5.) There are 40

Mathematics

1 answer:

Marina86 [1]3 years ago

7 0

50 dogs and 10 cats
This creates a 5:1 ratio and allows there to be 40 more dogs than cats. 50-10 equals 40

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Rectangle OPEN has diagonals intersecting at S. If m∠ENP=42 find m∠ EON, m∠ONP, m∠OSP, and m∠PSE

poizon [28]

Answer:

m∠EON = 48°

m∠ONP = 48°

m∠PSE = 90°

4 0

3 years ago

To approach the runway, a pilot of a small plane must begin a 10 degrees descent starting from a height of 1983 feet above the g

ddd [48]

<h3>Answer:</h3>

2.2 miles

<h3>Explanation:</h3>

The mnemonic SOH CAH TOA reminds you that

... Sin = Opposite/Hypotenuse

We are given an angle (10°) and its opposite side length (1983 ft), and we are asked to find the hypotenuse (the straight-line distance from the plane to the runway).

... sin(10°) = (1983 ft)/distance

Multiplying by distance and dividing by sin(10°), we have ...

... distance = (1983 ft)/sin(10°) ≈ 11419.6 ft

We want to express this in miles, so we have ...

... 11419.6 ft = (m mi)×(5280 ft/mi)

... (11419.6 ft)/(5280 ft/mi) = m mi ≈ 2.163 mi

Rounding to tenths, the distance is ...

2.2 miles

_____

<em>Comment on the question</em>

The distance from the plane to the airport is different than the horizontal distance from the airport at which the descent must start. The latter distance is the "adjacent" leg of the triangle, so must be found using the tangent function. Rounded to tenths, it is 2.1 miles.

8 0

3 years ago

The demand for a daily newspaper at a newsstand at a busy intersection is known to be normally distributed with a mean of 150 an

AURORKA [14]

Answer:

171 newspapers.

Step-by-step explanation:

Problems of normally distributed samples are 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 problem, we have that:

$\mu = 150, \sigma = 25$