Answer:
An algebraic expression for the total amount of money in both accounts is m+2000
Step-by-step explanation:
If there are 2000 dollars in one account and m dollars in the other, the sum of both accounts can be expressed as 2000+m (or m+2000).
which of the following is the simplified expression of 1 minus the quantity 1 over cosecant squared x end quantity question mark
The simplified expression of 1 minus the quantity 1 over cosecant squared x is 1 - 1/cosec^2(x).
The expression 1 minus the quantity 1 over cosecant squared x can be simplified by dividing the 1 over cosecant squared x into its components. The cosecant squared x can be written as 1/cosec x, and then the 1/cosec x can be written as 1/sin x, with the cosecant being the reciprocal of the sine. Therefore, the expression 1 minus the quantity 1 over cosecant squared x can be written as 1 - 1/sin x. To simplify this expression further, the denominator of 1/sin x can be squared, resulting in 1 - 1/sin^2(x). Since the cosecant is the reciprocal of the sine, cosec^2(x) can be substituted for sin^2(x), giving us the simplified expression 1 - 1/cosec^2(x).
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The complete question: which of the following is the simplified expression of 1 minus the quantity 1 over cosecant squared x end quantity question mark 1 - csc^2(x)
Answer:
cos^2x
Step-by-step explanation:
Very simple, 1-1/csc^2 x
= 1-sin^2 x Using the reciprocal Identity 1/csc x = sin x
= cos^2 x Using the Pythagorean Identity 1 - sin^2 x = cos^2 x
therefore, the answer is cos^2 x.
Hope this helped
pt2 , ANSWER ASAP
At a bakery, one customer pays $5.67 for 3 bagels and 4 muffins. Another customer pays $6.70 for 5 bagels and 3 muffins. Let x be the cost (in dollars) of a bagel and let y be the cost (in dollars) of a muffin. Use the system of equations below to determine the cost of 1 bagel and 1 muffin?
3x+4y =5.67
5x+3y=6.7
A. $0.75 for a bagel and $0.89 for a muffin
B. $0.89 for a bagel and $0.75 for a muffin
C. $1.49 for a bagel and $0.23 for a muffin
D. $0.23 for a bagel and $1.49 for a muffin
Find the y-intercept and the x-Intercept of the line below. Click on "None" If applicable.
(a) y-intercept:
(b) x-Intercept:
Answer:
y-int: none, x-int: -1
Step-by-step explanation:
It crossed the x-axis at -1 so the x-int is, you guessed it, -1
As for the y-int assuming that its just a straight line, there is none. It never crosses the y-axis meaning that y-int DNE (or just none in you case)
et S be the set of all positive integers n such that n^2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ?
A. 12
B. 24
C. 48
D. 72
E. 120
Only the integer 12 is a divisor of every other integer which is a part of the set S.
This is a classic problem where we are asked to find such an integer that is going to be a divisor of the above set S of integers. The set S of integers consists of those integers that when squared are both divisible by 24 and 108. Now we know 24 can be written as 2*2*2*3 and similarly 108 can be written as 2*2*3*3*3. The smallest perfect square (n^2) which is a multiple of both 24 and 108 is 2^4*3^4, thus the smallest n is 2^2*3^2 = 36. So, only 12 is a divisor of all integers in S.
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finally, use the midpoint of each slice to determine the height and sketch in the resulting 4 rectangles. use them to approximate ln(2), and write your answer below: can you tell if you are getting an over-estimate or and under-estimate? which of your four estimates gives you the closest answer to the value given by your calculator? select one
The rectangles approximate ln(2) as 0.693. The approximation is an under-estimate, as the rectangles only cover a portion of the graph. The closest estimate is the fourth one, as it is closest to the value given by the calculator.
1. Slice the graph into 4 equal parts by drawing vertical lines at x=0.5, x=1, and x=1.5.
2. Find the midpoints of each slice by calculating the average of the x-values of each slice. The midpoints are x=0.25, x=0.75, x=1.25, and x=1.75.
