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3 years ago

Write an expression that is equal to 3 × 2 1/4

Mathematics

1 answer:

Vera_Pavlovna [14]3 years ago

5 0

Convert the mixed number 2 1/4 into an improper fraction: 9/4.

Then multiply this 9/4 by 3: 27/4, or 6 3/4.

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Probability of father and mother born in Michigan independent.

raketka [301]

Answer:

A. no, not independent

Step-by-step explanation:

Let A = "father born in Michigan" and B = "mother born in Michigan".

If A and B are independent, then ...

P(A|B) = P(A)

The table tells us ...

P(A|B) = P(A&B)/P(B) = 0.29/0.73 ≈ 0.397

and

P(A) = 0.48

Since 0.48 ≠ 0.397, we must conclude that the events are not independent.

6 0

3 years ago

A luxury resort is offering an incentive discount. If you book your room six months in advance, you will save 15% off the price

Anna [14]

Answer:the total discounted cost for your stay is $1948.2

Step-by-step explanation:

If you book your room six months in advance, you will save 15% off the price of the room. You decide to take advantage of the offer and book a room for 6 nights. If the original price per night for the room is $382, this means that the value of the discount would be

15/100 × 382 = 0.15 × 382 = $57.3

The cost of the room for a night would be

382 - 57.3 = $324.7

Since you are staying for six nights,

the total discounted cost for your stay would be

324.7 × 6 = $1948.2

8 0

3 years ago

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 Difference\Sum of Cubes, SOAP can vary depending on how an expression is given to you. They resemble each other though.

6 0

3 years ago

Find the equation of the line Use exact numbers

GaryK [48]

Your Y intercept is 5
Y= mx + 5
Rises -5 / runs 2.5 so
Y= -2x + 5

8 0

3 years ago

What is the geometrick mean of 27 and 8 with the pothagereom theorem

enyata [817]

Answer:

x = 6√6

Step-by-step explanation:

27/x = x/8

x² = 27 × 8

x = √(27 × 8)

x = √(9 × 4 × 6)

x = 3 × 2 × √6

x = 6√6

5 0

2 years ago

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