Answer:
3.8
Step-by-step explanation:
a=3.79 or 3.8km
√(9.4^2 - 8.6^2)
A_____is a solid consisting of a square,a point not in the same plane as the square and all the points between them
A square rug has an inner square in the center. The side length of inner square is x inches and the width of the outer region is 2 inches. What is the area of the outer part of the rug?
Answer:
so Area of Outer part = 8x + 16 square inches
Step-by-step explanation:
2 squares.
inner square dimension is x inches by x inches.
width of outer region= 2inches.
We want the area of the border around the inner square.
so
Area of border = B = Area of Large - Area of Inner
B = (x+4)^2 - x^2
B = x^2 + 8x + 16 - x^2
B = 8x + 16 square inches
so Area of Outer part = 8x + 16 square inches
To find the area of the outer part of the rug, we need to follow these steps:
1. Calculate the area of the entire square rug including the inner square.
2. Calculate the area of the inner square.
3. Subtract the area of the inner square from the area of the entire rug to find the area of the outer part.
The side length of the inner square is x inches.
Since the width of the outer region is 2 inches on all sides, this width will be added to each side of the inner square twice (once for each side of the corner) when calculating the side length of the entire rug. Thus, the entire side length of the rug will be x + 2 + 2 inches, which simplifies to x + 4 inches.
Now let's perform the calculations step-wise:
Step 1: Calculate the area of the entire square rug.
The formula for the area of a square is side length squared (A = side^2), so the area of the entire rug is (x + 4)^2 square inches.
Step 2: Calculate the area of the inner square.
Using the same formula (A = side^2), the area of the inner square is x^2 square inches.
Step 3: Subtract the area of the inner square from the area of the entire rug.
Now we subtract the area of the inner square from the area of the entire rug to find the area of the outer region:
Area of the outer part = Area of the entire rug - Area of the inner square
Area of the outer part = (x + 4)^2 - x^2
To make it clearer, let's expand (x + 4)^2 using the distributive property (FOIL: First, Outer, Inner, Last):
(x + 4)^2 = (x + 4)(x + 4)
= x*x + 4*x + 4*x + 4*4
= x^2 + 4x + 4x + 16
= x^2 + 8x + 16
So the Area of the outer part is:
Area of the outer part = x^2 + 8x + 16 - x^2
Area of the outer part = 8x + 16 square inches
This is the area of the outer part of the rug.
The probability that a student guesses the correct answer to a four-choice multiple choice question is
P(correct) = 0.25. How many correct answers should a student expect to guess on a test with 68
four-choice multiple choice questions?
answer asap pls
Since we already know that there is a 25% chance to guess the correct answer to a multiple choice question, all we have to do is multiply .25 and 68 to get the expected amount of answers a student can possibly guess. We multiply .25 since it is the decimal form of 25% and 68 is our total questions.
.25 x 68 = 17
Therefore, a student can expect to guess 17 answers correct on a test with 68 multiple choice questions.
Answer:
the answer is 17
Step-by-step explanation:
Hope this helps!
what does it mean that there is an equal theoretical probability of each outcome ?
Answer:
there is equal probability for each outcome
Step-by-step explanation:
Let's say you are flipping a coin.
The possible outcomes are : Head and Tail
Probability(Head) = 1/2
Probability(Tail) = 1/2
In this case, there is equal theoretical probability of each outcome
What is the mean and mad of this data set?
n=7
The number of gerbils seen per day:
2,3,5,7,8,8,9
Answer:
The mean number of gerbils seen per day is 6.
The mean absolute deviation of the data is 2.29.
Step-by-step explanation:
The mean of a data set is the value that represents the entire data set. It is the average value.
The formula to compute the mean of a data set is:
[tex]\bar x=\frac{1}{n}\sum X[/tex]
The mean absolute deviation (MAD) of a data set is the average distance amid each value and the mean. The MAD provides us with an idea about the deviation in the data set.
