Answers
Therefore , the solution of the given problem of function comes out to be 4 log2 + 3/4 is the are required.
What is meant by the word function?A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.
Here,
Given :
=> f(x) = x.2ˣ
=>A = [tex]\int\limits^2_{-1} x.2^{x}[/tex]dx
=> A = [tex]2^{x} \int\limits^2_{-1} x. + x\int\limits^2_{-1} 2^{x}[/tex]
=> [ xlog2 + x²/2 + x²log2 ]₋₁²
=> log2 + 3/4 + 3log2
=> 4 log2 + 3/4
Therefore , the solution of the given problem of function comes out to be 4 log2 + 3/4 is the are required.
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Related Questions
Regan has Rs.10,000 in total. He lent a part of it to Sandip and the remaining to Saline. If Saline paid Rs.2160 more interest than Regan at the end of 3 years and at the rate of 18% simple interest rate. Find how much money did Regan give to Sandip and Saline. (Assume 365 days in a year)
Answers
The Rs. 10,000 Regan lent to Sandip and Saline and the Rs.2160 more interest Saline paid than Sandip after 3 years at an 18% simple interest rate, indicates by expressing the amounts using equations, that the amount Regan gives to Sandip and Saline is Rs. 3,000 and Rs. 7,000 respectively.
What is an equation?An equation is the presentation of a statement of the equivalence between quantities, or expressions, by joining the expressions with a '=' sign.
The amount Regan has = Rs. 10,000
Let x represent the amount Regan lent to Sandip, we get;
The amount Regan lent to Saline = 10,000 - x
The interest rate of the loan Regan lent to Sandip and Saline = 18% simple interest
The interest Saline paid to Regan after 3 years, using simple interest = Rs. 2160 + The interest Saline paid to Regan
The simple interest formula is; I = P·R·T/100
Where;
P = The principal amount loaned
R = The interest rate = 18%
T = The time or duration of the loan = 3 years
Therefore;
(10000- x) × 18/100 × 3 = 2160 + x × 18/100 × 3
5400 - 0.54·x = 2160 + 0.54·x
5400 - 2160 = 0.54·x + 0.54·x = 1.08·x
3240 = 1.08·x
x = 3240 ÷ 1.08 = 3000
The amount Regan lent to Sandip, x = Rs. 3000
The amount Regan lent to Saline = 10,000 - x
x = 3000
10,000 - x = 10,000 - 3000 = 7,000 (substitution property)
The amount Regan lent to Saline = Rs. 7,000
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Wyatt says that 0.6 has the same value as 0.600 do you agree explain
Answers
Answer:
Yes, the zeros can be used as place holders. When using place holders, the value does not change.
Find the volume of the pyramid.
7 m
12 m
The volume is
16 m
cubic meters.
Answers
The value of volume of pyramids is 448 cubic meter.
How to calculate volume of pyramid?A triangular pyramid's volume can be calculated using the formula Volume= 1/3 Base area Height. The side, height, and slant height of a triangular pyramid are the three parameters needed to calculate its surface area.
The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."
Given,
Length=12m
Width=7m
height=16m
volume =l * w * h / 3
= 12*7*16/3
= 448 cubic meter
Therefore volume of pyramid is 448 cubic meter .
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Seacausus stadium has a seating capacity for 25,000 spectators. The stadium has 25 exits and can be vacated in 20 minutes. The time taken to exit the stadium varies directly with the number of spectators and inversely with the number of exits. Determine the time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional.
Answers
The time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional is 28 minutes
How to determine the time taken for 21,000 spectators to vacate the stadium?
A variation is a relation between a set of values of one variable and a set of values of other variables
Let E, N and T represent the number of exits, the number of spectators and the time taken to exit the stadium respectively
We can write the variation as:
T α N/E
T = kN/E (where k is constant of proportionality)
when N = 25,000, E = 25, T = 20:
T = kN/E
k = TE/N
k = (20×25)/25000 = 0.02
when N = 21,000 and E = 15:
T = kN/E
T = (0.02×21,000)/15 = 28 minutes
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what’s the perimeter of a rectangle that’s
6m
6m
9m
9m
Answers
Answer:
30
Step-by-step explanation:
perimeter is the outside of a shape so just add them all together honestly
Line g has an equation of y= 1/3x–1. Parallel to line g is line h, which passes through the point (10,2). What is the equation of line h?
Answers
Y-2=1/3x-10/3 move -2 to the other side by adding both sides by 2
Y=1/3x-10/3+2 add like terms
Then Y=1/3x-4/3 is your answer
The difference between ( -7×-7) + -(7×7) is
A)98. B)28
C)0. D)-28
Answers
To find the difference between (-7*-7) + -(7*7), we first need to calculate the values of each expression.
(-7*-7) = 77 = 49
-(77) = -49
The difference between these two values is 49 - (-49) = 49 + 49 = 98.
Therefore, the answer is A) 98.
The Correct answer is Option (A) = 98.
We need to determine the value of each part and calculate their difference. after that.
Here, (-7*-7)= 49
and, -(7*7) = -49
Now, their difference is to be calculated as follows:
=49 - (-49)
= 49+ 49
= 98.
So, the answer is 98.
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7x-2y=10 slope intercept form
Answers
Answer:
7/2
Step-by-step explanation:
7x – 2y = 10
using ( y = mx + b) as our guideline
where m is the slope
7x – 2y = 10
subtract 7x from both sides
7x – 7x – 2y = 10 – 7x
–2y = 10x – 7x
when arranged in slope form
–2y = –7x + 10
divide both sides by (–2) to get y
[tex] \frac{ \\ - 2y}{ - 2} = \frac{ - 7x}{ - 2} + \frac{10}{ - 2} [/tex]
[tex]y = \frac{ \\ 7y}{2} - 5[/tex]
[tex]the \: slope \: will \: be \: \frac{ \\ 7}{2} [/tex]
This is our answer.
i hope i
What is the pattern?
Answers
A photographer plans to frame photos that measure
7 inches long and 6 inches wide. Because his
frames are larger than the photographs, he will
make a mat of uniform width to fill the area between
the photograph and the frame.
Define a unit for each quantity in the worksheet.
Then enter a variable for the mat width and use
this variable to write expressions for the other
quantities.
Answers
A unit for each quantity in the worksheet for the mat width are 5.357 inches.
How is the area of a rectangle calculated?The size of a rectangle. A = l × b. Once the length and width are known for any rectangle, the area may be determined. The area of the rectangle is calculated as a square-unit dimension by multiplying length and width.
How do you determine the size of a rectangle frame?Add the height and the width together to get the area of a rectangle. Given that each side of a square is the same length, all you need to do to determine its area is multiply the length of one of its sides by itself.
Length = 7 inches
Width = 6 inches
Area of photograph = length width = 7 6 = 42
Total area of photograph and frame = 84
frame length ( 7 + 2x)
frame width ( 6 + 2x)
Total area = Total area of photograph and frame
( 7 + 2x) ( 6 + 2x) = 84
2 + 13x - 21 = 0
x = 5. 357
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What is negation example?
Answers
Let's say we have an expression P^A then the negation of P^A will be not( P^A ). This is an example of negation.
As the name suggests negation means the negative of a term or expression and it comes under the branch of mathematical logical reasoning.
When not word is added in front of an expression it becomes the opposite , this is how we negate something. A statement is only admissible if it is always true or always false.
It is sometimes required in mathematics to find the inverse of a particular mathematical statement, this is when negation is used. Negation thus, refers to the process of determining the inverse of a given assertion.
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1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
Answers
x = 6 does not satisfy the given equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that an equation, 5(x – 3) = x + 13
Checking if x = 6 satisfy the equation or not,
5(x – 3) ? x + 13
5(6-3) ? 6+13
5×3 ? 19
15 ≠ 19
Hence, x = 6 does not satisfy the equation.
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1. If triangle ABC has the following measurements, find the measure of angle A. a = 17 b = 21 C = 25 42.3° 137.7° 56.2° 81.5°
Answers
Answer: Triangle ABC is a right triangle, because it satisfies the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
c^2 = a^2 + b^2
25^2 = 17^2 + 21^2
625 = 289 + 441
625 = 730
Since it is a right triangle, angle A is the angle opposite side a, which is the side that is the length of 17.
A right triangle also has one angle which is always 90 degree, that is the angle opposite the hypotenuse, so the remaining angle is A, which is 90- angle C, which is
90 - 42.3 = 47.7 degree.
Therefore the measure of angle A is 47.7°
So the correct answer is C. 42.3°
Step-by-step explanation:
4x(3 +5) Please answer :(
Answers
Answer: 32x
Step-by-step explanation:
4x (3 + 5)
add 3 and
⇒ 4x (8)
⇒ 32x answer .
hope that helps...
How do you solve longest side?
Answers
The cosine rule tells us
The third side (or c lets say):
c^2 = a^2 + b^2 - 2ab•cos(A)
i need the correct answer only 2 try’s and due in 15 min
Answers
The sample space between A to C is A,B,C
What is the probability?The likelihood that a sample point will occur is quantified by its probability.
The likelihood of a sample point
According to tradition, statisticians have adopted the following guidelines.
Any sample point's probability can be between 0 and 1.
The probability of every sample point in a sample space added together is 1.
Let's say we run a straightforward statistical experiment. One coin is flipped. Heads or tails are the possible results of the coin flip. These results taken as a whole serve as our experiment's sample space. Each result stands in for a single sample point in the sample space. What is each sample point's probability?
Solution: the total of all sample points' probability
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Can anyone help me solve this equation: x^{2} +5x+6=0
Answers
Answer: x= -2, -3
Step-by-step explanation: Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Is the inverse of every linear function also a function?
Answers
In most cases, the inverse of a linear function is also a linear function.
What is a linear function?The term "linear function" in mathematics applies to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.
Here, stands for the line's gradient and b for the y-axis intercept (which is sometimes called the vertical intercept).
These functions' graphs are mirror images of one another when viewed along the line y=x.
As a result, the points on the graph of f(x) are the points on the graph of f(x) that have been turned around.
A linear function's inverse is typically also a linear function.
Therefore, in most cases, the inverse of a linear function is also a linear function.
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1/5t + 2 - 2 = 17 - 2
Answers
Answer:
[tex]t=75[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{5} t+2-2=17-2[/tex]
Lets solve for [tex]t[/tex].
Subtract 2 from 2.
[tex]\frac{1}{5} t=17-2[/tex]
Subtract 2 from 17.
[tex]\frac{1}{5} t=15[/tex]
Combine [tex]\frac{1}{5}[/tex] and [tex]t[/tex].
[tex]\frac{t}{5} =15[/tex]
Multiply both sides of the equation by 5.
[tex]\frac{t}{5}*5 =15*5[/tex]
[tex]t=75[/tex]
solve for x and graph the solution on the number line below 7+x<16
Answers
Step-by-step explanation:
x<16-7x<11.....................
I need to know how to solve e,d,f im so confused it’s about angles in a circle
Answers
When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.
what is circle ?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about the center at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.
given
in 6th figure
61° + 52° + x = 180° ( sum of exterior angle )
113° + x = 180°
x = 67°
y = 67°
When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.
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a number is at least 16
Answers
SO MANY POINTS
Each of the problems below describes two different games you can play with a random number generator. In each case, you will win if the random number generator gives you the indicated kind of number. Find the theoretical probability that you win each game below. Decide and justify whether Game I or Game II in each part, (a) through (c), gives you a better chance of winning.
Picking a prime number from the integers between 1 and 20
Picking a multiple of from the integers between 1 and 20
Picking a multiple of from the integers between 1 and 40
Answers
b. In Game I, you have a theoretical probability of winning of 8/20 or 0.4. In Game II, you have a theoretical probability of winning of 0/20 or 0. Therefore, Game I gives you a better chance of winning.
c. In Game I, you have a theoretical probability of winning of 8/40 or 0.2. In Game II, you have a theoretical probability of winning of 0/40 or 0. Therefore, Game I gives you a better chance of winning.
Answer:
Game 1
Equal chance
Game 2
Step-by-step explanation:
A BETTER CHANCE OF WINNING
Each of the problems below describes two different games you can play with a random number generator. In each case, you will win if the random number generator gives you the indicated kind of number. Find the theoretical probability that you win each game below. Decide and justify whether Game I or Game II in each part, (a) through (c), gives you a better chance of winning.
Game I
a.Picking a prime number from the integers between 1 and 20
b.Picking a multiple of 5 from the integers between 1 and 20
c.Picking a multiple of 7 from the integers between 1 and 40
Hint:
Find the percent chance that each event will occur and compare the results.
a.Picking a prime number from the integers between 21 and 40
b.Picking a multiple of 5 from the integers between 1 and 40
c.Picking a multiple of 6 from the integers between 1 and 25
Answer:
Game 1
Equal chance
game 2
If f(x) =x - 5 and g(x) = 2x + 3, find values for each of the following.
a. f(g(1)) =
b. g(f (2)) =
c. g(g(0)) =
d. (f 0 9) (-2) =
e. (g o f) (3) =
f. (f o f) (-1) =
Answers
When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.
what is function ?Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions
given
a) f(g(1)
g(1) = 5 and f(g(1)) = 0
b) g(f (2))
f(2) = -3
g(f (2)) = -2
so When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.
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An art store manager buys easels for 10.20 each. He marks up the cost by 75% to get the selling price. What is the selling price of each easel
Answers
Answer:
17.85
Step-by-step explanation:
175% * 10.20 = 17.85
Four more then the quotient of 12 and a number x
Answers
Use to convert the expression into a fraction
Expand the fraction to get the least common denominator
Use the commutative property to reorder the terms
Any expression multiplied by remains the same solution= 4x+12/x
A) A sequence is defined using this term-to-term rule.
Un+1 = 2un+ 20
If uy = 8, find u2
b) Another sequence is defined using this term-to-term rule,
unty = ku,+r
where k and rare constants.
Given that u, = 37, uz = 188 and ug = 943, find the value of k and
the value of r.
Answers
The Value of the two constants K and R are 5 and 3 respectively.
a) To find u2, you can substitute u1 = 8 into the term-to-term rule to get:
u2 = 2u1 + 20 = 2(8) + 20 = 36
So u2 = 36.
b) To find the values of k and r, you can use the given values of u1, u2, and u3 to set up a system of equations. Using the term-to-term rule:
u2 = ku1 + ru3 = ku2 + rSubstituting in the given values:
u2 = 188 = k(37) + ru3 = 943 = k(188) + rSolving for r and k, we get:
k = 5 and r = 3.
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2x + 2y = -10
What is the slope and y intercept?
Answers
Answer:
Slope: -1; y-intercept: -5
Step-by-step explanation:
Given:
2x + 2y = -10
Question:
What is the slope and y intercept?
Work:
The "template" for the slope of a line is: y = mx + b. "m" is the slope, "x" is a variable, and "y" is the y-intercept.
2x + 2y = -10 (We need to get 2x on the other side so lets subtract 2x on both sides since subtraction is the inverse of addition)2y = -2x - 10 2y = -2x - 10 (We are almost done. Now, all we need to do is get rid of the 2 that is the coefficient of the variable "y" and we are done.)y = -x - 5y = -x - 5 (The y-intercept is -5 and the slope is -1)Answer: Slope = -1; y-intercept = -5Hope this helped! :D
Mr.Parrillo’s class has adopted a section of a highway to keep clean.If 1/3 of the section is 3/4 how long is the whole section
Answers
The whole section is 9/4 unit.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Mr.Parrillo’s class has adopted a section of a highway to keep clean.
1/3 of the section is 3/4.
To find the length of the whole section:
Multiply by 3.
So,
The length of the whole section = 3 (3/4)
The length of the whole section = 9/4
Therefore, 9/4 unit is the length.
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What are the 3 names of angles?
Answers
Angles are classified into three. They are acute angles, obtuse angle and right angle.
Therefore the three names of angles are - acute angles, obtuse angle and right angle.
Acute angles are angles that measure less than 90 degrees. They are smaller than a right angle and are often described as "sharp."
Right angles are angles that measure exactly 90 degrees. They are often represented by a square corner or the letter "L" shape.
Obtuse angles are angles that measure greater than 90 degrees but less than 180 degrees. They are larger than a right angle and are often described as "blunt."
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