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4 years ago

Find the number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1.

Mathematics

2 answers:

Volgvan4 years ago

8 0

<h2>Answer:</h2>

The number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1 are:

<h2>Step-by-step explanation:</h2>

We are asked to find the number of positive three-digit even integers whose digits are among 9, 8, 7, 5, 3, and 1.

We know that a number is even if the last digit of the number is divisible by 2 i.e. even.

Hence, the only digits among the given digits which is even is: 8

Now, at the first place any of the 6 digits could come up.

( Since, the digits could be repeated)

Also, at the second palace any of the 6 digits could come up.

Hence, the total number of such numbers possible are:

6×6×1=36

agasfer [191]4 years ago

6 0

Answer:

Step-by-step explanation:

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Please consider the attached image for complete question.

We have been given that measure of arc WY is 76° and and measure of arc XZ is 112°. We are asked to find the difference of of the measures of angle WPY and angle XPY.

First of all we will find the measure of angle WPY using intersecting secants theorem. Intersecting secants theorem states that measure of angle formed by two intersecting secants inside a circle is half the sum of intercepting arcs.

$m\angle WPY=\frac{1}{2}(\widehat{WY}+\widehat{XZ})$

$m\angle WPY=\frac{1}{2}(76^{\circ}+112^{\circ})$

$m\angle WPY=\frac{1}{2}(188^{\circ})$

$m\angle WPY=94^{\circ}$

We can see that angle WPY and angle XPY are linear angles, so they will add up-to 180 degrees.

$m\angle WPY+m\angle XPY=180^{\circ}$

$94^{\circ}+m\angle XPY=180^{\circ}$

$94^{\circ}-94^{\circ}+m\angle XPY=180^{\circ}-94^{\circ}$

$m\angle XPY=86^{\circ}$

Now we need to find difference of both angles as:

$m\angle WPY-m\angle XPY=94^{\circ}-86^{\circ}$

$m\angle WPY-m\angle XPY=8^{\circ}$

Therefore, the difference of the measures of angle WPY and angle XPY is 8 degrees.

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Step-by-step explanation:

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