The ages of the five family members as required are; 3, 10, 13, 42 and 42.
What are the ages of the five family members?As evident, in the task content, let a, b , c , d , e represents the ages of the family members in ascending order.
Since the median of the ages is; 13, it follows that the the third term, c = 13.
Also, since the mode is 42, it follows that; d = e = 42.
Also, since the range of the ages is 39, it follows that; 42 - a = 39 and consequently a = 3.
Finally, since the mean age is 22; it follows from the mean formula that;
22 = ( 3 + b + 13 + 42 + 42 ) / 5
110 = b + 100
b = 10.
Ultimately, the ages of the five family members as required are; 3, 10, 13, 42 and 42.
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An item has a listed price of 30$. If the sales tax rate is 8%, how much is the sales tax (in dollars)?
Answer:
32.4
Step-by-step explanation:
8% of 30 is 2.4. So, 2.4 + 30 is 32.4.
3
The volume of a sphere is given by V = Tr³, where r is the radius.
Find the inverse function. Describe what it represents.
The inverse function is v⁻¹ = ( v/T)^1/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that the formula of the volume of the sphere is,
⇒ v = 4/3 πr³
T = 4/3π
Now,
To determine the inverse function we can solve the formula for the term r as;
⇒ v = 4/3 πr³
Multiply by 3/4 we get;
⇒ 3v/4 = πr³
Divide by π both side, we get;
⇒ 3v/4π = r³
Substitute r = v⁻¹ in above equation, we get;
⇒ v⁻¹ = ( v/T)^1/3
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if Joaquin bought a lawn mower for $519.20 on a 20% off sale what was the original price of the mower
Answer: The original price of the lawn mower was $649
Step-by-step explanation:
If Joaquin bought the lawn mower for $519.20 after a 20% discount, it means that he paid only 80% of the original price. We can use this information to calculate the original price of the mower by setting up the following equation:
0.8x = 519.20
where x is the original price of the lawn mower. To solve for x, we can divide both sides of the equation by 0.8:
x = 519.20 / 0.8
x = $649
z=-4+5i what is |z|=√
Answer:


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Class 11
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>>The complex number z satisfying the equa
Question

The complex number z satisfying the equations ∣z∣−4=∣z−i∣−∣z+5i∣=0, is
This question has multiple correct options
A
3−i
B
23−2i
C
−23−2i
D
0
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Updated on : 2022-09-05
Solution

Verified by Toppr
Correct options are B) and C)
We have two equation ∣z∣−4=0 and ∣z−i∣−∣z+5i∣=0
Putting z=x+iy i.e x2+y2=16 ....(1)
and ∣x+iy−i∣=∣x+iy+5i∣
⇒x2+(y−1)2=x2+(y+5)2
⇒y=−2 ...(2)
Putting y=−2 in (1),
x2+4=16⇒x=±2
Step-by-step explanation:
Hence the complex numbers z satisfying the given equation are
z1=23−2i and z2=−23−2i
please help!! Describe an octant's main features
An octant's main features are :
Axes Positive and negative regions Quadrants What are the main features of an octant ?An octant is formed by three perpendicular axes, labeled X, Y, and Z. These axes intersect at a common point called the origin. Each octant contains both positive and negative values along the X, Y, and Z axes. The positive region is located on one side of each axis, while the negative region is on the other side.
Each of the three axes divides an octant into two quadrants. These quadrants are numbered from 1 to 8, with quadrant 1 being in the positive X, Y, and Z regions and quadrant 8 being in the negative X, Y, and Z regions.
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……………Help with 22-27…………
The equations of the lines in slope-intercept form are:
22. y = -1/2x + 3.
23. y = 2x - 3.
24. y = -x
25. y = -2x + 4.
26. y = 3/2x - 2.
27. y = 5/2x - 1/2
28. y = x + 3
29. y = -x + 2
30. y = -1/4x + 9/4
How to Find the Equation of a Line in Slope-intercept Form?The equation of a line is y = mx + b, in slope-intercept form, where:
m = slope = rise/run = change in y / change in x
b = y-intercept or the point where the graph intercepts the y-axis.
22. Slope (m) = rise/run = -1/2
y-intercept (b) = 3
Substitute m = -1/2 and b = 3 into the equation, y = mx + b:
y = -1/2x + 3.
23. Slope (m) = rise/run = 4/2 = 2
y-intercept (b) = -3
Substitute m = 2 and b = -3 into the equation, y = mx + b:
y = 2x - 3.
