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3 years ago

Find the Solution of the equation -2x + 7 = 7

Mathematics

1 answer:

Basile [38]3 years ago

8 0

Answer:

x = 0

Step-by-step explanation:

-2 x 0 + 7 = 7

-2 x 0 = 0

0 + 7 = 7

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Prove that sequence an = (3^n)/(2n)! is monotone

krek1111 [17]

When $n=1$ , you have $a_1=\dfrac3{2!}=\dfrac32$ .

When $n=2$ , you have $a_2=\dfrac{3^2}{4!}=\dfrac38$ .

Clearly, $a_1>a_2$ .

Assume $a_k$ . Now when $n=k+1$ , you have

$a_{k+1}=\dfrac{3^{k+1}}{(2k+2)!}=\dfrac3{(2k+2)(2k+1)}\times\dfrac{3^k}{(2k)!}=\dfrac3{(2k+2)(2k+1)}a_k$

Therefore by induction the sequence is monotone (decreasing).

5 0

3 years ago

If james rolls the number cube 250 times, predict the number of times it will land on an odd number

Mars2501 [29]

Answer:

Let's find the possible outcomes of rolling odd.

1,3,5 are all odd. We have 3 outcomes.

Now find the possible outcome of a power of 2.

2 is 21, 4 is 22. We have 2 DIFFERENT outcomes.

(If these outcomes overlapped, we would have to subtract to get unique outcomes. In this case, these outcomes are different)

Now, we find the total number of possible outcomes.

A dice has 6 different outcomes.

Now add up the desired outcomes, 3+2=5

and so the probability is 56

Step-by-step explanation:

3 0

3 years ago

I NEED HELP WITH #36

Roman55 [17]

Answer:

2 3/4 in

Step-by-step explanation:

The sum of the marked distances is equal to the total distances shown:

... (1 5/8) + ? + (1 5/8) = 6

... ? = 6 - (1 5/8 + 1 5/8) . . . . . subtract the constants on the left

... ? = 6 - (2 5/4) . . . . . . . . . . . add the numbers in parentheses

... ? = 6 - 3 1/4 . . . . . . . . . . . . rewrite the number in parentheses (2+5/4 = 2 + 1 1/4)

... ? = (6 -3) -1/4 = 3 -1/4 . . . . . see below

... ? = 2 3/4

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<em>Comment on subtacting mixed numbers</em>

Some folks find it convenient to subtract by adding. To find the difference between 3 1/4 and 6, they would start by adding 3/4 to make 4, then add 2 to make 6. Then they see the difference is 3/4 + 2 = 2 3/4.

Here, I chose to subtract 3 1/4 by subtracting 3, then subtracting 1/4. After subtracting 3 from 6, I get 3, from which I now need to subtract 1/4. It should be clear that taking 1/4 away from 3 will leave 2 3/4. (One of the units has been converted to 4/4 to make the subtraction of 1/4 possible.)

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<em>Comment on doubling a fraction</em>

As part of this problem, we needed to add 1 5/8 to itself. We did that by doubling the integer part, and doubling the fraction. When a fraction has an even denominator, it is easy to double it: replace the denominator with half its value — 2×(5/8) = 5/4, where the denominator 4 is half the denominator 8.