Perform the operation given that a = {−3, −2, −1, 0, 1, 2, 3}, b = {−4, −2, 0, 2, 4}, and c = {0, 1, 2, 3, 4}. (enter your answers as a comma-separated list.) b ∪ (a ∩ c)
Final answer:
The operation b \\u222a (a \\u2229 c) combines the unique elements of set b with the intersection of sets a and c, resulting in the set {-4, -2, 0, 1, 2, 3, 4}.
Explanation:
The student is asked to perform the operation b \\u222a (a \\u2229 c), given three sets a, b, and c. To do this, we need to first find the intersection of sets a and c, which is the set of elements that are both in a and in c. Then we find the union of set b with this intersection, which includes all the elements that are either in b or in the intersection of a and c.
Set a: {-3, -2, -1, 0, 1, 2, 3}
Set b: {-4, -2, 0, 2, 4}
Set c: {0, 1, 2, 3, 4}
First, find the intersection: a \\u2229 c = {0, 1, 2, 3}.
Next, find the union with set b: b \\u222a (a \\u2229 c) = {-4, -2, 0, 1, 2, 3, 4}.
The final result is the set {-4, -2, 0, 1, 2, 3, 4}, which contains all unique elements from both sets b and the intersection of a and c.
On Monday, 490 students went on a trip to the zoo. All 8 buses were filled and 10 students had to travel in cars. How many students were in each bus?
How to solve an expression with variables in the exponents?
Answer:
use logarithms
Step-by-step explanation:
Taking the logarithm of an expression with a variable in the exponent makes the exponent become a coefficient of the logarithm of the base.
__
You will note that this approach works well enough for ...
a^(x+3) = b^(x-6) . . . . . . . . . . . variables in the exponents
(x+3)log(a) = (x-6)log(b) . . . . . a linear equation after taking logs
but doesn't do anything to help you solve ...
x +3 = b^(x -6)
There is no algebraic way to solve equations that are a mix of polynomial and exponential functions.
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Some functions have been defined to help in certain situations. For example, the "product log" function (or its inverse) can be used to solve a certain class of equations with variables in the exponent. However, these functions and their use are not normally studied in algebra courses.
In any event, I find a graphing calculator to be an extremely useful tool for solving exponential equations.
To solve an expression with variables in the exponents, you apply the rules of exponents.
Explanation:When solving an expression with variables in the exponents, you need to apply the rules of exponents. Here are the key rules:
For example, (27x^3)(4x^2) can be simplified to 108x^5.
6b^2-13+6=0 Quadratic equations by factoring
You buy 8 gallons of gasoline at p dollars per gallon and pay $23.20. Write an equation to find the price of one gallon of gasoline. Then find the price of one gallon of gasoline.
Answer:
The price of 1 gallon of gasoline is $2.90.
Step-by-step explanation:
You buy 8 gallons of gasoline at p dollars per gallon and pay $23.20.
We get the expression:
[tex]8p=23.20[/tex]
We can find one gallon as: p=[tex]\frac{23.20}{8}[/tex]
=> p = $2.90
Hence, the price of 1 gallon of gasoline is $2.90.
Three friends were born in consecutive years. The some of their birth years is 5982.find the year in which each person was born
one of the advantages to an employer of pay employees piece-rate or commissions is that the employees paid based solely on their performance what is one disadvantage of this type of pay
Disadvantages of the Piece-Rate Pay System:
Hindered Production -- It's virtually impossible to predict how much product can be created within a set time under this system, because the system doesn’t easily lend itself to regulating and encouraging a production line.
Sick or Injured Workers -- Working for piece-rate pay means that workers might come to work when they are ill, thereby risking the health of their coworkers. This could shut down or seriously reduce production output. Additionally, depending on the materials and equipment, if workers are working too quickly in an attempt to produce more, workers could potentially injure themselves, which could open up the company to liability.
Reduced Quality -- When the focus is on quantity, the output the quality may suffer. Such a system requires dedicated employees who are determined to learn their craft thoroughly and then to increase the output. Employees are human, however, and it can be difficult to work at a rapid pace over a long duration. This can mean that employees may continue to work at a rapid pace but that production may produce items of reduced quality.
(edge 22)
sarah competes in a long jump competion. her first jump is 4.25m. her best jump is 12% more than this. however, her best jump is 15% lower than the winning jump. work out the of the winning jump.
The winning jump is approximately 5.60 meters.
1. We start by denoting Sarah's first jump distance as [tex]\( x \)[/tex] meters.
2. We calculate Sarah's best jump distance, which is 12% more than her first jump, giving [tex]\( 1.12x \).[/tex]
3. We know Sarah's best jump is 15% lower than the winning jump, so we set up an equation equating her best jump to 0.85 times the winning jump.
4. Solving for the winning jump, we find [tex]\( \frac{1.12x}{0.85} \).[/tex]
5. Substituting the value of Sarah's first jump [tex](\( x = 4.25 \))[/tex], we find that the winning jump is approximately 5.60 meters.