24. Slope (m) = rise/run = -2/2 = -1
y-intercept (b) = 0
Substitute m = -1 and b = 0 into the equation, y = mx + b:
y = -x + 0
y = -x
25. Slope (m) = rise/run = -2/1 = -2
y-intercept (b) = 4
Substitute m = -2 and b = 4 into the equation, y = mx + b:
y = -2x + 4.
26. Slope (m) = rise/run = 3/2
y-intercept (b) = -2
Substitute m = 3/2 and b = -2 into the equation, y = mx + b:
y = 3/2x - 2.
27. Slope (m) = rise/run = 5/2
y-intercept (b) = -0.5 = -1/2
Substitute m = 5/2 and b = -1/2 into the equation, y = mx + b:
y = 5/2x - 1/2
28. Slope (m) = change in y / change in x = (5 - 3) / (2 - 0) = 2/2 = 1
y-intercept (b) = 3
Equation is, y = x + 3
29. Slope (m) = change in y / change in x = (-1 - 4) / (3 -(-2)) = -5/5 = -1
Substitute (x, y) = (3, -1) and m = -1 into y = mx + b, to find b:
-1 = -1(3) + b
-1 = -3 + b
-1 + 3 = b
2 = b
b = 2
The equation would be: y = -x + 2
30. Slope (m) = change in y / change in x = (3 - 2) / (-3 - 1) = 1/-4 = -1/4
Substitute (x, y) = (1, 2) and m = -1/4 into y = mx + b, to find b:
2 = -1/4(1) + b
2 = -1/4 + b
b = 2 + 1/4
b = 9/4
The equation would be: y = -1/4x + 9/4
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How do you find Van t Hoff?
The formula for Van 't Hoff's law, which is also known as the law of osmotic pressure, is: П = iMRT, where: Π is the osmotic pressure of the solution,
i is the van 't Hoff factor, which is a measure of the number of particles a solute molecule dissociates into in solution, M is the molar concentration of the solute, R is the gas constant, and T is the absolute temperature. Van 't Hoff is a term used to refer to a Dutch chemist named Jacobus Henricus van 't Hoff, who was known for his work on solutions, chemical equilibrium, and the laws of thermodynamics. To find Van 't Hoff, you can do any of the following: Research: You can learn about Van 't Hoff by doing research on his life and work. There are many online and offline resources available that provide information about his contributions to chemistry and his scientific achievements. Education: If you are a student of chemistry, you are likely to encounter Van 't Hoff's name in your coursework. You can learn about his theories and concepts in your chemistry classes or by consulting your textbooks. Application: You can apply Van 't Hoff's laws and principles in solving problems related to chemical equilibrium, colligative properties of solutions, and other thermodynamic concepts. This may involve using mathematical formulas and equations that are based on his work. In summary, Van 't Hoff refers to a Dutch chemist known for his work in thermodynamics, solutions, and chemical equilibrium. You can learn about his contributions to chemistry through research, education, and application of his principles in problem-solving.
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A tiling pattern is defined by the pattern rule equation n = 5+ 3p, where p is the
position number and n is the number of tiles. How many tiles would there be in
position 26?
Step-by-step explanation:
n=5+3p
when p=26,
n=5+3×26=83
20. A popular pizza parlor charges $12 for a large cheese pizza plus $1.50 for each additional topping. The
total cost, C, of a pizza with T toppings can be represented by C = 1.50T + 12. What is the domain in
the context of the problem situation?
Answer:
efgdfhncdrt gguhd r g sixtieth sex
Mayerlin has xx dimes and yy nickels. She has no more than 20 coins worth no less than $1.30 combined. Solve this system of inequalities graphically and determine one possible solution.
what are the inequalities?
Answer: look at the image for the answers and solutions
Step-by-step explanation:
The function C approximates the number of calories recommended per day for
a dog, based on the weight, in pounds, of the dog.
The table gives values of C for selected values of p, where C(p) represents the
recommended number of calories per day for a dog that weighs p pounds.
Recommended Number of Calories for Dogs
p (pounds) C(p)
A2.F.BF.A.la
a.
C(x) = 18p +22
b. C(x) = 22p+ 18
?
11
22
33
Which of the equations shown most closely approximates C?
44
55
66
77
88
250
450
750
1000
1250
1500
1700
1880
C.
C(x) = 40(1.06)
d. C(x) = 48(1.07)"
The equation most closely approximates C is C(x) = 22p+ 18.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that function, C calculates the number of calories recommended per day for a dog based on the dog's weight in pounds.
The equation can be written as:-
C(x) = 22p+ 18.
Here the dependent variable is C(x) and the dependent variable is p. So the value of C(x) will always depend upon the variable p.
