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2 years ago

What is the value of x in the equation 3x- 4y =65, when y= 4?

Mathematics

2 answers:

Alecsey [184]2 years ago

4 0

Answer: The required value of x when y = 4 is 27.

Step-by-step explanation: We are given to find the value of x in the following equation when y = 4 :

$3x-4y=65~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To find the value of x, first we should write equation (i) as y as the dependent variable.

From equation (i), we have

$3x-4y=65\\\\\Rightarrow 3x=65+4y\\\\\Rightarrow x=\dfrac{65+4y}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Now, substituting y = 4 in equation (ii), we get

$x\\\\\\=\dfrac{65+4y}{3}\\\\\\=\dfrac{65+4\times4}{3}\\\\\\=\dfrac{65+16}{3}\\\\\\=\dfrac{81}{3}\\\\=27.$

Thus, the required value of x when y = 4 is 27.

Alexus [3.1K]2 years ago

3 0

3x-4y=65

3x=65+4y

x=(65+4y)/3, when y=4

x=(65+4*4)/3

x=(65+16)/3

x=81/3

x=27

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A local company makes snack-size bags of potato chips. Each day, the company produces batches of 400 snack-size bags using a pro

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Probability that a sample of 40 bags has an average weight of at least 2.02 ounces is 0.103.

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We are given that the company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. Assume the amount placed in each of the 400 bags is normally distributed and has a standard deviation of 0.1 ounce.

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The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, the probability that a sample of 40 bags has an average weight of at least 2.02 ounces is given by = P( $\bar X$ $\geq$ 2.02 ounces)

P( $\bar X$ $\geq$ 2.02) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\geq$ $\frac{2.02-2}{\frac{0.1}{\sqrt{40} } }$ ) = P(Z $\geq$ 1.265) = 1 - P(Z < 1.265)

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The above probability is calculated using z table by looking at value of x = 1.265 which will lie between x = 1.26 and x = 1.27 in the z table which have an area of 0.89707.

Therefore, probability that a sample of 40 bags has an average weight of at least 2.02 ounces is 0.103.

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