Alyssa draws a ray in her notebook. what is the minimum number of points through which the ray is drawn?
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<h3><u><em>Question:</em></u></h3>
On the first day, a total of 40 items were sold for $356. Pies cost $10 and cakes cost $8. Define the variables, write a system of equations to find the number of cakes and pies sold, and state how many pies were sold.
<h3><em><u>Answer:</u></em></h3>The variables are defined as:
"c" represent the number of cakes sold and "p" represent the number of pies sold
The system of equations used are:
c + p = 40 and 8c + 10p = 356
18 pies and 22 cakes were sold
<h3><em><u>Solution:</u></em></h3>Let "c" represent the number of cakes sold
Let "p" represent the number of pies sold
Cost of 1 pie = $ 10
Cost of 1 cake = $ 8
Given that total of 40 items were sold
number of cakes + number of pies = 40
c + p = 40 ------ eqn 1
<u><em>Given items were sold for $356</em></u>
number of cakes sold x Cost of 1 cake + number of pies sold x Cost of 1 cake = 356
8c + 10p = 356 ----- eqn 2
<u><em>Let us solve eqn 1 and eqn 2</em></u>
From eqn 1,
p = 40 - c ---- eqn 3
Substitute eqn 3 in eqn 2
8c + 10(40 - c) = 356
8c + 400 - 10c = 356
-2c = - 44
c = 22
<em>Substitute c = 22 in eqn 3</em>
p = 40 - c
p = 40 - 22
p = 18
Thus 18 pies and 22 cakes were sold
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