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1 year ago

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Write two numbers that when rounded to the greatest place value have an estimated sum of 11,000 and an estimated difference of 3

,000. Then find the exact sum and the exact difference. Provide a detailed explanation as to how you reached your answers and why they will work.

1 answer:

lianna [129]1 year ago

8 0

Answer:

x + y = 10,999.5 (rounded up to 11000)

x - y = 3,000.3 (this would be rounded down to 3000)

Step-by-step explanation:

Assume;

Two numbers are x, y

So,

x + y = 11,000 .......eq1

x - y = 3,000 .........eq2

eq1 + eq2

So,

2x =14,000

x = 7,000

So y = 4,000

For rounding number

x = 6,999.9 (rounded up to 7,000)

y = 3,999.6 (rounded up to 4,000)

Sum;

x + y = 10999.5 (rounded up to 11000)

x - y = 3000.3 (this would be rounded down to 3000)

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Answer:

(a) Probability that a sheet selected at random from the population is between 30.25 and 30.65 inches long = 0.15716

(b) Probability that a standard normal random variable will be between .3 and 3.2 = 0.3814

Step-by-step explanation:

We are given that the population of lengths of aluminum-coated steel sheets is normally distributed with;

Mean, $\mu$ = 30.05 inches and Standard deviation, $\sigma$ = 0.2 inches

Let X = A sheet selected at random from the population

Here, the standard normal formula is ;

Z = $\frac{X - \mu}{\sigma}$ ~ N(0,1)

(a) <em>The Probability that a sheet selected at random from the population is between 30.25 and 30.65 inches long = P(30.25 < X < 30.65) </em>

P(30.25 < X < 30.65) = P(X < 30.65) - P(X <= 30.25)

P(X < 30.65) = P( $\frac{X - \mu}{\sigma}$ < $\frac{30.65 - 30.05}{0.2}$ ) = P(Z < 3) = 1 - P(Z >= 3) = 1 - 0.001425

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Therefore, P(30.25 < X < 30.65) = 0.9985 - 0.84134 = 0.15716 .

(b)<em> Let Y = Standard Normal Variable is given by N(0,1) </em>

<em> Which means mean of Y = 0 and standard deviation of Y = 1</em>

So, Probability that a standard normal random variable will be between 0.3 and 3.2 = P(0.3 < Y < 3.2) = P(Y < 3.2) - P(Y <= 0.3)

P(Y < 3.2) = P( $\frac{Y - \mu}{\sigma}$ < $\frac{3.2 - 0}{1}$ ) = P(Z < 3.2) = 1 - P(Z >= 3.2) = 1 - 0.000688

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Therefore, P(0.3 < Y < 3.2) = 0.99931 - 0.61791 = 0.3814 .

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The table shows data from Vicente's Form 1040. Gross income $75,000 Standard deduction $12,000 Taxable income $63,000 Total inco

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Suppose they are working today t hrs, and his department will complete 43 packages per hour today.

It means they are going to make 43 t packages today.

This 43 t packages includes those 44 too , which they are short of yesterday due to picnic.

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Subtracting 39 t in both sides

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