Answers
The y-axis on the graph, that shows us the cost, goes from 2 to 2 units.
To find the cost at option one, the red line, we look in the graph where the line is when x = 80.
For x= 80, y= 58
Now, the same for option 2:
For x = 80, y= 44.
58-44 = 14
Answer: The difference is 14.
Related Questions
Solve the given quadratic inequality. Write the answer in interval notation.
Answers
A cat is stuck in the tree and the fire department needs a ladder to rescue the cat. The fire truck available has a 95-foot ladder, which starts 8 feet above ground. Unfortunately, the fire truck must park 75 feet away from the tree. If the cat is 60 feet up the tree, does the cat get rescued? If not, what ladder length is need to allow the cat to be rescued?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given scenario
STEP 2: Describe how to answer the question
The question forms a right angle triangle. where the height of the cat on the tree is the opposite side of the triangle. The distance between the cat and the tree is the adjacent side of the triangle .
Recall the 95 foot ladder can only start 8 feet above the ground .The diagram is represented above:
The ladder height should be the hypotenuse of the triangle.
using Pythagoras's theorem,
[tex]hypotenuse^2=opposite^2+adjacent^2[/tex]STEP 3: Write the given sides
[tex]\begin{gathered} adjacent=75fto \\ opposite=52ft \\ hypotenuse=x\text{ ft} \end{gathered}[/tex]STEP 4: find x
[tex]\begin{gathered} x^2=75^2+52^2 \\ x^2=5625+2704 \\ x^2=8329 \\ x=\sqrt{8329}=91.26335519 \\ x\approx91.26ft \end{gathered}[/tex]The expected length of the ladder should be approximately 91.26ft. Since the ladder is 95 foot, therefore the cat will be rescued with the given ladder.
A random variable X follows a normal distribution with a mean of 150 and a standard deviation of sigma. If we know that P(120 < X < 180) = 0.95, then, according to the 68-95-99.7 rule, the value of sigma is approximately:
a.
20
b.
15
c.
40
d.
30
e.
60
Answers
The value of sigma according to the 68-95-99.7 rule is 15.
What is the 68-95-99.7 rule?This is the informal term that is used in statistics to remember the percentage of values that are in the interval of a distribution in statistics.
We have the mean = 150
the interval is given as P(120 < X < 180)
based on this rule, 95 percent of the data lies in the u - 20 and u + 20 region
Such that we would have
u - 2α < x < u + 2α = 0.95
we have
u - 2α = 120
150 - 2α = 120
2α = 150 - 120
2α = 30
divide through by 2
α = 15
Sigma is given as 15
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find the value of XA. 11√ 41inB. 11 inC. 33 inD. 35 in
Answers
From the diagram provided, we have a right angled triangle with the hypotenuse (side facing the right angle) given as 55, while one of the other two sides is given as 44.
We shall apply the pythagoras' theorem as follows;
[tex]c^2=a^2+b^2[/tex]Where,
c = hypotenuse,
a and b = the other sides.
Therefore, we'll now have;
[tex]\begin{gathered} c^2=a^2+b^2 \\ 55^2=44^2+c^2 \\ 3025=1936+c^2 \end{gathered}[/tex]Next step, we'll subtract 1936 from both sides of the equation;
[tex]\begin{gathered} 3025-1936=1936-1936+c^2 \\ 1089=c^2 \end{gathered}[/tex]Add the square root sign to both sides of the equation;
[tex]\begin{gathered} \sqrt[]{1089}=\sqrt[]{c^2} \\ 33=c \end{gathered}[/tex]ANSWER
Therefore, the correct answer is option C, that is 33 inches.
Explain how you found the diagonal length of the package.
