The length of CD is 6 inches.
We can start by finding the area of triangle EDC
Area of triangle EDC = Area of triangle EDB - Area of triangle EBC
= 60.5 - 27.5
= 33
Using the formula for the area of a triangle, we can write
Area of triangle EDC = (1/2) * CD * ED
Substituting the given values, we get
33 = (1/2) * CD * 11
Multiplying both sides by 2 and then dividing by 11, we get
CD = 6
Therefore, CD is 6 inches.
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Find the 49th term.
-15, -10, -5, O, 5, ...
49th term = [?]
1st term + common difference(desired term - 1)
Enter
Answer:
49th term = 225
Step-by-step explanation:
The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.
An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.
The general formula, for the nth term of an arithmetic progression, is thus:
Tn = a + (n - 1)d, where a = first term, and d = common difference.
In the sequence: -15, -10, -5, 0, 5...,
a = -15, and d = -10--15 = 5
T49 = -15 + (49 - 1)5 = 225
∴ 49th term = 225
PLEASE HELP!!!! I NEED HELP ASAP PLEASE!!!!!!!! IM TRYING SO HARD TO GET MY GRADE UP !!!
Determine the likelihood that the following event will occur:
Rolling a number greater than 7 on a number cube with sides numbered 1 through 6.
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Determine the likelihood that the following event will occur:
Picking the 8 of Hearts from a standard deck of playing cards.
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Determine the likelihood that the following event will occur:
A spinner with 6 equal sections labeled 1 through 6 lands on a number less than 7.
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Determine the likelihood that the following event will occur:
Flipping a coin and having it land with the heads side facing up.
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Determine the likelihood that the following event will occur:
Rolling a sum of 14 with two number cubes with sides 1-6.
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What is the probability of rolling an even number on a dice? The dice is numbered 1-6
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The following M & M colors are in the bowl: 4 yellow, 6 orange, 3 green, 5 blue, 2 brown. What is the probability of selecting a blue candy?
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A number cube is labeled 1 through 6. The probability of randomly rolling a 4 is 1 over 6. What is the probability of not rolling a 4?
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Determine the likelihood that the following event will occur:
Picking a purple ball from a bag containing 7 purple balls and 1 green ball.
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Answer:
Step-by-step explanation:
Rolling a number greater than 7 on a number cube with sides numbered 1 through 6: The probability of rolling a number greater than 7 on a number cube with sides numbered 1 through 6 is 0, as it is not possible to roll a number greater than 6 on a standard six-sided die.
Picking the 8 of Hearts from a standard deck of playing cards: The probability of picking the 8 of Hearts from a standard deck of playing cards is 0, as there is no 8 of Hearts in a standard deck of playing cards.
A spinner with 6 equal sections labeled 1 through 6 lands on a number less than 7: The probability of a spinner with 6 equal sections labeled 1 through 6 landing on a number less than 7 is 1, as all the sections are labeled with numbers less than 7.
Flipping a coin and having it land with the heads side facing up: The probability of flipping a coin and having it land with the heads side facing up is 0.5 or 50%, assuming the coin is fair and has two equally likely sides.
Rolling a sum of 14 with two number cubes with sides 1-6: The probability of rolling a sum of 14 with two number cubes with sides 1-6 is 0, as the highest possible sum that can be obtained by rolling two number cubes with sides 1-6 is 12 (6 + 6).
What is the probability of rolling an even number on a dice? The dice is numbered 1-6: The probability of rolling an even number on a dice numbered 1-6 is 0.5 or 50%, as there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5) on a standard six-sided die.
The following M & M colors are in the bowl: 4 yellow, 6 orange, 3 green, 5 blue, 2 brown. What is the probability of selecting a blue candy? The probability of selecting a blue candy from the bowl is 5/20 or 1/4, as there are 5 blue candies in the bowl out of a total of 20 candies.
A number cube is labeled 1 through 6. The probability of randomly rolling a 4 is 1 over 6. What is the probability of not rolling a 4? The probability of not rolling a 4 on a number cube labeled 1 through 6 is 5/6, as there are 5 possible outcomes that are not 4 (1, 2, 3, 5, and 6) out of a total of 6 possible outcomes.
Picking a purple ball from a bag containing 7 purple balls and 1 green ball: The probability of picking a purple ball from a bag containing 7 purple balls and 1 green ball is 7/8, as there are 7 purple balls out of a total of 8 balls in the bag.
im sorry I don't know how to delete this but i now realize that my awnser was completely wrong.
onsider a partial output from a cost minimization problem that has been solved to optimality. Final Shadow Constraint Allowable Allowable Name Value Price R.H. Side Increase Decrease Labor Time 700 700 100 200 The Labor Time constraint is a resource availability constraint. What will happen to the dual value (shadow price) if the right-hand-side for this constraint decreases to 400? The Labor Time constraint is a resource availability constraint. What will happen to the dual value (shadow price) if the right-hand-side for this constraint decreases to 400? O It will remain at -6. It will become a less negative number, such as -4. It will become zero. O It will become a more negative number, such as -8. . It will become zero or less negative.
If the right-hand-side for the Labor Time constraint decreases to 400, the dual value (shadow price) will become a more negative number, such as -8.
This is because the constraint is tighter, and the reduced availability of labor time will make the resource more valuable in the cost minimization problem. The new allowable increase in the right-hand-side will be smaller and the allowable decrease will be larger, reflecting the increased importance of meeting the resource constraint. This is because the decrease in resource availability means that the value of an additional unit of that resource has increased, leading to a higher cost of not having enough of it.
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a survey by the national consumers league estimated the nationwide proportion to be 0.41 using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.03 ?
We'd need a sample size of at least 659 to estimate the population proportion with a periphery of error of 0.03.
To find the sample size demanded a confidence interval with a periphery of error of 0.03, we need to use the following formula
n = ( zσ/ E) * ( zσ/ E) * pq
where
z is the z- score corresponding to the asked position of confidence( let's assume 95 confidence, which corresponds to a z- score of 1.96)
σ is the population standard deviation( which is unknown in this case, so we'll use a conservative estimate of0.5)
E is the periphery of error( which is0.03)
p is the estimated proportion( which is0.41)
q = 1- p
Plugging in the values, we get
n = (1.960.5/0.03) * (1.960.5/0.03*0.41( 1-0.41) ≈658.72
Rounding up, we get a sample size of 659. thus, we'd need a sample size of at least 659 to estimate the population proportion with a periphery of error of 0.03, assuming a 95 confidence position and a population proportion estimate of 0.41.
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a bacteria culture starts with 40 bacteria and grows at a rate proportional to its size. after 2 hours there are 180 bacteria. find the number of bacteria after 5 hours.
The number of bacteria after 5 hours is approximately 1013.8.
We can use the formula for exponential growth to solve this problem. If a population grows at a rate proportional to its size, then we can writ
N(t) = N₀ × e^(rt),
where N(t) is the size of the population at time t, N₀ is the initial size of the population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.
We know that the culture starts with 40 bacteria, so N₀ = 40. We also know that after 2 hours, the size of the population is 180. We can use this information to solve for r:
180 = 40 × e^(2r)
180/40 = e^(2r)
ln(180/40) = 2r
r = ln(180/40)/2
r ≈ 0.6931
Now we can use the formula to find the size of the population after 5 hours:
N(5) = 40 × e^(0.6931×5)
N(5) ≈ 1013.8
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Please help me with this homework
Answer:47
7•7
Step-by-step explanation:
The name of the rule used in Normal Distribution Curves is called the
A) Kings Rule
B) Queens Rule
C) Students Rule
D) Empirical Rule
7. Volunteer drivers are needed to bring 80 students to the championship baseball
game. Drivers either have cars, which can seat 4 students, or vans, which can seat 6
students. The equation 4c +6v = 80 describes the relationship between the number
of cars c and number of vans v that can transport exactly 80 students.
Answer: To solve for c and v, we need to use the equation:
4c + 6v = 80
We have two variables and one equation, so we need another equation to solve for c and v. We can use the fact that the number of students transported by the drivers is 80. Since each car can seat 4 students and each van can seat 6 students, we can write:
4c + 6v = 80
c + v = number of drivers
Since we want to minimize the number of drivers, we want to minimize the value of c + v. We can use substitution to solve for c and v in terms of one variable. Solving for c in terms of v from the first equation, we get:
4c + 6v = 80
4c = 80 - 6v
c = (80 - 6v)/4
Substituting this expression for c into the second equation, we get:
c + v = number of drivers
(80 - 6v)/4 + v = number of drivers
Multiplying both sides by 4 to clear the fraction, we get:
80 - 6v + 4v = 4(number of drivers)
80 - 2v = 4(number of drivers)
20 - 0.5v = number of drivers
We want to minimize the value of c + v, so we want to minimize the value of v. Since v must be a whole number, we want to find the smallest integer value of v that satisfies the equation. We can plug in integer values of v and find the corresponding value of c, and check if the sum of c and v is less than or equal to the current minimum. Starting with v = 1, we get:
v = 1 -> c = 19.5 -> c + v = 20.5
v = 2 -> c = 18.0 -> c + v = 20.0
v = 3 -> c = 16.5 -> c + v = 19.5
v = 4 -> c = 15.0 -> c + v = 19.0
v = 5 -> c = 13.5 -> c + v = 18.5
v = 6 -> c = 12.0 -> c + v = 18.0
The smallest integer value of v that satisfies the equation is v = 6, which gives c = 12. Therefore, we need 12 cars and 6 vans to transport 80 students.
Step-by-step explanation:
GIVE THE DOMAIN FOR WHICH THE GRAPH IS NONLINEAR (CURVED).
what is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes? (round your answer to four decimal places.)
The Probability that a student will complete the exam 0.2676.
The probability of completing the exam in one hour or less is:
[tex]P (x < 60)[/tex]
= [tex]P (z < (60-83)/13)[/tex]
=[tex]P (z < -1.77)[/tex]
= 0.0384.
The probability that a student will complete the exam in more than 60 minutes, but less than 75 minutes is.
[tex]P (60 < x < 75)[/tex]
= [tex]P (x < 75)-P (x < 60)[/tex]
Now,
[tex]P (x < 75)[/tex]
=[tex]P (z < (75-83)/13)[/tex]
= [tex]P (z < -0.62)[/tex]
=0.2676.
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The incline of a skateboard ramp is 5.5 feet long .If the height of the ramp is 3 feet ,what is the angle of elevation that the ramp makes with the ground ?round to the nearest degree
Answer:
The ramp makes a 33.06° or 33° angle with the ground.
Step-by-step explanation:
Given: h = 5.5 ft
o = 3 ft
Let's call the angle as angle A
The ramp forms a right triangle. We can then use the concept of pythagorean theorem.
Since the angle of elevation is opposite the height of 3ft and hypotenuse is given as 5.5 ft then we can use sinA = opposite/hypotenuse
Solve:
sin A = 3ft/5.5ft
sin A = 0.5454
A = Arcsin 0.5454
A = 33.06°
2)
Phillip has 8 red balls, 3 green balls, 6 yellow balls, 3 orange balls, 13 black balls
and 15 blue balls in his bag.
Mean: | 0,2, Median :
Mode:
Range
The results of the balls in Phillip's bag are:
The mean = 8.
The median = 7.
The mode = blue
The range = 12
How do we calculate the Mean, Median, Mode and Range?The mean (or the average) is the sum of all the values divided by the total number of values. Let's calculate the mean for the given data:
Total number of balls = 8 + 3 + 6 + 3 + 13 + 15 = 48
Mean = (8 + 3 + 6 + 3 + 13 + 15) / 6 = 48 / 6 = 8
Mean = 8.
The median is the middle value when a set of values is arranged in ascending or descending order.
Let's arrange the given data in ascending:
3, 3, 6, 8, 13, 15
As the total number of values is even, the median will be the average of the two middle values, which are 6 and 8.
Median = (6 + 8) / 2 = 7
The median = 7.
The mode is the value that appears most frequently in a set of values. Let's find the mode of the given data:
Red balls: 8
Green balls: 3
Yellow balls: 6
Orange balls: 3
Black balls: 13
Blue balls: 15
Blue balls have the highest frequency (i.e., 15) among all the colors.
The range is the difference between the highest and lowest values in a set of values. Let's find the range of the given data:
Highest value = 15 (blue balls)
Lowest value = 3 (green balls and orange balls)
Range = Highest value - Lowest value = 15 - 3 = 12
Range = 12.
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What is the better estimate?
10 quarts or 10 gallons.
2 cups or 2 quarts.
The better estimate is 10 gallons and 2 quarts.
What are meaurements?10 gallons is a better estimate than 10 quarts because a gallon is larger than a quart. In fact, there are 4 quarts in a gallon. Therefore, 10 gallons is equivalent to 40 quarts, which is clearly larger than 10 quarts.
2 quarts is a better estimate than 2 cups because a quart is larger than a cup. In fact, there are 4 cups in a quart. Therefore, 2 quarts is equivalent to 8 cups, which is clearly larger than 2 cups.
Thus, the better estimates are 10 gallons and 2 quarts.
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It depends on the context in which the estimates are being used.
What is gallons?Gallons are a unit of measurement for volume commonly used in the United States and other countries. It is often used to measure the volume of liquids, such as gasoline, water, or milk.
Define Quarts?
It is a British unit of liquid or dry capacity equal to ¹/₄ gallon or 69.355 cubic inches or 1.136 liters.
If the estimates are for measuring liquid volume, then 10 gallons would be a better estimate than 10 quarts as it is a larger unit of measurement.
Similarly, if the estimates are for measuring liquid volume, then 2 quarts would be a better estimate than 2 cups as it is a larger unit of measurement.
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is $60 a resonable tax for a purchase of $120 what likey caused herschel to make the mistake
the pages per book in a library are normally distributed with a population standard deviation of 45 pages and an unknown population mean. a random sample of 15 books is taken and results in a sample mean of 305 pages. what is the correct interpretation of the 99% confidence interval? select the correct answer below: we estimate that 99% of the books in the library have between 275 and 335 pages. we estimate with 99% confidence that the sample mean is between 275 and 335 pages. we estimate with 99% confidence that the true population mean is between 275 and 335 pages.
Therefore, the 99% confidence interval for the population mean is 305 - 30 to 305 + 30, which is between 275 and 335 pages.
The correct interpretation of the 99% confidence interval is that we estimate with 99% confidence that the true population mean is between 275 and 335 pages. This is because the confidence interval is based on the sample mean and the standard deviation of the sample, and it provides a range of values within which we can be reasonably confident that the true population mean lies. The fact that the sample was randomly selected helps to ensure that the estimate is representative of the overall population of books in the library. The population standard deviation of 45 pages is used to calculate the standard error of the mean, which in turn is used to construct the confidence interval.
We estimate with 99% confidence that the true population mean is between 275 and 335 pages.
Explanation:
1. A random sample of 15 books is taken from the library.
2. The sample mean (305 pages) is calculated from the random sample.
3. The population standard deviation is given as 45 pages.
4. To construct a 99% confidence interval for the population mean, we need to use the standard deviation and the sample mean.
5. The formula for the margin of error in a confidence interval is: Margin of Error = Z-score * (Standard Deviation / [tex]\sqrt{SampleSize}[/tex])
6. For a 99% confidence interval, the Z-score is approximately 2.576.
7. Margin of Error = 2.576 * (45 / √15) ≈ 30
8. The confidence interval for the population mean is: (Sample Mean - Margin of Error) to (Sample Mean + Margin of Error)
9. Therefore, the 99% confidence interval for the population mean is 305 - 30 to 305 + 30, which is between 275 and 335 pages.
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the correct interpretation of the 99% confidence interval is:
"We estimate with 99% confidence that the true population mean is between 275.08 and 334.92 pages."
Based on the given information, we can calculate the 99% confidence interval for the true population mean of pages per book in the library.
Here are the steps to calculate the confidence interval:
Identify the given information:
population standard deviation [tex](\sigma) = 45[/tex] pages, sample size [tex](n) = 15[/tex] books, and sample mean [tex](\bar x) = 305[/tex] pages.
Calculate the standard error (SE) of the sample mean:
[tex]SE = \sigma / \sqrt n = 45 / \sqrt 15 \approx 11.62.[/tex]
The critical value (z) for a 99% confidence level:
[tex]z \approx 2.576[/tex] (from a standard normal distribution table or using a calculator).
Calculate the margin of error (ME):
[tex]ME = z \times SE \approx 2.576 \times 11.62 \approx 29.92.[/tex]
Determine the confidence interval:
[tex](\bar x - ME, \bar x + ME) = (305 - 29.92, 305 + 29.92) \approx (275.08, 334.92).[/tex]
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Please only do 9,11, and 13! And please help!! 40 points!!!
9. The volume of the triangular pyramid is given by:
V = (1/3)Bh
Here, B is the base area.
The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:
h = sqrt(26.7² - 11.7²) = 23.274 km
The area if the base is:
B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km
Now, the volume is:
V = (1/3)(136.89)(15) = 2053.35 cubic km
Hence, the volume of the triangular pyramid is 2053.35 cubic km.
9. The volume of the triangular pyramid is 2053.35 cubic km. 11. The area of the shaded portion is 348.19 cubic in 13. The slant height of the cone is 8.53 meters.
What is Pythagoras Theorem?A fundamental conclusion in geometry relating to the lengths of a right triangle's sides is known as Pythagoras' theorem. According to the theorem, the square of the length of the hypotenuse, the side that faces the right angle, in any right triangle, equals the sum of the squares of the lengths of the other two sides, known as the legs.
9. The volume of the triangular pyramid is given by:
V = (1/3)Bh
Here, B is the base area.
The base is shaped as a right triangle thus, using the Pythagoras Theorem we have:
h = √(26.7² - 11.7²) = 23.274 km
The area if the base is:
B = (1/2)bh = (1/2)(11.7 km)(23.4 km) = 136.89 sq. km
Now, the volume is:
V = (1/3)(136.89)(15) = 2053.35 cubic km
Hence, the volume of the triangular pyramid is 2053.35 cubic km.
11. The volume of a cone is given by:
V = (1/3)πr²h
The dimension of the bigger cone is radius is 9 in, and height 15 in:
V1 = (1/3)π(9 in)²(15 in) = 381.7 cubic in
The dimension of the smaller cone is radius is 4 in, and height 10 in:
V2 = (1/3)π(4 in)²(10 in) = 33.51 cubic in
Now, the area of the shaded portion is:
V1 - V2 = 381.7 - 33.51 = 348.19
13. The volume of a cone is given by:
V = (1/3)πr²h
Substituting the values we have:
542.87 = (1/3)π(6 m)²h
h = 542.87 / [(1/3)π(6 m)²] = 6.05 m
Now, using the Pythagoras Theorem for the slant height we have:
s² = r² + h²
s² = (6 m)² + (6.05 m)²
s² = 72.9
s = √(72.9) = 8.53 m
The slant height of the cone is 8.53 meters.
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what is the smallest number of consumers that timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level?
Answer:
To calculate the minimum sample size required for a given margin of error and confidence level, we can use the following formula:
n = (z^2 * p * (1-p)) / E^2
where:
n is the sample sizez is the z-score for the desired confidence level (in this case, 99%, which corresponds to a z-score of 2.576)p is the estimated proportion of the population that has the characteristic of interest (since we don't have an estimate for p, we can use 0.5, which will give us the largest possible sample size)E is the desired margin of error (in this case, 0.05)Substituting the values, we get:
n = (2.576^2 * 0.5 * (1-0.5)) / 0.05^2
n = 664.3
Rounding up to the nearest whole number, the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level is 665.
Explain why the triangles are similar, then find AB. Hint: redraw as 2 triangles
We can see that they are similar because the ratio of the corresponding sides of the triangle are the same = 5/3.
What is triangle?A triangle is a polygon with three sides and three angles. It is one of the most basic shapes in geometry and is formed when three non-collinear points are connected by straight lines. The three sides of a triangle can have different lengths, and the three angles can have different measures. Triangles can be classified based on their sides and angles.
BC/DE = AD/AB
15/9 = AB/6
AB = (15 × 6)/9 = 90/9 = 10.
15/9 = 10/6 = 5/3.
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The probability Milo will be assigned math homework is 0. 35 the probability Milo will be assigned math and writing is 0. 20 the probability Milo will be assigned either is 0. 65 what is the probability of writing homework being assigned?
The probability Milo will be assigned a writing homework is equal to 0,50.
Let us consider the event 'A' represents the assigned Math's homework.
And 'B' represents the assigned writing homework.
Probability of Milo assigned math homework = 0. 35
⇒P(A) = 0.35
Probability of Milo assigned math and writing homework = 0. 20
⇒P(A∩B ) = 0.20
Probability of Milo assigned either homework = 0. 65
⇒P(A∪B) = 0.65
Let the Probability of Milo assigned writing homework = P(B)
Using the Formula of probability we get,
P(A∪B) = P(A) + P(B) - P(A∩B )
Substitute the value we have,
⇒ 0.65 = 0.35 + P(B) - 0.20
⇒P(B) = 0.65 - 0.15
⇒P(B) = 0.50
Therefore, the probability of writing homework being assigned to Mila is equal to 0.50.
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A 10-ft chain weighs 25 lb and hangs from a ceiling. Find the work done (in ft-lb) in lifting the lower end of the chain to the ceiling so that it is level with the upper end.
The work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 250 ft-lb.
The work done in lifting the lower end of the chain to the ceiling can be calculated using the formula for work, which is given by:
Work = force x distance
In this case, the force is the weight of the chain, which is 25 lb, and the distance is the length of the chain, which is 10 ft.
So, the work done in lifting the lower end of the chain to the ceiling is:
Work = 25 lb x 10 ft
Work = 250 ft-lb
Therefore, the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 250 ft-lb.
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The work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 125 ft-lb.
The work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 125 ft-lb.
To find the work done in lifting the lower end of the chain to the ceiling, we need to consider the average weight of the chain as it is being lifted.
1. First, find the weight per foot of the chain:Weight of chain = 25 lbLength of chain = 10 ftWeight per foot = (25 lb) / (10 ft) = 2.5 lb/ft2.
Determine the average weight being lifted:Since you're lifting the chain from one end, the average weight you're lifting is half of the chain's total weight.
Average weight = (25 lb) / 2 = 12.5 lb3. Calculate the work done:Work done = Force x DistanceForce = Average weight = 12.5 lbDistance = Length of chain = 10 ftWork done = (12.5 lb) x (10 ft) = 125 ft-lb
So, the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end is 125 ft-lb.
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professional scouts are timing a football player running a 40-yard dash to determine how his speed compares to other players they may want on their team. what type of analysis are the scouts using?
The scouts are using quantitative analysis.
The total length of these planks is 92 metres. Work out the number of planks of length 2 metres in Ben workshop.
Answer: 13
Step-by-step explanation:
Find a congruence transformation that maps triangle RST to triangle UVW
A congruence transformation that maps triangle RST to triangle UVW is a reflection along the line y = 1, followed by a translation 2 units right and down by 1 units.
A congruence transformation that maps triangle RST to triangle UVW is a rotation of 180°, followed by a translation 2 units left and down by 5 units.
What is a transformation?In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.
By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-image underwent a sequence of congruence transformation to produce the image.
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The shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, determine what percentage of the circle is shaded
If the shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, the percentage of the circle is shaded is: 31.83% .
What percentage of the circle is shaded?We can start by finding the area of the entire circle. The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius. Since the diameter of the circle is 10 cm, the radius is half of that, or 5 cm. Therefore, the area of the entire circle is:
A = π(5 cm)^2 = 25π cm^2
Next, we can find what percentage of the circle is shaded by dividing the shaded area by the total area of the circle and multiplying by 100:
Percentage shaded = (shaded area / total area) x 100
Percentage shaded = (25 cm^2 / 25π cm^2) x 100
Percentage shaded = 100 / π ≈ 31.83%
Therefore, approximately 31.83% of the circle is shaded.
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Please help offering 15 points
More people that rode the roller coaster are between the ages of 11 and 30, than people that are between the ages of 41 and 60 is the best description of the data which is obtained by using the arithmetic operations.
What are arithmetic operations?
Any real number may be explained using the four basic operations, also referred to as "arithmetic operations." Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.
We are given a chart. From the chart we get the following data:
Number of people aged 11 - 20 riding roller coaster = 20
Number of people aged 21 - 30 riding roller coaster = 15
Number of people aged 31 - 40 riding roller coaster = 10
Number of people aged 41 - 50 riding roller coaster = 5
Number of people aged 51 - 60 riding roller coaster = 0
Using addition operation, we get
Total people = 20 + 15 + 10 + 5 + 0
Total people = 40
Now,
Total riders between 11 - 30 = 20 + 15
Total riders between 11 - 30 = 35
Similarly,
Total riders between 41 - 60 = 5 + 0
Total riders between 41 - 60 = 5
Hence, the fourth option is the correct answer.
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Solve for y. Express your answer as a proper or improper fraction in simplest terms. -1/4=-1/4+1/8y
Step-by-step explanation: Solve for y by simplifying both sides of the equation, then isolating the variable. y = 0
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Think of a cube whose edges are 6 cm long. 1). The volume of the cube is_______cm³. 2). The total area of the cube is_________cm².
Answer:
Step-by-step explanation:
For the volume, it would be length times width times height, and it is a cube, so they are all the same, meaning it would be 6*6*6. That is equal to 216 cm3, which is the answer for the first one. The total area, meaning surface area, would be found by finding the area of one side, which is 6*6, which is 36, and then multiplying by the number of sides, because it is a square, cube. The surface area is also 216 cm2.
1) 216 cm3 (cm^3)
2) 216 cm2 (cm^2)
miss austin gives her class 6 sets of data and asks them to identify which data set can most accurately be summarized by the mean. what topic is she covering?
Miss Austin is covering the topic of central tendency in statistics, specifically the mean. By giving her class 6 sets of data and asking them to identify which one can be most accurately summarized by the mean, she is testing their understanding of how the mean represents the average value of a set of data.
This also involves understanding how to calculate the mean and interpret its value in relation to the other values in the dataset. Therefore, Miss Austin is helping her class develop skills in data analysis and statistical reasoning. The use of the term "set" is not clear, but assuming it means "sets of data," it is relevant to the topic being covered.
Miss Austin is covering the topic of "Descriptive Statistics" in her class. Specifically, she is focusing on the concept of "mean" as a measure of central tendency to summarize data sets. By asking her students to identify which data set can most accurately be summarized by the mean, she is teaching them how to understand the appropriateness of using the mean for different sets of data.
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Practice & Problem Solving Leveled Practice 7. What is the surface area of the cylinder represented by the net? Uses as part of your answer 10 ft 16 ft
the surface area of the cylinder represented by the given net is approximately 166.306 square feet.
What is the surface area of the cylinder?To calculate the surface area of a cylinder using its net, we need to identify the different components of the net and their measurements.
Without the specific net provided, I will assume a standard net of a cylinder, consisting of two circles for the top and bottom faces, and a rectangle for the lateral (side) surface.
Given that the measurements provided are 10 ft and 16 ft, we can assume that the height of the cylinder is 10 ft and the circumference of the circular bases is 16 ft.
The surface area of a cylinder is given by the formula:
Surface Area [tex]= 2 \times \pi \times r \times (r + h)[/tex]
where r is the radius of the circular base and h is the height of the cylinder.
Since the circumference of the circular base is given as 16 ft, we can calculate the radius (r) using the formula:
Circumference [tex]= 2 \times π times r[/tex]
[tex]16 = 2 \times π \times r[/tex]
[tex]r = 16 / (2 \times \pi)[/tex]
[tex]r v\ approx 2.546 ft[/tex] (rounded to three decimal places)
Now that we know the radius (r) and the height (h) of the cylinder, we can substitute these values into the formula for surface area:
Surface Area [tex]= 2 \times π \times 2.546 \times (2.546 + 10)[/tex]
Surface Area [tex]\approx 166.306 ft^2[/tex] (rounded to three decimal places)
Therefore, the surface area of the cylinder represented by the given net is approximately [tex]166.306[/tex] square feet.
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if x is a nonnegative real number, then the expression √ x is called the
If x is a non-negative real number, then the expression √ x is called the Principal square root. The answer is Principal Square Root.
What is Principal Square Root?
The positive square root of a non-negative real integer is the principal square root. It is the one and only non-negative real number that, when squared, yields the given non-negative real number. The principal square root of 9 is 3, for example, because 3 multiplied by itself equals 9.
The radical sign (√) is frequently used to represent the principal square root. The term √x denotes Principal square root of x. The sign can be used to indicate the negative square root of x in some settings, but this is less frequent.
The principal square root notion is significant in mathematics, including algebra, geometry, and calculus. It's used to solve equations, simplify expressions, and calculate lengths and distances. It's also used in a wide range of scientific and engineering applications.
Therefore, if x is a non-negative real number, then the expression √ x is called the Principal square root.
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If x is a nonnegative real number, then the expression √ x is called the square root of x. The square root of a nonnegative real number is a value that, when multiplied by itself, equals the original number.
If x is a nonnegative real number, then the expression √x is called the "principal square root" of x. The principal square root of a nonnegative real number x is the nonnegative real number that, when multiplied by itself, equals x. In other words, if y = √x, then y * y = x. This ensures that the result is also a nonnegative real number.
For example, the square root of 4 is 2 because 2 multiplied by 2 equals 4. The square root function is denoted by the symbol √ and is used to find the positive number that, when squared, gives the input value.
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