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deff fn [24]
3 years ago
5

A man receives an annual increase of #30000 and after a period of 10 years service, the man has the salary of #1014. Find his in

itial salary​
Mathematics
1 answer:
Paladinen [302]3 years ago
7 0

I think you intended writing #30 as his pay rise instead of #30000. I solved the problem using #30 as his annual pay rise.

Answer:

The man's initial salary was #714

Step-by-step explanation:

Extracting the key information from the question:

*** A man got a pay raise for 10 years.

*** His current salary is #1,014

*** He gets a pay raise of #30 annually.

*** We are simply required to calculate his initial salary before he started receiving pay rise.

Now, To calculate his initial salary before he started receiving pay rise, let us denote that initial salary that we are currently unaware of by "a".

Since his salary as at today is #1,014 and he has also received this pay rise of #30 for 10 years, we can calculate his initial salary before he started receiving pay rise every year with the following equation:

a + 30(10) = 1014

That is -

Initial salary + [pay rise × number of years] = current salary.

a + 30(10) = 1,014

a + 300 = 1014

a = 1014 - 300

a = #714

Therefore the man's initial salary was #714

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The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 48,564 miles, with a standard
DerKrebs [107]

Answer:

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 48564, \sigma = 3293, n = 281, s = \frac{3293}{\sqrt{281}} = 196.44

What is the probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct?

This is the pvalue of Z when X = 48101. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{48101 - 48564}{196.44}

Z = -2.36

Z = -2.36 has a pvalue of 0.0091

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

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Start by going in the order of decimals and what ever you end at, put this number on top
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3 years ago
Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y) → (0, 0) x4 − 34y2 x2 + 17y2
HACTEHA [7]

Answer:

<h2>DNE</h2>

Step-by-step explanation:

Given the limit of the function \lim_{(x,y) \to (0,0)} \frac{x^4-34y^2}{x^2+17y^2}, to find the limit, the following steps must be taken.

Step 1: Substitute the limit at x = 0 and y = 0 into the function

= \lim_{(x,y) \to (0,0)} \frac{x^4-34y^2}{x^2+17y^2}\\=  \frac{0^4-34(0)^2}{0^2+17(0)^2}\\= \frac{0}{0} (indeterminate)

Step 2: Substitute y = mx int o the function and simplify

= \lim_{(x,mx) \to (0,0)} \frac{x^4-34(mx)^2}{x^2+17(mx)^2}\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^4-34m^2x^2}{x^2+17m^2x^2}\\\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^2(x^2-34m^2)}{x^2(1+17m^2)}\\\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^2-34m^2}{1+17m^2}\\

= \frac{0^2-34m^2}{1+17m^2}\\\\=  \frac{34m^2}{1+17m^2}\\\\

<em>Since there are still variable 'm' in the resulting function, this shows that the limit of the function does not exist, Hence, the function DNE</em>

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3 years ago
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