Solution :
a).
1. The domain of C(x)
[tex]$x \in [0, \infty)$[/tex]
Range of c(x) is [tex]$[0, \infty)$[/tex]
Since the negative value do not make any sense.
2. C(x) = Ax + b
Intercept here denotes the fixed cost (that is when x = 0)
The slope indicates the marginal cost (that is increase in cost per unit of quantity)
3. Revenue is maximum marginal revenue = 0
(that is when at the top of the parabola)
4. Profit = R(x) -C(x)
5. Range of P(x) is important so that we have the idea in mind about the maximum loss and the maximum profit for a particular quantity.
6 and 7 -- insufficient data.
15(2x -10) + 4x= -3(15x + 4)
The value of x in the equation 15(2x - 10) + 4x = -3(15x + 4) is 1.7
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
Given the equation:
15(2x - 10) + 4x = -3(15x + 4)
Solving the parenthesis:
30x - 150 + 4x = -45x - 12
Collect like terms:
30x + 4x + 45x = -12 + 150
79x = 138
Dividing both sides by 79:
x = 1.7
The value of x is 1.7
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Which of the following is an example of a statistical experiment?
A Twenty people in a neighborhood are asked if they want more streetlights on the street.
OB. More streetlights are installed on one street and people are then asked if they like the change.
OC. The number of accidents on the street is compared to last year's rate.
OD. People are asked to call a number to comment about the need for new streetlights.
Answer:
B. More streetlights are installed on one street and people are then asked if they like the change.
Step-by-step explanation:
An experiment is a type of research method that involves manipulating one or more variables and measuring their effects on other variables. In this case, the experiment is to change the color of the product packaging and see how many people like the change. This is because the outcome of the experiment (the number of people who like the change) depends on chance and can be measured using numerical data. The other options are not experiments, but surveys or observations. Surveys involve asking people questions and collecting their opinions or preferences. Observations involve watching and recording people's behavior or reactions without interfering with them.
A simple gable roof is to cover a span of 32 feet. If it is to have a 7:12 pitch, how tall will the ridgeline be above the house?
The ridgeline will be 18.67 feet above the house.
What will be the height of the ridgeline above the house?Generally, a height refers to the measurement of someone or something from head to foot or from base to top.
To find the height of the ridgeline, we will use the formula: Height = (Pitch / 12) * Span
Given data:
Pitch = 7
Span = 32 feet
Inputting the values, we have:
Height = (7 / 12) * 32
Height = 0.5833 * 32
Height = 18.6656
Height = 18.67 feet.
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Write the coordinates of the vertices after a dilation with a scale factor of 1 2 , centered at the origin.
The coordinates of the vertices after a dilation of the scale factor would be:
W' = (2.5, 5)V' = (0, -5)U' = (2.5, -5)How to dilate the vertices ?To perform a dilation with a scale factor of 1/2 centered at the origin, we multiply the coordinates of each vertex by the scale factor.
Given the vertices:
W = (5, 10)
V = (0, -10)
U = (5, -10)
After applying the dilation with a scale factor of 1/2, the new coordinates of the vertices would be:
W' = (5 * 1/2, 10 x 1/2) = (2.5, 5)
V' = (0 * 1/2, -10 x 1/2) = (0, -5)
U' = (5 * 1/2, -10 x 1/2) = (2.5, -5)
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I need help please guys
The solution is :
After the row operation replaces the second row, the augmented matrix is : [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]
Here, we have,
The designated sum can replace either row. Consult your curriculum materials for the intent.
Here, we'll replace row 2 with the sum.
3(2, -2, 5) +(-6, 3, -4) = (3(2)-6, 3(-2)+3, 3(5)-4) = (0, -3, 11)
After the row operation replaces the second row, the augmented matrix is ... [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]
Hence, The solution is :
After the row operation replaces the second row, the augmented matrix is : [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]
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Identify one example of each angle pair in the diagram to the right.
