a) The set Z (integers) is not open.
b) The set O = ∩(i=1 to ∞)Oi, where Oi = (-1/i, 1/i), is open.
a) The set Z (integers) is not open.
An open set is a set that does not contain its boundary points.
In the case of the set of integers, every point in the set is a boundary point since there are no open intervals around any integer that lie entirely within the set.
Therefore, the set Z is not open.
b) The set O = ∩(i=1 to ∞)Oi, where Oi = (-1/i, 1/i), is open.
Each individual interval Oi = (-1/i, 1/i) is an open interval, and the intersection of open sets is also an open set.
This means that for any point x in O, there exists an open interval around x that is entirely contained within O.
Therefore, O is an open set.
Neither set Z nor set O is closed.
In the case of set Z, it does not contain all of its boundary points since the boundary points include all non-integer numbers.
set O is not closed since it does not contain its boundary points, which include the points -1 and 1.
Neither set Z nor set O is compact.
A compact set is a set that is both closed and bounded. As mentioned earlier, neither set Z nor set O is closed.
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Write a rule for the nth term of the geometric sequence:
a3=54, a6=1458
Answer:
tn = -1350 + 468n
Step-by-step explanation:
First, we need to find the difference.
1458 - 54 / 6 - 3
= 468
Now we need to find the first term.
t3 = t1 + (n - 1) (d)
54 = t1 + (3 - 1)(468)
54 = t1 + (2)(468)
54 = t1 + 936
-882 = t1
The rule is:
tn = -882 + (n-1) (468)
tn = -882 + 468n - 468
tn = -1350 + 468n
All
bags of marbles from Esteban's Marble Company have 7 green marbles
for every 4 purple marbles. If a bag has 56 green marbles, how many
purple marbles are in the bag?
There are 32 purple marbles in the bag.
All bags of marbles from Esteban's Marble Company have 7 green marbles for every 4 purple marbles.
To find out the number of purple marbles, let's represent the ratio of the number of green marbles to purple marbles as 7:4.
Since the ratio of green marbles to purple marbles is constant for all bags of marbles, we can create the following equation:
x/4 = 56/7 where x is the number of purple marbles in the bag.
To solve for x, we can cross-multiply:7x = 224
Dividing by 7 on both sides,
x = 32
Hence, the number of purple marbles in the bag is 32.
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Find the standard form of:
x^2+3y^2+4x=5
-9x^2+25y^2-54x-50y-281=0
Answer:
2 + 3 2+ 4 = 5 − 9 2 +2 5 2 − 5 4 − 5 0 − 2 8 1 = 0
Step-by-step explanation:
There really isn't an easier way to put that, sorry :/
Hope this helped, and please mark as brainliest <3
In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If 10000 students participated in the poll, how many chose Orange?
Answer:
2100
Step-by-step explanation:
10,000 x 21%
10000 x 0.21 = 2100
Pls help me I don't get it.
Pls indicate steps
I'm having trouble reading, could you type out what is on the picture? I'll edit my answer then.
Answer:
x = -3, y = 3
Step-by-step explanation:
multiply the equation 3y - x = 12 by 3:
=> 9y - 3x = 36
now add the two equation 9y - 3x = 36 and 3x + 4y = 3 together to eliminate x and solve for y:
=> 9y - 3x = 36
+) 4y + 3x = 3
______________
13y = 39
=> y = 3
substitute y = 3 into the original equation 3y - x = 12 to solve for x:
3(3) - x = 12
=> -x = 12 - 9
=> -x = 3
=> x = -3
given the equation y = 2x - 8, what is the slope and the y-intercept?
After considering the given data and performing a series of serious calculations we conclude that the evaluated slope of the given line is 2, under the condition that the given line equation [tex]y = 2x - 8.[/tex]
Here we have to apply the principles of coordinate geometry, to evaluate the dedicated slope engaged to a line.
The given equation [tex]y = 2x - 8[/tex]is present in the slope-intercept form,
[tex]y = mx + b,[/tex]
Here as we can see that
the slope is m and b is the y-intercept.
Hence, the slope of the given line is 2 and the y-intercept is -8, this can be seen in the diagram given below.
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PL Price of adm Cost per ride Total cost PL Price of ad Cost per ride. I NEED HELLLLPPPPPP ASAPPPPP
Explanation is in a file
bit.[tex]^{}[/tex]ly/3a8Nt8n
Some chocolate bars are scored (split apart) into equal parts to make them easy to break apart and share. Simon wants to share five chocolate bars equally among four people. The chocolate bars are scored in four equal parts. How should Simon share all the chocolate bars so four people each have an equal share? Show all your mathematical thinking.
Answer:
If every bar is scored into 4 parts, then Simon has 5*4 parts in total = 20 parts.
To split them between 4 people, each person gets 20/4 parts - 5 parts in total. The way to realize this the easiest would be to give each person a single bar, and then split the last bar into 4 parts and give each person one of them.
If the means of 4,6,9,Y, 16 and 19 is 13, what is the value of y
Answer:
-246
Step-by-step explanation:
Add all the numbers together and divide by the amount of numbers added to find the mean. -246 is the only right answer.
Answer:
14
Step-by-step explanation:
To get the mean, you have to add all the numbers together, and then divide them by how many numbers there are. Here, i'll show you.
There are 6 numbers, including [tex]Y[/tex], which we need to find out.
The Equation: [tex]\frac{4+6+9+Y+16+19}{6} = 13[/tex]
We can simplify this equation into, [tex]\frac{54 + Y}{6} = 13[/tex]To find [tex]Y\\[/tex], we can do the inverse, and multiply [tex]13[/tex] by [tex]6[/tex].
(The 6 on the left side of the equation is then cancelled out)
[tex]\frac{54+Y}{6} = 13[/tex] becomes [tex]54 +Y =13[/tex] × [tex]6\\[/tex][tex]13[/tex] × [tex]6 = 78[/tex] so then [tex]54 + Y = 78[/tex]For this final equation to be true, [tex]Y[/tex] would have to equal [tex]14[/tex].
Hope the rest of your math goes well :)
Lets be a given function. A graphical interpretation of the 3-point central difference formula for approximating f'(x) is the slope of the line joining the points of absuissas Xoth h with h > 0.
T/F
True. The graphical interpretation involves calculating the slope of the line connecting two points on the graph of the function, with the distance between the points denoted as h, where h is greater than zero.
The 3-point central difference formula is a numerical approximation technique used to estimate the derivative of a function at a specific point. In this formula, the slope of the line joining two points on the graph of the function is used to approximate the derivative.
To apply the 3-point central difference formula, three points on the graph are considered: (x-h, f(x-h)), (x, f(x)), and (x+h, f(x+h)), where h is a positive value. These three points create two lines: one connecting (x-h, f(x-h)) and (x, f(x)), and the other connecting (x, f(x)) and (x+h, f(x+h)).
The slope of the line joining the points (x-h, f(x-h)) and (x+h, f(x+h)) is then calculated, which represents the approximation of the derivative at x using the 3-point central difference formula. The distance between the two x-coordinates, h, is taken to be greater than zero to ensure that the points are not too close together, allowing for a more accurate estimation of the derivative.
Therefore, the statement is true, as the graphical interpretation of the 3-point central difference formula involves calculating the slope of the line joining the points with a positive value of h.
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If a pack of highlighter costs 2.40 what is the cost Per highlighter, in dollars and cent
From the information you gave me, I am going to guess it is a 4 pack of highlighters.
Answer: $0.60 per highlighter
Explanation: To find the unit rate of an item, take the price ($2.40) and divide it by the amount of the product included (4).
Hey I know this is kind of a lot but can someone pls help.
Answer:
J) x = 6; slope is undefined
Step-by-step explanation:
Choice F is incorrect because the equation and slope. Choice G is incorrect because the slope. And, Choice H is incorrect because the equation and the slope.
