Enrollment in finite mathematics plus enrollment in calculus is less than 300.
The first step in solving a word problem is identifying the variables. The variables in any algebraic expression is the unknown value, and to solve it we usually assign a letter to represent it (x and y being the most commonly used).
In the question above, we already know that the number of student enrollees is less than 300 and not equal to 300 (might as well be just 20, we do not know) but we do know that it is NOT EQUAL TO 300, but less than.
Also we do not know the number of those enrolled for finite mathematics, so we shall call that f. Those that enrolled for calculus we shall call c. Since both categories are less than 300, the two variables f and c can now be written as an inequality which reads,
f plus c is less than 300
That is;
f + c ⊂ 300
You can make 8 pancakes with 5g of butter. How much butter do you need for 12 pancakes.
Which graph best represents this system of equations and its solution? 2x = 6 − y 5x − 4y = 28
Find the x -intercept and the y-intercept of the graph of the equation.-x+2 y=-7Good evening I am having a hard time getting this math is there any way you can help me?
Answer:
• x-intercept =7
,• y-intercept = -3.5
Explanation:
Given the linear equation
[tex]-x+2y=-7[/tex]x-intercept
The x-intercept is the value where the line crosses the x-axis.
We calculate this by setting y=0
[tex]\begin{gathered} \text{When y=0} \\ -x+2y=-7 \\ -x+2(0)=-7 \\ -x=-7 \\ x=7 \end{gathered}[/tex]The x-intercept is 7.
y-intercept
The y-intercept is the value where the line crosses the y-axis.
We calculate this by setting x=0
[tex]\begin{gathered} \text{When x=0} \\ -x+2y=-7 \\ -0+2y=-7 \\ 2y=-7 \\ Divide\text{ both sides by 2} \\ \frac{2y}{2}=-\frac{7}{2} \\ y=-3.5 \end{gathered}[/tex]The y-intercept is -3.5.
The table shows Mr. Blackwell's total earnings as a car salesman for different sale amounts.
Graph the points on the coordinate plane and connect them with a straight line.
A graph of the points on the coordinate plane with a straight line is shown in the image attached below. An equation in slope-intercept to represent the relationship is y = 125x + 500.
How to calculate the slope of a line?In order to determine the equation of this line in slope-intercept, we would first of all calculate its slope. Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope, m = (3,000 - 1,750)/(20 - 10)
Slope, m = 1,250/10
Slope, m = 125.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.c represents the intercept.At point (10, 1,750), we have;
y - 1,750 = 125(x - 10)
y - 1,750 = 125x - 1,250
y = 125x - 1,250 + 1,750
y = 125x + 500
Read more on slope here: https://brainly.com/question/11586413
#SPJ1
Answer:
Step-by-step explanation:
OPTION ONE GRAGH A GRAGH B OPTION TWO APPERAS TO INCREASE LESSAPPERAS TO INCREASE MOREIS LESSINCREASES MOREINCREASES LESS
To emphasize the slow increase in profits, it would be best for Bradley to use Graph A for his presentation.
Bradley should use this graph for his presentation because the profit appears to increase less on this graph (regardless both graphs show the same information)
Josh opens a savings account with a $300 deposit. He won't add or withdrawal any money. The
account earns 2% simple interest. What is the total amount that Josh will have on his savings at
the end of 5 years?
O $6
O $306
O $30
O $330
The most appropriate choice for simple interest will be given by-'
Amount of money Josh have at the end of 5 years = $330
Fourth option is correct
What is simple interest?
Simple interest ( SI) is the interest earned on a certain principal at a certain rate over a certain period of time,
If P is the principal, rate is r %, time is t years,
SI = [tex]\frac{p \times r \times t}{100}[/tex]
Adding Principal and simple interest will give the amount
Here,
Principal deposited by Josh= $300
Rate of interest = 2%
Time = 5 years
Simple interest = [tex]\frac{300 \times 2 \times 5}{100}\\[/tex]
= $30
Amount of money Josh have at the end of 5 years = $(300 + 30)
= $330
Fourth option is correct
To learn more about simple interest, refer to the link:
https://brainly.com/question/25793394
#SPJ9
Find the coordinates of the midpoint of a segment with the given endpoints.C(0,5) and D(-4,-5)
We have the following:
[tex]m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})_{}[/tex]resolving:
[tex]\begin{gathered} m=(\frac{0+(-4)_{}}{2},\frac{5+(-5)_{}}{2})_{} \\ m=(-\frac{4}{2},\frac{0}{2}) \\ m=(-2,0) \end{gathered}[/tex]Therefore, the midpoint is:
[tex]m=(-2,0)[/tex]18 red marbles; 6 to 9
27 blue marbles are there in the bag.