The formula to calculate the value of MAD is:
[tex]MAD=\frac{1}{n}\sum |x-\bar x|[/tex]
The data set for the number of gerbils seen per day is:
S = {2, 3, 5, 7, 8, 8, 9}
Compute the mean of the data as follows:
[tex]\bar x=\frac{1}{n}\sum X[/tex]
[tex]=\frac{1}{7}\times [2+3+5+7+8+8+9]\\\\=\frac{1}{7}\times 42\\\\=6[/tex]
The mean number of gerbils seen per day is 6.
Compute the mean absolute deviation of the data as follows:
[tex]MAD=\frac{1}{n}\sum |x-\bar x|[/tex]
[tex]=\frac{1}{7}\times [|2-6|+|3-6|+|5-6|+|7-6|+|8-6|+|8-6|+|9-6|]\\\\=\frac{1}{7}\times 16\\\\=2.2857\\\\\approx 2.29[/tex]
Thus, the mean absolute deviation of the data is 2.29.
Final answer:
The mean of the data set (2, 3, 5, 7, 8, 8, 9) is 6, and the mean absolute deviation (MAD) is approximately 2.29.
Explanation:
Finding the Mean and MAD of a Data Set
The mean (average) of a data set is found by adding up all the numbers in the set and then dividing by the count of those numbers. In the provided data set (2, 3, 5, 7, 8, 8, 9), the mean is calculated as follows:
Sum of the numbers = 2 + 3 + 5 + 7 + 8 + 8 + 9 = 42Count of numbers (n) = 7Mean = Sum / n = 42 / 7 = 6The mean absolute deviation (MAD) is found by calculating the absolute differences between each number in the set and the mean, averaging those absolute differences:
Absolute differences from the mean: |2-6|, |3-6|, |5-6|, |7-6|, |8-6|, |8-6|, |9-6|Absolute differences are: 4, 3, 1, 1, 2, 2, 3Sum of absolute differences = 4 + 3 + 1 + 1 + 2 + 2 + 3 = 16MAD = Sum of absolute differences / n = 16 / 7 ≈ 2.29Therefore, the mean of the data set is 6, and the MAD is approximately 2.29.
a fish tank is 24 inches long. 16 inches deep and 10 inches tall. The tank is filled halfway. How much water is in the tank?
The fish tank, when filled halfway with a height of water at 5 inches, contains 1920 cubic inches of water based on its dimensions of 24 inches by 16 inches by 5 inches.
Explanation:To calculate the volume of water in the fish tank when it is filled halfway, we need to use the tank's dimensions and consider only half the height, as it is filled to that level. The tank measures 24 inches long, 16 inches deep (width), and 10 inches tall. Since it is filled halfway, the water level is at 5 inches high.
Volume of the tank is calculated by the formula for the volume of a rectangular prism: Volume = Length × Width × Height. So we calculate half the volume: Volume = 24 inches × 16 inches × 5 inches. The calculations would be: 24 × 16 × 5 = 1920 cubic inches.
Therefore, the fish tank has 1920 cubic inches of water when filled halfway.
Click the prime number cards to build composite numbers to 50.
Answer:
See Explanation
Step-by-step explanation:
A prime number is a number that has only two factors, by 1 and itself.
A composite number on the other hand are numbers which have more than two factors.
To determine the number of prime cards needed to build each composite number, we first express the number as a product of its prime factors.
These are:
4=2X2
6=2X3
8=2X2X2
9=3X3
10=2X5
12=2X2X3
14=2X7
15=3X5
16=2X2X2X2
18=2X3X3
20=2X2X5
21=3X7
22=2X11
24=2X2X2X3
26=2X13
27=3X3X3
28=2X2X7
30=2X3X5
32=2X2X2X2X2
33=3X11
34=2X17
35=5X7
36=2X2X3X3
38=2X19
39=3X13
40=2X2X2X5
42=2X3X7
44=2X2X11
45=3X3X5
46=2X2X13
48=2X2X2X2X3
49=7X7
50=2X5X5
Therefore for each of the numbers, those are the prime number cards to be used.
