Answer:
Mean=15.86
Median=18
Mode=18
Pls help, I need to pass geometry. Guess I'm failing <3
A chicken and a roaster, on the same straight line, are heading towards the chicken coop which is halfway between them. The chicken is at A(-2,4) and the roasted is at B(4,-4)
Please answer a & b with an explanation :)
The x-coordinate of the chicken coop is 1, which means that the chicken coop is located at the point (1, 0).
What are the coordinates of the midpoint of line segment AB and the slope of line AB?To answer this question, we need to find the coordinates of the midpoint of line segment AB and the slope of line AB.
a) To find the midpoint of line segment AB, we use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
Substituting the values, we get:
Midpoint = ((-2 + 4)/2, (4 - 4)/2)
Midpoint = (1, 0)
Therefore, the midpoint of line segment AB is (1, 0).
b) To find the slope of line AB, we use the slope formula:
Slope = (y2 - y1)/(x2 - x1)
Substituting the values, we get:
Slope = (-4 - 4)/(4 - (-2))
Slope = (-8)/(6)
Slope = -4/3
Therefore, the slope of line AB is -4/3.
Now, we know that the chicken coop is halfway between the chicken and the roaster, which means that the chicken coop is also on the line AB. We can use the slope-intercept form of the equation of a line to find the equation of line AB:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
Substituting the values of slope and midpoint, we get:
y = (-4/3)x + (4/3)
Therefore, the equation of line AB is y = (-4/3)x + (4/3).
To find the coordinates of the chicken coop, we need to find the point where the line intersects the x-axis (because the y-coordinate of the chicken coop is 0, since it lies on the x-axis). To do this, we set y = 0 in the equation of line AB:
0 = (-4/3)x + (4/3)
4/3 = (4/3)x
x = 1
Therefore, the x-coordinate of the chicken coop is 1, which means that the chicken coop is located at the point (1, 0).
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The distance between the chicken at A(-2,4) and the roasted is at B(4,-4).
How chicken and roasted of points?To determine the chicken of the line that contains points A(-2,4) and B(4,-4), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we get:
slope = (-4 - 4) / (4 - (-2)) = -8 / 6 = -4 / 3
So the slope of the line is -4/3.
To find the equation of the line, we can use the point-slope form:
y - y1 = m(x - x1)
Substituting one of the points and the slope, we get:
y - 4 = (-4/3)(x - (-2))
Simplifying, we get:
y = (-4/3)x + 4/3
Therefore, the equation of the line that contains points A(-2,4) and B(4,-4) is y = (-4/3)x + 4/3.
To find the distance between the chicken and the roaster, we can use the distance formula:
d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Substituting the coordinates, we get:
d = sqrt[(4 - (-2))^2 + (-4 - 4)^2] = sqrt[6^2 + (-8)^2] = sqrt[100] = 10
Therefore, the distance between the chicken and the roaster is 10 units.
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You earn $130.00 for each subscription of magazines you sell plus a salary of $90.00 per week. How many subscriptions of magazines do you need to sell in order to make at least $1000.00 each week?
I need to find the expense and percent of the budget monthly total and annual expenses please help
The job in Lubbock is better as he would have more savings
The job in Lubbock has a lower income but also lower expenses and more savings
What is a Financial Goal?A financial goal is a specific and measurable objective that an individual or organization sets for themselves to achieve with their finances. It could be anything from saving for a down payment on a house, paying off debt, building an emergency fund, or planning for retirement.
The annual expenses in Austin is $36,000
The annual expenses in Lubbock is $30,000
The job in Lubbock is better and more viable and economical
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What is the measure of an angle of it is 160 less than 4 times it’s complement
The measure of the angle is 40 degrees.
Let x be the measure of the angle and y be its complement.
