Therefore , the solution of the given problem of function comes out to be the number of tractors that should be produced to incur minimum cost is 500.
What is function?The study of numbers and their variables, as well as our surrounds, structures, and both real and imagined locations, are all included in the mathematics curriculum. A function is a visual representation of the relationship between the quantities of inputs and the corresponding outputs for each. Simply described, a function is a collection of inputs that, when integrated, produce unique outputs for each input. Each role is given a country, city, or scope (also known as a realm).
Here,
The total cost function is:
C(x) = 23000 - 20x + 0.02x²
To find the minimum cost, we need to find the value of x that minimizes the total cost.
One way to do this is to find the vertex of the parabola that represents the total cost function.
The vertex of the parabola y = ax² + bx + c has an x-coordinate of -b/2a and a y-coordinate of c - b²/4a.
In this case, a = 0.02, b = -20, and c = 23000.
So, the x-coordinate of the vertex is:
x = -b/2a = -(-20)/(2 × 0.02) = 500
The minimum cost occurs at this x-value, so the number of tractors that should be produced to incur minimum cost is 500.
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answer please and make answers clear
h(-2) = 3
h(0) = 0
h(5) = 3/4
This can be solved by using the concept of function.
What is function?In arithmetic, a function from one set to another, X to Y, allocates precisely one element of Y to each element of X. Both of the set X and the set Y usually known as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.
A function with the name f is defined by the formula y=f(x). This is understood to mean "y is a function of x." The input value, also known as an independent variable, is represented by the letter X. The outcome value, or dependent variable, is denoted by the letter y, or f(x).
This is a piece wise-defined function:
For h(-2):
h(-2) = 3
For h (0):
h(0) = (x + 1)²- 1
h(0) = (0 + 1)² - 1
h(0) = 1 - 1
h(0) = 0
For h(5):
h(5) = -1/4 x + 2
h(5) = -1/4(5) + 2
h(5) = 3/4
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Which option is a possible solution to a system of linear equations?
0
y = 2x + 1
(1, 2)
y = 5
Answer:
y=5
Step-by-step explanation:
i think it is ahhhh&hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
The number of people who go out to movies at a local theater has decreased by 32%. Originally 450 people would go to see movies over a typical weekend. How many would be expected now?
We would expect 306 people to go to see movies now, after the 32% decrease.
How are expectations determined?The expected value is calculated in statistics and probability analysis by multiplying each conceivable outcome by the likelihood that each outcome will occur, then adding up all of those values. By calculating anticipated values, investors can choose the scenario that is most likely to provide the desired outcome.
We must subtract 32% from the original number of persons in order to arrive at the anticipated number of people who would currently attend movies.
Let x represent the predicted proportion of moviegoers in the present. The following equation can be created:
x = 450 - 0.32*450
By condensing this equation, we obtain:
x = 450 - 144
x = 306
As a result, given the 32% decline, we would anticipate 306 individuals to attend movies this week.
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use the given conditions to write an equation for the line in point-slope form and slope-intercept form
The equation of the line in point slope form is y + 6 = 3 (x + 3), and the line in slope intercept form is y = 3x + 3.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
We have the points on the line given.
(-3, -6) and (2, 9)
Slope of the line = (9 - -6) / (2 - -3) = 15/5 = 3
Equation of a line in point slope form is,
y - y₁ = m (x - x₁)
where (x₁, y₁) is a point on the line and m is the slope.
Substituting a point (-3, -6) and the slope = 3, we get,
y - -6 = 3 (x - -3)
y + 6 = 3 (x + 3), which is the point slope form.
Equation of a line in slope intercept form is,
y = mx + c
where m is the slope and c is the y intercept.
Substituting m = 3 and (x, y) = (2, 9),
9 = (3 × 2) + c
c = 9 - 6 = 3
Equation in slope intercept form becomes,
y = 3x + 3
Hence the point slope form and slope intercept form of the given line are y + 6 = 3 (x + 3) and y = 3x + 3 respectively.
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Identify the surface area of a sphere with a radius of 18 inches to the nearest tenth. Use 3.14 for π.
A. 4,147.9 in2
B. 8,134.2 in2
D. 4,069.4 in2
C. 16,201.4 in2
On the last day of a Shakespeare class, an English teacher asked her students which play they liked the best, and she recorded the results to date.
Hamlet 2
Twelfth Night 8
A Midsummer Night's Dream 2
What is the experimental probability that the next student to respond likes Hamlet best?
