Using the Empirical Rule, the interval that contains 68% of the scores is [81.5, 90.5].
<h3>What does the Empirical Rule state?</h3>
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
68% of the scores are within 1 standard deviation of the mean, hence the bounds of the interval are:
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Answer:
No
Step-by-step explanation:
The factors of 3 are 3, 1.
The factors of 11 are 11, 1.
The common factors of 3 and 11 are 1, intersecting the two sets above.
In the intersection factors of 3 ∩ factors of 11 the greatest element is 1.
Therefore, the greatest common factor of 3 and 11 is 1.
Answer: 35 inches.
Step-by-step explanation:
We know that:
hypotenuse = 5*y in
cathetus 1 = (x + 8) in
cathetus 2 = (x + 3) in
The perimeter of the triangle is 76 inches, then:
5*y + (x + 8) + (x + 3) = 76
5*y + 2*x + 13 = 76
We also know that the length of the hypotenuse minus the length of the shorter leg is 17 in.
The shorter leg is x + 3, then:
5*y - (x + 3) = 17
Then we have the equations:
5*y + 2*x + 11 = 76
5*y - (x + 3) = 17
With only these two we can solve the system, first we need to isolate one of the variables in one of the equations, i will isolate x in the second equation.
x = 5*y - 3 - 17 = 5*y - 20
x = 5*y - 20
Now we can replace this in the other equation, we get:
5*y + 2*x + 11 = 76
5*y + 2*(5*y - 20) + 11 = 76
15*y - 40 + 13 = 76
15*y - 29 = 76
15*y = 76 + 29 = 105
and remember that the hypotenuse is equal to 5*y, then we want to get:
3*(5*y) = 105
5*y = 105/3 = 35
5*y = 35
Then te length of the hypotenuse is 35 inches.
Answer:
-14. Aunque podría estar equivocado. Espero poder ayudar
Step-by-step explanation: