The average value of both f(x) and g(x) on 0≤x≤2 is 1/4. The average value of (f.g) on 0≤x≤2 is 0 and the statement avg(f) . avg(g) = avg(f . g) is false.
avg value of a function = 1/(b - a) ∫f(x) with limts a and b. Here a and b are the constraints under which the average has to be calculated.
a)
Hence average value of f(x) on 0≤x≤2
= 1/2 ∫f(x) with 0 and 2 as intervals
Since integration is basically the area under the curve we get
avg of f(x) = 1/2[area under curve from 0 to 1 + Area under the curve from 1 to 2]
Since from 0 to 1, the figure is a triangle and beyond that a straight line we get
1/2[1/2 X 1 X 1 + 0]
= 1/4 sq units
b)
Similarly, the average value of g(x) on 0 ≤ x ≤ 2
1/2[area from 0 to 1 + area from 1 to 2]
= 1/2[0 + 1/2]
= 1/4 sq units
c) here we need to find the average of f(x) . g(x)
Here we see that f(x) is 0 from x = 1 to x = 1 while g(x) id 0 from x = 0 from x = 1
Hence we see that on multiplying the functions, the resultant has to be a 0 function.
Hence its average value will be 0.
d)
Average(f) . Average(g) = 1/4 X 1/4
= 1/16
Average of (f.g) = 0
Hence the statement is false
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Complete Question
The figure attached to the left is a graph of f(x), and below to the right is g(x).
The figure below to the left is a graph of f(x), a
(a) What is the average value of f(x) on 0≤x≤2? avg value = __________
(b) What is the average value of g(x) on 0≤x≤2? avg value = __________
(c) What is the average value of f(x) . g(x) on 0≤x≤2? avg value = _________
(d) Is the following statement true?
Average(f) . Average(g)=Average(f.g)
A. Yes
B. No
16 quarts of soil are used to completely fill 5 flower pots. If each pot holds the same amount of soil, how many quarts will each pot hold?
How many quarts of soil are used to fill 3 flower pots?
9.6 quarts
First, find the unit rate, which is that when you divide 16 and 5 and you will get 3.2, then you multiply it with 3 for the 3 flower pots, and that's how you end up with the answer
In a circle with radius 5.1, an angle intercepts an arc of length 30.3. Find the angle in
radians to the nearest 10th.
Answer:
5.9 radian
Step-by-step explanation:
Applying,
S = 2πrФ/360°................. Equation 1
Where s = length of the arc, r = radius, Ф = angle.
make Ф the subject of the equation
Ф = 360S/(2πr)........... Equation 2
From the question,
Given: S = 30.3, r = 5.1
Constant: π = 3.14
Substitute into equation 2
Ф = (360×30.3)/(2×5.1×3.14)
Ф = 340.58°
Ф = (340.58×2×3.14)/360
Ф = 5.9 radian
Find the Average Rate of Change of the table below for the interval 2 < x < 5
The AROC is 3 for the interval 2 < x < 5, which is the correct answer that would be option (A).
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
The table is given in the question as follows:
x y
0 -2
1 -3
2 0
3 3
4 6
5 9
We have to determine the Average Rate of Change in the table below for the interval 2 < x < 5
As per the given table, the required AROC would be as:
⇒ (9 - 3)/(5-3)
⇒ 6/2
Apply the division operation, and we get
⇒ 3
Hence, the correct answer would be option (A).
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Determine the missing angle measure.
Answer:
Step-by-step explanation:
Since you already know that one of the angles is 21 degrees, this helps you A LOT. In total the line is 180 degrees so to find x you just do 180-21 which equals 159
x+ 159 degrees
Jaylen has a fun-size bag SweetTarts. Inside the bag are 4 pink, 1 blue, 2 yellow, 3 purple and 2 green SweetTarts. What is the probability of drawing a yellow SweetTart three time in a row if each SweetTart selected is eaten before the next SweetTart is drawn?
The probability of picking a yellow sweet tart three times in a row is 0
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here, There are 4 pink, 1 blue, 2 yellow, 3 purple and 2 green SweetTarts. P(yellow ball three times in a row) = 2/12 ×1/11 ×0/10
= 0
Hence, The probability of picking a yellow sweet tart three times in a row is 0
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The reputation of a city has been decreasing exponentially since 1990. In 1990, the population was 1,000,000. In 2010, the population was 560,000. If t represents time in years since 1990, which of the following equations
best models the decay of the population?
Answer:
i think you have to soleve that srry
What properties does the shape below have? Why is it not a parallelogram?
Answer:
Parallelograms have two symmetries but this kite had only one symmetry
Define symmetry-The symmetry that a figure has if it can be divided by a line into two parts that are mirror images.
Observe my example why its not a parallelogram...
Hope this helps plz like and brainly :D
Much would be appreciated <3
The integral 1 π(y2−y4) dy 0 represents the volume of a solid. Describe the solid.
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the y axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
The correct option is (d). The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
The difference between the areas beneath the two curves that form a boundary is the area between the curves. You will then have the area between the two curves, or the difference, between them.
In the cartesian coordinate system, a plane is divided into four areas by the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.Use washer method:The washer method enables us to use cylindrical discs with holes to compute the volume of solids in a rotation.
As we have mentioned, the washer method is an extension of the disk method. This technique is established so that we can also calculate for the volume of the solid returned by rotating the region bounded by two curves over the x and y axis.[tex]$$\begin{aligned}& V=\int_a^b \pi\left(x_1^2-x_2^2\right) d y \\& =\int_0^1 \pi\left(y^2-\left(y^2\right)^2\right) d y \\& =\int_0^1 \pi\left(y^2-y^4\right) d y\end{aligned}$$[/tex]
Therefore, the solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y² around the y axis.
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On a negatively skewed curve, which is true?
The statistical model is not good, and this is true for a negatively skewed curve.
What means negatively skewed curve?It is a statistical term implies that a curve is skewed at the left side.
In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.
Which is true for negatively skewed curve?In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.
In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.
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Jak starts to save at age 40 for a vacation home that he wants to buy for his 50th birthday. He will contribute $1000 each quarter to an account, which earns 2.1% interest, compounded annually. What is the future value of the investment, rounded to the nearest dollar, when jak is ready to purchase the vacation home?
Answer:
[tex]P=\$40840[/tex]
Step-by-step explanation:[tex]I=840[/tex]
From the question we are told that:
Time interval [tex]t=50-40=>10years[/tex]
Annual contribution [tex]X= 4*1000=>\$4000[/tex]
Annual interest rate [tex]r=2.1\%[/tex]
Generally the 10 years interest I is mathematically given by
[tex]I=X*t*r[/tex]
[tex]I=4000*0.021*10[/tex]
[tex]I=840[/tex]
Generally the equation for the future value of the investment [tex]P[/tex] is mathematically given by
[tex]P=X*t+840[/tex]
[tex]P=(4000*10)+840[/tex]
[tex]P=\$40840[/tex]
What is dual expression?
The Dual of Boolean Expression is defined as an expression that is obtained by interchanging the addition and multiplication and interchanging the 0's and 1's .
What is a Boolean Expression ?
The Boolean Expression is defined as an logical statement which results in the Boolean value which can either be True or False.
Sometimes, the synonyms is used to express statement such as ‘Yes’ for ‘True’ and ‘No’ for ‘False’. and also, 1 and 0 are used for digital circuits for True , False .
If in the Boolean expression , the addition and multiplication are interchanged and the binary 0 and 1 are also interchanged then the resulting expression will be called as a Dual Of Boolean Expression .
The given question is incomplete , the complete question is
What is Dual Boolean Expression ?
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Please help I will give 15 points
Answer:
THE FIRST ONE
Step-by-step explanation:
Can anyone help explain this math equation like I gotta turn this math in by midnight tonight!! I will give brainlist btw!!
Answer: 1) 288 inch^3
2) 960 inch^3
3) 188 cm^3
4) 44 inch^3
5) 396 ft^3
6) 552 inch^3
Step-by-step explanation:
1) (2*3)(3*2)(2*4)=288 inch^3
2) (4*5)(4*3)(4*1)=960 inch^3
3) 4*4*8+3*4*5=188 cm^3
4) 2*2*8+2*6*1=44 in^3
5) 4*6*6+6*6*7=396 ft^3
6) 8*6*10+4*3*6=552 in^3
please help me!!10points
Answer:
167 feet
Step-by-step explanation:
Please see the attached image.
(90-42)°=48°
The tangent of an angle is the opposite side relative to that angle divided by the adjacent side.
tan(48°)=x/150
x=tan(48°)*150
x≈167
Answer: 167 feet
Work out the area of this shape. Give your answer
in cm².
4 cm
4 cm
10 cm
Answer:
48cm^2
Step-by-step explanation:
Rectangle=LxW
Triangle=bh/2
Rectangle: 10x4=40cm^2
Triangle: 4x4=16/2=8cm^2
40+8=48cm^2
Hope this helps :)
Find the distance between point k and point L.
The distance between points L and K is 4 units.
What is the distance formula between two points?The distance formula between two points (x₁, y₁) and (x₂, y₂) is gien by,
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].
Given, Are two points L and K.
The coordinate points of L(- 2, 6) and K(- 2, 2).
Therefore, The distance between points L and K is,
[tex]|LK| = \sqrt{(- 2 + 2)^2 + (2 - 6)^2}[/tex].
[tex]|LK| = \sqrt{16}[/tex].
[tex]|LK| = 4[/tex].
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Find the missing side lengths. Leave your answers as radicals is simplest form.
The absolute value function graphed below can also be represented by a piecewise function.
Determine which function is represented by the graph.
please help!!!
Answer:
Step-by-step explanation:
Trust me
Please help me with this homework question. No silly answers please and no bots, links, etc! I will mark brainliest to whoever gets this right. Thank you!
Answer:
T = (m × 20) + 25
(2.5 × 20) + 25 = 75
75 minutes
110 - 25 = 85
85 ÷ 20 = 4.25
4.25 kilograms
hello please help i’ll give brainliest
Answer:
ocean crust is thinner
Step-by-step explanation:
Answer:
Oceanic crust is thinner
hope this helped
Step-by-step explanation:
Find the value of x.
x+16
9
Answer:
x = - 7
Step-by-step explanation:
given that the 3 angles in the triangle are congruent, then the triangle is equilateral with the 3 sides congruent , then
x + 16 = 9 ( subtract 16 from both sides )
x = - 7
Answer:
x=-7
Step-by-step explanation:
The triangles sides are all the same in length, therefore, you need all the sides to be equal to 9.
-12+16=4 This addition problem does not equal to 9 so it is not correct.
-7+16=9 This is correct because -7+16 or 16-7 = 9.
-9+16=7 This addition problem does not equal to 9 so it is not correct.
-11+16=5 This addition problem does not equal to 9 so it is not correct.
So, x = -7.
Rewrite the radical by extracting all possible roots and write your answer in radical form 75x4y7−−−−−−√
Answer:
[tex]\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{75x^4y^7[/tex]
Required
Rewrite
Express 75 as 25 * 3
[tex]\sqrt{75x^4y^7} = \sqrt{25 * 3x^4y^7}[/tex]
Split
[tex]\sqrt{75x^4y^7} = \sqrt{25} * \sqrt{3x^4y^7}[/tex]
This gives:
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3x^4y^7}[/tex]
Express y^7 as y^6 * y
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3*x^4 * y^6 * y}[/tex]
Split
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} *\sqrt{x^4} * \sqrt{y^6} * \sqrt{y}[/tex]
Express square roots as exponents
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^{(4 * \frac{1}{2})} * y^{(6* \frac{1}{2})} * \sqrt{y}[/tex]
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^2 * y^3 * \sqrt{y}[/tex]
Rewrite the factors
[tex]\sqrt{75x^4y^7} = 5 * x^2 * y^3* \sqrt{3} * \sqrt{y}[/tex]
[tex]\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3} * \sqrt{y}[/tex]
Combine roots
[tex]\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3y}[/tex]
[tex]\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}[/tex]
What do () mean in math?
Parentheses are employed to indicate changes to the usual order of operations.
Define round brackets.The well-known () symbols, often known as "round brackets," are used in pairs to group things together or designate the order of operations in an equation. You will frequently need to employ brackets in math when forming or resolving equations. They support number grouping and operation definition.
Mention other brackets as well.{}, [] are other type of brackets.
In mathematical expressions, parentheses are employed to indicate changes to the usual order of operations (precedence rules). In an expression like, the portion of the expression enclosed in parentheses,, is first assessed, and the outcome is then incorporated into the remaining portions of the expression.
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How do you write 5 more than a number?
x+5 is the way we can write 5 more than a number.
In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra.
Using the knowledge provided above, we must translate the mathematical statement provided in the question into an algebraic expression. Let's say that number is "x". The result of adding 5 to the provided number is a number that is 5 greater than this number. Thus, a number that is 5 more than x is equal to x+5. As a result, "5 more than a number" is represented by the algebraic expression "x+5".
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80 board game is on sale for 20 percent off
How much is the board game?
Answer:
the answer is 64 dollars or pounds or whichever currency
Answer:
The bord game is 64$.
Step-by-step explanation:
80/10=8
8*(8-2)=
64$
A rectangle frame needs to be constructed so that its width and length are in a ratio of 3:4 and its diagonal is 25 inches. What is the perimeter of the frame?
Answer:
70 inches
Step-by-step explanation:
From the diagram attached,
Assuming the width, lenght and diagonal of the rectangle forms a right angle triangle.
Applying pythagoras theorem,
a² = b²+c²................... Equation 1
Where a = diagonal = 25 inches, b = width = 3x inches, c = length = 4x inches
Substitute these values into equation 1 and solve for x
25² = (4x)²+(3x)²
625 = 14x²+9x²
625 = 25x²
25x² = 625
x² = 625/25
x² = 25
x = √25
x = 5 inches.
Therefore,
Width(w) = 3×5 = 15 inches
Length(l) = 4×5 = 20 inches
Perimeter (P) = 2(l+b)
P = 2(15+20)
P = 2(35)
P = 70 inches
Hence the perimeter of the frame is 70 inches
For what value of n is n-2] + 2 equal to 0?
Answer:
n=0
Step-by-step explanation:
0 - 2 = -2
-2 + 2 = 0
find the area of the shaded regions below. give your answer as a completely simplified exact value in terms of π (no approximations)
Answer:
Step-by-step explanation:
the area of the hemisphere is 1/2 [tex]\pi[/tex][tex]r^{2}[/tex]
the radius is 1/2 the diameter,
the diameter is also the hypotenuse of the isosceles triangle
[tex]d^{2}[/tex] = [tex]4^{2}[/tex]+[tex]4^{2}[/tex]
[tex]d^{2}[/tex] = 32
d =[tex]\sqrt{32}[/tex]
r = 1/2[tex]\sqrt{32}[/tex]
1/2[tex]\pi[/tex](1/2[tex]\sqrt{32}[/tex])^2
1/2[tex]\pi[/tex](1/4*32)
(32/8 )*[tex]\pi[/tex]
4[tex]\pi[/tex] ( the entire upper hemisphere )
area of the triangle is 1/2* 4 *4 = 8
then the exact area of the parts of the circle would be
4[tex]\pi[/tex] - 8
Convert one three fifths to a percent find that percent of 30 Divide your answer by 25% of 16
Answer:
40%
Step-by-step explanation:
1 and 3/5 as a fraction is 8/5 which as a percent is 160%.
25% of 16 is 4
160%/4 = 40%
helppp PLEASEE !!! lol
Answer:
3.14 x 3.8^2 = 45.3416
* find the surface area
hope this helped
Step-by-step explanation:
Answer:
if your going by 3 as pie you would do this:
Step-by-step explanation:
3*3.8*3.8=43.32