5 - 2z + 8z = ___
1 answer:
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Answer:
We conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.
Step-by-step explanation:
We are given that a survey showed that among 785 randomly selected subjects who completed four years of college, 144 of them are smokers.
Let p = <u><em>population proportion of smokers among those with four years of college</em></u>
So, Null Hypothesis, : p
27% {means that the rate of smoking among those with four years of college is more than or equal to the 27% rate for the general population}
Alternate Hypothesis, : p < 27% {means that the rate of smoking among those with four years of college is less than the 27% rate for the general population}
The test statistics that will be used here is <u>One-sample z-test</u> for proportions;
T.S. = ~ N(0,1)
where, = sample proportion of smokers =
= 0.18
n = sample of subjects = 785
So, <em><u>the test statistics</u></em> =
= -5.68
The value of z-test statistics is -5.68.
<h2>Also, the P-value of the test statistics is given by;</h2>P-value = P(Z < -5.68) = Less than 0.0001
Now, at a 0.01 level of significance, the z table gives a critical value of -2.3262 for the left-tailed test.
Since the value of our test statistics is less than the critical value of z, so we have <u><em>sufficient evidence to reject our null hypothesis</em></u> as it will fall in the rejection region.
Therefore, we conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.
Answer:
The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.
⇒The water level in the pool cannot exceed 14 feet.
Step-by-step explanation:
The question is on inequalities
Given;
Length= x ft
depth= x-6 ft
Width= x-8 ft
volume ≤ 1680 ft³
Forming the inequality to find length x of the pool
Volume= base area × depth
base area × depth ≤ volume
x(x-8) × (x-6) = 1680
(x²-8x )(x-6) = 1680
x(x²-8x) -6 (x²-8x)=1680
x³-8x²-6x²+48x=1680
x³-14x²+48x=1680
x³-14x²+48x-1680 ≤ 0
⇒The water level in the pool cannot exceed 14 feet...why?
taking the value of x at maximum to be 17 according to the graph, then maximum depth will be;
d=x-6 = 17-6=11 ft
⇒11 ft is less than 14ft
