Find all points having an x-coordinate of 4 whose distance from the point (-2,-1) is 10

1 answer:

8 0

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\
10=\sqrt{(4-(-2))^2+(y-(-1))^2}\\
10=\sqrt{6^2+(y+1)^2}\\
10=\sqrt{36+y^2+2y+1}\\
10=\sqrt{y^2+2y+37}\\
100=y^2+2y+37\\
y^2+2y-63=0\\
y^2+9y-7y-63=0\\
y(y+9)-7(y+9)=0\\
(y-7)(y+9)=0\\
y=7 \vee y=-9\\\\
\boxed{(x,y)=\{(4,-9),(4,7)\}}

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Breyers is a major producer of ice cream and would like to test the hypothesis that the average American consumes more than 17 o

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Answer:

The p-value would be 0.0939

Step-by-step explanation:

We can set a standard t-test for the Null Hypothesis that $H_0: 18.2\geq 17$

The test statistic then takes the form

$t=\frac{18.2-17}{3.9/\sqrt{15}}=1.317$

with this value we then can calculate the probability that is left to the right of this value $P(X>1.317)$ . From theory we know that t follows a standard normal distribution. Then $P(X>1.317)=0.0939$ which is smaller than the p-value set by Breyers of 0.10