Answers
You have already found the slope, which is 2
m =( y2-y1)/(x2-x1)
= (9200-9000)/(225-125)
= 200/100
= 2
The question tells us that it is a linear function
y = mx +b is the slope intercept form of a linear function
m is the slope and b is the initial value
c(n) = mn+b
c(n) = 2n+b
Using one of the points in the table we can find b
(125,9000)
9000 = 2(125) +b
9000 = 250+b
9000-250 = b
8750 = b
The initial value is 8750
This is also the estimate of c(0) because the initial value is when n=0
We can write the equation
c(n) = fixed cost + unit cost * number of units
The fixed cost is the initial value
the unit cost is the slope or m
c(n) = 8750 + 2n
Related Questions
I need help to solve. This is my daily practice assignment
Answers
The scenario formed a right triangle with an adjacent side of 24.2 ft. and included an angle of 37°.
First, let's recall the three main trigonometric functions.
[tex]\text{ Sine }\Theta\text{ = }\frac{Opposite\text{ Side}}{\text{Hypotenuse}}[/tex][tex]\text{ Cosine }\Theta\text{ = }\frac{Adjacent\text{ Side}}{Hypotenuse}[/tex][tex]\text{ Tangent }\Theta\text{ = }\frac{Opposite\text{ Side}}{Adjacent\text{ Side}}[/tex]In the scenario, the height of the flagpole appears to be the Opposite Side of the right triangle formed.
Since the function that we will be equating involves the Opposite Side and Adjacent Side of a right triangle, we will be applying the Tangent Function to find the height of the flagpole.
We get,
[tex]\text{ Tangent }\Theta\text{ = }\frac{Opposite\text{ Side}}{Adjacent\text{ Side}}[/tex][tex]Tangent(37^{\circ})\text{ = }\frac{x}{24.2}[/tex][tex]\text{ Tangent (37}^{\circ})\text{ x 24.2 = x}[/tex][tex]\text{ 18.23600801249 = x}[/tex][tex]\text{ 18.2 ft. }\approx\text{ x}[/tex]Therefore, the height of the flagpole is 18.2 ft.
Consider the equation below.x3 – 3x2 – 4 = 1/x-1+ 5The solutions to the equation are approximately x=and x=
Answers
Question:
Solution:
Consider the following equation:
[tex]x^3-3x^2-4=\frac{1}{x-1}+5[/tex]this is equivalent to:
[tex]x^3-3x^2=\frac{1}{x-1}+5+4[/tex]that is:
[tex]x^3-3x^2=\frac{1}{x-1}+9[/tex]Multiplying both sides by (x-1), we obtain:
[tex](x-1)(x^3-3x^2)=1+9(x-1)[/tex]this is equivalent to:
[tex](x-1)x^3-3x^2(x-1)=1+9(x-1)[/tex]solving for x, we obtain that the correct solutions are:
[tex]x\text{ }\approx0.90672[/tex]and
[tex]x\approx\: 3.68875[/tex]what is 11.77 hr converted to hours and min
Answers
We are asked to convert 11.77 hours into hours and minutes. The first step is to divide the whole number from its decimal part, that is:
[tex]11.77\text{ hours=11 hours+ 0.77 hours}[/tex]Now we convert the decimal hours into minutes. To do that we use the conversion factor 1h = 60 minutes. We get:
[tex]0.77\text{hour}\frac{60\min}{1hour}=46.2\min [/tex]Therefore, 11.77 hours is approximately 11 hours and 46 minutes.
Graph J(2,-1), K(4,-5), and L(3,1) and reflect across the x=-1. Please draw the line of reflection.
Answers
You have the following points:
J(2,-1), K(4,-5), L(3,1)
To reflect the previous points around the line x = -1, consider the horizontal distance of each point to the given line x=-1. The reflected point is obtained by using the same distance to the line but in the other side.
You proceed as follow:
J(2,-1)
the distance of the previous point to the line x=-1 is 2-(-1) = 3. You subtract this value to x = -1. Thus, the x-coordinate of the new point is:
-1-3 = -4
and the new point is:
J(2,-1) => J'(-4,-1)
For K(4,-5) you have:
distance to the line x=-1 is 4-(-1) = 5. Subtract this value to the line.
-1-5 = -6
and the new point is:
K(4,-5) => K'(-6,-5)
For L(3,1):
distance to the line x=-1 is 3-(-1) = 4.
-1-4 = -5
and the new point is:
L(3,1) => L'(-5,1)
A plot of the original and reflected points is given below:
where the figure with black lines is the original figure and the figure with blue lines is the reflected one.
Makayla was scuba diving. She started at at-80 5/9 meters below the surface. She then swam up 20 2/9 meters from her storting location for a break. Alwhat location did she stop for her break compared to sea level?
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Answer:
543/9 meters below the surface.
Explanation:
First, we need to transform the mixed numbers into fractions, so 80 5/9 meter and 20 2/9 meters are equivalent to:
[tex]\begin{gathered} A\frac{b}{c}=\frac{A\cdot c+b}{c} \\ 80\frac{5}{9}=\frac{80\cdot9+5}{9}=\frac{725}{9} \\ 20\frac{2}{9}=\frac{20\cdot9+2}{9}=\frac{182}{9} \end{gathered}[/tex]Now, to calculate the location where she stops for a break, we need to take 182/9 and subtract it from 725/9. So:
[tex]\frac{725}{9}-\frac{182}{9}=\frac{725-182}{9}=\frac{543}{9}[/tex]Therefore, Makayla stops for a break at 543/9 meters below the surface.
The functions f and g are defined as follows.g(x) = 4x-2-Xf(x)=-3x-1Find f (5) and g(-3).Simplify your answers as much as possible.f(s) = 0:Х?&(-3) = 0
Answers
We need to find f(5) and g(-3)
First, we will solve f(5), for this, we have the following function:
[tex]\begin{gathered} f(x)=-3x-1 \\ f(5)=-3\cdot(5)-1 \\ f(5)=-15-1 \\ f(5)=-16 \end{gathered}[/tex]Second, we will solve g(-3), for this, we have the following function:
[tex]\begin{gathered} g(x)=4x^2-x \\ g(-3)=4(-3)^2-(-3) \\ g(-3)=4\cdot9+3 \\ g(-3)=36+3 \\ g(-3)=39 \end{gathered}[/tex]In conclusion, f(5) = -16 and g(-3) = 39
4x = 2 + 14, A = -3 b=3 C = -3 D = 4
Answers
4x = 2 + 14
4x = 16
4 is multiplying on the left, then it will divide on the right
x = 16/4
x = 4
Hi. I think I am over thinking this question. Can you show me how this works step by step?
Answers
We know that:
MN = 7.3
DC = 8.7
M and N are midpoints of AD and BC respectively.
Since DC - MN = 8.7 - 7.3 = 1.4 and M and N are midpoints, we must have:
AB = 7.3 - 1.4 = 5.9
Simplify the expression to a polynomial in standard form: (3x + 10) (2x² - 2x + 3)
Answers
Step 1
Write out the question.
[tex]\begin{gathered} (3x+10)(2x^2\text{ - 2x + 3)} \\ =3x(2x^2-2x+3)+10(2x^2\text{ - 2x + 3)} \\ =6x^3-6x^2+9x+20x^2\text{ - 20x + 30} \\ =6x^3+14x^2^{}-11x+30^{} \end{gathered}[/tex]Which line is parallel to this one: y=2/3x-9A.y=3/2x+8B.y=2/3x-9C.y=2/3x-1D.y=-3/2x+7
Answers
to find the line parallel to th egiven line:
[tex]y=\frac{2}{3}x-9[/tex]the line parallel to the given equation is
[tex]y=\frac{2}{3}x-1[/tex]The graph is,
I need help to graph the line this is a study guide check point it gives you the answer if you do not know it but I don’t want just the answer on how to do it I want the explanation of it being worked out
Answers
Given:
[tex]y=2x[/tex]To graph the given equation, we can plug in any values for x to get values for y as shown below:
Example 1:
Let x= 0
We plug in x= 0 into y=2x:
[tex]\begin{gathered} y=2x \\ y=2(0) \\ \text{Simplify} \\ y=0 \end{gathered}[/tex]Based on the above values of x and y, our point is (0,0).
Example 2:
We let x =2:
[tex]\begin{gathered} y=2x \\ y=2(2) \\ \text{Simplify} \\ y=4 \end{gathered}[/tex]It means that the point is (2,4).
