Answer:
59 to 66
Step-by-step explanation:
Mean test scores = u = 74.2
Standard Deviation = 
= 9.6
According to the given data, following is the range of grades:
Grade A: 85% to 100%
Grade B: 55% to 85%
Grade C: 19% to 55%
Grade D: 6% to 19%
Grade F: 0% to 6%
So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.
6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for 0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)
The formula for z score is:
For z = -1.56, we get:
For z = -0.88, we get:
Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)
Answer:
y - 1 = 3/2(x - 6)
Step-by-step explanation:
First, we need to find the slope of the given equation. Without a graph, the easiest way to do this is by isolating y.
2x + 3y = 18
3y = -2x + 18 (Subtract 2x from both sides)
y = -2/3x + 6 (Divide both sides by 3)
The slope is -2/3. Perpendicular lines have opposite reciprocal slopes, so a line perpendicular to this one would need to have a slope of 3/2. We're given a point for this line, so we can write the equation for it in point-slope form.
Point-Slope Form: 
y - 1 = 3/2(x - 6)
If necessary, this can also be written in slope-intercept form by solving for y.
Because Stephen always gets $25 it doesn't change making it the Dependent Variable, but how many lawns she mows can change making it Independent.
Dependent = $25
Independent = Lawns Mowed
Answer:
2
Step-by-step explanation:
For some angle "a", the sine and cosine are related by ...
sin(a) = cos(π/2 -a)
That is,
sin(7π/16) = cos(π/16)
sin(5π/16) = cos(3π/16)
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Then your sum becomes ...
sum = sin(π/16)² +sin(3π/16)² +cos(3π/16)² +cos(π/16)²
If we let α = π/16 and β = 3π/16, this can be written as ...
sum = (sin(α)² +cos(α)²) +(sin(β)² +cos(β)²)
sum = 1 + 1
sum = 2
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The identity sin(α)² +cos(α)² = 1 is sometimes called the Pythagorean identity.
Answer:
done
Step-by-step explanation:
2x+11=39