Write your answer as a fraction or whole number.
The experimental probability that the next student to respond likes Hamlet best is 1/6 or 0.1667 as a decimal.
Calculating Experimental Probability of a Shakespeare Play Survey in an English ClassIn this problem, we are given the results of a survey conducted in an English class to determine which Shakespeare play the students liked the best. The teacher recorded the number of students who liked each of the three plays: Hamlet, Twelfth Night, and A Midsummer Night's Dream.
To calculate the experimental probability, we first need to find the total number of students who have responded to the survey so far. From the information given, we know that 2 students liked Hamlet best, 8 students liked Twelfth Night best, and 2 students liked A Midsummer Night's Dream best. Therefore, the total number of students who have responded so far is: 2 + 8 + 2 = 12
Next, we need to determine how many of these 12 students liked Hamlet best. We know from the data given that 2 students liked Hamlet best, so the number of students who liked Hamlet best is: 2
Finally, we can calculate the experimental probability that the next student to respond likes Hamlet best. We do this by dividing the number of students who liked Hamlet best (2) by the total number of students who have responded so far (12): 2/12
Simplifying this fraction, we get: 1/6
Therefore, the experimental probability that the next student to respond likes Hamlet best is 1/6 or 0.1667 as a decimal. This means that if we were to randomly select a student from the class and ask them which Shakespeare play they liked the best, there is a 1 in 6 chance that they would choose Hamlet.
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Please hurry class ends in 20 minutes
Answer:
33 inches
Step-by-step explanation:
Use triangle calculator online
The specific gravity of a substance is defined as the ratio of its density to the density of water. The density of steel is 487 pounds per cubic foot and the density of water is 62.4 pounds per cubic foot. Calculate the specific gravity of steel.
Answer:
Step-by-step explanation:
hashhshd
Answer:
≈ 7.8
Step-by-step explanation:
Specific gravity of steel = Density of steel / Density of water
Density of steel = 487 pounds per cubic foot
Density of water = 62.4 pounds per cubic foot
Specific gravity of steel = 487 / 62.4
Specific gravity of steel ≈ 7.8
Therefore, the specific gravity of steel is approximately 7.8.
solve
5 1/8 + 2 5/8=
Answer:7 3/4
Step-by-step explanation:
(5*8+1)/8+(8*2+5)/8=41/8+21/8=62/8=7 6/8=7 3/4
25
Find five consecutive odd integers if the sum of the first three integers is 7 more than
the sum of the last two.
nswer: The numbers are? Please help
Answer:
Step-by-step explanation:
We can represent the 5 consecutive odd integers as:
1. x
2. x + 2
3. x + 4
4. x + 6
5. x + 8
"...the sum of the first three integers", then, is
x + (x + 2) + (x + 4)
That is "the sum of the last two plus 7", which is
(x + 6) + (x + 8) + 7.
The connecting word "is" means there is an equals sign right there. Therefore,
x + (x + 2) + (x + 4) = (x + 6) + (x + 8) + 7 which simplifies down to
3x + 6 = 2x + 21 after we combine like terms.
x = 15. That means the first integer is 15, the next one is 17, the third one is 19, the fourth one is 21, and the fifth one is 23.
Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 2x^2 - 4x + 6. Complete parts a through d below. Find the average rate of change of profit as x changes from 3 to 5. $ ____ per item
The average rate of change of profit as x changes from 3 to 5 is $12 per item.
How to determine the average rate of changeTo find the average rate of change of profit as x changes from 3 to 5, we need to find the change in profit divided by the change in x over that interval:
Average rate of change = (P(5) - P(3)) / (5 - 3)
We can find P(5) and P(3) by plugging those values of x into the profit equation:
P(5) = 2(5)^2 - 4(5) + 6 = 36
P(3) = 2(3)^2 - 4(3) + 6 = 12
Substituting these values, we get:
Average rate of change = (36 - 12) / (5 - 3)
Average rate of change = 24 / 2
Average rate of change = 12
Hence, the average rate is $12 per item.
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PLEASE HELP!
Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.
Answer:picture is not clear on my side, please re-upload thx!
Step-by-step explanation:
You are planning a three day trip to Seattle, Washington in October. Use the fact that on each day, it could be sunny or rainy, and that each day is equally likely to be sunny or rainy to answer the following question. What is the probability that it rains all three days.
