Rational Functions

In 1918, women were allowed to join the Marine Corps to handle the clerical duties, while the men fought in World War I. Prior to World War II, the United States Marine Corps Women’s Reserve was formed. Eventually Congress passed the Women’s Armed Services Integration Act. Women could then join the regular component of the Marine Corps, but the number of women could not exceed 2% of the total number of Marines.


By 1965, during the Vietnam War, there were 2700 women in the Marines. Women could participate in a wider variety of duties including radio operator, parachute rigger, quartermaster, auto mechanic, telegraph operator, and aerial gunnery instructor. But it was not until 1967 that a law was passed removing the restriction on the number of women in the Marines. In addition, women could be promoted to the rank of colonel. Within the next ten years, women would be able to work in all aspects of the Marine Corps except the infantry, artillery, armor, and the pilot/air crew.


In 2008, there were 9782 women in the Marine Corps on active duty, or about 5% of the Marines on active duty. Currently, women now receive combat training and are accepted into special skill schools that were traditionally only available to the male Marines. Also, women are working in non-traditional jobs and in certain other areas that were previously restricted. Women in the Marine Corps serve proudly and honorably next to their male counterparts in any area the United States Marine Corps requires. The number of women in the United States Marine Corps can be modeled by:


W = 414x^2 - 3341x + 9403 / 0.04x^2 - 0.32x + 1

where x is the number of years since 2000


Graph the model to find the number of women in the Marine Corps between 2000 and 2009.

Use your graph to estimate the number of female Marines in 2006.

Identify the x-intercepts of this function, if any.

Identify the vertical and horizontal asymptotes of the graph of this function, if any.

Use the function to estimate the number of women in the Marine Corps in 2015.

Give two reasons why the number of women in the Marine Corps could exceed your answer from Exercise 5.

Using the algebraic equation and the graph given, number of extra days it will take Kathrine to make 20 necklaces than it will take her to make 20 bracelets is: 8 - 5 = 3 days.

An algebraic equation, like the one given, models word problems, and can be used to find unknown numbers.

Thus:

y = 4× represents the rate Kathrine uses to make bracelets, where,

x = number of days

y = total number of bracelets made

Find the number of days (x) it takes to make 20 bracelets.

Substitute y = 20 into y = 4x:

20 = 4x

20/4 = x

x = 5 days.

Create an algebraic equation in the form of, y = kx, for the rate of necklace Kathrine makes using the graph.

Thus, using the point, (4, 10), substitute x = 4 and y = 10 into y = kx and find k.

10 = k(4)

10/4 = k

k = 2.5

The algebraic equation for rate of necklace made is: y = 2.5x

Number of days Kathrine will use to make 20 necklaces would be:

20 = 2.5x

20/2.5 = x

x = 8 days.

Number of days to make 20 bracelets = 5 days

Number of days to make 20 necklaces = 8 days

In summary, using the algebraic equation and the graph given, number of extra days it will take Kathrine to make 20 necklaces than it will take her to make 20 bracelets is: 8 - 5 = 3 days.

Learn more about algebraic equations on:

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Answer:

There is only one solution, and that is x=−2 and y=7

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Rewrite the given equation as b^(2x) = b^8.

The exponents 2x and 8 must be equal, and so 2x = 8, and x = 4

Answer:

(E/2)/n = k

So when doing this you have to isolate K since your solving for “k”.

In order to do this you have to perform the inverse of every variable or number in order to isolate K.

In this case you divide 2 and then N.

Answer: A B C

Step-by-step explanation:

- 2/9

Step-by-step explanation:

(2/3 - 5/6)÷3/4

we'll first sort out the first part by equalizing denominators

(2/3 × 2/2) - 5/6 = 4/6 - 5/6 = -1/6

dividing by fraction is The Same as multiplying by it's inverse

= - 1/6 × 4/3 = - 4/ 18 = -2 × 2 = - 2/9

----------

2 × 9

Cp = 15000

L % = 2 %

First Let's find loss :

Final equation:

I am pretty lazy to use latex adjust with it xD

Answer:

wait a minuate which school you study i study in indian school salalah

Answer:

it's either 32 or 16f I don't know though

Answer:

16f

Step-by-step explanation:

We can combine like terms here by adding the coefficients:

9f + 7f = (9+7)f = 16f

x = -2

y = 1

let's multiply second equation by 4 to get a common coefficient of y variable.

16x-8y=-40

add the equations

3×+8y=2

16x-8y=-40

----------------

3x+16x = -38

19x = -38

x = -2

substitute x

3×-2 + 8y = 2

-6 + 8y = 2

8y = 2+6

y = 1

check the answer

-6+8 = 2

-8-2= -20

Answer:

19 1-point shots and 32 2-point shots

Step-by-step explanation:

Let x be the amount of 1-point shots they made and y be the amount of 2-point shots they made then...

x+y=51

x+2y=83

We can solve this equation using elimination. In this case, we can eliminate x be subtracting the two equations.

-y=-32

Divide both sides by -1

y=32

Plug this back into the equation to solve for x

x+32=51

Subtract 32 from both sides

x=19

They scored 19 1-point shots and 32 2-point shots.

Final price of gaming system, with the discount 20% and taxes 12% applied is represented by composite function as,

[tex]c[p(g)] =0.896p \\[/tex]

Composite function is the function in which the one function is dependent on the other function. The one function is written inside the other function to show the such relationship between the two function.

Given information-

The sale on the gaming system are of 20 percent.

The total local tax on the discounted price is 12%.

The function which expressed the sale on gaming system is,

[tex]p(g) = 0. 8g[/tex]

The function which expressed the tax on discounted price is,

[tex]c(p) = 1. 12p.[/tex]

The sale on the gaming system are of 20 percent and The function which expressed the sale on gaming system is,

[tex]p(g) = 0. 8g[/tex]

Now the local tax is applied on the discounted price after the 20 percent sell. Thus the function of discounted price will be a written inside the function of local tax as,

[tex]c[p(g)] =1.12p(0.8) \\c[p(g)] =0.896p \\[/tex]

The above function is the required function, which tales the final price of the gaming system is 0.896 times the original price.

The final price of gaming system, with the discount 20% and taxes 12% applied is represented by composite function as,

[tex]c[p(g)] =0.896p \\[/tex]

Learn more about the composite function here;

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Answer:

0.33

Step-by-step explanation:

i found this answer from knowing common sense. 33 hundredths is 0.33. thus making 33 pennies; 0.33

46 - 11

35 fruits will go into each smoothie

Answer:

same as the above

Step-by-step explanation:

Hope this answer helps you

Answer:

14g

Step-by-step explanation:

Combine like terms

8g–4g+10g = (8-4+10)g = (4+10)g = 14g

Hi!

I can help you with joy!

Solve by Combining Like Terms:

[tex]\bold{8g-4g+10g}[/tex]

[tex]\bold{4g+10g}[/tex]

[tex]\bold{14g}~(\text{Answer})[/tex]

Hope it helps!

Enjoy your day!

Ask me if you have any doubts.

~Misty~

Answer:

3/3, 6/3, 18/6, 32/8, 25/5

Step-by-step explanation:

You can do many different combinations but that is just one combination you can do that equals 1, 2, 3, 4, and 5.

Answer:

The answer is 1716

Step-by-step explanation:

214.50x8=1716

Answer:

D.  17,15,13,11

Step-by-step explanation:

The expression states that the next term in this sequence is formed by subtracting 2 from the preceding (n-1) result.  We know that for n = 1 that f(1) = 17.

f(n) is f(n-1) - 2

so

f(2) = f(1) - 2

f(2) = 17 - 2 or 15

f(3) = f(2) - 2

f(3) = 15 - 2 or 13

f(4) = f(3) - 2

f(4) = 13 - 2 or 11

 . . . .

 . . . .

 . . . .

and so on.

