Answer:
B) BC'= 8, m A'= 28°
Step-by-step explanation:
When dilating a figure, it increases its size or decreases. In this case, as it is dilating by a factor of 1/2, you can assume it decreases.
To find the value of the new figure, A'B'C', you have to multiply the factor times the lengths of the triangle, or, the only one they are asking for in this case, the length BC':
- BC' = BC×1/2
- BC' = 16×1/2
- BC' = 8
The angles, otherwise, do not change. When figures are dilated, they are similar. The properties of similar figures are that they have congruent angles, therefore, the same angles. They do not have any effect caused by the factor, so m A' stays at 28°.
Greatest common factor = 1
Answer:
a. 81.5%
Step-by-step explanation:
The z-score for 400 is ...
Z = (X -μ)/σ = (400 -500)/100 = -1
The z-score for 700 is ...
Z = (700 -500)/100 = 2
The empirical rule tells you that 68% of the distribution is within ±1σ of the mean, and 95% is within ±2σ of the mean. Half of that first number is in the range Z = -1 to 0, and half that second number is in the range Z = 0 to +2. So, the probability you want is ...
(1/2)(68%) + (1/2)(95%) = 81.5% . . . . matches choice A