Answer:
Step-by-step explanation:
Since the probability of rain on any given day is 0.5, and the weather on each day is independent of the others, we can calculate the probability of it raining all three days by multiplying the probabilities of rain on each individual day:
P(rain on day 1) x P(rain on day 2) x P(rain on day 3) = 0.5 x 0.5 x 0.5 = 0.125
Therefore, the probability of it raining all three days of your trip to Seattle in October is 0.125, or 12.5%.
Consider the surface defined by the following equation and complete parts a. through d. below. Z-7x = 0 a. Identify and briefly describe the surface. O A. The surface is a cylinder with values above and below the xy-plane whose trace in any plane parallel to the xy-plane is the square root function. OB. The surface is a cylinder whose values are always above the xy-plane and whose trace in any plane parallel to the xz-plane is the square root function. O C. The surface is a cylinder whose values are always above the xy-plane and whose trace in any plane parallel to the xz-plane is a parabola. OD. The surface is a cone above the xy-plane, opening away from the xy-plane and centered around the z-axis.
The equation Z-7x = 0 defines a plane in three-dimensional space, where Z is the vertical axis and x is one of the horizontal axes.
What is coordinate?A coordinate is a set of values that specifies the position of a point or an object in a given space or system. In mathematics, the most common coordinate systems are the Cartesian coordinate system and the polar coordinate system. In the Cartesian coordinate system, a point in two-dimensional space is represented by an ordered pair (x,y), where x is the horizontal coordinate (also known as the abscissa) and y is the vertical coordinate (also known as the ordinate).
Here,
Specifically, this plane is parallel to the y-axis and intersects the Z-axis at (0,0,0) with a slope of 7.
None of the answer choices provided correctly describe this surface. The surface is a plane, not a cylinder or cone, and its trace in any plane parallel to the xy-plane is a line (not a square root or parabolic function). Therefore, the correct answer is not given among the choices provided.
Note that if we solve the equation Z-7x = 0 for Z, we get Z = 7x, which is a linear function with slope 7 that passes through the origin. This means that the surface defined by Z-7x = 0 is a plane that is parallel to the y-axis and intersects the three coordinate axes at (0,0,0), (1,7,0), and (0,0,7).
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4/5*7
In simplest form
Answer:
5 3/5
Step-by-step explanation:
First, you write 4/5 x 7/1.
Next, you multiply 4x7 = 28.
Then, you multiply 5x1 = 5.
Now, you have an improper fraction--28/5.
You then divide 28/5 = 5 3/5.
No simplifying is needed.
Result: 5 3/5
A sofa regularly sells for $550. The sale price is $456.50. Find the percent decrease of the sale price from the regular price.
To find the percent decrease, we first need to find the amount of the decrease, which is the difference between the regular price and the sale price:
$550 - $456.50 = $93.50
So the amount of the decrease is $93.50.
To find the percent decrease, we divide the amount of the decrease by the original price and then multiply by 100:
($93.50 / $550) x 100 ≈ 17.0%
Therefore, the percent decrease of the sale price from the regular price is approximately 17.0%.
PLSS ANSWER QUICKY I BEG YALL
The discounted price per yard for ribbons and for fabrics is A. Ribbon costs $ 1. 50 per yard and fabric costs $ 5. 75 per yard.
How to find the discounted price ?You can find the discounted price by using the options and then multiplying the prices given, by the purchases of Gwen and Penelope to find out which price is right.
If the discounted price of ribbons were $ 1.50 per yard and the fabric was $ 5. 75 per yard, then the cost to Gwen would be:
= ( 1. 50 x 6 ) + ( 10 x 5. 75 )
= $ 66. 50
For Penelope :
= ( 1. 50 x 5 ) + ( 8 x 5. 75 )
= $ 53. 50
These are the amounts spent so these are the discounted prices.
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What is the exponent in the expression 4 to the power of 5?
A. 4
B. 5
C. 9
D. 20
Answer:
B. 5
Step-by-step explanation:
The expression "4 to the power of 5" can be written as 4^5. Here, 4 is the base, and 5 is the exponent. So the exponent in the expression 4 to the power of 5 is option B, 5.
simplify:
• 4 cos² θ + 4 sin² θ
• tan² θ cos² - sin² θ
• 1 + tan² θ
Answer:
1. 4
2. [tex]cos^2(sin^2(0))tan^2(0)[/tex]
3. sec^2 theta
Hope it helped!
