In 2005 there were 14000 students at college A, with a projected enrollment increase of 750 students per year. In the same year there were 35000 students at college B with a projected enrollment decline of 1000 students per year. According to these projectors when will the colleges have the same enrollment? What will be the enrollment in each college at that time

Answer:

A

Step-by-step explanation:

Remark

Just as a guess, the answer should be A or B. It's always a good idea to estimate an answer so that if you get something really far away, you know it is incorrect.

Equation

Set up a proportion for the problem

26/30 is the basic ratio of the home fans wearing the right color

x/45000 is the ratio of those in the entire stadium.

Solution

26/30 = x / 45000                 Cross multiply

30x = 26 * 45000                  Simplify the right

30x = 1170000                        Divide by 30

30x/30 = 1170000/30    

x = 39000 And that is A

Answer: 13 1/3

Step-by-step explanation:

To find the area of a rectangle, multiply the length by the width.

Answer:

You can't make any triangle

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

so

In this problem

[tex]2+1>2[/tex]

[tex]3>2[/tex] -----> is not true

therefore

You can't make any triangle.

By factoring out and simplifying, we can see that given expression is divisible by both 30 and 37.

The method for solving this question involves using certain properties of numbers and exponents. Firstly, observe the expressions (36^5-6^9) and (38^9-38^8). You can factor out 6^5 from the first expression and 38^8 from the second expression, giving you 6^5(6^4-1) and 38^8(38-1) respectively.

You will notice that 6^4-1 is 1295 and 38-1 is 37.  Both 1295 and 37 are divisible by 37, rendering the whole expression divisible by 37. Moreover, 1295 is divisible by 5 and 6^1 is divisible by 6, making the expression divisible by 5*6 = 30.

Therefore, the whole expression is divisible by both 30 and 37.

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To prove the divisibility of the expression, we factor and simplify it. The expression is divisible by both 30 and 37 due to its factors.

To prove that the value of the expression b(36^5 - 6^9)(38^9 - 38^8) is divisible by 30 and 37, we can factor out 6 from both terms in each parenthesis.

This gives us b(6^4)(6^9 - 1)(38^8)(38 - 1).

Next, we divide each term by 6, giving us b(6^3)(6^9 - 1)(38^8)(38 - 1)/6.

We can simplify this expression further by factoring out 2 from both terms in the first parentheses, giving us 2^3b(6^6)(6^3 - 1)(38^8)(38 - 1)/6.

Now we can see that the expression is divisible by both 30 and 37, since it contains factors of 2, 3, 5, and 37.

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Answer:

n = - 12

Step-by-step explanation:

Isolate the term in n by subtracting 4 from both sides

[tex]\frac{n}{-2}[/tex] = 6 ( multiply both sides by - 2 )

n = 6 × - 2 = - 12

Answer:

Step-by-step explanation:

The correct answer is B. The reason why is that you want the total number of floors traveled, so putting each number in an absolute value equation puts it as a positive value. 9 + 12 + 5 + 8 = 34 total floors traveled. Hope that helps.

The length and width of the rectangle is 12 and 10 respectively.

Let the consecutive integers be :

Area of rectangle = Length × width

120 = a(a + 2)

120 = a² + 2a

a² + 2a - 120 = 0

a² - 10a + 12a + 120 = 0

a(a - 10) + 12(a - 10)

a = 10 or a = -12

The width cannot be negative, Hence, width = 10

Length = a + 2

Length = 10 + 2

Length = 12

The length and width of the rectangle is 12 and 10 respectively.

Answer:

$5

Step-by-step explanation:

25/5=5

$5

Wouldn’t it be 5$ a person to pay for a car wash? Because if you think of it this way they made 25$ and it cost 5$ so you would take 25 divided by five . Please correct me if I’m wrong

Answer: s, v, w, & x = 13      y = 20        z = 20 + 13√3

Step-by-step explanation:

First, you need to understand the side lengths of each special triangle in the drawing.

A 45°- 45°- 90° triangle has corresponding sides of a - a - a√2

A 30°- 60°- 90° triangle has corresponding sides of b - b√3 - 2b

The hypotenuse of the 45-45-90 triangle is 13√2, so its legs are 13.

So A F = 13 → s = 13 and w = 13

     FB = 13 → x = 13

     EC = 13 → v = 13

Since the x-value of C is 20, then the x-value of E is also 20 → y = 20

ED is opposite of the 60° angle of the 30-60-90 triangle so ED is EC√3.  Since EC = 13, then ED = 13√3.

AE + ED = AD

20 + 13√3 = AD → z = 20 + 13√3

Answer:

f ( -2 ) = 30

g ( -2 ) = 3

Step-by-step explanation:

when it says f(x) and then has f(-2) - you fill in all x's in the equation with -2.. like this:

f(x) = -7(-2-2) +2                         g(x) = 2(-2)^2 -5

f(x) = -7(-4) +2                             g(x) = 2(4) -5

f(x) = 28 + 2                                g(x) = 8 - 5

f(x) = 30                                      g(x) = 3

hope this helps!!