Take for example, the number 50, the prime numbers that will be used to build 50 are the prime factors of 50.
50=2 X 5 X 5
Therefore, its prime factors are 2 and 5.
We will use the following prime number cards:
1 card with prime number 22 cards with prime number 5What is the first month in which Maria's amount of land exceeds Lucia's amount of land?
Answer:
7th Month
Step-by-step explanation:
The number of hectares of Lucia's land grows arithmetically by 5 hectares each month.
Whereas, the number of hectares of Maria's land grows geometrically with a common ratio of 1.4 every month.
Writing this as sequence expressions:
For Lucia,
First term, a=11 hectares
Common difference, d=5
Therefore:
[tex]T(n)=a+(n-1)d[/tex]
[tex]11+5(n-1)=11+5n-5\\=6+5n[/tex]
For Maria,
First term, a=6 hectares
Commons ratio=1.4
[tex]T(n)=ar^{n-1}\\=6*1.4^{n-1}[/tex]
Next, we compute and compare the results for values of n of these two equations:
[tex]Lucia, T(n)=6+5n[/tex]
[tex]Maria,T(n)=6*1.4^{n-1}[/tex]
[tex]Lucia, T(1)=6+5=11[/tex]
[tex]Maria,T(1)=6*1.4^{1-1}=6[/tex]
[tex]Lucia, T(2)=6+5(2)=16[/tex]
[tex]Maria,T(2)=6*1.4^{2-1}=8.4[/tex]
[tex]Lucia, T(3)=6+5(3)=21[/tex]
[tex]Maria,T(3)=6*1.4^{3-1}=11.76[/tex]
[tex]Lucia, T(4)=6+5(4)=26[/tex]
[tex]Maria,T(4)=6*1.4^{4-1}=16.56[/tex]
[tex]Lucia, T(5)=6+5(5)=31[/tex]
[tex]Maria,T(5)=6*1.4^{5-1}=23.05[/tex]
[tex]Lucia, T(6)=6+5(6)=36[/tex]
[tex]Maria,T(6)=6*1.4^{6-1}=32.27[/tex]
[tex]Lucia, T(7)=6+5(7)=41[/tex]
[tex]Maria,T(7)=6*1.4^{7-1}=45.18[/tex]
Therefore, in the seventh month, Maria's land will exceed that of Lucia.
At midnight, a passenger train left the station. Two hours later, a freight train left the same station
traveling on the same track in the same direction. At 8 a.m. the passenger train was 120 miles ahead
of the freight train. Find the rate of each train if the passenger train traveled 5 mph faster than the
freight train. ENTER ONLY THE NUMBER (do not enter variables, punctuation marks, units, symbols
or equals signs).
