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3 years ago

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Mixed in a drawer are 44 blue socks, 88 white socks, and 44 gray socks. You pull out two socks, one at a time, without looki

ng. Find the probability of getting 2 socks of the same color.

1 answer:

MrRissso [65]3 years ago

3 0

Answer:

The probability of getting 2 socks of the same color is 1/3.

Step-by-step explanation:

In the drawer,

Number of blue socks = 4

Number of white socks = 8

Number of gray socks = 4

Total number of socks = 4 + 8 + 4 = 16

Total ways to select 2 socks form 16 socks is

$^{16}C_2=\dfrac{16!}{2!(16-2)!}=120$

Total ways to select 2 socks of the same color is

T = Possible ways of (2 blue + 2 white +2 gray) socks

= $^{4}C_2+^{8}C_2+^{4}C_2$

= $6+28+6$

= $40$

The probability of getting 2 socks of the same color is

$Probability=\dfrac{\text{Total ways to select 2 socks of the same color}}{\text{Total ways to select 2 socks form 16 socks}}$

$Probability=\dfrac{40}{120}$

$Probability=\dfrac{1}{3}$

Therefore, the probability of getting 2 socks of the same color is 1/3.

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The function f(x) varies directly with x, and f(x) = 45 when x = 9.

Paladinen [302]

Answer:

Option C = 15

Step-by-step explanation:

In principle when a function <em>f(x) </em>varies directly with <em>x</em> it suggests that any changes in x results in the equivalent changes in<em> f(x)</em>. If we have two variables, i.e. <em>y</em> representing<em> f(x)</em> and <em>x</em> representing itself, any increment/decrement in <em>x</em> will result to the same increment/decrement in <em>y</em> by a factor <em>a, thus we can say that y = ax, implying y and x have the same ratio. </em>

In the given question we know that <em> $f(x) = 45$ </em> when $x=9$ <em>, </em>which translates as

$f(x=9) = 45$

This tells us that $f(x)$ varies by a factor (lets call it) $a$ for a given value of $x$ .

To find this factor we can just divide 45 with 9 which gives: $\frac{45}{9} = 5$

Thus the factor $a$ here is $a=5$ which finally tells us that

$f(x) = 5x$ Eqn (1) our original function.

Since we now know our function we can plug in the value for $x=3$ and solve for $f(x=3)$ as follow:

$f(x=3)= 5*3$

$f(x=3) = 15$

$f(3) = 15$

Looking at the given options in the question we can conclude that the correct answer is Option C = 15

3 0

3 years ago

Hamburger buns come in packages of 8. Hamburger patties come in packages of 10.

Vadim26 [7]

Answers/Step-by-step explanation:

A. LCM

B. Greatest Common Factor(GCF) shows the largest whole number, in this case patties and buns, would be a part of the whole that matches both numbers. Neil is unable to buy parts of packages because that not how most stores do business. Least common multiple(LCM) is the number that is both closest in value to the original number while being equal for all numbers. in that case, Neil is buying whole packages so it would work.

C. Neil would buy 4 packages of hamburger patties and 5 packages of hamburger buns. He could make 20 burgers.

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3 years ago

F. -10x >45<br> Solve the two step inequality

Daniel [21]

Answer:

x < -4.5

Step-by-step explanation:

<u>Step 1: Solve for x</u>

-10x / -10 > 45 / -10

When dividing or multiplying by a negative, the sign flips.

x < -4.5

Answer: x < -4.5

4 0

4 years ago

What are the solution(s) to the quadratic equation 9x^2=4?

Irina18 [472]

Answer:

x = 2/3 or x = -2/3

Step-by-step explanation:

Solve for x over the real numbers:

9 x^2 = 4

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by 9:

x^2 = 4/9

Hint: | Eliminate the exponent on the left-hand side.

Take the square root of both sides:

Answer:x = 2/3 or x = -2/3

8 0

3 years ago

(10 points) Consider the initial value problem y′+3y=9t,y(0)=7. Take the Laplace transform of both sides of the given differenti

Rashid [163]

Answer:

The solution

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3 t}$

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Consider the initial value problem y′+3 y=9 t,y(0)=7

<em>Step(i)</em>:-

Given differential problem

y′+3 y=9 t

<em>Take the Laplace transform of both sides of the differential equation</em>

L( y′+3 y) = L(9 t)

<em>Using Formula Transform of derivatives</em>

<em> L(y¹(t)) = s y⁻(s)-y(0)</em>

<em> By using Laplace transform formula</em>

<em> </em> $L(t) = \frac{1}{S^{2} }$ <em> </em>

<em>Step(ii):-</em>

Given

L( y′(t)) + 3 L (y(t)) = 9 L( t)

$s y^{-} (s) - y(0) + 3y^{-}(s) = \frac{9}{s^{2} }$

$s y^{-} (s) - 7 + 3y^{-}(s) = \frac{9}{s^{2} }$

Taking common y⁻(s) and simplification, we get

$( s + 3)y^{-}(s) = \frac{9}{s^{2} }+7$

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

<em>Step(iii</em>):-

<em>By using partial fractions , we get</em>

$\frac{9}{s^{2} (s+3} = \frac{A}{s} + \frac{B}{s^{2} } + \frac{C}{s+3}$

$\frac{9}{s^{2} (s+3} = \frac{As(s+3)+B(s+3)+Cs^{2} }{s^{2} (s+3)}$

On simplification we get

9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Put s =0 in equation(i)

9 = B(0+3)

<em> B = 9/3 = 3</em>

Put s = -3 in equation(i)

9 = C(-3)²

<em>C = 1</em>

Given Equation 9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Comparing 'S²' coefficient on both sides, we get

9 = A s²+3 A s +B(s)+3 B +C(s²)

<em> 0 = A + C</em>

<em>put C=1 , becomes A = -1</em>

$\frac{9}{s^{2} (s+3} = \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}$

<u><em>Step(iv):-</em></u>

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

$y^{-}(s) =9( \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}) + \frac{7}{s+3}$

Applying inverse Laplace transform on both sides

$L^{-1} (y^{-}(s) ) =L^{-1} (9( \frac{-1}{s}) + L^{-1} (\frac{3}{s^{2} }) + L^{-1} (\frac{1}{s+3}) )+ L^{-1} (\frac{7}{s+3})$

<em>By using inverse Laplace transform</em>

<em></em> $L^{-1} (\frac{1}{s} ) =1$ <em></em>

$L^{-1} (\frac{1}{s^{2} } ) = \frac{t}{1!}$

$L^{-1} (\frac{1}{s+a} ) =e^{-at}$

<u><em>Final answer</em></u>:-

<em>Now the solution , we get</em>

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3t}$

5 0

3 years ago