Annie is creating a stencil for her artwork using a coordinate plane. The beginning of the left edge of the stencil falls at (2,
2 answers:
Answer:
(A)(12, 9)
Step-by-step explanation:
Provided:
The starting point of the stencil's left edge is at (2, -1).
A designated point, referred to as Q on the stencil, is located at (4, 1).
Point Q divides the stencil in a 1:4 ratio.
We are tasked with determining the endpoint of the stencil.
Mathematically, Point Q segments the stencil internally in a 1:4 ratio.
For calculating the internal division of a line segment with initial point and end point
in the ratio m:n, we apply the formula
,
, Q(x,y)=(4,1), m:n=1:4
Consequently:
The selected choice is A.
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Answer:
At the α = 0.10 level, there is no substantial evidence indicating that the average vertical jump for students at this school differs from 15 inches.
Step-by-step explanation:
A hypothesis test is necessary to verify the assertion that the average vertical jump of students diverges from 15 inches.
The null and alternative hypotheses are:
The significance level is set at 0.10.
The sample mean recorded is 17, and the sample standard deviation is 5.37.
The degrees of freedom are calculated as df=(20-1)=19.
The t-statistic is:
The two-tailed P-value corresponding to t=1.67 is P=0.11132.
<pSince this P-value exceeds the significance level, the result is not significant. Therefore, the null hypothesis remains unchallenged.At the α = 0.10 level, there is no compelling evidence that the average vertical jump of students at this school deviates from 15 inches.
Answer:
Upon solving for y, we find:
By substitution, we have:
Thus, we arrive at:
And for x, we determine:
This gives us a length of 76 and a width of 12.5.
Step-by-step explanation:
We are dealing with a rectangle. The formula for the perimeter is:
Here, x denotes the length and y the width. The following conditions can be established:
Substituting these values yields:
When we solve for y, we find:
By substitution, we obtain:
Thus, we conclude:
The length is found to be 76, while the width measures 12.5.