Lin understands that expanding is using the distributive property, but she doesn’t understand what factoring is or why it works. How can Kiran explain factoring to Lin?
Answer:
doing this so other guy gets brainliest
Step-by-step explanation:
Can someone please tell me the answers
Answer:
3. [tex]190yd^{2}[/tex] 4. [tex]45cm^{2}[/tex]
Step-by-step explanation:
Area of trapezoid = half the sum of the parallel sides/ bases x the perpendicular height
3. Area of trapezoid = [tex]\frac{(b_{1} +b_{2} )h}{2}[/tex]
= [tex]\frac{(17+21)10}{2}[/tex]
= [tex]\frac{380}{2}[/tex]
= [tex]190yd^{2}[/tex]
4. Area of trapezoid = [tex]\frac{(b_{1} +b_{2} )h}{2}[/tex]
= [tex]\frac{(4.5+5.5 )9}{2}[/tex]
= [tex]\frac{90}{2}[/tex]
= [tex]45cm^{2}[/tex]
hope this helps :)
The cost of renting a bicycle, y, for
x hours can be modeled by a linear
function. Renters pay a fixed insurance
fee of $12 plus an additional cost of $10
per hour, for a maximum of 6 hours.
What is the range of the function for this
situation?
Answer:
Step-by-step explanation:
9x - 1 / 2 + 9/2 x = 0.128886 (43)
2 / 5x - 1b = 4/3 - 1 - 1 = 2x (4)
= x1 + 24 - 3/4 + 8
9/3 - 1 x = /3
Please help me with this
Answer:
join
Step-by-step explanation:
meet./vyc-hwbw-svg
Answer:
see explanation
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
(1)
Here m = 2 and (a, b) = (- 1, 3 ) , then
y - 3 = 2(x - (- 1) ), that is
y - 3 = 2(x + 1)
(2)
Here m = - 5 and (a, b) = (4, 0 ) the coordinates of the x- intercept
y - 0 = - 5(x - 4) , that is
y = - 5(x - 4)
ANSWER ASAP PLEASE!
Diana & Henry are choosing candy toppings for their ice cream. Diana
will randomly choose a candy topping and Henry will also randomly
choose a candy topping. The candy topping choices are Butterfinger,
Snickers, MilkyWays, Crunch Bar, Starburst, and Skittles. What is the
probability that Diana and Henry will both choose Butterfinger?
a. 1/30
b. 1/36
c. 1/12
d. 1/6
Answer:d
Step-by-step explanation: there are 6 candys and only one is butterfinger therefore it would be 1/6
Answer:
answer should be 1/36
option (b)
good day mate
explanation : the sample space is 36 and butterfinger comes only once to both of them.
One house key weighs 1/2
ounce.
Which model represents the total weight in ounces of 5 house keys?
Answer: 5/2
Step-by-step explanation:
If 1 house key weighs 1/2 ounce,
Then do 5×1/2 which is 5/2
or [tex]\frac{1key}{5key} \frac{1/2ounce}{?}[/tex]
With this cross multiply and get 1x=5/2
giving a total of 5/2 again when divided by 1.
I am the smallest number u can make that is greater than 617,500| what number am I
Answer:
Step-by-step explanation:
That'd be 617,501. This is greater than 617,500.
Find the area of the circle or semicircle. use 3.14 for pi
where's the circle? :v
Find the area of the figure.
Answer:
192.2
Step-by-step explanation:
The formula for area of a rectangle is A= base times height’
15.5 x 12.4= 192.2
A builder has an 6-acre plot divided into 1 4 -acre home sites. How many 1 4 -acre home sites are there?
Complete question :
A builder has an 6-acre plot divided into 1/4 -acre home sites. How many 1/4 -acre home sites are there?
