At her ranch, Georgia starts an animal shelter to save cats. After the first three days, she has 34 male cats and 13 female cats. She decides to only accept cats in male-female pairs from then on. In this problem, we find the largest number of pairs of cats she can accept to her shelter and still have at least 60% of her dogs be male.

(a) Let d be the number of pairs of cats she accepts. How many male cats will she have total? Female cats? Total cats?

(b) Write an inequality that means that the percentage of cats at her shelter that are male is at least 60%.

(c)Solve the inequality and determine the largest number of pairs of animal she can accept to her shelter and still have at least 60% of her dogs be male.

Answers

Answer 1

Step-by-step explanation:

I know that both sides of the cats, males and females, receive the same # of new cats.

I write an equation, (not an inequality though):

3((34+2x)/5)=2((13+2x)/5)

From here on, I solve for x. I get x = -38. I know we can't have negative pairs and we're only bringing in more cats, and not taking any away. I add 38, and try to see what percentage of cats are male, and I get fairly close, getting to about 62.5% I think. Then, I divide 38 by 2, getting 19, and see what else I can get. I try to find a value between the 38 and lesser 19 so as to find a value which will give me a male cat percentage of 60%. I get about 57.5% with 19 plugged in, which is when I see that hey, the differences are the same. What I then do is find the average of 19 + 38, which is 57.5. I round that to 58, and I get the right answer.

I see that perhaps my solution wasn't really orthodox or anything, but with a little bit of trial and error and a bit of my creative thinking, I guess I managed to solve the problem. What worries me though is this is the first problem in the "questions" section of the inequalities section of AoPS, so I'm definitely struggling to deal with the concepts.


Related Questions

Please put all these in order. Will give brainleast if answered correctly.

Answers

Answer: I can’t see the pic it’s blank

Step-by-step explanation:

Step-by-step explanation:

The answer is two because when you have one pen and buy another one it becomes two pens

Short Answer
Note: Your teacher will grade your response to ensure you receive proper credit for your answer
Describe how you would estimate the square root of a number that is not a perfect square without using a calculator

Answers

Answer:

The square root must be between the square roots of the perfect squares just above and just below your number.

For example the square root of 89 must be between 9 and 10.

Step-by-step explanation:

What is the area of cross-section ADGF of this right rectangular prism?



A.
20 square units
B.
48 square units
C.
52 square units
D.
65 square units

Answers

Answer:

C.52 square units

Step-by-step explanation:

We are given that

Length of cross-section ADGF,l=13units

Length of cross-section ADGF, b=4 units

We have to find the area  of cross-section ADGF of this right rectangular prism.

We know that

Area of rectangle=[tex]l\times b[/tex]

Using the formula

Area of cross-section ADGF of this right rectangular prism

=[tex]13\times 4[/tex]

Area of cross-section ADGF of this right rectangular prism=52square units

Option C is correct.

C.52 square units

Answer:

i hope this helps

Step-by-step explanation:

1/6(x + 6) = 11 What is x

Answers

Answer:

x = 60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

[tex]\frac{1}{6}[/tex](x+6)=11

[tex]\frac{1}{6}[/tex]x + 1 = 11

[tex]\frac{1}{6}[/tex]x +1 -1 = 11 -1

[tex]\frac{1}{6}[/tex]x * 6 = 10 *6

x = 60

To double check

[tex]\frac{1}{6}[/tex](60+6)=11

10+1 = 11

11 = 11

Helen plays basketball. For free throws, she makes the shot 75% of the time. Helen must now attempt two free throws. The probability that Helen makes the second free throw given that she made the first is 0.85. What is the probability that she makes both free throws?

Answers

Answer: 0.6375

Step-by-step explanation:

Let's assume that the event that she'll make the first shot is given as P(A) while making the second shot is P(B). Therefore, P(A/B) = 0.85

Therefore, the probability that she makes both free throws will be denoted as:

= 0.75 × 0.85

= 0.6375

Condense to a single logarithm : log 12 18+3 log 12 2

Answers

Answer:

2 or [tex] \log_{12} 144 [/tex]

Step-by-step explanation:

I assume 12 is the base.

[tex] \log_{12} 18 + 3 \log_{12} 2 = [/tex]

[tex] = \log_{12} 18 + \log_{12} 2^3 [/tex]

[tex] = \log_{12} (18 \times 8) [/tex]

[tex] = \log_{12} 144 [/tex]

[tex] = \log_{12} 12^2 [/tex]

[tex] = 2\log_{12} 12 [/tex]

[tex] = 2 [/tex]

The entire expression simplifies to 2, but if you need the simplest log expression, then you can use

[tex] \log_{12} 144 [/tex]

Elijah needs to buy some cat food. At the nearest store, 6 bags of cat food costs $24.75. How much would Elijah spend on 3 bags of cat food

*ONLY TYPE THE AMOUNT/ROUND TO THE NEAREST HUNDRED*

Answers

Answer: the original answer is 75.25 but rounded to the hundredths would be 100

Step-by-step explanation: brainliest please? ^^

A
walking path across a park is represented by the equation y = -3x - 6. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 3). Identify the equation that represents the new path.