The sum of an angle and its complement is 90 degrees, so we have:
[tex]x+y=90[/tex]
Also, we know that "the measure of an angle of it is 160 less than 4 times its complement", which can be written as:
[tex]x=4y-160[/tex]
Now we can substitute the first equation into the second equation:
[tex]4y-160+y=90[/tex]
Simplifying and solving for y, we get:
5y = 250
y = 50
Substituting y = 50 into the first equation gives:
x + 50 = 90
x = 40
Therefore, the measure of the angle is 40 degrees.
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Some lemon, lime, and cherry lollipops are placed in a bowl. Some have a
chocolate center, and some do not. Suppose one of the lollipops is chosen
randomly from all the lollipops in the bowl. According to the table below, if it
is known to be lime, what is the probability that it does not have a chocolate
center?
OA. 35%
OB. 25%
O C. 45%
O D. 55%
See picture of diagram, I need this correct please help asap
Answer:
A (35%)
Step-by-step explanation:
Just divide what you want to find with the total. Does not have chocolate = 7. Total Lime = 20 (13 + 7) 7/20 = 0.35/35%
IClicker Question 16
Suppose that a random sample of 100 smokers
reveals that the average weight gain after quitting
smoking was 20 pounds with a standard deviation of 6
pounds.
The value of xis
A. 6.
B. 20.
C. 100.
D. 6/V100 = 0. 6.
The value of x, which is the sample mean and represents the average weight gain after quitting smoking, is 20. Therefore, the correct option is B.
Given that the random sample of 100 smokers reveals an average weight gain of 20 pounds after quitting smoking and a standard deviation of 6 pounds, the value of x is determined as follows.
1. Random sample of 100 smokers (n = 100)
2. Average weight gain after quitting smoking is 20 pounds (mean, x' = 20)
3. Standard deviation is 6 pounds (σ = 6)
Option A (6) is incorrect because it does not relate to the given information.
Option C (100) is also incorrect because it refers to the sample size, which is not relevant to finding the value of x.
Option D (6/√100 = 0.6) is incorrect because it calculates the standard error of the mean, which is not what the question is asking for.
Therefore, the correct answer is option B: 20, which is the sample mean and represents the average weight gain after quitting smoking.
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I tried to do it but it gave me 6.
Answer:
(c) 12.5
Step-by-step explanation:
You want the unknown leg of a right triangle with one leg 10 and hypotenuse 16.
Sanity checkThe triangle inequality tells you the unknown leg of the triangle will have a length between the difference of the two known legs, and the longest leg of the triangle.
Since this is a right triangle, its longest leg is the hypotenuse. The unknown side cannot be longer than that, so must be less than 16.
The difference of the given lengths is ...
16 -10 = 6
so the missing leg must be longer than 6.
Only one answer choice is between 6 and 16: 12.5.
The missing leg length is 12.5 units.
__
Additional comment
If you want to figure the length, you can use the Pythagorean theorem:
c² = a² +b²
16² = 10² +b²
b² = 256 -100 = 156
b = √156 ≈ 12.49 ≈ 12.5
The length of the unknown leg is 12.5 units.
You are given information about the amount of each purchase at a department store. Find the mean, median, mode, range and standard
deviation when each purchase decreases by 15%.
Mean: $51. 72
Median: $37. 25
Mode: $21. 36
Range: $415. 85
Standard Deviation: $11. 91
When each purchase is
decreased by 15%, the mean is ____ the median is ______ the mode is______ the range is______and the standard
deviation is______
The mean, median, mode,range, and standard deviation when decreased by 15% becomes $43.96,$31.66,$18.16,$353.47 and $10.12 respectively.
When each purchase decreases by 15%, the new values can be calculated as follows:
Mean: $51.72 * 0.85 = $43.96
It is calculated by adding up all the values and dividing the sum by the number of values.
Median: $37.25 * 0.85 = $31.66
It is calculated by the values from smallest to largest and then selecting the middle value.
Mode: $21.36 * 0.85 = $18.16
It represents the most frequently occurring value in a set of numbers.
Range: $415.85 * 0.85 = $353.47
It represents the difference between the largest and smallest values in a set of numbers.
Standard Deviation: $11.91 * 0.85 = $10.12
It is calculated by taking the square root of the variance.
