Answers:
a. The company needs to sell 100 units to reach the maxmum profit.
b. The company's maximum profit is $5,000.
Solution:
a. How many unit does the company need to sell to reach the maximum profit?
p(x)=-0.5x^2+100x
This is a quadratic equation, and its graph is a parabola vertical (because the veriable "x" is square). Comparing with the general form:
p(x)=ax^2+bx+c; a=-0.5, b=100, c=0
a=-0.5<0 (negative), then the parabola opens downward, and it has a maximimun value (maximum profit) at its vertex.
We can find the abscissa of the vertex (units that the company needs to sell to reach the maximum profit using the following formula:
x=-b/(2a)
Replacing b by 100 and a by -0.5 in the formula above:
x=-100/[2(-0.5)]
x=-100/(-1)
x=100
The company needs to sell 100 units to reach the maximum profit.
b. What's the company's maximum profit?
To determine the maximum profit we substitute the value of "x" obrained in part "a" in the quadratic equation:
x=100→p(100)=-0.5(100)^2+100(100)
p(100)=-0.5(10,000)+10,000
p(100)=-5,000+10,000
p(100)=5,000
The company's maximum profit is $5,000.
Emilio has 5 bag of birdseed.Each bag has about 28 ounces of birdseed.if he divides the birdseed equally into 3 containers about how much birdseed will he put in each containers.
There were 630 concert tickets sold. Each ticket cost $21. How much money was raised from selling the tickets
Answer:
$13,230
Step-by-step explanation:
you need to multiply the cost of the ticket by the amount of tickets sold,
630 x 21 = $13,230
At the city museum, child admission is $6.40 and adult admission is $9.70 . On Wednesday, twice as many adult tickets as child tickets were sold, for a total sales of $980.40 . How many child tickets were sold that day?
complete the solution of the equation. fine the value of y when x equals 4.
-3x+9y=-57
y = - 5
substitute the value of x = 4 into the equation and solve for y
- 12 + 9y = - 57 ( add 12 to both sides )
9y = - 45 ( divide both sides by 9 )
y = [tex]\frac{-45}{9}[/tex] = - 5
-3(-4)+9y=-57
12+9y=-57
9y=-57-12
9y=-69
9y/9=69/9
y=-23/3
How does the distributive property work
The frequency table shows the favorite college football teams of middle school students what fraction of the students choose the Sooners write the fraction as a decimal
what does the table look like
i cant seem to figure this out please help. and if its okay may you please put in steps?
Where is the error with this solution?
2 + 3 * (5 + 4)
Step 1: 2 + 3 * 9
Step 2: 5 * 9
Step 3: 45
Step # =
The error happens in step 2 when the person decided to add 2+3 to get 5. The order of operations PEMDAS says that we have to do multiplication (M) before addition (A). So this is what the steps should look like:
2+3*(5+4)
2+3*9
2+27
29
The proper answer is 29
If f(x)=x/2+8 what is f(x) when x=10
Hey there,
So the answer is 13.
The explanation is:
We are asked to find f(10), so let's evaluate this function at 10 by plugging this in for x.
So, as we know about the 10, the f(x) is going to be this- f(10).
We put f(10)= 10 over 2 + 8= 5+8 = 13
We have to flip the 8.
So you answer should be 13
Hope this helps...
-Justin0208
Convert 6 over 15 to a decimal.
The Answer is 0.4
My work:
6 / 15 = .4
Veronica brought her turtle out of its aquarium for 15 minutes every night for 7 days how many total minutes did she bring her turtle out of his aquarium write another scenario that uses the same numbersVeronica brought her turtle out of its aquarium for 15 minutes every night for 7 days. How many total minutes did she bring her turtle out of his aquarium? Type an scenario that uses the same numbers
Total of 105 minutes
An Hour and 5 mins
May has baby rabbits. She lets them roam outside freely every (7)days for 15 minutes
Which of the following functions is graphed below?
A. y = |x - 8| + 2
B. y = |x - 8| - 2
C. y = |x + 8| + 2
D. y = |x + 8| - 2
Answer:
A
Step-by-step explanation:
You have a spanish club meeting every fourth day and math club meeting every tenth day. Today you have both meetings. In how many days will you have both meetings on the same day again?
I believe in 20 days. We have to think about a number both 4 and 10 go into. The 1st number they both go into is 20. Hope it helps
The cast of the school play had a party at the drama teachers house.There were 20 cookies and 40 carrot sticks served as refreshments.Each cast member had the same amount of whole carrot sticks. Nothing was left over and the drama teacher did not eat. How many cast members might have been at the party??
60/4=15 and 20/4=5 there were 4 cast members at the party and they each ate 15 carrot sticks, your welcome
The cast members might have been at the party are
20 members – each gets 1 cookie and 2 carrot sticks, or 10 – each gets 2 cookies and 4 carrot sticks, or 5 – each gets 4 cookies and 8 carrot sticks, or 4 – each gets 5 cookies and 10 carrot sticks, or 2 – each gets 10 cookies and 20 carrot sticks, or 1 – gets it all: 20 cookies and 40 carrot sticksWhat is refreshments?Something to eat or drink during an event such as a meeting or party. . A more alert and comfortable state, especially after eating or drinking.