Let's denote Sarah's first jump distance as [tex]\( x \)[/tex] meters.
According to the problem:
- Sarah's best jump is 12% more than her first jump: [tex]\( 1.12x \).[/tex]
- Sarah's best jump is 15% lower than the winning jump.
Let's calculate Sarah's best jump distance:
[tex]\[ \text{Best jump} = 1.12x \][/tex]
Now, let's find the winning jump distance:
[tex]\[ \text{Best jump} = 0.85 \times \text{Winning jump} \][/tex]
Since Sarah's best jump equals 0.85 times the winning jump:
[tex]\[ 1.12x = 0.85 \times \text{Winning jump} \][/tex]
To find the winning jump distance, we'll divide Sarah's best jump by 0.85:
[tex]\[ \text{Winning jump} = \frac{1.12x}{0.85} \][/tex]
Now, let's substitute the value of Sarah's first jump:
[tex]\[ \text{Winning jump} = \frac{1.12 \times 4.25}{0.85} \][/tex]
[tex]\[ \text{Winning jump} = \frac{4.76}{0.85} \][/tex]
[tex]\[ \text{Winning jump} \approx \frac{4.76}{0.85} \][/tex]
[tex]\[ \text{Winning jump} \approx 5.60 \][/tex]
So, the winning jump is approximately 5.60 meters.
Complete question
sarah competes in a long jump competion. her first jump is 4.25m. her best jump is 12% more than this. however, her best jump is 15% lower than the winning jump. work out the of the winning jump.
4[(6 - 1) + 3(5 - 2)] 44 46 56
The numerical expression 4[(6 - 1) + 3(5 - 2)] evaluates step-by-step following the order of operations. Operations within the parentheses are performed first, followed by multiplication, resulting in a final answer of 56
The student's question involves evaluating a numerical expression, which is a concept in mathematics. We have the expression 4[(6 - 1) + 3(5 - 2)] and want to calculate its value step by step following the order of operations:
First, perform the operations inside the parentheses: (6 - 1) = 5 and (5 - 2) = 3.Next, multiply by 3 within the parentheses: 3(5 - 2) becomes 3 * 3 = 9.Now, add the results within the square brackets: 5 + 9 = 14.Finally, multiply the result by 4: 4 * 14 = 56.Hence, the correct answer to the expression is 56
1. The price of a set of luggage was reduced by $35 for a pre-holiday sale. After the holiday, the set's price tag was marked with an additional discount of 35% of the price during the pre-holiday sale. Let P represent the price of the set of luggage before the sale Which of the following gives an expression representing the price of the set of after the holiday and the final price of the set, if it's original price P was $200?
a) P-0.35*(P-35); $107.25
b) 0.65*(P)-35; $107.25
c) 0.65*(P-35; $107.25
d) 0.65p-22.75; $95.00
what is the simplified form of the following expression 7m2+6.5n-4n+2.5m2-n
Answer:
The simplified form of the provided expression is [tex]9.5m^2+1.5n[/tex].
Step-by-step explanation:
Consider the provided expression.
[tex]7m^2+6.5n-4n+2.5m^2-n[/tex]
Arrange the like terms together.
[tex]7m^2+2.5m^2+6.5n-4n-n[/tex]
Add and subtract the like terms as shown below:
[tex]9.5m^2+1.5n[/tex]
Thus, the simplified form of the provided expression is [tex]9.5m^2+1.5n[/tex].
Danielle's basic cell phone rate each month is $29.95. Add to that $5.95 for voice mail and $2.95 for text messaging. This past month Danielle spent an additional C dollars on long distance. Her total bill was $77.70. How much did Danielle spend on long distance?
Choose the point slope form of the equation below that represents the line passing through the point (-6,4) and (2,0)
Answer: [tex]y=\dfrac{-1}{2}(x-2)[/tex]
Step-by-step explanation:
The equation of a line passing through points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Given : The points from which line is passing : (-6,4) and (2,0)
Then , the equation of the line, in point slope form, that passes through (-6,4) and (2,0)will be :-
[tex](y-(0))=\dfrac{4-0}{-6-2}(x-2)\\\\\Rightarrow\y=\dfrac{4}{-8}(x-2)\\\\\Rightarrow\ y=\dfrac{-1}{2}(x-2)[/tex]
Which of the following is the largest volume? 4.5 x 102 m3 4.5 x 107 cm3 4.5 x 104 dm3 5.0 x 108 mm3 (the 100's are actually 10^2 and other numbers)
if a line is tangent to a circle,then it is perpendicular to the radius drawn to that point of tangent.
Use the square root property of equality to solve (x – 3)2 = –4
Answer:
3+2i
Step-by-step explanation:
Mr. Miller owns two hotels and is ordering towels for the rooms. He ordered 27 hand towels and 48 bath towels for a bill of $540 for the first hotel. He ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel. What is the cost of one hand towel and one bath towel?