The number of hours of daylight on the summer
solstice (the 172nd day of the year) is 15.3 and
the number of hours of daylight on the winter
solstice (the 355th day of the year) is 9.1.
Complete the function below to model this data.
Hint: The period is 365 days.
The completed function to model the data is:
[tex]y = 3.1cos(\frac{2\pi }{365} (x-15.3)) + 12.2[/tex]
What is Amplitude?A periodic variable's amplitude is a gauge of its change over a single period.
A non-periodic signal's magnitude in relation to a standard value is its amplitude. There are several ways to define amplitude, and they are all dependent on how much the extreme values of the variable deviate from one another.
To find the amplitude:
max - min/2=15.3-9.1/2
= 3.1
The wavelength is 365
The midpoint is 12.2
The max position is 15.3
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determine whether the data described below are qualitative or quantitative and explain why. the numbers of cases of flu treated at a certain hospital in different years
The data described, the numbers of cases of flu treated at a certain hospital in different years, are quantitative data.
Why is this quantitative data ?Quantitative data is any data that can be measured or expressed in numerical terms. In this case, the data is expressed as the number of cases of flu treated at the hospital in different years. This type of data can be analyzed using mathematical and statistical methods to obtain insights and patterns.
The information provided, specifically the numbers of flu cases treated at a certain hospital in various years, is quantitative information because it is expressed numerically.
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The graph below is the function f(x)
The correct statements regarding the function are given as follows:
f(2) is defined.The function is not continuous at x = 2.What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
To the left of x = 2, the graph of the function approaches x = 2 at y = 2, hence:
lim x-> 2^- f(x) = 2.
To the right of x = 2, the graph of the function approaches x = 2 at y = 1, hence:
lim x-> 2^+ f(x) = 1.
Due to the different lateral limits, the function is not continuous at x = 2, and the limit is not defined.
Due to the closed circle, the function is defined at x = 2, with a numeric value of y = 2.
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Write one complete sentence to interpret the solution of the graph below.
The interpretation of the solution of the graph can be: the solution (6, 64) on the graph represents that after 6 minutes, there are 64 gallons of water.
How to Interpret the Solution of a Graph?The solution to a system that is plotted on a graph is the coordinates of the point interception of the graph.
Therefore, the solution (6, 64) represents a point on the graph of a relationship between time in minutes (represented by the x-axis) and water in gallons (represented by the y-axis).
The solution tells us that at 6 minutes, the water level is 64 gallons. In other words, (6, 64) on the graph, represents the amount of water in the tank over time.
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13. In a football game, the Tigers scored 9 touchdowns and the Leopards scored 5 touchdowns.
Each touchdown is worth 6 points. What equation can be used to find how many more points
the Tigers scored than the Leopards? Use p to represent the number of points.
Write your equation and answer to the problem in the box.
and p =
O
14. Last month, Mr. Foreman spent $105 on landscaping, $448 on utility bills, $115 on his cell-
phone bill, and $143 on his cable-Internet bill. He received a credit of $21 on his cell-phone bill.
He estimated his total expenses for these bills for last month to be about $780. Use estimation
strategies to see if Mr. Foreman's estimate is correct.
So, in response to the above question, we can state that The projected sum is $800, or around $780. Hence, equation of Mr. Foreman's estimation is accurate.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Nine touchdowns by the Tigers, each earning six points, for a total of nine times six or 54 points.
The Leopards scored 5 touchdowns for a total of 5 x 6 = 30 points, each of which was worth 6.
We may deduct the total points scored by the Leopards from the total points scored by the Tigers to see how many more points the Tigers scored than the Leopards:
Leopards' points minus Tigers' points equals 54 - 30 = 24.
As a result, the formula is p, where p = 24, where Tigers' points Equal Leopards' points.
Hence, the Tigers outscored the Leopards by 24 points.
$105 + $448 + $115 + $143 - $21 = $790
We have the following by rounding the numbers to the closest tens:
$110 + $450 + $120 + $140 - $20 = $800
The projected sum is $800, or around $780. Hence, Mr. Foreman's estimation is accurate.
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Cuanto costaba un abrigo que , tras experimentar una rebaja del 40% y a continuación una subida del 30% ahora cuesta 56,16€?
Por lo tanto, el precio original del abrigo era de 72€
Para resolver este problema, primero debemos determinar el precio original del abrigo antes de las rebajas.
Sea x el precio original del abrigo.
Después de aplicar la primera rebaja del 40%, el precio del abrigo sería:
x - 0.4x = 0.6x
Luego, tras la subida del 30%, elprecio se incrementaría al 130% del precio anterior:
1.3(0.6x) = 0.78x
Sabemos que este precio final es de 56,16€, por lo que podemos resolver la ecuación:
0.78x = 56.16
x = 72
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whats the answer to the question
The height of the flagpole based on the information is 23 feet.
How to calculate the heightLet's start by converting the height of the person's shadow to feet, since the length of the flagpole's shadow is given in feet. There are 12 inches in a foot, so 54 inches is 54/12 = 4.5 feet.
Now we can set up a proportion to solve for the height of the flagpole:
(person's height) / (person's shadow length) = (flagpole height) / (flagpole shadow length)
Plugging in the values we know, we get:
5.75 / 4.5 = x / 18
5.75 * 18 = 4.5 * x
103.5 = 4.5x
Dividing both sides by 4.5, we get:
x = 103.5 / 4.5
x = 23
So the height of the flagpole is 23 feet.
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The ramp is place from a ditch to a main road 2 feet above the ditch if a length of the ramp is 12ft how far away is the bottom of the ramp from the road
Answer:
See My Attached Work For Answer. (POV THIS WAS HARD!!!)
Step-by-step explanation:
I'll give brainliest
Answer: C) (1, -1)
Step-by-step explanation:
[tex]\boldsymbol{\sf{\underline{\diamond System \ of \ equations \ by \ the \ reduction \ method:} }}[/tex]
[tex]\boldsymbol{\sf{We\:have\:the\:system\:of\:equations \ --\to \ \left \{ {{x+2y=1 \ } \atop {2x-3y=5 }} \right. }}[/tex]
Multiply the first equation by 2, and the second equation by -1, then both equations must be added.
[tex]\boldsymbol{\sf{\star \ 2(x+2y=-1) }}\\ \boldsymbol{\sf{\star -1(2x-3y=5) }}[/tex]
We add these equations to eliminate x.
[tex]\boldsymbol{\sf{\star \ 7y=-7 }}[/tex]
Then we solve 7y=-7 for y (divide by 7).
[tex]\boldsymbol{\sf{\star \ \dfrac{7y}{7}=\dfrac{-7}{7} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ y=-1}}}[/tex]
We place the found value of y, in one of the original equations y to solve for x.
[tex]\boldsymbol{\sf{\star \ x+2y=-1}} \\ \\ \boldsymbol{\sf{\star \ x+2(-1)=-1}}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}[/tex]
Simplify (We add x to both sides.)
[tex]\boldsymbol{\sf{\star \ 0+(x)=-x+1+(x) }}\\ \\ \boldsymbol{\sf{\star \ x=1}}\\ \\ \boldsymbol{\sf{\star -2=-1-x}}[/tex]
Add (2) to both sides.
[tex]\boldsymbol{\sf{\star \ -2+(2)=-x-1+(2) }}\\ \\ \boldsymbol{\sf{\star \ 0=-x+1 }}[/tex]
We divide by 1.
[tex]\boldsymbol{\sf{\star \ \dfrac{x}{1}=\dfrac{1}{1} }}\\ \\ \boxed{\boldsymbol{\sf{\star \ x=1}}}[/tex]
[tex]\underline{\bf{ \ \ x,y \ answer\ \ \ \ }}\\\boxed{\boldsymbol{\sf{x=1,y=-1 }}}[/tex]
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which of the following gives the proportion of items in each bin? a. relative frequency b. frequency c. bin proportion d. class size
The proportion of items in each bin is given by the:
a. relative frequency.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The concept of probability was presented because it is the same concept of relative frequency, which gives the proportion of items in each bin.
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Together, teammates Pedro and Ricky got 2685 base hits last season. Pedro had 285 more hits than Ricky. How many hits did each player have?
Answer:
Ricky has 1204 hits and Pedro has 1481 hits.
Step-by-step explanation:
Answer: pedro had 1,200 and ricky had 1,485
Step-by-step explanation: all i did was 2685 - 285 which equals 2,400. then i did 2,400 divided by 2 which was 1,200, pedro had 1.200 hits.
1,200 add 285 equals 1,485. ricky has 1,485. to double check add 1,200 and 1,485 and you should get 2,685
