can you show me how to get the answer to A chef makes 3 containers of soup that fill a total of 120 bowls. Each container of sou
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Given:
In a set of 3 numbers the first is a positive integer, the second is 3 more than the first and the 3rd is a square of the second.
To find:
The equation for the given situation if the sum of the numbers is 77.
Solution:
a. Let the first number in the set is x.
The second is 3 more than the first. So, the second number is .
The 3rd number is a square of the second. So, the third number is .
Therefore, the first, second and third numbers are respectively.
b. The sum of the numbers is 77.
First number + Second number + Third number = 77
c. So, the equation in terms of x is:
Therefore, the required equation is .
d. On simplification, we get
Subtract 77 from both sides.
Therefore, the simplified form of the required equation is .
Answer:
We conclude that the actual percentage of households is equal to 30%.
Step-by-step explanation:
We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.
Their marketing people survey 150 households with the result that 43 of the households have three cell phones.
Let p = <u><em>proportion of households that have three cell phones NOT known.</em></u>
So, Null Hypothesis, : p = 30% {means that the actual percentage of households is equal to 30%}
Alternate Hypothesis, : p
30% {means that the actual percentage of households different from 30%}
The test statistics that would be used here <u>One-sample z-test for proportions;</u>
T.S. = ~ N(0,1)
where, = sample proportion of households having three cell phones =
= 0.29
n = sample of households = 150
So, <u><em>the test statistics</em></u> =
= -0.27
The value of z test statistic is -0.27.
<u>Also, P-value of the test statistics is given by;</u>
P-value = P(Z < -0.27) = 1 - P(Z 0.27)
= 1 - 0.6064 = <u>0.3936</u>
<u>Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.</u>
Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <em><u>we fail to reject our null hypothesis</u></em>.
Therefore, we conclude that the actual percentage of households is equal to 30%.