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2 years ago

Which strategy best explains how to solve this problem?

Mathematics

2 answers:

Rufina [12.5K]2 years ago

5 0

Answer:

Use objects to model the problem. Is your answer. i had this on my old test

Rufina [12.5K]2 years ago

4 0

This is a geometric sequence because each term is twice the value of the previous term. So this is what would be called the common ratio, which in this case is 2. Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a(n)=nth value, a=initial value, r=common ratio, n=term number

In this case we have r=2 and a=1 so

a(n)=2^(n-1) so on the sixth week he will run:

a(6)=2^5=32

He will run 32 blocks by the end of the sixth week.

Now if you wanted to know the total amount he runs in the six weeks, you need the sum of the terms and the sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r) where the variables have the same values so

s(n)=(1-2^n)/(1-2)

s(n)=2^n-1 so

s(6)=2^6-1

s(6)=64-1

s(6)=63 blocks

So he would run a total of 63 blocks in the six weeks.

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Which expression is equivalent to 3(4y)<br> I WILL MARK BRAINLIEST

Anastaziya [24]

Answer:

Step-by-step explanation:

Well 12y is the most obvious answer.

Anything that makes 12 is good enough.

4(3y) is another answer

12(y)

1(12y)

6(2y)

2(6y

7 0

3 years ago

Consider the following game, played with three standard six-sided dice. If the player ends with all three dice showing the same

ddd [48]

Answer:

$P(A) = \frac{1}{36}$

$P(B) = \frac{15}{36}$

$P(U) = \frac{11}{36}$

Step-by-step explanation:

From the question we are told that

The number of dice is $n = 3$

Generally for all three dice to show the same number the second and the third dice must have the same outcome as the outcome of the first dice.

This means that the number of outcome the first die can have is 6 (6 sides), the number of outcome which the second and the third dice can have is 1 (they must match the first )

So the probability that all three dice show the same number on the first roll is mathematically represented as

$P(A) = \frac{6}{6} * \frac{1}{6} * \frac{1}{6}$

=> $P(A) = \frac{1}{36}$

Generally for two of the three dice show the same number after the first roll then the number of outcome for one of the dice would be is 6 , the number of outcome for another one must be 1(i.e it must match the first ) , the number of outcome for the remaining one must be 5 (i.e it can show any of the remaining 5 sides which the first and second dice are not showing )

Now the number of ways of selecting this 2 dice that show the same number from the 3 dice is mathematically represented as

$N = ^3C_2$

Here C stands for combination

$N = ^3C_2 = 6$

So the probability that exactly two of the three dice show the same number after the first roll is mathematically represented as

$P(B) = N \frac{1}{6} * \frac{5}{6}$

=> $P(B) = \frac{15}{36}$

Generally from the question we are told that if two dice match, the player re-rolls the die that does not match.

Now the probability that the die that did not match the first time will match the second time is

$P(E ) = \frac{1}{6}$

Generally if that one die does not show the same number in the second round , the probability that it will match in the third round is

$P(R) = \frac{5}{6} * \frac{1}{6}$

Generally the probability that he wins (i.e when all three are showing the same number ) and exactly two is showing the same number is mathematically represented as

$P(K) = P(E)* P(B) + P(R)* P(B)$

=> $P(K) = \frac{1}{6} * \frac{15}{36} + \frac{5}{6} * \frac{1}{6} * \frac{15}{36}$

=> $P(K)= \frac{165}{1296}$

So the probability that the player wins, conditioned on exactly two of the three dice showing the same number after the first roll is mathematically represented as

$P(U) = \frac{\frac{165}{1296}}{\frac{15}{36} }$