Find the volume of the figure below. Use 3.14 for pi. Round your answer to the nearest
tenths place if necessary.
Answers
The volume of cone as per given figure is 314cm³.
The following mathematical operation must be carried out in order to determine a cone's volume: V = Π(h/3)r². The surface area of the circular portion of a cone is simply πr2. The lateral face wrapping around this base is calculated as πrl, or if you aren't given the slant height, you can use the formula πr√(r2+h2).
To calculate the volume of a cone, we apply the following formula:
, where V = volume
h = height
r = radius
π = pi
(h = height of cone, r= radius of cone)
Given:
Height of cone = 12 cm
Radius of cone = 5 cm
Volume of cone, V = 3.14 * (12/3 )* 5* 5
= 3.14 * 20 * 5
= 3.14 * 100
= 314 cm³
Therefore, The volume of cone as per given figure is 314cm³.
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Related Questions
The central train station in a large city is located at the intersection of tracks A, B, and C as shown below. pls pls pls respond now!!!!
Answers
a.) The position of the train moving from station A to station B after 10 minutes 20 km east
b.) The position of the train moving from station A to station B after 10 minutes, if station B is assumed to be the origin is 50 km west
c.) The position of the train moving from station A to station B after 10 minutes, if station C is assumed to be the origin is 80 km west
How do we know?we have that:
Railway station - A B C
Distance(km) - 0 30 60
Starts from A , train reaches B be in 15 minutes
Starts from A , train reaches C be in 30 minutes
a.)
If A is origin
As train covers 30km = 15 minutes
⇒ 15 minutes = 30 km
1 minute = km
⇒ 10 minutes = 2×10 = 20 km
The position of the train moving from station A to station B after 10 minutes = 20 km east
b.)
If B is origin then , the position of the train moving from station A to station B after 10 minutes = 30 + 20 = 50 km west
c.)
If C is the origin then , the position of the train moving from station A to station B after 10 minutes = 60 + 20 = 80 km west
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#possible complete question:
Three railway stations, A, B, and C, are situated on a straight railway route. Station B is at 30 km in the east from station A and station C is at 60 km in east from station A. A train, with a constant average velocity, starts from A and reaches B in 15 minutes, and reaches C in 30 minutes. Assuming that station A is the origin, find the following:
a. The position of the train moving from station A to station B after 10 minutes.
b. The position of the train moving from station A to station B after 10 minutes, if station B is assumed to be the origin.
c. The position of the train moving from station A to station B after 10 minutes, if station C is assumed to be the origin.
Can you pls help? This is geometry
Answers
The equation of the circle is (x - 2)²+ (y - 3)² = 169
Define circleA circle is a two-dimensional form that may be described as a collection of points that are equally spaced apart from a central fixed point. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points at a certain radius from the centre.
The following is the equation for a circle with centres (a, b) and radius r:
(x - a)² + (y - b)² = r²
In this case, the center of the circle is A(2,3), and a point on the circle is B(7,15). The radius of the circle may be calculated using the distance formula:
r = √((7 - 2)² + (15 - 3)²) = √(5² + 12²) = 13
So the equation of the circle is:
(x - 2)² + (y - 3)² = 13²
(x - 2)²+ (y - 3)² = 169
Therefore, the equation of the circle is (x - 2)²+ (y - 3)² = 169
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3. A function can have zero to many parameters, and it can return this many values.a. zero to manyb. noc. only oned. a maximum of tene. None of these
Answers
A function can have zero to many parameters, and it can return only one (option c).
In mathematics, a function is a rule that maps each element from one set, called the domain, to a unique element in another set, called the range.
The number of parameters a function can take determines the number of arguments required to call the function.
For instance, a function f(x) takes one parameter, and it requires one argument to be called.
On the other hand, a function g(x,y,z) takes three parameters, and it requires three arguments to be called. However, a function h() takes no parameters and does not require any argument to be called.
Hence the correct option is (c).
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Which is not a legal python statement
a) print("x")
b) 3 + 4 = x
c) x = 3 + 4
d) x = eval(input("Enter x: "))
Answers
This statement tries to assign a value to an expression (3 + 4), which is not allowed in Python. In Python, we can only assign values to variables using the = operator.
Option a) print("x") is a legal Python statement that prints the string "x" to the console.
