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3 years ago

You just got a new job with the Biden Administration as a House Clerk working full time (40 hours a week) with

Mathematics

1 answer:

avanturin [10]3 years ago

3 0

Answer:

Step-by-step explanation:

You are making alot of money but you can't pay off all of this and still have money left over

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Two distinct number cubes, one red and one blue, are rolled together. Each number cube has sides numbered 1 through 6. What is t

Pani-rosa [81]

Answer:

$\frac{2}{3}$

Step-by-step explanation:

Given: Two distinct number cubes, one red and one blue, are rolled together

To find: probability that the outcome of the roll is an even sum or a sum that is a multiple of 3

Solution:

If two dices are rolled together, possible outcomes are as follows:

(1,1) (1,2)(1,3)(1,4)(1,5)(1,6)

(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)

(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

So, total number of outcomes = 36

In order to find probability that the outcome of the roll is an even sum or a sum that is a multiple of 3, favourable outcomes are

(1,1) (1,2)(1,3)(1,5)

(2,1)(2,2)(2,4)(2,6)

(3,1)(3,3)(3,5)(3,6)

(4,2)(4,4)(4,5)(4,6)

(5,1)(5,3)(5,4)(5,5)

(6,2)(6,3)(6,4)(6,6)

Number of favourable outcomes = 24

Probability that the outcome of the roll is an even sum or a sum that is a multiple of 3 = Number of favourable outcomes/Total Number of outcomes = $\frac{24}{36} =\frac{2}{3}$

5 0

4 years ago

What is the solution to this equation?

QveST [7]

Step-by-step explanation:

$10x - 15x + 5 = - 45 + 20 \\ or \: 10x - 15x = - 45 + 20 - 5 \\ or \: - 5x = - 45 + 15 \\ or \: - 5x = - 30 \\ or \: \frac{ - 5x}{ - 5} = \frac{ - 30}{ - 5} \\ or \: x = 6 \\ \\ therefore \: the \: value \: of \: x \: is \: 6.$

<h3> D. The value of X is 6. I hopes</h3><h3> it helps you ☺️.......</h3>

Thank you ☺️

6 0

3 years ago

Rewrite with only sin x and cos x. <br><br> sin 3x

xeze [42]

$\bf sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\\\\\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\
cos(2\theta)=
\begin{cases}
\boxed{cos^2(\theta)-sin^2(\theta)}\\
1-2sin^2(\theta)\\
2cos^2(\theta)-1
\end{cases}\\\\
-------------------------------\\\\
sin(3x)\implies sin(2x+x)\implies sin(2x)cos(x)+cos(2x)sin(x)$

$\bf 2sin(x)cos(x)cos(x)~+~[cos^2(x)-sin^2(x)]sin(x)
\\\\\\
\stackrel{like~terms}{\stackrel{\downarrow }{2sin(x)cos^2(x)}~~+~~\stackrel{\downarrow }{sin(x)cos^2(x)}}-sin^3(x)
\\\\\\
3sin(x)cos^2(x)-sin^3(x)$

8 0

3 years ago

Jocelyn finds the blueprints for her house in the basement. The kitchen floor measures 12 inches long and 15 inches wide on the

Svetach [21]

Answer:

Step-by-step explanation:

48 ft by 60 ft

6 0

3 years ago

Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3. (2 points) Select one: a. x = -4

Kay [80]

Answer:

Step-by-step explanation:

$\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}$

Domain:

$x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3$

solution:

$\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}$

use <em>(a - b)(a + b) = a² - b²</em>

$\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}$

multiply both sides by (x - 3) ≠ 0

$\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}$

cancel (x - 3)

$\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3$

subtract $\frac{4(x-3)}{x}$ from both sides

$\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}$