Therefore, the correct equation will be C(x) = 22p+ 18.
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E = (children who go to the park),
T = {children who play tennis) ,
G = {children who play golf}
120 children go to the park. 50 play tennis. 75 play golf. 25 do not play tennis or golf.
(a) Show this information in the Venn diagram.
(b) How many children play both golf and tennis?
Answer:
125 children play tennis and golf
don't forget to follow me ,
What is the prime factorization of 51?
The prime factorization of 51 is 3 * 17.
What is the value of (2^(2014)+2^(2012))/(2^(2014)-2^(2012))? (A) -1 (B) 1 (C) (5)/(3) (D) 2013 (E) 2^(4024)
The value of the exponential equation is A = 5/3
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = [ 2²⁰¹⁴ + 2²⁰¹² ] / [ 2²⁰¹⁴ - 2²⁰¹² ] be equation (1)
On simplifying the equation , we get
Taking the common factor as 2²⁰¹² , we get
A = 2²⁰¹² [ 2² + 1 ] / 2²⁰¹² [ 2² - 1 ]
On further simplification , we get
A = ( 2² + 1 ) / ( 2² - 1 )
A = ( 4 + 1 ) / ( 4 - 1 )
A = 5/3
Therefore , the value of A is 5/3
Hence , the equation is A = 5/3
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Which inequality represents all the solutions of 4(3x + 2) < 5(3x − 2)? Select the correct answer.
Answer:
x > 6
Step-by-step explanation:
4(3x+2) < 5(3x-2)
12x+8 < 15x-10
12x-15x < -10-8
-3x < -18
3x > 18
x> 6
A car salesman earns 5% on the sale of a BMW sold for $103,100. What is his take home pay that day?
Answer:
$5155
Step-by-step explanation:
We know
A car salesman earns 5% on the sale of a BMW sold for $103,100.
5% = 0.05
What is his take-home pay that day?
We take
103,100 times 0.05 = $5155
SO he takes home $5155.
Step-by-step explanation:
Looks like we're trying to find out what 5% of 103,100 is. We first need to convert the percent into a decimal and then multiply.
[tex]5\% = 0.05[/tex]
Now we can multiply
[tex](0.05)(103100) = 5155[/tex]
line u - Line v, what is the value of x?
Question 9
Triangle ABC has vertices of
A (2,4)
B (3,7)
C (7,4)
What will be the vertices of Triangle A'B'C' after a dilation of k = 2, centered at point A?
A'
B’
C’
I NEED HELP
The coordinates of the triangle after the dilation of k = 2 is given by
A' ( 4 , 8 ) , B' ( 6 , 14 ) and C' ( 14 , 8 )
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as ABC
Now , let the dilated triangle be represented as A'B'C'
And , the coordinates of the triangle ABC are
The coordinate of A = A ( 2 , 4 )
The coordinate of B = B ( 3 , 7 )
The coordinate of C = C ( 7 , 4 )
And , the dilation factor k = 2
So , the new coordinates of the dilated triangle are
The coordinate of A' = A' ( 4 , 8 )
The coordinate of B' = B' ( 6 , 14 )
The coordinate of C' = C' ( 14 , 8 )
Hence , the triangle is dilated by a scale factor of 2
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For what value of x is the given parallelogram a rhombus?
The value of x the given parallelogram a rhombus is 18
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The quadrilateral that is a rhombus
The diagonals of rhombus bisect each other
Using the above as a guide, we have the following:
Angle 1 = A
Substitute the known values in the above equation, so, we have the following representation
5x - 30 = 3x + 6
Evaluate
2x = 36
Divide
x = 18
Hence, the value is 18
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Rewrite in simplest terms: 6(4y+8)−2y
The simplification process of the expression 6(4y+8)−2y involves distributing '6' to '4y' and '8', and then combining like terms, yielding the simplified expression as 22y+48.
Explanation:To rewrite the given expression in simplest terms, distribute the 6 to the terms inside the parentheses:
6 * 4y = 24y6 * 8 = 48Now subtract 2y:
24y + 48 - 2y = 22y + 48So, the expression 6(4y+8)−2y can be simplified to 22y + 48.
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(Likelihood MC)
A collector has items including baseball cards, gold coins, and stamps in a box. If P(gold coin) 50%, interpret the likelihood of randomly selecting a gold coin from the box.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Answer: The likelihood of randomly selecting a gold coin from the box is "Likely."
When the probability of an event is 50%, it means that there is an equal chance of the event happening or not happening. In this case, the probability of randomly selecting a gold coin from the box is 50%, so it is likely to occur.
Step-by-step explanation:
please help!! i’m confused
The method that can be used to prove that the triangles are congruent is B. AAS.
How to prove the congruence ?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
There are two angles in the two triangles that are shown to be equal and there is also a side of one triangle that is equal to anther side. These triangles are therefore congruent.
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Which rational function has the most solutions in common with the function y=2x+6
Answer: Rational functions are defined as the ratio of two polynomials. A rational function has the most solutions in common with the function y = 2x + 6 if their graphs intersect at the most points.
If a rational function has the same degree as the polynomial function y = 2x + 6, which is degree 1, and has a leading coefficient that is the same sign as the leading coefficient of y = 2x + 6, then their graphs will intersect at the most points.
One such rational function that has the same degree as y = 2x + 6 and has a leading coefficient that is the same sign is:
y = (2x + 6) / 1
So the rational function y = (2x + 6) / 1 has the most solutions in common with the function y = 2x + 6.
Step-by-step explanation:
A triangle has integer side lengths 2, 5 and x. What is the median of all possible
values of x?
The median of all possible values of x is 5.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
To find the median of all possible values of x, we need to find all the possible values of x first.
By the triangle inequality, we know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, we can write:
2 + 5 > x
2 + x > 5
5 + x > 2
Simplifying each inequality, we get:
7 > x
x > 3
x > -3
The smallest possible integer value for x is 4 and the largest possible integer value for x is 6.
Therefore, the possible integer values for x are 4, 5, and 6.
Since we have an odd number of values, the median is simply the middle value, which is 5.
Therefore, the median of all possible values of x is 5.
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Show all work to multiply (2+√-25)(4-√-100).
Product of multiplication of (2+√-25) and (4-√-100) is 58.
What are complex numbers?Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1).
For example, 6+7i is a complex number, where 6 is a real number and 7i is an imaginary number.
Given complex numbers
(2+√-25) and (4 -√-100)
√-25 = √(5² . -1) = 5√-1
i = √-1
√-25 = 5i
√-100 = √(10² . -1)
√-100 = 10i
Multiplying both numbers
(2+√-25) . (4 -√-100)
then
= (2 + 5i) . (4 - 10i)
Using FOIL method
(a + b)(c + d) = ac + ad + bc + bd
= 8 - 20i + 20i - 50i²
= 8 - 50i²
i² = -1
= 8 + 50
= 58
Hence, 58 is the product of multiplication of (2+√-25)(4-√-100)
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Graph the line that has a slope of 1/4 and includes the point (0,4).
.
Answer: y = mx+b
y = -1x+1/4
Step-by-step explanation:
Divide 3x³ - 2x² + 4x - 3 by x² + 3x + 3.
The quotient of the division is 3x - 11 with a remainder of 37x + 21
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
Divide 3x³ - 2x² + 4x - 3 by x² + 3x + 3.
Using the long division method of quotient, we have
x² + 3x + 3 | 3x³ - 2x² + 4x - 3
The division steps are as follows
3x - 11
x² + 3x + 3 | 3x³ - 2x² + 4x - 3
3x³ + 9x² + 9
------------------------------------------------
-11x² + 4x - 12
-11x² - 33x - 33
------------------------------------------------
37x + 21
Hence, the quotient is 3x - 11
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Using the Rule of 70, what approximate interest rate would be needed for an investment
of $14,000 to double by the end of 32 years?
A22.49
B 45.7%
C 2.19%
Leo's rent is due a few days before he expects to receive his paycheck from work. He takes out a payday loan for $200 to cover some of his rent and will pay it back when he gets his paycheck. The lender charges $15 for every $100 borrowed, which needs to be paid back in 2 weeks.
Leo needs to pay back a total of $215 in two weeks.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Leo takes out a payday loan for $200 to cover some of his rent and will pay it back when he gets his paycheck and the lender charges $15 for every $100.
Now, (15/100)×100% = 15%.
Therefore, He has to pay back,
[(100 + 15)/100]×200.
= (115/100)×200.
= 1.15×200.
= $230.
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4.) You roll a number cube twice. Find the probability that the first roll shows a five, and then
che second roll shows a six.
The probability of rolling a 5 and then 6 is 1/36
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
Number cube rolled twice
The sample space of each number cube is
Sample space = {1. 2. 3. 4. 5. 6}
From the above entries, we have
P(5) =1/6
P(6) = 1/6
Using the above as a guide, we have the following:
P = 1/6 * 1/6
Evaluate
P = 1/36
Hence, the probability is 1/36
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