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xenn [34]
1 year ago
12

11) A building casts a shadow of 100 feet. The angle of elevation from the end of the shadow to the top of the

Mathematics
1 answer:
svp [43]1 year ago
5 0

Answer:

≈ 27 ft

Step-by-step explanation:

using the tangent ratio in the right triangle formed by the building and the ground.

tan15° = \frac{opposite}{adjacent} = \frac{?}{100} ( multiply both sides by 100 )

100 × tan15° = ? , then

? ≈ 27 ft ( to the nearest whole number )

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How many 7 digit phone numbers are there assuming the first digit can't be a 0 or a 1?
Anettt [7]
The first digit can be any one of the numbers 2-9 That a total of 8 numbers.

The next 6 digits can be any permutation of 6  from the numbers  0 to 9.
(10 numbers)

nPr  =  n! / r!

so here we have  10P6  = 10! / 6!  =  10*9*8*7  =  5040

So final answer  is 8 * 5040 = 40,320
7 0
3 years ago
One solution to the problem below is 5 what ya the other solution a^2-25=0
Alex

-5

a^2-25=0

a^2=25

take the square root of both sides

a=5, and -5

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3 years ago
Express the following as a pecentage:16 out of 40
Irina-Kira [14]

the answer is 40 percent

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3 years ago
Find the mean 9,1,8,3,2,1 graphically.
adelina 88 [10]
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4 0
2 years ago
The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2617 and standard deviation
Eduardwww [97]

Answer:

a) N(2617, 586)

b) 0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c) 0.4013 = 40.13% of the customers consume over 2764 calories

d) 3981 calories.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 2617, \sigma = 586

a. What is the distribution of X?

Here we first place the mean, then the standard deviation.

N(2617, 586)

b. Find the probability that the customer consumes less than 2409 calories.

This is the pvalue of Z when X = 2409. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{2409 - 2617}{586}

Z = -0.355

Z = -0.355 has a pvalue of 0.3613

0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c. What proportion of the customers consume over 2764 calories?

This is 1 subtracted by the pvalue of Z when X = 2764. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{2764 - 2617}{586}

Z = 0.25

Z = 0.25 has a pvalue of 0.5987

1 - 0.5987 = 0.4013

0.4013 = 40.13% of the customers consume over 2764 calories

d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?

Top 1%, so the 100-1 = 99th percentile.

The 99th percentile is the value of X when Z has a pvalue of 0.99. So it is X when Z = 2.327. So

Z = \frac{X - \mu}{\sigma}

2.327 = \frac{X - 2617}{586}

X - 2617 = 2.327*586

X = 3980.6

Rounding to the nearest calorie, 3981 calories.

7 0
2 years ago
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