The blades on a wind turbine trace a circular path with radius 100 feet. Suppose the turbine spins at 20 revolutions per minute. What is the linear velocity, in miles per hour (1 mile equals 5,280 feet), of a point on the tip of a blade? Round the answer to the nearest tenth.
The linear velocity of a point on the tip of a blade on a wind turbine is approximately 0.05 miles per hour.
Explanation:To find the linear velocity of a point on the tip of a blade on a wind turbine, we need to convert the rotational speed to linear speed. The formula to do this is linear speed = radius × angular speed. In this case, the radius is 100 feet and the turbine spins at 20 revolutions per minute. First, we convert the revolutions per minute to radians per second by multiplying by 2π/60. Then, we multiply the angular speed by the radius to find the linear speed.
Angular speed = 20 revolutions per minute × 2π/60 = 20π/60 = π/3 radians per second
Linear velocity = 100 feet × π/3 = 100π/3 feet per second
Finally, to convert the linear velocity to miles per hour, we divide by 5280 (since 1 mile equals 5280 feet).
Linear velocity = (100π/3) / 5280 ≈ 0.05 miles per hour
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At one vehicle inspection station, 13 of 52 trucks and 11 of 88 cars failed the emissions test. assuming these vehicles were representative of the cars and trucks in that area, what is the standard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations?
[tex]SE=\sqrt{p(1-p)\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}[/tex]
where p is the pooled sample proportion, [tex]n_1[/tex] is the size of sample 1, and [tex]n_2[/tex] is the size of sample 2.The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 In(9t+4), where y is the number of lawn mowers sold. How many mowers will be sold 4.5 years after a model is introduced? Round your answer to the nearest whole number. Show your work to find the number of mowers for credit.
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A sewing pattern calls for 1/2 meter of red ribbon and 1/5 meter of blue ribbon. What is the unit rate in meters of red ribbon per meter of blue ribbon?
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A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 7 milliliters of compound B. If a chemist wants to make 684 milliliters of the drug, how many milliliters of compound A are needed?
300 minutes equals how many hours
Given the following functions f(x) and g(x), solve (f ⋅ g)(2) and select the correct answer below: (1 point)
f(x) = 2x2 − 10
g(x) = x + 9
−22
22
−66
66
Answer:
-22
Step-by-step explanation:
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Calculate the slope of a line that intersects points (6,2) and (-4,-3).
A. 1/2
B. 2/3
C. 4/5
D. 7/8
The slope of the line passing through the points (6,2) and (-4,-3) is calculated using the slope formula (y2 - y1) / (x2 - x1), resulting in a slope of 1/2.
To calculate the slope of a line that intersects points (6,2) and (-4,-3), we use the slope formula, which is (change in y) / (change in x), or (y2 - y1) / (x2 - x1). Here, we consider point 1 to be (6,2) and point 2 to be (-4,-3).
Using the formula:
y2 = -3y1 = 2x2 = -4x1 = 6Substituting the values into the formula gives us the following calculation:
Slope = (-3 - 2) / (-4 - 6)
Slope = (-5) / (-10)
Slope = 1/2
Therefore, the correct answer is A. 1/2.
If g(x)= 2x^4+3x^3-x^2, find g(-1)
The hyperbola with center at (4, 5), with vertices at (0, 5) and (8, 5), with b = 2.
Answer:
Step-by-step explanation:
The correct answer is (x-4)^2/16 - (y-5)^2/4 = 1
you have a bottle of water with a leak. after 2 second,there are 28 ounces left in the bottle. after 6 seconds, there are 20 ounces left in the bottle. how fast is the bottle losing water
Answer:
rate of losing water = 8 ounce per 4 sec or 2 ounces per sec.
Step-by-step explanation:
Given : after 2 second,there are 28 ounces left in the bottle. after 6 seconds, there are 20 ounces left in the bottle.
To find : how fast is the bottle losing water.
Solution : WE have given that
After 2 second water left in bottle = 28 ounces.
After 6 second water left in bottle = 20 ounces.
We can see with in ( 6 - 2) ,4 second bottle lose their 8 ounce water.
Therefore, rate of losing water = 8 ounce per 4 sec or 2 ounces per sec.
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Which of these is a point-slope equation of the line that is perpendicular to y-25=2(x-10) and passes through (-3,7)
Answer: y - 7= -1/2 (x+3)
Step-by-step explanation:
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In a class of 147 students, 95 are taking math(m), 75 are taking science (s), 52 are taking both math and science. What is the probability of randomly choosing a student who is taking neither math nor science? Round your answer to the nearest tenth
Answer:
31/147
Step-by-step explanation:
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Anwar says that the shape below is a parallelogram. is he correct that a kite is a parallelogram explain
Suppose that an open box is to be made from a square sheet of cardboard by cutting out squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 576 cubic inches, find the original dimensions of the sheet of cardboard.
5y^2 - 2y - 7 are (5y - 7) and ( )
The standard guidelines for fluid intake recommend that a 10dash20-kg child should have 1000 mL of fluid plus 50 mL for each full kilogram of body weight over 10 kg per day. How many 8-ounce glasses of fluid should a 43-pound child have each day? The 43-pound child should drink about nothing 8-ounce glasses of fluid each day.
The pyramid shown has a square base that is 14 centimeters on each side. The slant height is 15 centimeters. What is the surface area of the pyramid?
Brady has collected the following data. 11, 15, 15, h, 11. If the range of Brady's data is 9, what is the value of h?
To solve this question, let's start by understanding what the range of a data set means. The range is the difference between the highest value and the lowest value in the set.
