use set notation to represent the following
the set of integers that are multiples of 5
Answers
The set of integers that are multiples of 5 can be represented using set notation as:
{...,-10, -5, 0, 5, 10, 15, 20, 25, 30, ...}
In set notation, this can be written as:
{ x | x ∈ ℤ, x is a multiple of 5 }
where "x" represents an element in the set, "ℤ" represents the set of integers, and the condition "x is a multiple of 5" specifies the property that the element must satisfy.
Related Questions
Your income determines your credit score
true or false
Answers
Your income determines your credit score
False.
Your income can sometimes affect your credit score, but it's not based on it. Your credit score is based on your Payment history, Credit history, and debt.
Point K is located at ( 1 , 2 ) on the following coordinate plane. A square that has a perimeter of 20 units will be drawn so that K is one vertex of the square. Which three ordered pairs could represent the location of another vertex of the square? Select the three correct answers.
Answers
Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).
To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.
One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.
Using the distance formula, we get:
\(\sqrt{(x-1)^{2} +(y-1)^{2} }\) = 5
Simplifying and squaring both sides, we get:
(x-1)^2 + (y-2)^2 = 25
Expanding the left side and simplifying, we get:
\(x^{2}\) - 2x + \(y^{2}\) - 4y + 20 = 0
Completing the square for x and y, we get:
\((x-1)^{2}\) + \((y-1)^{2}\) = \(6^{2}\)
This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.
Using this method, we can find several possible locations of the other vertices of the square. Three of them are:
(7, 2), (-5, 2), (1, 8)
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Elizabeth has $26 left after shopping at the mall. She bought 2 shirts for $22.99 each, a drink for $2.02, and 2 books for $16 each. How much money did she start with?
Answers
Step-by-step explanation:
22.99 × 2 + 2.02 + 16 × 2 + 26= $106
Choose what the expressions below best represent within the context of the word problem.
Answers
x best represent the width of the rectangle and x + 12 best represents the length of the rectangle.
How to find the width and length of a rectangle?The length of the rectangle is 12 inches more than it width.
The width of the rectangle can be found as follows:
The perimeter of the rectangle is 42 inches.
Therefore,
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthHence,
perimeter of a rectangle = 2(l + w)
The length of the rectangle is 12 inches more than it width.
Therefore,
let
x = width
Hence,
length = 12 + x
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how do you solve this equation step-by-step? (below)
4a + 8 - 2a - 3 = 45
Answers
Answer:
a=20
Step-by-step explanation:
Answer:
Step-by-step explanation:
4a-2a+8-3=45
2a+5=45
2a+5-5=45-5
2a/2=40/2
a=20
(03.01 MC)
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
three to the fourth power all over nine equals three squared
By simplifying 9 to 32 to make both powers base three and adding the exponents
By simplifying 9 to 32 to make both powers base three and subtracting the exponents
By finding the quotient of the bases to be one third and simplifying the expression
By finding the quotient of the bases to be one third and cancelling common factors
Answers
The correct answer is By finding the quotient of the bases to be one third and canceling common factors. Option D.
The Quotient of Powers Property states that when dividing two powers with the same base, you can subtract the exponents. In the given expression, we have three to the fourth power divided by nine.
To simplify this expression using the Quotient of Powers Property, we first need to recognize that nine can be written as three squared, since 3 multiplied by itself gives 9.
So, we have (3^4) / (3^2). According to the Quotient of Powers Property, we subtract the exponents: 4 - 2.
This gives us 3^(4-2), which simplifies to 3^2. Therefore, the expression three to the fourth power all over nine equals three squared.
It states that we find the quotient of the bases to be one third and cancel common factors. In this case, the bases are 3 and 3, and their quotient is indeed one third. Additionally, there are no common factors that can be canceled, as the expression does not contain any variables or additional terms.
Therefore, By finding the quotient of the bases to be one third and canceling common factors. accurately describes the steps involved in simplifying the expression using the Quotient of Powers Property.
We find the quotient of the bases (one third) and cancel common factors (which is not applicable in this case). Option D is correct.
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Note the complete question is
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
Three to the fourth power all over nine equals three squared
A.) By simplifying 9 to 32 to make both powers base three and adding the exponents
B.) By simplifying 9 to 32 to make both powers base three and subtracting the exponents
C.) By finding the quotient of the bases to be one third and simplifying the expression
D.) By finding the quotient of the bases to be one third and cancelling common factors
Submit your answers to the following questions. Be sure to explain your reasoning for each; it is helpful to draw this out to get started to see any quantitative patterns that develop.
If you write the counting numbers in rows of 7 numbers each, like shown below (but you keep going), where all the number line up in seven vertical columns as you go. (Note in the example below, the number 13 is in the 2nd row and the 6th column.)
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
In which column would the number 100 land?
In which row?
