Consider the universal set R,R, define the interval A=[−7,1],A=[−7,1], interval B=(−1,5),B=(−1,5), and CC be the negative real numbers. Complete the following exercises in interval notation.
1. A∪B=A∪B=
2. A∩B∩C=A∩B∩C=
3. A∩(B∪C)=A∩(B∪C)=
4. A^c ∪ B^c∪ C^c=
5. (C−A)∪(B−C)=(C−A)∪(B−C)=
Final answer:
The question involves calculating various set operations in interval notation, including the union, intersection, and complements using intervals A, B, and set C (negative real numbers) within the universal set of real numbers R.
Explanation:
The student is working with set operations in interval notation, particularly focusing on the union, intersection, and complement relative to the set of real numbers R. Given intervals A=[-7,1], B=(-1,5), and set C being the negative real numbers, we need to perform various set operations.
A⋃B is the union of A and B, which is the set of all elements in either A or B.A∩B∩C is the intersection of A, B, and C, which represents all elements common to all three sets.A∩(B⋃C) represents the intersection of A with the union of B and C.A¹ ⋃ B¹ ⋃ C¹ is the union of the complements of A, B, and C relative to the universal set R.(C-A)⋃(B-C) represents the union of the set difference of C and A with the set difference of B and C.which decimal is least in value
0.511 0.57 0.453 0.582
explain ehy the square root of 64 has a positive and a negative value.
Amy has set aside $150 a month for her cell phone bill. The cost for a monthly cell phone plan is a $65 access fee plus $20 per gigabyte of data used. Which expression represents the amount of money Amy has left from her monthly budget after she pays her cell phone bill?
The expression to represent the amount of money Amy has left from her monthly budget after paying her cell phone bill is $85 - $20x.
Explanation:To find the amount of money Amy has left from her monthly budget after paying her cell phone bill, we need to subtract the cell phone bill from her monthly budget. Amy has $150 a month and the cell phone bill consists of a $65 access fee plus $20 per gigabyte of data used.
Let's represent the amount of data used in gigabytes as 'x'. So, the expression to represent the amount of money Amy has left is:
$150 - ($65 + $20x)
This expression simplifies to:
$85 - $20x
So, the amount of money Amy has left from her monthly budget after paying her cell phone bill is $85 - $20x.
The expression that represents the amount of money Amy has left from her monthly budget after she pays her cell phone bill is $150 - ($65 + $20x).
Explanation:Amy has set aside $150 a month for her cell phone bill. The cost for a monthly cell phone plan is a $65 access fee plus $20 per gigabyte of data used. To calculate the amount of money Amy has left from her monthly budget after she pays her cell phone bill, we need to subtract the total cost of the cell phone plan from her budget. So, the expression that represents the amount of money Amy has left is:
$150 - ($65 + $20x)
Where x represents the number of gigabytes of data Amy has used.
PLEASE HELP!! IM VERY STUCK.
Although she's only in middle school, Tameka loves to drive go-carts! Her favorite place to drive go-carts, Drivers Delight, has 3 circular tracks. Track 1 has a radius of 60 feet. Track 2 has a radius of 85 feet. Track 3 has a radius of 110 feet.
a. Compute the circumference of Track 1.
b. Compute the circumference of Track 2.
Answer:
Circumference of Track 1 is 377.14 feet and circumference of Track 2 is 534.29 feet.
Step-by-step explanation:
Consider the provided information.
Drivers Delight, has 3 circular tracks. Track 1 has a radius of 60 feet. Track 2 has a radius of 85 feet. Track 3 has a radius of 110 feet.
Part (A)
Compute the circumference of Track 1.
Track 1 has a radius of 60 feet.
The formula used to find the circumference of the circle is: [tex]2\pi r[/tex]
The circumference of Track 1 is:
[tex]2\pi r=2\times \frac{22}{7}\times 60[/tex]
[tex]2\pi r=377.14 [/tex]
Thus, circumference of Track 1 is 377.14 feet.
Part (B)
Compute the circumference of Track 2.
Track 2 has a radius of 85 feet.
The circumference of Track 2 is:
[tex]2\pi r=2\times \frac{22}{7}\times 85[/tex]
[tex]2\pi r=534.29 [/tex]
Thus, circumference of Track 2 is 534.29 feet.
Tim found a jacket that was 25% off. The original price was $45.00. What was the sale price?
The area of a rectangle is 4.9 square units. The length is 2.5 units and the width is y units. What is the value of y? y=1.96 y=2.4 y=7.4 y=12.25
Answer:
1.96
Step-by-step explanation:
how can you quickly calculate 20 percent of any bill amount?
Answer:
There are many ways to do this calculation. Few are listed below.
1. Whenever we say percent, that means divided by hundred. And any number divided by 100 will result in putting a decimal to two places left. Like 20% will becomes [tex]\frac{20}{100}[/tex] = 0.20
And you can multiply the bill amount with 0.20 mentally.
2. You can also simply divide the total bill amount by 5, it will be equal to 20% of the total bill amount. Like if bill amount is $200.
[tex]\frac{200}{5}=40[/tex] and [tex]0.20\times200=40[/tex]. Both values are same.
Jeremy drew a polygon with four right angles and four sides with the same length. Name all the polygons that he could have drawn
Each night Ann and her family empty their pockets, purses, and wallets and place all of the pennies, nickels, dimes, and quarters in a large container. Ann helps her father count the money. If there are 145 pennies, 42 dimes, & 12 quarters, how much money did she count?
