The required value of impulse is 88 N-s and the mass of the cart is 8.8 kg.
How to find the impulse?Newton's Second Law relates an object's acceleration as a function of both the object's mass and the applied net force on the object.
Given data:
The speed of cart is, v = 10 m/s.
We are given the Force-time graph for which the area of the force-time graph will provide the value of impulse. So from the graph, the maximum force is,
F = 22 N
And time interval is,
t = 4.5 s - 0.5 s
t = 4 s
So, the impulse is,
I = Area of graph
I = F × t
I = 22 × 4
I = 88 N-s
Now the standard expression for the impulse as per the impulse-momentum theorem is,
I = ΔP (Change in momentum)
I = m ×( v - u )
Here, u is the final velocity, and since the cart stops finally, then u = 0 m/s. And m is the mass of the cart.
Solving as,
88 = m ×( v - u )
88 = m ×( 10 - 0 )
m = 8.8 kg
Thus, we can conclude that the required value of impulse is 88 N-s and the mass of car is of 8.8 kg.
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which of the following satisfies ? 3m-5=10
Answer:3-7=5
Step-by-step explanation: 3-7=5
abc x abc x abc in condensed form
The condensed form of the expression abc x abc x abc is (abc)^3
Expressing the expression in a condensed formWhen we have the same base raised to different exponents that are being multiplied together, we can simplify or condense the expression by adding the exponents.
In this case, we have the same base "abc" being raised to the exponent of 1 three times, so we can write it as:
abc x abc x abc
To condense this expression, we add the exponents 1+1+1=3, and write it as:
(abc)^3
So, the condensed form of the expression "abc x abc x abc" is "(abc)^3".
This is an example of the exponent rule for multiplying powers with the same base.
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Use the formula KE= mv^2/2 where m=mass, V= velocity, KE = kinetic energy. If dev has a mass of 60kg and is running at a constant velocity with 150 J of KE. What is his velocity?
Dev's velocity is [tex]\sqrt{5}[/tex]. Thus option B.
What is kinetic energy?Kinetic energy is a amount of energy possessed when an object is in motion. Such that;
KE = 1/2 m v^2
Where m = mass, v = velocity
It is measured in Joules.
From the given question, we have;
KE = 1/2 m v^2
2KE = m v^2
v^2 = 2KE/ m
= (2*150)/ 60
= 300/ 60
= 5
V = (5)^1/2
The velocity of Dev is B. [tex]\sqrt{5}[/tex].
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An object is thrown upward at a speed of 145 feet per second by a machine from a height of 2 feet off the ground. The height h of the object after t seconds can be found using the equation
When will the height be 230 feet?
seconds
When will the object reach the ground?
seconds
Answer:
Step-by-step explanation:
The equation for the height h of the object after t seconds is given by:
h = -16t^2 + 145t + 2
To find when the height will be 230 feet, we can set h = 230 and solve for t:
230 = -16t^2 + 145t + 2
We can simplify this equation by moving all the terms to one side:
16t^2 - 145t + 228 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 16, b = -145, and c = 228. Plugging in these values, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)
t = (145 ± sqrt(21025 - 14592)) / 32
t = (145 ± sqrt(6433)) / 32
t ≈ 0.56 seconds or t ≈ 9.17 seconds
Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.
To find when the object will reach the ground, we can set h = 0 and solve for t:
0 = -16t^2 + 145t + 2
Again, we can simplify this equation by moving all the terms to one side:
16t^2 - 145t - 2 = 0
Using the quadratic formula again, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)
t = (145 ± sqrt(21249)) / 32
t ≈ 9.51 seconds or t ≈ 0.15 seconds
Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.
~~~Harsha~~~
An inductor of l = 250 is subjected to a voltage v(t) = 8 e-4t V:
A. Knowing that, integrate both sides to determine the current i(t). You may assume that the initial current is zero.
B. Given that the absorbed power is, determine the total stored energy.
A. The current flowing through the inductor at time T is given by i(T) = (2/250) * (1 -[tex]e^{-4t}[/tex])A B. The total stored energy in the inductor from t = 0 to t = T is given by W(T) = 2( [tex]e^{-4t}-e^{-8t}[/tex]) J.
Describe Integration?Finding the region beneath a curve or the entire accumulation of a quantity over a given period is the goal of the mathematical procedure known as integration. It is the inverse operation of differentiation and is frequently employed in a number of scientific, mathematical, and engineering disciplines.
Finding an antiderivative—a function that, when separated from the original function being integrated—is a necessary step in the integration process. The symbol for this antiderivative is frequently ∫f(x) dx, where f(x) is the function being integrated and dx denotes an incredibly minute change in x. The outcome of the integration is a family of functions that differ from one another by a constant quantity called the integration constant.
A. We know that v(t) = L di(t)/dt, where L is the inductance of the inductor and i(t) is the current flowing through it at time t. We can rearrange this equation to get di(t)/dt = v(t)/L, and then integrate both sides with respect to time from t = 0 to t = T to get:
∫[0, T] di(t)/dt dt = ∫[0, T] v(t)/L dt
After integrating the left side, we get:
i(T) - i(0)
This becomes i(T) as the starting current is zero. When the right side is integrated, we get:
(1/L) ∫[0, T] v(t) dt
When we replace the given phrase for v(t), we obtain:
(1/L) ∫[0, T] 8 -[tex]e^{-4t}[/tex] dt
When we incorporate this expression, we get:
(1/L) * (-2 [tex]e^{-4t}[/tex] ) |[0, T]
When the integration and simplification limitations are swapped out, we obtain:
i(T) = (2/L) * (1 - [tex]e^{-4t}[/tex] ) A
As a result, the current through the inductor at time T can be calculated as follows:
i(T) = (2/250) * (1 - [tex]e^{-4t}[/tex] ) A
B. As of time T, the inductor's total stored energy is given by:
W(T) = (1/2) L i²(T)
We obtain the following by substituting the expression for i(T) from section A:
W(T) = (1/2) * 250 * [(2/250) * (1 - [tex]e^{-4t}[/tex] )]²
Simplifying, we get:
W(T) = 2.5 * [(1 - [tex]e^{-4t}[/tex] )²] J
We integrate this expression with regard to time from t = 0 to t = T to determine the total energy stored from t = 0 to t = T:
W(T) = ∫[0, T] 2.5 * [(1 - [tex]e^{-4t}[/tex] )²] dt
We can rewrite this integral as follows by replacing the supplied expression for p(t):
W(T) = (1/8) ∫[0, T] p(t) dt
Integrating p(t) in relation to time results in:
p(t) = 64 ( [tex]e^{-4t}-e^{-8t}[/tex])
∫[0, T] p(t) dt = 16 ( [tex]e^{-4t}-e^{-8t}[/tex]) J.
When we use this expression to solve for W(T), we obtain:
W(T) = 1/8 * 16 ( [tex]e^{-4t}-e^{-8t}[/tex]) J.
Simplifying, we get:
W(T) = 2 ( [tex]e^{-4t}-e^{-8t}[/tex]) J.
As a result, the formula for the total energy stored in the inductor from t = 0 to t = T is as follows:
W(T) = 2 ( [tex]e^{-4t}-e^{-8t}[/tex]) J.
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BRAINLIEST find the volume and surface area of a hypotenuse of a triangular right base that is 25 m . 7m height 24 m base? 22m length?
The volume and surface area of a triangular prism is 1,848 cubic meters and 1,694 square meters.
What is surface area?
The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
the volume and surface area of a right triangular prism with base dimensions of 24 m and 7 m height and a length of 22 m.
The volume of a right triangular prism is given by the formula:
V = (1/2) * b * h * l
where b is the base width, h is the height, and l is the length. Plugging in the given values, we get:
V = (1/2) * 24 m * 7 m * 22 m = 1,848 m³
Therefore, the volume of the right triangular prism is 1,848 cubic meters.
The surface area of a right triangular prism is given by the formula:
SA = 2 * (b * h + l * h + b * l)
Plugging in the given values, we get:
SA = 2 * (24 m * 7 m + 22 m * 7 m + 24 m * 22 m) = 1,694 m²
Therefore, the surface area of the right triangular prism is 1,694 square meters.
Hence, the volume and surface area of a triangular prism are 1,848 cubic meters and 1,694 square meters.