Answers

Answer:

We are given the path, y=-3x-6

The general form of the straight line is 'y=mx+b', where 'm' is the slope and 'b' is the y-intercept.

Thus, the slope of the given line is -3.

As, we have that the incipient path is perpendicular to the given path.

And, we ken that, 'Product of slopes of perpendicular lines is -1'.

Since, the incipient path passes through the point (-3,3). Superseding the values in the general form, we get,

b= 3+1

b= 4.

Step-by-step explanation:

Help please! Thank youuuuuy

Answers

Step-by-step explanation:

can an.y gi.rl message me. i have no power to inbox

anyone think they could help me with this question???

Answers

Answer:

61

Step-by-step explanation:

As we can see the triangles are congruent so

< F = < C ( being corresponding angles of congruent triangle)

< C = 29

Now

<A +<B + <C = 180° { being sum of angles of triangle }

5x + 1 + 90 + 29 = 180°

5x = 180° - 120°

5x = 60°

x = 12°

<A = 5 * 12° + 1 = 61°

Hope it will help :)

Given the point (3, 4) and the slope of 6, find y when x = 27. (1 point)

Answers

Step-by-step explanation:

use the slope and coordinates to find the equation of line then substitute the value of X in the equation to find Y.

if it helps pls mark me brainliest

Complete the following proofs.

Given: Points R, S, T, Q on circle O



Prove: m Arc RS + m Arc ST + m Arc TQ = m Arc RQ

Answers

Answer:

Points R, S, T, Q on circle O is given

and points are central arc

Step-by-step explanation:

17 >n +4
I rlly need help now

Answers

Answer:

n=13

Step-by-step explanation:

Step 1: Flip the equation.

Step 2: Subtract 4 from both sides.

Write the equation of the line that passes through the points (8, 14) and (-2,-16) in slope-intercept form.

Answers

Answer:

y = 3x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (8, 14) and (x₂, y₂ ) = (- 2, - 16)

m = [tex]\frac{-16-14}{-2-8}[/tex] = [tex]\frac{-30}{-10}[/tex] = 3 , then

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (8, 14 ) , then

14 = 24 + c ⇒ c = 14 - 24 = - 10

y = 3x - 10 ← equation of line

I’ll give brainlist to anyone that can help me

Answers

Answer:

80 ft

Step-by-step explanation:

if 1 = 20 then 20 is width but ? is length

1=20

2=40

3=60

4=80

since 4 in is length then actual length is 80ft

Answer:

80ft

Step-by-step explanation:

hope this helps

Carlos tiene un terreno cuadrado que mide 8 m por lado. ¿Cuál es el área del terreno?¿Qué operación permite obtenerla?

Answers

Answer:

32 ,multiplica 8 por 2 en cuanto lo vi lo resolví

the cost of contructing a 63mcube wall is rs 84000. find the volume of each brick if the cost of a bric is rs 13

Answers

Answer:

0.00975 m^3 each

Step-by-step explanation:

rs 84000 / rs 13 = 6461.539 bricks

63 m^3 / 6461.539 = 0.00975 m^3 each

1 + 7x
The sum of two numbersis 23. The greater number
is b. Select the expression that represents the lesser
number.

Answers

Answer:

Step-by-step explanation:

a+b = 23

a<b

a = 23-b

Drop the answer love:)





Or.. i'll drop ur ip<3




mwa

Answers

-16x=-114.
X=7.13
Hope this helps.

First okay and second umm my what?! Lol

The answer is : - 112

We add 14 to both side

-16x - 14 = -126

       + 14    +14

-16x      =  - 112.    <- that’s the answer

Then we divide both sides by 16

X          =  7

Ta -Da!!

Also I’ll leave this.....

If the sales tax rate is 7.5% in New York State, then how much sales tax would you pay in Albany for a $34 pair of pants? What is the final cost?

Answers

Answer:

Sales Tax $2.55

Final Cost $36.55

Step-by-step explanation:

Finding sales tax

34 * 7.5%= 2.55

Multiply the tax with the original cost, that will be your sales tax

Finding final cost

34 + 2.55= 36.55

Add your sales tax with the original cost, now you have the final total

The sales tax in one state is 5%. Write a function rule for finding the total cost of an item with selling price x. Then find the total cost of CD player with a selling price of $110

Answers

Answer:

Total Cost = 1.05x

CD Player cost = 110*1.05 = $115.50

Step-by-step explanation:

find the value of a and b of a+root5 is (root5+root3)(root5-root3)​

Answers

Given:

Consider the value of [tex]a+b\sqrt{5}[/tex] is [tex](\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex].

