The standard deviation for the data must be approximately $111.93.
How to calculate the standard deviationSince we are given a range of values that encompasses about 95% of the data, we can assume that this range is within two standard deviations of the mean.
Thus, we can set up the following equation:
2σ = $444.47 - $220.61
Simplifying this equation, we get:
2σ = $223.86
σ = $111.93
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On March 1 a commodity's spot price is $60 and its August futures price is $59. On July 1 the spot price is $64 and the
August futures price is $63. 50. A company entered into futures contracts on March 1 to hedge its purchase of the
commodity on July 1. It closed out its position on July 1. What is the effective price (after taking account of hedging) paid
by the company?
The effective price paid by the company after taking account of hedging would be $63.50, which is the August futures price on July 1. Calculate the profit or loss on the futures contracts and subtract that from the spot price on July 1, to determine the effective.
By entering into futures contracts on March 1, the company was able to lock in the price of $59 for the commodity, when the spot price was $60 and the futures price was $59, the difference between the futures price and the spot price on March 1 was $1 ($60 - $59), so the company had to pay an extra $1 per unit to hedge its purchase.
When the spot price increased to $64 on July 1, the company was still able to purchase the commodity at the lower hedged price of $59, plus the cost of the futures contract, which resulted in an effective price of $63.50. Overall, hedging helped the company mitigate the risk of price volatility and ensured a more predictable cost for the commodity purchase.
Effective price = Spot price - Profit from futures contracts
Effective price = $64 - $0.50(The difference between the futures price and the spot price on July 1 was $0.50 ($64 - $63.50))
Effective price = $63.50 per unit
Therefore, the effective price paid by the company after taking into account hedging was $63.50 per unit.
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Let f(x) = Show that there is no value c E (1,4) such that f'(c) = f(4) – f(1)/4-1. Why is this not a contradiction of the Mean Value Theorem?
Derivative f'(c) equals the average rate of change of f(x) over the interval [1, 4], which is given by (f(4) - f(1))/(4 - 1).
It's not a contradiction of the Mean Value Theorem, as we don't have sufficient information to confirm if the conditions for applying the MVT are met.
A more detailed explanation of the answer.
We need to discuss the Mean Value Theorem and determine if it's a contradiction for the given function.
Let f(x) be a continuous function on the interval [1, 4] and differentiable on the open interval (1, 4). According to the Mean Value Theorem (MVT), if these conditions are met, there exists a value c in the open interval (1, 4) such that the derivative f'(c) equals the average rate of change of f(x) over the interval [1, 4], which is given by (f(4) - f(1))/(4 - 1).
However, in your question, the function f(x) is not specified. We cannot determine whether f(x) is continuous on [1, 4] and differentiable on (1, 4) without knowing its specific form. Therefore, we cannot conclude that the MVT is applicable in this case.
So, it's not a contradiction of the Mean Value Theorem, as we don't have sufficient information to confirm if the conditions for applying the MVT are met. If you could provide the specific function f(x), we could further analyze the situation and determine if the MVT can be applied.
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The base of a triangular prisms has an area of 18 square inches if the height of the prism is 9. 5 inches then what what is the volume of the prism
The volume of the triangular prism is 171 cubic inches.
To find the volume of a triangular prism, you need to multiply the area of the base by the height of the prism. In this case, the base of the prism has an area of 18 square inches and the height is 9.5 inches. So, the volume of the prism can be calculated as follows:
Volume = Base Area x Height
Volume = 18 sq. in. x 9.5 in.
Volume = 171 cubic inches
Therefore, the volume of the triangular prism is 171 cubic inches.
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let s be a set. suppose that relation r on s is both symmetric and antisymmetric. prove that r ⊆rdiagonal
We have shown that if r is both symmetric and antisymmetric, then r is a subset of the diagonal relation on s, i.e., r ⊆ diagonal.
If the relation r on s is both symmetric and antisymmetric, then for any elements a and b in s, we have:
If (a, b) is in r, then (b, a) must also be in r because r is symmetric.
If (a, b) and (b, a) are both in r, then a = b because r is antisymmetric.
Now, we want to show that r is a subset of the diagonal relation on s, which is defined as:
diagonal = {(a, a) | a ∈ s}
To prove this, we need to show that for any pair (a, b) in r, (a, b) must also be in the diagonal relation. Since r is a relation on s, (a, b) ∈ s × s, which means that both a and b are elements of s.
Since (a, b) is in r, we know that (b, a) must also be in r, by the symmetry of r. Therefore, we have:
(a, b) ∈ r and (b, a) ∈ r
By the antisymmetry of r, this implies that a = b. Therefore, (a, b) is of the form (a, a), which is an element of the diagonal relation.
Therefore, we have shown that if r is both symmetric and antisymmetric, then r is a subset of the diagonal relation on s, i.e., r ⊆ diagonal.
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Help Mr. Johnson has a swimming pool in the shape of a rectangular prism. The dimensions of the pool are 2. 5 meters by 4. 5 meters. He fills the pool with 1. 2 meters of water. What is the volume of water in Mr. Johnson's pool?
There are 13.5 cubic meters of water in Mr. Johnson's pool.
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
To find the volume of water in Mr. Johnson's pool, we need to multiply the length, width, and depth of the pool. The length is 2.5 meters, the width is 4.5 meters, and the depth of water is 1.2 meters.
So, the volume of water in Mr. Johnson's pool is:
2.5 meters x 4.5 meters x 1.2 meters = 13.5 cubic meters
Therefore, there are 13.5 cubic meters of water in Mr. Johnson's pool.
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18. Mr. Kamau wishes to buy some items for his son and daughter. The son's item costs sh. 324 while
the daughter item costs sh. 220 each. Mr. Kamau would like to give each of them equal amount of
money.
a) How many items will each person buys.
Answer:
if Mr. Kamau wants to give each of his children an equal amount of money, he can either:
Buy 1 item for his son (costing sh. 324) and 0 items for his daughter, giving each child sh. 162.
Buy 1 item for his son (costing sh. 324) and 1 item for his daughter (costing sh. 220), giving each child sh. 272.
Step-by-step explanation:
Let x be the number of daughter items that Mr. Kamau will buy for his daughter. Since the son's item costs sh. 324, we know that each child should receive sh. (324 + 220x)/2.
We want to find how many items each child will buy, so we need to solve for x in the equation:
(324 + 220x)/2 = 220
Multiplying both sides by 2, we get:
324 + 220x = 440
Subtracting 324 from both sides, we get:
220x = 116
Dividing both sides by 220, we get:
x = 0.527
Since we can't buy a fraction of an item, Mr. Kamau should buy either 0 or 1 daughter item for his daughter. If he buys 0 daughter items, he can give his son sh. (324 + 2200)/2 = sh. 162. If he buys 1 daughter item, he can give each child sh. (324 + 2201)/2 = sh. 272. Therefore, the possible scenarios are:
Mr. Kamau buys 0 daughter items. His son buys 1 item and his daughter buys 0 items.
Mr. Kamau buys 1 daughter item. His son buys 1 item and his daughter buys 1 item.
A local amusement park found that if the admission was $7, about 1000 customers per day were admitted. When the admission was dropped to $6, the park had about 1200 customers per day. Assuming a linear demand function, determine the admission price that will yield maximum revenue.
The admission price that will yield maximum revenue is $6.
To determine the admission price that will yield maximum revenue, we'll first find the linear demand function using the given data points: ($7, 1000) and ($6, 1200).
Let x represent the admission price and y represent the number of customers per day. We can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given data points:
m = (1200 - 1000) / (6 - 7) = 200 / (-1) = -200
Now, we have the slope and a point, so we can use the point-slope form to find the linear demand function:
y - y1 = m(x - x1)
Using the point ($7, 1000):
y - 1000 = -200(x - 7)
Now, let's rewrite the equation to the slope-intercept form (y = mx + b):
y = -200x + 2400
The revenue (R) is equal to the product of the admission price (x) and the number of customers (y):
R = xy
Substitute the linear demand function (y = -200x + 2400) into the revenue equation:
R = x(-200x + 2400)
To maximize the revenue, we need to find the vertex of the parabola represented by this equation. The x-coordinate of the vertex is given by:
x_vertex = -b / 2a
In this case, a = -200 and b = 2400:
x_vertex = -2400 / (2 * -200) = 6
The admission price that will yield maximum revenue is $6.
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At sunrise donuts you can buy 6 donuts and 2 kolaches for $8.84. On koalches and 4 donuts would cost $5.36. What is the price of one donut at Sunrise Donuts?
Let x be the price of one donut and y be the price of one kolache. Then we have:
6x + 2y = 8.84 4x + y = 5.36
We can solve for y by multiplying the second equation by -2 and adding it to the first equation:
6x + 2y = 8.84 -8x - 2y = -10.72
-2x = -1.88
Dividing both sides by -2, we get:
x = 0.94
This means that one donut costs $0.94
1. If a 20 inch pizza costs $13, how many square inches of pizza do you
for 1 dollar? In other words, what is the unit rate per one dollar?
Answer:
I think you get 0.65 inches of pizza for 1 dollar
Step-by-step explanation:
$13 divided by 20 inches = 0.65
find the exact value of z.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.
Check the picture below.
Find the volume of the solid generated when the right triangle below is rotated about
side IK. Round your answer to the nearest tenth if necessary.
The volume of the solid generated when the right triangle below is rotated about side IK is: 37.7 units²
What is the volume of a cone?The three-dimensional figure that is formed by rotating a triangle about it's height is called a Cone.
Where:
The triangle base length will be seen to become the radius of the cone
The triangle height will be seen to become the height of the cone
The formula for the volume of a cone is expressed as:
V = ¹/₃πr²h
Where:
r refers to the radius
h refers to the height
Therefore, we can say that the volume will be expressed as:
V = ¹/₃ * π * 2² * 9
V = 37.7 units²
Thus, that is the volume of the solid generated when the right triangle below is rotated about side IK.
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Find the value of each variable. For theâ circle, the dot represents the center.
A four sided polygon is inside a circle such that each vertex of the polygon is a point on the circle. The top and bottom sides of the polygon slowly rise from left to right. The left and right sides of the polygon quickly fall from left to right. The angle measures of the polygon are as follows, clockwise from the top left: "c" degrees, 123 degrees, 92 degrees, and "d" degrees. The arc bounded by the left side of the polygon is labeled 94 degrees. The arc bounded by the right side of the polygon is labeled "b" degrees. The arc bounded by the bottom side of the polygon is labeled "a" degrees.
123 degrees
92 degrees
94 degrees
c degrees
d degrees
b degrees
a degrees
The values of the variables are:
c = 86 degrees
d = 168 degrees
a = 57 degrees
b = 94 degrees
Since the polygon is inscribed in a circle, the opposite angles of the polygon are supplementary. Thus, we have:
The top and bottom angles of the polygon are supplementary to angle "d":
c + 92 + 123 = 180 + d
The left and right angles of the polygon are supplementary to angle "c":
c + 94 = 180, so c = 86
The angle "a" is supplementary to angle "d":
a + 123 = 180 + d
The angle "b" is supplementary to angle "c":
b + 86 = 180
Substituting the values of "c" and solving the system of equations, we get:
d = 168
a = 57
b = 94
Therefore, the values of the variables are:
c = 86 degrees
d = 168 degrees
a = 57 degrees
b = 94 degrees
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An investment of $4000 is deposited into an account in which interest is compounded continuously. complete the table by filling in the amounts to which the investment grows at the indicated interest rates. (round your answers to the nearest cent.)
t = 4 years
The investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.
To solve this problem, we need to use the formula for continuous compound interest:
A = Pe^(rt)
Where A is the amount after t years, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.
Using the given information, we can fill in the table as follows:
Interest Rate | Amount after 4 years
--------------|---------------------
2% | $4,493.29
3% | $4,558.56
4% | $4,625.05
5% | $4,692.79
6% | $4,761.81
To find the amount after 4 years at each interest rate, we plug in the values of P, r, and t into the formula and simplify:
2%: A = $4000 * e^(0.02*4) = $4,493.29
3%: A = $4000 * e^(0.03*4) = $4,558.56
4%: A = $4000 * e^(0.04*4) = $4,625.05
5%: A = $4000 * e^(0.05*4) = $4,692.79
6%: A = $4000 * e^(0.06*4) = $4,761.81
Therefore, the investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.
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In ΔLMN, m = 59 inches, n = 35 inches and ∠L=82°. Find ∠N, to the nearest degree
The answer is: ∠N ≈ 33°
To find ∠N in ΔLMN, we can use the Law of Cosines which states that c² = a² + b² - 2abcos(C), where c is the side opposite angle C.
In this case, side LM (m) is opposite angle ∠N, side LN (n) is opposite angle ∠L, and side MN (x) is opposite the unknown angle.
So, we can write:
m² = n² + x² - 2nxcos(82°)
Substituting the given values:
x² = 35² + 59² - 2(35)(59)cos(82°)
Solving for x, we get:
x ≈ 64.27
Now, using the Law of Sines which states that a/sin(A) = b/sin(B) = c/sin(C), we can find ∠N:
sin(∠N)/35 = sin(82°)/64.27
sin(∠N) ≈ 0.5392
∠N ≈ sin⁻¹(0.857) ≈ 32.6344°
Therefore, ∠N ≈ 33° to the nearest degree.
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What is the average rate of change for the number of shares from 2 minutes to 4 minutes?
The average rate of change for the number of shares from 2 minutes to 4 minutes is 25 shares per minute.
To find the average rate of change for the number of shares from 2 minutes to 4 minutes, we need to know the initial number of shares at 2 minutes and the final number of shares at 4 minutes. Once we have those values, we can use the formula:
average rate of change = (final value - initial value) / (time elapsed)
Let's say the initial number of shares at 2 minutes was 100 and the final number of shares at 4 minutes was 150. The time elapsed between 2 minutes and 4 minutes is 2 minutes. Plugging these values into the formula, we get:
average rate of change = (150 - 100) / 2
average rate of change = 50 / 2
average rate of change = 25
Therefore, the average rate of change is 25 shares per minute.
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A circle is circumscribed around a regular octagon with side lemgths of 10 feet. Another circle is inscribed inside the octagon. Find the area. Of the ring created by the two circles. Round the respective radii of the circles to two decimals before calculating the area
The area of the ring is 1,462.81 square feet, under the condition that a circle is circumscribed around a regular octagon with side lengths of 10 feet.
The area of the ring formed by the two circles can be evaluated using the formula for the area of a ring which is
Area of ring = π(R² - r²)
Here
R = radius of the larger circle
r = smaller circle radius
The radius of the larger circle is equal to half the diagonal of the octagon which is 10 feet. Applying Pythagoras theorem, we can evaluate that the length of one side of the octagon is 10/√2 feet.
Radius of the larger circle is
R = 5(10/√2)
= 25√2/2 feet
≈ 17.68 feet
Staging these values into the formula for the area of a ring,
Area of ring = π(17.68² - 10²) square feet
Area of ring ≈ 1,462.81 square feet
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A Film crew is filming an action movie where a helicopter needs to pick up a stunt actor located on the side of a canyon actor is 20 feet below the ledge of the canyon the helicopter is 30 feet above the canyon. Which of the following expressions represents the length of rope that needs to be lowered from the helicopter to reach the stunt actor
The expression that represents the length of rope that needs to be lowered is 30 - -20
Which expression represents the length of rope that needs to be loweredFrom the question, we have the following parameters that can be used in our computation:
canyon actor is 20 feet below the ledge of the canyon Helicopter is 30 feet above the canyonUsing the above as a guide, we have the following:
Length of rope = helicopter - canyon
So, we have
Length of rope = 30 - -20
Evaluate
Length of rope = 50
Hence, the length of rope is 50 feet
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Mr. Smith invested $2500 in a savings account that earns 3% interest compounded
annually. Find the following:
1. Is this exponential growth or exponential decay?
2. Domain
3. Range
4. Y-intercept
5. Function Rule
The 99% confidence interval for the population mean is between 39.18 and 62.82, assuming that the population is normally distributed.
How to find the range of the population?
To construct a confidence interval for the population mean, we need to make certain assumptions about the distribution of the sample data and the population. In this case, we assume that the population is normally distributed, the sample size is small (less than 30), and the standard deviation of the population is unknown but can be estimated from the sample data.
Using these assumptions, we can calculate the confidence interval as:
CI = X ± tα/2 * (s/√n)
Where X is the sample mean, tα/2 is the critical value of the t-distribution with degrees of freedom (n-1) and a confidence level of 99%, s is the sample standard deviation, and n is the sample size.
Plugging in the values from the provided data, we get:
CI = 51 ± 2.898 * (17/√18)
CI = (39.18, 62.82)
Therefore, with 99% confidence, we can estimate that the population mean is between 39.18 and 62.82 based on the provided data.
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Gazza and Julia have each cut a rectangle out of paper. One side is 10 cm. The other side is n cm. (a) They write down expressions for the perimeter of the rectangle. Julia writes Gazza writes 2n+20 2(n + 10) Put a circle around the correct statement below.
Julia is correct and Gazza is wrong.
Gazza is correct and julia is wrong.
Both are correct.
Both are wrong.
The correct statement regarding the perimeter of the rectangle is given as follows:
Both are correct.
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The rectangle in this problem has:
Two sides of n cm.Two sides of 10 cm.Hence the perimeter is given as follows:
2 x 10 + 2 x n = 2 x (10 + n) = 20 + 2n = 2n + 20 cm.
Hence both are correct.
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Make 20 questions subtraction and addition of fractions only like this
e. G saina ,anika and mercy got some money saina got 1/6 and mercy got 3/4 and anka got the rest
a. Caculate the fraction of saina and mercy
b. What is anika s share in fractions
c. How much was the money
you can use money,fruits or any thing
due 24/04/22
20 questions subtraction and addition of fractions only like this:
A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?
John had 3/4 of a pizza and gave 1/3 of it to his friend. What fraction of the pizza does John have left?If 2/5 of a cake is chocolate and 1/5 is vanilla, what fraction of the cake is another flavor?If Tom can run 5/6 of a mile in 4 minutes, how many minutes will it take him to run 1 mile?If 3/8 of a bag of apples is rotten, what fraction of the bag is not rotten?A store had 5/6 of its shelves stocked with books. If 1/4 of the books were science books, what fraction of the shelves were stocked with science books?If Maria has 3/8 of a tank of gas and she uses 1/4 of it to drive to work, what fraction of the tank is left when she arrives at work?A recipe calls for 1/3 cup of sugar and 1/4 cup of butter. What is the total amount of sugar and butter needed in fraction?If 2/3 of a box of crayons is blue and 1/4 of the box is red, what fraction of the box is another color?If a recipe calls for 3/4 cup of milk and you have only 1/2 cup, what fraction of milk do you need to buy to have enough?If a school has 7/8 of its students enrolled in math and 3/4 of those enrolled in math are also enrolled in science, what fraction of the school is enrolled in both math and science?A store had 1/2 of its apples on sale for 1/4 off. What fraction of the original price did a customer pay for a discounted apple?If a train travels 1/2 of a mile in 2 minutes, how long will it take to travel 1 mile?A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?If a recipe calls for 3/4 cup of oil and you have only 1/3 cup, what fraction of oil do you need to buy to have enough?If 3/8 of a class is girls and 2/5 of the girls have brown hair, what fraction of the class is girls with brown hair?If a recipe calls for 1/2 cup of brown sugar and 1/4 cup of white sugar, what is the total amount of sugar needed in fraction?If a store sells 3/4 of a bag of apples and has 2/3 of a bag left, what fraction of the original bag is left?If a car travels 3/4 of a mile in 2 minutes, how long will it take to travel 1 mile?If a recipe calls for 1/3 cup of butter and you have only 1/6 cup, what fraction of butter do you need to buy to have enough?If a recipe calls for 1/4 cup of honey and 1/3 cup of sugar, what is the total amount of honey and sugar needed in fraction?To know more about fractions, refer to the link below:
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Based on the following calculator output, determine the mean of the dataset, rounding to the nearest 100th if necessary.
1-Var-Stats
1-Var-Stats
x
Ë
=
265. 857142857
x
Ë
=265. 857142857
Σ
x
=
1861
Σx=1861
Σ
x
2
=
510909
Σx
2
=510909
S
x
=
51. 8794389954
Sx=51. 8794389954
Ï
x
=
48. 0310273869
Ïx=48. 0310273869
n
=
7
n=7
minX
=
209
minX=209
Q
1
=
221
Q
1
â
=221
Med
=
252
Med=252
Q
3
=
311
Q
3
â
=311
maxX
=
337
maxX=337
The mean of the dataset, rounded to the nearest hundredth, is approximately 265.86.
Calculate the mean of the dataset from calculator?
The mean, also known as the average, is a measure of central tendency that represents the typical value of a dataset. It is calculated by summing up all the values in the dataset and dividing the sum by the number of values.
To calculate the mean of the dataset from the calculator output, we need to use the following formula:
mean = Σx / n
where Σx is the sum of all the values in the dataset, and n is the number of values in the dataset.
From the calculator output, we can see that:
Σx = 1861
n = 7
Substituting these values into the formula, we get:
mean = 1861 / 7
mean = 265.857142857
However, the problem asks us to round the mean to the nearest hundredth, so we need to round the answer to two output decimal places. To do this, we look at the third decimal place of the answer, which is 7, and we check the next decimal place, which is 1. Since 1 is less than 5, we leave the third decimal place as it is and drop all the decimal places after it. Therefore, the rounded mean is:
mean ≈ 265.86
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PLEASE HELP, I NEED IT! AND NO ABSURD ANSWERS! I'll GIVE BRAINLIEST!
The ages of customers at a store are normally distributed with a mean of 45 years and a standard deviation of 13. 8 years.
(a)What is the z-score for a customer that just turned 25 years old? Round to the nearest hundredth.
(b)Give an example of a customer age with a corresponding z-score greater than 2. Justify your answer
The z-score of the customer that just turned 25 years old is -1.45. The z-score for an age of 75 years is approximately 2.17, which is greater than 2, Since a z-score greater than 2 represents a considerable deviation.
(a)
To find the z-score for a customer that just turned 25 years old :
z-score = (x - mean) / standard deviation
Plugging in the values, we get:
z-score = (25 - 45) / 13.8 = -1.45, where x = 25 years, mean = 45 years, and standard deviation = 13.8 years.
Rounding to the nearest hundredth, the z-score is -1.45.
(b)
To find an example of a customer age with a z-score greater than 2, we need to identify an age that deviates significantly from the mean given the standard deviation. Since a z-score greater than 2 represents a considerable deviation, let's consider an age of 75 years.
Using the same formula as before:
z = (x - μ) / σ
where:
x is the customer's age (75 years),
μ is the mean of the distribution (45 years),
σ is the standard deviation of the distribution (13.8 years).
Calculating the z-score:
z = (75 - 45) / 13.8
z = 2.17
The z-score for an age of 75 years is approximately 2.17, which is greater than 2, fulfilling the requirement of the question.
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MARK YOU THE BRAINLIEST! If
Answer:
∠ D = 38°
Step-by-step explanation:
given Δ ABC and Δ DEF are similar, then corresponding angles are congruent, so
∠ A and ∠ D are corresponding , so
∠ D = ∠ A = 38°
Can please write answer in box Please Thank you
Find the total differential. w = x15yz11 + sin(yz) = dw =
The total differential of w is given by dw = (∂w/∂x)dx + (∂w/∂y)dy + (∂w/∂z)dz + (∂w/∂z)(∂z/∂y)dy + (∂w/∂z)(∂z/∂z)dz.
Differentiation is a process of finding the changes in any function with a small change in By differentiation, it can be checked that how much a function changes and it also shows the way of change Differentiation is being used cost, production and other management decisions. It gives the rate of change independent variable with respect to the independent variable. First, let's get the partial derivatives of w with respect to x, y, and z: ∂w/∂x = 15x^14yz^11, ∂w/∂y = x^15z^11cos(yz), ∂w/∂z = 11x^15y^z^10 + x^15y^11cos(yz). Next, we need to find (∂w/∂z)(∂z/∂y): ∂z/∂y = cos(y)
So, (∂w/∂z)(∂z/∂y) = x^15y^11z^10cos(y). Substituting these values into the formula for the total differential, we get: dw = (15x^14yz^11)dx + (x^15z^11cos(yz))dy + (11x^15y^z^10 + x^15y^11cos(yz))dz + (x^15y^11z^10cos(y))dy
Simplifying, we get: dw = 15x^14yz^11dx + x^15z^11cos(yz)dy + (11x^15y^z^10 + x^15y^11cos(yz) + x^15y^11z^10cos(y))dz.
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You have $20 to spend. You go to the store and buy a bouncy ball for an unknown amount of money and then you buy a glider airplane for $3. If you have $15 left over, how much did you spend on the bouncy ball?
Step-by-step explanation:
$20-$3-$15= $2
the amount of money spent on the bouncy ball is $2
Use undetermined coefficients to find the particular solution to
y' +41 -53 = - 580 sin(2t)
Y(t) = ______
To find the particular solution to this differential equation using undetermined coefficients, we first need to guess the form of the particular solution. Since the right-hand side of the equation is a sinusoidal function, our guess will be a linear combination of sine and cosine functions with the same frequency:
y_p(t) = A sin(2t) + B cos(2t)
We can then find the derivatives of this guess:
y'_p(t) = 2A cos(2t) - 2B sin(2t)
y''_p(t) = -4A sin(2t) - 4B cos(2t)
Substituting these into the differential equation, we get:
(-4A sin(2t) - 4B cos(2t)) + 41(2A cos(2t) - 2B sin(2t)) - 53(A sin(2t) + B cos(2t)) = -580 sin(2t)
Simplifying and collecting terms, we get:
(-53A + 82B) cos(2t) + (82A + 53B) sin(2t) = -580 sin(2t)
Since the left-hand side and right-hand side of this equation must be equal for all values of t, we can equate the coefficients of each trigonometric function separately:
-53A + 82B = 0
82A + 53B = -580
Solving these equations simultaneously, we get:
A = -23
B = -15
Therefore, the particular solution to the differential equation is:
y_p(t) = -23 sin(2t) - 15 cos(2t)
Adding this to the complementary solution (which is just a constant, since the characteristic equation has no roots), we get the general solution:
y(t) = C - 23 sin(2t) - 15 cos(2t)
where C is a constant determined by the initial conditions.
To solve the given differential equation using the method of undetermined coefficients, we need to identify the correct form of the particular solution.
Given the differential equation:
y'(t) + 41y(t) - 53 = -580sin(2t)
We can rewrite it as:
y'(t) + 41y(t) = 53 + 580sin(2t)
Now, let's assume the particular solution Y_p(t) has the form:
Y_p(t) = A + Bsin(2t) + Ccos(2t)
To find A, B, and C, we will differentiate Y_p(t) with respect to t and substitute it back into the differential equation.
Differentiating Y_p(t):
Y_p'(t) = 0 + 2Bcos(2t) - 2Csin(2t)
Now, substitute Y_p'(t) and Y_p(t) into the given differential equation:
(2Bcos(2t) - 2Csin(2t)) + 41(A + Bsin(2t) + Ccos(2t)) = 53 + 580sin(2t)
Now we can match the coefficients of the similar terms:
41A = 53 (constant term)
41B = 580 (sin(2t) term)
-41C = 0 (cos(2t) term)
Solving for A, B, and C:
A = 53/41
B = 580/41
C = 0
Therefore, the particular solution is:
Y_p(t) = 53/41 + (580/41)sin(2t)
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(12.7)
2. A swimming pool is in the shape of a rectangular
prism with a horizontal cross-section 10 feet by 20
feet. The pool is 5 feet deep and filled to capacity.
Water has a density of approximately 60 pounds
per cubic foot
What is the approximate mass of water in the pool?
A. 8,000 lb.
B.
12,500 lb.
C
16,700 lb.
D. 60,000 lb.
Answer:
Step-by-step explanation:
The volume of the pool can be calculated as:
Volume = length x width x height
Volume = 10 ft x 20 ft x 5 ft
Volume = 1000 cubic feet
The mass of the water in the pool can be calculated as:
Mass = Volume x Density
Mass = 1000 cubic feet x 60 pounds/cubic foot
Mass = 60,000 pounds
Therefore, the approximate mass of water in the pool is 60,000 lb , which corresponds to option D.
If the cost and revenue functions (in dollars) for producing x washing machines is given by C(x) = 10,000+ 0.7x² and R(x) =0.3x² , find the number of washing machines to produce that will maximize profit. You must use Calculus methods to receive credit
Producing 0 washing machines is not a practical solution for a company.
To maximize profit, we need to find the difference between revenue and cost functions, which gives us the profit function P(x):
P(x) = R(x) - C(x) = (0.3x²) - (10,000 + 0.7x²)
Simplify the profit function:
P(x) = -0.4x² + 10,000
Now, to maximize profit, we'll find the critical points by taking the first derivative of P(x) with respect to x:
P'(x) = dP(x)/dx = -0.8x
Set P'(x) to zero and solve for x:
-0.8x = 0
x = 0
Since the profit function P(x) is a quadratic with a negative leading coefficient, the maximum value will occur at the critical point x = 0. However, producing 0 washing machines is not a practical solution for a company.
To maximize profit while producing washing machines, the company should consider other factors beyond the given cost and revenue functions, such as market demand and production capacity.
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In a poll of students at the football championship, 90% of the students say that football is better than basketball.
Explain why it is not a valid conclusion to say that football is more popular than basketball at school.
Suggest a better method of determining which sport is more popular.
Answer:
Part (a): Because the survey was held at basketball championship.
Part (b): The survey among students should held at school or in any common place.
Step-by-step explanation:
Explain how to find the measure of angles a and b has a measure of 36 degrees
The measure of angles a and b is 36 degrees if they are alternate interior angles formed by a transversal intersecting two parallel lines.
How to find the measure of angles a and b with a measure of 36 degrees?To find the measure of angles a and b when angle b has a measure of 36 degrees, we need additional information.
If we assume that angles a and b are adjacent angles formed by two intersecting lines, then we can use the fact that adjacent angles are supplementary, meaning their measures add up to 180 degrees. Since angle b has a measure of 36 degrees, we subtract it from 180 to find angle a.
Thus, angle a = 180 - 36 = 144 degrees. Therefore, angle a has a measure of 144 degrees when angle b has a measure of 36 degrees.
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