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Troyanec [42]
3 years ago
14

A plane is flying at an altitude of 17,000 feet. The angle of depression from the plane to the airport on the ground is 21°. Wha

t is the distance between the plane and the airport to the nearest 10th of a foot
Mathematics
1 answer:
viva [34]3 years ago
6 0

Answer:

47,433.0 feet

Step-by-step explanation:

Using the SOH CAH TOA identity

Height of the plane = opposite = 17000feet

distance between the plane and the airport = hypotenuse = x

Angle of depression = 21 degrees

Since Sin theta = opp/hyp

Sin 21 = 17000/x

x = 17000/sin21

x = 17000/0.3584

x = 47,433.0

Hence the distance between the plane and the airport to the nearest 10th of a foot is 47,433.0 feet

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Jumbo eggs in Australia, on average, are supposed to weigh 68g. Margot is in charge of a quality control test that involves weig
Andrej [43]

Answer:

0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g

Step-by-step explanation:

To solve this question, we use the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean weight of 67g and a sample standard deviation of 1g.

This means that \mu = 67, \sigma = 1

Sample of 4

This means that n = 4, s = \frac{1}{\sqrt{4}} = 0.5

What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?

This is the pvalue of Z when X = 68.5. So

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

By the Central Limit Theorem

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

Z = \frac{68.5 - 67}{0.5}

Z = 3

Z = 3 has a pvalue of 0.9987

0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g

6 0
3 years ago
Read 2 more answers
Can y’all help me *********
melisa1 [442]

Answer:

33. The sheep pen is 16 square yards

Step-by-step explanation:

You can divide the rhombus inside into two triangles. Each triangle has a base of 4 yards and height 4 yards.

Area of triangle: A = 0.5*b*h = 0.5(4)(4) = 8

Since there are 2, then 2*8 = 16 square yards.

7 0
2 years ago
8.6 mi<br> 18 mi<br> A) 53.2 mi?<br> C) 106.4 mi?<br> E) 212.8 mi?<br> B) 221 mi?<br> D) 110.5 mi?
GenaCL600 [577]

Answer:

C

Step-by-step explanation:

4 0
3 years ago
joey made a deposit into an account that earns 6% simple interest.After three years, joey had earned $400. How much was joey's i
Sergio [31]

Answer:

Step-by-step explanation:

To find the amount deposited, we will simply use the formula for calculating simple interest.

Simple Interest = pxrxt/100     (fraction)

Where p = principal

      R= Rate

           T= Time

Principal is the initial amount deposited which we are ask to find.

R is given to be 6%  and T is the time which is given in years

Simple interest is the interest earned over the year which is given to be $400

Lets substitute our variable into the equation

Simple Interest = pxrxt/100    (fraction)

$400  = P × 6 × 3   /     100

$400 = 18p/100    (fraction)

We will then cross multiply

$40 000  =   18 P

To get  the value of P, we divide both-side of the equation by 18

4000/18 = 18p/18     (fractions)

$2222.22 =  P

P = $2222.22

credits: ummuabdallah

3 0
3 years ago
Read 2 more answers
There are approximately 3.2
gladu [14]
So, using the number 3,200,000 deaths per year, you want to divide it until it reaches deaths per minute.
3,200,000 divided by 365 (for days)
8767.123 divided by 24 (for hours)
365.297 divided by 60 (for minutes)
and so you get 
6.088 deaths per minute

Hope this helped.
8 0
3 years ago
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