Answer:
0.448 seconds
Step-by-step explanation:
d = -16t² -4t + 412
find t when d = 407
substituting d = 407 into the equation:
407 = -16t² -4t + 412 (subtract 407 from both sides)
-16t² -4t + 412 - 407 = 0
-16t² -4t + 5 = 0 (multiply both sides by -1)
16t² + 4t - 5 = 0
solving using your method of choice (i.e completing the square or using the quadratic equation), you will end up with
t = (-1/8) (1 + √21)= -0.70 seconds (not possible because time cannot be negative)
or
t = (-1/8) (1 -√21) = 0.448 seconds (answer)
Answer:
The measure of the angle JKG is:
m∠JKG = 56°
Step-by-step explanation:
<u>Given</u>
m∠JKG = 76-2x
m∠FHK = 6x-4
J is a midpoint of the segment FG and K is a midpoint of the segment GH.
<u>To determine</u>
m∠JKG = ?
Given that J is a midpoint of the segment FG and K is a midpoint of the segment GH. Thus, making two similar triangles, ΔJGK and ΔFGH
We know that two triangles are similar if the only difference is size. So, the angles remain the same.
so m∠JKG and m∠FHK are equal.
i.e.
m∠JKG = m∠FHK
substitute m∠JKG = 76-2x and m∠FHK = 6x-4
76-2x = 6x-4
6x+2x = 76 + 4
8x = 80
divide both sides by 8
8x/8 = 80/8
x = 10
Therefore, the value of x = 10
As
m∠JKG = 76-2x
substitute x = 10
m∠JKG = 76 - 2(10)
= 76 - 20
= 56°
Therefore, measure of the angle JKG is:
m∠JKG = 56°
Remainder of question:
Find the probability distribution of x
Answer:
The random variable x is defined as: X = {0, 1, 2, 3, 4}
The probability distribution of X:
P(X = 0) = 0.656
P(X = 1) = 0.2916
P(X= 2) = 0.0486
P(X=3) = 0.0036
P(X = 4) = 0.0001
Step-by-step explanation:
Sample size, n = 4
Random variable, X = {0, 1, 2, 3, 4}
10% (0.1) of the homeowners are insured against earthquake, p = 0.1
Proportion of homeowners who are not insured against earthquake, q = 1 - 0.1
q = 0.9
Probability distribution of x,
Answer:
The answer is B
Step-by-step explanation:
x/-y is equivalent to -(x/y)
