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PtichkaEL [24]
3 years ago
10

Nicole has a machine that will produce a number from 1 through 50 when she pushes a button. If she

Mathematics
1 answer:
BaLLatris [955]3 years ago
8 0
Total outcome is 50 [because the number produced by the machine is from 1 to 50]

Question a:

Multiple of 10 are 10, 20, 30, 40, 50
There are five possible outcomes for multiple of 10
P(Multiple of 10) = 5/50 = 1/10

Question b:

Number 1 to 50 will be all the outcomes that are not 100
There are 50 possible outcomes
P(not 100) = 50/50 = 1

Question c:

Multiple of 4 that are less than 50 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
There  are 12 possible outcomes for multiple of 4
We want 'not multiple of 4' so we need to do 50 - 12 = 38 outcomes
P(not a multiple of 4) = 38/50 = 19/25

Question d:

One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9
There are 9 possible outcomes
P(one-digit number) = 9/50
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Step-by-step explanation:

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Polynomial expressions with matching​
yuradex [85]

Answer:

The difference of 27x³ and 8y³ → [3x - 2y][9x² + 6xy + 4y²]

The difference of 27x³ and 64y³ → [3x - 4y][9x² + 12xy + 16y²]

The sum of 27x³ and 64y³ → [3x + 4y][9x² - 12xy + 16y²]

The sum of 27x³ and 8y³ → [3x + 2y][9x² - 6xy + 4y²]

Step-by-step explanation:

For the first two, we use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

\displaystyle 3x - 2y = \sqrt[3]{27x^3 - 8y^3} \\ 3x - 4y = \sqrt[3]{27x^3 - 64y^3}

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign in your given expression, which will be a plus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ - 64y³

[3x - 4y][9x² + 12xy + 16y²]

↑ ↑ ↑

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ - 8y³

[3x - 2y][9x² + 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Now, for the last two, we use the Sum of Cubes [(a³ + b³)(a² - 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

\displaystyle 3x + 2y = \sqrt[3]{27x^3 + 8y^3} \\ 3x + 4y = \sqrt[3]{27x^3 + 64y^3}

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign is in your given expression, which will be a minus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ + 64y³

[3x + 4y][9x² - 12xy + 16y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ + 8y³

[3x + 2y][9x² - 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

I am delighted to assist you anytime!

* As you can see, when using the <em>Difference\Sum of Cubes</em>, SOAP can vary depending on how an expression is given to you. They resemble each other though.

6 0
2 years ago
Please help !!!!!picture shown
NeX [460]
I seef(x)  between 0 to 1 is goes to xfinity but in the negative direction
We can say it is large neagtive numbet when x is between 0 and 1
5 0
3 years ago
If right I’ll mark brainlest
zubka84 [21]

Answer:

154m^2

Step-by-step explanation:

I hope this helps.

4 0
3 years ago
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