Now write the counting numbers in rows of 6 numbers each. What’s the location of 100 in this array?
Write arrays with other length rows. Find a way to predict in which row and column 100 will land for any array of numbers.
Answers
The number 100 would land in column 2
The number 100 would land in row 14The location of 100 in rows of 6 numbers is row 16 and column 3The location of 100 in rows of n numbers is row q and column rIn which column would the number 100 land?Given that we have the array of numbers
The length of each row in the array is 7
Dividing 100 by 7, we have
100/7 = 14 Remainder 2
This means that
Column = 2
In which row would the number 100 land?In (a), we have
100/7 = 14 Remainder 2
This means that
Row = 14
The location of 100 in rows of 6 numbersHere, we have
The length of each row in the array is 6
Dividing 100 by 6, we have
100/6 = 16 Remainder 3
So, the location of 100 in rows of 6 numbers is row 16 and column 3
Predicting the row and column 100 will landLet the length of each row in the array be n
Dividing 100 by n, we have
100/n = q Remainder r
This means that the location of 100 in rows of n numbers is row q and column r
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ide in
Which phrases from the text contain words with strong
connotations that help describe the violence in
Honduras? Check all that apply.
Answers
Answer: “fear of gangs that controlled”, “enforced a 6 p.m. curfew”, “shot on the spot”, and “bodies littered the dirty streets”.
Step-by-step explanation:
xA radioactive isotope is decaying at a rate of 20% every hour. Currently there are 15 grams of the substance.
Questions:
A. Write an equation that will represent the number of grams present after n hours
B. How much will be left after 24 hours (one day)? (Round to the nearest hundredth)
C. After how many hours will there be approximately one gram left?
Answers
B. After 24 hours, approximately 2.49 grams will be left.
C. After approximately 18.13 hours, there will be approximately one gram left.
A. To represent the number of grams present after n hours, we can use the equation:
N(n) = 15 × (1 - 0.2)^n
Where:
N(n) is the number of grams present after n hours,
15 is the initial amount of the substance in grams,
0.2 represents the decay rate of 20% per hour, and
^n represents the exponentiation operation.
B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:
N(24) = 15 × (1 - 0.2)^24
Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.
C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:
1 = 15 × (1 - 0.2)^n
To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:
log(0.8)(1/15) = n
Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.
Therefore, the answers are:
B. After 24 hours, approximately 2.49 grams will be left.
C. After approximately 18.13 hours, there will be approximately one gram left.
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could someone help me find the measures of this Rhombus? im very confused right now and need an explanation on thisThe measures you need to find:NK=NL=ML=JM=M
Answers
We shall take a quick reminder of the properties of a rhombus.
All sides are equal in measure
The opposite sides are parallel
The diagonals bisect each other at right angles
Opposite angles are equal in measure
Therefore, we can deduce the following from the given rhombus;
If JL bisects MK, then
\(\begin{gathered} MN=NK=\frac{MK}{2} \\ MN=NK=\frac{24}{2} \\ MN=NK=12 \end{gathered}\)If MK bisects JL, then line
\(\begin{gathered} JN=NL=\frac{JL}{2} \\ JN=NL=\frac{20}{2} \\ JN=NL=10 \end{gathered}\)Also, in triangle MJN,
MN = 12,
JN = 10,
Angle J = 50
Angle N = 90
Therefore angle M = 40
(All three angles in a triangle sum up to 180)
Therefore, in right angled triangle MJN, with the right angle at N,
\(\begin{gathered} MN^2+JN^2=JM^2 \\ 12^2+10^2=JM^2 \\ 144+100=JM^2 \\ 244=JM^2 \\ \sqrt[]{244}=JM \\ JM=15.6 \end{gathered}\)All sides are equal, therefore,
JM = ML = 15.6
Since line MK has been bisected by line JL, then
\(\angle KNL=90\)Also angle MJL equals 50, and line JL bisects angle J, then
\(\angle MJL=\angle KJL=50\)If angle MJL and angle KJL both measure 50, then angle MJK equals 100 (50 + 50).
Opposite angles of a rhombus are equal, hence
\(\angle MJK=\angle MLK=100\)If KJL = 50, and JNK = 90, then
\(\begin{gathered} \angle JKM+\angle KJL+\angle JNK=180\text{ (angles in a triangle sum up to 180)} \\ \angle JKM+50+90=180 \\ \angle JKM=180-50-90 \\ \angle JKM=40 \end{gathered}\)If JKM = 40, then
\(\begin{gathered} \angle JKM=\angle LKM=40 \\ \angle JKL=\angle JKM+\angle LKM \\ \angle JKL=80 \\ \angle JKL\text{ and }\angle JML\text{ are opposite angles. Therefore,} \\ \angle JML=80 \end{gathered}\)So the answers are;
NK = 12
NL = 10
ML = 15.6
JM = 15.6
5.6.8 let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e). show that this need not be true if f is continuous but not uniformly continuous.
