Step-by-step explanation:
a. The null hypothesis is generally an exact value and the alternative hypothesis is the one we are trying to show. We are trying to show that the population mean is different from $24.57, so the hypotheses are as follows:
Null: The population mean hourly wage in the manufacturing industry is the same as the population mean hourly wage in the goods-producing industries
Alternative: The population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries
b.
Because we know the population standard deviation, we can use a z test
Plugging in the values:
Expected population mean: 24.57
Sample average: 23.89
Sample size: 30
Population standard deviation: 2.4, we get 0.1207 as our p-value.
c. Using a = 0.05, our p-value is greater than that, so we can not conclude the alternative hypothesis (The population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries)
d. Using a critical value calculator, we can find that for a two-tailed approach, the critical value would be 1.96. This would mean that the z score would have to be greater than 1.96 or less than -1.96 for the results to be significant. The population mean we would plug in here is 24.57, while the raw score would be 23.89 and the standard deviation would be 2.4. The z score we get is -0.283, which is not in the values specified (>1.96 or <-1.95) so we cannot conclude the alternative hypothesis
Answer:
or 2.738
Step-by-step explanation:
Let’s just look at the triangle on the top with the on the top and x on the bottom. (Basically the top half to the equilateral triangle)
There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem:
We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b= or
Plugging these values into the equation:
x^2+ (\frac{\sqrt{10} }{2})^{2}=\sqrt{10} ^{2}
This approximately equals 2.738
The formula for the surface area is 2(lw + lh + wh). So all you have to do is plug the values in.
Box A:
2(lw + lh + wh)
2( (4x6) + (4x25) + (6x25) ).
2(24+100+150)
2(274)
548=Surface Area
Box B:
2(lw + lh + wh)
2( (9x5) + (9x11) + (5x11) ).
2(45+99+55)
2(199)
398=Surface Area
Box C:
2(lw + lh + wh)
2( (10x5) + (10x8) + (5x8) ).
2(50+80+40)
2(170)
340=Surface Area
Answer:
12 squared unit
Step-by-step explanation:
Answer:
-23a + 64
Step-by-step explanation:
-8(-2a + 4a - 8) - 7a
First combine like terms
-8(2a - 8) - 7a
Then distribute
-16a + 64 -7a
Combine like terms
-23a + 64