Answer:
Step-by-step explanation:
Let Q have coordinates x and y
<u>Using midpoint formula we find the values of x and y</u>
- (- 3 + x)/2 = 5 ⇒ -3 + x = 10 ⇒ x = 10 + 3 ⇒ x = 13
- (6 + y)/2 = 8 ⇒ 6 + y = 16 ⇒ y = 16 - 6 ⇒ y = 10
- Q = (13, 10)
<h3>Answer: As a fraction, HC is 21/4 units long</h3><h3>In decimal form, HC is 5.25 units long.</h3>
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Work Shown:
Let x = HC and y = BH
AH = 12-x since AH = 12-HC and x = HC
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See the attached drawing below. The altitude BH forms three similar triangles which makes the proportion below possible
HC/BH = BH/AH
x/y = y/(12-x) ... substitution
x(12-x) = y^2 ... cross multiply
y^2 = -x^2+12x
note how I isolated y^2 instead of y. We will use this equation later.
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Focus on triangle AHB. Use the pythagorean theorem
(BH)^2 + (AH)^2 = (AB)^2
(y)^2 + (12-x)^2 = (9)^2
y^2 + 144-24x+x^2 = 81
-x^2+12x + 144-24x+x^2 = 81 ... replace y^2 with -x^2+12x
-x^2+12x + 144-24x+x^2-81 = 0
-12x + 63 = 0
-12x = -63
x = -63/(-12)
x = 5.25 <<-- answer in decimal form
x = 5 + 0.25
x = 5 + 1/4
x = 20/4 + 1/4
x = 21/4 <<-- answer as a fraction
Construct a probability mass function (pmf) for x, the dollar amount won by a contestant in this game is 1/18.
What is a probability math example?
- Probability is the measurement of how likely something is to happen.
- As an example, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head.
- We write P(heads) = 12 here. The four most popular approaches to probability are axiomatic, classical, empirical, and subjective.
from above total number of chips =4+6+5+2+1 =18
hence Probabilty of win 0 P(0)=4/18
P(1) =6/18
P(5) =5/18
P(10) =2/18
P(100)=1/18
x P(x) xP(x)
0 0.22 0.00
1 0.33 0.33
5 0.28 1.39
10 0.11 1.11
100 0.06 5.56
8.39
therefore expeted value =8.39
Learn more about probability
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1. 198.56
Step-by-step explanation:
To find the volume of a cylinder, you need to find the area of the cross-section (one of the circles on the side) and multiply it by the length.
Area of the circle = π = π x (5.3/2) x (5.3/2) = π x 2.65 x 2.65 = 7.0225π
Volume of the cylinder = 7.0225π x 9 = 63.2025π = 198.56 2. V
=
a
base
×
h
V
=
π
r
2
×
h
V
=
π
(
d
2
)
2
×
h
V
=
π
(
6.6
2
)
2
×
9.9
V
=
338.7
c
m
3
Hopefully this helps!
