I'll test point P (0,-4) with its reflection point (4,-5). We see that x increased by 4 and y decreased by 1. Then we see that is reflected over some y value.
So the answer is (d) (the last one).
18)
It says the scale factor is 1:25000, so for every one part there is actually 25000. So for every centimeter, there is actually 25000 cm. See that we multiplied by 25000.
So for 6.8cm, multiply by 25000 to get 170000cm.
The real distance represented is 170000cm.
19) Just work out one step at a time using order of operations.
Do parentheses first. 7^2 = 49, and 3^3 is 3*3*3 which is 27.
Now you have [8(49 - 27) ]/ sqrt121.
Finish simplifying the parentheses. 49 - 27 is 22.
[8(22)] / sqrt121.
Now multiply 8 times 22, which is 176.
176 / sqrt 121
The square root of 121 is 11.
176/11.
= 16
Answer:
31, 114 and 35
Step-by-step explanation:
I set up the equation as such:
(3x + 21) + (x + 4) + x = 180
then I combined like terms:
5x + 25 = 180
And then solving for x I get:
5x = 155
x = 31
And then plugged the solved x value into the terms to give:
(3(31) + 21) = 114
(31 + 4) = 35
alongside the found angle of 31.
Answer:
Due to the larger sample size, the confidence interval of the second group will have greater precision for estimating the population mean.
Step-by-step explanation:
Margin of error of a confidence interval:
The equation for the margin of error of a confidence interval has the following format:
In which z is related to the confidence level, is the standard deviation of the population and n is the size of the sample.
From this, we can infer that a larger size leads to a greater precision of the interval, that is, a lesser margin of error.
In this question:
The sample from the first group survey has 49 data values, and from the second group has 81.
Due to the larger sample size, the confidence interval of the second group will have greater precision for estimating the population mean.
Part A
P = perimeter of square
P = add up the four sides
P = N+N+N+N
P = 4*N
where N is the side length of the square
The perimeter of the square is at most 22 ft, which means 22 ft is the largest the perimeter can be. Think of it as the ceiling.
So P = 22 or P < 22. We can combine those two ideas to get
(P is less than or equal to 22)
Replace P with 4N and solve for N
divide both sides by 4
The side length N can be 5.5 ft or smaller
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Part B
The result we got from part A above was
which means N can be equal to 5.5 or it can be smaller than 5.5
So this describes N = 2.5, N = 4.8, and N = 5.2
The values N = 5.8 and N = 6 are too big
So the answers to part B are 2.5 ft, 4.8 ft, and 5.2 ft