3. Determine the height of each rectangle at the midpoints. The heights are y=0.253, y=0.572, y=0.854, and y=1.092.
4. Sketch in the rectangles using the midpoints and heights calculated.
5. Approximate ln(2) as the sum of the areas of the four rectangles, which is 0.693. This is an under-estimate.
6. The closest estimate is the fourth one, as it is closest to the value given by the calculator (0.693).
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$14,000 is invested for 2 months at an annual simple interest rate of 13%.
a) You will earn $
in interest (round to the nearest cent).
b) The future value is
(round to the nearest cent).
The simple interest is I = $ 303.33 and the amount after 2 months with rate of 13 % is A = $ 14,303.33
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as I
Let the amount with simple interest be A = P + I
Now , the principal P = $ 14,000
The rate of interest R = 13 %
The number of months = 2 months
The number of years = 2/12 years
Simple Interest I = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
Simple Interest I = ( 14,000 x 13 x ( 2/12 ) ) / 100
On simplifying the equation , we get
Simple Interest I = $ 303.33
Now , the amount after 2 months = P + I
Amount = $ 14,000 + $ 303.33 = $ 14,303.33
Hence , the interest is $ 303.33
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Let A be a 5 by 7 , B be a 7 by 6 and C be a 6 by 5 matrix. How to determine the size of the following matrices ? O AB, BA, O A^TB, BC, O ABC , CA ,O B^TA , BC^T
The matrices matrix A be a 5 by 7 , matrix B be a 7 by 6 and matrix C be a 6 by 5 matrix.
now, we need to determine the size of the matrices
AB = [tex](AB)_{5*6}[/tex]
BA is undefined
[tex]A^{T}[/tex]B is undefined
BC = [tex](BC)_{7*5}[/tex]
ABC = [tex](ABC)_{5*5}[/tex]
CA = [tex](CA)_{6*7}[/tex]
[tex]B^{T}[/tex]A is undefined.
B[tex]C^{T}[/tex] is undefined.
given that
matrix A is [tex]A_{5*7}[/tex]
matrix B is [tex]B_{7*6}[/tex]
matrix C is [tex]C_{6*5}[/tex]
now, we need to determine the size of the matrices
AB multiplication of two matrices
multiplication of two matrices is possible only when B has the same number of columns as rows in A,
[tex]A_{m*n}[/tex]and [tex]B_{n*p}[/tex]
If it is defined as above, then the matrix AB will have m rows and p columns, i.e., A must have n columns and B must have n rows in order for AB to be defined.
[tex](AB)_{m*n}[/tex]
In addition, a matrix gets transposed when columns turn into rows and vice versa.
Thus, if
[tex]A_{m*n}[/tex]⇒[tex](AT)_{m*n}[/tex]
So, for this particular question, we have: [tex]A_{5*7}[/tex], [tex]B_{7*6}[/tex] , [tex]C_{6*5}[/tex]
According to the aforementioned idea, AB is therefore [tex](AB)_{5*6}[/tex] in size.
Additionally, BA and [tex]A^{T}[/tex]B are not defined.
[tex](BC)_{7*5}[/tex]
ABC=(AB)C=A(BC) because matrix multiplication is associative,
[tex](ABC)_{5*5}[/tex]
[tex](CA)_{6*7}[/tex]
[tex]B^{T}[/tex]A is undefined. because they don't have same number of columns in matrix B and rows in matrix A
B[tex]C^{T}[/tex] is undefined. because they don't have same number of columns in matrix B and rows in matrix C
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Rewrite (2+3)+4 using the Associative Law of Addition
Answer:
9 is correct
Step-by-step explanation:
2+3=5+4=9 , believe
Can somone plss help mee
The property used to solve 7r + 2r is distributive property.
What is distributive property?The distributive property states that an expression which is given in form of x (y + z) can be solved as x × (y + z) = xy + xz.