Answer:
speed of freight train = 40 MPH
speed of passenger train = 45MPH
Step-by-step explanation:
Let the speed of freight train be X miles per hour
speed of passenger train is 5 mph more than speed of freight train
Therefore speed of passenger train is X + 5 mph
we will use the formula to calculate distance which is givn below
distance travelled by any object is = speed * time
______________________________________________
Time at which the distance between the train are calculated = 8 AM
for freight train
since it started at 2 AM morning and traveled until 8 AM
duration for which it traveled = 8 - 2 = 6 hours
distance traveled by freight train in those 6 hours = speed of freight train * duration for which it travelled = X * 6 = 6X ----equation A
______________________________________________
for passenger train
since it started at 00.00AM morning and traveled until 8 AM
duration for which it traveled = 8 - 0 = 8 hours
distance traveled by passenger train in those 8 hours = speed of passenger train * duration for which it travelled = X + 5 * 8
= 8X + 40 ------- equation B
_______________________________________________
Distance between passenger train and freight train at 8 AM = 120 miles
also distance can be calculated using distance calculated above in equation A and B
Distance between passenger train and freight train at 8 AM in terms if X = distance traveled by passenger train in 8 hours - distance travelled by freight train in 6 hours = 8X + 40 - 6X = 2X + 40
2X + 40 distance is equal to 120 miles as given in question
therefore
2X + 40 = 120
2X = 120 -40
X = 80/2 = 40
therefore speed of freight train = X = 40 MPH
speed of passenger train = X + 5 = 40 + 5 = 45MPH
venice mowed 6 lawns in 9 hours . what was her rate of mowing in hours per lawn
Answer:
1.5 hours per lawn
Step-by-step explanation:
Take the hours and divide by the number of lawns
9 hours / 6 lawns
1.5 hours per lawn
multiply (x – 4)(x + 3)
Answer:
x^2-x-12
Step-by-step explanation:
I used the box method its easier than foil method if that helps in the future
which ordered pair describes a translation of 6 units up up and 4 units left
Answer:
The correct answer for this is [tex](-4,6)[/tex].
Step-by-step explanation:
As it can be seen from the attached graph image:
The y-axis increases in positive values when we move in up direction i.e. we have +y-axis in upward direction.The y-axis decreases and keeps on becoming more and more negative values when we move in down direction i.e. we have -y-axis in downward direction.The x-axis increases in positive values when we move in right direction i.e. we have +x-axis in right direction.The x-axis decreases and keeps on becoming more and more negative values when we move in left direction i.e. we have -x-axis in left direction.Now, according to question, the translation is performed 6 points up i.e. towards positive y-axis and 4 points towards left i.e. towards negative x-axis.
And, as per rule, the co-ordinates are represented as [tex](x,y)[/tex] where [tex]x[/tex] is the x-co-ordinate and [tex]y[/tex] is y-co-ordinate.
So, the answer here is [tex](-4,6)[/tex].
ABCD is a trapezium calculate the area of ABCD
Answer:
The area of trapezium is 87.5 cm square.
Step-by-step explanation:
Calculate are of trapezium by:
Base 1 (10cm)+ Base 2 (15cm) divided by 2 and times height (7cm)
Please mark brainiest
A scientist needs 4.8 liters of a 12% alcohol solution. She has available a 22% and a 10% solution. How many liters of the 22% and how many liters of the 10% solutions should she mix to make the 12% solution?
Liters of 10% solution =
Liters of 22% solution =
pls someone help!!
Answer:
4.0 L of 10%0.8 L of 22%Step-by-step explanation:
For mixture problems, it is convenient to define a variable to represent the amount of the greatest contributor. Let x represent the amount of 22% solution in the mix. Then 4.8-x is the amount of 10% solution.
The amount of alcohol in the mix is ...
0.22x +0.10(4.8-x) = 0.12(4.8)
Eliminating parentheses, we have ...
0.22x -0.10x +0.10(4.8) = 0.12(4.8)
Subtracting (0.10)(4.8) and combining x-terms gives ...
0.12x = 0.02(4.8)
x = (0.02/0.12)(4.8) = 0.8 . . . . . divide by the x-coefficient
The scientist needs 0.8 L of 22% solution and 4.0 L of 10% solution.
What is the value of P(X=2 or X=0)=?
Answer:
0.4
Step-by-step explanation:
The conditions are mutually exclusive (X cannot be both 0 and 2), so the probability is the sum of the individual probabilities:
P(x = 2 or 0) = P(x=2) +P(x=0)
P(x = 2 or 0) = 0.1 +0.3
P(x = 2 or 0) = 0.4
What is the GCF of 96x5 and 64,27
Marissa's Beauty Salon has six hair dryers that each require 500 watts when switched
on. How much would it cost to run all six dryers for 7 hours, at a cost of $0.15 per kWh?