Option c) x = 3 + 4 is a legal Python statement that assigns the value 7 to the variable x.
Option d) x = eval(input("Enter x: ")) is a legal Python statement that prompts the user to enter a value for x, evaluates the input expression, and assigns the result to the variable x.
Write the transformation matrix and the resultant matrix that will translate the triangle, (-2, 4), given the triangles vertices are at A(-1, 3), B(0, -4) and C(3, 3).
Answers
The new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:
|-3 -2 1 |
| 7 0 7 |
| 1 1 1 |
Define translationIn mathematics, a translation refers to a geometric transformation that moves every point in a figure or a space by the same distance in a given direction. In other words, it involves sliding a figure or a point to a new location without changing its size, shape, or orientation.
To translate the triangle by a vector (x, y), we use the following transformation matrix:
|1 0 x|
|0 1 y|
|0 0 1|
For the given triangle with vertices at A(-1, 3), B(0, -4), and C(3, 3), let's assume we want to translate it by a vector (−2, 4). Then the transformation matrix for translation is:
|1 0 -2|
|0 1 4 |
|0 0 1 |
To apply this transformation matrix to each vertex of the triangle, we represent the vertices as column vectors and multiply them by the matrix:
| -1 | | 1 0 -2 | | -3 |
| 3 | -> | 0 1 4 | = | 7 |
| 1 | | 0 0 1 | | 1 |
| 0 | | 1 0 -2 | | -2 |
| -4 | -> | 0 1 4 | = | 0 |
| 1 | | 0 0 1 | | 1 |
| 3 | | 1 0 -2 | | 1 |
| 3 | -> | 0 1 4 | = | 7 |
| 1 | | 0 0 1 | | 1 |
So, the new vertices of the triangle after the translation are A'(-3, 7), B(-2, 0), and C(1, 7), which form the resultant matrix:
|-3 -2 1 |
| 7 0 7 |
| 1 1 1 |
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1/2 + 1/6 least multiple that is the same add using renamed fraction
Answers
To add these two fractions, we need to rename them so they have a common denominator of 6.
1/2 = 3/6
1/6 = 1/6
Now we can add them together:
3/6 + 1/6 = 4/6
Simplifying 4/6 gives us 2/3.
Therefore, 1/2 + 1/6 = 2/3.
Answer: 2/3
Step-by-step explanation: 1/2 converted to 6ths is 3/6 add them together and it’s 4/6 simplify that and it’s 2/3
suppose that ann selects a ball by first picking one of two boxes at random and then selecting a ball from this box. the first box contains three orange balls and four black balls, and the second box contains seven orange balls and four black balls. what is the probability that ann picked a ball from the second box if she has selected an orange ball? (enter the value of the probability in decimal format and round the final answer to two decimal places.)
Answers
The probability that Ann picked a ball from the second box given that she selected an orange ball is 0.56 or 56% (rounded to two decimal places).
We can use Bayes' theorem to calculate the probability that Ann picked a ball from the second box given that she selected an orange ball.
Let A be the event that Ann selected an orange ball, and B be the event that Ann picked a ball from the second box. We want to find P(B|A), the probability that Ann picked a ball from the second box given that she selected an orange ball.
We know that there are two boxes, each with a probability of 1/2 of being selected. The probability of selecting an orange ball from the first box is 3/7, and the probability of selecting an orange ball from the second box is 7/11. Therefore, the probability of selecting an orange ball overall is:
P(A) = P(A|B)P(B) + P(A|B')P(B')
= (7/11)(1/2) + (3/7)(1/2)
= 25/42
Now we can use Bayes' theorem:
P(B|A) = P(A|B)P(B)/P(A)
= (7/11)(1/2)/(25/42)
= 14/25
Therefore, the probability that Ann picked a ball from the second box given that she selected an orange ball is 0.56 or 56% (rounded to two decimal places).
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a student performs an experiment where they flip a coin 3 times . if they perform this experiment 200 times, predict the number of repetitions the experiment that will results in exactly two of the three flips landing on tails
Answers
We can predict that out of 200 repetitions of the experiment, approximately 75 of them will result in exactly 2 of the 3 flips landing on tails.