Given that the range of Brady's data is 9, and we have the following data points: 11, 15, 15, h, 11, we can use this information to determine the value of h.
1. Identify the smallest value in the data set (without considering h for now). The smallest value given is 11.
2. Identify the largest value in the data set (without considering h for now). The largest value given is 15.
3. Since the range of the data is 9, we can calculate what the new highest and lowest value could be if h were to be the extremum.
If h were the largest value, then:
h - smallest value = 9
h - 11 = 9
h = 9 + 11
h = 20
If h were the smallest value, then:
largest value - h = 9
15 - h = 9
h = 15 - 9
h = 6
4. Now that we have two potential values for h (20 if it’s the maximum, and 6 if it’s the minimum), we have to decide which value is correct. Remember that the range is the difference between the largest and smallest values, so whichever potential value of h does not coincide with a number already in the data set is likely the correct value.
Since the current largest value in the data set without h is 15, and the current smallest value is 11, using h = 20 would yield a new range greater than 9 (20-11 = 9), and using h = 6 would also yield a range greater than 9 (15-6 = 9). But we are only looking for an existing range of 9. Thus, we must consider whether 20 or 6 would form a range of exactly 9 with the current set of numbers.
- If h = 20, it would become the new largest number and the range would be simply h - smallest value, which is 20 - 11 = 9, which is correct.
- If h = 6, it would become the new smallest number and the range would be largest value - h, which would be 15 - 6 = 9, which is also correct.
In this case, both h = 20 and h = 6 satisfy the condition for the range to be 9. However, we should look at the data set to see which data point (h) is not already present because the range should be the difference of two distinct (unique) data points.
In examining the given data set, we see that we already have a smallest value of 11 and a largest value of 15.
To maintain the range of 9 with the given data (without h), h could take on either the value which provides a max-min of 9 and is not already in the data set. In this scenario, both potential values 6 and 20 meet the criteria, since neither is present in the original data set.
Therefore, Brady’s h can be either 6 or 20 and still satisfy the given conditions.
Rachel says that Graph R has a greater constant of variation that Graph S. Which statement explains whether Rachel is correct?
For this case we have that by definition the constant of variation of a line is given by the slope m, of said line.
Where:
[tex]m = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
To find the slope of a line it is necessary to find two points through which the line passes.
To solve the given problem, we find the slopes of the lines shown in the graphics R and S:
Graphic R:
It is observed that the line passes through the following points:
[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (2,1)[/tex]
Substituting in the formula of the slope we have:
[tex]m_ {R} = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
[tex]m_ {R} = \frac {1-0} {2-0}[/tex]
[tex]m_ {R} = \frac {1} {2}[/tex]
Thus, the slope of the line of the graph R is given by: [tex]m_ {R} = \frac {1} {2}[/tex]
Graphic S:
It is observed that the line passes through the following points:
[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (1,2)[/tex]
Substituting in the formula of the slope we have:
[tex]m_ {S} = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
[tex]m_ {S} = \frac {2-0} {1-0}[/tex]
[tex]m_ {S} = \frac {2} {1}[/tex]
[tex]m_ {S} = 2[/tex]
Thus, the slope of the line of the graph R is given by: [tex]m_ {S} = 2[/tex]
[tex]m_ {S}> m_ {R}[/tex]
then, the graph S has a variation constant greater than the graph R.
Answer:
The graph S has a variation constant greater than the graph R.
Rachel's idea is wrong
Answer:
It’s D
Step-by-step explanation:
Chris Shopper received a $1,000 discount loan to purchase a washer and dryer. The loan was offered at 12% for 120 days. What are the proceeds? $40.00 $144.00 $960.00 $1,440.00
Answer:
The correct answer is 960.
Step-by-step explanation:
120/360=0.333
Remember to use 360 because a bank year is 360 days.
Then you use the interest formula:
I= P×R×T
I=1000×0.12×0.333
39.99=I
Now take 1000 because your principal is 1000, and subtract that from 1000
1000-39.99=960
A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?
You planted 488 acres of corn last season. you sold all your corn: 8,120 bushels in August and 64,100 bushels in September. what is your yield pet acre, rounded to the nearest bushel per acre
Answer:
There will be approx 148 bushels in per acre.
Step-by-step explanation:
You planted 488 acres of corn last season.
you sold all your corn: 8,120 bushels in August and 64,100 bushels in September.
Total bushels = [tex]8120+64100=72220[/tex]
Now, this amount of bushels were in 488 acres of land.
So, per acre will contain = [tex]72220/488=147.99[/tex]≈ 148 bushels
Hence, there will be approx 148 bushels in per acre.
Find the value of x.
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Hazel covered a box with felt. The dimensions of the box are shown in the figure below: A rectangular prism is shown. The length of the rectangular prism is labeled as 11 inches, the height is labeled as 6 inches, and the width is labeled as 8 inches. The felt costs 9¢ per square inch. She will only pay for the felt used to cover the box, even if there is waste or extra. How much money did Hazel spend on the felt? $18.18 $27.72 $36.36 $45.54
Write parametric equations of the line 2x-y=3
Answer: The required parametric equation is y=2t-3.
Step-by-step explanation:
Since we have given that
2x+-y=3
We need to rewrite in parametric equation:
The parametric equation is written as
[tex]f(x)=y=at+b[/tex]
So, Arranging the given equation in the above equation, we get
[tex]2x-y=3\\\\2x-3=y\\\\f(x)=y=2x-3[/tex]
And then put x = t, to get the exact parametric form.
Hence, the required parametric equation is y=2t-3.
Use the quadratic formula to solve the equation. If necessary, round answers to the nearest hundredth. 5x2 + 16x – 84 = 0