Hence, the graph of y=2x is:
which of the following statements about the function f(x)=x2-2x-2 is true
Answers
Express f (x) = x^2 -2x in the form f(x) = (x - h ) ^2 - k
x^2 - 2x = +2
h = -b/2a and k = h^2
a = 1 , b= -2
h= -(-2)/ 2(1) = 2/2 = 1
k = h^2 = 1^2 = 1
So, x^2 - 2x = (x-1) ^2 - 1
To rewrite the complete equation
f(x) = (x - 1)^2 - 1 - 2
f(x) = (x - 1)^2 - 3,
[tex]f(x)=(x-1)^2-3[/tex]The minimum value is is -3
Option D is the answer
In a normal distribution, what percentage of the data falls within 2 standarddeviations of the mean?
Answers
In a normal distribution, 68% of data will fall within two standard deviations of the mean
help.par1. What is the product of 2/10 and 4/9?A. 6/19B. 4/45c. 9/20D. 11/14
Answers
To perform a product of fractions, we multiply the numerator with denominator and denominator with denominator:
[tex]\frac{2}{10}\cdot\frac{4}{9}=\frac{2\cdot4}{10\cdot9}[/tex]And solve:
[tex]\frac{2\cdot4}{10\cdot9}=\frac{8}{90}[/tex]And simplify:
[tex]\frac{8}{90}=\frac{4}{45}[/tex]The answer is option B. 4/45
using exponential growthif the starting population of 5 rabbits grow at 200% each year, how many will there be in 20 years?
Answers
grow at 200% each year
so, population becomes twice in each year, then after 20 years:
[tex]\text{population}=5\times2^{20}=5\times1048576=5242880[/tex]answer: population is 5,242,880 after 20 years
A casting director wishes to find one male and one female to cast in his play. If he plans to audition 10 males and 14 females, in how many different ways can this be done?
Answers
There are 10 males and 14 females.
So the order doesn't matter and we cant repeat a person.
Given the before information, we are going to use combinations
[tex]c=\frac{n!}{r!(n-r)!}=[/tex]Where n is the total of people and r the election, so:
For males:
n=10
r=1
[tex]c=\frac{10!}{1!(10-1)!}=10[/tex]For females:
n=14
r=1
[tex]C=\frac{14!}{1!(14-1)!}=14[/tex]Finally, multiply both results:
10* 14 = 140
Therefore, there are 140 ways that the casting can be done.
jackie made lunches for the family picnic. Dhe put 8 carrots sticks in each lunch and had no leftovers carrot sticks. which of the following shows how many corrot stick she might have started with?a. 26b. 38c. 44d. 48
Answers
Since putting 8 sticks in each lunch box doesn't give any leftover, that means that number of carrot sticks she had is a multiple of 8.
Pretty simply!
Let's see the multiples of 8.
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, ....
Out of the choices, only 48 is a multiple of '8'.
Therefore,
D is correct
The product of two positive consecutive odd integers is 195. Create and solve an equation to find the value of the integers. What is the sum of the two integers?
Answers
Let's define the next variables:
x: the first odd integer
y: the next odd integer
Since they are consecutive:
x + 2 = y
The product of them is 195, then:
x*y = 195
Replacing the y from the first equation into the second one:
x*(x + 2) = 195
x*x + x*2 - 195 = 0
x² + 2x - 195 = 0
Solving with help of the quadratic formula:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-195)}}{2\cdot1} \\ x_{1,2}=\frac{-2\pm\sqrt[]{784}}{2} \\ x_1=\frac{-2+28}{2}=13 \\ x_2=\frac{-2-28}{2}=-15 \end{gathered}[/tex]Given that we are only interested in positive integers, the solution x = -15 is discarded.
Therefore, the integers are 13 and 15
The sum of them is 13 + 15 = 28
A data set has a mean of 58 and a standard deviation of 17. All of the data values are within three standard deviations of the mean. Which of the following could be the minimum and the maximumvalues of the data set?Minimum 5: Maximum 106Minimum 5; Maximum 111Minimum 8: Maximum 111Minimum 2, Maximum 109
Answers
To answer this question, we can use the standard normal distribution, and use the z-scores for finding the minimum and maximum values in the distribution.
The z-score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]We have that the maximum and minimum are within three standard deviations. The z-scores are a measure of the standard deviations from the population mean. Then, the values are for minimum, z = -3, and for maximum, z = 3.
The population's mean is equal to 58 (mu), and the standard deviation is equal to 17.
