Explain how to work out these type of questions please!
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Answer:
We conclude that the proportion of student body in favor of him is significantly less than or equal to 50%.
Step-by-step explanation:
We are given that Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent.
A random sample of 100 students was taken. Fifty-five of them favored Mike.
<em>Let p = </em><u><em>proportion of the students who are in favor of Mike.</em></u>
So, Null Hypothesis, : p
50% {means that the proportion of student body in favor of him is significantly less than or equal to 50%}
Alternate Hypothesis, : p > 50% {means that the proportion of student body in favor of him is significantly more than 50%}
The test statistics that would be used here <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of students body in favor of Mike =
= 0.55
n = sample of students taken = 100
So, <em><u>test statistics</u></em> =
= 1.01
The value of z test statistics is 1.01.
<em>Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.</em>
<em>Since our test statistic is less than the critical value of z as 1.01 < 1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><u><em>we fail to reject our null hypothesis</em></u><em>.</em>
Therefore, we conclude that the proportion of student body in favor of him is significantly less than or equal to 50% or proportion of the students in favor of Mike is not significantly greater than 50 percent.
The expression which is equivalent to 6 Superscript 4 times 6 cubed and posses same value as this expression is,
Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The given statement for the expression is 6 Superscript 4 times 6 cubed. This expression cab be written as,
Suppose the equivalent expression of this equation is n. Thus,
The 4 power of number 6 means that the number 6 should be multiplied 4 times.
Hence, the expression which is equivalent to 6 Superscript 4 times 6 cubed and posses same value as this expression is,
Learn more about the equivalent expression here;
First we will convert those radian angles to degrees, since my mind works better with degrees. Let's work one at a time. First, 
. If we start at the positive x-axis and measure out 315 we end up in the 4th quadrant with a reference angle of 45 with the positive x-axis. The side across from the reference angle is -1, the side adjacent to the angle is 1, and the hypotenuse is sqrt2. The cotangent of this angle, then is 1/-1 which is -1. As for the second one, converting radians to degrees gives us that 
. Sweeping out that angle has us going around the origin more than once and ending up in the first quadrant with a reference angle of 30° with the positive x-axis. The side across from the angle is 1, the side adjacent to the angle is √3, and the hypotenuse is 2. Therefore, the secant of that angle is 2/√3.