Alternate exterior angles are ∠9 and (∠1 + ∠2)
Consecutive interior angles are ∠7 and ∠4
Consecutive exterior angles are ∠9 and ∠∠3
Vertical angles are ∠2 and ∠5
Linear pairs are ∠7 and ∠8
We have,
Alternate exterior angles: Pairs of angles on opposite sides of a transversal line, formed by two parallel lines, and located outside the intersected lines.
Consecutive interior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located between the intersected lines.
Consecutive exterior angles: Pairs of angles on the same side of a transversal line, formed by two parallel lines, and located outside the intersected lines.
Vertical angles: Pairs of non-adjacent angles formed by the intersection of two lines, sharing the same vertex and having equal measures.
Linear pair: A pair of adjacent angles formed by the intersection of two lines, sharing a common side, and whose measures add up to 180 degrees.
So,
Alternate exterior angles
= ∠9 and (∠1 + ∠2)
Consecutive interior angles
= ∠7 and ∠4
Consecutive exterior angles
= ∠9 and ∠∠3
Vertical angles
= ∠2 and ∠5
Linear pair
= ∠7 and ∠∠8
Thus,
Alternate exterior angles are ∠9 and (∠1 + ∠2)
Consecutive interior angles are ∠7 and ∠4
Consecutive exterior angles are ∠9 and ∠∠3
Vertical angles are ∠2 and ∠5
Linear pairs are ∠7 and ∠8
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(b) The co-ordinates of three points are A(7, 4), B(-1, -2) and C(3t, 5-4t). (i) Find the value of t if the three points are collinear.
Answer:
Step-by-step explanation:
To determine the value of t if the three points A(7, 4), B(-1, -2), and C(3t, 5-4t) are collinear, we can use the concept of slope. If the points are collinear, the slopes between any two pairs of points should be equal.
The slope between points A and B is given by:
m₁ = (y₂ - y₁) / (x₂ - x₁)
= (-2 - 4) / (-1 - 7)
= (-6) / (-8)
= 3/4
Now, let's calculate the slope between points B and C:
m₂ = (y₂ - y₁) / (x₂ - x₁)
= (5 - (-2)) / (3t - (-1))
= (7) / (3t + 1)
Since the points are collinear, the slopes m₁ and m₂ should be equal. Therefore, we can set up the equation:
3/4 = 7 / (3t + 1)
To solve for t, we can cross-multiply and solve the resulting equation:
4(7) = 3(3t + 1)
28 = 9t + 3
25 = 9t
t = 25 / 9
Therefore, the value of t that makes the points A(7, 4), B(-1, -2), and C(3t, 5-4t) collinear is t = 25/9.
Answer:
6/7
Step-by-step explanation:
If the three points are collinear, then the slope of the line passing through any two of the points should be the same as the slope of the line passing through the other two points.
Let's find the slope of the line passing through points A and B:
slope AB = (y2-y1)/(x2-x1)
= (-2-4)/(-1-7)
= -6/-8
= 3/4
Now let's find the slope of the line passing through points B and C:
slope BC = (y2-y1)/(x2-x1)
= (5-4t-(-2))/(3t-(-1))
= (7-4t)/(3t+1)
Since the three points are collinear, slope AB = slope BC:
3/4 = (7-4t)/(3t+1)
Cross-multiplying and simplifying:
12t + 4 = 28-16t
28t = 24
t = 24/28
t = 6/7
Therefore, the value of t is 6/7 if the three points A, B, and C are collinear.
A bag contains 14 blue marbles, 6 green marbles and 8 purple marbles. What is the likelihood of randomly drawing a blue marble?
Answer:
0
Step-by-step explanation:
because 6 plus 8 eqaul 14
Can someone please answer and provide an explanation for these problems?
Answer:
50) Midpoint: (5.5, 0)
51) Midpoint: (6, -8)
Step-by-step explanation:
We can find the midpoint between two points using the midpoint formula, which is m = (x1 + x2) / 2, (y1 + y2) / 2, where
m is the midpoint,(x1, y1) are one point,and (x2, y2) are another point50) We can allow (10, 10) to be our (x1, y1) point and (1, -10) to be our (x2, y2) point:
x-coordinate of midpoint of (10, 10) and (1, -10):
(10 + 1) / 2
11 / 2
5.5
y-coordinate of midpoint of (10, 10) and (1, -10):
(10 + (-10)) / 2
(10 - 10) / 2
0 / 2
0
Thus, the midpoint of the line segment with the endpoints (10, 10) and (-1, 10) is (5.5, 0).
