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2 years ago

Please help solve this using L.C.M and explain the steps plz ty.

Mathematics

1 answer:

Reptile [31]2 years ago

6 0

9514 1404 393

Answer:

(x, y) = (2, 3)

Step-by-step explanation:

The first step is to find the least common multiple of the denominators of each of the equations. If the denominators have no common factors, a reasonable choice is their product. Here, it works to start with the fractions that must be added, then compare the LCM found to the denominator on the right to see if any further factors must be included.

First equation:

LCM = 3×4 = 12

12(2x/3 -y/4) = 12(7/12) . . . . . multiply the equation by 12

8x -3y = 7 . . . . . . . . . simplify

Second equation:

LCM = 4×5 =20

20(3x/4 -2y/5) = 20(3/10) . . . . multiply equation by 20

15x -8y = 6 . . . . . . simplify

Solve by elimination

We can eliminate the y-variable by subtracting 3 times the second equation from 8 times the first:

8(8x -3y) -3(15x -8y) = 8(7) -3(6)

19x = 38 . . . . . simplify

x = 2 . . . . . . . divide by 19

Substituting into the first equation gives ...

8(2) -3y = 7

3y = 9 . . . . . . add 3y-7

y = 3 . . . . . divide by 3

The solution is ...

(x, y) = (2, 3)

_____

There are many ways to solve such a system of equations. Using the LCM to eliminate fractions is one way to start. You can also do the arithmetic with the fractions intact, though most folks don't care to. In addition to the elimination method used here, you can use matrix or graphical methods, substitution, or any of the variations of Cramer's Rule.

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From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that ag

Jlenok [28]

Answer:

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.

Step-by-step explanation:

1) Data given and notation

$\bar X=18.1$ represent the mean age when smokers first start to smoke varies

$s=1.3$ represent the standard deviation for the sample

$\sigma=2.1$ represent the population standard deviation

$n=37$ sample size

$\mu_o =5.7$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean starting age is at least 19, the system of hypothesis would be:

Null hypothesis: $\mu\geq 19$

Alternative hypothesis: $\mu < 19$

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{18.1-19}{\frac{2.1}{\sqrt{37}}}=-2.607$