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Doss [256]
1 year ago
11

Reference the attached image for the problem to solve. Thank you very much

Mathematics
1 answer:
ExtremeBDS [4]1 year ago
6 0

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for calculating relative frequency

Relativefrequency=\frac{number\text{ of required events}}{number\text{ of total events}}

STEP 2: Calculate the relative frequency

\begin{gathered} number\text{ of club}=12 \\ number\text{ of total cards}=52 \end{gathered}

By substitution,

Relative\text{ }frequency=\frac{12}{52}=\frac{3}{13}

The relative frequency in a fraction in its simplest form is 3/13

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We have been given an image of a circle. We are asked to find the value of each variable.

We can see that angle b corresponds to diameter of circle. We know that the measure of an angle that is inscribed to the diameter of a circle is 90 degrees . Therefore, the value of b will be 90.

we can see that angle is an inscribed angle of arc 99 degrees. We know that measure of an inscribed angle is half the measure of inscribed arc.

a=\frac{1}{2}\cdot 99

a=49.5

Therefore, the value of a is 49.5 units.

We know that measure of all angles of a triangle is 180 degrees. The measure of 3rd angle will be half the measure of c, so we can set an equation as:

a+b+\frac{1}{2}c=180

49.5+90+\frac{1}{2}c=180

139.5+\frac{1}{2}c=180

139.5-139.5+\frac{1}{2}c=180-139.5

\frac{1}{2}c=40.5

\frac{1}{2}c\cdot 2=40.5\cdot 2

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Two Social Security numbers (see Exercise 8.12) match zeros if a digit of one number is zero iff the corresponding digit of the
Roman55 [17]

Answer:

Proved

Step-by-step explanation:

From the given parameters, we have:

n = 9 i.e. the length of each security numbers

r = 2 i.e. 2 security numbers

Required

In 513 security numbers, 2 must have matching zeros

To do this, we make use of Pigeonhole principle.

First, we calculate the number of all security numbers not having matching zeros.

Each of the 9 digits can be selected in 2 ways.

2 ways implies that each digit is either 0 or not

So, total selection is:

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Apply Pigeonhole principle

The principle states that: suppose there are n items in m containers, where n>m, then there is at least one container that contains more than 1 item.

This means that if there are 512 security number without matching zeros, then there is 1 (i.e. 512 + 1) with matching zeros.

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