We are going to find the raw score, x, for the minimum and maximum values 3 standard deviations below and above the mean. Then, we have:
Minimum
[tex]-3=\frac{x-58}{17}\Rightarrow-3\cdot17=x-58\Rightarrow x=-51+58\Rightarrow x=7[/tex]Maximum
[tex]undefined[/tex]Listed are the fractions of the total number of books Allisa put in a bookcase 2/5 history books 1/3 math books 1/10 art books Allisa will fill the remainder of the bookcase with science books Drag and drop the fractions into the boxes that show the fraction of the total number of books that are history, math, or art books in the bookcase and the fraction of the total number of books that will be science
Answers
Answer:
Books in Bookcase = 5/6
Science Books = 1/6
Explanation:
Given:
Total number of books Alissa put in a bookcase;
2/5 history books
1/3 math books
1/10 art books
We can go ahead and determine the fraction of the total number of books that are history, math, or art books in the bookcase by adding the given fractions together as seen below;
[tex]\frac{2}{5}+\frac{1}{3}+\frac{1}{10}=\frac{12+10+3}{30}=\frac{25}{30}=\frac{5}{6}[/tex]So the fraction of the total number of books that are history, math, or art books in the bookcase is 5/6
Let x represent the fraction of the total number of books that will be science.
We can go ahead and determine the value of x by subtracting the fraction of the total number of books that are history, math, or art books in the bookcase from 1;
[tex]x=1-\frac{5}{6}=\frac{6-5}{6}=\frac{1}{6}[/tex]So the fraction of the total number of books that will be science is 1/6
What other number is a part of this fact family? 3,4,
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The other number that is a part of the fact family of 3,4 is 7.
According to the question,
We have the following information:
Two numbers of the fact family is 3 and 4.
Now, we know that in a fact family, if two numbers are given then the third number can be found by adding the two given numbers.
(More to know: fact family is often used to prove commutative property of addition. It can be used to find any number of other numbers of fact family are given.)
4+3 = 3+4 = 7
Hence, the other number that is a part of the fact family of 3,4 is 7.
To know more about fact family here
https://brainly.com/question/12557539
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B. The perimeter of this rectangle is 20 centimeters. What is the value of X
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Statement Problem: Find the value of x in the diagram below, given the perimeter of a rectangle as 20centimeters.
Solution:
The perimeter of a rectangle is;
[tex]P=2(l+w)[/tex]Where the length and width of the given rectangle is;
[tex]\begin{gathered} l=(x+3)cm \\ w=(x+1)cm \end{gathered}[/tex]Thus, the value of x is;
[tex]\begin{gathered} 2(l+w)=20 \\ 2(x+3+x+1)=20 \\ \text{Divide both sides by 2},\text{ we have;} \\ \frac{2\mleft(x+3+x+1\mright)}{2}=\frac{20}{2} \\ x+3+x+1=10 \\ \text{Collect like terms, we have;} \\ 2x+4=10 \\ \end{gathered}[/tex]Then, we subtract 4 from both sides of the equation, we have;
[tex]\begin{gathered} 2x+4-4=10-4 \\ 2x=6 \\ \text{Divide both sides by 2, we have;} \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]The value of x is 3
Car X weighs 136 pounds more than car Z. Car Y weighs 117 pounds more than car Z. The total weight of all three cars is 9439 pounds. How much does each car weigh?
Answers
Let x, y and z denote the weighs of car X, car Y and car Z, respectively.
We know that car X weighs 136 more than car Z, this can be express by the equation:
[tex]x=z+136[/tex]We also know that Y weighs 117 pounds more than car Z, this can be express as:
[tex]y=z+117[/tex]Finally, we know that the total weight of all the cars is 9439, then we have:
[tex]x+y+z=9439[/tex]Hence, we have the system of the equations:
[tex]\begin{gathered} x=z+136 \\ y=z+117 \\ z+y+z=9439 \end{gathered}[/tex]To solve the system we can plug the values of x and y, given in the first two equations, in the last equation; then we have:
[tex]\begin{gathered} z+136+z+117+z=9439 \\ 3z=9439-136-117 \\ 3z=9186 \\ z=\frac{9186}{3} \\ z=3062 \end{gathered}[/tex]Now that we have the value of z we plug it in the first two equations to find x and y:
[tex]\begin{gathered} x=3062+136=3198 \\ y=3062+117=3179 \end{gathered}[/tex]Therefore, car X weighs 3198 pound, car Y weighs 3179 pounds and car Z weighs 3062 pounds.
Find the area of the figure. zyd 13 / yd The area of the figure is yd?
Answers
The area of the given parallelogram is:
A = b·h
b: base = 13 1/5 = (65 + 1)/5 = 66/5 = 13.2 yd
h: height = 27 1/2 = 13.5 yd
A = (13.2 yd)(13.5 yd) = 178.2 yd²
which equation describes the line with a slope of 2/3 that passes through the point
Answers
Option (a)
Given:
The value of slope is, m = -2/3.
