Answer:
Step-by-step explanation:
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The online program at a certain university had an enrollment of 580 students at its inception and an enrollment of 1725 students 3 years later
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
The online program at a certain university had an enrollment of 580 students at its inception and an enrollment of 1725 students 3 years later. Assume that the enrollment increases by the same percentage per year. a) Find the exponential function E that gives the enrollment t years after the online program's inception. b) Find E(11), and interpret the result. c) When will the program's enrollment reach 5500 students?
Let E0 be the number of students that enrolled at inception
E(t) be the number of students that enrolled at any time t
At inception i.e at t = 0, E0 = 580
The exponential function E that gives the enrollment at inception will be expressed as;
E(t) = E0e^kt (note that the exponential power is positive since number of students keep increasing yearly).
At inception:
E(0) = 580e^k(0)
E(0) = 580(1)
E(0) = 580
If after 3years, enrollment increases to 1725 students i.e at t = 3, E(t) = 1725. The equation becomes;
E(3) = P0e^kt
E(3) = 580e^3k
1725 = 580e^3k
Make k the subject of the formula:
e^3k = 1725/580
e^3k = 2.9741
Apply ln to both sides of the equation
ln(e^3k) = ln(2.9741)
3k = 1.08995
k = 1.08995/3
k = 0.3633
The exponential function E that gives the enrollment t years after the online program's inception will be expressed as;
E(t) = E0e^kt
Given E0 = 580 and k = 0.3633
E(t) = 580e^0.3633t
b) To get E(11), we will substitute t = 11 into the resulting expression in (a) above to have;
E(t) = 580e^0.3633t
E(11) = 580e^0.3633(11)
E(11) = 580e^3.9965
E(11) = 580×54.4074
E(11) = 31,556.287
E(11) ≈ 31,556 students
This means that about 31,556students enrolled 11years later.
c) To know when the program's enrollment reach 5500 students, we will set E(t) to 5500, E0 to 580 and k to 0.3633 and calculate the value of t
From the equation E(t) = 580e^0.3633t
5500 = 580e^0.3633t
e^0.3633t = 5500/580
e^0.3633t = 9.4828
Apply ln to both sides
ln(e^0.3633t) = ln(9.4828)
0.3633t = 2.2495
t = 2.2495/0.3633
t = 6.19
t ≈ 6years
This means that the program's enrollment will reach 5500 students 6 years later.
The three volumes of Lord of the Rings sit in order on a shelf. Each is 1 1/4 inches thick, comprising an inch of pages and 1/8 inch for each cover. A bookworm bores from page 1, volume I, to the last page of volume III. How far does it travel?
Answer:
4 2/4 (NOT SIMPLIFIED)
Step-by-step explanation:
Comprising means made of (aka including). You just add 1 1/4+1 1/4+1 1/4.
=3 3/4
The 1/8 is for the front and back cover. The bookworm ate through 3 volumes so there is 6 covers. So times 1/8 by 6. I turned the 6 into a fraction by putting it over 1. So now you have 1/8×6/1=6/8. Now you are going to add the 3 3/4 to the 6/8. You are going to turn the whole fraction to an improper. You are going to multiply the whole number(3) to the denominator(4), add that to the numerator(3) , and put it over the original denominator (4)= 15/4. Now you are going to set up the problem were you add the 6/8 to the 15/4. To add fractions the denominator have to be the same. With this problem you have two options: you can either do an equation to change the 6/8 denominator equal to 4 or an equation to change the 15/4 denominator equal to 8. Either one would work fine. I'm going to show you how to set the 6/8 denominator to 4.
1. Set it up as an equation 6/8=x/4
2. Find what gets the first denominator to the second in this case dividing by 2 6/8=x/4
3. What you do to the bottom is what you have to do with the top. So to find x, you need to divide 6 by 2= 3
So now your new equation is now 3/4+15/4. Adding this should give you 18/4, but most likely you have to write it as a proper fraction. To do this you are going to divide the 18 by 4. Your remainder will become your new numerator and the 4 will still be you denominator. The number times 4 fully goes into 18 will be your new whole number.
