MacGyver wants to estimate the width of a river so he can get to the other side to save the world. He makes the measurements pictured. How wide is the river? Will he be able to do it?
Answers
Answer:
Wideness ≈ 40 m
He will be able to do it .
Step-by-step explanation:
He wants to estimate the width of a river so he can get to the other side to save the world . The width of the river is the side AB. From the scale above 2 right angle triangle are formed . The smaller triangle is CDE and the larger triangle is CAB.
The angle ECD can be gotten below
tan C = opposite/adjacent
tan C = 8/6
tan C = 1.3333
C = tan⁻¹ 1.333
C = 53.1301022854
C = 53. 13°
∠ACB = ∠ECD (vertically opposite angles)
Using the angle to find the wideness of the river AB in triangle CAB.
tan C = opposite/adjacent
tan 53.13° = AB/30
AB = 30 tan 53.13
AB = 30 × 1.33332837108
AB = 39.9998511323
AB ≈ 40 m
He will be able to do it.
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What is the width of a triangle that has a 15 cm height and hypotenuse of 19 cm
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1. Answer is 4.5 km / hr.
... because you divide the time but the distance so for this question you divide 22.5 by 5 and that's your answer. do the same for every question! hope this helps.
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Final answer:
The probability that the average percent of fat calories is more than 40 for a group of 16 individuals is 0.1151 and the first quartile for the average percent of fat calories is 34.82.
Explanation:
The problem presented is one of statistics, specifically dealing with the normal distribution. When dealing with the normal distribution, there are a few key facts to know. The mean (μ) is the average value of the data, the standard deviation (σ) measures the spread of the data, and the Z-score measures how many standard deviations an element is from the mean. It appears that you're asked to find the probability that the average percent of fat calories is more than 40 for a group of 16 individuals and the value corresponding to the first quartile.
- For (a), remember that when dealing with averages, the standard deviation gets divided by the square root of the number of observations. Therefore, the new standard deviation becomes 10/√16 = 2.5. The Z-score can then be calculated by subtracting the mean from the observed value and dividing by the new standard deviation. That is, Z = (40 - 37) / 2.5 = 1.2. You can then refer to a Z-table to find the probability associated with this Z-score. However, since the question is asking for more than 40, you need to subtract the resulting probability from 1. Rounded to four decimal places, the probability that the average percent of fat calories is more than 40 is 0.1151.
- For (b), the first quartile (Q1) is the value corresponding to the 25th percentile. This corresponds to a Z-score of -0.674 (from the Z-table). You can then use the formula Q1 = μ + Zσ to obtain Q1 = 37 - 0.674*2.5 = 34.815. Therefore, the first quartile for the average percent of fat calories is 34.82 (after rounding to two decimal places).
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Final answer:
The probability that the group consumes more than 40% of fat calories is 0.8849 (or 88.49%). The first quartile for the average percent of fat calories is 34.26%.
Explanation:
This problem requires the use of normal distributions and the calculation of z-scores, which is a quantitative measure that describes a value's relationship to the mean of a group of values. Knowing the mean (μ) and standard deviation (σ), you can calculate the z-score.
In part a) the problem asks for the probability that a sample of 16 individuals has an average fat calories consumption over 40%. First, we calculate the z-score.
z = (X - μ) / (σ/ √ n ), where n is the sample size. So, z = (40 - 37) / (10 / √ 16) = 1.2. Using a standard normal distribution table, we find that the probability corresponding to this z-value is ~0.1151. However, since the question is asking for more than 40%, we subtract this from 1 (1 - 0.1151 = 0.8849). So, the chance that the average of this sample would have more than 40% fat calories is 0.8849, or 88.49%.
For part b), the first quartile (also known as the 25th percentile) is the point at which 25% of the data fall below it. With a standard normal distribution, this z-value is approximately -0.674. We plug this into our z-score formula to find: X = μ + Zσ = 37 -0.674(10) =34.26%. Therefore, the point where 25% of individual average fat calories fall below it is 34.26%.
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A.16
B.64
C.256
D.none of these
Answers
Answer:
64π in²
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr²
where r is the radius.
The radius of a circle is half the diameter. For the circle shown, the radius is ...
r = d/2 = (16 in)/2 = 8 in
Then the area is ...
A = π(8 in)² = 64π in²
_____
Often, units are left off, so the appropriate choice might be 64π.
_____
If you want to be technically correct (at the expense of getting your answer marked wrong), you can select "None of the above." That is because none of the offered choices have the correct units: square inches. You may want to discuss this with your teacher.