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1 month ago

How many pairs of whole numbers have a sum of 110

Mathematics

1 answer:

Inessa [12.5K]1 month ago

5 0

The term "whole numbers" has various interpretations.

Some sources define them as any integer, positive or negative.

Others, especially in mathematics, consider whole numbers as non-negative integers.

Here, we adopt the mathematical definition: whole numbers are zero or positive integers.

To find all pairs of whole numbers summing to 110, we enumerate:

0 + 110 = 110

1 + 109 = 110

2 + 108 = 110

...

54 + 56 = 110

55 + 55 = 110

Since 56 + 54 repeats a previous pair (54,56), we stop at 55 + 55. In total, there are 56 such pairs.

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The idle time for taxi drivers in a day are normally distributed with an unknown population mean and standard deviation. If a ra

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Answer:

$172-2.51\frac{16}{\sqrt{23}}=163.626$

$172+2.51\frac{16}{\sqrt{23}}=180.374$

Hence, in this case, the 98% confidence interval would be (163.626;180.374)

Step-by-step breakdown:

Previous concepts

A confidence interval represents a range that is likely to encompass a population value within a specific confidence level, typically expressed as a percentage whereby a population mean falls between an upper and lower limit.

The margin of errorindicates the span of values surrounding the sample statistic in a confidence interval.

A normal distributionillustrates a probability distribution that is symmetrical around the mean, signifying that values near the mean occur more frequently than those farther away from it.

$\bar X=172$ denote the sample mean

$\mu$ population mean (the variable of interest)

s=16 signifies the sample standard deviation

n=23 represents the sample size

The solution to the query

The equation for the confidence interval of the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

To determine the critical value $t_{\alpha/2}$ , we first need to calculate the degrees of freedom, which is expressed as:

$df=n-1=23-1=22$

Since the confidence level is 0.98 or 98%, we find the value of $\alpha=0.02$ and $\alpha/2 =0.01$ using tools like Excel or a calculator, where the Excel command would be: "=-T.INV(0.01,22)". This yields $t_{\alpha/2}=2.51$

Having all components ready, we can substitute into formula (1):

$172-2.51\frac{16}{\sqrt{23}}=163.626$

$172+2.51\frac{16}{\sqrt{23}}=180.374$

Thus, for this case, the 98% confidence interval will be (163.626;180.374)

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Geraldine has 200 feet of fencing. She wants to fence in a rectangular area. Which function A(w) represents the area of land tha

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21 day ago

What is the domain of the function graphed below?

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The function is applicable within the segments of x:
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Importantly,
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1 month ago

Read 2 more answers

The line width of a tool used for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micromete

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Answer:

a. 0.82%

b. 71.11%

c. 0.564 micrometer

Step-by-step explanation:

To find the z value for each measurement, we must calculate and determine the percentage they correspond to, and the difference will give us the percentage between those two statistics.

The equation for z is:

z = (x - m) / (sd)

Here, x is the value being evaluated, m denotes the mean, and sd represents the standard deviation.

For 0.62 copies, we calculate:

z = (0.62 - 0.5) / (0.05)

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This translates to 0.9918.

Therefore, p (x > 0.62) = 1 - 0.9918

p (x > 0.62) = 0.0082 = 0.82%

For 0.47 copies, we have:

z = (0.47 - 0.5) / (0.05)

z = -0.6, which equates to 0.2742.

For 0.63 copies:

z = (0.63 - 0.5) / (0.05)

z = -2.6, which yields 0.9953.

Hence, p (0.47 > x > 0.63) = 0.9953 - 0.2742

p (0.47 > x > 0.63) = 0.7211 = 72.11 %

For x copies, we find:

p = 0.9 corresponds to z = 1.28.

Thus, 1.28 = (x - 0.5) / (0.05)

From which we derive:

x = 1.28*0.05 + 0.5

x = 0.564 micrometer

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