You mix the letters m,a,t,h,e,m,a,t,i,c,a and l thoroughly without looking you draw one letter probability p(A) . write the prob
1 answer:
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Answer:
Option A. one rectangle and two triangles
Option E. one triangle and one trapezoid
Step-by-step explanation:
step 1
we know that
The area of the polygon can be decomposed into one rectangle and two triangles
see the attached figure N 1
therefore
Te area of the composite figure is equal to the area of one rectangle plus the area of two triangles
so
step 2
we know that
The area of the polygon can be decomposed into one triangle and one trapezoid
see the attached figure N 2
therefore
Te area of the composite figure is equal to the area of one triangle plus the area of one trapezoid
so
The net pay is the amount left after taxes and deductions have been removed from the gross pay.
Her monthly gross pay is: $4111.93
The deductions are:
Let her gross pay be x.
So, we have:
So, we have:
Express percentage as decimals
Add 102 to both sides
Divide both sides by 0.95
Rewrite as:
Hence, her monthly gross pay is: $4111.93
Read more about gross and net pay at:
Answer:
(a) P(X > $57,000) = 0.0643
(b) P(X < $46,000) = 0.1423
(c) P(X > $40,000) = 0.0066
(d) P($45,000 < X < $54,000) = 0.6959
Step-by-step explanation:
We are given that U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542.
Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246.
<em>Let X = annual salaries in the metropolitan Boston area</em>
SO, X ~ Normal()
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = average annual salary in the Boston area = $50,542
= standard deviation = $4,246
(a) Probability that the worker’s annual salary is more than $57,000 is given by = P(X > $57,000)
P(X > $57,000) = P( >
) = P(Z > 1.52) = 1 - P(Z
1.52)
= 1 - 0.93574 = <u>0.0643</u>
<em>The above probability is calculated by looking at the value of x = 1.52 in the z table which gave an area of 0.93574</em>.
(b) Probability that the worker’s annual salary is less than $46,000 is given by = P(X < $46,000)
P(X < $46,000) = P( <
) = P(Z < -1.07) = 1 - P(Z
1.07)
= 1 - 0.85769 = <u>0.1423</u>
<em>The above probability is calculated by looking at the value of x = 1.07 in the z table which gave an area of 0.85769</em>.
(c) Probability that the worker’s annual salary is more than $40,000 is given by = P(X > $40,000)
P(X > $40,000) = P( >
) = P(Z > -2.48) = P(Z < 2.48)
= 1 - 0.99343 = <u>0.0066</u>
<em>The above probability is calculated by looking at the value of x = 2.48 in the z table which gave an area of 0.99343</em>.
(d) Probability that the worker’s annual salary is between $45,000 and $54,000 is given by = P($45,000 < X < $54,000)
P($45,000 < X < $54,000) = P(X < $54,000) - P(X $45,000)
P(X < $54,000) = P( <
) = P(Z < 0.81) = 0.79103
P(X $45,000) = P(
) = P(Z
-1.31) = 1 - P(Z < 1.31)
= 1 - 0.90490 = 0.0951
<em>The above probability is calculated by looking at the value of x = 0.81 and x = 1.31 in the z table which gave an area of 0.79103 and 0.9049 respectively</em>.
Therefore, P($45,000 < X < $54,000) = 0.79103 - 0.0951 = <u>0.6959</u>