The ratio of the measures of the angles in a triangle is 5 to 2 to 3 what's the measure of one angle

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

4 0

5x + 2x + 3x = 180
10x = 180
x = 18

Angles are 36, 54, 90

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The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i

kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.

Recall the formula for the sum of consecutive positive integers,

$\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2$

Now,

$1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016$

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

$\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224$

numbers, and their sum is

$\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400$

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of $1+9\times2=19$ .

So, the sum of the first 1234 terms in the sequence is 2419.

8 0

2 years ago

I need help with my math please help.

Misha Larkins [42]

The lines are more then you think they are

7 0

3 years ago

Read 2 more answers

In a standard normal distribution, what z value corresponds to 17% of the data between the mean and the z value?

hjlf

You're looking for a value $z$ such that

$\mathbb P(0$

Because the distribution is symmetric, the value of $z$ in either case will be the same.

Now, because the distribution is continuous, you have that

$0.17=\mathbb P(0$

The mean for the standard normal distribution is $0$ , and because the distribution is symmetric about its mean, it follows that $\mathbb P(Z$ .

$0.17=\mathbb P(Z$

You can consult a $z$ score table to find the corresponding score for this probability. It turns out to be $z\approx0.4399$ .