David conducts his own study. He selects a random sample of 50 students and asks if they are getting 9 hours of sleep per night.
Thirty of the 50 students are not getting enough sleep.
Does David’s sample result provide convincing evidence that more than 50% of all students at the school are not getting enough sleep?
Does David’s sample result provide convincing evidence that more than 50% of all students at the school are not getting enough sleep?
1 answer:
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Answer:
StartFraction 50 miles Over 1 hour EndFraction = StartFraction 200 miles Over question mark hours EndFraction
Step-by-step explanation:
For constant speed, miles and hours are proportional. One possible equation is ...
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<em>Comment on the solution</em>
I personally like to put the unknown in the numerator, so the equation can be solved in one step. The equation above requires two steps: one to cross-multiply, and one to divide by 50.
I might write the equation as ...
(? hours)/(200 mi) = (1 hour)/(50 mi) . . . . multiply by 200 mi to solve
Another way to write the equation is matching the ratios of times to corresponding miles:
(? hours)/(1 hour) = (200 mi)/(50 mi)
This only requires simplification to solve it: ? = 4.
Answer: y = 7cos(0.4π x) - 3
<u>Step-by-step explanation:</u>
The equation of a cosine function is: y = A cos(Bx - C) + D where
- Amplitude (A) is the distance from the midline to the max (or min)
- Period (P) is the length of one cosine wave --> P = 2π/B
- Phase Shift (C/B) is the horizontal distance shifted from the y-axis
- Midline (D) is the vertical shift. It is equal distance from the max and min
<u>Midline (D) = -3</u>
(-1.25, -3) is given as a point on the midline. We only need the y-value.
<u>Horizontal stretch (B) = 0.4π</u>
The max is located at (0,4) and also at (5, 4). Thus the period (length of one wave) is 5 units.
→ B = 0.4π
<u>Phase Shift (C) = 0</u>
The max is on the y-axis so there is no horizontal shift.
<u>Amplitude (A) = 7</u>
The distance from the midline to the max is: A = 4 - (-3) = 7
<u>Equation</u>
Input A = 7, B = 0.4π, C = 0, and D = -3 into the cosine equation.
y = A cos(Bx - C) + D
y = 7cos(0.4π x - 0) - 3
y = 7cos(0.4π x) - 3