Describe Probability?Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is used to quantify the uncertainty associated with a particular event or outcome. In simpler terms, probability is a measure of the likelihood that a certain event will occur, expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
There are different types of probability, including classical probability, empirical probability, and subjective probability. Classical probability is based on the assumption of equally likely outcomes, while empirical probability is based on actual observations or experiments. Subjective probability, on the other hand, is based on personal judgment or belief.
The probability of getting tails on any single flip of a fair coin is 1/2. Since we are flipping the coin three times, the probability of getting exactly two tails is given by the binomial probability formula:
P(exactly 2 tails) = (number of ways to get 2 tails out of 3) * (probability of getting tails)² * (probability of getting heads)¹
The number of ways to get 2 tails out of 3 is given by the binomial coefficient "3 choose 2", which is 3. So we have:
P(exactly 2 tails) = 3 * (1/2)² * (1/2)¹ = 3/8
This means that the probability of getting exactly 2 tails in one trial of flipping the coin 3 times is 3/8.
To predict the number of repetitions out of 200 that will result in exactly 2 tails, we can multiply the probability of getting exactly 2 tails in one trial by the total number of trials:
Number of repetitions with exactly 2 tails = P(exactly 2 tails) * total number of trials
Number of repetitions with exactly 2 tails = (3/8) * 200
Number of repetitions with exactly 2 tails = 75
Therefore, we can predict that out of 200 repetitions of the experiment, approximately 75 of them will result in exactly 2 of the 3 flips landing on tails.
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4. Find volume. Show work, round to 2 decimal places.
*cone*
Answers
Answer: 80
Step-by-step explanation:
Choose the correct phrase in the piece.
Answers
a rancher has 10,000 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures, with an internal fence parallel to one of the rectangular sides. what is the maximum area of each pasture? round to the nearest square foot.
Answers
For a 10,000 linear feet of fencing and wants to enclose a rectangular field, the maximum area of each pasture is equals to the 2,083,333.33 square feet .
A rancher wants to enclose about 10,000 linear feet of fencing in a rectangular field. There are two equal pastures. Let, W the Width and L the Length with 3 pieces. The total length will be equal to 2W + 3L. As we know, the Area of rectangle, A = L×W ---(1)
Perimeter of rectangle = 10,000 feet, so sum of all sides of rectangle, 2W + 3L = 10000
Solve for determining value of L, 3L
= 10000 - 2W
[tex]L = \frac{ 10000 - 2W }{3}[/tex]
Substitutes for L into the first equation, A = L×W
[tex]A = W(\frac{ 10000 - 2W }{3})[/tex]
For maximum area, set the 1st derivative = 0.
differentiating above Area equation w.r.t W,[tex] A = \frac{(10000 \: W - 2W^2)}{3}[/tex]
[tex] \frac{dA}{dW} = \frac{d(\frac{10000 \: W - 2W^2}{3})}{dW}[/tex]
=> [tex]\frac { 1}{3}(10000 - 4W) = 0 [/tex]
=> W = 2500 meters
Now, using above relation, 2W + 3L= 10000
=> 5000 + 3L = 10000
=> 3L = 5000
=> L = 1667 meters
Area = 2500× 5000/3 = 4,166,666.67 sq feet. Now, maximum area of each pasture
= 4,166,666.67/2 = 2,083,333.33333 sq. feet. Hence, required value is 2,083,333.33 sq. feet.
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Chester has 49 CDs. Tony has 1/7 as many as Chester. How many CDs does Tony have?
Answers
Answer:7
Step-by-step explanation: you divide 49 by 7 which gives you 7
Answer:
7
Step-by-step explanation:
1/7 of 49 would be equal to divided 49 by 7 to find 1 seventh of 49
49/7 = 7
so 1/7 of Chesters 49 CDS is equal to 7 CDS that Tony has.
hope this helps :)
help me asap
pls i need to find z this R.4 ixl for special right triangles
Answers
Answer:
3 cm
Step-by-step explanation:
because the correct answer is 3cm
Does the data in this table represent a function?
X -4 2 -4 2 -4
y -3 1 5 8 9
A. No, it is not a function.
B. Yes, a linear function.
C. Yes, a nonlinear function.
Answers
Answer:
A
Step-by-step explanation:
It is not a function because both x-values -4 and 2 have multiple y-values. Try the vertical line test if you don't understand.
A. No, it is not a function.
Step-by-step Explanation:
A function is a set of ordered pairs where each input (x) has only one output (y).