Proof. (1): To prove {f(xn)} is a Cauchy sequence just need to prove ∀ > 0, ∃N, s.t.,∀n, m > N,
have |f(xn) − f(xm)| < . Since f is uniformly continuous on set E, thus ∀ > 0, ∃δ > 0, s.t.,
∀x, y ∈ E, if |x − y| < δ,then |f(x) − f(y)| < .as {xn} is a Cauchy sequence, then ∃N, s.t.,
∀n, m > N, |xn − xm| < δ, thus |f(xn) − f(xm)| < which proves {f(xn)} is a Cauchy sequence.
(2): for example f(x) = 1
x
, x ∈ (0, 2) which is continuous but not uniformly continuous. {
1
n
} is
a Cauchy sequence, however, {f(xn)} does not converge which proves that it is not a Cauchy
sequence.
Answers
Showing that this need not be true if f is continuous but not uniformly continuous.
Given :
let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e).
( 1 )
If f is uniformly continuous on E, then given ε > 0 there is δ > 0 such that if x, y are in E and |x−y| < δ,
then |f(x) − f(y)| < ε. Let (xn) be a Cauchy sequence in E. Then given δ > 0 there is N such that if p, q > N,
then |xp − xq| < δ, and thus |f(xp) − f(xq)| < ε, implying that (f(xn)) is a Cauchy sequence.
( 2 )
Let E = {1, 1/2, 1/3, · · } and f(1/n) = 1 is n is odd, f(1/n) = −1 if
n is even. Then f is continuous but not uniformly continuous. The sequence (xn) = (1/n) in E is Cauchy but the
sequence (f(xn)) = (1, −1, 1, −1, · · ·) is not Cauchy.
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Calculator
What is the volume of this figure?
Enter your answer in the box.
ft³
8 ft
25 ft
4 ft
20 ft
5 ft
Answers
The volume of the figure, by splitting it into two cuboids comes to be 3300 ft³.
What is the volume of a cuboid?The volume of a cuboid is the product of its three dimensions i.e. length, breadth, and height.
Let us split the given figure into two cuboids
The dimensions of one cuboid = 20 ft*25 ft *5ftThe dimension of the other cuboid = 4 ft*25ft * 8ftSo, the volume of the figure will be the sum of the volume of both the cuboids.
So, the volume of the cuboid with dimensions 20 ft x 25 ft x 5ft
= 20 x 25 x 5
=2500 ft³.
The volume of the cuboid with dimensions 4 ft x 25ft x 8ft
=4 x 25x 8
=800 ft³.
So, the volume of the figure = 2500 + 800 =3300 ft³.
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A clothing company produces denim jeans. The jeans are made and sold with either a regular cut or a boot-cut. To estimate the proportion of all customers in Tacoma, WA, who prefer boot-cut jeans, a marketing researcher examined sales receipts for a random sample of 178 customers who purchased jeans from the firm’s Tacoma store. 56 of the customers in the sample purchased boot-cut jeans. Construct the 99% confidence interval to estimate the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans and interpret the confidence interval (please write the interval boundaries to THREE decimal places
Answers
Answer:
99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].
Step-by-step explanation:
We are given that a marketing researcher examined sales receipts for a random sample of 178 customers who purchased jeans from the firm’s Tacoma store. 56 of the customers in the sample purchased boot-cut jeans.
Firstly, the Pivotal quantity for 99% confidence interval for the population proportion is given by;
P.Q. = \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) ~ N(0,1)
where, \(\hat p\) = sample proportion of customers who purchased boot-cut jeans = \(\frac{56}{178}\) = 0.315
n = sample of customers = 178
p = population proportion of customers who prefer boot-cut jeans
Here for constructing 99% confidence interval we have used One-sample z test for proportions.
So, 99% confidence interval for the population proportion, p is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) < 2.58) = 0.99
P( \(-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) < \({\hat p-p}\) < \(2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) ) = 0.99
P( \(\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) < p < \(\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) ) = 0.99
99% confidence interval for p = [ \(\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\), \(\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\)]
= [ \(0.315-2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }\) , \(0.315+2.58 \times {\sqrt{\frac{0.315(1-0.315)}{178} } }\) ]
= [0.225 , 0.405]
Therefore, 99% confidence interval for the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans is [0.225 , 0.405].
The interpretation of the above confidence interval is that we are 99% confident that the proportion of all customers in Tacoma, Washington, who prefer boot-cut jeans will lie between 0.225 and 0.405.
The length and width of a rectangular laptop have a ratio of 8 to 5. The width of the table is 40 in. Find the length of the table.