Answers
First find diagonal of base D =√( 10^2 + 10^2)= √200
Then find diagonal lenght L = √ (D^2 + 10^2) = √ (200 + 100) =√300
L= √300 = √3•√100 = √3• 10
L= √3•10 = 10•√3 (by conmutative property)
The population of Canada, as estimated every five years since 1960, is shown in the table. 1. . Calculate the finite differences for the data set.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data set
STEP 2: Find the finite difference
We first find the differences in the output values which is the population as seen below
[tex]\begin{gathered} 19.68-17.91=1.77 \\ 21.32-19.68=1.64 \\ 23.21-21.32=1.89 \\ 24.59-23.21=1.38 \\ 25.94-24.59=1.35 \\ 27.79-25.94=1.85 \\ 29.35-27.79=1.56 \\ 30.77-29.35=1.42 \\ 32.31-30.77=1.54 \\ 34.01-32.31=1.70 \\ 35.75-34.01=1.74 \end{gathered}[/tex]STEP 3: Find the second order difference
[tex]\begin{gathered} 1.64-1.77=-0.13 \\ 1.89-1.64=0.25 \\ 1.38-1.89=-0.51 \\ 1.35-1.38=-0.03 \\ 1.85-1.38=0.47 \\ 1.56-1.85=-0.29 \\ 1.42-1.56=-0.14 \\ 1.54-1.42=0.12 \\ 1.70-1.54=0.16 \\ 1.74-1.70=0.04 \end{gathered}[/tex]STEP 4: Find the third order difference
[tex]undefined[/tex]There is one male snake, and the rest are female. She needs one vitamin pill for every female snake. How many vitamin pills does she need if the number of snakes is: a. 10b. 6C. X
Answers
We are told that there is one male snake, and the rest are female.
She needs one vitamin pill for every female snake.
1. If there are 10 snakes, this means that if one is male, the number of female snakes are:
[tex]10-1=9\text{ females}[/tex]Sine one vitamin pill is needed for each female snake, she would need 9 vitamin pills.
2. If there are 6 snakes, this means that if one is male, the number of female snakes are:
[tex]6-1=5\text{ females}[/tex]Sine one vitamin pill is needed for each female snake, she would need 5 vitamin pills.
3. If there are X snakes, this means that if one is male, the number of female snakes are:
[tex]X-1=(X-1)\text{ females}[/tex]Sine one vitamin pill is needed for each female snake, she would need (X-1) vitamin pills.
Consider the following system of equations.ſ x - 4y = -34x - 2y = -12Step 2 of 2: Determine if the point (3, 1) lies on both of the lines in the system of equations by substituting theordered pair into both equations.
Answers
Given:
x - 4y = -3
4x - 2y = -12
To determine if the point (3, 1) lies on both of the lines in the system of equations:
Substitute (3, 1) in the first equation, we get
3 - 4(1) = -3
3 - 4 =-3
-1 = -3
But,
[tex]-1\ne-3[/tex]Substitute (3, 1) in the second equation, we get
4(3) - 2(1) = -12
12 - 2 = -12
10 = -12
But,
[tex]10\ne-12[/tex]Hence, the answer is, No.
The point (3, 1) does not lie on both of the lines in the system of equations.
How is the input force different from the output force?
Responses
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is applied to the problem, and the output force is the movement that results.
The input force is applied to the problem, and the output force is the movement that results.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
Answers
The input force different from the output force is D. The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object."
What is a simple machine?A simple machine is a mechanical device that alters the magnitude or direction of a force. In general, they are the most basic systems that exploit mechanical advantage to multiply force.
A simple machine is a mechanical device that adjusts the direction or amplitude of a force. According to Newton's third law, if object A exerts a force on object B, object B will exert a force of same size and opposite direction on object A.
In that situation, the input force is done by object A, and the output force is done by object B as a reaction.
With this in mind, we can see that the proper answer is: "The input force is applied to the simple machine, and the output force is the force applied to an item."