However, in this table, the input x=-4 has two different outputs, y=-3 and y=5. Similarly, the input x=2 also has two different outputs, y=1 and y=8.
Therefore, it violates the definition of a function, and the correct answer is A. No, it is not a function.
5. Graph f(x)=x + 3
x-2
Answers
Answer:
1) f(-2) = -2 + 3
2) f(-2) = 1
Find the area of the figure. Round to the nearest tenth, if necessary.
Answers
From the given dimensions, area of the figure is approximately equal to 75.8 cm².
What is a regular polygon?A regular polygon is a closed shape with straight sides and equal-length edges, as well as equal angles between those sides. Examples of regular polygons include equilateral triangles, squares, and hexagons. The number of sides a regular polygon has is referred to as its order, while the measure of each interior angle of a regular polygon can be calculated using the formula (n-2) x 180/n, where n represents the number of sides.
From the image we can see that, ABHI is a square with sides 6 cm, BCDGH is a regular pentagon with sides 6 cm (BH = AI = 6 cm) and DEFG is a rectangle with length 11 cm and breadth 6 cm ( DG = AI = 6 cm).
To find the area of the figure we have to find the area of each shape and add it together.
Area of square = side × side = 6 × 6 = 36 cm²
Area of regular pentagon = [tex]\frac{1}{4} \sqrt{5(5+25)a^{2} }[/tex]
= [tex]\frac{1}{4} \sqrt{5(5+25)6^{2} }[/tex]
= [tex]\frac{1}{4} \sqrt{25 + 10*1.41*36}[/tex]
= [tex]\frac{1}{4} \sqrt{532.6 }[/tex]
≈ 5.77 cm²
Area of rectangle = 2(l + b) = 2(11 + 6) = 34 cm²
Therefore area of the figure = 36 cm² + 5.77 cm² + 34 cm² ≈ 75.8 cm².
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HELPPPP ASAPPP WILLL GIVE BRAINLEST
Answers
Answer:
2) The smallest amount of fabric Amy can buy is 78 inches = 2 1/6 yards, so she will need 2 1/4 yards of fabric.
3) $2.25(5) + $0.35(2) + $0.25(3) + $0.60 = $13.30 before sales tax
Sales tax is $13.30 × .08 = $1.06
Total is $13.30 + $1.06 = $14.36
What is the value of the digit 7 when 2.7 is multiplied by 10 to the 2nd power
Answers
Answer:
When 2.7 is multiplied by 10 to the 2nd power, it becomes 270. The digit 7 is in the ones place, so the value of the digit 7 is 7.
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs *Not all tiles will be used*
Match the correct volume formula with each described figure
1. V = 1/2 * pi * x ^ 3;
2. V = x ^ 3;
3. V = 1/3 * x ^ 3;
4. V = 1/2 * pi * x ^ 3;
5. V = 1/2 * x ^ 3;
6. V = pi * x ^ 3
A. a prism with a height of x cm and a square base with side length of x cm
B. a cylinder with a radius of x and height of cm
C. a pyramid with a height of x cm and a square base with a side length of x cm
D. a cone with a radius of x cm and height of x cm
Answers
A. a prism with a height of x cm and a square base with side length of x cm = option 2
B. a cylinder with a radius of x and height of cm= option 6
C. a pyramid with a height of x cm and a square base with a side length of x cm = option 3.
How to match the correct formula with the statements given ?For statement A=
The formula for a square based prism= a²h
where a= X
h = X
Vol = x³
For statement B;
The formula for a cylinder=πr²h
where r= X, h= X
Vol= π×x³
For statement C;
The formula for a square based pyramid= 1/3a²h
a = X
H = X
Vol = 1/3 * x³
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Let h(x) be the number of hours it takes
a new factory to produce x engines. The
company's accountant determines that
the number of hours it takes depends on
the time it takes to set up the machinery
and the number of engines to be
completed. It takes 6.5 hours to set up
the machinery to make the engines and
about 5.25 hours to completely
manufacture one engine. The
relationship is modeled with the
function b(x)=6.5+5.25%
1. Determine the x and y-
intercepts of the function.
2. Is the function increasing or
decreasing?
Answers
Based on the information, the y-intercept is (0, 6.5).
The function is increasing.