Answers
SOLUTION
Write out the given information
\(\begin{gathered} \text{ratio of the length to width is 8;5} \\ \text{Hence } \\ \text{length:width = 8:5} \end{gathered}\)Then
\(\begin{gathered} \text{The width of the table=40in} \\ \text{Let the length of the table =L inches } \end{gathered}\)Then
Appplying the principle of ratio, we have
\(\begin{gathered} \text{the ratio of the length of the rectangular laptop=the ratio of the table} \\ \text{Hence } \\ \frac{8}{5}=\frac{L}{40} \end{gathered}\)Taking the cross product of the equation above, we have
\(\begin{gathered} 5L=40\times8 \\ \\ \end{gathered}\)Divide both sides by 5, we have
\(\begin{gathered} \frac{5L}{5}=\frac{40\times8}{5} \\ \text{Then} \\ L=8\times8=64in \\ L=64in \end{gathered}\)Hence,
The length of the table is 64 inches
PLEASEEE HELP ASAP!!!
A 90% confidence interval for a proportion is found to be (0.52, 0.58) . What is the sample proportion?
Answers
Answer:
Its 0.55
Step-by-step explanation:
I just took the test
Choose a relationship model that will reach $0 in the same number of days as this scenario: Mika has $12 and spends $2 each day.
Answers
Answer:
Step-by-step explanation:
Since we have given that
Amount that Mike has = $12
Amount he spends each day = $2
Let the number of days be 'x'.
Let the amount remaining at the end be 'y'.
So, According to question, it becomes,
Hence, our required expression would be
Solve 4|x + 7| = 24.
O A. x= -13 and x = -1
OB. x = 13 and x = -1
O C. x= 13 and x = -13
OD. x= -13 and x = 1
Answers
Simplify:
2
(
3
x
)
+
(
x
+
10
)
2(3x)+(x+10)
Answers
Answer:
7x+10
Step-by-step explanation:
2x(3x)+1x(x+10)
6x+1x+10
7x+10
For each exercise, identify the error(s) in planning the solution or solving the
problem. Then write the correct solution.
1. Is (-5, -1) a solution of y > - x + 3?
y>-x+3
-13-5+3
-1>-2
-5>4 true (-5, -1) is a solution.
Answers
Answer: im sowwy but what are you asking lol srrry ima soopid person
Step-by-step explanation:
2x (3x+20) find the value of X
Answers
Answer:
6x^2+40x
Step-by-step explanation:
2x(3x+20)
6x^2 +40x
That's your answer. you won't be able to find x
Please help me I don’t understand and I will mark brainlyest
Answers
h ≥ 4 3/4 ft tall because they are tall enough and they can be taller to ride
Best describes , whats the best possible answer
Answers
Answer:
D?
Step-by-step explanation:
I'm not completely sure, but there are 2 different 180 degree lines that y falls on. On one line (y+70=180) it is for sure 110 degrees
When measured on the other line it is (y+70+x=180) I'm not too familiar with this??
Solve for the Value of R
Answers
Answer:
whats the question
i do not wan t have to do this again so in return ill give brain to the the first answer correct and 5 stars and thanks
Answers
Point A is at (5, 6) on the coordinate plane. It is reflected over the y-axis to create point B. Point A is then reflected over both axes to create point C. What is the area of the triangle that results from connecting the three points?
Answers
The area of the triangle which is formed as described is; 60.
What is the area of the triangle formed?According to the task content, when Point A(5,6) is reflected over the y-axis, the point B formed is; (-5,6) and when reflected over both axis, the point C formed is; (-5,-6).
It therefore follows that the length of segments AB and BC which represents the base and height of the triangle formed are; 10 and 12 respectively.
Therefore, the area of the triangle is; (1/2) × 10 × 12 = 60.
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Best decimal to represent 5 3/7
Answers
Answer:
to the nearest tenth: 5.4
to the nearest hundredth: 5.43
Step-by-step explanation:
Keep the whole number 5 by itself
divide 3 by 7 and add that as the decimal with 5
Answer:
5.4285714286
Step-by-step explanation:
Calculation:
5+3/7
= 5.4285714286
= 542.85714286%
Question 8 of 10
Simplify (7 + 1)2 – (11 + 32) - 4.
Answers
Answer:
Does anyone watch shaurya aur anokhi ki on star plus an Indian serial you'll love it I guarantee
John ran up and $88 Bill last Saturday the service was excellent so we decided to leave a 30% tip for the waitress how much was his tip
Answers
$26.40
ten percent is 88 divided by 10= 8.8
8.8 multiplied by 3 is 26.40
Which answer is an example of systematic sampling?
asking every fifth person their age
asking your neighbors if they approve of the mayor
submitting an online survey
counting everyone who attends a game
Answers
Answer:
Asking every 5th person their age
Step-by-step explanation:
I just did the quiz
sorry if it's confusing I just need help lol
Answers
Step-by-step explanation:
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