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I am Lyosha [343]
4 years ago
7

Say a certain service industry has 78.9 thousand jobs in 2003, but expects to increase at an average annual rate of 2.65 thousan

d jobs yearly from 2003 to 2013. If this holds true, what will be this industry’s percent increase from 2003 to 2013? a. 28% b. 30% c. 33% d. 40%
Mathematics
2 answers:
lesantik [10]4 years ago
8 0
You just multiply 2.65 thousand * 10 and you get 26.5 thousand.
After that you divide that number (26.5) by 78.9 and you get your answer
Answer = 33%
AysviL [449]4 years ago
7 0

Answer:

the answer is C

Step-by-step explanation:

C. 33%

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Does anyone know the answer to this? Algebra 2
natulia [17]

Answer:

Step-by-step explanation:

Sinθ = \frac{\text{Opposite side}}{\text{Hypotenuse}}

If, sinθ = -\frac{1}{2} and π < θ < \frac{3\pi }{2}

Since, sinθ is negative, angle θ will be in IIIrd quadrant.

And the measure of angle θ will be (180° + 30°)

θ = 210°

It's necessary to remember that tangent and cotangent of angle θ in quadrant III are positive.

Therefore, cos(210°) = -\frac{\sqrt{3} }{2}

tan(210°) = \frac{1}{\sqrt{3} }

csc(210°) = -\frac{1}{2}

sec(210°) = -\frac{2}{\sqrt{3} }

cot(210°) = √3

3 0
3 years ago
Perform the following operations s and prove closure. Show your work.
nadezda [96]

Answer:

1. \frac{x}{x+3}+\frac{x+2}{x+5} = \frac{2x^2+10x+6}{(x+3)(x+5)}\\

2. \frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16} = \frac{1}{(x+2)(x-4)}

3. \frac{2}{x^2-9}-\frac{3x}{x^2-5x+6} = \frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}

4. \frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3} = \frac{1}{(x-2)(x-4)}

Step-by-step explanation:

1. \frac{x}{x+3}+\frac{x+2}{x+5}

Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)

=\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}\\=\frac{x^2+5x+(x)(x+3)+2(x+3)}{(x+3)(x+5)} \\=\frac{x^2+5x+x^2+3x+2x+6}{(x+3)(x+5)} \\=\frac{x^2+x^2+5x+3x+2x+6}{(x+3)(x+5)} \\=\frac{2x^2+10x+6}{(x+3)(x+5)}\\

Prove closure: The value of x≠-3 and x≠-5 because if there values are -3 and -5 then the denominator will be zero.

2. \frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16}

Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)

Factors of x^2+5x+6 = x^2+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)

Putting factors

=\frac{x+4}{(x+3)(x+2)}*\frac{x+3}{(x-4)(x+4)}\\\\=\frac{1}{(x+2)(x-4)}

Prove closure: The value of x≠-2 and x≠4 because if there values are -2 and 4 then the denominator will be zero.

3. \frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}

Factors of x^2-9 = (x)^2-(3)^2 = (x-3)(x+3)

Factors of x^2-5x+6 = x^2-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)

Putting factors

\frac{2}{(x+3)(x-3)}-\frac{3x}{(x+3)(x-2)}

Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)

\frac{2(x-2)-3x(x+3)(x-3)}{(x+3)(x-3)(x-2)}

=\frac{2(x-2)-3x(x+3)}{(x+3)(x-3)(x-2)}\\=\frac{2x-4-3x^2-9x}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-9x+2x-4}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}

Prove closure: The value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.

4. \frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3}

Factors of x^2-5x+6 = x^2-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)

Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)

\frac{x+4}{(x-2)(x+3)}\div\frac{(x-4)(x+4)}{x+3}

Converting ÷ sign into multiplication we will take reciprocal of the second term

=\frac{x+4}{(x-2)(x+3)}*\frac{x+3}{(x-4)(x+4)}\\=\frac{1}{(x-2)(x-4)}

Prove Closure: The value of x≠2 and x≠4 because if there values are 2 and 4 then the denominator will be zero.

5 0
3 years ago
B. Find the equation of the line through (-3, 3) with slope 4.
yarga [219]

Answer:

Step-by-step explanation:

use the formula y=mx+b. the first number in the parenthesis is -3 so that is x. 3 is y and the slope is m

so it is 3=4(-3)+b

4 0
3 years ago
Water in a Play Pool
8_murik_8 [283]

Answer:

6

Step-by-step explanation:

66

8 0
3 years ago
A tank is being filled with gasoline at a rate of 4.5 gallons per minute. The gas tank contained 1.5 gallons of gasoline before
denis-greek [22]

Answer:

4.5x - y = -1.5

Step-by-step explanation:

y - total

x - minutes

finding the slope intercept form is way easier

slope intercept form: y = 4.5x + 1.5

now, just put it into standard form:

Ax + By = C

4.5x - y = -1.5

remember that x in standard form can't be negative

8 0
3 years ago
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