A person has a taco stand. He has found that his daily costs are approximated by C(x)=x²-20 x+340, where C(x) is the cost, in dollars, to sell x units of tacos. Find the number of units of tacos he should sell to minimize his costs. What is the minimum cost?
The person should sell ? units of tacos to minimize the costs. The minimum cost is $ ?.
(Simplify your answers. Type integers or fractions.)
Answers
The cost function, C(x) = x² - 20·x + 340, where x is the units sold, indicates;
The person should sell 10 units of tacos to minimize the costs. The minimum cost is $240
What is a function in mathematics?A function is the definition of the relationship between the input and output variables of an ordered pair, such that each input has one output.
The daily cost function for the sale of Tacos is, C(x) = x² - 20·x + 340
Where;
C(x) = The cost of selling x tacos
x = The number of units of tacos sold
The function in the question is a quadratic function and the positive coefficient of x² indicates that the graph of the function which is a parabola, is concave upwards.
The vertex of the parabola, of the equation, f(x) = a·x² + b·x + c, is at the point where, x = b²/(2·a)
Comparison with the equation, C(x) = x² - 20·x + 340, indicates that we have;
a = 1
b = -20
c = 340
The x-coordinate of the vertex, which is the minimum point of a concave up parabola is; x = (20)/(2×1) = 10
The number of units sold that yields minimum cost is; x = 10
The number of units the person should sell to minimize the cost is 10.
The minimum cost is therefore;
C(10) = 10² - 20 × 10 + 340 = 240
The minimum cost is $240
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Related Questions
"I'm thinking of a number. If you multiply it
by 5 and then take away 7, you will got 53.
What is my number?"
Equation:
Answer:
Answers
Answer: 12
Equation: 12 times 5 - 7.
Step-by-step explanation: 12 times 5 is 60 and take away 7 would be 53.
Hoped This Helped!
Answer: 9.2
The temperature T, in degrees Fahrenheit, t hours after 6 AM is given by:
T(t)= -1/2t^2+8t+32
0≤1≤ 12
What is the warmest temperature of the day? When does this happen?
Answers
The warmest temperature or "maximum" temperature means we need to find the derivative of the function.
T = -(t^2)/2 + 8t + 32
dT/dt = -t +8
A maximum/minimum occurs when the derivate(gradient) = 0
Therefore, dT/dt = 0
0 = -t + 8
t = 8
Putting t = 8 back into the original equation gives.
T(8) = 64 degF
So the warmest temperature is 64 degF 8 hours after 6am so at 2pm
What number can you add to √7 to get a rational number?
√7
-√7
0
7
Answers
Answer: -√7 because it will cancel out to equal 0
cual es la solucion de este numero entero (+4)+(+12)
Answers
Answer:
16
Step-by-step explanation:
12+1=13
13+1=14
14+1=15
15+1=16
1+1=2
2+1=3
3+1=4
---------
4+6=10
10+6=16
(6+6=12)
The number of laps Amelie swam daily for the past 3 weeks is shown in the dot plot. A number line going from 2 to 10. 3 dots are above 2. 2 dots are above 3. 3 dots are above 4. 5 dots are above 5. 4 dots are above 6. 2 dots are above 7. 1 dot is above 10. Use the dot plot to complete the statements. The dot plot shows that Amelie swam 3 laps times. Amelie most frequently swam laps. The data distribution is .
Answers
Regarding the data-set, we have that:
The dot plot shows that Amelie swam 3 laps two times.Amelie most frequently swam 5 laps.The data distribution is left skewed.What is shown by the dot plot?The dot plot shows the absolute frequencies of each observation, hence we have that:
Amelie swam two laps three times.Amelie swam three laps two times.Amelie swam four laps three times.Amelie swam five laps five times. -> most frequent due to the highest number of dots.Amelie swam six laps four times.Amelie swam seven laps two times.Amelie swam ten laps one time.The distribution is analyzed considering the mean and the median.
The mean is given by the sum of all observations divided by the number of observations, hence:
Mean = (2 x 3 + 3 x 2 + 4 x 3 + 5 x 5 + 6 x 4 + 7 x 2 + 10 x 1)/(3 + 2 + 3 + 5 + 4 + 2 + 1) = 4.85.
There are 20 observations, hence the median is composed by the mean of the 10th and of the 11 observation, which are both of five, hence the median is of five.
Since the median is greater than the median, the data distribution is left skewed.
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Answer:
5, skewed right
For some particular website, the password must start with one of the letters W, X, Y, or Z. Then there must be 5 more charaters, and each of those characters may be a numeric digit or a letter of the alphabet. How many different passwords are possible?