This question is based on the concept of solving a two linear equation.
Thus, the cost of one bath towel is $9 and one hand towel is $4.
Given:
Number of ordered of hand towels is 27 and bath towels is 48 and for a bill of $540 for the first hotel.
Number of ordered of hand towels is 50 and bath towels is 24 and for a bill of $416 for the other hotel.
We need tom determined the cost of one hand towel and one bath towel.
According to the question:
Let the hand towels be h and bath towels be b.
Therefore, equation of first hotel is
27h + 48b = 540........(1)
Equation of second hotel is
50h + 24b = 416.........(2)
Now, solving both equation for h and b.
Equation (2) multiplying by -2.
-100 h -48 b = - 832..................(3)
Now, solve equation (1) and (3)
27h + 48b = 540 and -100h - 48b = - 832
⇒ -73 h = - 292
⇒ h = -292 / -73
⇒ h = 4
Therefore, the cost of 1 hand towel is $4.
Now, putting the value of h = 4 in equation (1).
⇒ 27(4) + 48b = 540
⇒ 108 + 48b = 540
⇒ 48b = 540 - 108
⇒ 48b = 432
⇒ b = 432/48
⇒ b = 9
Therefore, the cost of 1 bath towel is $9.
Thus, the cost of one bath towel is $9 and one hand towel is $4.
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After 5 years, Rachel’s amount in her savings account is $7446.52. Her account earned interest at 4.32% APR and was compounded daily. How much did she invest?
Simplify 2x^4y^5 * 3x^5y^7z^3
Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?
Answer:
f(x) intersect the x-axis ate ( 4 , 0 ) and ( -1/3 , 0)
Step-by-step explanation:
Given function, [tex]f(x)=3x^2-11x-4[/tex]
We need to find this function cuts x-axis at what point.
let, [tex]y=3x^2-11x-4[/tex]
We know that points on x-axis has y-coordinate equal to 0.
So, we put y = 0 to find value of x.
By putting y = 0, we get
[tex]0=3x^2-11x-4[/tex]
[tex]3x^2-11x-4=0[/tex]
solving by quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-11)\pm\sqrt{(-11)^2-4\times3\times(-4)}}{2\times3}[/tex]
[tex]x=\frac{11\pm\sqrt{121+48}}{6}[/tex]
[tex]x=\frac{11\pm\sqrt{169}}{6}[/tex]
[tex]x=\frac{11\pm13}{6}[/tex]
[tex]x=\frac{11+13}{6}\:\:and\:\:x=\frac{11-13}{6}[/tex]
[tex]x=\frac{24}{6}\:\:and\:\:x=\frac{-2}{6}[/tex]
[tex]x=4\:\:and\:\:x=\frac{-1}{3}[/tex]
Therefore, f(x) intersect the x-axis ate ( 4 , 0 ) and ( -1/3 , 0)
The equation for perimeter of square p=4s . what is the formula solved for p
20 is equal to 5 less than twice a number.
My sister's 14 years old my brother said that his age minus 12 is equal to my sister say how old is my brother
What is the slope of line represents by the equation y=-1/2x+1/4
I have another math question
Explain the error in each statement Three points have to be collinear
Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use. How much of the 15% alcohol solution should Bruce use?
The amount of 15% alcohol Bruce should use ls 20 mL
Using the equation given in the question :
0.10x + 0.15(50 - x) = 0.12(50)
0.10x + 7.5 - 0.15x = 6
Collect like terms
-0.05 = 6 - 7.5
-0.05x = - 1.5
x = 1.5 / 0.05
x = 30 mL
The amount of 15% solution to be used is related can be calculated thus :
Amount of 15% solution = 50 - x
Amount of 15% solution = 50 - 30 = 20mL
Therefore, 20mL of 15% solution is required.
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f(x)=3^x and x=-5 help
A) 1/729
B) -15
C) 1/243
D) -125
A plane is flying at an altitude of 23,760 feet. Which expression can be used to find the altitude in miles?
The altitude of the plane in miles will be 4.5144 miles.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a plane is flying at an altitude of 23,760 feet. The height of the plane in miles will be calculated as,
Height = 23760 feet
1 feet = 0.00019 miles
Height = 23760 x 0.00019 miles
Height = 4.5144
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Jennifer spent $150 at a craft fair to rent a booth. she sells knit blankets for $25 each. how would you 1.) wright the equation(slope) 2.) how many blankets does Jennifer need to sell to break even
Answer: Jeniffer wins $25 per blanket. and she must pay $150 to renth the booth.
a) So the equation of Jennifer's profit is P(x) = $25*x - $150.
where x is the number of blankets that she sells, 25*x is positive because that is the money she wins, and the 150 is negative because is the money that she has to pay for the rent.
b) For breaking even, the profit must be equal to zero, it means that she doesn't lose or win anything. Then we do P(x) = 0 = $25*x - $150.
then 25*x = 150
x = 150/25 = 6
So she must sell 6 blankets to break even.