The roster method to write the set A' as {13, 16, 17}.
- "Set" is a collection of distinct objects, which can be numbers or other elements.
- "Roster method" is a way of listing all the elements in a set by separating them with commas and enclosing them within braces { }.
Now, let's find set A', which is the complement of set A with respect to set U. This means that A' contains all the elements in U that are not in A.
U = {12, 13, 14, 15, 16, 17, 18}
A = {12, 14, 15, 18}
To find A', we will list the elements from set U that are not in set A:
A' = {13, 16, 17}
So, using the roster method, the complement of set A (A') is written as:
A' = {13, 16, 17}
In summary, the roster method is useful for listing all the elements in a set. By finding the complement of set A with respect to set U, we can use the roster method to write the set A' as {13, 16, 17}.
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Maggie Ryan is pricing materials for a deck project. She notes that deck
boards are sold in standard lengths by the foot as follows: 6 feet for
$5.88, 8 feet for $8.79, 10 feet for $10.68, 12 feet for $13.43, 14 feet for
$15.65, 16 feet for $17.88, 18 feet for $20.99, and 20 feet for $24.99. What
is the price per foot for each length?
According to the notes of Maggie the price for per foot length of deck division board is -6 feet for $5.88 = $0.98,8 feet for $8.79 = $1.09 ,10 feet for $10.68 = $1.06 ,12 feet for $13.43 = $1.11 .
What is division?One of the four fundamental mathematical operations—the others being addition, subtraction, and multiplication—is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.
Here,
The first record for deck board noted by Maggie is -
The length of the deck board = 6 feet
Price for 6 feet of deck board = $5.88
Use the division method -
Price for 1 feet of deck board = 5.88/6
Price per feet of deck board = $0.98
The second record for deck board noted by Maggie is -
The length of the deck board = 8 feet
Price for 6 feet of deck board = $8.79
Use the division method -
Price for 1 feet of deck board = 8.79/8
Price per feet of deck board = $1.09
The third record for deck board noted by Maggie is -
The length of the deck board = 10 feet
Price for 6 feet of deck board = $10.68
Use the division method -
Price for 1 feet of deck board = 10.68/10
Price per feet of deck board = $1.06
The fourth record for deck board noted by Maggie is -
The length of the deck board = 12 feet
Price for 6 feet of deck board = $13.43
Use the division method -
Price for 1 feet of deck board = 13.43/12
Price per feet of deck board = $1.11
The fifth record for deck board noted by Maggie is -
The length of the deck board = 14 feet
Price for 6 feet of deck board = $15.65
Use the division method -
Price for 1 feet of deck board = 15.65/14
Price per feet of deck board = $1.11
The sixth record for deck board noted by Maggie is -
The length of the deck board = 16 feet
Price for 6 feet of deck board = $17.88
Use the division method -
Price for 1 feet of deck board = 17.88/16
Price per feet of deck board = $1.11
The seventh record for deck board noted by Maggie is -
The length of the deck board = 18 feet
Price for 6 feet of deck board = $20.99
Use the division method -
Price for 1 feet of deck board = 20.99/18
Price per feet of deck board = $1.16
The eighth record for deck board noted by Maggie is -
The length of the deck board = 20 feet
Price for 6 feet of deck board = $24.99
Use the division method -
Price for 1 feet of deck board = 24.99/20
Price per feet of deck board = $1.24
Therefore, the value for deck board per foot length is $0.98, $1.09, $1.06, $1.11, $1.11, $1.11, $1.16, $1.24.
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Quadrilateral DABC was dilated to form quadrilateral EFGH.
The scale factor for the dilation from the quadrilateral EFGH to form DABC is the fraction 3/5.
What is scale factorScale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.
Considering the coordinates (1/2, 3/4) and (3/10, 9/4) centered at the original, we will observe the the point 1/2 was increased by 3/5 to become 3/10 at the x–axis, that is;
1/2 × 3/5 = 3/10
Also, the point 3/4 was increased by 3/5 to become 9/20 at the y–axis, that is;
3/4 × 3/5 = 9/20
Therefore, 3/5 is the scale factor of the dilation for the quadrilateral EFGH to DABC.
