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mezya [45]
4 years ago
14

The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1800 hours and a standard deviation

of 35 hours. Using the empirical rule, what percentage of light bulbs last between 1765 hours and 1835 hours?
Mathematics
1 answer:
DedPeter [7]4 years ago
6 0

Answer: 68% of light bulbs last between 1765 hours and 1835 hours.

Step-by-step explanation:

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is 1800 hours and the standard deviation is 35 hours.

1 standard deviation = 1 × 35 = 35

1800 - 35 = 1765 hours

1800 + 35 = 1835 hours

Therefore, 68% of light bulbs last between 1765 hours and 1835 hours.

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3 years ago
Shopping While shopping for clothes, Tracy spent $28 less than 2 times what Daniel spent. Tracy
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Answer:

Daniel spent $ 19.

Step-by-step explanation:

Given that, while shopping for clothes, Tracy spent $28 less than 2 times what Daniel spent, and Tracy spent $ 10, to determine how much Daniel spent the following equation must be performed:

Daniel: X

Tracy: 2X - 28 = 10

2X - 28 = 10

2X = 10 + 28

X = 38/2

X = 19

2x19 - 28 = X

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So, Daniel spent $ 19.

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4 years ago
5x-2y=12<br><br>6x+2y=32<br><br>find the solution
diamong [38]

Answer:

(4,4)

Step-by-step explanation:

There are two ways that you can solve this. You can solve it with the help of technology or you can solve it traditionally. I will show how to do it in both ways so you can pick which way you want to solve it.

<em>Traditional Method:</em>

5x - 2y = 12

6x + 2y = 32

Look at the variables and numbers in both equations. One of them has to be the same value but have to have opposite signs. The 2y in both equations are the same value but have different signs. That's what we want. We can add everything in the equation now. (5x + 6x), (-2y + 2y), and (12 + 32).

11x = 44

To get x alone, Divide each side by 11. Then we will get the value of x.

11/11x = 44/11

x = 4

Horray! We got x, but what about y? Pick one of the equations. I will go with 5x - 2y = 12. Substitute the x value inside the equation.

5(4) - 2y = 12

20 - 2y = 12

-2y = -8

y = 4

Good! We figured out y. Now we know the solution! The solution is (4,4).

<em>Technology Method:</em>

Grab a graphing calculator. Enter the equations. You will see two lines. Look at where they intersect. The point where they intersect is the solution. That line is (4,4). You could also do this on a piece of paper by graphing the equations.

I hope this helps! Let me know if you need any more help or if I got anything wrong.

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3 years ago
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