The correct option is X.

Step-by-step explanation:

From the given figure it is clear that:

1. Pyramid has 4 congruent triangles and a square base.

2. Color of 2 triangles is blue and another two triangles have black and white lines.

3. Triangles with same color or same design can't be on the opposite sides.

Option W is incorrect because it contains 3 blue triangles.

Options Y and Z are incorrect because triangles with same color or same design are on the opposite sides.

Only option X fulfill the above condition.

Therefore the correct option is X.

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Answer:

She drank 12 ounces so, 12 minus 2 1/4 = 9 3/4 ounces of water.

Step-by-step explanation:

It’s 88 cause if you see in the other side is 44+44 and what does That Equal =88

Answer: The correct answer is 9.

Step-by-step explanation: In order to solve this problem you need to divide the 45 books by the 5 book shelves. 45 / 5 = 9. Divided equally, there will be 9 books on each shelf.

[tex]45 \div 5 = 9[/tex]

Aisha can place 9 books on each shelf.

I absolutely love these.

Your answer would be A since "h" is how many hours has pass and "J" is your jogging.

A + B = C.

Your "A" is the number of jogs you have, "B" is "h", and your "C" is "j".

Hopefully this helps!

Answer:

A) is what you are kooking for Bro

Step-by-step explanation:

Good day to you!

Answer: SECOND OPTION

Step-by-step explanation:

Substitute any value of n shown in the table attached into each function given in the options, and observe if you obtain the value of [tex]a_n[/tex] shown in the table.

Let's substitute n=1 (According to the table, you need to obtain [tex]a_n=3[/tex]):

For the first option:

[tex]f(1)=1+3=4[/tex]

For the second option:

[tex]f(1)=7(1)-4=3[/tex]  THIS IS THE FUNCTION

For the third option:

[tex]f(1)=3(1)+7=10[/tex]

 For the fourth option:

[tex]f(1)=1+7=8[/tex]

Therefore, the answer is the second option.

ANSWER

[tex]f(n) = 7n - 4[/tex]

EXPLANATION

The terms of the sequence are;

[tex]3,10,17,24,31,...[/tex]

This implies that,

[tex]a_1=3[/tex]

The constant difference is

[tex]d = 10 - 3 = 7[/tex]

The nth term of the sequence is;

[tex]a_n=a_1+d(n-1)[/tex]

[tex]a_n=3+7(n-1)[/tex]

[tex]a_n=3+7n - 7[/tex]

[tex]a_n=7n-4[/tex]

Or

[tex]f(n) = 7n - 4[/tex]

The correct choice is B.

Answer:

Yeah true

Step-by-step explanation:

Because it makes sense

It is true that when developing a proof, focusing on the "given" information is crucial as it forms the foundation of the logical argument leading to the conclusion that needs to be proven.

When developing a plan for a proof, it is indeed important to look at the "given" information. This is true because in the context of mathematical proofs, the "given" information represents the starting point from which you will build you argument to reach a conclusion. These are the facts, definitions, or previously proven theorems that can be used in establishing the validity of the statement you are tasked to prove.

To develop a successful proof, one generally follows a systematic approach:

This structured approach to problem-solving involves using what you know to logically arrive at a conclusion that was previously unknown or needs to be proven. This method not only applies to mathematics but also to other fields that require logical reasoning and evidence-based conclusions.

Answer:

what is √25x^2y^2/√xy in simplest from? Assume x≥o and y≥0

The correct answer to this question is 5√xy

Step-by-step explanation:

The given expression in its simplest form is [tex]5 \sqrt{xy}[/tex]

From the question,

We are to evaluate sqrt 25x^2y^2/sqrt xy in its simplest form.

First, we will write the given expression properly

The given expression is

[tex]\frac{\sqrt{25x^{2} y^{2} } }{\sqrt{xy} }[/tex]

Now, the expression can be evaluated as shown below

[tex]\frac{\sqrt{25x^{2} y^{2} } }{\sqrt{xy} }[/tex]

[tex]\frac{\sqrt{25 } \times \sqrt{x^{2} y^{2}} }{\sqrt{xy} }[/tex]

This becomes

[tex]\frac{5 \times xy }{\sqrt{xy} }[/tex]

This becomes

[tex]\frac{5 \times xy}{(xy)^{\frac{1}{2} } }[/tex]

This can be written as

[tex]5 \times xy \div (xy)^{\frac{1}{2} }[/tex]

By applying one of the laws of indices

We get,

[tex]5 \times (xy)^{1-\frac{1}{2} }[/tex]

[tex]5 \times (xy)^{\frac{1}{2} }[/tex]

[tex]5 \times \sqrt{xy}[/tex]

[tex]5 \sqrt{xy}[/tex]

Hence, the given expression in its simplest form is [tex]5 \sqrt{xy}[/tex]

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Answer:

7/39 = 17.94%

Step-by-step explanation:

Town          Students     Relative Frequency

Wilmette   12 boys + 7 girls = 19 19/39 = 48.72%

Glencoe    9 girls + 4 boys = 13 13/39 = 33.33%

Kenilworth  2 boys + 5 girls = 7  7/39 = 17.94%

Total         39 students         39/39 = 100%

Another approach to solve probability is the Relative Frequency. A frequency is the number of times an event occurs. To solve for the relative frequency, it’s the ratio of the frequency of an event to the total outcomes. From the question, it is clear that for each town, it was subdivided into boys and girls but the word students represent the combined number of boys and girls for a particular town. so finding the probability that a student called at random to answer a question is from kenilworth is simply the ratio of students from kenilworth over the total number of students in the class.  

I'm not 100% but i think its A: 3

For this case we have that by definition of power properties:

[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]

We have the following expression:

[tex]\frac {5 ^ 6} {5 ^ 2} = a ^ b[/tex]

It can be rewritten as:

So:

[tex]\frac {5 ^ 6} {5 ^ 2} = 5 ^ {6-2} = 5 ^ {4} = a ^ b[/tex]

So, [tex]b = 4\ and\ a = 5[/tex]

Answer:

Option B

Let's reason through it.

We are given the inequality that says, in English, that the absolute value of ten times x is greater than -2.

Let's consider three cases:

x is negative

- When x is negative the number in the absolute value will be negative. But because it is inside the absolute value, the number becomes positive. Therefore, for any x that is negative (however small or large), the left side will be positive. Any positive value (however small) is greater than a negative value, so the inequality is satisfied in this case.

x is positive

- When x is positive, the number inside the absolute value will be positive. The absolute value of a positive number is itself, so the left hand side will be positive again. Then, for all positive values of x (however small or large), the inequality will be satisfied because any positive value is larger than -2.

x is zero

- Even in the case of zero, when the left hand side will be zero, the equality is satisfied. This is because zero is greater than -2. If this doesn't immediately make sense, imagine the two numbers on the number line. 0 is to the right of -2, so it is larger.

Since we cannot find a value for x that does not satisfy the inequality, the solution to the inequality is all values of x. See the attached image.

Answer:

All values are solutions

Step-by-step explanation:

Answer:

they are equal

Step-by-step explanation:

rectangle- 8 + 8 = 16

                 2 + 2 =4

rectangles perimeter is  20

square  5 X 4 = 20

sqaures perimeter is 20

Answer:

The rectangular shape has a perimeter of 18 cm. The square shape has a perimeter of 20 cm. The square perimeter is larger by 2 cm.

Step-by-step explanation:

Answer:

32.8

Step-by-step explanation:

153.30-125.50

153.3-120.5=33.8 This is how you get the answer

Answer:

5m^5-m^3-3

Step-by-step explanation:

What you do is you have to distribute the negative sign into the equation.

-m^5-2m^3+4m-6. Next, you will either add or subtract from the other equation.

6m^5-m^5=5m^5.

m^3-2m^3=-m^3.

-4m+4m=0m or you don't put anything.

3-6=-3. Then you put it all together to get.

5m^5-m^3-3 as your answer.

Answer:

33 grams

Step-by-step explanation:

We multiply the total weight of the choco. bar (94 grams) by 0.36 to obtain the number of grams of cocoa present:

0.36(94 grams) = 33.04 grams.

The bar contains 33.04 grams of cocoa.  Round this up to 33 grams.

Answer: 33.84 gr

Step-by-step explanation:

You have the following information given in the problem:

- Hans chocolate bar is 36% cocoa.

- The chocolate bar weighs 94 grams.

Therefore, to calculate the amount of grams of cocoa it contains (which you can call x), you must multiply the weight of the chocolate bar by the percentafe of cocoa it has

Therefore, you obtain the following result:

[tex]x=94gr*0.36\\x=33.84gr[/tex]

Answer:

Cleo wants to select a shirt from a collection of 13 shirts.   1/13

selecting a card from the spades suit.

rolling a six-sided die.

At a class picnic, the teacher wants to decide which game to  

play: baseball, basketball, tennis, volleyball, soccer, or field hockey.

flipping a coin.

Roxanne wants to decide which one of two pair of shoes she

should wear to a party

spinning a spinner divided into five equal sections.

Clayton wants to take one of his five kids with him to the  

supermarket.  

Step-by-step explanation:

Roxanne wants to decide which one of two pair of shoes she

should wear to a party.    1/2

Clayton wants to take one of his five kids with him to the  

supermarket.     1/5

At a class picnic, the teacher wants to decide which game to  

play: baseball, basketball, tennis, volleyball, soccer, or field hockey.

1/6

Cleo wants to select a shirt from a collection of 13 shirts.   1/13

selecting a card from the spades suit.

There are 13 cards in a suit  so 1/13

rolling a six-sided die.

1/6

flipping a coin.

two sides on a coin

1/2

spinning a spinner divided into five equal sections.

1/5

Card from spades suit--->Cleo with 13 shirts

6 sided die-----> Class picnic

Flipping a coin---->Roxanne with party shoes

spinning spinner with 5 sections---> Cleo takes one of his kids to the supermarket