Answer:
24 home sites
Step-by-step explanation:
Given :
Total size of land = 6 - acre
Size of each home site = 1/4 acre
Number of home sites obtainable from the 6-acre land :
Total size of land ÷ size of each home site ;
6 ÷ 1/4
6 * 4/1
= 24
Hence, 24 home sites are on the plot of land.
Hello, can someone please assist me with this problem.
Write a linear (y= mx + b), quadratic ( y= ax^2), or exponential (y=a(b)^x) function that models the data.
The type of function that models the data in the table is linear and the equation is y = 4x - 1
Identifying the type of function that models the data in the table?From the question, we have the following table of values that can be used in our computation:
The table of values
The above definitions imply that
As x increases by 1
y increases by 4
This means that the function is a linear function
Also, we have
Slope = 4/1
So, we have
Slope = 4
The equation is then calculated as
y = Slope * x + y-intercept
From the table, we have
y-intercept = -1
So, we have
y = 4x - 1
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What is the difference between the greatest and least amounts of rain?
Answer:
1 inch
Step-by-step explanation:
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CAN SOMEONE PLEASE HELP ME
Jlvesh is analyzing the flight of a few of his model rockets with various equations. In each equation, h is
the height of the rocket in centimeters, and the rocket was fired from the ground at timet = 0, where t is
measured in seconds.
Jivesh also has a more powerful Model B rocket. For this rocket, he uses the equation h=-90t4 + 300t.
When is the height of the Model B rocket 250 centimeters? Round your answers to the nearest
hundredth.
After t =
seconds, the rocket will have reached a height of 250 centimeters.
Answer:
After t = 1.67 seconds, the rocket will have reached a height of 250 centimeters.
Step-by-step explanation:
Given
[tex]h = -90t^2 + 300t[/tex] --- correct expression
Required: When does height = 250 cm
To do this, we have:
[tex]h = 250[/tex]
This gives:
[tex]250 = -90t^2 + 300t[/tex]
Rewrite as:
[tex]90t^2 - 300t + 250 = 0[/tex]
Divide through by 10
[tex]9t^2 - 30t + 25 = 0[/tex]
Expand
[tex]9t^2 - 15t - 15t + 25 = 0[/tex]
Factorize:
[tex]3t(3t - 5) -5(3t - 5) = 0[/tex]
[tex](3t - 5)(3t - 5) = 0[/tex]
This gives:
[tex]3t - 5 = 0[/tex]
Solve for 3t
[tex]3t = 5[/tex]
Solve for t
[tex]t = \frac{5}{3}[/tex]
[tex]t = 1.67s[/tex]
John had 8 marbles and 4 red marbles in the bag. He took 1 marble from the bag and then replaced it and then took a second marble. What is the probability that john gets a red marble and then a red marble again?
A: 1/9
B: 3/4
C: 1/3
D: 1/11
Answer:
1/4
Step-by-step explanation:
P(red,red) = 4/8 x 4/8 = 1/2 x 1/2 = 1/4
Write the equation of a line in slope intercept form that passes through (3,-2) and (0,-5)
Answer:
y=x-5
Step-by-step explanation:
First, you find the slope by -2-(-5)/3-0. This would be 3/3 which is equal to 1. Then you plug in the x with any point you want. I'm going to use (3,-2). The equation should look like -2=3+y. Now we find what is y. Therefore for this equation to be true. Y is equal to -5. Now put it all together. Y=x-5. You can use the other point to check my answer! Hope that helps!!
In one year, a principal of $1000 led to an accumulation of $1100 .
The annual percentage yield ( APY ) for this investment is 9 % .
True
False
In one year, a principal of $1000 led to an accumulation of $1100. The annual percentage yield ( APY ) for this investment is 9 %. False.
The annual percentage yield (APY) is not 9% in this case. The APY takes into account the compounding of interest over the course of a year and provides a more accurate representation of the actual return on the investment. In this scenario, the investment of $1000 growing to $1100 in one year represents a simple interest rate of 10%. The APY would be higher than 10% if the interest was compounded.
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