3. The rectangle below has an area of 297 in. Find the length of the diagonal.
1 answer:
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Step-by-step explanation:
a) The graph of a normal curve with a mean of 64" and a standard deviation of 3.5" is a bell-shaped curve with its
maximum value at x = 64.
Important points:
mean - 3 deviations: 64 - 3(3.5) = 64 - 10.5 = 53.5
mean - 2 deviations: 64 - 2(3.5) = 64 - 7 = 57
mean - 1 deviation: 64 - 3.5 = 60.5
mean: = 64
mean + 1 deviation: 64 + 3.5 = 67.5
mean + 2 deviations: 64 + 2(3.5) = 64 + 7 = 71
mean + 3 deviations: 64 + 3(3.5) = 64 + 10.5 = 74.5
b) If there are 3000 plants, approximately how many will be taller than 71"?
71" is 2 standard deviations above the mean. The region between two standard deviations below the mean and two standard deviations holds approximately 95% of the plants.
Therefore there will be approximately 5% of the plants divided equally between being taller than two standard
deviations above the mean and being shorter than two standard deviations below the mean. Thus, there will be
approximately 2.5% of the plants taller than 71": 0.025 x 3000 = 75 plants.
or
the z-score for 71
= (71-64)/35 = 2
going to your tables, or some other suitable source for standard deviation, we find
P(z < 2) = .9772
P(z > 2) = .0228
.0228(3000) = 68.4
or appr 68 plants
Answer:
2; 5; 8
Step-by-step explanation:
To fill in the table, we need to generate an equation to represent the relationship between x and y.
First, find the slope using the two pairs given, (5, -1) and (25, 11):
m = ⅗.
Next, using the point-slope form, we can use a point/coordinate pair and the slope to derive an equation as follows.
Where,
m = ⅗.
Plug in the values
Subtract 1 from both sides
Use the equation above to fill out the table by plugging each value of x into the equation to get the corresponding values of y for each x value.
✔️When x = 10:
✔️When x = 15:
✔️When x = 20: