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Alenkasestr [34]

2 years ago

12

John has $50 in his bank account. He gets his usual allowance of $20 and mows two lawns, earning $10 each. He puts that money in

the bank. Then John spends $45 on a video game.

1 answer:

Nat2105 [25]2 years ago

4 0

He has 45 dollars left

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Yuki888 [10]

It is 30 degrees. Add 90 and 60 to get 180. Then subtract that from 180, since all triangles interior angles add to 180. You’ll get 30.

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3 years ago

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This recipe makes 7 portions of chocolate mousse.

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3 years ago

If the unit price for watermelon is $0.24 per pound and Jared pays $1.68 for a watermelon, how many pounds does his watermelon w

Vanyuwa [196]

The watermelon weighs 7 pounds

Proof:

remove the decimal points then divide 168 by 24

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3 years ago

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3. A company with loud machinery needs to cut its sound intensity to 44% of its original level. By how many decibels would the l

sergeinik [125]

Answer: <em>3. The correct option is: A) 3.57 decibels.</em>

<em>6. The correct option is: B) $ln(\frac{x^2}{c^5})$ </em>

Step-by-step explanation:

3. Sound intensity is cut to 44% of its original level. That means, if the original sound intensity was 100, then now sound intensity will be 44.

So, $I_{0}= 100$ and $I= 44$

Using the formula $L= 10log(\frac{I}{I_{0}})$ , we will get.....

$L= 10log(\frac{44}{100})\\ \\ L= 10log(0.44)\\ \\ L= 10(-0.3565...)=-3.565...\approx -3.57$

<em>(Rounded to the nearest hundredth)</em>

So, the loudness would be reduced by 3.57 decibels.

6. Given expression is: $2ln(x) - 5ln(c)$

First applying the property $m*log(x)= log(x^m)$ , we will get.....

$ln(x^2)-ln(c^5)$

Now using the formula, $log(a)-log(b)= log(\frac{a}{b})$ , we will get....

$ln(x^2)-ln(c^5) = ln(\frac{x^2}{c^5})$

Thus, the answer as a single natural logarithm is $ln(\frac{x^2}{c^5})$

8 0

3 years ago

A group of high school athletes has an average GPA of 2.7 with a standard deviation of 0.9. a)Find the percentage of athletes wh

mart [117]

Answer:

a) The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is 3.645.

Step-by-step explanation:

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:

$\mu = 2.7, \sigma = 0.9$

a)Find the percentage of athletes whose GPA more than 1.665.

This is 1 subtracted by the pvalue of Z when X = 1.665. So

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

$Z = \frac{1.665 - 2.7}{0.9}$

$Z = -1.15$

$Z = -1.15$ has a pvalue of 0.1251

1 - 0.1251 = 0.8749

The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is more than 85.31 percent of the athletes in the study. Compute his GPA.

His GPA is X when Z has a pvalue of 0.8531. So it is X when Z = 1.05.

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

$1.05 = \frac{X - 2.7}{0.9}$

$X - 2.7 = 1.05*0.9$

$X = 3.645$

John's GPA is 3.645.

8 0

3 years ago