18/4=4.5
What is the answer to x - 3 = -10
Answer:
x = -7
Step-by-step explanation:
x - 3 = -10
Add 3 to each side
x - 3+3 = -10+3
x = -7
Between which two integers is the positive value of the square root of 75?
Answer:
8 and 7
Step-by-step explanation:
the square root of 75 is approximately 8.66025 or 5√3 in radical form
What if the perimeter of the table?
Step-by-step explanation:
13? i forgot all this math XD
negative thirty-one less than s is greater than 93
Answer:
s > 62
Step-by-step explanation:
Write it out: s - (-31) > 93Simplify: s + 31 > 93Subtract 31 from each side, so it now looks like this: s > 62I hope this helps!
The inequality which represents the given statement is given by s > 62.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
The given statement is "negative thirty-one less than s is greater than 93". This statement must be transformed into form of an inequality.
We know that an inequality comes when a number is greater than or less than another number . Here the variable is the unknown number 's'. This meant the expression can be written as :
s - (-31) > 93
Simplifying this inequality we get :
s + 31 > 93
s > 93 - 31
s > 62
Therefore , the inequality which represents the given statement is given by s > 62.
Learn more about inequalities here :
brainly.com/question/25275758
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The product of 6 and a is 30
Answer:
30 divided by 6=5
Step-by-step explanation:
a=5
5 times 6 is the product of 30
A doctor studying nutrition collected data on the weights (in kilograms) of infants in North Africa. The table below shows the mean weights for infants of different ages in the study. Plot the data in a scatter plot.
Answer:
Step-by-step explanation:
Got it correct on Khan Academy
4x – 3y = 20
2x + y = 30
Using the two equations above, solve for y.
Answer:
4x-3y+20
Step-by-step explanation:
x=6.875
y=2.5
2x+y=30
x=12.5
y=-5
Kira owes Mark $5, and Mark owes Kira $7. Which statement means the same thing?
Answer:
mark owes Kira $2
I think
ionic bonds occur between?
Answer:
Ionic bonds usually occur between metal and nonmetal ions. For example, sodium (Na), a metal, and chloride (Cl), a nonmetal, form an ionic bond to make NaCl. In a covalent bond, the atoms bond by sharing electrons. Covalent bonds usually occur between nonmetals.
An ionic bond is held together by the electrostatic attraction between ions that are near one another. Electrostatic attraction is the attraction between atoms that have opposite charge and holds the atoms together in ionic bonds.
Write a cubic binomial with constant -8.
Answer:
27a³ -8
Step-by-step explanation:
A binomial has two terms. If one of the terms is the constant -8, the other must be a cubic term, something with a variable to the third power.
27a³ -8 . . . . . a cubic binomial with a constant of -8
1. Which of the following is a true statement? *
To square a number, multiply the number by 2.
The inverse of squaring a number is to divide the number by 2.
To square a number, multiply the number by itself.
O A perfect square is a number whose square root is an even number.
Answer:
To square a number, multiply the number by itself.
Step-by-step explanation:
100(z-0.2)=-10(5z+0.8)
Answer:
Z= 0.08
Or
Z= 2/25
Step-by-step explanation:
100(z-0.2)=-10(5z+0.8)
Opening all the bracket
100z - 20= -50z - 8
Collecting like terms, and at Same time adding up this like terms
100z +50z = -8+20
150z= 12
Dividing bith sides of the equation by 150 to look for the value of z
(150/150)(z)=12/150
Z= 0.08
Or
Z= 2/25
Two consecutive numbers have a sum of 27. What is the smaller number?
Answer:
13
Step-by-step explanation:
The value halfway between them is their average: 27/2 = 13.5.
The smaller number is 13.
__
The larger number is 14.
If CE= 7x+4
x+3 + 8x-9 = 7x+4
what expression is equivalent
Answer:
-4x^2, -3x, -5
Step-by-step explanation:
-4x^2 + 2x - 5 (1 + x)
-4x^2 + 2x - 5 + 5x
-4x^2 - 3x - 5
Find the triangle of the following figure: A. 30cm2 B: 36cm2 C. 18cm2 D. 15cm2
Answer:
D. 15cm2
Step-by-step explanation:
To find the area of a triangle, you multiply the base (10cm) and height of the triangle (3cm) and divide that by 2. So 10×3=30. Then, you need to divide this by 2. Since 30 is an even number, you won't get a decimal. So 30/2=15. And dont forget your units!
Julie travels 3 times as fast as Bill. Traveling in opposite directions, they are 190 miles apart after 2.5 hours. Find their rates of travel.
Answer:
Step-by-step explanation:
Let b
Bill's rate of travel = x
Let Julie's rate of travel = 3x
The time each travels is 2.5 hours
Together they travel a distance of 190 miles
d = r*t
Bill's distance covered is r * t = 2.5x
Julie's distance travel is 2.5 * 3x = 7.5x
The total distance = Bill + Julie
2.5x + 7.5x = 190
10x = 190
x = 190/10
x = 19
Bill's distance = 2.5 * 19 = 47.5
Julie's distance = 19 * 7.5 = 142.5
Rate = distance / time
Bill's rate = 47.5 / 2.5 = 19 miles per hour.
Julie's rate = 142.5/2.5 = 57 miles per hour
Is there an easier way?
You should notice that Bill's rate is just x which is 19 miles / hour
You can also notice that Julie is going 3 times as fast or 19*3 = 57
Find the greatest common factor of 30p4q3, 45p6q5, 90p9q4
Answer:
no cule bro
Step-by-step explanation:
Answer:
15p4q3
Step-by-step explanation:
Question 20 of 33
The table below compares the number of lawns Sam mowed with the amount
of money he earned. What is a logical conclusion to make about the amount
Sam would earn for mowing 7 lawns?
Number of lawns mowed
Total money earned
1
$25
3
$75
5
$125
7
?
Write <, >, or = between the pair of numbers to form a true statement.
0.848
0.84800
Even though 0.84800 has two more zeroes at the end, this is still the same number as 0.848.
0.84800 -> 0.848
Therefore, 0.848 = 0.48400
Best of Luck!
A domain consists of the values 1, 2, 3, and 2. A range consists of the values 5, 10, 15, and 20. The 1 in the domain corresponds to the 5 in the range, the first 2 in the domain corresponds to the 10 in the range, the 3 in the domain corresponds to the 15 in the range, and the second 2 in the domain corresponds to the 20 in the range. Does this relation represent a function? Explain.(1 point)
It does not represent a function. The domain value of 2 corresponds to two values within the range.
It does not represent a function. Each value in the domain corresponds to exactly one value in the range.
It does represent a function. Each value in the domain corresponds to exactly one value in the range.
It does represent a function. The domain value of 2 corresponds to two values within the range.
Answer:
It does not represent a function. The domain value of 2 corresponds to two values within the range.
Step-by-step explanation:
Given the function:
Domain : Range
1 => 5
2 => 10
3 => 15
2 => 20
For a relation to be considered a function, every domain value should have exactly 1 range value assigned to it or mapped to it.
In order words, a domain value should not have different range values.
In the relation given, domain value of 2, has more than 1 range value, 10 and 20, assigned to it. It does not have exactly 1 range value.
Therefore, the relation does not represent a function because the domain value of 2 corresponds to two values (10 and 20), within the range.
Answer:
It does not represent a function. The domain value of 2 corresponds to two values within the range.
Step-by-step explanation:
When two times a number is decreased by 3, the result is 11. What is the number?
Answer:
7
Step-by-step explanation:
let the unknown number be x
so x times 2 minus 3=11
it will now be 2x-3=11
the -3will cross the equal sign and change to +3
2x=11+3 which will be 2x=14
divide both sides by 2 and the final answer will be x=7
You intend to estimate a population mean mu with the following sample. 45.3, 42.3, 53, 49, 15.2, 52.3, 45.6, 39.6, 39.4, 16.1, 54.4.You believe the population is normally distributed. Find the 99.9% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places (because the sample data are reported accurate to one decimal place).
Answer:
A 99.9% confidence interval for the population mean is [22.31, 59.91] .
Step-by-step explanation:
We are given the following sample values;
X = 45.3, 42.3, 53, 49, 15.2, 52.3, 45.6, 39.6, 39.4, 16.1, 54.4.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = [tex]\frac{\sum X}{n}[/tex] = 41.11
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex] = 13.59
n = sample size = 11
Here for constructing a 99.9% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 99.9% confidence interval for the population mean, [tex]\mu[/tex] is;
P(-4.587 < [tex]t_1_0[/tex] < 4.587) = 0.999 {As the critical value of t at 10 degrees of
freedom are -4.587 & 4.587 with P = 0.05%}
P(-4.587 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 4.587) = 0.999
P( [tex]-4.587 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}{[/tex] < [tex]4.587 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.999
P( [tex]\bar X-4.587 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+4.587 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.999
99.9% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-4.587 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+4.587 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]41.11-4.587 \times {\frac{13.59}{\sqrt{11} } }[/tex] , [tex]41.11+4.587 \times {\frac{13.59}{\sqrt{11} } }[/tex] ]
= [22.31, 59.91]
Therefore, a 99.9% confidence interval for the population mean is [22.31, 59.91] .
f(x) = x - 5, translated 6 units to the right.
Answer:
[tex]g(x) = x - 11[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x - 5[/tex]
Required
Translate to the right by 6 units
When a function is translated to the right, the resulting function becomes
[tex]g(x) = f(x - h)[/tex]
Where h is the number of units moved;
Since; h = 6
[tex]g(x) = f(x - h)[/tex]
becomes
[tex]g(x) = f(x - 6)[/tex]
Solving for f(x - 6);
[tex]f(x) = x - 5[/tex]
Substitute x - 6 for x
[tex]f(x - 6) = x - 6 - 5[/tex]
[tex]f(x - 6) = x - 11[/tex]
This implies that [tex]g(x) = x - 11[/tex] is the result of the translation
Noah is shopping for new socks. He sees many different options. one bag has 12 socks for $9.99, another bag has 20 socks for $14.99, and the third bag with 10 socks for $19.99. which is the best deal for socks?
Answer:
20 socks fit $14.99 is the best deal out of the 3
Step-by-step explanation:
Here, we want to know the bag that contain the best deals for socks .
The best way to go about this is to know the unit prices of socks in each of the bags.
Let’s proceed;
12 socks for $9.99
The unit price here is 9.99/12 = 0.8325 per socks
20 socks for 14.99
Unit price here is 14.99/20 = 0.7495
10 socks for 19.99
The unit price here is 19.99/10 = 1.999
Out of all these options , we can see that the second option is actually the cheapest and offers what we should be pick as we are looking for suppliers since it charges the lowest;
So the best deal for socks is in the bag of 20 socks for $19.99
1.81 repeating as a fraction
Answer: 1 73/90 if the decimal is 1.81 and the one is repeating
If the .81 is repeating then 1 9/11
Step-by-step explanation:
Answer:
20/11
Step-by-step explanation:
let 0.(81) = x
--> 100x = 81.(81)
--> 100x - x = 81.(81) - 0.(81)
--> 99x = 81
--> x = 81/99 = 9/11
1.(81) = 1 + 0.(81) = 1 + x = 1 + 9/11 = 20/11
Can someone help me with my algebra homework and explain how you got it ?
Answer: D
Step-by-step explanation:
This problem seems to ask for the slope of the line. If not by counting, we can use the slope formula to solve. The formula is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Let's use (1,2) and (2,-1).
[tex]m=\frac{-1-2}{2-1} =\frac{-3}{1}=-3[/tex]
Now, we know that the slope is -3.
We also know that A and C are eliminated because the line is going down, which signifies negative. We would be left with B and D. We know that B is incorrect because the slope would be less steep if B were to be the answer. Therefore, D is the correct answer.
WILL MARK BRAINLIEST
List all of the number sets that contain the number 15.
A. rational numbers and integers
B. rational numbers, integers, and natural numbers
C. rational numbers, integers, and whole numbers
D. rational numbers, integers, natural numbers, and whole numbers
Answer: D
Step-by-step explanation: