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Olegator [25]
3 years ago
5

An airplane travels 460 miles from San Diego to San Francisco in 2.5 hours, going against the wind. The return trip is with the

wind, and takes only 2 hours. Find the rate of the airplane with no wind. Find the rate of the wind.
Please & Thanks! <3
Mathematics
1 answer:
hammer [34]3 years ago
5 0
Distance=rate times time
distance=460
rate-wind=rate against wind
rate+wind=rate with wind
2.5=time aginst wind
2=time with wind
so
460=(rate-wind) times 2.5
and
460=(rate+wind) times 2

solve for rate
460=(rate-wind) times 2.5
divide both sides by 2.5
184=rate-wind

460=(rate+wind) times 2
divide by 2
230=rate+wind

we have
184=rate-wind
230=rate+wind
add them

184=rate-wind
<u>230=rate+wind +
</u>414=2rate+0wind
414=2rate
divide by 2
207=rate

answer is 207 miles per hour
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3 years ago
Assume that the average life of a refrigerator is 14 years, with the standard deviation given in part (a) before it breaks. Supp
fiasKO [112]

Answer:

The guarantee should be made of X = 1.555 + 14\sigma years, in which \sigma is the standard deviation given in part (a).

Step-by-step explanation:

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.

Assume that the average life of a refrigerator is 14 years

This means that \mu = 14

The standard deviation given in part (a) before it breaks.

This will be the value of \sigma

However, the company does not want to replace more than 6% of the refrigerators under guarantee. For how long should the guarantee be made?

We need to find the 100 - 6 = 94th percentile, which is X when Z has a pvalue of 0.94. So X when Z = 1.555. So

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

1.555 = \frac{X - 14}{\sigma}

X = 1.555 + 14\sigma

The guarantee should be made of X = 1.555 + 14\sigma years, in which \sigma is the standard deviation given in part (a).

7 0
3 years ago
What is the simplest form of this expression w^2(-4w^2-2)+(-5w^2)(-2w^2-2)
VikaD [51]
Answer:
6w⁴ + 8w²

Explanation:
Before we begin, remember the following:
xᵃ * xᵇ = x⁺ᵇ
+ve * -ve = -ve
-ve * -ve = +ve
+ve * +ve = +ve

To solve this problem, we will follow the following steps:
1- get rid of the brackets using the distributive property
2- combine like terms

This can be shown as follows:
w²(-4w² - 2) + (-5w²)(-2w² - 2)
w²(-4w²) + w²(-2) + (-5w²)(-2w²) + (-5w²)(-2)
-4w⁴ - 2w² + 10w⁴ + 10w²
w⁴(-4+10) + w²(-2+10)
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Hope this helps :)

7 0
3 years ago
Read 2 more answers
Andre has 45 sheets of paper and needs to buy more. A store has 5 reams of paper, and each
maks197457 [2]

Answer:

The practical domain of the function is the set of all integers from 1 to 5, inclusive.

Step-by-step explanation:

It is given the initial number of sheets of paper is 45.

A store has 5 reams of paper, and each ream contains 500 sheets of paper.

Let f(x) represent the number of sheets after purchasing x reams.

f(x)=500x+45

Domain is the set of input. In other words domain is the set of x-values.

Since number of reams can not be a negative or fraction value, therefore, the domain of the function is {1,2,3,4,5}.

Andre needs to buy more sheets, so number of reams of paper can not be 0.

Thus, the practical domain of the function is the set of all integers from 1 to 5, inclusive.

8 0
3 years ago
si tienes una mesa de 25m de largo por 10 de ancho ¿ en cuanto varíaran cada una de sus dimensiones para que sin alterar su supe
Murrr4er [49]

responder: 8,75

Cada dimensión será de 8,75 porque si la longitud es de 25 m de largo y el ancho es 10, si los sumamos y obtendremos 35. Así que 35 dividido entre 4 es 8,75

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3 years ago
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