Answers
241,864,704 many different passwords are possible.
The total characters of the password is six in which it is given that first character should start with W, X, Y or Z. So the first character can be filled in 4 ways.
For next five characters it can be any letter of the alphabet or any numeric digit so it will be 26 + 10 = 36.
So second, third, fourth, fifth and sixth space can be taken by 36 characters.
Therefore the total no. of passwords will be 4 * 36 * 36 * 36 * 36 * 36 that is equal to 241,864,704.
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a baker's dozen (13) of cookies is on sale for $4.94. how much does each cookie cost
Answers
Answer:
0.41
Step-by-step explanation:
$4.94/12=0.41
Answer: $0.39.
Step-by-step explanation: $4.94. Divided by 13 = $0.38
If <1 and <2 are complementary, what are the measures of the backed when
Answers
The measures of the angles are m∠1 = 69° and m∠2 = 29°
How to find the measures of an angle?
*Triangles always have angles that add up to 180 degrees. As a result, you may find the unknown angles by taking the specified angles of a triangle and subtracting them from 180.
*Finding Unknown Measurements Using Exterior Angles
Two angles that together total 180 degrees are known as supplementary angles. These two angles combine to form a straight angle when put side by side
m∠1 = (4x-7)°
m∠2 = (x+12)°
As the two angles are complementary
4x-7+x+12=90°
5x+5=90°
5x=90-5
5x=85
x=[tex]\frac{85}{5}[/tex]
x=17
Therefore
m∠1 = 4(17)-7
m∠1 = 61°
m∠2 = 17+12
m∠2= 29°
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For the parallelogram, if m / 2 = 4x - 20 and m /4 = 3x - 11, find m / 1. The diagram is not drawn to scale.
Answers
For a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°.
As per the question statement, a parallelogram has (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, and [∠2 = (4x - 20)] and [∠4 = (3x - 11)],
Then, we are required to calculate the measure of ∠1.
To solve this question, first we will need to know about two important properties of a parallelogram,
(a) The sum of all the four interior angles of a parallelogram is equal to 360°,
(b) Opposite angles of a parallelogram are equal.
Now since our concerned parallelogram has (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles,
Therefore, (∠1 = ∠3) and (∠2 = ∠4),
And [(4x - 20) = (3x - 11)]...[∵(∠2 = ∠4)]
Or, [(4x - 3x) = (20 - 11)]
Or, [x = 9]
Therefore, [∠2 = ∠4 = (4x - 20) = 16°].
Now, [(∠1 + ∠2 + ∠3 + ∠4) = 360°]
Or, [(∠1 + ∠2 + ∠1 + ∠2) = 360°]...[∵(∠1 = ∠3) and (∠2 = ∠4)]
Or, [{(∠1 + ∠1 ) + (∠2 + ∠2)} = 360°]
Or, [(2∠1 + 2∠2) = 360°]
Or, [2∠1 = {360 - (2 * 16)}°]
Or, [2∠1 = (360 - 32)°]
Or, [2∠1 = 328°]
Or, [∠1 = (328/2)°]
Or, [∠1 = 164°]
That is, for a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°
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Write the equation in standard form using integers.
y+3=3/4(x+5)
The equation in standard form is _____
Answers
Answer:
-3x + 4y = 3
Step-by-step explanation:
Ax + By = C standard form
y + 3 = 3/4 (x + 5) | ×4
4(y + 3) = 3(x + 5)
4y + 4·3 = 3x + 3·5
4y + 12 = 3x + 15
-3x + 4y = 15 - 12
The equation in standard form is -3x + 4y = 3
Without computing, which best describes the value of (1/4) / 274?
(A) About one
(B) Much greater than one
(C) Much less than one
(D) There is not enough information
Answers
Answer:
Step-by-step explanation:
1/4 is already less than 1.
When you divide 1/4 by 274, you get much less than 1.
Much less than 1
Write the equation in slope-intercept form of the line that is parallel to the given line and passes through the given point.
y = 2x + 1; (6, -1)
Answers
The equation of line in slope - intercept form is, y = 2x - 13.
What is slope-intercept form of the line?
Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.
Consider the given equation of line y = 2x + 1.
And the point given is, (6, -1).
We have to find the equation of line parallel to the given line and passes through the point (6, -1).
First we have to find the slope of the parallel line.
Since, Slope of the parallel line is same as the slope of the given line.
Here, the slope of the line is 2.
So, the slope of the parallel line is also 2.
Now consider the point slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex](x_1, y_1)=(6, -1) , m = 2[/tex]
⇒
[tex]y-(-1)=2(x-6)\\y+1=2x-12\\y=2x-12-1\\y=2x-13[/tex]
Hence, the equation of the line parallel to the given line in slope intercept form is, y = 2x - 13.
