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3 years ago

The value of y varies directly with x. If x = 5 when y = 12, what is the value of x whon y = 30?

Mathematics

1 answer:

Brrunno [24]3 years ago

5 0

Step-by-step explanation:

y = kx, where k is a real constant.

When y = 12, x = 5.

=> (12) = (5)k, k = 2.4.

Therefore when y = 30,

x = y/k = (30)/(2.4) = 12.5.

The answer is 12.5.

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A right triangle has one leg that measures 7 inches, and the second leg measures 10 inches. How long is the hypotenuse?

faltersainse [42]

Answer:

Hypotenuse≈ $12.21$

Step-by-step explanation:

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3 years ago

The manufacturer of an electronic device claims that the probability of the device failing during the warranty period is 0.005.

Zielflug [23.3K]

Answer:

The value is $P(X \ge 15) = 0.5$

Step-by-step explanation:

From the question we are told that

The probability of the device failing during the warranty period is $p = 0.005$

The sample size is $n = 3000$

The random variable considered is x = 15

Generally this is distribution is binomial given the fact that there is only two out comes hence

X which is a variable representing a randomly selected selected electronic follows a binomial distribution i.e

$X \~ \ B(n , p)$

Now the mean is mathematically evaluated as

$\mu = n * p$

=> $\mu = 3000 * 0.005$

=> $\mu =15$

The standard deviation is mathematically represented as

$\sigma = \sqrt{np(1 -p )}$

=> $\sigma = \sqrt{3000 * 0.005 * (1 - 0.005 )}$

=> $\sigma = 3.86$

Now given that n is very large, then it mean that we can successfully apply normal approximation on this binomial distribution

$P(X \ge 15) = P( \frac{X - \mu}{\sigma } \ge \frac{x - \mu}{\sigma } )$

Now applying Continuity Correction we have

$P(X \ge (15-0.5)) = P( \frac{X - \mu}{\sigma } > \frac{(15 -0.5) - 15}{3.86 } )$

Generally $\frac{X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X)$

$P(X \ge (15-0.5)) = P(Z >-0.130 )$

From the z-table

$P(Z >-0.130 ) =0.5$

Thus

$P(X \ge 15) = 0.5$

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3 years ago

You attend a karaoke night and hope to hear your favorite song. The karaoke song book has 900 different songs (your favorite son

Afina-wow [57]

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2 years ago

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.

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1 year ago