Round to the nearest cent.
We have been given that Marissa's Beauty Salon has six hair dryers that each require 500 watts when switched on.We are asked to find the cost to run all six dryers for 7 hours, at a cost of $0.15 per kWh.
First of all, we will find watts of energy used to switch on 6 hair dryers.
[tex]\text{Watts used per hour}=\text{Wattage per hour}\times \text{Number of hair dryers}[/tex]
[tex]\text{Watts used per hour}=500\text{ Watts}\times 6[/tex]
[tex]\text{Watts used per hour}=3000\text{ Watts}[/tex]
Now we will convert watts into kilowatts. We know that 1 kW is equal to 1000 W.
[tex]3000\text{ Watts}=\frac{3000}{1000}\text{ kW}=3\text{ kW}[/tex]
So 3 kW are used for 7 dryers for 1 hour. Now we will multiply 3 kW by 7 to find kWs used in 7 hours as:
[tex]\text{kWs used in 7 hours}=3\times 7=21[/tex]
Since the cost of 1 kWh is $0.15, so to find cost for 21 kW/h, we will multiply $0.15 by 21.
[tex]\$0.15\times 21=\$3.15[/tex]
Therefore, it will cost $3.15 to run all six dryers for 7 hours.
A corporation maintains a large fleet of company cars for Its sales people. To check the average number of miles driven per month per car this year, a random sample of 40 cars is examined. The mean and standard deviation for the samples are 2752 mi/mo., and 350 mi/mo., respectively. It is known that the average number of miles driven per car per month was 2600 and sigma = 350 from the previous records. Test the claim that the mean mileage driven per car per month is different from that of the previous records. Let alpha = 0.05. a. State the requirements. Does it meet the appropriate requirements? b. State H_0 and H_a. c. Compute the test statistic. d. Find the critical value and p value. State your conclusion and interpret.
Jerome solved the equation below by graphing. log Subscript 2 Baseline x + log Subscript 2 Baseline (x minus 2) = 3 Which of the following shows the correct system of equations and solution? y 1 = StartFraction log x Over log 2 EndFraction + StartFraction log (x minus 2) Over log 2 EndFraction, y 2 = 3; x = 3 y 1 = StartFraction log x Over log 2 EndFraction + StartFraction log (x minus 2) Over log 2 EndFraction, y 2 = 4; x = 4 y 1 = log x + log (x minus 2), y 2 = 3; x = 33 y 1 = log x + log (x minus 2), y 2 = 3; x = 44
Answer:
x=4
Step-by-step explanation:
The solution for the logarithmic equation is x = 4 and it is graphically shown in the figure.
What is graphing a logarithmic function?Every logarithmic function is the inverse function of an exponential function, we can think of every output on a logarithmic graph as the input for the corresponding inverse exponential equation.
For the given situation,
The equation is
[tex]log_{2}x+log_{2}(x-2) =3[/tex]
⇒ [tex]log_{2} (x)(x-2)=3[/tex]
⇒ [tex]log_{2}(x^{2} -2x)=3[/tex]
we know that [tex]y=log_{b} x[/tex] can be written as [tex]x=b^{y}[/tex]
⇒ [tex]x^{2} -2x=2^{3}[/tex]
⇒ [tex]x^{2} -2x-8=0[/tex]
⇒ [tex](x-4)(x+2)[/tex]
⇒ [tex]x=4[/tex] or [tex]x=-2[/tex]
The solution for the logarithmic function is shown in the graph below.
Hence we can conclude that the solution for the logarithmic function is x = 4.
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Which number is irrational?
