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Liula [17]
3 years ago
5

Evaluate. –345 + 562 – (–209)

Mathematics
1 answer:
Elena L [17]3 years ago
6 0
Subtracting a negative is the same as adding a positive.
–345 + 562 – (–209)
–345 + 562 + 209
217 + 209
426
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For a particular diamond mine, 81% of the diamonds fail to qualify as "gemstone grade". A random sample of 92 diamonds is analyz
Fed [463]

Answer:

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 92, p = 0.81

So

\mu = E(X) = np = 92*0.81 = 74.52

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{92*0.81*0.19} = 3.76

Find the probability that more than 79% of the sample diamonds fail to qualify as gemstone grade.

This is 1 subtracted by the pvalue of Z when X = 0.79*92 = 72.68. So

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

Z = \frac{72.68 - 74.52}{3.76}

Z = -0.49

Z = -0.49 has a pvalue of 0.3121

1 - 0.3121 = 0.6879

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

4 0
3 years ago
What is the result when the number 39 is decreased by 3%?
dlinn [17]

Answer:

New value =

39 - Percentage decrease =

39 - (3% × 39) =

39 - 3% × 39 =

(1 - 3%) × 39 =

(100% - 3%) × 39 =

97% × 39 =

97 ÷ 100 × 39 =

97 × 39 ÷ 100 =

3,783 ÷ 100 =

37.83

Step-by-step explanation:

3 0
2 years ago
-7+2<br><br><br> Chises: 6 5 -5 9
Allushta [10]
The answer is -5 isjsjshsj
3 0
2 years ago
Alan and his classmates performed a linear regression analysis on the data set shown below and found that the line of best fit t
stealth61 [152]

Answer:

C. y=\frac{4}{5}x+7

Step-by-step explanation:

Alan and his classmates found that the line of best fit through the data had the equation y=-\frac{5}{4}x+18

The slope of this line is m=-\frac{5}{4}

If a line would intersect this line of best fit at right angles, then the two lines are perpendicular to each other.

The slopes of perpendicular lines are negative reciprocals of each other,

Hence that line must have slope \frac{-1}{-\frac{5}{4}} =\frac{4}{5}

Therefore we look for a line whose slope is \frac{4}{5} from the given options.

That line is the third option y=\frac{4}{5}x+7

5 0
3 years ago
If ad = 16 and ac = 4y - 44, find the value of y then find ac and dc​
SashulF [63]

Answer:

x=13

Step-by-step explanation:

7 0
3 years ago
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