<h3>
Answer: 52.8 minutes</h3>
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How I got that answer:
The interval 0 < t < 30 has the midpoint of 15 since (0+30)/2 = 15
The interval 30 < t < 60 has the midpoint 45 because (30+60)/2 = 45
We add up the endpoints and then divide by 2 to get the midpoint.
Repeat this for each of the intervals mentioned.
From top to bottom, the midpoints are:
Notice we add 30 to each midpoint to get the next one. This is directly due to the fact that each interval is 30 units wide (eg: 90-60 = 30).
Multiply each midpoint by the corresponding frequency for a given row.
- 15*7 = 105
- 45*27 = 1215
- 75*12 = 900
- 105*4 = 420
Then add up those products.
105+1215+900+420 = 2640
Lastly, we divide this over the sum of the frequencies 7+27+12+4 = 50 to get 2640/50 = 52.8
The average time spent on homework is estimated to be about 52.8 minutes
Note that the majority of the the students (27) are in the 30 < t < 60 interval, so the mean of 52.8 fits this interval perfectly. It's closer to the right endpoint of the interval due to the fact the other 12+4 = 16 students are above this, and they make up the second most majority compared to the 27.
The reason why 52.8 is an estimate rather than the actual mean is because we are estimating each interval by picking out the midpoint each time. The midpoint is at the direct center, so it's the best guess we can do.
Answer:
Cos 68
Step-by-step explanation:
Given the expression 2cos² 34° - 1, we are to expression as a single trig ratio.
Let the angle be theta
Recall that sin²theta + cos²theta = 1
sin²theta = 1 - cos²theta ... 1
also Cos 2theta = Cos²theta - sin²theta ... 2
Substitute 1 into 2
Cos 2theta = Cos²theta - (1-cos²theta)
Cos 2theta = Cos²theta - 1 + cos²theta
Cos 2theta = 2Cos²theta - 1
Replace theta with 34
Cos 2(34)= 2Cos²(34)- 1
Cos 68 = 2Cos²(34)- 1
Hence the single trig expression is Cos 68
Answer:
The answer is 15
Step-by-step explanation:
hope this helps
Answer:
Step-by-step explanation:
Multiply 8 and 6 by 3.5 and then times them together.
8x3.5=28
6x3.5=21
28x21=588