To find:

The values of a and b.

Solution:

According to the given information,

[tex]a+b\sqrt{5}=(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex]

[tex]a+b\sqrt{5}=(\sqrt{5})^2-(\sqrt{3})^2[/tex]            [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]a+b\sqrt{5}=5-3[/tex]

[tex]a+b\sqrt{5}=2[/tex]

It can be written as

[tex]a+b\sqrt{5}=2+0\sqrt{5}[/tex]

On comparing both sides, we get

[tex]a=2,b=0[/tex]

Therefore, the value of a is 2 and the value of b is equal to 0.

Solve for xxx.
Your answer must be simplified.
15 < -5 x

Answers

Answer:

x < - 3

Step-by-step explanation:

Given

15 < - 5x

Divide both sides by - 5, reversing the symbol as a result of dividing by a negative quantity

- 3 > x , that is

x < - 3

The simplified expression is x < -3.

What is an inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is the condition of being unequal. It is used most often to compare two numbers on the number line by their size.

For the given situation,

The expression is 15 < -5x

⇒ [tex]15 < -5 x[/tex]

Divide both sides by -5,

⇒ [tex]\frac{15}{-5} < \frac{-5}{-5} x[/tex]

When we divide an inequality with negative number, we need to change the sign,

⇒ [tex]-3 > x[/tex]

⇒ [tex]x < -3[/tex]

Hence we can conclude that the simplified expression is x < -3.

Learn more about inequalities here

https://brainly.com/question/22406619

#SPJ2

Write the equation 9 = -5x + 4 in the form ax + b = c, where c = 9.
What are the values of a and b?

Answers

Answer:

a = - 5x and b= 4

Step-by-step explanation:

So it becomes - 5x +4=9

Hope this helps pls tell if any mistakes

Answer:

dil bende ingilizce göründüğü için anlamıyoruuumm

someone who can actually give the answer please answer this please! do not put nothing crazy or get reported!!
Find the zeros of this polynomial.

Answers

Answer:you’ll find the answer just by understanding and looking at the photo

Step-by-step explanation:

el área de un mosaico es de 900cm2 ¿cuánto mide por lado cada mosaico​

Answers

Answer:

El lado de cada mosaico tiene una longitud de 30 cm.

Step-by-step explanation:

El area de un mosaico cuadrado es:

[tex]A=l^{2}[/tex]

Donde l es el lado del mosaico.

Entonces, si sabes que el area es 900 cm², el lado valdra:

[tex]900=l^{2}[/tex]

[tex]l=\sqrt{900}[/tex]

[tex]l=30\: cm[/tex]

Por lo tanto el lado de cada mosaico tiene una longitud de 30 cm.

Espero te haya servido!

Your parents are building a pool that is 7 ft wide and 12 ft long. They want to put a walkway around the pool that is x ft wide on all sides. Write a polynomial that represents the combined area of the pool and walkway. Answer needs to be in standard form and use x as your variable.

Answers

Answer:

Combined area = 4[tex]x^{2}[/tex] + 38x + 84

Step-by-step explanation:

The rectangle formed by the pool and walkway is 12 + 2x long and 7 + 2x wide.

Area of the rectangle = lw = (2x + 12)(2x + 7) = 4[tex]x^{2}[/tex] + 38x + 84

Nebi has already typed 250 words. He then starts a timer and finds that he types 150 words in 3 minutes. If Nebi types at a constant rate, write a linear equation to represent the number of words w Nebi types m minutes after starting the timer.

Answers

Answer:

198

Step-by-step explanation:I

Answer: w= 150m

Step-by-step explanation:

MARK BRAINLIEST

if f(x)=3x-4 and g(x)=x^2 -1
what is f(g(-3))?

a) -34
b) 8
c) 20
d) 168

Answers

Answer: C) 20
Explanation: Subsitute (-3) into the g(x) equation so you get g(-3)= (-3)^2-1= 9-1=8
Then replace the x as 8 in f(x) and you get 3(8)-4=24-4= 20.

Estimate the answer by rounding each fraction to the nearest whole number and then adding. 13 7/10 + 10 1/8

Answers

9514 1404 393

Answer:

  24

Step-by-step explanation:

The rounded numbers are ...

  13 7/10 = 13.7 ⇒ 14

  10 1/8 = 10.125 ⇒ 10

The sum of the rounded numbers is 14 +10 = 24.

The estimate of the sum is 24.

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