How to calculate the interceptBased on the information, we can use the variable x. This will be:
0 = 6.5 + 5.25%x
-6.5 = 5.25%x
x = -6.5 / 5.25% ≈ -123.81
There's no x intercept due to the negative value which doesn't make sense in this scenario.
In order to find the y-intercept, we set x = 0 and evaluate b(x):
b(0) = 6.5 + 5.25% × 0 = 6.5
Therefore, the y-intercept is (0, 6.5).
The function b(x) is increasing since the coefficient of x is positive (5.25%). This means that as the number of engines produced (x) increases, the time it takes to manufacture the engines also increases.
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Solve the simultaneous equation
x² + y² = 1
5x+12y +13=0
Answers
The two solutions to the system of equations are (x,y) = (7/5,-3) and (x,y) = (144/65,-12/13).
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x.
We can use substitution to solve this system of equations.
First, we solve the second equation for one of the variables, say x:
5x + 12y + 13 = 0
5x = -12y - 13
x = (-12/5)y - (13/5)
Next, we substitute this expression for x into the first equation:
x² + y² = 1
[(-12/5)y - (13/5)]² + y² = 1
Expanding the square and simplifying, we get:
y² + [(144/25)y² + (312/25)y + (169/25)] + y² = 1
(26/5)y² + (312/25)y + (144/25) = 0
Multiplying both sides by 25 to eliminate the fractions:
26y² + 312y + 144 = 0
Dividing by 4 to simplify:
6.5y² + 78y + 36 = 0
Using the quadratic formula:
y = (-b ± sqrt(b² - 4ac)) / 2a
where a = 6.5, b = 78, and c = 36.
Plugging in these values:
y = (-78 ± sqrt(78² - 4(6.5)(36))) / 2(6.5)
y = (-78 ± sqrt(4761)) / 13
y = (-78 ± 69) / 13
y = -3 or -12/13
If y = -3, then substituting into the equation for x gives:
x = (-12/5)(-3) - (13/5) = 7/5
So one solution is (x,y) = (7/5,-3).
If y = -12/13, then substituting into the equation for x gives:
x = (-12/5)(-12/13) - (13/5) = 144/65
So another solution is (x,y) = (144/65,-12/13).
Therefore, the two solutions to the system of equations are (x,y) = (7/5,-3) and (x,y) = (144/65,-12/13).
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Triangulation
Here are two-five pointed stars. Both figures A and B are polygons.They are both composed of line segments and are
two dimensional. Neither have curves. Do you agree with the statement?
Answers
A plane is an infinite two-dimensional figure.
We have,
When two planes intersect, they form a line.
The vector equation for the line of intersection is given by
r = r₀ + tₓ
where r₀ is a point on the line
tₓ is the cross product of the normal vectors of the two planes.
The parametric equations for the line of intersection are given by
x = a , y = b and z = c
where a, b and c are the coefficients from the vector equation
r = a (i) + b (j) + c (k)
The line of intersection will be perpendicular to the normal of both the planes
The line of intersection lies on both the planes
Therefore , a line is observed at the intersection of two planes
Given data ,
A line is one-dimensional, a segment is a part of a line and is also one-dimensional, and a point is zero-dimensional.
A plane, on the other hand, is a flat, two-dimensional surface that extends infinitely in all directions.
It has length and width, but no thickness, and can be thought of as an infinitely large sheet of paper.
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complete question:
Which of the following is an infinite two-dimensional figure?
A. A line
B. A plane
C. A segment
D. A point
Explain how you would find the highest point the rider achieved on this jump.
A. What would be the two quantities you would measure for x and y?
B. What would your equation possibly look like? Put the picture on a grid and show some possible points
C. What points could you use to find the maximum height? How would you use those points? Be specific
Answers
Answer:
Step-by-step explanation:
36
Find the area.
Area =
6 m
10 m
square meters
Answers
Answer:
32m
Step-by-step explanation:
area= L×B
L= 10m ×2 =20m
B= 6m×2 =12m
Area= 20m + 12m = 32m
When we add together the NPV and the false omission rate for any test, why is the sum always 100%?
Answers
The sum of the NPV and false omission rate for any test will always be 100%.
Explaining why is the sum always 100%?The NPV (Negative Predictive Value) is the proportion of people who test negative for a condition and actually do not have it, while the false omission rate is the proportion of people who have the condition but test negative for it.