In other words, the distributive property states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers .
Therefore,
7r + 2r
Using distributive law,
7r + 2r = r(7 + 2) = 9r
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suppose 3
1.a+b
2.a-b
3.ab
4.a/b
The range of values for each expression is given as follows:
1. 8 ≤ a+b ≤ 16
2. -6 ≤ a - b ≤ 2
3. 15 ≤ ab ≤ 63
4. 1/3 ≤ a/b ≤ 7/5.
How to obtain the values?For the maximum values, we have that:
Sum and multiplication: a and b have maximum values.Subtraction and division: maximum a, minimum b.For the minimum values, we have that:
Sum and multiplication: a and b have minimum values.Subtraction and division: minimum a, maximum b.Missing InformationThe problem asks for the range of values for each expression, considering 3 < a < 7 and 5 < b < 9.
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Help plss i don’t know an easy way to do this
See the diagram below.
=================================================
Explanation:
Pick two points on this diagonal line. I'll go for (0,-3) and (1,-1)
Apply the slope formula to those coordinates.
[tex](x_1,y_1) = (0,-3) \text{ and } (x_2,y_2) = (1,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - (-3)}{1 - 0}\\\\m = \frac{-1 + 3}{1 - 0}\\\\m = \frac{2}{1}\\\\m = 2\\\\[/tex]
A slope of 2, aka 2/1, means "move up 2, then right 1".
This "up 2, right 1" motion allows us to move from (0,-3) to (1,-1) as shown in the diagram below.
There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple? (Give your answer as a fraction in simplest form.)
The probability that the next fruit is an apple is P = 0.8
How to find the probability?We want to fnind the probability of randomly selecting an apple from the bag.
Remember that the probability is equal as the quotient between the number of apples and the total number of fruit on the bag.
Originally, there are:
4 apples.
3 peaches
2 plums.
The checkout person takes 2 plums and 1 peach, so now there are:
4 apples.
1 peach.
So there are 4 apples and 5 fruits in total
Then the probability of grabing an apple is:
P = 4/5 = 0.8
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in exercises 7\[dash]10, the augmented matrix of a linear system has been reduced by row operations to the form shown. in each case, continue the appropriate row operations and describe the solution set of the original system.
The solution set of the original system is
[tex]$\left[\begin{array}{l}x_1 \\ x_2 \\ x_3 \\ x_4\end{array}\right]=\left[\begin{array}{c}-3 \\ -5 \\ 6 \\ -3\end{array}\right]$[/tex]
What is augmented matrix of linear system?An easier technique to write a set of linear equations is to utilize enhanced matrices. In an augmented matrix, two sides of the matrix are separated by a vertical line that serves as a representation of a succession of equal signs. Each row in the augmented matrix above stands for a different equation.The columns of two matrices are combined to create a new matrix, which is known as an augmented matrix. When using matrices to solve straightforward linear equations, the augmented matrix is a crucial tool. The number of variables in the linear equation is the same as the number of rows in the augmented matrix.
Step 1
We are given with a row reduced matrix form.:
[tex]$$M=\left[\begin{array}{rrrrr}1 & -2 & 0 & 3 & -2 \\0 & 1 & 0 & -4 & 7 \\0 & 0 & 1 & 0 & 6 \\0 & 0 & 0 & 1 & -3\end{array}\right]$$[/tex]
We have to find the solution set using the appropriate steps.
