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PLEASE HELP BY TODAY!!! NO WORK NEEDED!!!

soldi70 [24.7K]

The answer is 76 degrees

3 0

3 years ago

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Which ordered pair is a solution of y = x - 4?

Katarina [22]

Answer:

The correct answer is (-3,-7). This is because you can plug it in and the two sides are equal to each other. When you plug -3 in for x, you subtract for from it and get -7 since the y term is -7 the answer is -7=-7, thus (-3, -7) is the answer.

Step-by-step explanation:

Hope this helps :)

5 0

3 years ago

A team of runners is needed to run a 1/4 -mile relay race. If each runner must run 1/16 mile, how many runners will be needed?

gtnhenbr [62]

Answer:

You will need four runners.

Step-by-step explanation:

If you multiply 1/16 by four you will get 4/16, which is simplified to 1/4

8 0

3 years ago

Jina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Jina drove h

NISA [10]

Answer:

264 miles

Step-by-step explanation:

Using the relation ...

distance = speed · time

we can rearrange to get ...

speed = distance/time

We can choose to let d represent the distance we want to find. Then Jina's speed going to the mountains is d/6. Her speed coming home is then d/6+22. It takes Jina 4 hours at that speed to cover the same distance, so we have ...

d = 4(d/6 +22)

d = 2/3d +88 . . . . eliminate parentheses

1/3d = 88 . . . . . . . subtract 2/3d

d = 264 . . . . . . . . . multiply by 3

Jina lives 264 miles from the mountains.

3 0

3 years ago

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A company manufactures a brand of lightbulb with a lifetime in months that is normally distributed with mean 3 and variance 1. A

Ratling [72]

Answer:

The smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772 is 16.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

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.

n values from a normal distribution:

The mean is $\mu n$ and the standard deviation is $s = \sigma\sqrt{n}$

A company manufactures a brand of lightbulb with a lifetime in months that is normally distributed with mean 3 and variance 1.

This means that $\mu = 3, \sigma = \sqrt{1} = 1$

For n bulbs:

The distribution for the sum of n bulds has $\mu = 3n, \sigma = \sqrt{n}$

What is the smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772?

We want that: $S_{n} \geq 40 = 0.9772$ .

This means that when X = 40, Z has a pvalue of 1 - 0.9772 = 0.0228, that is, when $X = 40, Z = -2$ . So

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

$-2 = \frac{40 - 3n}{\sqrt{n}}$

$-2\sqrt{n} = 40 - 3n$

$3n - 2\sqrt{n} - 40 = 0$

Using $y = \sqrt{n}$

$3y^2 - 2y - 40 = 0$

Which is a quadratic equation with $a = 3, b = -2, y = -40$

$\Delta = b^{2} - 4ac = (-2)^2 - 4(3)(-40) = 484$

$y_{1} = \frac{-(-2) + \sqrt{484}}{2*3} = 4$

$y_{2} = \frac{-(-2) - \sqrt{484}}{2*3} = -...$

Since y and n have both to be positive:

$y = \sqrt{n}$

$\sqrt{n} = 4$

$(\sqrt{n})^2 = 4^2$

$n = 16$

The smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772 is 16.

4 0

3 years ago