Circle Q is centered at the origin with radius r. Point P(x, y) lies on circle Q. Make a conjecture. How can you find an equatio
n relating the radius to the coordinates of point P? Check all that apply. Notice that ΔPQS forms a right triangle.
Because ΔPQS is a right triangle,
apply the Pythagorean theorem.
x² + y² = r²
Because ΔPQS is a right triangle,
apply the Pythagorean theorem.
x² + y² = r²
2 answers:
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In a basket, 5/9 of the fruits are apples and the rest are oranges. 3/10 of the apples are green in colour. There are 15 green apples. How many fruits are there in the basket?
Answer:
15.7 in
Step-by-step explanation:
A slice of a round pie is a sector of a circle.
The perimeter of a slice is the arc length s plus twice the radius r.
P = s + 2r
s = rθ = r(16/360) = r/22.5. So,
16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5
16 × 22.5 = 46r
360 = 46r
r = 7.826
D = 2r = 2 × 7.826 = 15.7 in
The diameter of the cake should be 15.7 in.
Check:
It checks.
Answer:
a) Mean blood pressure for people in China.
b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.
d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg
f) 157.44mmHg
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If X is two standard deviations from the mean or more, it is considered unusual.
In this question:
a.) State the random variable.
Mean blood pressure for people in China.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
This is 1 subtracted by the pvalue of Z when X = 135.
has a pvalue of 0.6179
1 - 0.6179 = 0.3821
38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
This is the pvalue of Z when X = 141.
has a pvalue of 0.7140
71.30% probability that a person in China has blood pressure of 141 mmHg or less.
d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So
X = 125
has a pvalue of 0.4483
X = 120
has a pvalue of 0.3632
0.4483 - 0.3632 = 0.0851
8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
From b), when X = 135, Z = 0.3
Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.
f.) What blood pressure do 90% of all people in China have less than?
This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then
X = 120
So
157.44mmHg