How to find the number of blue marbles?Given,
A bag contains 18 red marbles.
The ratio of red marbles to blue marbles is 6:9
Solution:
From the given ratio of 6:9,
If 6 part is red marble, then 1 part = 18/6 =3
Therefore,
The number of blue marbles is 9*3 = 27
Thus, there are 27 blue marbles in the bag.
To learn more about ratios, refer
https://brainly.com/question/2914376
#SPJ13
Joe has 3/4 cup of paint in a container. He uses 1/3 cup on a project and then adds another 1/2 cup. How much paint does he have now?
Answer:
Step-by-step explanation:
The cup of paint he has now is 11/12.
What is the amount of paint he has now?We are basically going to add or subtract the quantity of cup added or used respectively.
Initially, he has 3/4 cup of paint.
He uses 1/3 cup out of the 3/4 cup of paint, so we subtract 1/3 from 3/4:
= 3/4 - 1/3 = 5/12
He adds another 1/2 cup, so we add 1/2 to what we have left previously (5/12):
= 5/12 + 1/2 = 11/12
Therefore, the amount of paint he has now is 11/12 cup
Learn more about fractions on:
https://brainly.com/question/7678465
#SPJ1
i need help with mat equation
[tex]\qquad \textit{power of a complex number} \\\\\ [\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)] \\\\[-0.35em] ~\dotfill\\\\ z=2[\cos(104^o)~~ + ~~i\sin(104^o)] \\\\\\ z^2=2^2[\cos(2\cdot 104^o)~~ + ~~i\sin(2\cdot 104^o)] \\\\\\ z^2=\underset{polar}{4[\cos(208^o)~~ + ~~i\sin(208^o)]}~\hfill \implies ~\hfill z^2\approx \underset{rectangular}{\stackrel{4\cos(208^o)}{-3.532}~~,~~\stackrel{4\sin(208^o)}{-1.878} i}[/tex]
Larissa invested $19,000 in an eleven-year CD giving 7.5% interest, but needed to withdraw $2,500 after four years. If the CD’s penalty for early withdrawal was one year’s worth of interest on the amount withdrawn, how much money did Larissa have when the CD reached maturity, not including the amount she withdrew?
Answer:
$32190
Step-by-step explanation:
19,000 x 1.3 = 24700
24700-2500=22200
22200 x 1.45 = 32190
Malik just returned from a spring break volunteer trip. He is shopping for a photo album that will showcase his photos from the trip. The albums range in photo capacity and orientation. Horizontally Vertically 50 photos 2 3 100 photos 2 7 150 photos 6 8 What is the probability that a randomly selected photo album holds exactly 50 photos or 150 photos? Simplify any fractions.
Answer:
Explanation:
The total number of photo albums showcased:
[tex]\begin{gathered} =2+3+2+7+6+8 \\ =28 \end{gathered}[/tex]The number that holds exactly 50 photos = 2+3 = 5
[tex]P(\text{album holds 50 photos)=}\frac{5}{28}[/tex]The number that holds exactly 150 photos = 6+8 =14
[tex]P(\text{album holds 50 photos)=}\frac{5}{28}[/tex]T
the cost to rent a ski boat is $174.83 . Six friends each pay $34. How much change would a group of friends receive?
If $34 are paid six times, the group will pay in total:
$34 x 6 = $204
Since, the cost to rent a ski boat is $174.83, in order to find the change the group will receive we just need to substract it:
$204 - $174.83 = $29.17
Jeanine Baker makes floral arrangements. She has 13 different cut flowers and plans to use 4 of them. How many different selections of the 4 flowers are possible?
715 different selections of the 4 flowers are possible.
What is combination?Combinations are based entirely on grouping. Combinations can be used to determine how many different groups that can be created from the available items.
The scaling factor can be calculated if both the original dimensions and the new dimensions are known. There are two terms that must be grasped in order to use the scale factor. Scaling refers to the process of increasing or decreasing a figure's size. Scaling up refers to the process of increasing a figure's size.
Given:
n= 13,r= 4
Using Combination
[tex]^{13}c_4[/tex]
=13! / 4! (13 - 4)!
=13! / 4! 9!
= 13 x 12 x 11 x 10 x 9!/ 4! 9!
= 13 x 12 x 11 x 10 / 4 x 3 x 2
=13 x 11 x 5
= 715
Hence, 715 different selections of the 4 flowers are possible.
Learn more about combination here:
https://brainly.com/question/28720645
#SPJ1
calculate the the population standard division of the data set 5,4,5,3 to 6 round to the nearest hundred
Do you have a picture of your question?
3. Students performed in a play on a Friday and a Saturday. For both performances,adult tickets cost a dollars each and student tickets cost s dollars each.On Friday, they sold 125 adult tickets and 65 student tickets, and collected $1,200. OnSaturday, they sold 140 adult tickets and 50 student tickets, and collect $1,230.125a + 65 = 1,200140a + 50s = 1,230This situation is represented by this system of equations:a. What could the equation 265a + 115s = 2,430 mean in this situation?b. The solution to the original system is the pair a = 7 and s = 5. Explain why itmakes sense that this pair of values is also the solution to the equation265a + 115s = 2,430.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
students play:
125a + 65s = 1,200 ===> Friday
140a + 50s = 1,230 ===> Saturday
Step 02:
system of equations:
a.
a = adult tickets
s = students tickets
265a + 115s = 2,430
On this day, they sold 265 adults tickets and 115 students tickets, and collect $2,430.
b.
original solution:
a = 7
s = 5
265(7) + 115(5)= 2,430
1855 + 575 = 2430
2430 = 2430
It is verified that the original solution is also valid for this equation.
That is the full solution.
Dude my sister posted this one
Answer:
do i need to do the right or wrong answer
im pretty sure that there is 12
Step-by-step explanation:
Find all of the zeros of this function and use them to sketch a rough graph.
The zeroes of the function f(x) = x⁵ - 8x³ - 9x are x = 0, 3, - 3, i, and - i.
Consider the function,
f(x) = x⁵ - 8x³ - 9x
x⁵ - 8x³ - 9x = x( x⁴ - 8x² - 9 )
Factoring: x⁴ - 8x² - 9
The coefficient of x⁴ is 1, the coefficient of -8x² is - 8, and - 9 is the constant term.
x⁴ - 8x² - 9 = x⁴ - 9x² + x² - 9 = x²( x² - 9 ) + 1( x² - 9 )
x⁴ - 8x² - 9 = ( x² - 9 ) ( x² + 1 )
So,
x⁵ - 8x³ - 9x= 0
x( x⁴ - 8x² - 9 ) = 0
x( x² - 9 ) ( x² + 1 ) = 0
x( x - 3 )( x + 3 ) ( x² + 1 ) = 0
Therefore, the zeroes of the function are:
x = 0, x = 3, x = - 3, and
x² + 1 = 0
x² = - 1
x = ± √( - 1 ) = ± i
Learn more about zeroes here:
brainly.com/question/28185780
#SPJ1
there is a .9987 probability that a randomly selected 27-year old male lives through a year. a life insurance company charges $154 for insuring that the male will live through the year. if the male does not survive the year, the policy pays out $100,000 as a death benefit
Using probability we know that the expected value of the insurance company is $141.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.So, the expected value of the insurance company:
Probability = 0.9987So, 1.0000 - 0.9987 = 0.0013Now, get the expected value as follows:
E(x) = 0.9987 × 154 + 0.0013(-9987)E(x) = 153.7998 + (-12.9831)E(x) = 153.7998 - 12.9831E(x) = 140.8167Rounding off: $141
Therefore, using probability we know that the expected value of the insurance company is $141.
Know more about probability here:
https://brainly.com/question/25870256
#SPJ13
The complete question is given below:
There is a .9987 probability that a randomly selected 27-year-old male lives through a year. a life insurance company charges $154 for ensuring that the male will live through the year. if the male does not survive the year, the policy pays out $100,000 as a death benefit.
What is the expected value for the insurance company?
Round 287.9412 to the nearest tenth. Do not write extra zeros.
To round the number 287.9412 to the nearest tenth.
First, we identify the tenth digit.
• The tenth digit is 9.
,• The digit after 9 is 4
Since the digit after 9 is less than 5, we simply cut off the numbers after 9.
Therefore:
287.9412 = 287.9 (correct to the nearest tenth).
Answer:
287.9
Step-by-step explanation:
Determine the constant of proportionality for the relationship.
p equals 2 over 150
p = 0.0133
p = 75
p = 150
The constant of proportionality for the relationship is p = 75.
How to express proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
In other words, a proportional relationship is one in which two quantities vary directly with each other.
It can be represented as follows:
y = px
where
p = constant of proportionalityx and y are the variablesTherefore, when we are given the variables the constant of proportionality can be found as follows:
where
y = 150
x = 2
p = y / x
p = 150 / 2
Therefore,
p = 75
Complete question: Determine the constant of proportionality for the relationship: y = px where y = 150 and x = 2
learn more on proportional relationship here: https://brainly.com/question/17228462
#SPJ1
Which of the following is the simplified form of the expression 15z-9-3z-z+8?
Answer:
11z - 1
Step-by-step explanation:
What line gets the proportionality between y and x of 4/3
Round 6,252 to the nearest hundred
To the nearest hundred, 6300 is round 6,252.
What formula is used to round numbers to the nearest hundred?100 closest to the whole number
Look at the tens digit to know how close a number is to 100. Round up when the tens digit is 5 or above. You should round down if the tens digit is 4 or fewer. 3281 has 8 as the tens digit.
Which method of teaching rounding is the simplest?The best technique to get children to round to the closest 10 is to model rounding using two-digit numbers. Ask your youngster to imagine a rounded number, then ask what comes before and after that amount, and only fill in those two numbers.
To know more about round numbers visit:-
https://brainly.com/question/28562556
#SPJ13
Assume the point (10,20) belongs to the graph of f(x) what point belongs to the graph of y = f( x - 5 )(15,20) (10,25) (5,20) (10,15)
Answer:
(15, 20)
Explanation:
If the point (10,20) belongs to the graph of f(x), a function that satisfies this point for example could be:
[tex]f(x)=2x[/tex]When x is replaced with x-5, we have:
[tex]\begin{gathered} f(x-5)=2(x-5) \\ =2x-10 \end{gathered}[/tex]Therefore, when x=15
[tex]\begin{gathered} f(x-5)=2(15)-10 \\ =30-10 \\ =20 \end{gathered}[/tex]A point that belongs to the graph of y = f(x-5) is (15, 20).
A solid figure is composed of rectangular prism and a right triangular prism. The figure and some of its dimensions are sown in this diagram.
Whats the volume of the figure? (5 ft, 5ft, 2 ft, 4 ft, and 7ft.)
Answer:
volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length.
Step-by-step explanation:
Does the point(1, 1)satisfy the in equality 11x + 8y ≥ 20?
Answer:
Step-by-step explanation:
A bookstore sells 6 books for $82.50. Which table represents the relationship
between number of books and the total price?
Answer: A
Step-by-step explanation: to find the base price, you would do 82.5 to give you a rate of 0.0727 (repeating) book per dollar. then if you do that with 7 and 8 in the same table, t gives you the same rate so A would be the answer.
Answer:
A
Step-by-step explanation:
We don't actually need to do any math to figure this out. We can use process of elimination and logical thinking.
we know it's not B because the prices are too close to each other, there is also the fact that 3 books should cost half of 82.50, and 15.75 isn't half of 82.50.
it's not D because 21 books cannot cost 33.75 dollars if 6 books cost 82.50.
it's not c because 12 books should be double the cost of 82.50, which it isn't.
therefore it must be A
hope this helps :D
Sorry the picture is a little tight I can't find the value of A and I keep getting the wrong answer which is really frustrating. I think I just need a little assistance.
The slope of the line can be calculated using the points (2,2) and (6,10):
[tex]\begin{gathered} m=\frac{10-2}{6-2} \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]Since the point (a,8) should belong to the same line, the slope should be the same using the points (a,8) and any other point. Since the slope is 2, use the points (a,8) and (2,2):
[tex]\begin{gathered} 2=\frac{8-2}{a-2} \\ =\frac{6}{a-2} \end{gathered}[/tex]We got this expression for a:
[tex]2=\frac{6}{a-2}[/tex]Take the reciprocal of both sides of the equation:
[tex]\frac{1}{2}=\frac{a-2}{6}[/tex]Multiply both sides by 6:
[tex]\begin{gathered} \frac{6}{2}=a-2 \\ \Rightarrow a-2=3 \end{gathered}[/tex]Add 2 to both sides of the equation:
[tex]a=5[/tex]Therefore, a=5.
Help needed! please help math
The Mercury is 5.745 × 10^9 kilometers closer to the sun.
In this question, we have been given the approximate average distance from the sun to Neptune and Mercury.
Mercury : 5.79 × 10^9 kilometers
Neptune : 4.5 × 10^7 kilometers
We need to find how much Mercury is closer to the sun.
To find the distance by which Mercury is closer to the sun, consider the difference (5.79 × 10^9) - (4.5 × 10^7)
In the above difference the exponents of 10 are different.
So, we consider the 10^7
we write 5.79 × 10^9 as 579 × 10^7
So the difference would be,
(579 × 10^7) - (4.5 × 10^7)
= (579 - 4.5) × 10^7
= 574.5 × 10^7 km
= 5.745 × 10^9 km
Therefore, the Mercury is 5.745 × 10^9 kilometers closer to the sun.
Learn more about exponent here:
https://brainly.com/question/11709654
#SPJ1
