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3 years ago

7

Your English teacher has decided to randomly assign poems for the class to read. The syllabus includes 2 poems by Shakespeare, 3

poems by Coleridge, 5 poems by Tennyson, and 4 poems by Lord Byron. What is the probability that you will be assigned a poem by Coleridge and then a poem by Lord Byron?

1 answer:

Ivanshal [37]3 years ago

3 0

$|\Omega|=14\cdot13=182\\
|A|=3\cdot4=12\\\\
P(A)=\dfrac{12}{182}=\dfrac{6}{91}$

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The sum of a number and its reciprocal is <br> 61<br> 30<br> .<br> Find the numbers.

Maksim231197 [3]

Let's say the number is hmmm "a", its reciprocal would then be 1/a
thus $\bf a+\cfrac{1}{a}=\cfrac{61}{30}$

solve for "a"

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There are seven roads that lead to the top of a hill. How many different ways are there to reach the top and then go back down?

rjkz [21]

Answer:

two I have no idea of the question

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The graph of the quadratic function y = ax^2 + bx + c is given.<br> Find a + b + c.

andrey2020 [161]

Answer:

$\frac{145}{24}\approx 6$ ***

Answers may vary depending on the person reading the graph.

It is hard to tell what they think crosses nicely.

For example, I decided that the graph crossed nicely at the following points:

$(0,3)$

$(2,8)$

$(6,5)$

Step-by-step explanation:

I see that the graph crosses at $(0,3)$ , $(2,8)$ , and $(6,5)$ .

The equation $y=ax^2+bx+c$ tells us the $y$ -intercept is $c$ since when $x=0$ we have $y=a(0)^2+b(0)+c=0+0+c=c$ .

The $y$ -intercept for our graph is $3$ . Therefore, $c=3$ .

So far we have the equation:

$y=ax^2+bx+3$ .

Let's enter the other points creating a system of linear equations to solve:

$8=a(2)^2+b(2)+3$

$5=a(6)^2+b(6)+3$

Let's simplify:

$8=4a+2b+3$

$5=36a+6b+3$

Let's subtract 3 on both sides:

$5=4a+2b$

$2=36a+6b$

I choose to solve the system by elimination.

Let's multiply the top equation by -3:

$-15=-12a-6b$

$2=36a+6b$

Now adding the equations results in:

$-13=24a$

Divide both sides by 24:

$\frac{-13}{24}=a$

Now using one of the equations we can find $b$ :

$5=4a+2b$ with $a=\frac{-13}{24}$

$5=4\frac{-13}{24}+2b$

$5=\frac{-13}{6}+2b$

Add 13/6 on both sides:

$5+\frac{13}{6}=2b$

$\frac{30+13}{6}=2b$

$\frac{43}{6}=2b$

Divide both sides by 2:

$\frac{43}{2(6)}=b$

$\frac{43}{12}=b$

So we have the equation:

$y=\frac{-13}{24}x^2+\frac{43}{12}+3$

Let's evaluate $a+b+c$ now:

$\frac{-13}{24}+\frac{43}{12}+3$

$\frac{-13+86+72}{24}$

$\frac{73+72}{24}$

$\frac{145}{24}$

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3 years ago

Simplify. Assume that a is a positive integer and a>2. (a-2)!/a!

Paul [167]

Answer:

C. 1 / (a(a - 1))

Step-by-step explanation:

View Image

Just know that:

n! = n(n-1)!

= n(n-1)(n-2)!

= n(n-1)(n-2)(n-3)!

= ...

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Change to an improper fraction 4 2/3=

barxatty [35]

Solutions

To solve the problem the first step is to m<span>ultiply the whole number by the fraction's denominator (4 x 3).Add the numerator (2) to the product.

4 * 3 = 12

12 + 2 = 14

= 14/3 </span>

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