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32. Challenging. Read this one very carefully. Carla runs a small business where she makes artificial flower arrangements. A customer has placed a large order for 100 identical arrangements. Carla has made a list of supplies that she needs to make the entire order. Each arrangement needs a plastic molding. It will cost Carla $3.25 for each plastic molding. She also needs 4 packages of colored netting, which sell for $15.00 each. However, the company she orders from has a special on the netting packages. If you buy 3 packages of netting, you get a package for free. Polyester fabric is another item she will need. She needs 180 square feet of polyester fabric that sells for $5.20 per square yard. Lastly she needs artificial stems. She will need 6 stems per arrangement and they are sold in packs of 10. The cost for one pack of artificial stems is $2.50. if Carla sells each arrangement for $20.00,How much money will Carla make off the order once she subtracts her expenses for the supplies.
Answers
Substract expenses
Carlas expenses are
1. 100 Arrangements
2. Plastic molding PM = 3.25
3. Colored netting CN = 15
4. Four packages netting = 3 packages
5. 180 feet2 ,. 1 yard2=5.20
6. 10 stems = 2.5x10 = $25
7. Arrangement price AP = 20.00
Then substract
20 minus 3.25 = 16.75
16.75 x100= $1675
4. 4 packages nettingx 15 = $60 - $15 = $45
5. Now
In 180 feet2 ,there are 60 yards2
then polyester price is 60x5.2= $312
6. She needs 100x6= 600 stems
600/10 = 60 packs
60 packs x 2.50= $150
Then answer is
Carla's money = 1675 - 45 - 312 - 150 = $1168 dollars
An elliptical-shaped path surrounds a garden, modeled by quantity x minus 20 end quantity squared over 169 plus quantity y minus 18 end quantity squared over 289 equals 1 comma where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent?
Answers
In general, the equation of an ellipse centered at (h,k) and axis equal to a and b, and parallel to the y-axis is
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1,a>b[/tex]And the maximum distance between two points on the ellipse is equal to the length of the major axis; in our case,
[tex]\begin{gathered} a^2=289,b^2=169 \\ \Rightarrow a=17,b=13 \end{gathered}[/tex]Therefore, the answer is 17 feet, the major axis.
NO LINKS!! Show all work where necessary to get full credit Part 2
Answers
21. Circle R
A circle is named using its center.22. RV
A radius connects the center to a point on the circle.23. ZV
A chord connects two points on the circle.24. TX
A diameter passes through the center of the circle and connects two points on the circle.25. RV
See 22 and 24.26. 4 feet
The diameter is twice the radius, 2(2)=4.Answer:
21. R
22. RU
23. VZ
24. BE
25. RU
26. 4 feet
Step-by-step explanation:
Question 21
A circle is named by its center.
Therefore the name of the given circle is R.
Question 22
The radius of a circle is a straight line segment from the center to the circumference.
Therefore, the radii of the given circle are:
RZ, RT, RU, RV, RW and RX.Question 23
A chord is a straight line segment joining two points on the circumference of the circle.
Therefore, the chords of the given circle are:
WZ, TX and VZ.Question 24
The diameter of a circle is the width of the circle at its widest part. It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circumference.
Therefore, the diameters of the given circle are:
TX and WZ.Question 25
As the diameters are TX and WZ, they contain the radii RZ, RT, RW and RX.
Therefore, the radii that are not contained in the diameter is:
RU and RV.Question 26
The diameter is twice the length of the radius.
Therefore, if the radius of the circle is 2 feet:
⇒ Diameter = 2 × 2 = 4 feet.
A manufacturing company currently uses 15 workers to load and unload trucks. Each worker can move an average of 15 boxes per minute. A robotics firm has built a robot that can load and unload boxes at the rate of 21 boxes per minute. How many robots will it take to do the same job as the 15 humans?
Answers
It will take 11 robots to do the same job as the 15 humans
Explanation:Given:
Workers in use = 15
Each worker can move an average of 15 boxes per minute.