51) We can allow (3, -6) to be our (x1, y1) point and (9, -10) to be our (x2, y2) point:
x-coordinate of midpoint of (3, -6) and (9, -10):
(3 + 9) / 2
12 / 2
6
y-coordinate of midpoint of (3, -6) and (9, -10):
(-6 + -10) / 2
(-16) / 2
-8
Thus, the midpoint of the line segment with the endpoints (3, -6) and (9, -10) is (6, -8).
can somebody please help me with this asap!
The diameter of the second pile of phosphate is 53.5 ft.
We have,
Conveyor belt:
Cone shape:
Diameter = 48.6 ft
Radius = D/2 = 24.3 ft
Height = 15.3 ft
Volume.
= 1/3 x π x r² x h
= 1/3 x 3.14 x 24.3 x 24.3 x 15.3______(1)
Shorter conveyor belt:
Cone shape:
Diameter = D
Height = (15.3 - 2.7) = 12.6 ft
Volume.
= 1/3 x π x (D/2)² x h
= 1/3 x 3.14 x (D/2)² x 12.6_______(2)
Since (1) and (2) are equal.
24.3 x 24.3 x 15.3 = (D/2)² x 12.6
(D/2)² = 717.02
D²/4 = 717.02
D² = 717.02 x 4
D² = 2868.09
D = 53.55
D = 53.5 ft
Thus,
The diameter of the second pile of phosphate is 53.5 ft.
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Which of the following is not the solution of system of inqualities
(1,0) (8,0). (0,4). (3,0)
The points (1,0) (8,0). and. (3,0) are not the solution of system of inqualities
How to deterine which is not the solution of system of inqualitiesFrom the question, we have the following parameters that can be used in our computation:
The graph
Also, we have the following ordered pairs
(1,0) (8,0). (0,4). (3,0)
From the graph, we have the following ordered pairs in the shaded region
(0, 4)
Other points (1,0) (8,0). and. (3,0) are not in the shaded region
This means that (1,0) (8,0). and. (3,0) are not the solution of system of inqualities
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Lydia has four straws of different lengths, and she is trying to form a right triangle. The lengths are 8, 9, 15, and 17 units. Which three lengths should she use? Justify your answer.
The set of 3 lengths that make a right triangle is {8, 15, 17}
Which three lengths should she use?Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.
So if the 3 sides are A, B, and C, such that:
A < B < C
We will have:
A² + B² = C²
Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:
8² + 15² = 17²
289 = 289
That equationis true, thus, these 3 lengths make a right triangle.
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I just need someone to draw the tree diagram for the picture below not to much
According to the information, there are thousands of different lunch options in this restaurant.
How to calculate the number of different lunches in the restaurant?To calculate the number of different lunches in the restaurant we must carry out the following mathematical procedure. We must multiply the different options as shown below:
4 green options x 5 protein options x 8 vegetable options x 4 extra options x 6 topping options = 4 x 5 x 8 x 4 x 6 = 4,800 different lunch options.
Based on the above, we can infer that 4,800 different lunch options can be created with the available ingredients.
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PLEASE HELP WITH THIS! PLEASE! SURFACE AREA. I HAVE NO CLUE!!
Answer: 626 yd^2
Step-by-step explanation: First you need to split the figure into 2 rectangular prisms (see attached image). The tallest rectangular prism has a length of 12 yd, a width of 3 yd, and a height of 11 yd. The shorter one has a length of 12yd, a width of 4 yd, and a height of 4 yd. The surface area equation is SA=2(wl+hl+hw). First solve for the taller rectangular prism. SA=2(3x12+11x12+11x3). SA=2(36+132+33). SA=2(201). SA=402 yd^2. Now solve for the smaller rectangular prism. SA=2(4x12+4x12+4x4). SA=2(48+48+16). SA=2(112). SA=224 yd^2. Lastly, add both values together. 402+224=626 yd^2.
