In 2005, there were 12,300 students at college A, with a projected enrollment increase of 500 students per year. In the same year there were 18,550 students at college B with a projected enrollment decline of 750 students per year. According to these projections, when will the colleges have the same enrollment? What will the enrollment in each college at that time?

Answer:

Step-by-step explanation:

The formula of a volume of a sphere:

[tex]V=\dfrac{4}{3}\pi R^3[/tex]

We have V = 36(3.14) cm³ = V = 36π cm³. Substitute:

[tex]\dfrac{4}{3}\pi R^3=36\pi[/tex]      divide both sides by π

[tex]\dfrac{4}{3}R^3=36[/tex]           multiply both sides by 3

[tex]4R^3=108[/tex]            divide both sides by 4

[tex]R^3=27\to R=\sqrt[3]{27}\\\\R=3\ cm[/tex]

The diameter D = 2R.

Therefore D = 2(3 cm) = 6cm

Answer:

D. g(x)= {x+2}-3 is the answer

Step-by-step explanation:

1) shift 2 units to the right ( Talking about the X-axis Image that you are on the origin point on the x-axis moving to right is positive moving to the left is Negative.)

So x will be 2 or x+2 or 0,2

2) Shift 3 units down is talking about the Y-axis( Imagine you are at the origin (0,0) Moving up is positive moving down is negative)

So it will be -3

That why my answer is what it is

Hopes this help you!

Answer: 552 cubic meters

Step-by-step explanation: You want to find the volume. To do this, multiply each number with each other. 7 times 9 times 8 is 504 and 3 times 8 times 2 is 48. Then, add the two products. 504 plus 48 is 552.

Answer:

Option B.

Step-by-step explanation:

Domain of any function is defined by all the values of x for which the given function is valid.

In other words for any function if we put the value of x and we get a unique value of y, then x - values are considered as the domain of the function and y- values as range.

From the given graph we can easily say all the values of x greater than (-3) is the domain set.

Therefore, Option B. is the answer.

Answer:

1)  40°

2) 40°

3) 100°  

Step-by-step explanation:

The sum of angels of a triangle is: 180°

The ratio of angles are: 4x,4x,10x

The sum of ratios: 4x + 4x + 10x

=> 18x

Therefore,

=> 18x = 180

=> x = 180/18

=> x = 10

So, required angels are:

The angles of the triangular supports of the wooden table are 40 degrees, 40 degrees, and 100 degrees.

The sum of the angles in any triangle is 180 degrees. Given that the angles are in the ratio 4x : 4x : 10x, we can find the value of x by setting up the equation:

4x + 4x + 10x = 180

Combining like terms, we get:

18x = 180

To find the value of x, we divide both sides of the equation by 18:

x = 180 / 18

x = 10

Now that we have the value of x, we can find the measures of the three angles:

First angle = 4x = 4 * 10 = 40 degrees

Second angle = 4x = 4 * 10 = 40 degrees

Third angle = 10x = 10 * 10 = 100 degrees

 The answer is: [tex]40^\circ, 40^\circ, 100^\circ.[/tex]

➷ 3x + 9 = 12

Subtract 9 from both sides:

3x + 9 - 9 = 12 - 9

As you can see, the '9' would cancel out on the left side:

3x = 3

Divide both sides by 3:

x = 1

➶ Hope This Helps You!

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3x + 9 =12

To solve for x you need to get it by itself.

First subtract 9 from both sides of the equation:

3x = 3

Now divide both sides by 3

x = 3/3

x = 1

Answer:

‐15−8= ‐15 + -8

‐15−(‐8)= ‐15 + 8

Step-by-step explanation:

‐15−8 = -23

‐15 + -8 = -23

‐15−(‐8) = -7

-15+8 = -7

Answer:

‐15−8= ‐15 + -8

‐15−(‐8)= ‐15 + 8

Answer:

B

Step-by-step explanation:

7 + x = 84

Subtract 7 from both sides.

x = 77

Answer should be C

hope this helped you.

Answer:

[tex]8a^3b^3c^4(\sqrt[3]{bc} )[/tex]  C. should be your answer

Step-by-step explanation:

Answer:

Not sure sorry,but can you please help me on the following:

Step-by-step explanation:

Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?

Answer:

Step-by-step explanation:

How nice question 7s it

Answer:

(7x8 + 4y32) • (7x8 - 4y32)

Step-by-step explanation:

P.1 (49 • (x16)) - 24y64

P.2 72x16 - 24y64

P.3 (7x8 +4y32) • (7x8 - 4y32)

the answer would be (x+7)(x-7)

Answer:

(x+7)(x-7)

The factors are -7 and 7

Step-by-step explanation:

Given the function x²-49, to find the factors, we will factorise the expressed using the different of two square.

If a and b are two numbers, then based on difference of two square;

a²-b² = (a+b)(a-b)

Applying this to the function in question

x²-49

= x²-7²

= (x+7)(x-7)

The factors can be gotten by equating the function to zero according to factor theorem.

(x+7)(x-7) = 0

x+7 = 0 and x-7 = 0

x = -7 and 7

[tex]\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \log_2(x-1)=\log_8(x^3-2x^2-2x+5) \\\\\\ \log_2(x-1)=\log_{2^3}(x^3-2x^2-2x+5) \\\\\\ \log_{2^3}(x^3-2x^2-2x+5)=\log_2(x-1) \\\\\\ \stackrel{\textit{writing this in exponential notation}}{(2^3)^{\log_2(x-1)}=x^3-2x^2-2x+5}\implies (2)^{3\log_2(x-1)}=x^3-2x^2-2x+5[/tex]

[tex]\bf (2)^{\log_2[(x-1)^3]}=x^3-2x^2-2x+5\implies \stackrel{\textit{using the cancellation rule}}{(x-1)^3=x^3-2x^2-2x+5} \\\\\\ \stackrel{\textit{expanding the left-side}}{x^3-3x^2+3x-1}=x^3-2x^2-2x+5\implies 0=x^2-5x+6 \\\\\\ 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}[/tex]

Answer: third option

Step-by-step explanation:

To solve the exercise you must apply the proccedure shown below:

- Find the value of irrational number given in the problem (By definition, an irrational number cannot be written as a simple fraction, where the numerator and the denominators are integer.

- Then the value in decimal number is the following:

[tex]\sqrt{115}=10.72[/tex]

- The number 10.72 is located between the integer 10 and the integer 11.

Answer:

Part A: Up 9

Part B: Up 6

Step-by-step explanation:

Part A: The graph appears to be a cosine graph since it starts at a peak on the y-axis. Normally a cosine graph starts at (0,1). This graph begins at (0,10). It has been shifted up y a translation by 9.

Part B: Each trig equation has a basic structure f(x) = a sin (x+b) + k where:

A vertical translation is a vertical shift and is represented by the value in k added outside of the function. In the equation f(x) = 2sin(θ + 120°) + 6, k = 6. The vertical translation is 6.

Answer:

p should equal -4

Step-by-step explanation:

7.32

10 = 73.2

100 = 732

1000 = 7320

0.006

10 = 0.06

100 = 0.6

1000 = 6

The decimal place moves to the right depending on how many zeros the number has.

For example, if you had 0.6 multiplied by 100, you would move 2 decimal places to the right because 100 has two zeros.

Answer:

Step-by-step explanation:

[tex]The\ factors\ of\ 8:\ 1,\ 2,\ 4,\ 8\\\\8=1\cdot8\\8=2\cdot\boxed4\\8=4\cdot2\\8=8\cdot1[/tex]

Answer:

Linear

y = -30x + 100

Step-by-step explanation:

The table has a set of inputs with matching outputs. The behavior of the outputs will determine the type of function. The outputs appear to descend at a constant subtraction rate of -30 each time.

70 - 30 = 40

40 - 30 = 10

10 - 30 = -20

etc.

A constant addition or subtraction rate is a slope. Since the function has a slope, this is a linear function.

To write the function you'll need a slope and a y-intercept. Recall, the y-intercept is where x = 0. This is not in the table but can be found by reversing the process by adding 30 + 70 = 100.

Substitute m = -30 and b = 100 into y = mx+b for the equation.

y = -30x + 100

Answer:

Step-by-step explanation:

the answer is f(x)= 100-30x

Answer:

50% and 50%, they are both the same!

When breeding a patchwork fish (Bb) with a fish that only has Blue Scales (BB), there is a 50% chance of having fish with red scales (Bb) and a 0% chance of having fish with patchwork scales (bb).

When breeding a patchwork fish (Bb) with a fish that only has Blue Scales (BB), the offspring will have a 50% chance of having red scales (Bb) and a 50% chance of having blue scales (BB). This is because the blue scales are dominant over the red scales, represented by the capital 'B', and the patchwork scales are recessive, represented by the lowercase 'b'.

To calculate the probability of having fish with red scales, we divide the number of offspring with red scales (Bb) by the total number of possible offspring, and then multiply by 100. So the probability is 50%.

To calculate the probability of having fish with patchwork scales, we divide the number of offspring with patchwork scales (bb) by the total number of possible offspring, and then multiply by 100. Since the fish that only has blue scales does not carry the patchwork gene, there will be no offspring with patchwork scales. Therefore, the probability is 0%.

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Answer:

16,21,15

Step-by-step explanation:

The solutions are 16, 21, and 15. The only value that is not a solution is 11 since 11 is less than 15

Inequality expressions are expressions separated by an unequal sign

Given the inequality expression 15 ≤ y

On swapping sides, the inequality sign will change to have y ≥ 15

Based on the table, we need to select yes for values that are greater than or equal to 15 and select no if otherwise

Based on the given value, the solutions are 16, 21, and 15. The only value that is not a solution is 11 since 11 is less than 15

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Im pretty sure this is the answer

12x-6y+2

it will travel 343m•7. this is 2401 meters.

The distance of the sound in 7 seconds will be 2401 meters.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that sound travels in waves. in dry air at 20 Celsius, sound travels about 343 meters in one second.

The distance travelled by the sound in 7 seconds will be calculated as,

Distance = 343 x time

Distance = 343 x 7

Distance = 2401 meters

Therefore, the distance of the sound in 7 seconds will be 2401 meters.

To know more about an expression follow

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The probability of rolling an odd number on a six-sided die is 1/2 or 50%, calculated by dividing the 3 odd outcomes (1, 3, and 5) by the total of 6 possible outcomes.

If you roll a single six-sided die, the question asks what is the probability of rolling an odd number. A six-sided die has three odd numbers (1, 3, and 5) and three even numbers (2, 4, and 6). Therefore, the probability of rolling an odd number is calculated by dividing the number of odd outcomes by the total number of possible outcomes.

The formula for probability is Probability = Number of favorable outcomes / Total number of possible outcomes. In this case, there are 3 favorable outcomes (rolling a 1, 3, or 5) out of 6 possible outcomes (since a die has 6 sides). Therefore, the probability is 3/6, which simplifies to 1/2.

So, if you roll a single six-sided die, the probability of rolling an odd number is 1/2 or 50%.

Answer:

The first three numbers in the pattern would be 6, 12, and 18 since the rule pattern goes by six. I'm not sure if this is what you were looking for but I hope I helped!

Answer:

To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.

this will show u i searched it and wrote half in my words

Answer:

315 in^2

Step-by-step explanation:

Triangles

Area of the two triangular faces.

Area = 1/2 * h * b

h = 7 in

b = 11 in

Area = 1/2 * 7 * 11

Area = 1/2 * 77

Area = 38.5

But there are 2 faces

Area = 38.5 * 2

Area = 77 in^2

Area Left Face

Area left face = height * width

Area left face = 14 * 8

Area left face = 112 in^2

Area Right face

Area Right face = w*h

w = 9

h = 14

Area = w*h

Area right face = 126 in^2

Total Area

Total Area = 126 + 112 + 77

Total Area = 315 in^2

Step-by-step explanation:

2/3=10/15 (divide 15 by 3 to get 5, then multiply both numerator and denominator by 5 to set equivalent)

3/5=9/15

10/15 is greater than 9/15, so during the 1st week there were more boy campers

During the first week of a summer camp, there were more boy campers.

To determine during which week there were more boy campers, we need to compare the fractions of boys in each week. In the first week, 2 out of 3 campers were boys, which can be written as a fraction as 2/3. In the second week, 3 out of 5 campers were boys, which can be written as a fraction as 3/5. To compare these fractions, we need to find a common denominator. In this case, the lowest common denominator is 15, which is the total number of campers each week. Multiplying the numerator and denominator of each fraction by 5 and 3 respectively, we get 10/15 for the first week and 9/15 for the second week. Therefore, during the first week, there were more boy campers.

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5:1, 5/6, or 84%(rounded).

There is one chance of rolling a 2 and since it is against rolling a 2, you have a 5 other numbers you could get.

Answer:

B) The initial number of subscribers.

Step-by-step explanation:

The given equation is:

[tex]y=42000(0.96)^{t}[/tex]

[tex]y=42000(1-0.04)^{t}[/tex]

We can compare this equation with the general model of exponential growth/decay:

[tex]y=A(1-r)^{t}[/tex]

Here A represents the initial amount, r represents the rate of decay and t represents the time in years.

Comparing both equations, we can see that 42,000 represents the Initial Quantity which in this case is the initial number of subscribers.

So option B gives us the correct answer.

Answer:

B) the initial number of subscribers

Step-by-step explanation:

Answer: the answer is three sorry if its wrong.

Step-by-step explanation:

Your answer will be 3