Answer:
And using a calculator, excel or the normal standard table we have that:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the weigths of a population, and for this case we know the distribution for X is given by:
Where 
and 
Since the distribution for X is normal then we know that the distribution for the sample mean 
is given by:
We can find the probability required with the following z score formula:
And replacing we got:
And using a calculator, excel or the normal standard table we have that:
Answer:
<u>r=6</u>
Step-by-step explanation:
3 = r/2
6 = r
(5 + 7x + 6)/2 = 3x + 9
7x + 11 = 6x + 18
7x - 6x = 7
x = 7
EF = 3x + 9
= 3(7) + 9
= 21 + 9
= 30
Your question seems to be -7 +(1/8) -(-9) + (1/2) but then there is a decimal in front of the next -2 so that makes no sense unless that is a period before starting a new equation. You can simply type this beginning section into a calculator to get your answer of (21/8), but I have a feeling you just tried to copy and paste a test question and it did not format correctly in your question so is probably much more complicated than using a calculator.
A better idea would be to write it in math terms instead of words, then find a common denominator so you can simplify. Writing it out in words makes it too hard for your brain to think about it in terms of math.
Answer:
Measure of ∠B = 51°.
Step-by-step explanation:
The sum of the measures of any triangle will always add up to 180°. Also the sum of two supplementary angles, or angles that are side by side on a straight line, will also add up to 180°. In order to find the measure of ∠B, you need to first find the measure of ∠C. ∠C is supplementary to the angle of 113°, so we can find ∠C: 180 - 113 = 57°. Now that we know ∠A and ∠C, we can solve for ∠B: 180 = 72 + 57 + ∠B or 180 = 129 + ∠B, subtracting 129 from both sides, we get ∠B = 51°.