Finally the word "refreshment". While English adapted the term in the 15th century from several Gallic sources, according to the OED it meant the physical refreshment of a person or thing by food, drink, rest, coolness, etc.
Enjoying refreshment is a welcome break in the world of the day, and it also means that we leave working time for social elements, sharing coffee improves the mood and has a uniting effect, we are better able to deal with problems that arise within the team.
To learn more about refreshment, refer;
https://brainly.com/question/23702175
#SPJ2
84 is 60% of what number?
To convert a percent to a decimal, you divide by 100.
60% = 0.60
If x is the unknown number, the word is means equal
84 = 0.60 * x
Divide both sides by 0.60
84/0.60 = (0.60/0.60)* x = x
140 = x
x * .60 = 84
x = 84 / .60
x = 140
What is 30 divide by 8,350
The Answer is 0.00359281437 Hope this helps :D
Write the equation of the line that passes through the points (-1,2) and (6,3) in slope intercept form
Answer:
[tex]y =\frac{x}{7} +\frac{15}{7}[/tex]
Step-by-step explanation:
Given that the line passes through two points (-1,2) and (6,3)
Slope of the line passing through (x1,y1) and (x2,y2) is
[tex]\frac{y2-y1}{x2-x1}[/tex]
Hence slope of our line =
(3-2)/(6+1) = 1/7
So in slope intercept form the equation would be
y = 1/7 x +C
to find C
Since (-1,2) lies on the line substitute these in the line equation
2 = 1/7(-1)+c
C = 2+1/7 = 15/7
Hence equation in slope intercept form is
[tex]y =\frac{x}{7} +\frac{15}{7}[/tex]
The equation of the line that passes through the points (-1,2) and (6,3) in slope intercept form is y = 1/7x + 15/7.
Explanation:The question is asking for the equation of a line passing through two given points in slope-intercept form. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line and b is the y-intercept.
Firstly, to find the slope (m), you use the formula: m = (y2 - y1)/(x2 - x1). Substituting the given points into this formula: m = (3 - 2) / (6 - (-1)) = 1/7. Thus, the slope of the line is 1/7.
To then find the y-intercept (b), we substitute the slope and one of the points into the equation: 2 = 1/7 * (-1) + b. Solving for b, we find that b = 2 + 1/7 = 15/7.
So, the equation of the line that passes through the points (-1,2) and (6,3) in slope-intercept form is y = 1/7x + 15/7.
Learn more about slope-intercept form here:https://brainly.com/question/37778219
#SPJ3
PLZZZZZZZZZZZZ HELP ASAP FIRST ONE TO ANSWER WILL GET BRAINLYEST!!!!!!!!!!!!!!!!!!!!!!Find the yx ratio in each table.
Table A
x y
4 5
8 10
16 20
Table B
x y
8 6
12 9
20 15
Enter your ratios in the boxes in simplest form.
25,
Table A yx ratio = ?
Table B yx ratio = ?
Answer:
so depending if you want x to y ratio or y to x switch the lowe numbers around.
Step-by-step explanation:
table A is 5/4
Table B is 3/4
Just divide the y and x to get the ratio.
if the movie theater seats 328 people, what is the maximum amount of money the theater can bring?
328*12= 3936
$3936.00
The total money a theater can bring in is calculated by multiplying the number of seats by the price of a ticket. Without knowing the ticket price, a specific answer cannot be provided.
Explanation:To determine the maximum amount of money the movie theater can bring in, we need to know the price of a single ticket. For example, if each ticket costs $10, then the total amount of money possible would be 328 multiplied by $10 which equates to $3280. However, without knowing the cost of a ticket, we cannot give a specific answer.
Learn more about Multiplication for Revenue Calculation here:https://brainly.com/question/34319486
#SPJ3
Write the equation of the horizontal line given m = 0 that passes through the point (3,-2).
Answer:
y = -2
Step-by-step explanation:
Since the line is horizontal, all points have the same y-coordinate, -2. The y-intercept is the point (0, -2), so b = -2. The line is horizontal, so the slope is m = 0 which is given.
Use the slope-intercept form of the equation of a line and plug in the information you have.
y = mx + b
y = 0x + (-2)
y = -2
a company produces tables determines that its cost of producing and selling x tables is given by the function C(x)=50x+3000. the company is going to sell the bats for $70 per bat. how many table must be sold for the firm to break even
Cost of producing and selling x tables is given by the function C(x)=50x+3000
x is the number of tables produced
Each table is sold for $70
So selling price of x tables S(x) = 70x
Now we find the number of table must be sold for the firm to break even
Break even occurs when selling price = cost price
That is S(x) = C(x)
70x = 50x + 3000
Subtract 50x on both sides
20x = 3000
x = 150
150 tables must be sold for the firm to break even
The cost of gallon of orange juice is $3.50 what is the maximum number of containers you can buy for $15?
1 gallon - 3.5 $
x gallons - 15 $
X= (1×15)/3.5=4.3
You can't buy a third of gallon, so the maximum number is 4
Answer: 4 gallons
Make an equation to solve this problem. The cost of a gallon of orange juice is $3.50, so we can show this using the expression 3.50o, where o represents the number of gallons of orange juice that someone buys.
We can put the expression 3.50o into an equation, and make the expression equal to 15 because that is the amount of money you supposedly have.
3.50o = 15, divide both sides of the equation by 3.50.
o = 4.28571428571, but you cannot have a fraction or decimal of a gallon of orange juice, so we would always round these kinds of problems down to the nearest whole number.
4.28571428571 rounds down to 4 gallons of orange juice, so the answer is 4 gallons of orange juice is the maximum amount you can buy with $15.
What is the answer ? is 5 6 7 8 8 9 8 8 8 8 8 4 4 4 4 4 4 4 4 4 4
I might be right or not but i am 50% sure that the answer is:
6 kilometers.
please tell me if im wrong!
Answer:
Likely 6 kilometers, sorry if I am incorrect.
Step-by-step explanation:
If this is measuring displacement, it SHOULD be 6 km
What is 7.33, 2.66, 6.88, 4.71, 4.13, 4.77, 1.76, 3.98, 3.44, and 3.66 rounded to the nearest tenth.
7.33=7.30
2.66=2.70
6.88=6.90
4.71=4.70
4.13=4.10
4.77=4.80
1.76=1.80
3.98=4.00
3.44=3.40
3.66=3.70
hope i could help ya out!! :)
100.7 x 0.009 (basic math im in 5th grade)
Answer
0.9063
Step-by-step explanation:
(100.7)*(0.009)
The result of multiplying 100.7 by 0.009 and rounding to the hundredths place is 0.91, considering that you round up when the next digit is 5 or greater.
When multiplying 100.7 by 0.009, a calculator might show an extended result such as 0.9063. However, if we need to report our answer rounded to the hundredths place, we would need to consider the digit in the thousandths place to determine whether to round up or down. In this case, the digit to be dropped is a 7, which is greater than 5, so we would round up for our final answer.
Thus, after rounding, the final answer would be 0.91.
What is the value of the discrimination for the quadratic equation -3=-x^2+2x
-3 = -x^2 + 2
Solution:
Multiplying by -1 throughout;
3 = x^2 - 2x
x^2 - 2x - 3 = 0
Using the quadratic formula;
x = (b^2 +/- [tex]\sqrt{b^2 -4ac}[/tex]) × 1/2a
x = (2 +/- 4) × 1/2
x = 3 or -1
Find the slope and y-intercept if the line. Y = 2x + 5
The slope is the number withe the variable X.
The y-intercept is the number at the end of the equation.
Slope = 2
y-intercept = 5
seeing as thought y=mx+b m=2 and b=5
What is -8/15 as a decimal
-0.533333333
-hope this helps
Your school’s football team scored 49 points your team score was 19 more than the opponent score s write and solve an equation to find the opponents score
Hello!
A way to write this problem as an equation can be seen as such (using s for the opponent's score)
[tex]49=s+19[/tex] or alternatively as [tex]s=49-19[/tex]
When you solve for s, we find that the opponent scored a total of 30 points during the football game.
Hope this helps.
lunch, Heather eats a jelly sandwich every 5th day and drinks milk every 4th day. If she had a jelly sandwich and milk today, how many days will pass before she will have both again?
The least common multiple of 4 and 5 is 20, so Heather will have both a jelly sandwich and milk again on the 20th day from today.
The question asks us to determine how many days will pass before Heather will again have both a jelly sandwich and milk if she eats a jelly sandwich every 5th day and drinks milk every 4th day. To find when these two events will coincide again, we need to find the least common multiple (LCM) of the two numbers representing the days on which these events occur.
We find that the,
LCM of 4 and 5 is 20.
Therefore, Heather will have both a jelly sandwich and milk on the 20th day from today. This is because 20 is the smallest number that is a multiple of both 4 and 5, which means it is the first day where both schedules will align again.
What is the smallest power of 10 that would exceed 234,567,890?
Questions is asking about what is the smallest power of 10 that would exceed 234,567,890.
To find that first we need to check how the powers of 10 changes the size of number. So let's find poers of 10 as shown below:
[tex]10^1=10[/tex]
[tex]10^2=100[/tex]
[tex]10^3=1000[/tex]
[tex]10^4=10000[/tex]
[tex]10^5=100000[/tex]
[tex]10^6=1000000[/tex]
[tex]10^7=10000000[/tex]
[tex]10^8=100000000[/tex]
On this pattern we see that as the exponent increases by 1 then a zero increases in the output.
In given number 234567890, there are 9 digits. So we need at least 9 zeroes which is
1000000000 or [tex]10^9[/tex]
Clearly 1000000000 exceeds 234567890.
Hence the final answer is that exponent of 10 will be 9.