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Reika [66]
2 years ago
5

Three consecutive even numbers have a sum between 84 and 96.

Mathematics
1 answer:
ELEN [110]2 years ago
5 0

Answer:

a. 84 < n + (n + 2) + (n + 4) < 96

b. 26 < n < 30


Step-by-step explanation:

Let n = 1st number

n+2   2nd  even number

n+4 = 3rd even number

The sum of these 3 numbers is

n+n+2+n+4

It must be between 84 and 96  (it does not include this 84 and 96)

84< n+n+2+n+4 < 96


Now we need to solve this

Combine like terms

84 < 3n +6< 96

Subtract 6 from all sides

84 -6 < 3n+6-6 < 96 -6

78 < 3n < 90

Divide all sides by 3

78/3 < 3n/3 < 90/3

26 < n< 30


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3 years ago
On two tests so far this year, a student received a 78 and a 93. The student wants an average between 80 and 90 inclusive. What
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3 years ago
Calculate a critical z-score for a left-tailed, right-tailed, or two-tailed test.
muminat

Answer:

a. Z = -1.175.

b. Z = 1.34.

c. |Z| = 2.054.

d. |Z| = 1.28.

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

a. The critical z-score for a left-tailed test at a 12% significance level

Left-tailed test: The region of interest is the 12th percentile or below.

Thus, the critical z-score is Z with a p-value of 0.12, so Z = -1.175.

b. The critical z-score for a right-tailed test at a 9% significance level

Right-tailed test: The region of interest is the 100 - 9 = 91th percentile and above.

Thus, the critical z-score is Z with a p-value of 0.91, so Z = 1.34.

c. The critical z-score for a two-sided test at a 4% significance level is 1.75.

Two-tailed test: The region of interest is between the 4/2 = 2th percentile and the 100 - (4/2) = 98th percentile.

Thus, the critical z-score is |Z| with a p-value of 0.02 or 0.98, so |Z| = 2.054.

d. The critical z-score for a two-sided test at a 20% significance level is 0.85.

Region of interest is between the 20/2 = 10th percentile and the 100 - (20/2) = 90th percentile.

Thus, the critical z-score is |Z| with a p-value of 0.1 or 0.9, so |Z| = 1.28.

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