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zaharov [31]
2 years ago
8

"Woohoo! The school carnival is here! You think about all the fun carnival games that you love to play every year. Then you reme

mber that some of the probability concepts you learned about in math class could help you here. Time to play!"

Mathematics
1 answer:
Lena [83]2 years ago
5 0

Answer:

14

Step-by-step explanation:

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What numbers are always prime numbers?
VashaNatasha [74]
2 ,3,5,7,11,17,19,23,29,31, 37,41,43,47,53,59,61
67,71,73,79,83,89,97.....
4 0
3 years ago
Help me please ASAP please help
Mekhanik [1.2K]

Answer:

the volume is 15.7 in. 3............

4 0
3 years ago
Old Navy has a sale on $15 shirts: buy 3
UNO [17]

The amount that the would be paid after 40% discount is $27

<h3>Word Problem</h3>

Given Data

  • Cost of a shirt = $15
  • Discount = 40%

Let us find the cost of three shirt

= 15*3

= $45

Let us find 40% discount of $45

= 40/100*45

= 0.4*45

= $18

Let us find the amount after discount

= 45-18

= $27

Learn more about word problem here:

brainly.com/question/25693822

7 0
1 year ago
Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator
SpyIntel [72]
\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}
\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)

When x=3, you're left with

147=49a_1\implies a_1=\dfrac{147}{49}=3

When x=\sqrt2 or x=-\sqrt2, you're left with

\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}

Adding the two equations together gives -10=2a_5, or a_5=-5. Subtracting them gives 2\sqrt2=2\sqrt2a_4, a_4=1.

Now, you have

5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)
5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)
2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that a_2x^4=2x^4 and a_3(-3)(-2)=6a_3=-6. These alone tell you that you must have a_2=2 and a_3=-1.

So the partial fraction decomposition is

\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}
7 0
3 years ago
How do we know what sign goes outside of the bracket when factoring binomials?
Xelga [282]
I'm assuming you're asking about negative or positive signs here. When I factor binomials, it depends on what would make factoring simpler for me. And how you're factoring the binomial too.

More often than not, it's going to be positive. For example, 4x^2 - 2x = 0. That would factor out to be 2x(2x-1) = 0. The sign outside is going to be positive because it's simpler to solve that way. Here, x is equal to 0 and equal to 1/2. Taking out a negative in this case would complicate the solving process.
3 0
3 years ago
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