Find the area of the following shape.
2 answers:
Answer:
57 units^2
Step-by-step explanation:
First find the area of the triangle on the left
ABC
It has a base AC which is 9 units and a height of 3 units
A = 1/2 bh = 1/2 ( 9) *3 = 27/2 = 13.5
Then find the area of the triangle on the right
DE
It has a base AC which is 6 units and a height of 1 units
A = 1/2 bh = 1/2 ( 6) *1 = 3
Then find the area of the triangle on the top
It has a base AC which is 3 units and a height of 3 units
A = 1/2 bh = 1/2 ( 3) *3 = 9/2 = 4.5
Then find the area of the rectangular region
A = lw = 6*6 = 36
Add them together
13.5+3+4.5+36 =57 units^2
Answer:
Total Area = 57 sq. units
Step-by-step explanation:
will make it simple and short
Total Area = A1 + A2 + A3
A1 = (7 + 6) * 6/2 = 39 sq. units (area of a trapezoid)
A2 = 1/2 (9 * 3) = 13.5 sq. units (area of a triangle)
A3 = 1/2 (3 * 3) = 4.5 sq. units (area of a triangle)
Total Area = 39 + 13.5 + 4.5 = 57 sq. units
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Answer:
a) A. The population must be normally distributed
b) P(X < 68.2) = 0.7967
c) P(X ≥ 65.6) = 0.3745
Step-by-step explanation:
a) The population is normally distributed having a mean () = 64 and a standard deviation (
) =
b) P(X < 68.2)
First me need to calculate the z score (z). This is given by the equation:
but μ=64 and σ=19 and n=14,
and
Therefore:
From z table, P(X < 68.2) = P(z < 0.83) = 0.7967
P(X < 68.2) = 0.7967
c) P(X ≥ 65.6)
First me need to calculate the z score (z). This is given by the equation:
Therefore:
From z table, P(X ≥ 65.6) = P(z ≥ 0.32) = 1 - P(z < 0.32) = 1 - 0.6255 = 0.3745
P(X ≥ 65.6) = 0.3745
P(X < 68.2) = 0.7967
Answer:
The p value for this case would be given by:
Since the p value is higher than the significance level provided we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 20 ounces.
Step-by-step explanation:
Information provided
represent the sample mean
represent the population deviation
sample size
represent the value that we want to test
represent the significance level
z would represent the statistic
represent the p value
Hypothesis to test
We want to test if the true mean is at least 20 ounces, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing the info given we got:
The p value for this case would be given by:
Since the p value is higher than the significance level provided we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 20 ounces.