Answer: The correct option is (D) P″(9, -12) and Q″(15, -3).
Step-by-step explanation: Given that triangle PQR is dilated by a scale factor of 1.5 to form triangle P′Q′R′. This triangle is then dilated by a scale factor of 2 to form triangle P″Q″R″.
The co-ordinates of vertices P and Q are (3, -4) and (5, -1) respectively.
We are to find the co-ordinates of the vertices P″ and Q″.
<u>Case I :</u> ΔPQR dilated to ΔP'Q'R'
The co-ordinates of P' and Q' are given by

<u>Case II :</u> ΔP'Q'R' dilated to ΔP''Q''R''
The co-ordinates of P'' and Q'' are given by

Thus, the co-ordinates of the vertices P'' and Q'' are (9, -12) and (15, -3).
Option (D) is CORRECT.
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Answer:
9
Step-by-step explanation:
<em>Degrees of freedom</em> is the number of values in the final calculation of a statistic that are free to vary. Degrees of freedom are related to sample size and calculated by n-1 where n is the <em>sample size</em>.
The Supervisor selects 10 teddy bears as sample from 5000 teddy bears produced daily. Therefore in this situation, there are 10-1=9 degrees of freedom
The width is half the length, so is
width = (1/2)*length
width = (1/2)*(<span>3.2a + 0.18b) cm
width = (1.6a +0.09b) cm
The perimeter of the rectangle is twice the sum of length and width.
perimeter = 2*(length + width)
perimeter = 2*((3.2a +0.18b) cm + (1.6a +0.09b) cm)
perimeter = 2*(4.8a +0.27b) cm)
perimeter = (9.6a +0.54b) cm
Sasha did not get this answer, so apparently ...
her reasoning was not correct.</span>
Answer:
A) The probability is 0.95 that the percent of adults living in the United States who are satisfied with their health care plans is between 63.6% and 68.4%.
Step-by-step explanation:
A polling agency reported that 66 percent of adults living in the United States were satisfied with their health care plans. The estimate was taken from a random sample of 1,542 adults living in the United States, and the 95 percent confidence interval for the population proportion was calculated as (0.636, 0.684).
This means that we are 95% sure that the true proportion of adults living in the United States who were satisfied with their health care plans is between 0.636 and 0.684.
So the correct answer is:
A) The probability is 0.95 that the percent of adults living in the United States who are satisfied with their health care plans is between 63.6% and 68.4%.
<span>With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first.</span>