = ∫ f(x,y) dy from 0 to 1-x
= ∫ 24xy dy from 0 to 1-x
= 12x(1-x)² for 0 < x < 1
Similarly, the marginal pdf of Y can be found by integrating the joint pdf over all possible values of x:
f(y) = ∫ f(x,y) dx from 0 to 1-y
= ∫ 24xy dx from 0 to 1-y
= 12y(1-y)² for 0 < y < 1
To check for independence, we need to verify if f(x,y) = f(x)f(y) for all x and y. However, if we multiply the marginal pdfs, we get:
f(x)f(y) = 144xy(1-x)²(1-y)² for 0 < x < 1 and 0 < y < 1
This is not the same as the joint pdf, so X and Y are not independent.
(b) To find P(Y > 2X), we need to integrate the joint pdf over the region where Y > 2X:
P(Y > 2X) = ∫∫ f(x,y) dA over the region where Y > 2X
= ∫∫ 24xy dA over the region where Y > 2X
= ∫∫ 24xy dxdy over the region where 0 < y < 2x and x+y < 1
= ∫[0,1/2] ∫[y/2,1-y] 24xy dxdy
= 3/16
Therefore, P(Y > 2X) = 3/16.
(c) The marginal pdf of X is given by:
f(x) = ∫ f(x,y) dy from 0 to 1-x
= ∫ 24xy dy from 0 to 1-x
= 12x(1-x)² for 0 < x < 1
Same result we get in part (a).
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X and Y are not independent.
P(Y > 2X) = 3/16.
Marginal pdf of X = 12x(1-x)² for 0 < x < 1
Briefly explain about what method is used to answer each part of the question?(a) To determine if X and Y are independent, we need to check if the joint pdf can be factored into the product of the marginal pdfs:
f(x,y) = 24xy if 0 < x, 0 < y, x + y < 1, and zero otherwise.
Marginal pdf of X can be calculated by integrating the joint pdf over the all possible values of y:
f(x) = ∫ f(x,y) dy from 0 to 1-x
= ∫ 24xy dy from 0 to 1-x
= 12x(1-x)² for 0 < x < 1
Similarly, the marginal pdf of Y can be found by integrating the joint pdf over all possible values of x:
f(y) = ∫ f(x,y) dx from 0 to 1-y
= ∫ 24xy dx from 0 to 1-y
= 12y(1-y)² for 0 < y < 1
To check for independence, we need to verify if f(x,y) = f(x)f(y) for all x and y. However, if we multiply the marginal pdfs, we get:
f(x)f(y) = 144xy(1-x)²(1-y)² for 0 < x < 1 and 0 < y < 1
This is not the same as the joint pdf, so X and Y are not independent.
(b) To find P(Y > 2X), we need to integrate the joint pdf over the region where Y > 2X:
P(Y > 2X) = ∫∫ f(x,y) dA over the region where Y > 2X
= ∫∫ 24xy dA over the region where Y > 2X
= ∫∫ 24xy dxdy over the region where 0 < y < 2x and x+y < 1
= ∫[0,1/2] ∫[y/2,1-y] 24xy dxdy
= 3/16
Therefore, P(Y > 2X) = 3/16.
(c) The marginal pdf of X is given by:
f(x) = ∫ f(x,y) dy from 0 to 1-x
= ∫ 24xy dy from 0 to 1-x
= 12x(1-x)² for 0 < x < 1
Same result we get in part (a).
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calculate the sound level (in decibels) of a sound wave that has an intensity of 2.15 µw/m2.
The sound level is 63.3 decibels
How to determine the intensityThe formula for calculating sound intensity in expressed as;
L = 10 × log10(I/I0),
Given that the parameters are expressed as;
L represents the sound levelI is the intensity of the sound wave(W/m²From the information given, we have to convert the intensity to W/m²
We have;
2.15 µW/m² is equivalent to 2.15 × 10⁻⁶ W/m².
Substitute the values, we have;
L = 10 × log₁₀(2.15 × 10⁻⁶ / 1 × 10⁻¹²
Divide the values, we have;
L = 10 × log₁₀(2.15 × 10⁶).
Find the logarithmic value
L = 10 × 6.3
Multiply the values
L = 63.3 decibels
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write a quadratic polynomial, sum of whose zeroes is 2 and product is -8
Answer:
x^2 +2x-8
Step-by-step explanation:
Here, we want to write the quadratic polynomial given the sum of the root and the product
mathematically, we can have the factors as -2 And +4
So we have the equation as;
(x-2)(x + 4)
= x^2+ 2x - 8
What is the slope of the line that passes through the points ( 9 , − 10 ) and ( 14 , 5 ) ? Write your answer in simplest form.
Answer: The slope of the line that passes through the points ( 9 , − 10 ) and ( 14 , 5) is 3.
Step-by-step explanation:
To calculate the slope of the line, we apply the following formula:
\(\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff \ m=\dfrac{y_2-y_1}{x_2-x_1} }}\)
where m is the slope of the line.
The points are:
\(\boldsymbol{\sf{\diamond \ x_1=9, \ y_1=-10 }}\\ \\ \boldsymbol{\sf{\diamond \ x_2=14, \ y_2=5 }}\)
We substitute our data in the formula and solve, then
\(\boldsymbol{\sf{m=\dfrac{5-(-10)}{14-9}=\dfrac{15}{5}=3 }}\)
The slope of the line that passes through the points ( 9 , − 10 ) and ( 14 , 5) is 3.
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What is the slope of the line that passes through the points (9 , -10 ) and (14 , 5)? Write your answer in simplest form.
From inspection on the given problem:
\( \sf{(x_1, y_1) = (9, -10)}\)\( \sf{(x_2, y_2) = (14, 5)}\)To calculate the slope of the line passing through the given points, we must use the formula below:
\( \sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}\)Substitute the given values into the slope formula and solve for m:
\( \sf{m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{5 - (-10)}{14 - 9} = \dfrac{15}{5} = \pmb{3}}\)
Therefore, the slope of the line that passes through the given points is 3.
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sin²(240°) how to solve
Answer:
3/4
Step-by-step explanation:
sin^2(240°)
=sin^2(360-120)
=sin^2(-120)
={-sin^2(120)}
=(-\(\sqrt({3} /2)^2\)
=3/4
Step-by-step explanation:
i hope so u can see sorry
and it is correct
Precalculus to wa
Please help Ik the language
Answer:
In mathematics education, precalculus or College algebra is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.
Step-by-step explanation:
Dude you can search this stuff up
What is the quotient of -3/7and -1/3? -1 1/8 -1/8 1/8 1 1/8
Answer:
1 2/7
Step-by-step explanation:
Quotient means division
-3/7 ÷-1/3
Copy dot flip
-3/7 * -3/1
9/7
7/7 + 2/7
1 2/7
Angle ABC has a measure of 125° Angle ABC is rotated 75° about point B to create angle A'B'C'. What is
the measure, in degrees, of angle A'B'C
Answer:
The measure of ∠A'B'C' is 125°
Step-by-step explanation:
The given information are;
The measure of ∠ABC = 125°
The transformation applied to ∠ABC = 75° rotation about point B
The vertices of the image formed after rotation = ∠A'B'C'
Therefore, given that a rotational transformation is a form of rigid transformation, we have that the size and shape of the figure in the preimage = The size and shape of the figure of the image
Therefore, the measure of m∠ABC = The measure of m∠A'B'C'.
The measure of the angle A'B'C' which is created by rotating angle ABC 75° about point B is 125 degrees.
What is rotation of figure?Rotation of a figure is the transformation of it about a point in either clockwise or anticlockwise direction. By rotating, a figure changes the coordinate point of the figure.
The following information regarded to angle ABC are given.
Angle ABC has a measure of 125° Angle ABC is rotated 75° about point B to create angle A'B'C'.Angle A'B'C is formed after the rotation.The rotation of 75 degree is applied on the given angle ABC from the point B. This will change the coordinate points of the point A and point C.
As it is known that the rotation changes the coordinate point and the position of the shape but does not change the shape and size of the original figure.
Hence, the measure of the angle A'B'C' which is created by rotating angle ABC 75° about point B is 125 degrees.
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A bag contains:
.
5 red marbles
6 blue marbles
3 green marbles
4 black marbles
• 2 yellow marbles
A marble will be drawn from the bag and replaced 100 times. What is a reasonable prediction
for the number of times a green or black marble will be drawn?
F 14
G 65
H7
J 35
Answer:
j.35 times
Step-by-step explanation: