Answer: 5 years
14,800 students enrolled
Step-by-step explanation:
Let x represent the number of years and
Let y represent the number of students enrolled
College A: y = 12,300 + 500x
College B: y = 18,550 - 750x
Use substitution Method to solve:
12,300 + 500x = 18,550 - 750x
+750x +750x
12,300 + 1250x = 18,550
-12,300 -12,300
1250x = 6250
x = 5
Input x = 5 into one of the equations to solve for y.
y = 12,300 + 500x
= 12,300 + 500(5)
= 12,300 + 2500
= 14,800
Determine whether the table could represent a function that is linear, exponential, or neither. If the function is exponential or linear, find a function that passes through the points. If the function is neither exponential nor linear, type NONE.
x 1 2 3 4
f(x)70 40 10 -20
f(x)=
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
If you roll a single six-sided die, what is the probability of rolling an odd number? A. B. C. D. 3
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.
Explanation: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%.
a six sided die is tossed. Determine the odds against rolling a 2.
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.
Will mark BRAINLIEST!!!
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:
What happens if you breed a patchwork fish (Bb) with a fish that only had Blue Scales (BB)?
a. What is the probability of having fish with red scales? _____%
b. What is the probability of having fish with patchwork scales?____%
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).
Explanation: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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Factor. 49x16−16y64
Answer:
(7x8 + 4y32) • (7x8 - 4y32)
Step-by-step explanation:
P.1 (49 • (x16)) - 24y64
P.2 72x16 - 24y64
P.3 (7x8 +4y32) • (7x8 - 4y32)
Multiply each of the following numbers 7.32, and 0.006 by 10, 100, and 1,000. Then explain the pattern you can use to find the products. *
Your answer
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.
add 5 to p then divide 7 by the result
Answer:
p should equal -4
Step-by-step explanation:
what value of x makes the equation below true?
Answer:
B
Step-by-step explanation:
7 + x = 84
Subtract 7 from both sides.
x = 77
Between what two consecutive integers does .... lies?
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.
Which number is a factor of 8?
4
7
5
6
Answer:
4Step-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]
Subscriptions to a popular fashion magazine have gone down by a consistent percentage each year and can be modeled by the function y = 42,000(0.96)t. What does the value 42,000 represent in the function? A) The decay factor of subscribers. B) The initial number of subscribers. C) The number of time intervals. D) The number of subscribers after t years. Submit
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:
PLS HELP 20 POINTS
Carrie built a fort to plain in by connecting two boxes.The first box is 7 meters long,9 meters wide and 8 meters high.The second box is 3;meters long, 8 meters wide, and 2 meters high how many cubic meters of space does Carrie have to play in?
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.
What is x please
3x +9 = 12
➷ 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!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
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
use the distributive property to write an expression that is equivalent to each expression. -2(-6x + 3y - 1)
Im pretty sure this is the answer
12x-6y+2
Helppppp Plsssss Asap!! Show your work!! Thanks.
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!
Find the surface area of this triangular prism
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
sound travels in waves. in dry air at 20 Celsius ,sound travels about 343 meters in one second. how many meters will ,sound travels in 7 seconds?
it will travel 343m•7. this is 2401 meters.
The distance of the sound in 7 seconds will be 2401 meters.
What is an expression?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.
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For each value of Y, determine whether it is a solution to 15Greater than or equal to Y
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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{ 5x - y = 5
{ 5x - 3y = 15
solve the system using substitution
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
The supports of a wooden table are in the shape of a triangle. Find the angles are in the ratio 4x : 4x : 10x
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:
4(x) = 4(10) = 40°4(x) = 4(10) = 40°10(x) = 10(10) = 100°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]
What are the factors of x2 − 49? (x − 1)(x + 49) (x − 7)(x − 7) (x − 7)(x + 7) Prime
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
During the first week of a summer camp 2 out of 3 campers were boys. During the second week 3 out of 5 were boys. There were a 15 total campers each week. During which week were there more boy campers. Explain
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.
Explanation: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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‐15−8= ‐15 + __
= __
Enter numbers to evaluate ‐15−(‐8).
‐15−(‐8)= ‐15 + __
=__
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
what is the domain of the function
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.
9. Consider a pattern that begins with 28 and each consecutive number is six more than the previous term. What are the first three terms of this pattern?
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!
How to solve logarithmic equations as such
[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]
Part A: Explain how to determine the value of the vertical translation, d, for the graph of g(x). (2 points)
Part B: Explain how to determine the value of the vertical translation, d, for the graph of f(x) = 2sin(θ + 120°) + 6. (3 points)
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 is the vertical stretchb is the horizontal shiftk is the vertical shiftA 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.
a sphere has a volume of 36 (3.14) cm cube. what is the diameter of the sphere
Answer:
Diameter = 6 cmStep-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
You run 7 miles in one hour and 21 miles in three hours
Answer: the answer is three sorry if its wrong.
Step-by-step explanation:
Your answer will be 3