The slope of a line of best fit is undefined when _____.
select all that apply
(1) the x values of the data set are constant
(2) the y values of the data set do not change when the x values change
(3) the slope of the line of best fit is vertical
(4) the slope is of the line of best fit is horizontal.
(5) the x values of the data set increase at an unspecified rate as the y values decrease
The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. This is because a horizontal line has a slope of zero
The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. A line of best fit is a straight line that is used to represent the data on a scatter plot. It is the line that best fits the data points in a scatter plot.
The slope of a line of best fit is the rate of change of the y-coordinate relative to the x-coordinate.. In other words, there is no rate of change of the y-coordinate relative to the x-coordinate when the line is horizontal.
The x values of the data set increase at an unspecified rate as the y values decrease. This means that the line of best fit has a negative slope. A negative slope means that the y-coordinate decreases as the x-coordinate increases.
In other words, there is a rate of change of the y-coordinate relative to the x-coordinate. The slope of the line of best fit is the value of this rate of change.
The slope of a line of best fit is used to determine the direction and strength of the relationship between two variables.
A positive slope means that the variables are directly proportional, while a negative slope means that they are inversely proportional. The slope of a line of best fit can be calculated using the formula y2 - y1 / x2 - x1.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
2=a
7=b
Step-by-step explanation:
a+14=6a+4
-a
14=5a+4
-4
10=5a
/5
2=a
9b+8=10b+1
-1
9b+7=10b
-9b
7=1b
/1
7=b
Answer:
WZ=7
XY=7
WX=2
ZY=2
Step-by-step explanation:
9b+8=10b+1
Take 9b to 10b and 1 to 8 to form the equation
8 - 1 =10b - 9b
7 = b
a + 14 =6a + 4
Take a to 6a and 4 to 14 to form the equation
14 - 4 =6a - a
10 =5a
Simplify the answer
10/5 =5a/5
Five divide by five 1 and 10 divided by 5 is 2
Answer is therfore
2 = a
How long must 100 be invested at a rate of 4% to earn 32.00 in interest
area of a floor 19m by 12 m is
Answer:228m
Step-by-step explanation: 19m x 12m = 228m
Answer: 228m
Step-by-step explanation: Just multiply 19m by 12m. That's how you find area.
100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
The required exact value of sin(585 degrees) is -0.707
The sine function is periodic with a period of 360 degrees.
Therefore,
= sin(585 degrees)
= sin(585 degrees - 360 degrees)
= sin(225 degrees).
The sine function has a negative value in the third quadrant, and 225 degrees is in the third quadrant.
Therefore,
sin(225 degrees) = -sin(45 degrees)
= -(1/sqrt(2)) = -0.7071.
Therefore, the exact value of sin(585 degrees) is -0.7071.
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Hi
Please help on question asap if the answer is correct I'll rate you five stars a thanks and maybe even brainliest!
What do you notice about the values?
0.9 amps ÷0.03v=30 ohms.
1.9amps÷0.07v=27.149 ohms
3.1. amps ÷0.10v =31 ohms
3.9. amps ÷ 0.12v =032.5 ohms
5. amps ÷0.15v=33.33 ohms
6.1. amps ÷0.19v=32.1053 ohms
In the given data, current and voltage are directly proportional, while the resistance is constant.
What is the relationship between current and voltage?The relationship between the voltage, current, and resistance in an electric circuit is described by Ohm's Law.
The law states that the voltage across a circuit is directly proportional to the current flowing in the circuit.
V ∝ I
V = IR
where;
R is the resistance, the proportionality constantFrom the given data set we can see that for each division of current by voltage we have almost a constant value of 30 ohms.
Thus, if we observe the values given in the data set, we can conclude that;
current and voltage are directly proportional, while the resistance is constant.
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Write an expression to represent: 6 times the difference of 5 and x
Answer:
6 * (5 - x)
Step-by-step explanation:
This expression calculates the difference between 5 and x, and then multiplies it by 6. The difference is obtained by subtracting x from 5, and then the entire result is multiplied by 6.