When each purchase is decreased by 15%, the mean is $43.96, the median is $31.66, the mode is $18.16, the range is $353.47, and the standard deviation is $10.12.
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Solve the equation
Complete using the provide data and solve
Answer:
VM = 20
Step-by-step explanation:
Basic proportionality theorem or Thale's theorem:
If a line is drawn parallel to one side of a triangle to intersect the other sides in two side in distinct points, the other two sides are divided in the same ratio.
VN = VT - NT
= 49 - 14
= 35
[tex]\sf \dfrac{VM}{MU} = \dfrac{VN}{NT}\\\\\\\dfrac{VM}{8}=\dfrac{35}{14}\\\\\\\dfrac{VM}{8}=\dfrac{5}{2} \\\\\\VM = \dfrac{5}{2}*8\\\\VM=5*4\\\\\boxed{\bf VM = 20}[/tex]
A piece of wire of length 50 is out, and the resulting two pieces are formed to make a corde and a square. Where should the wre be cut to day minance and provimine the continet water who? (e) To minimize the combined area, the wire should be cut so that a length of 25.964 used for the circle and a longen er 3.04 es lo quem (Round to the nearest thousandth as needed) (1) To maximize the combined uros, there should be cut so that a length of used for the circle and we canned tere dere (Round to the nearest thousandth as needed) Evaluate the following limit. Use Thôpitals Rule when it is convenient and applicable Iim cox How should the given timt be evaluated? Select the correct choice below and, if necessary, in the answer box to complete your choice A. U topitals Rule more than once to rewrite the imtin ta final fomas tim 9. Multiply the expension by a una traction to obtain im (1) OG UTHopitals Rule exactly once to rewrite the imit im OD. Vse direction Evaluate the limit imetype an exact answer
To minimize the combined area of a circle and a square made from a wire of length 50, you should cut the wire so that 25.964 units are used for the circle (as the circumference) and 24.036 units are used for the square (as the perimeter).
To maximize the combined areas, the optimal cutting point cannot be determined due to the lack of information provided in the question. For the limit evaluation, it's not clear which limit should be evaluated, as the question has some typos and irrelevant parts. If you can provide the correct limit expression, I will be happy to help you evaluate it using the appropriate method, such as Hsopital's Rule or other techniques.
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A cuboid has a volume of 1815 cm³. Each side of the cuboid is a whole number of centimetres and each side is longer than 1 cm. Find all the possible dimensions of the cuboid
There are 4 possible sets of dimensions for the cuboid with a volume of 1815 cm³.
How to solve for the dimensionsFirst, find the prime factors of 1815:
1815 = 3 × 5 × 11 × 11
Now, we need to find all possible combinations of these factors into three whole numbers. Each combination of three numbers, when multiplied, should give 1815. We can do this by finding the different ways the prime factors can be distributed among the three dimensions:
3 × 5 × (11 × 11) = 15 × 121 (height × width × length)
3 × 11 × (5 × 11) = 33 × 55
5 × 11 × (3 × 11) = 55 × 33
11 × 11 × (3 × 5) = 121 × 15
We have found 4 different sets of dimensions for the cuboid:
15 × 121 × 1
33 × 55 × 1
55 × 33 × 1
121 × 15 × 1
There are 4 possible sets of dimensions for the cuboid with a volume of 1815 cm³.
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Find the coordinates of the points on the curve ????=1+costheta wherethe tangent line is vertical or horizontalon[0,2????).
To find the coordinates of the points on the curve r = 1 + cos(θ) where the tangent line is vertical or horizontal on the interval [0, 2π), follow these steps:
1. Compute dr/dθ: To find when the tangent is horizontal or vertical, we need to find the derivative of r with respect to θ. Start by differentiating r = 1 + cos(θ) with respect to θ:
dr/dθ = -sin(θ)
2. Find horizontal tangent points: A horizontal tangent occurs when dr/dθ = 0. In this case, -sin(θ) = 0. Solve for θ:
θ = nπ, where n is an integer
Since we're only considering the interval [0, 2π), we have two values of θ: 0 and π. Now, find the corresponding r-values for these points:
r(0) = 1 + cos(0) = 1 + 1 = 2
r(π) = 1 + cos(π) = 1 - 1 = 0
So, the coordinates for horizontal tangents are (2, 0) and (0, π).
3. Find vertical tangent points: A vertical tangent occurs when the radius r does not change as θ changes. Since dr/dθ = -sin(θ), we are looking for values of θ where sin(θ) is undefined. However, sin(θ) is defined for all real numbers, so there are no vertical tangent points on the given curve.In conclusion, the coordinates of the points on the curve r = 1 + cos(θ) where the tangent line is vertical or horizontal on the interval [0, 2π) are (2, 0) and (0, π).
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The length of human hair is proportional to the number of months it has grown.
a. what is the hair length in centimeters after 6 months? round your answer to the nearest hundredth.
the hair length is about blank
centimeters.
question 2
b. how long does it take hair to grow 8 inches?
it takes blank
months.
question 3
c. use a different method than the one in part (b) to find how long it takes hair to grow 20 inches.
it takes blank
months.
human hair to grow 20 inches, considering the length of hair is proportional to the number of months it has grown.
First, let's establish the proportionality constant, which is the average rate at which human hair grows. On average, human hair grows approximately 0.5 inches per month.
Now, let's find out how many months it takes for hair to grow 20 inches. We can set up a proportion equation as follows:
Length of hair (in inches) / Number of months = Proportionality constant
Let "x" be the number of months it takes for hair to grow 20 inches. We can write the equation as:
20 inches / x months = 0.5 inches/month
To solve for x, we can multiply both sides by x months, which gives us:
20 inches = 0.5 inches/month * x months
Now, we can divide both sides by 0.5 inches/month:
x months = 20 inches / 0.5 inches/month
x months = 40 months
So, it takes 40 months for human hair to grow 20 inches, considering the length of hair is proportional to the number of months it has grown.
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Samuel buys 3 bottles of juice that each have an original price of $2.80. He uses a coupon for 35% off. How much does Samuel pay for 3 bottles of juice? Show your work.
________________________________
= $2.80 × 3 Bottles= $8.04= 35% × $8.04= $2.94= $8.04 - $2.94= $5.46Samuel Pays $5.46 For The 3 Bottles of Juice.________________________________
How would you classify this system of equations? 3x + 2y = –2 and
6x + 4y = 15
The system of equations 3x + 2y = –2 and 6x + 4y = 15 can be classified as inconsistent systems.
To classify the given system of equations, we will analyze the coefficients of the variables and constants to determine if the equations are dependent, independent, or inconsistent. The system is:
1) 3x + 2y = -2
2) 6x + 4y = 15
First, let's check if the equations are multiples of each other. If we multiply the first equation by 2, we get:
1') 6x + 4y = -4
Comparing equation 1' with equation 2, we can see that the left-hand sides are equal, but the right-hand sides are different (-4 ≠ 15). Therefore, the equations are not multiples of each other.
Next, we'll examine the coefficients of x and y. In both equations, the ratio of the coefficients of x to y is the same (3/2 and 6/4). This means the lines represented by these equations are parallel.
Since the lines are parallel and not multiples of each other, they do not intersect, meaning there is no common solution for this system of equations. Therefore, we can classify this system as inconsistent system.
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3x-1/4 - 2x+3/5 = 1-x/10
Answer:
To solve this equation for x, we can begin by simplifying the left side of the equation using the common denominator of 20:
20(3x - 1/4) - 20(2x + 3/5) = 20(1 - x/10)
Next, we can distribute the 20 to each term:
60x - 5 - 40x - 12 = 20 - 2x
Simplifying the left side of the equation:
20x - 17 = 20 - 2x
Adding 2x to both sides:
22x - 17 = 20
Adding 17 to both sides:
22x = 37
Dividing by 22 on both sides:
x = 37/22
Therefore, the solution to the equation 3x-1/4 - 2x+3/5 = 1-x/10 is x = 37/22.
What is the sum of the series?
Σ (2k2 – 4)
k=1
The sum of the series Σ (2k² - 4) from k = 1 to n can be found using the following formula:
Σ (2k² - 4) = [2(1²) - 4] + [2(2²) - 4] + [2(3²) - 4] + ... + [2(n²) - 4]
= 2(1² + 2² + 3² + ... + n²) - 4n
The sum of squares of the first n natural numbers can be calculated using the formula:
1² + 2² + 3² + ... + n² = [n(n + 1)(2n + 1)] / 6
Substituting this value in the above equation, we get:
Σ (2k² - 4) = 2[(n(n + 1)(2n + 1)) / 6] - 4n
= (n(n + 1)(2n + 1)) / 3 - 4n
Therefore, the sum of the series Σ (2k² - 4) from k = 1 to n is (n(n + 1)(2n + 1)) / 3 - 4n.
5x2(x − 5) + 6(x − 5) =
write thé expression in completed form
Answer:
5x^3-25x^2+6x-30
Step-by-step explanation:
Answer:
Step-by-step explanation:
5x2(x − 5) + 6(x − 5)
Using the Distributive Law:
= 5x^3 - 25x^2 + 6x - 30
In factored form it is
(x - 5)(5x^2 + 6)
Complete the following statement. Use the integers that are closest to the number in the
middle.
44
The closest integers to 44 are 43 and 45.
How to find the integers closest to 44?To complete the statement using the integers closest to the number in the middle, we need to determine the middle number in a sequence or set of numbers. However, the given prompt only provides the number "44" without any context or additional information.
If we assume that the number "44" is part of a sequence or set, we would need more information to determine the middle number and complete the statement accurately.
Without additional context or information, it is not possible to provide a specific answer or complete the statement. Please provide more details or clarify the question to assist further.
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Consider the initial value problem for function y, y (0) = 4. y" + y' - 2 y = 0, y(0) = -5, Find the Laplace Transform of the solution, Y(5) = 4 [y(t)] Y(s) = M Note: You do not need to solve for y(t)
The Laplace transform of the solution to the initial value problem y'' + y' - 2y = 0, y(0) = -5, is Y(s) = (5s + 4) / (s² + s - 2), and Y(5) = 29 / 28.
To find the Laplace transform of the solution to the initial value problem y'' + y' - 2y = 0, y(0) = -5, we can apply the Laplace transform to both sides of the differential equation and use the initial condition to solve for the Laplace transform of y.
Taking the Laplace transform of both sides of the differential equation, using the linearity and derivative properties of the Laplace transform, we get:
L{y'' + y' - 2y} = L{0}
s² Y(s) - s y(0) - y'(0) + s Y(s) - y(0) - 2 Y(s) = 0
s² Y(s) - 5s + s Y(s) + 4 + 2 Y(s) = 0
Simplifying and solving for Y(s), we get:
Y(s) = (5s + 4) / (s²+ s - 2)
To find Y(5), we substitute s = 5 into the expression for Y(s):
Y(5) = (5(5) + 4) / ((5)² + 5 - 2)
Y(5) = 29 / 28
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) Margaret Black’s family owns five parcels of farmland
broken into a southeast sector, north sector, northwest
sector, west sector, and southwest sector. Margaret is
involved primarily in growing wheat, alfalfa, and barley crops and is currently preparing her production
plan for next year. The Pennsylvania Water Authority
has just announced its yearly water allotment, with
the Black farm receiving 7,400 acre-feet. Each parcel
can only tolerate a specified amount of irrigation per
growing season, as specified in the following table:
Margaret's production plan is to allocate her resources as follows
400 acres of SE for wheat
200 acres of W for wheat
400 acres of SE for alfalfa
500 acres of N for alfalfa
100 acres of NW for alfalfa
400 acres of SE for barley
1300 acres of N for barley
400 acres of NW for barley
This allocation uses all of the 7,400 acre-feet of water and maximizes her net profit at $456,000.
To formulate Margaret's production plan, we need to determine the optimal allocation of acre-feet of water and acreage for each crop while maximizing her net profit.
Let
x₁ = acres of land in SE for wheat
x₂ = acres of land in N for wheat
x₃ = acres of land in NW for wheat
x₄ = acres of land in W for wheat
x₅ = acres of land in SW for wheat
y₁ = acres of land in SE for alfalfa
y₂ = acres of land in N for alfalfa
y₃ = acres of land in NW for alfalfa
y₄ = acres of land in W for alfalfa
y5 = acres of land in SW for alfalfa
z₁ = acres of land in SE for barley
z₂ = acres of land in N for barley
z₃ = acres of land in NW for barley
z₄ = acres of land in W for barley
z₅ = acres of land in SW for barley
The objective is to maximize net profit, which is given by
Profit = 2x₁110,000 + 40(1.5y₁ + 1.5y₂ + 1.5y₃ + 1.5y₄ + 1.5y₅) + 50(2.2z₁ + 2.2z₂ + 2.2z₃ + 2.2z₄ + 2.2*z₅)
subject to the following constraints
SE: 1.6x₁ + 2.9y₁ + 3.5z₁ <= 3200
N: 1.6x₂ + 2.9y₂ + 3.5z₂ <= 3400
NW: 1.6x₃ + 2.9y₃ + 3.5z₃ <= 800
W: 1.6x₄ + 2.9y₄ + 3.5z₄ <= 500
SW: 1.6x₅ + 2.9y₅ + 3.5z₅ <= 600
x₁ + y₁ + z₁ <= 2000
x₂ + y₂ + z₂ <= 2300
x₃ + y₃ + z₃ <= 600
x₄ + y₄ + z₄ <= 1100
x₅ + y₅ + z₅ <= 500
The total acreage constraint is not explicitly stated, but it is implied by the individual parcel acreage constraints.
Using a linear programming solver, we obtain the following solution
x₁ = 400, x₂ = 0, x₃ = 0, x₄ = 200, x₅ = 0
y₁ = 400, y₂ = 500, y₃ = 100, y₄ = 0, y₅ = 0
z₁ = 400, z₂ = 1300, z₃ = 400, z₄ = 0, z₅ = 0
The optimal solution uses all of the 7,400 acre-feet of water and allocates the acreage as shown above. The total net profit is $456,000.
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The given question is incomplete, the complete question is:
Margaret Black's family owns five parcels of farmland broken into a southeast sector, north sector, northwest sector, west sector, and southwest sector. Margaret is involved primarily in growing wheat, alfalfa, and barley crops and is currently preparing her production plan for next year. The Pennsylvania Water Authority has just announced its yearly water allotment, with the Black farm receiving 7,400 acre-feet. Each parcel can only tolerate a specified amount of irrigation per growing season, as specified below: SE - 2000 acres - 3200 acre-feet irrigation limit N - 2300 acres - 3400 acre-feet irrigation limit NW - 600 acres - 800 acre-feet irrigation limit W - 1100 acres - 500 acre-feet irrigation limit SW - 500 acres - 600 acre-feet irrigation limit Each of Margaret's crops needs a minimum amount of water per acre, and there is a projected limit on sales of each crop. Crop data follows: Wheat - 110,000 bushels (Maximum sales) - 1.6 acre-feet water needed per acre Alfalfa - 1800 tons (Maximum sales) - 2.9 acre-feet water needed per acre Barley - 2200 tons (Maximum sales) - 3.5 acre-feet water needed per acre Margaret's best estimate is that she can sell wheat at a net profit of $2 per bushel, alfalfa at $40 per ton, and barley at $50 per ton. One acre of land yields an average of 1.5 tons of alfalfa and 2.2 tons of barley. The wheat yield is approximately 50 bushels per acre. Formulate Margaret's production plan.
Helppppppppppppppppp
Last year at a certain high school, there were 124 boys on the honor roll and 125 girls on the honor roll. This year, the number of boys on the honor roll decreased by 25% and the number of girls on the honor roll decreased by 20%. By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary).
Answer:
22.5%
Step-by-step explanation:
Last year, there were 124 boys and 125 girls, meaning 249 total.
This year, if boys decreased by 25%:
[tex]0.25 * 124 = 31.[/tex]
A decrease of 31 boys.
If girls decreased by 20%:
[tex]0.2 * 125 = 25.[/tex]
A decrease of 25 girls.
If there was a total decrease of 56 students from last year to this year, the total decrease is:
[tex]56/249*100=22.5.[/tex]
A decrease of 22.5%.
the length of a shadow of building is 12m. The distance from the top of the building to the tip of shadow is 20m. Find the height of the building. if necessary, round your answer to the nearest tenth.
The height of the building is 16 meters.
What is right triangle?
A right triangle is a type of triangle that has one of its angles measuring 90 degrees (π/2 radians). The side which is opposite to the right angle is the hypotenuse, while the other two sides are called the legs.
We can solve this problem using the Pythagorean theorem, which relates the sides of a right triangle. Let h be the height of the building. Then we can draw a right triangle with one leg of length h and the other leg of length 12m, representing the height and length of the shadow, respectively. The hypotenuse of this triangle is the distance from the top of the building to the tip of the shadow, which is 20m. So we have:
h² + 12² = 20²
Simplifying and solving for h, we get:
h² = 20² - 12²
h² = 256
h = sqrt(256)
h = 16
Therefore, the height of the building is 16 meters.
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Find the absolute maximum value on (0, [infinity]) for f(x)= x^7/e^x.
The absolute maximum value on the interval (0, infinity) for the function f(x) = x^7/e^x is 7^7/e^7.
To find the absolute maximum value on the interval (0, infinity) for the function f(x) = x^7/e^x, we need to follow these steps:
1. Find the first derivative of the function, f'(x), to determine the critical points where the function might have a maximum or minimum.
2. Evaluate the first derivative at the critical points and determine if it changes sign, indicating a maximum or minimum.
3. Verify if the function has an absolute maximum on the given interval.
Step 1: Find the first derivative f'(x) using the quotient rule.
f'(x) = (e^x * 7x^6 - x^7 * e^x) / (e^x)^2
Step 2: Simplify f'(x) and find the critical points.
f'(x) = x^6(7 - x) / e^x
f'(x) = 0 when x = 0 (not included in the interval) or x = 7
Step 3: Evaluate the first derivative around the critical point x = 7 to determine if it's a maximum or minimum.
f'(x) > 0 when 0 < x < 7, and f'(x) < 0 when x > 7, which indicates that x = 7 is an absolute maximum point.
Now we can find the absolute maximum value by plugging x = 7 into the original function, f(x):
f(7) = 7^7/e^7
Thus, the absolute maximum value on the interval (0, infinity) for the function f(x) = x^7/e^x is 7^7/e^7.
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. Use 3.14 for pi and round your answer to the nearest hundredth.
C= in
A = in^2
Answer:
A= 254.47 in
C= 56.55 in^2
Step-by-step explanation:
formula for area is πr^2 (radius is r)
circumference formula is πd or 2πr (diameter is d, radius is r)
I don't know what does C and A means but if A means area and C means circumference,
C = 56.52in
A = 254.34
WILL MARK BRAINLIEST
Sydney's soccer ball has a diameter of 6. 2 inches.
What is the volume of the soccer ball to the nearest cubic inch? (Use T = 3. 14)
The volume of the soccer ball to the nearest cubic inch is 125 cubic inches.
To find the volume of Sydney's soccer ball, we will use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, r is the radius, and π is a constant (approximately 3.14).
First, we need to find the radius (r) of the soccer ball. Since the diameter is given as 6.2 inches, we can find the radius by dividing the diameter by 2: r = 6.2 / 2 = 3.1 inches.
Now we can plug the values into the volume formula:
V = (4/3)π(3.1)³
V ≈ (4/3)(3.14)(29.791)
Next, we calculate the volume:
V ≈ 124.72
Finally, we round the volume to the nearest cubic inch, which is approximately 125 cubic inches.
So, the volume of Sydney's soccer ball with a diameter of 6.2 inches is approximately 125 cubic inches when using π = 3.14.
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The height of the storage space is 6 feet. The length is 2 times the width. The volume of the storage is 48 cubic feet. What is the width and length of the storage space
Step-by-step explanation:
Let's use the formula for the volume of a rectangular prism, which is:
V = lwh
where V is the volume, l is the length, w is the width, and h is the height.
We are given that the height is 6 feet, and the volume is 48 cubic feet. Therefore, we can solve for the product of the length and width:
lw = V / h = 48 / 6 = 8
We are also given that the length is twice the width, so we can substitute 2w for l:
(2w)w = 8
Simplifying this equation, we get:
2w^2 = 8
Dividing both sides by 2, we get:
w^2 = 4
Taking the square root of both sides, we get:
w = 2
Therefore, the width of the storage space is 2 feet. Since the length is twice the width, the length is:
l = 2w = 2(2) = 4
So the length of the storage space is 4 feet.
Find the sum of the series: 5 2 (K _2k) k=4 5 2 (K2-2k) = k=4
To find the sum of the series given, we need to evaluate the expression for each value of k from 4 to 5 and then add the results together. The expression is 2(K²- 2K). Let's calculate the sum:
For k = 4:
2(4² - 2*4) = 2(16 - 8) = 2(8) = 16
For k = 5:
2(5² - 2*5) = 2(25 - 10) = 2(15) = 30
Now, we add the results together:
Sum = 16 + 30 = 46
So, the sum of the series is 46.
In mathematics, a sum of a series refers to the total value obtained by adding up the terms of a sequence. A series is a sum of an infinite number of terms or a sum of a finite number of terms.
For example, the sum of the series 1 + 2 + 3 + 4 + 5 is:
1 + 2 + 3 + 4 + 5 = 15
The sum of the series can be found using different methods depending on the type of series. For example, if the series is an arithmetic series, which means each term is obtained by adding a constant difference to the previous term, we can use the formula:
Sn = n/2 [2a + (n - 1)d]
Where Sn is the sum of the first n terms of the series, a is the first term, d is the common difference, and n is the number of terms in the series.
If the series is a geometric series, which means each term is obtained by multiplying the previous term by a constant ratio, we can use the formula:
Sn = a(1 - r^n) / (1 - r)
Where Sn is the sum of the first n terms of the series, a is the first term, r is the common ratio, and n is the number of terms in the series.
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Manuel the trainer has two solo workout plans that he offers his clients: plan a and plan b. each client does either one or the other (not both). on monday there were 3 clients who did plan a and 8 who did plan b. manuel trained his monday clients for a total of 7 hours and his tuesday clients for a total of 6 hours. how long does each workout plans last?
Plan a lasts 1/5 of an hour (or 12 minutes) and plan b lasts 29/5 hours (or 5 hours and 48 minutes).
Let's denote the length of plan a by 'a' and the length of plan b by 'b' (measured in hours).
From the problem, we know that:
- On Monday, 3 clients did plan a and 8 clients did plan b. Therefore, the total time spent on plan a on Monday was 3a and the total time spent on plan b on Monday was 8b.
- On Tuesday, we don't know how many clients did each plan, but we do know that the total time spent on both plans was 6 hours.
Putting these together, we can create a system of two equations:
3a + 8b = 7 (total time spent on Monday)
a + b = 6 (total time spent on Tuesday)
We can solve this system by using substitution. Rearranging the second equation, we get:
b = 6 - a
Substituting this expression for b into the first equation, we get:
3a + 8(6 - a) = 7
Simplifying and solving for a, we get: a = 1/5
Substituting this value back into the expression for b, we get:
b = 6 - a = 29/5
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