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An account earning 6.6% interest compounded continuously for 10 years would have a balance
of how much if the principal was $550.
$984.96
$1046.41
O$1064.14
Answer:
To find the final balance of an account earning interest compounded continuously, you can use the formula:
A = Pe^(rt)
where A is the final account balance, P is the initial principal (or starting) amount, r is the interest rate, and t is the time (in years) for which the interest is being calculated.
Substituting in the given values:
A = 550 * e^(0.066 * 10)
Therefore, the final balance would be approximately $1064.14.
Answer:
C) $1064.14
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
P = $550r = 6.6% = 0.066t = 10 yearsSubstitute the given values into the continuous compounding formula and solve for A:
[tex]\implies A=550e^{0.066 \times 10}[/tex]
[tex]\implies A=550e^{0.66}[/tex]
[tex]\implies A=550(1.93479233...)[/tex]
[tex]\implies A=1064.13578...[/tex]
Therefore, the balance of the account after 10 years would be $1064.14.
the function f(x)=a(1/2)^x is graphed below for a=4. Describe how the graph would change for a>4 and 1
The curve of the graph would move closer to the y-axis for a > 4
How to describe the graph?From the question, we have the following parameters that can be used in our computation:
f(x) = a(1/2)^x
Such that
a = 4
The graph of the function is added as an attachment
From the given parameters, we can see that the value of a is positive
This implies that an increment in the value of a would make the curve move closer to the y-axis
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Given the sequence below, find S7
(4374, 1458, 486,162,...}
The value of the 7th term of the Geometric sequence is 6
What is geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.
r is found by dividing the second term by first term.
The nth term of a geometric sequence is S(n) = ar^(n-1).
The common ratio in the sequence = 1458/4374 = 1/3
therefore S(7) = 4374×1/3^( 7-1)
= 4374× (1/3)⁶
= 4374/729
= 6
Therefore the value of the seventh term is 6
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What is the measure of x?
4
9
X=[?]vL
Give your answer in simplest form.
4 2 add y 2 root that
it's pretty easy and thanks for the high points ur welcome ur in the matrix kid
The function f(x)=x√ is horizontally stretched by a factor of 4 to form function g(x).
What is the equation of g(x)?
Enter your answer in the box.
The equation of the function g(x) will be √ [ (x) - 4 )].
A line that, in analytical geometry, is an asymptote of a curve is one where, as one or both of the x or y coordinates tend to infinity, the distance between the curve and the line approaches zero.
An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and related contexts.
Given that the function F(x) is √x and is horizontally stretched by a factor of 4 to form function g(x).
The equation of the stretched function can be written as:-
f(x) = √x
g(x) = √ [ (x) - 4 )]
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which ratios form a proportion iready
4/5 and 6/10 form a proportion.
Which ratios form a proportion iready ?A proportion is a statement that two ratios are equal. In order for two ratios to be considered a proportion, the two ratios must be multiplied by the same number to yield the same result.Doing so is called cross-multiplying. In this case, 4/5 can be cross-multiplied to get 8/10, which is equal to 6/10.Since 4/5 and 6/10 are both equal when cross-multiplied, they are considered a proportion.In addition to cross-multiplying to confirm that two ratios form a proportion, the two ratios can also be written as a fraction and simplified.In this case, the two ratios can be written as 4/5 = 6/10.The fraction can then be simplified to 2/3 = 3/5.This method of simplifying the fraction is another way to confirm that the two ratios are a proportion. In conclusion, 4/5 and 6/10 form a proportion because they are equal when cross-multiplied, and they simplify to 2/3 and 3/5, respectively.To learn more about ratios form a proportion iready refer to:
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HCF and LCM of 240 and 126
Please I will appreciate it
Answer:
the highest (hcf) would be 6 , while lowest (lcm) is 5,040
William just measured himself and found out he is 61 inches tall. The last time he measured, he was 50 inches tall. What percent taller is William now? %
Answer:
18.03
Step-by-step explanation:
Its pretty easy actually,
50x100 When we put 50 correct out of 61 possible into our formula, we get this: (50/61) x 100 = 81.97%
so , 100-81.97 = 18.03
Six familie went to the food fetival. Each family ha 2 adult and 4 childern. The entry fee for each child ticket cot $4, and an adult ticket cot $8. What would be the total cot of the fetival ticket?
The total cost of the festival tickets for 6 families with 2 adults and 4 children would be $192.
We can start by using the following equation to find the total cost of the child tickets:
Child tickets cost = Number of child tickets x Cost per child ticket
In this case, the number of child tickets is 4 children/family x 6 families = 24 children
The cost per child ticket is $4.
So, the total cost of the child tickets would be:
24 children x $4/child = $96
Similarly, we can find the total cost of the adult tickets:
Adult tickets cost = Number of adult tickets x Cost per adult ticket
In this case, the number of adult tickets is 2 adults/family x 6 families = 12 adults
The cost per adult ticket is $8.
So, the total cost of the adult tickets would be:
12 adults x $8/adult = $96
To find the total cost of the festival tickets, we can add the cost of the child tickets and the cost of the adult tickets:
Total cost = Child tickets cost + Adult tickets cost
$96 + $96 = $192
So, the total cost of the festival tickets for 6 families with 2 adults and 4 children would be $192.
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A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in squares from each corner and folding up the sides. The box is to hold 7623 in How big a piece of cardboard is needed?
The size of the cardboard piece required is 7627.0 in.
The formula for finding the size of a box is
2(L + W) + 8L + 8W = Perimeter of the cardboard piece
Where L = Length, W = Width
We need to find L and W to find the size of the cardboard piece.
7623 = 2(L + W) + 8L + 8W
7623 = 2L + 2W + 8L + 8W
7623 = 10L + 10W
7623/10 = L + W
762.3 = L + W
Let's take L = 500 and W = 262.3 (762.3 - 500 = 262.3)
Now we plug in the values of L and W in the original formula
2(500 + 262.3) + 8(500) + 8(262.3) = 7623
2(762.3) + 4000 + 2102.4 = 7623
1524.6 + 4000 + 2102.4 = 7623
7627.0 = 7623
Therefore, the size of the cardboard piece required is 7627.0 in.
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27 km = how many m ????????
Answer:
27000 m
Step-by-step explanation:
1km = 1000 m
27km = 27 x 1000 = 27000 m
So, the answer is 27000 m
Answer:27 km in meters is 27000 m
Step-by-step explanation:
multiply the length by 1000!
Type the correct answer in each box.
Alan, Bill, and Calvin are playing a game with collectible cards. At the moment, Alan has 11 less than 2 times the number of cards Bill has. Calvin has
1 more than 1 times the number of cards Bill has.
If Alan and Calvin have the same number of cards, the number of cards Bill has is 12
19
If Alan, Bill, and Calvin have all the cards in the deck, then the deck has
Reset
cards.
Next
The number of cards Alan and Calvin each have is
In given word problem the number of cards Alan has is 13 and Number of cards Calvin has is 13.
What is word problem?
A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Here , Let us take Number of card Alan has as A and Number of card bill has as B and Number of cards does Calvin has as C.
Now Alan has 11 less than 2 times the number of cards Bill has then,
=> A = 2B-11 ------------->1
And Calvin has 1 more than 1 times the number of cards Bill has then,
=> C = B+1 ----------> 2
Here Alan and Calvin has same number of cards then
=> 1 = 2
=> 2B - 11 = B +1
=> 2B-B = 11+1
=> B = 12
Now put B= 12 into 1 then
=> A = 2(12)-11= 24-11 = 13
Now put B= 12 into 2 then
=> C = 12+1 = 13
Hence the number of cards Alan has is 13 and Number of cards Calvin has is 13.
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Geometric mean of 2 and 22
Answer:
4,6,8,12
Hope it helps because im not sure if its right
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The triangle below is equilateral. Find the length of side x to the nearest tenth.
x
12
Answer:
6.9
Step-by-step explanation:
You want half the side length of an equilateral triangle with an altitude of 12.
Pythagorean theoremThe altitude shown divides the base into equal parts. If one of those parts is x, then the full side length is 2x. The Pythagorean theorem relates the side lengths of the right triangle:
(2x)² = x² +12²
3x² = 144 . . . . . . . . subtract x²
x² = 48 . . . . . . . . divide by 3
x = √48 = 4√3 . . . take the square root
x ≈ 6.9
__
Additional comment
You should be familiar with the fact that a 30°-60°-90° triangle has side lengths in the ratio 1 : √3 : 2. This means the shortest side (x) will have a length of 12/√3 ≈ 6.9, since the middle-length side is shown as having a length of 12.
Find the real solutions of the equations 7x to the fourth =56. Round your answers to two decimal places. Explain.
The equation 7x^4 = 56 can be rewritten as x^4 = 8. To find the real solutions of the equation, we take the fourth root of both sides:
What does a math equation mean?
Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
x = ∛8 = 2.
So the real solutions of the equation are x = 2.
Note: since the fourth root of 8 is 2, we can check that the equation holds true. i.e 7*2^4 = 56
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A toaster uses 1,200 watts. It is plugged into a 120-volt outlet. How many amps will the toaster draw?
Answer:
Step-by-step explanation:
10.00 amps
How does a graph show a functional relationship?
A graph can demonstrate a functional relationship by showing a line or curve that changes with the independent variable, indicating a direct relationship between the two variables.
A graph can show a functional relationship by showing a line or curve that consistently increases or decreases when the independent variable is changed. This will show a direct relationship between the two variables, and the pattern of the line or curve will show the functional relationship that exists.
A graph can demonstrate a functional relationship by showing a line or curve that changes with the independent variable, indicating a direct relationship between the two variables.
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Bivariate Probability Distribution
A bivariate probability distribution is a statistical distribution that describes the joint probability of two random variables. It provides the probability of each combination of values for the two variables. In simple words, it's a way to model the joint probability of two variables and the relationship between them.
A bivariate probability distribution is represented by a probability density function (pdf) or a probability mass function (pmf) depending on whether the variables are continuous or discrete. The function gives the probability of a given pair of values of the two variables. Bivariate probability distributions are useful in understanding the relationship between two variables and can be used to make predictions or draw inferences. It can be visualized using a scatter plot, a contour plot or a 3D plot. It can also be used to calculate the covariance and correlation between the two variables.
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Complete question:
Describe Bivariate Probability Distribution.
Cecilia types at a speed of 38 words per minute. Which graph correctly represents the total words Cecilia types over a 4 minute period?
The total words Cecilia types over a 4 minute period is 152 words
How to solve an equation?An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.
The slope intercept form of a linear equation is:
y = mx + b
where m is the slope and b is the y intercept.
Let y represent the total words that Cecilia types after x minutes.
Cecilia types at a speed of 38 words per minute. Hence:
y = 38x
After 4 minutes:
y = 38(4) = 152 word
The total words Cecilia types over a 4 minute period is 152 words
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Which expression is equivalent to
x²+7x+8/x²+2x-1
A) 5x +9
B) 5x/x²+2x-1
C) 5x+9/x²+7x+8
D) 5x+9/x²+2x-1
The expression that is equal to the provided expression, x2+7x+8, is 5x/x2+2x-1.
what is expression ?In math, it is possible to multiply, divide, add, or subtract. The following sentence form describes an expression: (Mathematical Operator, Number or Variable, Expression) Numbers, variables, and operations make constitute a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be compared.
given
expression = x²+7x+8/x²+2x-1
x²+8/x²+7x+2x-1
5x + 1/x2 + 2x -1
5x/x²+2x-1
The expression that is equal to the provided expression, x2+7x+8, is 5x/x2+2x-1.