Pass throught he point, (x1, y1) = (2,-3)
The objective is to find the equation of the line.
The general equation of straight line is,
[tex]y-y_1=m(x-x_1)[/tex]Now, substitute the given values in the above equation.
[tex]\begin{gathered} y-(-3)=-\frac{2}{3}(x-2) \\ y+3=-\frac{2}{3}(x-2) \end{gathered}[/tex]Hence, option (a) is the correct answer.
For which value of x does p(x)=-4 in the graph below
Answers
You have to identify which dot in the graph corresponds to p(x)=-4
p(x)=-4 → this expression indicates that the value of the "output" is -4, in the graph, it will correspond to the dot that has y-coordinate= -4
The dots in the graph have the following coordinates:
The coordinates are always given in the following order (x,y), the first coordinate corresponds to the value of x (input) and the second coordinate corresponds to the value of y (output)
From the dots, the only one that has the y-coordinate -4 is the one located in the fourth quadrant with coordinates (2,-4)
Rewrite the following into equivalent expressions using the GCF of both numbers and the distributive property.When complete, evaluate the expressions to check for equivalency.124 + 36
Answers
24 + 36
[tex]\begin{gathered} \text{factors of 24 = }\mleft\lbrace1,2,3,4,6,8,12,24\mright\rbrace \\ \text{factors of 36 = }\mleft\lbrace1,2,3,4,6,9,12,18,36\mright\rbrace \\ \text{GCF}=12 \\ 24=12\times2 \\ 36=12\times3 \\ (12\times2)+(12\times3) \\ 24+36=12(2+3) \end{gathered}[/tex]What are the center and the radius of the circle x2−2x+y2=0?A)The center is (1, 0), and the radius is 1.B) The center is (2, 0), and the radius is 2.C)The radius is 0, so the equation cannot represent a circle.D) The radius is negative, so the equation cannot represent a circle.
Answers
We want to know the center and the radius of the circle:
[tex]x^2-2x+y^2=0[/tex]We remember that the equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]In this case, we complete the square by adding 1 and substracting 1:
[tex]\begin{gathered} x^2-2x+1+y^2-1=0 \\ x^2-2x+1+y^2=1 \\ \text{Factoring the first three terms, we obtain:} \\ (x-1)^2+y^2=1 \end{gathered}[/tex]This means that the center is the point (1,0), and:
[tex]\text{Radius: }\sqrt[]{1}=1[/tex]9. Simplify: 7 - 5m - 10m* O 7+ 15m O 7-15m O 7-5m O 7 +5m
Answers
1) Simplifying 7 -5m -10m we'll need to combine like terms. So
7 -5m -10m Combine Like terms
7 -15m
2) Given the options, the answer is 7 -15m
Find a_1 for the geometric sequence with the given terms. a_3 = 54 and a_5 = 486
Answers
ANSWER
[tex]6[/tex]EXPLANATION
We want to find the first term of the sequence.
The general equation for the nth term a geometric sequence is written as:
[tex]a_n=ar^{n-1}[/tex]where a = first term; r = common ratio
Let us use this to write the equations for the third term and the fifth term.
For the third term, n = 3:
[tex]\begin{gathered} a_3=ar^2 \\ \Rightarrow54=ar^2 \end{gathered}[/tex]For the fifth term, n = 5:
[tex]\begin{gathered} a_5=ar^4 \\ \Rightarrow486=ar^4 \end{gathered}[/tex]Let us make a the subject of both formula:
[tex]\begin{gathered} 54=ar^2_{} \\ \Rightarrow a=\frac{54}{r^2} \end{gathered}[/tex]and:
[tex]\begin{gathered} 486_{}=ar^4 \\ a=\frac{486}{r^4} \end{gathered}[/tex]Now, equate both equations above and solve for r:
[tex]\begin{gathered} \frac{54}{r^2}=\frac{486}{r^4} \\ \Rightarrow\frac{r^4}{r^2}=\frac{486}{54} \\ \Rightarrow r^{4-2}=9 \\ \Rightarrow r^2=9 \\ \Rightarrow r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Now that we have the common ratio, we can solve for a using the first equation for a:
[tex]\begin{gathered} a=\frac{54}{r^2} \\ \Rightarrow a=\frac{54}{3^2}=\frac{54}{9} \\ a=6 \end{gathered}[/tex]That is the first term.