A robot has been built that can move an average of 21 boxes per minute
15 worker would move:
15 * 15 boxes = 225 boxes per minute.
The number of robots it will take to move 225 boxes is:
225/21 = 10.7
It will take 11 robots to do the same job as the 15 humans
How do I graph a line with a equation in slope intercept form?An example is y=-3x+3, how do I graph this?
Answers
we have
y=-3x+3
to graph a line we need at least two points
so
Find out the intercepts
y-intercept (value of y when the value of x is zero)
For x=0
y=-3(0)+3
y=3
y-intercept is (0,3)
x-intercept (value of x when the value of y is zero)
For y=0
0=-3x+3
3x=3
x=1
x-intercept is (1,0)
therefore
Plot the points (0,3) and (1,0)
and join them to graph the line
see the attached figure to better understand the problem
Given the formula for the nth term, state the first 5 terms of each sequence.t1= 800, tn= -0.25tn-1
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
t1 = 800
tn = - 0.25 tn-1
Step 02:
sequence:
t1 = 800
t2 = -0.25 (800) = - 200
t3 = -0.25 (-200) = 50
t4 = -0.25 (50) = -12.5
t5 = - 0.25 (-12.5) = 3.125
The answer is:
t1 = 800
t2 = - 200
t3 = 50
t4 = -12.5
t5 = 3.125
Find the missing side of this righttriangle.x816x= V[?]=Enter the number that belongs in the green box.Enter
Answers
As gien by the question
There are given that the right angle triangle.
Now,
To find the value of x, use Pythagoras theorem:
So,
From the Pythagoras theorem;
[tex]\begin{gathered} x^2+8^2=16^2 \\ x^2+64=256 \\ x^2=256-64 \\ x=\sqrt[]{192} \end{gathered}[/tex]Hence, the value of x is shown below:
[tex]x=\sqrt[]{192}[/tex]when taking a 19 question multiple choice test ,where each question has 3 possible answers ,it would be unusual to get or more questions correct by guessing alone consider "unusual " to be more than two standard deviations away from expected.
Answers
we have that
You have 1 in 3 probability of guessing the correct answer for a single question
you have 19 opportunities to guess
so
19*(1/3)=19/3=18/3+1/3=6 1/3
therefore
would be unusual to get 7 or more questions correct by guessing alone
For the equation 5x+36=x, Which value could be a solution
Answers
Solution;
[tex]\begin{gathered} 5x+36=x \\ 5x-x+36=x-x \\ 4x+36=0 \\ \end{gathered}[/tex][tex]\begin{gathered} 4x+36-36=0-36 \\ 4x=-36 \end{gathered}[/tex][tex]x=-\frac{36}{4}=-9[/tex]x=-9
At Joe's Café 1 cup of coffee and 3 doughnuts cost $7.54, and 2 cups of coffee and 2 doughnuts cost $8.32. What is thecost of 1 cup of coffee?
Answers
To answer this question, we can proceed as follows:
1. Let x be the cost of a cup of coffee.
2. Let y be the cost of a doughnut.
Then, we can express the question, algebraically, as follows:
[tex]\begin{cases}x+3y=7.54 \\ 2x+2y=8.32\end{cases}[/tex]Now, we can solve this linear equation system by
What is the slope of (-8, -3) and (-7, -6)
Answers
To find the slope, we use the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the given points.
[tex]m=\frac{-6-(-3)}{-7-(-8)}=\frac{-6+3}{-7+8}=\frac{-3}{1}=-3[/tex]Hence, the slope is -3.I was wondering if you could help me with this problem. I am not sure where to start solving it. Thank you.
