Answer:


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 grade points avergae of a population, and for this case we know the following properties
Where
and
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
So we can find the z score for the value of X=3.44 in order to see how many deviations above or belowe we are from the mean like this:

So the value of 3.44 is 2 deviations above from the mean, so then we know that the percentage between two deviations from the mean is 95% and on each tail we need to have (100-95)/2 = 2.5% , because the distribution is symmetrical, so based on this we can conclude that:

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Answer:
x ≤ – 3 or x ≥ 9.
Step-by-step explanation:
Given : 9x ≤ –27 or 4x ≥ 36.
To find : Solve the compound inequality.
Solution : We have given 9x ≤ –27 or 4x ≥ 36.
For 9x ≤ –27 .
On dividing both sides by 9.
x ≤ – 3.
For , 4x ≥ 36.
On dividing both sides by 4.
x ≥ 9.
We can write x ≤ – 3 or x ≥ 9.
Therefore, x ≤ – 3 or x ≥ 9.
Answer:
69.94 miles
Step-by-step explanation:
The distance d₁ the first ship moves after 3 hours is 3 hours × 15 miles per hours = 45 miles
The distance d₂ the second ship moves after 3 hours is 3 hours × 12 miles per hours = 36 miles.
The angle the first ship's direction makes in the North-East direction is 90° - 75° = 15°
The angle the second ship's direction makes in the South-West direction = 14°
The distance moved by the two ships form the side of a triangle. The angle, θ between the two ship directions is 14° + 90° + 15° = 119°
Using the cosine rule, we find the distance d between the two ships
d = √(d₁² + d₂² -2d₁d₂cosθ)
= √(45² + 36² -2×45×36cos119°)
= √(2025 + 1296- (-1570.78))
= √(3321 + 1570.78)
= √4891.78
= 69.94 miles
Answer:

Step-by-step explanation:
We want to simplify

Recall the reciprocal property:

We apply this property to get:

Also apply this property of exponents to get:


We simplify using the product property of exponents to get:
