Answer:
a: 0.8884
b: 0.9934
Step-by-step explanation:
We have µ = 300 and σ = 70. The sample size, n = 125.
For the sample to be within 8 units of the population mean, we would have sample values of 292 and 308, so we want to find:
P(292 < x < 308).
We need to find the z-scores that correspond to these values using the given data. See attached photo 1 for the calculation of these scores.
We have P(292 < x < 308) = 0.8884
Next we want the probability of the sample mean to be within 17 units of the population mean, so we want the values from 283 to 317. We want to find
P(283 < x < 317)
We need to find the z-scores that correspond to these values. See photo 2 for the calculation of these scores.
We have P(283 < x < 317) = 0.9934
Answer: 6.82
Step-by-step explanation:
So we know the Law of Sines which is that Sin A/a = Sin B/b = Sin C/c. The Sin on top of the fraction is the angle, and the letter on the bottom is the side opposite from that angle.
Our first step is going to be finding the last angle. We have 2 angles already, but one that's missing. We know that all triangles' angles add up to 180, so we can add 68+40=108. Then do 180-108 to get 72. Now we know the third and final angle.
Ok so back to Law of Sines. Now we can plug into that equation. We only need Sin A/a = Sin B/b (It doesn't matter what order you put them in). And remember the lowercase letter at the bottom represents the OPPOSITE side from one of the angles. Since the problem wants the side opposite Sin 68, let's set up a proportion.
Set up we have what we know. We know one side, and opposite that is the angle we already solved for. Now we can cross multiply and end up with:
Since we want to isolate x, we can divide each side by Sin 72.
x= 7(Sin 68)/Sin 72
So now let's put it into the calculator:
7(Sin 68)=6.2853
Now let's divide 6.2853/Sin 72
And you should be left with 6.82 if you round it!
Answer:
576 cm²
Step-by-step explanation:
Given:
Number of sections in a suncatcher (n) = 6
Each section is in the shape of a parallelogram.
Base of parallelogram = 12 cm
Height of parallelogram = 8 cm
Now, area of a parallelogram is given as:
Area of parallelogram = Base × Height
Area of 1 parallelogram = 12 cm × 8 cm = 96 cm²
Now, there are 6 parallelogram shaped sections.
So, area of the sections = area of 1 section × total number of sections
∴ Area of 6 sections = 96 cm² × 6 = 576 cm²
Therefore, the total area of the sections of a suncatcher is 576 cm².
Answer: 5 games
Step-by-step explanation: They need to win half their games for a .500 record and half or 30 is 15. They already won 10 so they need to win 15- 10 = 5 more games to have a .500 record.
A. Area = ½b × h
= ½ × 16 × 9
= 72
B. Area = b × h
= 26 × 18
= 468
C. Area = a²
= 11²
= 121
D. Area = ½(a+b) × h
= ½(6+21) × 8
= 108
Hope this helps :)
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