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write two different quadratic functions that goes through points (5,3) and (8,0)
Two quadratic functions that contains the points (5, 3) and (8, 0) are
How to find two possible quadratic functionsIn this problem we must find two possible quadratic functions that contains two points: (x, y) = (5, 3), (x, y) = (8, 0). The factor form of the quadratic function is now introduced:
y = a · (x - r₁) · (x - r₂)
Where:
r₁, r₂ - Rootsa - Constantx - Independent variable.y - Dependent variable.If we know that (x₁, y₁) = (5, 3) and (x₂, y₂) = (8, 0), then the two possible quadratic functions are:
3 = a · (5 - r₁) · (5 - r₂)
3 = a · [25 - 5 · (r₁ + r₂) + r₁ · r₂]
0 = a · (8 - r₁) · (8 - r₂)
0 = 64 - 8 · (r₁ + r₂) + r₁ · r₂
0 = 64 - 8 · r₁ - 8 · r₂ + r₁ · r₂
0 = 64 - 8 · r₁ + (r₁ - 8) · r₂
Now we clear r₂:
r₂ = (8 · r₁ - 64) / (r₁ - 8)
And we eliminate r₂ in the first equation:
3 = a · [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]
And variable a is now cleared:
a = 3 / [25 - 5 · [r₁ + (8 · r₁ - 64) / (r₁ - 8)] + r₁ · [(8 · r₁ - 64) / (r₁ - 8)]]
The function is graphed and two possible solutions are introduced below:
(r₁, a) = (6, 1), (r₁, a) = (10, 0.2)
And the values of r₂ are, respectively:
(r₁, a) = (6, 1):
r₂ = (8 · 6 - 64) / (6 - 8)
r₂ = - 16 / (- 2)
r₂ = 8
(r₁, a) = (10, 0.2):
r₂ = (8 · 10 - 64) / (10 - 8)
r₂ = 16 / 2
r₂ = 8
Finally, we complete and graph the resulting quadratic functions.
Case 1:
y = (x - 6) · (x - 8)
y = x² - 14 · x + 48
Case 2:
y = 0.2 · (x - 10) · (x - 8)
y = 0.2 · (x² - 18 · x + 80)
y = 0.2 · x² - 3.6 · x + 16
The graphs of the two quadratic functions are shown in the second image.
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baseball team 747 for the season this was 9 times the number the number
Hence ,the basketball team scored 83 points in the first game.
What is the basketball?Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular court, compete with the primary objective of shooting a basketball through the defender's hoop, while preventing the opposing team from shooting through their own hoop.
What is the team ?A team is a group of individuals (human or non-human) working together to achieve their goal.As defined by Professor Leigh Thompson of the Kellogg School of Management, team is a group of people who are interdependent with respect to information, resources, knowledge and skills and who seek to combine their efforts to achieve a common goal
Let x be the number of points scored in the first game.
According to the question,
747 = 9 x
now 9 divided by both sides,
x = [tex]\frac{747}{9}[/tex]
than we get:
x = 83
Therefore, the basketball team scored 83 points in the first game.
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Complete question is:
A basketball scored 747 points for the season.This was 9 times the number of points they scored in the first game.How many points were scored in the first game.
Find the surface area
Round to the nearest tenth
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 27 N acts on a certain object, the acceleration of the object is 9 m/s². If the force is changed to 24 N, what will the object's acceleration be?
*Worth 100 points and will award brainliest for the first correct answer.*
Given:
[tex]\vec F_{1} =27 \ N[/tex]
[tex]\vec F_{2} =24 \ N[/tex]
[tex]\vec a_{1} = 9 \ m/s^2[/tex]
Find:
[tex]\vec a_{2} = ?? \ m/s^2[/tex]
We know that [tex]\vec F= m \vec a[/tex]. Use [tex]\vec F_{1}[/tex] and [tex]\vec a_{1}[/tex] to find mass, m.
[tex]\Longrightarrow \vec F_{1} = m \vec a_{1} \Longrightarrow 27= m(9) \Longrightarrow m= \frac{27}{9} \Longrightarrow m= \boxed{ 3 \ kg }[/tex]
We now know the mass of the moving object we can now find [tex]\vec a_{2}[/tex].
[tex]\Longrightarrow \vec F_{2} = m \vec a_{2} \Longrightarrow 24= (3) \vec a_{2} \Longrightarrow \vec a_{2}= \frac{24}{3} \Longrightarrow \vec a_{2}= \boxed{ 8 \ m/s^2 } \ \therefore \ Sol.[/tex]
You are given that cos(A)=−5/13, with A in Quadrant II, and sin(B)=24/25, with B in Quadrant II. Find cos(A+B). Give your answer as a fraction.
The value for the trigonometric expression cos(A+B) is (5√7 - 288)/325
Explain trigonometry.
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It includes the study of trigonometric functions such as sine, cosine, and tangent, which are used to calculate unknown angles or sides of a triangle. Trigonometry has many practical applications in fields such as engineering, physics, and navigation.
According to the given information
We can use the trigonometric identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) to find cos(A + B).
Since cos(A) = -5/13 and A is in Quadrant II, we can use the Pythagorean identity sin²A + cos²A = 1 to find sin(A). Solving for sin(A), we get sin²A = 1 - cos²A = 1 - (-5/13)² = 144/169. Since A is in Quadrant II, sin(A) is positive, so sin(A) = √(144/169) = 12/13.
Similarly, since sin(B) = 24/25 and B is in Quadrant II, we can use the Pythagorean identity to find cos(B). Solving for cos(B), we get cos²B = 1 - sin²B = 1 - (24/25)² = 7/625. Since B is in Quadrant II, cos(B) is negative, so cos(B) = -√(7/625) = -√7/25.
Substituting these values into the identity for cos(A + B), we get:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
= (-5/13)(-√7/25) - (12/13)(24/25)
= (5√7)/(13*25) - (12*24)/(13*25)
= (5√7 - 288)/(13*25)
= (5√7 - 288)/325
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Adeline earns $28 for mowing lawns for 7 hours. If Adeline charges at the same rate, how many hours will it take her to earn $40?
Answer:
10 hours
Step-by-step explanation:
[tex] \frac{28}{7} = \frac{40}{h} [/tex]
[tex]28h = 280[/tex]
[tex]h = 10[/tex]
Please simplify the attachment
The evaluation of the expression consisting of surds indicates that we get;
(9·x + 42 - 69·√x)/(x - 49)
What are surds?A surd is a value under a square root sign, which can not be further simplified into fractions or whole numbers.
The expression (9·√x - 6)/(√x + 7), can be simplified by using the rationalization of surds technique as follows;
(9·√x - 6)/(√x + 7) = ((9·√x - 6)/(√x + 7)) × ((√x - 7)/(√x - 7))
(√x + 7) × (√x - 7) = ((√x)² - 7²) = (x - 49)
(9·√x - 6) × (√x + 7) = 9·x + 42 - 69·√x
Therefore; (9·√x - 6)/(√x + 7) = (9·x + 42 - 69·√x)/(x - 49)
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can you answer these two questions
The confidence interval can be expressed as a trilinear inequality: 82.9% < p < 95.7%.
The confidence interval in interval form is (0.1864, 0.3026).
How to calculate confidence interval?The given confidence interval, 89.3% ± 6.4%, means that we are 89.3% confident that the true value of the population parameter lies within a range of 6.4% above and below the sample estimate.
To express this in the form of a trilinear inequality, first find the upper and lower bounds of the interval.
Upper bound = 89.3% + 6.4% = 95.7%
Lower bound = 89.3% - 6.4% = 82.9%
Therefore, the confidence interval 89.3% ± 6.4% can be expressed in the form of a trilinear inequality as:
82.9% < p < 95.7%
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George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months. He followed the steps below to determine the number of cars he needs to sell in the next month to have a mean number of sales per month of 24.Step 1: Find the total cars needed to have a mean of 24: .Step 2: Find the total cars sold: .Step 3: Subtract the total cars sold from the total cars needed: .Step 4: State the answer: George needs to sell 26 cars next month. Where did George make his first mistake?Step 1Step 2Step 3Step 4
George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months.
George's first mistake was in Step 1 where he tried to find the total number of cars he needs to sell in the next month to have a mean number of sales per month of 24. To find this value, George should have multiplied the desired mean number of sales per month (24) by the total number of months (7) to get the total number of cars needed to have a mean of 24 over 7 months. However, it seems that George skipped this step and directly assumed that the total number of cars needed for a mean of 24 in the next month is simply 24.
Let's go through each step to explain
Step 1 Find the total cars needed to have a mean of 24
To find the total number of cars George needs to sell over the next 7 months to have a mean of 24 cars sold per month, he should multiply the desired mean (24) by the number of months (7)
Total cars needed = 24 * 7 = 168
Step 2 Find the total cars sold
To find the total number of cars George sold over the past 7 months, he should add up the individual sales for each month:
Total cars sold = 18 + 22 + 26 + 12 + 25 + 20 + 19 = 142
Step 3 Subtract the total cars sold from the total cars needed
To find the number of cars George needs to sell in the next month to meet his target mean of 24 cars sold per month over the past 8 months, he should subtract the total number of cars sold from the total cars needed
Cars needed in the next month = Total cars needed - Total cars sold
Cars needed in the next month = 168 - 142 = 26
Step 4 State the answer
George needs to sell 26 cars next month to have a mean of 24 cars sold per month over the past 8 months.
Therefore, George's mistake was in Step 1 where he did not correctly calculate the total number of cars he needs to sell over the next 7 months to have a mean of 24 cars sold per month.
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Factor the following polynomial. 98x^3 - 18x
For the following sequence: 6,15,24,33,.....
a) Write an expression for the nth term
b) Find the 10th term.
Answer:
a) The common difference between consecutive terms is 9. Thus, the nth term can be expressed as:
n(9)+(-3)
b) To find the 10th term, we substitute n=10 in the expression we just found:
10(9) + (-3) = 87
Therefore, the 10th term of the sequence is 87.
Find the measure of x in circle C shown below.
x =
(50 points will give brainiest for effort)
The measure of the value of x in the circle given is calculated as equal to: x = 12.
How to Find the Measure of x in the Circle?A semicircle is a two-dimensional shape that is half of a circle, consisting of a curved boundary or arc and a diameter or straight line segment that connects the two endpoints of the arc. This is always equal to 180 degrees.
Therefore, we have the equation:
12x + 6 + 3x - 6 = 180
Combine like terms:
15x = 180
Divide both sides by 15
x = 180/15
x = 12
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x^2 + 7y + 12 = ?
x = -1 y = 4
The value of the expression when x = -1 and y = 4 is 41.
Evaluating the expression [tex]x^2[/tex]+7y+12 when x = -1 and y = 4, we get:
[tex]x^2[/tex]+7y+12 = [tex](-1)^2[/tex] + 7(4) + 12 = 1 + 28 + 12 = 41
Therefore, the value of the expression when x = -1 and y = 4 is 41.
Here is the step-by-step solution:
Substitute x = -1 and y = 4 into the expression.
Evaluate the exponent.
Multiply 7 by 4.
Add 1, 28, and 12.
The answer is 41.
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solve 3/4 (5x- 3) + 8 = 17. show your work.
2+7•(-3)^2
Help me
How do I solve. ?
Answer:
To solve the expression 2 + 7 • (-3)^2, we follow the order of operations, also known as PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, we evaluate the exponent: (-3)^2 = 9 (because squaring a number means multiplying it by itself).
Next, we perform multiplication: 7 • 9 = 63.
Finally, we perform addition: 2 + 63 = 65.
So, the value of the expression 2 + 7 • (-3)^2 is 65.
please help studying my next grade:
12+6÷(82-33)x66
Answer:
3246
Step-by-step explanation:
To calculate this equation, we need to follow the order of operations, also known as PEMDAS. First, we evaluate anything inside parentheses, which in this case is (82-33), giving us 49. Next, we perform division, so we have 6 ÷ 49. Then, we multiply 49 and 66, resulting in 3234. Finally, we add 12 to 3234, leading to the final answer of 3246. Therefore, the value of the expression 12+6÷(82-33)x66 is 3246.
Answer:
3246
Step-by-step explanation:
find an equivalent expression to 2-4(x+1)-18
Answer:
Sure. Here are the steps on how to find an equivalent expression to 2-4(x+1)-18:
1. Expand the parentheses:
```
2-4(x+1)-18 = 2-4x-4-18
```
2. Combine like terms:
```
2-4x-4-18 = -4x-14
```
Therefore, the equivalent expression to 2-4(x+1)-18 is -4x-14.
2 - 4(x + 1) - 18 can be simplified as follows:
= 2 - 4x - 4 - 18 [distribute -4]
= -20 - 4x [combine like terms]
Therefore, an equivalent expression to 2-4(x+1)-18 is -20 - 4x.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday
49 55 42 46 47 42 38
Julia measured the high temperature in her town for one week. Using the chart above, find the mean absolute deviation for the high temperatures. Round your answer to the nearest tenth.
Be sure to show your work for finding:
the mean of the set of data
the distance of each number from the mean
the mean absolute deviation
the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.
How to solve the question?
To find the mean absolute deviation (MAD) for the high temperatures in Julia's town, we first need to find the mean temperature for the week.
To do this, we add up all the temperatures and divide by the number of temperatures:
(49 + 55 + 42 + 46 + 47 + 42 + 38) ÷ 7 = 43.3
The mean temperature for the week is 43.3 degrees.
Next, we need to find the distance of each temperature from the mean. To do this, we subtract the mean from each temperature:
|49 - 43.3| = 5.7
|55 - 43.3| = 11.7
|42 - 43.3| = 1.3
|46 - 43.3| = 2.7
|47 - 43.3| = 3.7
|42 - 43.3| = 1.3
|38 - 43.3| = 5.3
We take the absolute value of each difference to ensure that the distances are positive.
Now, we find the mean of the distances by adding up all the distances and dividing by the number of temperatures:
(5.7 + 11.7 + 1.3 + 2.7 + 3.7 + 1.3 + 5.3) ÷ 7 = 4.9
Therefore, the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.
In conclusion, the mean absolute deviation is a measure of the variability of a set of data. It is calculated by finding the mean of the absolute distances of each data point from the mean. In this case, the MAD is 4.9 degrees, indicating that the temperatures for the week were relatively close to the mean.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
The solution to the given composite function is; C: 4x² - 4x - 2
How to solve composite functions?From the question, we are given the individual functions as;
f(x) = x² - 3
g(x) = 2x - 1
Now when it comes to composite functions, we know that;
(f ° g)(x) = f[g(x)]
Substitute the known values in the above equation, so, we have the following representation
(f ° g)(x) = f(2x - 1) = (2x - 1)² - 3 = 4x² - 2x - 2x + 1 - 3 = 4x² - 4x - 2
This is the final solution of the composite function expression.
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The solution to the given composite function is; Option D: 2x² - 7
How to solve composite functions?Composite functions are defined as functions where the output of one function is used as the input of another. Wheb we have a function f and another function g, then the function fg(x), said as “ f of g of x”, is the composition of the two functions.
The given functions are:
f(x) = x² - 3
g(x) = 2x - 1
We want to find (g ° f)(x) . We know that:
(g ° f)(x) = g[f(x)]
Thus:
(g ° f)(x) = g(x² - 3)
= 2(x² - 3) - 1
= 2x² - 6 - 1
= 2x² - 7
This is the final result of the composite function expression.
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Find the mass of the triangular region with vertices (0, 0), (4, 0), and (0, 2), with density function ρ(x,y)=x^2+y^2.
The mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]
What is a triangle?A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.
According to the given information:The mass of a 2D region with variable density can be calculated using the double integral formula:
m = ∬R ρ(x,y) dA
where R is the region of integration, ρ(x,y) is the density function, and dA is the area element.
In this case, we have a triangular region with vertices (0, 0), (4, 0), and (0, 2), and the density function is ρ(x,y) = [tex]x^2 + y^2.[/tex]To set up the double integral, we need to determine the limits of integration for x and y.
Since the triangular region is bounded by the lines y = 0, y = 2, and x = (2/5)y, we can set up the integral as follows:
m = ∫0 ∫[tex]0^[/tex](2/5)y ([tex]x^2 + y^2)[/tex] dxdy
Integrating with respect to x first, we get:
m = ∫[tex]0^2 [(x^3/3) + xy^2]_0^(2/5[/tex])y dy
m = ∫[tex]0^2 [(8/375)y^5 + (4/15)y^3][/tex]dy
Evaluating the integral, we get:
m = [tex][(2/1875)y^6 + (2/5)y^4]_0^2[/tex]
m = (64/1875) + (16/5)
m = 136/375
Therefore, the mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]
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NO LINKS!! URGENT HELP PLEASE!!!!
Express the statement as an inequality part 10a^2
The inequality that represents the sentence that the absolute value of x is greater than 6 is given as follows:
|x| > 6.
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.The absolute value of x is represented as follows:
|x|.
The inequality that represents the absolute value being greater than six is gjven as follows:
|x| > 6.
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Answer:
|x| > 6
Step-by-step explanation:
The correct statement is: |x| > 6.
This means that the distance between x and 0 on the number line is greater than 6 units, so x can be any number greater than 6 or less than -6.
The options given are:
|x| < 6: This statement indicates that the distance of x from 0 on the number line is less than 6 units. In other words, x could be any value between -6 and 6, not including -6 and 6.|x| > 6: This statement indicates that the distance of x from 0 on the number line is greater than 6 units. Therefore, x could be any value less than -6 or greater than 6.|x| = 6: This statement indicates that the distance of x from 0 on the number line is exactly 6 units. Therefore, x could be either 6 or -6.|x| ≥ 6: This statement indicates that the distance of x from 0 on the number line is greater than or equal to 6 units. Therefore, x could be any value less than or equal to -6 or greater than or equal to 6.|x| ≤ 6: This statement indicates that the distance of x from 0 on the number line is less than or equal to 6 units. In other words, x could be any value between -6 and 6, including -6 and 6.Therefore, the correct statement is |x| > 6.
here's how to express the statement |x| > 6 as an inequality part 10a^2
| x | > 6
Squaring both sides of this inequality, we get:x^2 > 6^2
Simplifying, we get:x^2 > 36
Multiplying both sides by 10, we get:10x^2 > 360
So the inequality we get after multiplying both sides by 10 is:10x^2 - 360 > 0
Therefore, the inequality for |x| > 6 in terms of 10a^2 is:10x^2 - 360 > 0
Note that this inequality does not directly involve "a," as it is not mentioned in the original statement.
Please help me write a summary of the 3 rules on segments
1) When 2 chords intersect inside a circle, and 4 segments are formed
2) When 2 secants intersect outside a circle, and 4 segments are formed
3) When 1 secant and 1 tangent intersect outside a circle, and 3 segments are formed
The summary of the 3 rules on segments are written below.
How to write a summary of the 3 rules on segments?The three rules on segments in circles are:
1. When two chords intersect inside a circle, they create four line segments.
The product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the other chord.
2. When two secants intersect outside a circle, they create four line segments.
The product of the length of the secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.
3. When one secant and one tangent intersect outside a circle, they create three line segments.
The product of the length of the secant segment and its external segment is equal to the square of the length of the tangent segment.
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A cone has a radius of 6 m and a height of 24 m. What is the volume of the cone in terms of π? 864π m3 432π m3 288π m3 144π m3
The volume of the cone is 288π m³. Hence, the answer is option C, 288π m³.
What is cone?A cone is a shape created by connecting all the points of a circular base (which does not contain the apex) to a common point known as the apex or vertex using a series of line segments or lines. The height of the cone is determined by measuring the distance between its vertex and base.
The formula for the volume of a cone is given by V = (1/3)πr²h, where r is the radius and h is the height.
Substituting the given values, we get:
V = (1/3)π(6²)(24)
V = (1/3)π(36)(24)
V = (1/3)(864π)
V = 288π
Therefore, the volume of the cone is 288π m³.
Hence, the answer is option C, 288π m³.
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If you deposit $2000 in an account paying 2% annual interest compounded monthly, how much money will you have in the account after 40 years?
Answer: To calculate the amount of money you will have in the account after 40 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount of money in the account after t years, P is the principal (the initial amount of money deposited), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $2000, r = 0.02 (since the interest rate is 2%), n = 12 (since the interest is compounded monthly), and t = 40. Plugging these values into the formula, we get:
A = 2000(1 + 0.02/12)^(12*40)
A = $5,837.85
So you will have $5,837.85 in the account after 40 years.