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-2x - 4y = 10
-3x-2y=-1
Answers
Answer:
3/5 elimination
Step-by-step explanation:
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Lydia buy 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas.
Answers
1. If you multiply the first equation by 2, the number to multiply the second equation by eliminating the y terms when making a linear combination is -3.
2a) The price per pound of apples is $1.25.
b) The price per pound of bananas is $0.75.
What is a system of equations?A system of equations involves two or more equations solved together.
Such equations are also known as simultaneous equations.
5x + 3y = 8.5 ... Equation 1
3x + 2y = 5.25 ... Equation 2
Multiply Equation 1 by 2:
5x + 3y = 8.5 ... (x 2)
= 10x + 6x = 17 ... Equation 3
Multiply Equation 2 by -3:
3x + 2y = 5.25 ... (x -3)
-9x -6y = -15.75 ... Equation 4
Add Equations 3 and 4:
10x + 6x = 17
+
-9x -6y = -15.75
= x = 1.25
Substitute x = 1.25 in Equation 1:
5x + 3y = 8.5
6.25 + 3y = 8.5
3y = 2.25
y = 0.75
Check variables in Equation 2:
3x + 2y = 5.25
= 3(1.25) + 2(0.75) = 5.25
= 3.75 + 1.5 = 5.25
5.25 = 5.25
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Question Completion:5x + 3y = 8.5
3x + 2y = 5.25
1. If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination?
2. Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas?
Mary borrowed $720 from her parents. She will make equal payments of $60 per month for 12 months to repay the loan. Which equation can Mary use to find out how much money she still owes after each loan payment?
Answers
Answer:
$0
Step-by-step explanation:
Answer:
She will owe 2,391
Step-by-step explanation:
760-60x12
Write each set in the indicated form.
If you need to use "..." to indicate a pattern, make sure to list at least four elements of the set
Answers
a. Roster form: { 3, 4,5, 6}
b. Set-builder form : {x | x is an integer, where x ≥ -5}
What is a Roster form?
A list of the elements of a set, each separated by a comma, enclosed in a group of curly brackets, can be used to describe the contents of the set. Roster form is the term for this method of describing a collection.
What is a set-builder form?
Set builder notation is defining a set by expressing its properties rather than simply listing its constituents. One or more variables and a rule specifying which elements are part of the set and which are not are included in the set builder notation.
Here,
a. It is given the set is A={x:x is an integer 3 ≤ x ≤ 6}.
Then the integers lying between 3 and 6 are 3,4,5,6.
So the roster form is
A={3,4,5,6}.
b. It is given that A = { -5, -4, -3, -2......}
then the set-builder form is
A = {x | x is an integer, where x≤ -5}
Hence,
a. Roster form: { 3, 4,5, 6}
b. Set-builder form : {x | x is an integer, where x ≥ -5}
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A sweater has an original price of $65. It is on sale for 25% off. What is the amount of the discount?
Answers
Answer:
16.25
65 x 0.25 = 16.25
If another type of question the total price would be 48.75 :)
If you took out a loan for $10,000 with a 2% interest rate & it was for 18 months. How much interest would pay?
Answers
The amount of interest he would pay for a loan of $10,000 with a 2% interest rate and for 18 months is $300
Amount of money taken as a loan = $10000
The rate of interest = 2%
The time period of interest is 18 months = 1.5 year
Interst = prt/100
= 10000x 2 x 1.5/100
= 300
Therefore, the amount of interest he would pay for a loan of $10,000 with a 2% interest rate and for 18 months is $300
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use synthetic division to find the quotient and remainder of the following. Write your answer on the form of
Answers
Answer:
Step-by-step explanation:
1. x^2 + 4x + 5/x-1
2. x^3-3x^2 + 9x-2 + 3/x+3
3. 2x^2 - 2x+5- 14/3x+1
4.3x2^2- 4x+3 - 13/ 2x-1
5. 3x^2 + 6x + 7 + 12/2x-3
I need help please
In a test of a sex-selection technique, results consisted of female babies and male babies.
1. Based on this result, what is the probability of a female being born to a couple using this technique?
2. Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
Answers
The probability of a female being born to a couple using this technique is 0.923.
Yes, it is effective in increasing the likelihood that a baby will be a female.
Given:
In a test of a sex-selection technique, results consisted of 215 female babies and 18 male babies.
Total = 215+18
= 233
1.
The probability of a female being born to a couple using this technique is:
p = 215/233
p = 0.923.
hence the probability of the female being born to a couple is 0.923.
2.
