Answer:
A Yes, a sequence of dilations and rigid motions carries one triangle onto the other
Step-by-step explanation:
Since two angles are marked with the same measures in each triangle, the triangles are similar by the AA postulate with no further action.
By some accounts it seems to be necessary to lay one figure on top of the other to demonstrate similarity. In order to do that, the smaller triangle would need to be dilated and translated (a rigid motion) to make it occupy the same space as the larger triangle.
Answer:
8
Step-by-step explanation:
hypotenuse = c = 17 feet
Height = a = 9 feet + 6 feet = 15 feet
Children's space = b
a^2 + b^2 = c^2
15^2 + b^2 = 17^2
225 + b^2 = 289 Subtract 225 from both sides
225-225+b^2=289-225
b^2 = 64 Take the square root of both sides.
sqrt(b^2) = sqrt(64)
b = 8
Since each child takes up 1 foot, 8 children can sit on side b.
Answer:
Due to the higher z-score, Jane did better in class.
Step-by-step explanation:
Z-score:
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Whoever's grade had the better z-score did better in class.
Mary's:
Mean of 85, standard deviation of 5, grade of 88. This means that
. So



Jane's
Mean of 80, standard deviation of 10, grade of 88. This means that
. So



Due to the higher z-score, Jane did better in class.
Answer:
Yes
Step-by-step explanation:
0.581 i used a calculator