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4 years ago

3x + 5y = 78

Mathematics

2 answers:

fenix001 [56]4 years ago

8 0

Answer: The correct option is (B) 6.

Step-by-step explanation: We are given to select the x co-ordinate of the point of intersection of the following lines.

$3x+5y=78~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-y=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

To find the x co-ordinate of the point of intersection, we need to solve the given system of equation to find the point of intersection.

From equation (ii), we have

$2x=y\\\\\Rightarrow y=2x~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of y from equation (iii) in equation (i), we get

$3x+5(2x)=78\\\\\Rightarrow 3x+10x=78\\\\\Rightarrow 13x=78\\\\\Rightarrow x=\dfrac{78}{13}\\\\\Rightarrow x=6.$

Thus, the x co-ordinate of the point of intersection of the given lines is 6.

Option (B) is CORRECT.

zysi [14]4 years ago

5 0

Hello here is a solution :
3x + 5y = 78 .... (1)
2x - y = 0 ... (2)
from (2) : y = 2x
in (1) : 3x+5(2x) =78
13x = 78
x= 6
but : y =2x y=2(6) = 12
answer : x=6

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Using the normal distribution, the percentages are given as follows:

a) 9.18%.

b) 97.72%.

c) 50%.

d) 4.27%.

e) 0.13%.

f) 59.29%.

g) 2.46%.

h) 50%.

i) 50%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

For this problem, the mean and the standard deviation are given as follows:

$\mu = 247, \sigma = 60$

For item a, the proportion is the p-value of Z when Z = 167, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (167 - 247)/60

Z = -1.33.

Z = -1.33 has a p-value of 0.0918.

Hence the percentage is of 9.18%.

For item b, the proportion is the p-value of Z when Z = 367, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (367 - 247)/60

Z = 2.

Z = 2 has a p-value of 0.9772.

Hence the percentage is of 97.72%.

For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (247 - 247)/60

Z = 0

Z = 0 has a p-value of 0.5.

Hence the percentage is of 50%.

For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (350 - 247)/60

Z = 1.72

Z = 1.72 has a p-value of 0.9573.

1 - 0.9573 = 0.0427.

Hence the percentage is of 4.27%.

For item e, the proportion is the p-value of Z when Z = 67, hence:

$Z = \frac{X - \mu}{\sigma}$

Z = (67 - 247)/60

Z = -3.

Z = -3 has a p-value of 0.0013.

Hence the percentage is of 0.13%.

For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:

X = 300:

$Z = \frac{X - \mu}{\sigma}$

Z = (300 - 247)/60

Z = 0.88.

Z = 0.88 has a p-value of 0.8106.

X = 200:

$Z = \frac{X - \mu}{\sigma}$

Z = (200 - 247)/60

Z = -0.78.

Z = -0.78 has a p-value of 0.2177.

0.8106 - 0.2177 = 0.5929.

Hence the percentage is 59.29%.

For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:

X = 400:

$Z = \frac{X - \mu}{\sigma}$

Z = (400 - 247)/60

Z = 2.55.

Z = 2.55 has a p-value of 0.9946.

X = 360:

$Z = \frac{X - \mu}{\sigma}$

Z = (360 - 247)/60

Z = 1.88.

Z = 1.88 has a p-value of 0.97.

0.9946 - 0.97 = 0.0246

Hence the percentage is 2.46%.

For items h and i, the distribution is symmetric, hence median = mean and the percentages are of 50%.

More can be learned about the normal distribution at brainly.com/question/24808124

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3 years ago