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Multiply 5.4 by 7:
Now divide 37.8 by 4:
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Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and
calculations to receive credit x^2 - 4x + y^2 + 8y = -4
1 answer:
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Answer:
Option (4) and Option (5)
Step-by-step explanation:
By calculating the second difference, if the second difference in a table is equal, table will represent the quadratic relationship.
In the given option, we analyze that table given in Option (4) will represent the quadratic relationship.
x y Ist difference IInd difference
0 4 - -
1 -4 -4 - (4) = -8 -
2 -4 -4 - (-4) = 0 0 - (-8) = 8
3 4 4 - (-4) = 8 8 - 0 = 8
Second difference of the terms in y are the same as 8.
Therefore, table of Option (4) represents the quadratic relationship.
Similarly, in Option (5) we will calculate the second difference of y terms.
x y Ist difference IInd difference
0 -4 - -
1 -8 -8 - (-4) = -4 -
2 -10 -10 - (-8) = -2 -2 - (-4) = 2
3 -10 -10 - (-10) = 0 0 - (-2) = 2
Here the second difference is same as 2.
Therefore, table of Option (5) will represent the quadratic relationship.
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%.