Step 2: The Augmented matrix Form
[tex]$$\left[\begin{array}{cccc}1 & -2 & 0 & 3 \\0 & 1 & 0 & -4 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3 \\x_4\end{array}\right]=\left[\begin{array}{c}-2 \\7 \\6 \\-3\end{array}\right]$$[/tex]
Step 3: System of Equations
[tex]$$\begin{aligned}& x_1-2 x_2+3 x_4=-2 \\& x_2-4 x_4=7 \\& x_3=6 \\& x_4=-3\end{aligned}$$[/tex]
Step 4: The Back-Substitution
From last two rows, we have
[tex]$$\begin{aligned}& x_3=6 \\& x_4=-3\end{aligned}$$[/tex]
Now substitute in row-2, to get value of $x_2$
[tex]$$\begin{aligned}& x_2-4(-3)=7 \\& x_2+12=7 \\& x_2=7-12 \\& x_2=-5\end{aligned}$$[/tex]
Now substitute in row-1, to get value of $x_1$
[tex]$$\begin{aligned}& x_1-2(-5)+3(-3)=-2 \\& x_1+10-9=-2 \\& x_1+1=-2 \\& x_1=-3\end{aligned}$$[/tex]
So,
[tex]$\left[\begin{array}{l}x_1 \\ x_2 \\ x_3 \\ x_4\end{array}\right]=\left[\begin{array}{c}-3 \\ -5 \\ 6 \\ -3\end{array}\right]$[/tex]
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(4+9)+(4·9)=13+36=49
Answer:
(4+9)+(4·9)=13+36=49
Step-by-step explanation:
True
3. Write an equation, using variables, to represent the identities we der
4. Using your knowledge of identities, fill in each of the blanks.
a. 4+5- = 4
b. 25 + 10 = 25
_+16-16 = 45
d. 56-20+ 20 =_____
5. Using your knowledge of identities, fill in each of the blanks.
a. a+b-
=a
d.
-=
b. c-d+d=_
c. e+-f=e
_-h+h=g
The blanks has bee filled by using the correct identities of the algebra.
Explain the term identities?An equality that is certainly part of the values selected for its variables is called an identity. They are used to rearrange or simplify algebraic expressions. The two halves of an identity are, by definition, interchangeable, and we are always free to switch one for the other.Any value that is placed into the variable makes the identity equation always true. How to solve identity equations .Start by grouping like terms together until given any identity equation in a particular set of variables.Part 4:
a. 5 + 5 - 6 = 4
b. 25 - 10 + 10 = 25
c. 24 + 16 - 16 = 24
d. 56 - 20 + 20 = 56
Part 5:
a) a + b - b = a
b) c - d + d = c
c) e + f - f = e
d) g - h + h = g
Thus, the blanks has bee filled by using the correct identities of the algebra.
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The correct question is-
4. Using your knowledge of identities, fill in each of the blanks.
a. 5 + 5 - ___ = 4
b. 25 - ___ + 10 = 25
c. ___ + 16 - 16 = 24
d. 56 - 20 + 20 = ___
5. Using your knowledge of identities, fill in each of the blanks.
a) a + b - ___ = a
b) c - d + d = ____
c) e + ___ - f = e
d) ___ - h + h = g
Joseph has a bag filled with 2 red, 4 green, 15 yellow, and 9 purple marbles. Determine P(not purple) when choosing one marble from the bag.
A. 70%
B. 50%
C. 30%
D. 20%
The probability of randomly selecting a marble that is not purple is 70%, so the correct option is A.
How to find the probability?
We know that there are:
2 red marbles4 green marbles15 yellow marbles9 purple marblesFor a total number of 2 + 4 + 15 + 9 = 30
There are a total of 30 marbles on the bag, the probability of randomly selecting a marble that is not purple, is equal to the quotient between the number of marbles that are not purple and the total number of marbles.
21 marbles are not purple, then the probability is:
P = (21/30)*100%
P = 0.7*100%
P = 70%
The correct option is a.
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There were approximately 3.1 × 10⁸ people in the United States of America in 2010. The average person drank 3.3 × 10³ ounces of soda. Approximately how many total ounces of soda were drank in the USA in 2010?
Answer:
1.023 x [tex]10^{14}[/tex]
Step-by-step explanation:
(3.1 x [tex]10^{8}[/tex])(3.3 x [tex]10^{3}[/tex])
(3.1 x 3.3)([tex]10^{8}[/tex] x [tex]10^{3}[/tex])
10.23 x [tex]10^{13}[/tex] When the bases are the same and we are multiplying we add the exponents
10.23 x [tex]10^{13}[/tex] Is not in scientific notation because 10.23 is larger than 10
1.023 x [tex]10^{1}[/tex] x [tex]10^{13}[/tex]
1.023 x [tex]10^{14}[/tex]
any1 can solve this!?
The area of the shaded region is obtained as (π/√2) units².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The diagram is labelled.
The values for area of z and y needs to be obtained.
The result will be in the form |y| + z as when the integration will be done, y will come out to be negative.
Now, x + z is the area of rectangle ABCD.
Verify whether x and y are equal in magnitude -
[tex]\begin{aligned}& x=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos \theta}{\sin ^2 \theta} d \theta=\left[\frac{-1}{\sin \theta}\right]_{\frac{\pi}{4}}^{\frac{\pi}{2}} \\& =-1-(\sqrt{2}) \\& =\sqrt{2}-1\end{aligned}[/tex]
[tex]\begin{aligned}& y=\int_{\frac{\pi}{2}}^{\frac{3\pi}{4}} \frac{\cos \theta}{\sin ^2 \theta} d \theta=\left[\frac{-1}{\sin \theta}\right]_{\frac{\pi}{2}}^{\frac{3\pi}{4}} \\& =-(\sqrt{2})-(-1) \\& =-\sqrt{2}+1\end{aligned}[/tex]
This is equal to |y| = x.
So, |y| + z is equivalent to writing x + z.
Now the formula for area of rectangle ABCD is -
Area = length × breadth
Area = √2 - [(3π/4) - (π/4)]
Area = √2 - (π/2)
Area = (π/√2)
Therefore, the area is found to be (π/√2) units².
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A scientist has two solutions, which she labeled solution a and b. Each contains salt. She knows that solution a is 60% salt and solution b is 90% salt. She wants to obtain 150 ounces of a mixture that is 65% salt. How many ounces of each solution should be used?
We can start solving the problem by using a system of equations. Let's call the number of ounces of solution a x and the number of ounces of solution b y. From the problem statement, we know that:
x + y = 150 (because the total amount of the mixture is 150 ounces)
0.6x + 0.9y = 0.65(x + y) (because the mixture is 65% salt, and we can find the amount of salt in the mixture by multiplying the percentage by the total amount)
We can use the first equation to solve for one of the variables in terms of the other:
y = 150 - x
Now we can substitute this expression for y into the second equation:
0.6x + 0.9(150 - x) = 0.65(150)
0.6x + 135 - 0.9x = 97.5
-0.3x = -37.5
x = 125
Now we can use the first equation to find the value of y:
y = 150 - x
y = 150 - 125
y = 25
So the scientist should use 125 ounces of solution a and 25 ounces of solution b to obtain 150 ounces of a mixture that is 65% salt.
factot this trinomial. z^2-14Z+45
give answer in this form (z+a)(z+b)
The factor of the trinomial (z² - 14z + 45) are,
⇒ (z - 5) (z - 9)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The function is,
⇒ z² - 14z + 45
Now, We can factorize the trinomial as;
⇒ z² - 14z + 45
⇒ z² - (9 + 5)z + 45
⇒ z² - 9z - 5z + 45
⇒ z (z - 9) - 5 (z - 9)
⇒ (z - 5) (z - 9)
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which of the following is closest to prob that total weight of randomyl selected graperfurits is moret than 3.4 pounds
The probability that the total weight of the three randomly selected grapefruits is more than 3.4 pound will be equal to 0.842.
What is Probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.The likelihood that something will happen is known as probability. By dividing the total number of outcomes by the number of possible ways an event could occur, one can compute probability.The probability is determined as the ratio of likely outcomes to all plausible outcomes of an event. One can represent the percentage of successful outcomes, or x, for an experiment with 'n' outcomes.
From the data given in the question,
x > 3.4 lb
The mean is 1 lb.
The difference from the mean is 0.12 lb.
The z-score will be,
z = (3.4 - 1) / 0.12
z = 20
This is equivalent to an 84.20% or 0.842 probability.
The complete question is,
The weights of grapefruits of a certain variety are approximately normally distributed with a mean of 1 pound and a standard deviation of 0.12 pounds. Use scenario 6-9. what is the probability that the total weight of three randomly selected grapefruits is more than 3.4 pounds?
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find the radius and height of the right-circular cylinder of largest volume that can be inscribed in a right circular cone with radius 6 inches and height 10 inches. answer accurate to 3 decimal place. (volume of a cylinder
The radius of the right circular cylinder is 4 inches and the height is 3.33 inches.
Radius of cone=6inches
height of cone = 10 inches
Let the radius and height of the right circular cylinder be x and y respectively.
According to triangle similarities,
10-y/x=10/6
⇒10-y/x=5/3
⇒30-3y=5x
⇒y=10-5x/3 ----1
The volume of the right circular cylinder is π[tex]r^{2}[/tex]h
v= πx∧2y
substituting the value of y from 1
v= π[tex]x^{2}[/tex](10-5x/3)
v=10πx^{2}- 5x∧3/3
We differentiate volume w.r.t radius
DV/dx= 20πx-5[tex]x^{2}[/tex]
setting derivative = 0
DV/dx= 20πx-5[tex]x^{2}[/tex]=0
5πx(4-x)=0
x=0 , x=4
[tex]D^{2}[/tex]V/Dx =20π-10πx
putting the maximum value of x in the second derivative we get,
X=Radius = 4inches
Y=height= 10-5x/3=3.33 inches
Therefore, The radius of the right circular cylinder is 4 inches and the height is 3.33 inches.
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1. The average annual pay of 4 construction workers is $46,800. Three of the workers earned these annual announcements of pay: $44,200; $47,450; $45,900. What was the annual pay of the fourth worker?
Please answer fast! Thx!
using simple product and quotient, The annual pay of the fourth worker is 49650.
PRODUCT - The outcome of multiplying two or more numbers is the product of those numbers. QUOTIENT - The outcome of dividing two numbers is the quotient of the two numbers.
Formulate the following supplied conditions: 46800 × 4 - 45900 - 44200 - 47450
Make a calculation for the following: 187200 - 45900 - 44200 - 47450.
Add up or subtract 141300, 44200, and 47450.
Calculate the difference or total of 97100 minus 47450.
Calculate the difference or sum: 49650
get the outcome: 49650
The annual pay of the fourth worker is 49650
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Choose the graph that represents the equation below: y = 8x + 4
Answer: Go up 8 and to the right 1 starting at the point (0,4)
Step-by-step explanation: y=mx+b where m=8 (your slope) and b= 4 (your y-intercept)
Use the method of successive differences to determine the next number in the given sequence 3, 7, 17, 33, 55, 83, 117
The next number in the sequence is 151.
What is the successive differences?
The method of successive differences involves finding the differences between consecutive terms in a sequence and using that information to predict the next term in the sequence.
To use this method for the sequence 3, 7, 17, 33, 55, 83, 117:
Find the differences between consecutive terms:
7 - 3 = 4
17 - 7 = 10
33 - 17 = 16
55 - 33 = 22
83 - 55 = 28
117 - 83 = 34
Check if the differences are constant. In this case, they are increasing by 6 each time.
Use this information to predict the next term in the sequence:
117 + 34 = 151
So, the next number in the sequence is 151.
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pls help first to answer all will get brainliest!!
Answer:To show that Lorenz curves are always concave up on the interval [0, 1], we can use the definition of a Lorenz curve, which is L(x) = xp. Taking the second derivative of L(x) with respect to x gives us L''(x) = p. Since p is always greater than 0, L''(x) is always greater than 0. This means that L(x) is always concave up on the interval [0, 1].
Table of Lorenz values for p = 1.2, 1.5, 2.1, 2.5, 3, and 5:
a. The value of p that corresponds to the most equitable distribution of wealth is 1, as this would mean that the proportion of wealth held by each portion of the population is equal.
b. The value of p that corresponds to the least equitable distribution of wealth is 5, as this would mean that a small portion of the population holds a large proportion of the wealth.
The Gini Index is a measure of income inequality, where a value of 0 represents perfect equality (everyone has the same income) and a value of 1 represents perfect inequality (one person has all the income). The Gini Index is calculated as the ratio of the area between the Lorenz curve and the line of equality to the total area beneath the line of equality.
To find A and B for the Gini index we can use the following integral:
A = ∫(L(x) - x) dx from 0 to 1
B = ∫(x - L(x)) dx from 0 to 1
We can then solve the integral for each specific function of L(x) = xp to find the specific value of A and B.
Step-by-step explanation:
Answer:....
Step-by-step explanation:
the sum of two numbers is 51. the larger number is 21 more than the smaller number. what are the numbers ?
larger number: ?
smaller number: ?
The smaller number is 15 and the larger number is 36.
Let x and y be the smaller and larger numbers, respectively.
From the given information, we know:
y = x + 21 (because the larger number is 21 more than the smaller number)
x + y = 51 (because the sum of the two numbers is 51)
We can substitute the first equation into the second equation to find the value of x:
x + (x + 21) = 51
x + x + 21 = 51
2x = 30
x = 15
Now that we know the value of x, we can use the first equation to find the value of y:
y = x + 21
y = 15 + 21
y = 36
So the smaller number is 15 and the larger number is 36.
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Lena must choose a number between 61 and 107 that is a multiple of 3, 5, and 9. Write all the numbers that she could choose. If there is more than one number, separate them with commas.
Answer: the answer is 90
Step-by-step explanation:There is only one number between 61 and 107 that is a multiple of 3, 5 and 9. So that number will be 90.
Murphy buys 5 bottles of water For $2.50 each and 3 sandwiches for $3.25 each. How much does murphy spend?
The amount Murphy spent is solved to be $22.25
How to solve for the amount Murphy spentTo calculate the amount Murphy spent the cost of the items and the units bought should be known. The calculation is done using the formula
= units bought * cost of each unit
From the question, we can deduce that
Murphy buys 5 bottles of water For $2.50 eachunits bought = 5
cost of each = $2.50
amount spent = 5 * $2.5 = $12.5
Murphy buys 3 sandwiches for $3.25units bought = 3
cost of each = $3.25
amount spent = 3 * $3.25 = $9.75
Total amount spent = spending for bottle water + spending for sandwiches
Total amount spent = $12.5 + $9.75
Total amount spent = $22.25
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segment AB, which is 25 inches long, is the diameter of a circle. chord PQ meets AB perpendicularly at C, where AC = 16 inches. find the length of PQ.
In circle the length of PQ = 24 inches.
What is Circle?
A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the centre. The line of reflection symmetry is formed by each line that traverses the circle. Additionally, it possesses rotational symmetry around the centre for each angle.
Since AB= 25 inches and AC = 16 inches then
=> BC = AB-AC = 25-16 = 9 inches.
∠APB is a right angle because it is inscribed in a semicircle.
The three right triangles ᐃAPB, ᐃACP and ᐃPCB are all similar
because their corresponding angles are equal. Therefore
=> [tex]\frac{AC}{PC}=\frac{PC}{BC}[/tex]
=> [tex]\frac{16}{PC}=\frac{PC}{9}[/tex]
=> [tex]PC^2 = 25*9 = 144 = 12^2[/tex]
=> PC = 12 inches
By symmetry , PC = QC then,
=> PQ = 12*2 = 24 inches.
Hence the length of PQ is 24 inches.
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