WhaYou is 1/5 divided by 2/6
Based on the March expense statement, how much did Maria spend using her credit card?
A. $181.18
B. $117.57
C. $507.59
D. $25.28
In the figure, what percentage of the circles are shaded?
Answer: E. 25%
Step-by-step explanation: There are 12 circles in total. 3 out of those twelve are shaded in, making it in fraction form 3/12. dividing both the numerator in the denominator by 3 simplifies it into 1/4. which is subsequently, 25%
Before the new carpet is installed, all
the walls and the ceiling will be painted
with primer. If one gallon of primer
covers 300 square feet, how many
gallons of primer will be needed?
44 ft
8 ft
32 ft
You would need to purchase 6 gallons of primer.
What is the intermediate step in the form (x+a)^2=b as a result of complementing the square for the following equations
The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.
To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.
Add the square of half of the coefficient of x to both sides of the equation:
x² + 2x + (2/2)² = 319 + (2/2)²
x² + 2x + 1 = 320
The left-hand side of the equation can now be factored as a perfect square:
(x+1)² = 320
This is the equation in the form (x+a)²=b, where a=1 and b=320.
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The complete question is as follows:
What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?
x² + 2x = 319
Part of the population of 5,250 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected. How many elk are likely to be infected? Based on the sample, there will likely be infected elk in the wildlife preserve.
The likely population of the infected elk in the wildlife preserve is 840.
What is the likely population of the infected elk?A sample is a smaller group of the population. A sample is a representation of the population.
The fraction of infected elks in the sample to the total sample would be the same of the infected elks in the population to the total population of the elks.
Population of the infected elk = (infected elks in the sample / total sample) x number of elks in the preserve
(8/50) x 5250
= 0.16 x 5250 = 840
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which cellphone srvice provider was the first to be established in south africa
The first cellphone service provider to be established in South Africa was Vodacom. Vodacom was launched on April 1, 1994, and it became the country's first cellular network operator.
The company was a joint venture between Telkom, the national telecommunications company of South Africa, and Vodafone, a global telecommunications giant.
Vodacom introduced the GSM network to South Africa, providing mobile voice and data services to customers across the country. Its launch marked a significant milestone in the telecommunications industry in South Africa, as it brought mobile communication to the masses and revolutionized the way people connect and communicate.
Since its inception, Vodacom has played a pivotal role in the development of the telecommunications sector in South Africa. It has continually expanded its network coverage, introduced innovative services, and played an active role in bridging the digital divide in the country.
Today, Vodacom remains one of the leading mobile network operators in South Africa, providing a wide range of mobile services to millions of customers.
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The probable question may be:
Which cellphone service provider was the first to be established in south africa
A solid figure is separated into 2 rectangular prisms. The volume of rectangular prism A is 75 cubic yards. Rectangular prism
B has a length of 7 yards and a width of 3 yards. The total volume of the solid figure is 180 cubic yards. What is the height of
rectangular prism B?
The height of rectangular prism B is 5 yards.
Let's first find the volume of rectangular prism B:
The volume of the solid figure = Volume of prism A + Volume of prism B
180 = 75 + length × width × height of prism B
105 = length × width × height of prism B
We know that the length of prism B is 7 yards and the width is 3 yards,
Substitute those values:
105 = 7 × 3 × height of prism B
105 = 21 × height of prism B
height of prism B = 105/21
height of prism B = 5
Therefore, the height of rectangular prism B is 5 yards.
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A rectangle has an area of 114cm squared and a perimeter of 50 cm. What are its dimensions
If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.
Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².
So, we have:
lw = 114
Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.
So, we have:
2l + 2w = 50
We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:
l = 114/w
We can then substitute this expression for l in the second equation:
2(114/w) + 2w = 50
Multiplying both sides by w to eliminate the fraction, we get:
228 + 2w² = 50w
Rearranging and simplifying, we get a quadratic equation:
2w² - 50w + 228 = 0
We can solve for w using the quadratic formula:
w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5
Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:
l(5) = 114
l ≈ 22.8
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