Answer:
86%
Step-by-step explanation:
Let g represent the mean mark for the 10 girls in the class. Then the mean mark for the class was ...
10g +20(62%) = 30(70%)
g = 3(.7) -2(.62) . . . . . . . . . divide by 10 and subtract 2(.62)
g = .86 = 86%
The mean mark for girls was 86%.
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You can do this in your head if you consider it in terms of deviations from the mean. The second equation above can be rewritten and factored as ...
g = 70% +2(70% -62%)
That is, because there are 2 boys for every girl, the girl's score is above the mean by an amount that is 2 times the amount that the boy's score is below the mean. The boys' score is below by 8%, so the girls' score is above by 16%, so is 86%.
Answer:
35/4 minutes per mile
Step-by-step explanation:
rate = time/distance, therefore the answer is 35/4
Hey there!
150 short sleeves will be ordered
100 long sleeves will be ordered
Hope this helps!
Answer:
30%
Step-by-step explanation:
1/5 = 20%
so, 50 - 20 = 30
The normal vector to the plane <em>x</em> + 3<em>y</em> + <em>z</em> = 5 is <em>n</em> = (1, 3, 1). The line we want is parallel to this normal vector.
Scale this normal vector by any real number <em>t</em> to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:
(1, 0, 6) + (1, 3, 1)<em>t</em> = (1 + <em>t</em>, 3<em>t</em>, 6 + <em>t</em>)
This is the vector equation; getting the parametric form is just a matter of delineating
<em>x</em>(<em>t</em>) = 1 + <em>t</em>
<em>y</em>(<em>t</em>) = 3<em>t</em>
<em>z</em>(<em>t</em>) = 6 + <em>t</em>