-27
3
4.12
the mean weight of 9 players and 3 reserve players is 188 pounds what is the mean weight of the 3 reserve players
Answer:
83.56/p
Step-by-step explanation:
Let the weight of the players = p
Let the weight of the reserve players = r
Since there 9 players, there weight = 9p
And since there 3 reserve players, there weight = 3r
(9p + 3r) / 12 = 188
9p + 3r = 12 * 188
9p + 3r = 2256
Solve for r
r = 2256 / 27p
r = 83.56/p
Casey is going to wear a gray sportcoat and is trying to decide what tie he should wear to work. In his closet, he has 27 ties, 18 of which he feels go well with the sportcoat. If Casey selects one tie at random, determine the probablity and the odds of the tie going well or not going well with the sportcoat.
Answer:Probability of the tie going well [tex]=\frac{2}{3}[/tex]
Step-by-step explanation:
Given
There are 27 ties in closet out of which 18 go well with coat
and remaining 9 does not go well with coat
Probability of the tie going well [tex]=\frac{\text{Choosing a go well tie}}{\text{choosing a tie out of 27 }}[/tex]
Probability of the tie going well [tex]=\frac{18}{27}=\frac{2}{3}[/tex]
Probability of the tie not going well [tex]=\frac{\text{Choosing a not go well tie}}{\text{choosing a tie out of 27 }}[/tex]
Probability of the tie not going well [tex]=\frac{9}{27}=\frac{1}{3}[/tex]
Odds in favor of the tie going well is [tex]=18:9=2:1[/tex]
Odds against of the tie going well is [tex]=9:18=1:2[/tex]
The probability of picking a tie that matches the sport coat is 2/3 or .67, with the odds being 2:1. The probability of choosing a tie that does not match the sport coat is 1/3 or .33, with the odds being 1:2.
Explanation:The topic at hand is about probability and odds. Probability defines the likelihood that an event will occur out of all possible outcomes, while odds compare the likelihood of the event happening to it not happening.
In this situation, Casey has 27 ties in total. The probability of him picking a tie that goes well with the sport coat is the number of favorable outcomes – 18 ties – over the total number of outcomes – 27 ties. So, the probability would be 18/27 which simplifies to 2/3 or approximately .67.
The odds of this happening, on the other hand, are 18 to 9 or simplified to 2:1. This means that for every three ties he picks, two are likely to go well with the sport coat.
The probability of picking a tie that doesn't go well with the sportcoat is 9/27, which simplifies to 1/3 or approximately .33. The odds of this are 9 to 18, or simplified to 1:2. This means that for every three ties he picks, one is likely not to match the sport coat.
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Determine the zeros of the function 2x2 - 4x - 6 = 0.
Answer:
-1, +3
Step-by-step explanation:
The equation can be factored as ...
2(x² -2x -3) = 0
2(x -3)(x +1) = 0
The zeros are the values of x that make the factors zero:
x = 3, x = -1
The zeros are -1 and 3.
Help! Best Answer = Brainiest!
Answer:
12 = 2.5h + 4
Step-by-step explanation:
Which of the following figures does not have a line of symmetry?
Answer:
b
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
C cannot be folded upon any axis and lay upon itself.
Wyatt was his room and found 57 book under his bed he stacked the books on his desk each stack had the same number of books in it and no stack had fewer than 5 books how many stacks did Wyatt make and how many books were in each stack.
Answer:
There was 3 stacks of 19 books.
Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an independent restaurant will fail in the first year is 43 % . She obtains a random sample of 66 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year? Please give your answers precise to two decimal places.
Answer:
The mean of the number of restaurants that failed within a year is 28.38 and the standard deviation is 4.02.
Step-by-step explanation:
For each restaurant, there are only two possible outcomes. Either it fails during the first year, or it does not. The probability of a restaurant failling during the first year is independent of other restaurants. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In the city where she lives, the probability that an independent restaurant will fail in the first year is 43 %.
This means that [tex]p = 0.43[/tex]
66 independent restaurants
This means that [tex]n = 66[/tex]
Mean:
[tex]E(X) = np = 66*0.43 = 28.38[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = 4.02[/tex]
The mean of the number of restaurants that failed within a year is 28.38 and the standard deviation is 4.02.
Solve −5x = 30
I need help ASAP
Answer:
x = -6
Step-by-step explanation:
−5x = 30
Divide each side by -5
-5x/-5 = 30/-5
x = -6
Answer:
x=-6
Step-by-step explanation:
−5x = 30
divide both sides by -5 to isolate x
x=-6
I hope this helps! Please mark brainliest :)
Complete the expressions so that the expressions have the same value. 1.62÷0.8 and 16.2÷8 and 0.0162 ÷ 0.008 and 0.08 ÷ 0.08,all four of them are correct. There are actually two different ways to complete the expressions above with the given numbers so that each expression has the same value. Question 1, The value of all four expressions could be _ or_ . please help
The expressions 1.62 ÷ 0.8, 16.2 ÷ 8, and 0.0162 ÷ 0.008 all have the same value of 2.025, while 0.08 ÷ 0.08 has a different value of 1.
Explanation:To solve this problem, calculate each of the expressions:
1.62 ÷ 0.8 = 2.02516.2 ÷ 8 = 2.0250.0162 ÷ 0.008 = 2.0250.08 ÷ 0.08 = 1So, the first three expressions are the same because they all equal 2.025. However, the fourth expression is different because it equals 1. In the given question, they are not all equal. Thus, the values of three expressions could be 2.025, and the value of the fourth expression could be 1.
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In 2002, there were 972 students enrolled at Oakview High School. Since then, the number of students has increased by 1.5% each year. Write an exponential function to model the situation, then find the number of students enrolled in 2014. Is this considered growth or decay?
Answer:
[tex]N(t) = 972(1.015)^{t}[/tex]
Growth function.
The number of students enrolled in 2014 is 1162.
Step-by-step explanation:
The number of students in the school in t years after 2002 can be modeled by the following function:
[tex]N(t) = N(0)(1+r)^{t}[/tex]
In which N(0) is the number of students in 2002 and r is the rate of change.
If 1+r>1, the function is a growth function.
If 1-r<1, the function is a decay function.
In 2002, there were 972 students enrolled at Oakview High School.
This means that [tex]N(0) = 972[/tex]
Since then, the number of students has increased by 1.5% each year.
Increase, so r is positive. This means that [tex]r = 0.015[/tex]
Then
[tex]N(t) = N(0)(1+r)^{t}[/tex]
[tex]N(t) = 972(1+0.015)^{t}[/tex]
[tex]N(t) = 972(1.015)^{t}[/tex]
Growth function.
Find the number of students enrolled in 2014.
2014 is 2014-2002 = 12 years after 2002, so this is N(12).
[tex]N(t) = 972(1.015)^{t}[/tex]
[tex]N(12) = 972(1.015)^{12}[/tex]
[tex]N(12) = 1162[/tex]
The number of students enrolled in 2014 is 1162.
The exponential function that models the given situation is [tex]P(t) = 972 \times (1.015)^{t}[/tex]. By 2014, the number of students is approximately 1162, demonstrating growth.
To model the enrollment of students at Oakview High School using an exponential function, we start with the given data:
The initial number of students (P₀) in 2002: 972.
Annual growth rate: 1.5% or 0.015 as a decimal.
The exponential formula is:
[tex]P(t) = P_0 (1 + r)^t[/tex]
where:
P(t) is the population at time t.P₀ is the initial population.r is the growth rate.t is the number of years since the initial year.In our case, the exponential formula will be:
[tex]P(t) = 972 \times (1 + 0.015)^{t}\\P(t) = 972 \times (1.015)^{t}[/tex]
To find the number of students in 2014, calculate t as follows:
t = 2014 - 2002 = 12
[tex]P(12) = 972 \times (1.015)^{12}[/tex]
Compute the result:
P(12) ≈ 972 × 1.195618
P(12) ≈ 1162 students
This is an example of 'growth', as the number of students increases over time.