Answers
As shown at the graph, we need to find x and y
The angles (x+1) and (2y+1) are vertical
so, x + 1 = 2y + 1
so,
x = 2y eq.(1)
And the sum of the angles (x+1) , (3x + 4y) and (71 - 3y) are 180
So,
(x+1) + (3x + 4y) + (71-3y) = 180
x + 1 + 3x + 4y + 71 - 3y = 180
4x + y = 180 - 1 - 71
4x + y = 108
Substitute with x from eq (1) with 2y
4 * 2y + y = 108
8y + y = 108
9y = 108
y = 108/9 = 12
x = 2y = 2 * 12 = 24
So, x = 24 and y = 12
A line passes through the point −6, 3 and has a slope of 32 .Write an equation in slope-intercept form for this line.
Answers
The equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195.
What is the slope - intercept form of the equation of a straight line?
The slope - intercept form of the equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that passes through the point (−6, 3) and has a slope of 32.
We know that the slope - intercept form can be written as -
y = mx + c
Now, the slope of the line = [m] = 32
Since, the line passes through the point (-6, 3), we can write -
3 = 32 x -6 + c
3 = -192 + c
c = 3 + 192
c = 195
So, the equation of the straight line that passes through the point (-6, 3) will be -
y = 32x + 195
Therefore, the equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195
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Which angles are adjacent to each other? Select all that apply.
Answers
Answer:
I think it's all the options but I cant confirm.
Step-by-step explanation:
adjacent angles are angles that:
- have the same vertex
- share one side
How many and what type of solution(s) does the equation have?6p2 = 8p + 32 rational solutions1 rational solutionNo real solutions2 irrational solutions
Answers
We are going to solve the question using the quadratic formula
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{(b^2}-4ac)}{2a} \\ \text{where the quadratic equation is ax}^2+bx+c=0 \end{gathered}[/tex]The quadratic equation given is
[tex]\begin{gathered} 6p^2=8p+3 \\ 6p^2-8p-3=0 \\ \text{where a=6} \\ b=-8 \\ c=-3 \end{gathered}[/tex]By substitution we will have,
[tex]\begin{gathered} p=\frac{-(-8)\pm\sqrt[]{(-8)^2}-(4\times6\times-3)}{2\times6} \\ p=\frac{8\pm\sqrt[]{64+72}}{12} \\ p=\frac{8\pm\sqrt[]{136}}{12} \\ p=\frac{8\pm\sqrt[]{4\times34}}{12} \\ p=\frac{8\pm2\sqrt[]{34}}{12} \\ p=\frac{2(4\pm\sqrt[]{34)}}{12} \\ p=\frac{4\pm\sqrt[]{34}}{6} \\ p=\frac{4+\sqrt[]{34}}{6}\text{ or p=}\frac{4-\sqrt[]{34}}{6} \end{gathered}[/tex]Therefore,
With the roots gotten from the quadratic equation, we can therefore deduce that the solutions to the equation 6p²=8p+3 will give 2 irrational roots.
The correct answer is OPTION D
what is the volume of a right triangular pyramid whose base is 5 meters on each side and whose altitude is 4 meters? round to the nearest hundred
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Right triangular pyramid
base = 5 meters
altitude = 4 meters
Volume = ?
Step 02:
The volume of a right triangular pyramid
V = 1/3 B * h
B = 1/2 b * h
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\cdot5m\cdot4m \\ B=\text{ }10m^2 \end{gathered}[/tex][tex]V\text{ = }\frac{1}{3}\cdot10m^2\cdot4m=\text{ }13.3333m^3[/tex]The answer is:
The volume of the pyramid is 13.33 m³.
Determine the midpoint between A(2,13) and O (-4,3)
Answers
The midpoint between two points can be found by averaging their coordinates. This is done below:
[tex]\begin{gathered} x_m\text{ = }\frac{x_1+x_2}{2} \\ y_m\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]Using the above expressions we can apply the coordinates of the points we want to find, A(2,13) and O(-4,3).
[tex]\begin{gathered} x_m\text{ = }\frac{2\text{ -4}}{2} \\ x_m\text{ = }\frac{-2}{2} \\ x_m\text{ = -1} \end{gathered}[/tex][tex]\begin{gathered} y_m\text{ = }\frac{3+13}{2} \\ y_m\text{ = }\frac{16}{2} \\ y_m\text{ = 8} \end{gathered}[/tex]The coordinates of the midpoint are (-1,8).
Need help with a math word problem for homework. Thank you in advance
Answers
Given:
A client is making a 10-lb bag of trail mix
The chocolates cost $4 per pound and mixed nuts cost $7 per pound
the client has a budget of $6.1 per pound
We will use the variables c and n to represent the number of pounds for chocolates and nuts
So, we have the following system of equations:
[tex]\begin{gathered} c+n=10\rightarrow(1) \\ 4c+7n=6.1\cdot10\rightarrow(2) \end{gathered}[/tex]Solving the system by substitution method
From equation (1)
[tex]c=10-n\rightarrow(3)[/tex]substitute with (c) from equation (3) into equation (2)
[tex]\begin{gathered} 4(10-n)+7n=6.1\cdot10 \\ \end{gathered}[/tex]solve the equation to find (n)
[tex]\begin{gathered} 4\cdot10-4n+7n=6.1\cdot10 \\ -4n+7n=6.1\cdot10-4\cdot10 \\ 3n=21 \\ n=\frac{21}{3}=7 \end{gathered}[/tex]Substitute with (n) into equation (3) to find (c)
[tex]c=10-7=3[/tex]so, the answer will be:
The number of pounds of chocolates = c = 3 pounds
The number of pounds of nuts = n = 7 pounds
The line 3x + 4y - 7 = 0 is parallel to the line k . x + 12y + 3 = 0. What is the value of k?
Answers
The function is solved below
What is a function?
The function is instantly given a name, such as a, in functional notation, and its description is supplied by what it does to the input x, using a formula in terms of x. Instead of sine, put sine x. (x). Leonhard Euler invented functional notation in 1734. Some commonly used functions are represented with a symbol made up of many letters (usually two or three, generally an abbreviation of their name). In this scenario, a roman font is typically used, such as "sine" for the sine function, rather than an italic font for single-letter symbols. A function is also known as a map or a mapping, however some writers distinguish between "map" and "function."
The function can be written as
3x+4y-7 = 0
or, y = (-3/4)x + 7/4
so, slope = -3/4
and other function is
kx+12y+3 = 0
or, y = (-k/12)x - 1/4
so, slope = -x/12
Given the lines are parallel, so slopes are equal
i.e., -3/4 = -k/12
or, k = (3/4)12 = 9
Hence, the value of k is 9.
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#24Graph the function and tell wether or not it has a point of discontinuity at x = 0. If there is a discontinuity, tell wether it is removable or non removable.
Answers
We have the function:
g(x) = x/(x - 2)
Notice that if x = 2 the denominator equals zero and then we have a vertical asymptote at x = 2. Furthermore, if x = 0, g(0) = 0.
The graph of g(x) is shown below:
As you can notice, there is no a discontinuity at x = 0.
For which value(s) of x will the rational expression below equal zero? Che all that apply. (x - 5)(x+2) x + 1 A.-5 B. 2 c. 1 1 D. -1 E. 5 F. -2
Answers
The rational expression we have is:
[tex]\frac{(x-5)(x+2)}{x+1}[/tex]For a rational expression to be equal to 0, the numerator of the expression has to be equal to 0.
The numerator is: (x-5)(x+2)
That has to be equal to 0:
[tex](x-5)(x+2)=0[/tex]Here, we apply the zero product property, which tells us that if a product is equal to 0, one of the two elements, or the two elements, are equal to 0:
[tex]\begin{gathered} x-5=0 \\ x+2=0 \end{gathered}[/tex]We solve the two equations, and get the two values that will make the rational equation equal to 0:
[tex]\begin{gathered} x=5 \\ x=-2 \end{gathered}[/tex]Answer:
E. 5
F. -2