Answer:
True.
Step-by-step explanation:
These angles are congruent because lines DE and BC are parallel.
Answer:
Height: 3/2 inches
Length: 12 inches
Width: 4 inches
Step-by-step explanation:
Let x is the side length of the square
The height of the box by cutting squares off :x
- The new length of the cardboard = 15 -2x (because we cut from 4 corners)
- The new width of the cardboard = 7 -2x (because we cut from 4 corners)
The new volume of it is:
V = (15 -2x) (7 -2x) x
<=> V =
To maximum volume, we use the first derivative of the volume
<=> 
<=> 
<=> 2x -3 = 0 or 6x -35 = 0
<=> x = 3/2 or x = 35/6
To determine which value of x gives a maximum, we evaluate
= 24x -88
= 24(3/2) -88 = -52
= 24(35/6) -88 = 52
We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.
So the dimensions (in inches) of the box is:
Height: 3/2 inches
Length: 15-2(3/2) = 12 inches
Width: 7 - 2(3/2) = 4 inches
Using it's concept, it is found that the probability of being a girl and choosing lemonade is given by:
b. 0.2.
<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
In this problem, out of 130 people, 26 are girls who choose lemonade, hence the probability is given by:
p = 26/130 = 0.2, which means that option b is correct.
More can be learned about probabilities at brainly.com/question/14398287
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