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Given the function f(x) = -5x + 1, what is the value of x if f(x) = 11?
For the value of f (x) = 11, the value of x is
What is Function?A relation between a set of inputs having one output each is called a function.
We have to given that;
The function is,
⇒ f(x) = -5x + 1
And, f (x) = 11
Now, We have;
⇒ f(x) = -5x + 1
Substitute f (x) = 11, we get;
⇒ 11 = - 5x + 1
⇒ 5x = - 11 + 1
⇒ 5x = - 10
⇒ x = - 2
Thus, The value of x = - 2
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Find the 12th term -7, -3, 1,
Answer:
[tex] \sf \: 12th \: term = 37[/tex]
Step-by-step explanation:
Common difference (d) is,
→ d = a2 - a1
→ d = -3 - (-7)
→ d = -3 + 7
→ [ d = 4 ]
Now the 12th term will be,
→ a1 + (d × (n - 1))
→ -7 + (4 × (12 - 1))
→ -7 + (4 × 11)
→ -7 + 44
→ 37 => 12th term
Hence, the answer is 37.
What is the coefficient of X in 8 x/y *?
The polynomial 8X/Y has a coefficient of X of 8.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is often a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.
In the above polynomial 8X/Y, the coefficient of X is 8.
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Please explain what answer is it. And how do u show the work
Given the function g(x) = 6x + 2, find g(0)
To find g(0) we need to substitute x = 0 into the function g(x) = 6x + 2.
g(0) = 6(0) + 2 = 0 + 2 = 2
So, g(0) = 2
Therefore, the value of the function g(x) when x is equal to 0 is 2.
solve the following linear inequalities in one variable and show the solution set on the number line. 10<2x-1
The solution for given linear inequality will be x>11/2.
What are linear inequalities?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
e.g. y>x+2
Now,
Given linear inequality is
10<2x-1
i.e. x>11/2.
The number line is in image.
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Find the slope of the line passing through the points (7, 10) and (18, 25).
The slope of the line passing through the points is given by the equation Slope m = 15/11
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be represented as P = P ( 7 , 10 )
Let the second point be represented as Q = Q ( 18 , 25 )
Now , the slope of the line between the points is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 25 - 10 ) / ( 18 - 7 )
On simplifying the equation , we get
Slope m = 15/11
Hence , the slope of the line is m = 15/11
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Can you help me with this
Using the function f(x) = 500(0.67)^x :
A).f(0) = 500, f(1) = 335, f(2) = 224.45 and f(3) = 150.3815
B). 33% of bugs are eaten each day
C). 67% of the bugs remain each day
D). After day 7 will there remain fewer than 40 bugs in the farm.
Function of a function ruleThe function of a function rule is defined as the process that changes the input value to output.
day 1 will have 165 bugs eaten with a percentage evaluated as;
(165 × 100)/500 = 33%
day 2 will have 110.55 bugs eaten with a percentage evaluated as;
(110.55 × 100)/335 = 33%
day 3 will have 74.0685 bugs eaten with a percentage evaluated as;
(74.0685 × 100)/224.45 = 33%
day 1 will have 335 bugs remaining with a percentage evaluated as;
(335 × 100)/500 = 67%
day 2 will have 224.45 bugs remaining with a percentage evaluated as;
(224.45 × 100)/335 = 67%
day 3 will have 150.3815 bugs remaining with a percentage evaluated as;
(150.3815 × 100)/224.45 = 67%
At day 7;
f(7) = 500(0.67)⁷
f(7) = 30.30.
Therefore, 500, 335, 224.45 and 150.3815 are the respective population the days:0, 1, 2, and 3. for the function f(x) = 500(0.67)^x
33% of bugs are eaten each day
67% of the bugs remain each day and,
After day 7 will there remain fewer than 40 bugs in the farm.
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