When we add together the NPV and the false omission rate for any test, we are essentially considering all the cases where the test result is negative.
The NPV represents the proportion of people who truly do not have the condition and test negative for it, while the false omission rate represents the proportion of people who actually have the condition but test negative for it.
Together, these two values cover all possible cases where the test result is negative, which means that they represent the entirety of the negative results for the test.
Since the sum of all probabilities for an event must always equal 100%, the sum of the NPV and false omission rate must also equal 100%.
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What function is represented by the mapping diagram shown?
-2
00
6
2135
A. F(x)= x+3
B. F(x)= 3x
C. F(x) = 2x
D. F(x)=x-3
24600
2
8
Answers
Answer:c. F(x)=2x
Step-by-step explanation:
Hi
6. Sebastian recorded the price of gas each month for 12 months.
a. Draw a trend line on the scatter plot.
b. If the trend continues, what equation can he use to predict
the price of gas in future months?
Gas Price ($)
N
4
O
Gas Price
2 4 6 8 10 12
Month
X
Answers
The trend line for the y = 0.5x + 2 is attached accordingly. Note that the the predicted gas price for month 13 would be $8.50.
What is the explanation for the above response?a. To draw a trend line on a scatter plot, you need to perform a linear regression analysis. This involves finding the line of best fit that passes through the data points. The equation for a linear regression line is typically of the form y = mx + b, where y is the dependent variable (gas price in this case), x is the independent variable (month), m is the slope of the line, and b is the y-intercept.
Once you have the equation for the line of best fit, you can plot it on the scatter plot to visualize the trend. The slope of the line will tell you the direction and steepness of the trend (i.e., whether prices are increasing or decreasing, and how quickly).
b. To predict future values using the trend line, you can simply plug in the value of the independent variable (month) for the month you want to predict, and solve for the dependent variable (gas price). For example, if the equation for the trend line is y = 0.5x + 2, and you want to predict the gas price for month 13, you would plug in x = 13 and solve for y:
y = 0.5(13) + 2
y = 6.5 + 2
y = 8.5
So the predicted gas price for month 13 would be $8.50.
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Rewrite 84 + 36 in the form
a(b+c)
where a is the greatest common factor of 84 and 36
Answers
The GCF of 84 and 36 is 12.
The GCF of two non-zero integers, x(36) and y(84), is the greatest positive integer m(12) that divides both x(36) and y(84) without any remainder.
GCF of 36 and 84 by Listing Common Factors
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
There are 6 common factors of 36 and 84, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 36 and 84 is 12.
Rewrite in the form of a(b + c), a is the greatest common factor of 84 and 36
84/ 12 = 7
36/12 = 3
So, 12(84 + 36)
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Answer:
Less
Step-by-step explanation:
Look at the hundreds number in set L the numbers are greater in Set L than Set K.
What is the correct list of functions ordered from least to greatest by average rate of change over the interval 0 less than or equal to x less than or equal to 3
Answers
The correct list of functions ordered from 0 ≤ x ≤ 3 is:
h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x
Line connecting the interval's endpoints in order to compute the average rate of change for each function over range 0 x 3.
For f(x) = x^2, the slope between x = 0 and x = 3 is:
[tex](f(3) - f(0)) / (3 - 0) = (9 - 0) / 3 = 3[/tex]
For g(x) = 2x + 1:
[tex](g(3) - g(0)) / (3 - 0) = (7 - 1) / 3 = 2[/tex]
For h(x) = sin(x):
[tex](h(3) - h(0)) / (3 - 0) = (sin(3) - sin(0)) / 3[/tex] ≈ 0.279
For k(x) = e^x, the slope between x = 0 and x = 3 is:
[tex](k(3) - k(0)) / (3 - 0) = (e^3 - 1) / 3[/tex] ≈ 6.076
Therefore, correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3 is:
[tex]h(x) = sin(x) < f(x) = x^2 < g(x) = 2x + 1 < k(x) = e^x[/tex]
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--The complete Question is, Consider the following four functions:
f(x) = x^2
g(x) = 2x + 1
h(x) = sin(x)
k(x) = e^x
What is the correct list of functions ordered from least to greatest by average rate of change over the interval 0 ≤ x ≤ 3? --