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damaskus [11]
3 years ago
12

Carter rolls a fair number cube 18 times.Which is the best prediction for the number of times he will roll a number that is odd

and less than 3?
Mathematics
1 answer:
spin [16.1K]3 years ago
8 0

\frac{3}{18}
Simplified
\frac{1}{6}
There are 6 numbers on a die. So the probability over all to get either of those 6 numbers is 1/6 if you roll just once. The only number that is odd and less than 3 is 1. 1 is one of those 6 numbers so the probability to get a number odd and less than three in 18 rolls is 3/18 which is also 1/6 if it needs to be simplified
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A certain city's population is 120,000 and decreases 1.4% per year for 15 years.
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Answer:

  • Decay Problem.
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Step-by-step explanation:

The exponential function for growth/decay is given as:

P(t)=P_0(1 \pm r)^t, where:\\P_0$ is the Initial Population\\r is the growth/decay rate\\t is time

In this problem:

The city's initial population is 120,000 and it decreases by 1.4% per year.

  • Since the population decreases, it is a Decay Problem.
  • Decay rate, r=1.4% =0.014
  • Initial Amount =120,000

Therefore, the function is:

P(t)=120000(1 - 0.014)^t\\P(t)=120000(0.986)^t

When t=10 years

P(10)=120000(0.986)^10\\=104219.8\\\approx 104220 $ (to the nearest whole number)

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Find an equation for those points P such that the distance from P to A(0, 1, 2) is equal to the distance from P to B(6, 4, 2). W
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Answer:  The required equation for points P is 4x+2y=17.

Step-by-step explanation: We are give two points A(0, 1, 2) and B(6, 4, 2).

To find the equation for points P such that the distance of P from both A and B are equal.

We know that the distance between two points R(a, b, c) and S(d, e, f) is given by

RS=\sqrt{(d-a)^2+(e-b)^2+(f-c)^2}.

Let the point P be represented by (x, y, z).

According to the given information, we have

PA=PB\\\\\Rightarrow \sqrt{(x-0)^2+(y-1)^2+(z-2)^2}=\sqrt{(x-6)^2+(y-4)^2+(z-2)^2}\\\\\Rightarrow x^2+y^2-2y+1+z^2-4z+4=x^2-12x+36+y^2-8y+16+z^2-4z+4~~~~~~~[\textup{Squaring both sides}]\\\\\Rightarrow -2y+1=-12x-8y+52\\\\\Rightarrow 12x+6y=51\\\\\Rightarrow 4x+2y=17.

Thus, the required equation for points P is 4x+2y=17.

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3 years ago
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