Using the normal distribution, there is a 0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean 
and standard deviation 
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean
and standard deviation 
, as long as 
and 
.
The estimate and the sample size are:
p = 0.29, n = 207.
Hence the mean and the standard error are given as follows:
.
.
The probability that the sample proportion of households spending more than $125 a week is less than 0.31 is the <u>p-value of Z when X = 0.31</u>, hence:
By the Central Limit Theorem:
Z = 0.63
Z = 0.63 has a p-value of 0.7357.
0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
More can be learned about the normal distribution at brainly.com/question/4079902
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The equation of the line segment through A and B is given as
-7x + 3y = -21.5
In standard form,
3y = 7x - 21.5
y = (7/3)x - 7.1667
Line AB has a slope of 7/3.
Let the equation of line segment PQ be
y = mx + b
Because line segments AB and PQ are perpendicular, therefore
(7/3)*m = -1
m = -3/7
The equation of PQ is
y = -(3/7)x + b
To find b, note that the line passes through the point (7,6). Therefore
6 = -(3/7)*7 + b
6 = -3 + b
b = 9
The equation of PQ is
y = - (3/7)x + 9
or
7y = -3x + 63
3x + 7y = 63
Answer: 3x + 7y = 63
29990
10%=29990/10=2999
1%=2999/10=299.90
0.5%=299.90/2=149.95
6%=299.90x6=1799.40
6.5%=1799.50+149.95=$1949.35 tax
total +tax
29990+1949.35=$31395.35
Answer:
2587mm^3 approx!
Step-by-step explanation:
first you divide the nut into 6 part(in triangle now, by joining centre to each edge)
let's take one part of the triangular shape then area of that part can be found by using 1/2×base×height
i.e, 1/2×13×15=97.5(mm^2)
now when we consider depth of that traingular part,we will get volume of that part as area×depth
i.e, 97.5×6=585(mm^3)
now volume of all the 6 triangular part is 585×6=3510(in mm^3)
now take circular cavity in consideration, it's volume will be π(7^2)6=923(mm^3) approximately
now reqired volume will be volume of that hexagonal part minus that of circular cavity
=3510-923
=2587mm^3
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First figure out his total bill by adding up what he buys.
Now subtract the discount of $20 since his purchase was above $100:
