At Cascadia College, students need to take a 100 level Math and English courses plus an optional Philosophy course. In any quarter, the college needs to make available 4 less English sections than Math sections. In any quarter student demand for the optional Philosophy course is half as many sections as English sections. Available classrooms limit the total sections of all three courses to 44
Given these constraints how many sections of each course should the college make available each quarter to meet demand?
Math sections =
English sections =
Philosophy sections =
Answer:
Math sections = 20
English sections = 16
Philosophy sections = 8
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of Math sections.
y is the number of English sections.
z is the number of Philosophy sections.
Available classrooms limit the total sections of all three courses to 44.
This means that [tex]x + y + z = 44[/tex]
4 less English sections than Math sections.
This means that [tex]y = x - 4[/tex]
In any quarter student demand for the optional Philosophy course is half as many sections as English sections.
This means that [tex]z = \frac{y}{2} = \frac{x - 4}{2}[/tex]
Finding the number of Math sections:
We have both y and z as functions of x. So
[tex]x + y + z = 44[/tex]
[tex]x + x - 4 + \frac{x-4}{2} = 44[/tex]
[tex]2x + \frac{x-4}{2} = 48[/tex]
Multiplying everything by 2
[tex]4x + x - 4 = 96[/tex]
[tex]5x = 100[/tex]
[tex]x = \frac{100}{5}[/tex]
[tex]x = 20[/tex]
Then
[tex]y = x - 4 = 20 - 4 = 16[/tex]
[tex]z = \frac{y}{2} = \frac{16}{2} = 8[/tex]. So
Math sections = 20
English sections = 16
Philosophy sections = 8
PLEASE HELP I'LL GIVE BRAINLIEST!!!!!!!!! According to the Census Bureau, in 2014 California had an estimated population of 3.88 × 107 and Wyoming had a population of 5.84 × 105. Complete the following sentences.
3.8216 × 107 0.38216 × 107 3.8216 × 106 38.216 × 107 0.66 × 101
66.4 × 101 6.64 × 101
The population of California is __________ more than the population of Wyoming
Alternatively, the population of California is _________ times the population of Wyoming.
Answer:
The population of California is [tex]3.3216 * 10^{7}[/tex] more than the population of Wyoming.
Alternatively, the population of California is [tex]6.64 * 10^{1}[/tex] times the population of Wyoming.
Step-by-step explanation:
The first part is to take the numbers out of the scientific notation. The estimated population of California is 38,800,000, and the population of Wyoming is 584,000.
Not that we've done that, let's start with the first part of the problem.
"The population of California is __________ more than the population of Wyoming."
This is a statement of subtraction, because it's not asking how many TIMES more. So, we subtract Wyoming's population from California's population.
[tex]38,800,000 - 584,000 = 38,216,000.[/tex]
Putting that number into scientific notation is easy: move the decimal to the place in the number where there will only be one number in front of the decimal: 3.3216. How many number slots until you have only one number in front of the decimal? 7. So, we know that the power of 10 is going to be 7. So, the first part of the question answers to:
[tex]3.8216 * 10^{7} .[/tex]
Now for the second part.
"Alternatively, the population of California is _________ times the population of Wyoming."
This is a problem of division. The question is asking us to divide California's population by Wyoming's population.
[tex]\frac{38,800,000}{584,000} = 0.664383562 * 10^{2} .[/tex]
We need to have one number in front of the decimal point, so we move it behind the first 6, giving us 6.64. Because we did this, we need to bump the exponent from 2 to 1, leaving us with:
[tex]6.64 * 10^{1}.[/tex]
So, the answer to the question is:
1. [tex]3.8216 * 10^{7}.[/tex]
2. [tex]6.64 * 10^{1}.[/tex]
Hope this helped you, and I hope you get a perfect score!! :)
Answer:
The population of California is ( 3.8216 x 10⁶ ) more than the population of Wyoming.
Alternatively, the population of California is ( 6.64 x 10¹ ) times the population of Wyoming.
Step-by-step explanation:
I'm pretty sure this is what the other person was trying to say it was just very confusing.
Anyway I got this right on my mastery test.
so thx for the points
Sophie has 5 pieces of string that are each 5 feet long. Cooper has 4 pieces of string that are each
3 feet long. Estimate how much more string Sophie has than Cooper has. Enter your answer in the bo
Answer:
Sophie has 12 feet more
Step-by-step explanation:
If x = 4, what is the value of 10x + 147
Answer:
187
Step-by-step explanation:
10*4=40
40+147=187
Answer:
251
Step-by-step explanation:
x=4
104 +147=251
Find the length of side x
Answer:
≈3.464
Step-by-step explanation:
1. the required 'x' belongs to the hypotenuse of the given triangle. It means, the formula of its length is:
x=4*cos30°=4*sin60°, note sin60°=cos30°=√3/2≈0.866.
2. according to the formula above the required length 'x' is:
x=4*0.866=3.464 (or 2√3)
Which triangle most likely has the angles 56°, 48°, and 76°?
A. triangle A
B. triangle B
C. triangle C
D. triangle D
Answer:
c
Step-by-step explanation:
do this for brainliest! :)
Answer:
Question 13 is 27/2 (decimal form, 13.5, Mixed fraction 13 1/2)
Question 14 = 4
Step-by-step explanation:
hope this helped you:)
(This is fundamental Counting principle) choosing from 35 different flavors of ice cream; one, two or three scoops; and sugar or waffle cone.
Answer:
210
Step-by-step explanation:
35x3x2=210
A coordinate plane.
Which statements are true? Check all that apply.
The line that goes through the points (3,7) and (–2,7) is a horizontal line.
The equation x = –8 is a vertical line that goes through the point (–8,3).
The line that goes through the points (0,5) and (0,–7) is a vertical line.
The points on a horizontal line have the same x-coordinate.
Answer:
A , B, and C
Step-by-step explanation:
i just did it
If x is a positive integer, which of the following must be an even integer that is twice the value of an odd integer.
A. 2x
B. 2x + 1
C. 2x + 2
D. 4x + 1
E. 4x + 2
Which fraction is equivalent to (7-3)*3/10^4-10^2
A. 16/25
B. 1/25
C. 8/1125
D. 16/2475
Answer:
C.8/1125 is the answer......
Suppose has a solution. Explain why the solution is unique precisely when has only the trivial solution. Choose the correct answer.
Answer:
Because [tex]x = y[/tex], then the solution is unique.
Step-by-step explanation:
Given
[tex]Ax = b[/tex]
[tex]Ax=0[/tex]
See comment for complete question
Let there be two solutions x and y.
Such that:
[tex]Ax = b[/tex] and [tex]Ay = b[/tex]
Since:
[tex]Ax = Ay = b[/tex]
Then:
[tex]Ax - Ay = b - b[/tex]
[tex]Ax - Ay = 0[/tex]
This implies that:
[tex]Ax - Ay = A(x-y) = 0[/tex]
The only trivial solution is:
[tex]Ax - Ay = A(x-y) = 0[/tex]
Such that:
[tex]x -y = 0[/tex]
Then
[tex]x = y[/tex]
Because [tex]x = y[/tex], then the solution is unique.
Find the value of x.
35
21
Х
X=
= [?]
Help
Step-by-step explanation:
Using Pythagoras theorem
x=✓(35²-21²)=✓784=28 units
An ice company charges $8.16 for 6 bags of ice . If you buy 8 bags of ice how much would it cost you ?
Answer:
$10.88
Step-by-step explanation:
1. Find the cost of each bag
8.16/6 = $1.36
2. Then muti the cost of each bad with the ammount you are buying
1.36(8) = $10.88
F(t)=212-6t
what is the value of t when F (t) = 140?
Answer: -628
Step-by-step explanation:
F(140) = 212 - 6(140)
F(140) = 212 - 840
F(140) = -628
cos=0.985 rounded to nearest tenth
its something about cookies
Answer:
huh????
Step-by-step explanation:
Answer:
cool. i like cookies.
r+4 at r=13 help me
The value of the expression is 17.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
r + 4
When r = 13
r + 4
= 13 + 4
= 17
Thus,
The value is 17.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ5
In the triangle below, the measure of angle A = 52°. Find the measure of angle C.
Answer:
128°
Step-by-step explanation:
180-52=128
what is -6(a + 8) simplified?
Answer:
-6a-48
Step-by-step explanation:
Answer:
-6a - 48
Step-by-step explanation:
distribute
-6 x a = -6a
-6 x 8 = -48
put the answer together
-6a - 48
"Y varies directly as x". If y = 3 when x = 24, find y when x = 10.
Answer:
y=3x-24
Step-by-step explanation:
Divide 4 1/2 by the following unit fractions.
1/8
Answer:
The answer is 36
Step-by-step explanation:
First:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
92÷18
Applying the fractions formula for division,
=9×82×1
=722
Simplifying 72/2, the answer is
=36
Can you help me on question six?!
Answer: A (1:2)
Step-by-step explanation:
Since there are 12 puppies total and 8 of the puppies are yellow labs, there must be 12 - 8 = 4 black labs. Now, the ratio of black labs to yellow labs is 4:8 because there are 4 black labs and 8 yellow labs. However, we can simplify this ratio by dividing the entire ratio by 4. In this case, we would get (4/4):(8/4), which simplifies to 1:2, which is the answer.
help please (will mark brainliest or however you spell it)
A random number generator is set to produce integers from 1 to 10.
About how often would you expect to get an even number in 300 trials?
You would expect to get an even number about
times.
Answer:
you would expect to get 100-200 even numbers. but if u want an exact answer it would be 150 times.
Step-by-step explanation:
there are 5 even and odd numbers. so a 1/2 chance. and 1/2 of 300 is 150
s is inversely proportional to t.
When s
0.4, t = 4
Work out s when t = 0.8
Answer:
0.2
Step-by-step explanation:
Sorry i dk how to explain it
Grayson is going to invest $710 and leave it in an account for 17 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Grayson to end up
with $920?
Answer:
1.52%
Step-by-step explanation:
Miranda needs to add 68+19 mentally but is struggling.If she knows that 68+20=88 how can she use this to help.Use a similar approach to describe how Miranda could add 37+29 mentally
20 points Which of the following is NOT an advantage of using wind turbines to generate wind power? Wind turbines are not suitable for all geographical locations. O Wind turbines are affordable. Wind turbines do not emit carbon dioxide and do not require sunshine. O Wind turbines cause little disruption of ecosystems.
The option that does not describe an advantage of wind power is Wind turbines cause little disruption of ecosystems.
What is Wind power?Wind power is defined as the process by which the wind is utilized to generate mechanical power or electricity.
Wind power is the most sustainable, and renewable energy source which has a much smaller harmful influence on the environment as compared to the burning of fuels.
This is an environmentally friendly mechanism for synthesizing energy and electricity.
Wind turbines are not placed in large bodies of water that turbines are on land for the production of electricity.
Therefore, the option is Wind turbines cause little disruption of ecosystems.
To learn more about Wind power, refer to the link:
brainly.com/question/2031508
#SPJ6
The formula V equals S to the third power gives the volume V of a cube with the side length S the volume of a cube that has a side length of 3 inches is__?__ inches cubed
Answer:
27
Step-by-step explanation:
The formula for the volume of a cube is given as [tex]V=s^{3}[/tex]. if s=3in, then V=27inches cubed.