An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triang
le is x. Another side is 12 more than four times the length of the bottom of the triangle. The last side is 3 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle
2 answers:
ANSWER
EXPLANATION
The perimeter of the triangle is the distance around the triangle.
We need to apply our ability to convert word problems in to mathematical expressions.
we were told that the bottom of the triangle is units.
From the diagram perimeter
Four times the length of the bottom will be .
12 more than 4 times the bottom will be
Hence another side of the triangle is
Finally we were told that the last side is 3 more than the bottom, that will be
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Answer:
(a) The distribution of the sample proportion is Normal distribution.
(b) The probability that in this sample of 150 households that more than 50% own a 4K television is 0.00012.
Step-by-step explanation:
We are given that in the United States, 35% of households own a 4K television.
Suppose we take a random sample of 150 households.
<em>Let </em><em> = sample proportion of households who own a 4K television.</em>
The z-score probability distribution for sample proportion is given by;
Z = ~ N(0,1)
where, = sample proportion
p = population proportion of households own a 4K television = 35%
n = sample of households = 150
(a) The distribution of the sample proportion is related to the Normal distribution.
(b) Probability that in this sample of 150 households more than 50% own a 4K television is given by = P( > 0.50)
P( > 0.50) = P(
>
) = P(Z > 3.67) = 1 - P(Z
3.67)
= 1 - 0.99988 = 0.00012
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.67 in the z table which has an area of 0.99988.</em>
Therefore, probability that in this sample of 150 households more than 50% own a 4K television is 0.00012.