Hi there!
quarter:18
<u><em>1.Find common denominator in 4 and 1/2:</em></u>
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<u><em>2.Convert 4 2/4 into mixed number:</em></u>
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<u><em>3.Divide 18/4 by 1/4:</em></u>
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Therefore, there is 18 quarters in 4 1/2.
I: x-2y>=8
II:2x+y<=3
start by isolating y on a side
with I:
x-2y>=8
-2y>=8-x
2y<=x-8
y<=x/2-4
with II:
2x+y<=3
y<=-2x+3
now you can draw I' and II' and read of the solutions with the graph.
transform the inequalities into lines in slope intercept form by replacing the inequality with equality:
y<=x/2-4
->
y=x/2-4
y<=-2x+3
->
y=-2x+3
look at the inequalities to figure out if the area above or below is valid for each line (y<=... -> area below is valid->colored in the attached image)
the area in which all areas overlap is the solution space.
Answer:
The prism
Step-by-step explanation:
The surface area of a cube is:
where
L is the length of the side
For the cube in this problem,
L = 6 cm
So the surface area of the cube is
The surface area of a rectangular prism with squared base is:
where
L is the length of the base
h is the height of the prism
For the prism in this problem,
L = 3 cm
h = 12 cm
Therefore,
So, the prism has a greater surface area.
The probability the man will win will be 13.23%. And the probability of winning if he wins by getting at least four heads in five flips will be 36.01%.
<h3>How to find that a given condition can be modeled by binomial distribution?</h3>
Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ⁻ˣ⁾
A man wins in a gambling game if he gets two heads in five flips of a biased coin. the probability of getting a head with the coin is 0.7.
Then we have
p = 0.7
n = 5
Then the probability the man will win will be
P(X = 2) = ⁵C₂ (0.7)² (1 - 0.7)⁽⁵⁻²⁾
P(X = 2) = 10 x 0.49 x 0.027
P(X = 2) = 0.1323
P(X = 2) = 13.23%
Then the probability of winning if he wins by getting at least four heads in five flips will be
P(X = 4) = ⁵C₄ (0.7)⁴ (1 - 0.7)⁽⁵⁻⁴⁾
P(X = 4) = 5 x 0.2401 x 0.3
P(X = 4) = 0.3601
P(X = 4) = 36.01%
Learn more about binomial distribution here:
brainly.com/question/13609688
#SPJ1
Answer:
$23,330.66
Step-by-step explanation:
The compound interest function is ...
FV = P(1 +r/n)^(nt)
where P is the principal amount ($19,600), n is the number of compoundings per year (4), r is the interest rate (.035), and t is the number of years (5).
Putting these numbers into the formula and doing the arithmetic, we get ...
FV = $19,600(1 +.035/4)^(4·5) = $23,330.66