Yes it is effective in increasing the likelihood that a baby will be a female because the probability of female is higher than the probability of male to be born.
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HALP PLEASE EMERGENCY
Answers
Answer:
a.) The relation is linear
b.) Plot the given (x,y) coordinates on the given graph and connect them.
c.) The y-intercept is at y=2.
d.) m=4
e.) y=4x+2
Step-by-step explanation:
a.) The relation is linear because the values in the sequence of first differences are all equal:
6-2=4 10-6=4 14-10=4 18-14=4
c.) The y-intercept is the point on the graph where x=0. According to the given points, the y-intercept must be y=2.
d.)
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\(x_1,y_1)=(0,2)\\(x_2,y_2)=(4,18)\\m=\frac{18-2}{4-0}\\m=4[/tex]
e.) Plug slope (m) and y-intercept into the slope-intercept form to get y=4x+2.
(6,- 8); 2x + 3y = 6
A. Write in slope intercept form
B. Write equation in the form Ax+By=C
Answers
And you can change it into B part
A stack of books is 52 inches tall.
Each book is 1/2 inch thick. Which expression tells us how many books are in the stack?
Answers
Answer:
52 / (1/2)
Step-by-step explanation:
Divide the total height by the thickness of each book.
52 / (1/2)
12. The Height of the CN Tower is about 550 m. What is the height of the CN Tower in a scale drawing if the scale is 1:11 000?
Answers
The height of the CN Tower on scale drawing is 0.05.
What is scale?A scale is a group of levels or numbers that are applied to a certain system of measurement or comparison.
Given that,
The height of CN Tower = 550 m,
Also, the scale is 1/11000
Let the height of the CN Tower in the scale is x,
Then,
x/550 = 1/11000
⇒x= =550/11000
⇒x = 0.05
The height of the CN Tower on scale drawing is 0.05.
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Josie has $47 left on her checking account. If she writes a check for $55, what will Josie's balance be?
Answers
"I'm thinking of a number. If you multiply
it by 8 and then add 17, you will get 33.
What is my number?"
Equation:
Answer:
Answers
Answer: f = 2
please help me with this im struggling :(
Answers
The equation that best represent the relationship on the scatter plot is y = 6 / 5 x + 18 / 5.
How to find the equation of a scatter plot?The line of best fit is used to express a relationship in a scatter plot of different data points.
The line of best fit (or trendline) is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot.
Therefore, the line of best fit will pass through (2, 6)(7, 12) and (12, 18).
Therefore, the equation of the line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = 12 - 6 / 7 - 2
m = 6 / 5
Let's find y-intercept using (2, 6)
6 = 6 / 5(2) + b
6 - 12 / 5 = b
b = 18 / 5
Therefore, the equation is y = 6 / 5 x + 18 / 5
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Find x.
Please help me with this
Answers
Answer: a.
Step-by-step explanation:
As Mars revolves around the sun, it travels at a speed of approximately 15 miles per second. Convert this speed to kilometers per second. At this speed, how
many kilometers will Mars travel in 20 seconds? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers.
Answers
Mars travels at a rate of 24 km per second.
At this rate, Mars travel 480 km in 20 seconds.
What is speed?
The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time.
Here, we have
Mars revolves around the sun, it travels at a rate of approximately 15 miles per second.
1 mile = 1.6 km (given)
15 miles = 15 ×1.6 = 24 km
So, Mars travels at a rate of 24 km per second.
In 20 seconds, Mars will travel 24×20 =480km
Hence, Mars travels at a rate of 24 km per second.
At this rate, Mars travel 480 km in 20 seconds.
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Brandon made a model of a tower as shown below. It is composed of a square, prism, and a square pyramid. The height of the pyramid is 2 inches while The height of the prism 3 feet and the base of the prism is 8 inches long. What is the volume, to the nearest cubic inch, of the tower?
Answers
The volume, to the nearest cubic inch, of the tower is 2,347.
Brandon made a model of a tower, as shown in the figure. The tower is composed of a square prism and a square pyramid. The height of the pyramid is 2 inches. The height of the prism is 3 feet = 36 inches and the base of the prism is 8 inches long. Let the volumes of the tower, prism, and pyramid be represented by the variables V, V1, and V2.
V1 = L*B*H
V1 = 8*8*36
V1 = 2,304
The volume of the square prism is 2,304 cubic inches.
V2 = (1/3)a²h
V2 = (1/3)(8)²(2)
V2 = 42.67
The volume of the square pyramid is 42.67 cubic inches.
The volume of the tower is the sum of the volumes of the square prism and the square pyramid.
V = V1 + V2
V = 2,304 + 42.67
V = 2,346.67
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