Question 4 options:
$8.65
$11.65
$46.45
$199.00
On a map of Tennessee, one inch represents 15 miles. If Chattanooga and Nashville are 11.3 inches apart on the map, how many miles apart are the cities?
Which point below is not on the graph of p(x) = /36-x?
Answer:
(-35,1)
Step-by-step explanation:
The temperature dropped 2°F every hour for six hours what was the total number of degrees the temperature change in the six hours?
How is the quotient of a number and 6 decreased by 10 is equal to 2
Using algebraic equation to find the measures of the two angles described below Begin by letting X represent the degree measure of the angle supplement the measure of the angle is 17 times greater than its supplement what is the measure of the supplement what is the measure of the other angle
the quotient of a number and -2
Mr Grant needs 30 pieces of felt. He can buy them in packs of 10 or as single pieces. What are the different ways Mr Grant can buy felt?
In the figure, GK (with an arrow pointing right) bisects angle FGH.
(L = angle)
if mL FGK = 3v - 4 AND mL KGH = 2v +7
a) 33
b) 58
c) 11
d) 29
How to write 75 1/3 % as a fraction in simplest form
Answer:
The simplified form of the provided fraction is [tex]\frac{226}{3}\%[/tex].
Step-by-step explanation:
Consider the provided fraction.
The provided fraction can be written as:
[tex]75\frac{1}{3}\%[/tex]
Convert the provided mixed number into a proper fraction.
Multiply the number 75 with 3 and add 1 to the obtained number.
[tex]75\frac{1}{3}\%[/tex]
[tex]\frac{(75\times 3+1)}{3}[/tex]
[tex]\frac{225+1}{3}\%[/tex]
[tex]\frac{226}{3}\%[/tex]
Hence, the simplified form of the provided fraction is [tex]\frac{226}{3}\%[/tex].
To convert 75 1/3 % to a fraction in simplest form, first change the mixed number to an improper fraction, then write it over 100, and finally simplify by dividing both numerator and denominator by their greatest common divisor.
Explanation:To convert 75 1/3 % to a fraction in simplest form, start by understanding that a percent is a ratio whose denominator is 100. Therefore, 75 1/3 % can be expressed as the fraction 75 1/3 over 100.
First, convert the mixed number to an improper fraction. Multiply the whole number 75 by the denominator 3 and add the numerator 1:
75 * 3 = 225225 + 1 = 226Now, 75 1/3 as an improper fraction is 226/3. Write this as a fraction over 100:
226/3 % = (226/3) / 100 = 226/300
To simplify this fraction, we look for the greatest common divisor of 226 and 300, which is 2. Divide both the numerator and the denominator by 2 to get:
Numerator: 226 / 2 = 113Denominator: 300 / 2 = 150The fraction in simplest form is therefore 113/150.
A mother wants to invest $11,000.00 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $ 660.00, how much money was invested in the CD account?
The mother invested $5000 in the CD account and the remaining $6000 in a savings bond. This solution was arrived at by setting up a system of two equations, which we solved simultaneously.
Explanation:Let's denote the amount of money invested in the CD account as x and the amount in the savings bond as y. The total amount of money is $11000, so we can set up the first equation as: x + y = 11000.
Then, the mother earns interest from both accounts. The CD account earns 4%, that's 0.04x while the savings bond earns 7%, that's 0.07y. The total interest is stated to be $660, so we can have the second equation as: 0.04x + 0.07y = 660.
From the first equation, we can solve for y: y = 11000 - x and substitute it into the second equation which gives us: 0.04x + 0.07(11000 - x) = 660.
Solving for x, you should get approximately $5000. This means a balance of $6000 was invested in the bond (11000 - 5000). Therefore, the mother invested $5000 in the CD account.
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Compare and contrast expressions equations and inequalities
Simplify using exponents: B12/B5
Answer: call 267 188 3800 today
Step-by-step explanation:
what is 9 + t/12 = -3
the formula for the perimeter of a rectangle is P=2l, + 2w, where l is the length and w is the width. A rectangle has a perimeter of 24 inches. Find it's dimensions if it's length is 3 inches greater than it's width.
The dimensions of the rectangle are 7.5 inches and 4.5 inches, or w = 4.5 inches and l = 7.5 inches if the perimeter of a rectangle is P=2l, + 2w.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
The rectangle can be defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
P = 24 inches
l = 3 + w
P = 2l + 2w
24 = 2(3 + w) + 2w
24 = 6 + 2w + 2w
24 = 6 + 4w
24 - 6 = 4w
18 = 4w
w = 4.5 inches
l = 3 + 4.5 = 7.5 inches
Thus, the dimensions of the rectangle are 7.5 inches and 4.5 inches, or w = 4.5 inches and l = 7.5 inches if the perimeter of a rectangle is P=2l, + 2w.
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One photoshop charges $0.36 per print. Another photoshop charges $2.52 plus $0.08 per print. Juan finds that the cost of printing his photos is the same at either shop. How many photos does Juan have to print?
what is m equal to if 7m+12/8=2m-1/3
Dale finished a puzzle in 6 minutes. How many seconds is this?
math question down below
if a = 42 and b = 2 then find ab
If three people share seven cookies equally. How many cookies do each friend get in fractions?