The coefficient of determination r² is 0.769² = 0.591. This means that 59.1% of the data y can be explained by the linear relationship between x and y while the other 40.9% is still unexplained. The positive value for the correlation coefficient r means that as values for x increases, values for y also increase.
Answer:
The additional information required to prove ΔDEF ~ ΔPQR is the value of the ratio DE/PQ which has to be equal to three-halves for ΔDEF to be similar to ΔPQR
Step-by-step explanation:
Given DF/PR = FE/RQ = 3/2
The Side Side Side, SSS, similarity theorem states that where there are two triangles that have corresponding sides that are proportional to each other, the two triangles are said to be similar
Given ΔDEF and ΔPQR, have sides DF/PR = FE/RQ, to prove that ΔDEF and ΔPQR, then the additional information required is the ratio of the third sides of the triangles which is DE/PQ.
If DE/PQ = Three-halves, the two triangles ΔDEF and ΔPQR are similar, if not, that is DE/PQ ≠ Three-halves, then the two triangles ΔDEF and ΔPQR are not similar.
Answer:
(a) 93.19%
(b) 267.3
Step-by-step explanation:
The population mean and standard deviation are given as 502 and 116 respectively.
Consider, <em>X</em> be the random variable that shows the SAT critical reading score is normally distributed.
(a) The percent of the SAT verbal scores are less than 675 can be calculated as:
![P(X](https://tex.z-dn.net/?f=P%28X%3C675%29%3DP%28Z%3C%5Cfrac%7B675-502%7D%7B116%7D%29%5C%5C%20P%28X%3C675%29%3DP%28Z%3C%5Cfrac%7B675-502%7D%7B116%7D%29%5C%5CP%28X%3C675%29%3DP%28Z%3C1.49%29%5C%5CP%28X%3C675%29%3D%200.9319)
Thus, the required percentage is 93.19%
(b)
The number of SAT verbal scores that are expected to be greater than 575 can be calculated as:
![P(X>575)=P(\frac{x-502}{116}>\frac{575-502}{116}\\P(X>575)=P(Z>\frac{575-502}{116})\\P(X>575)=P(Z>0.6293)\\P(X>575)=0.2673](https://tex.z-dn.net/?f=P%28X%3E575%29%3DP%28%5Cfrac%7Bx-502%7D%7B116%7D%3E%5Cfrac%7B575-502%7D%7B116%7D%5C%5CP%28X%3E575%29%3DP%28Z%3E%5Cfrac%7B575-502%7D%7B116%7D%29%5C%5CP%28X%3E575%29%3DP%28Z%3E0.6293%29%5C%5CP%28X%3E575%29%3D0.2673)
So,
Out of 1000 randomly selected SAT verbal scores, 1000(0.2673) = 267.3 are expected to have greater than 575.
X = 0 is the smallest x can be. Anything smaller and it wouldn't make any sense because negative time values make no sense.
x = 7 is the largest x can be. Why? Because plugging in x = 7 leads to
f(x) = 1575 - 225x
f(7) = 1575 - 225*7
f(7) = 1575 - 1575
f(7) = 0
so at year 7, the value is 0 dollars. Any x value larger than 7 will produce negative dollar values, which make no sense.
Another way to get x = 7 is to notice that 1575 - 225x = 0 has the solution x = 7
We'd solve for x like so
1575 - 225x = 0
1575 = 225x
225x = 1575
x = 1575/225
x = 7
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So x = 0 is the smallest x can be and x = 7 is the largest x can be. This means the domain is
Answer: Choice D
Answer:
Step-by-step explanation:
(0, 1) (4, -2)
(-2 - 1)/(4 -0) = -3/4