PLEASE HELP!!! Solve -(6)^x-1+5=(2/3)^2-x by graphing. Round to the nearest tenth.
1 answer:
Answer:
x= 1.8
Step-by-step explanation:
We have been given the equation;
-(6)^(x-1)+5=(2/3)^(2-x)
We are required to determine the value of via graphing. To do this we can split up the right and the left hand sides of the equation to form the following two separate equations;
y = -(6)^(x-1)+5
y = (2/3)^(2-x)
We then proceed to graph the two equations on the same graph. The solution will be the point where the equations will intersect. Find the attachment below for the graph;
The value of x is 1.785. To the nearest tenth we have x = 1.8
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Answer:
We conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remained same.
Step-by-step explanation:
We are given that in a previous poll, 40% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week.
Suppose that, in a more recent poll, 456 of 1194 adults with children under the age of 18 reported that their family ate dinner together seven nights a week.
Let p = <u><em>proportion of families with children under the age of 18 who eat dinner together seven nights a week.</em></u>
SO, Null Hypothesis, : p
40% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remained same}
Alternate Hypothesis, : p < 40% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased}
The test statistics that would be used here <u>One-sample z test for</u> <u>proportions</u>;
T.S. = ~ N(0,1)
where, = sample proportion of families with children under the age of 18 who eat dinner together seven nights a week =
= 0.38
n = sample of adults = 1194
So, <u><em>the test statistics</em></u> =
= -1.424
The value of z test statistics is -1.424.
<u>Now, at 0.01 significance level the z table gives critical value of -2.326 for left-tailed test.</u>
Since our test statistic is more than the critical value of z as -1.424 > -2.326, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remained same.