Answer:

D and B

Step-by-step explanation:

using the recursive formula and f(1) = 17 , then

f(2) = f(1) - 2 = 17 - 2 = 15

f(3) = f(2) - 2 = 15 - 2 = 13

f(4) = f(3) - 2 = 13 - 2 = 11

first 4 terms are 17, 15, 13, 11 → D

-------------------------------------------------------

Using the recursive formula and f(1) = 5 , then

f(2) = 4f(1) = 4 × 5 = 20

f(3) = 4f(2) = 4 × 20 = 80

f(4) = 4f(3) = 4 × 80 = 320

first 4 terms are 5, 20, 80, 320 → B

Answer:

z-355=x

2z-80=y

x+y+z=2425 ft

Step-by-step explanation:

Smallest Yosemite falls- x

Largest Yosemite falls-y

Middle Cascades Falls- z

Answer:

1 / [tex]\sqrt{2}[/tex]

Step-by-step explanation:

In a 45,45,90 triangle, the two legs of the triangle are equal to each other and the hypotonus being x [tex]\sqrt{2}[/tex]. So that make the unknown sides 6 and 6[tex]\sqrt{2}[/tex]. When solving for cos(45) you divide the leg adjacent to the 45 (6) by the hypotonus (6[tex]\sqrt{2}[/tex]) This gives you 6/6[tex]\sqrt{2}[/tex]. You can simplify the 6s to get 1 / [tex]\sqrt{2}[/tex]

Explanation:

This is a 45-45-90 right triangle, aka isosceles right triangle.

The two legs are 6 units each, because the legs of isosceles triangles are the same length.

The hypotenuse is 6*sqrt(2) through the use of the pythagorean theorem.

From here we can say:

[tex]\cos\left(\text{angle}\right) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos\left(45^{\circ}\right) = \frac{6}{6\sqrt{2}}\\\\\cos\left(45^{\circ}\right) = \frac{1}{\sqrt{2}}\\\\[/tex]

It turns out that the '6' has nothing to do with the final answer, since the '6's cancel out. So we could change that 6 to any number we want, and the answer would still be the same.

Side note: Rationalizing the denominator will have [tex]\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}[/tex]

Answer:

2p^2 - 1p - 8     GCF= 2p

Step-by-step explanation:

The GCF of the following equation can be written as 2p.

So with this information, we can solve the equation.

2p^2 - 1p - 8

Let me know if I am correct.

Answer:

if we are simplifying, the answer is 6x⁴y²

Answer:

6x⁴y²

Step-by-step explanation:

2x³ × 3xy²

multiply 2x³ by 3xy²

= 6x⁴y²

Answer:

what is x then i can say

Step-by-step explanation:

?????????????????????? i dont gets it

Otherwise its already simplified.

Answer:

last one, x>-2.5

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

7m - 4

7(4) - 4

28 - 4

24

Therefore, the value of the expression 7m-4 when m=4 is 24

Answer:

1/2x

Step-by-step explanation:

It's exactly in between the steep slope and the flat line and the steep line's slope is x or 1x.

Answer:

Addition and Subtraction with different denominators. If the denominators are different then a common denominator needs to be found.

2 pages.

hope this helps

The volume of the triangular prism clay pot is 195 unit³

where

B = base area

H = height of the prism

Therefore,

Base area = area of a triangle

area of a triangle = 1 / 2 × base × height

Therefore,

B = 1 / 2 × b × h

b = 3 units

h = 5 units

B = 1 / 2  × 3 × 5

B = 15 / 2

B = 7.5 units²

Therefore,

H = 26 units

 B = 7.5 units²

V = 7.5 × 26

V= 195 unit³

learn more on triangular prism here: https://brainly.com/question/16537585

Answer:

? X 3= 6

3 X 3= 9

?= 6/3

?= 2

please mark as Brainliest

Answer:

2

Step-by-step explanation:

6 multiply by 3 to give 18

9 multiply by question mark we represent the question mark with x

so 18 divided by 9 gives 2

Answer:

Equation is Y=x/2

Step-by-step explanation: