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3 years ago

3x-2y=10. 4x-y=6. solve each of the pair of simultaneous linear equation by substitution method

Mathematics

1 answer:

brilliants [131]3 years ago

4 0

Answer:

x = 2/5, y= -22/5

Step-by-step explanation:

4x−y=6;3x−2y=10

Step: Solve4x−y=6for y:

4x−y+−4x=6+−4x(Add -4x to both sides)

−y=−4x+6

-y/-1 = -4x +6 over -1 (Divide both sides by -1)

y=4x−6

Step: Substitute4x−6for y in 3x−2y=10:

3x−2y=10

3x−2(4x−6)=10

−5x+12=10(Simplify both sides of the equation)

−5x+12+−12=10+−12(Add -12 to both sides)

−5x=−2

-5x/-5 = -2/5 (Divide both sides by -5)

x= 2 /5

Step: Substitute 2/ 5 for x in y=4x−6:

y=4x−6

y=4 ( 2/ 5 ) −6

y= −22 /5

(Simplify both sides of the equation)

x = 2/5, y= -22/5

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Step-by-step explanation:

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3 years ago

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Give a correct interpretation of a 99% confidence level of 0.328 < μ < 0.486.

stepladder [879]

Answer:

Step-by-step explanation:

Lower bound of the population mean is 0.328

Upper bound of the population mean is 0.486

Confidence level is 99%

Therefore, the correct interpolation of the confidence interval is that we are 99% confident that the true value of the population mean is between 0.328 and 0.486

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4 years ago

You have the numbers 1-24 written on slips of paper. If you choose one slip at random, what is the probability that you will not

ra1l [238]

The probability of selecting a number not divisible by 3 is: 2/3

Step-by-step explanation:

There are two methods to solve the question.

We can find the probability of numbers not divisible by 3
We can find the probability of numbers divisible by 3 and then find the complement of it

We will use the second method:

Given:

There are 24 slips

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24}

n(S) = 24

Let A be the event that the slip number is divisible by 3

Then

A = {3,6,9,12,15,18,21,24}

n(A) = 8

The probability of number divisible by 3 is:

$P(A) = \frac{n(A)}{n(S)}\\=\frac{8}{24}\\=\frac{1}{3}$

The sum of the probability of an event's occurrence and non-occurrence is 1. So the probability of numbers divisible by 3 will be subtracted from 1 to find the probability of selecting a number not divisible by 3.

The probability of selecting a number not divisible by 3 will be:

$=1-\frac{1}{3}\\=\frac{3-1}{3}\\=\frac{2}{3}$