The relation a into b represent all possible combinations of elements in a and b as ordered pairs.
The relation "a into b" refers to the cartesian product of the sets a and b, which is denoted by a × b. The cartesian product of two sets is a set of all possible ordered pairs, where the first element of each ordered pair comes from the first set, and the second element comes from the second set.
In this case, a = {0, 1, 2} and b = {-1, 1, 2}. So, their cartesian product a × b is the set of all possible ordered pairs (a, b), where a is an element of a and b is an element of b. Therefore, we have:
a × b = {(0, -1), (0, 1), (0, 2), (1, -1), (1, 1), (1, 2), (2, -1), (2, 1), (2, 2)}
This means that the relation a into b consists of all possible combinations of elements in a and b as ordered pairs.
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Assume that there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents. Scientists later investigate whether or not this bivariate relationship is moderated by age.
Age 16-20: r = 0.6 p = 0.01
Age 21+: r = 0.2 p = 0.05
T or F: Based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.
It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.
In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.
Let's first understand what is meant by the term "moderator.
"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.
Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.
As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.
So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.
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Simplify to create an equivalent expression.
2−4(5p+1)
Answer:
-2-20p OR -20p-2
Step-by-step explanation:
2-4(5p+1)
Rewrite (the spaces can help me to view the different parts):
2 -4(5p + 1)
Distribute:
2 -20p -4
Combine like terms:
-2-20p
Answer:
-2-20p OR -20p-2
Answer:
-2 - 20p
Step-by-step explanation:
First distribute 2 - 4 ( 5p + 1 )
Next do 2 - 20p - 4 and add 2+ - 4
Therefore, your answer is -2 - 20p
YALL JHITTS GO ADD MY T IK T OK
ITS >. * twoplayaany*
im following back
Answer:
Okay bestie ‼️
Step-by-step explanation:
Phil has 5 times as many toy race cars as Richard has. Phil has 425 toy race cars. How many race cars does Richard have? *
Answer:
85
Step-by-step explanation:
425 divided by 8= 85
Answer:
He as 85 race cars.
Step-by-step explanation:
Just divide 425 by 5 and you have your answer.
cammy is making gift bags. she has 28 kazoos, 70 stickers, and 84 headbands. she wants to make the greatest number of gift bags and have the same number of each type of prize in each bag. how many bags can she make?
By greatest common divisor , we can say the most bags that may be produced are 12, and each of those 12 bags will include two pencils, three candy bars, and four erasers.
what is greatest common divisor ?The biggest number that divides both of two integers is referred to as the greatest common divisor (gcd), or greatest common divisor. For instance, 5 is the largest common divisor of 20 and 15. This is so that 5 can divide both 20 and 15, which is a quality that higher numbers lack.
Since you have 36 candy bars, 24 pencils, and 48 erasers to divide among the gift bags and you want to divide the items evenly and not have any items left over, the calculation that follows must be done in order to determine, if you make the most gift bags possible, how many of each item would go in each bag:
It is necessary to find the three numbers' highest common divisor.
\(24 = 2, 3, 4, 6, 8, 12, 24\\36 = 2, 3, 4, 6, 9, 12, 18, 36\\48 = 2, 3, 4, 6, 8, 12, 24, 48\)
The maximum number of bags that may be produced is 12, as 12 is the largest common divisor of these integers.
Thus, there will be two pencils, three candy bars, and four erasers in each of the 12 bags.
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What are the zeros of f(x) = x2 - 12x+ 36?
A. X = -4 and x = 9
B. x = -6 only
C. x= -6 and x = 6
D. x = 6 only
Answer:
D
Step-by-step explanation:
x^2-12x+36
type into desmos and see where it touches the the line
The ability of a person to curl their tongue in a u-shape is determined by a dominant allele (t). if two parents that are heterozygous for the tongue curling trait have a child, what is the likelihood their child will be able to curl their tongue? 50% 25% 100% 75%
Answer:
^ They are correct :) ^
Step-by-step explanation:
I got it correct too.
Answer:
75%
Step-by-step explanation:
Tasha lists all the multiple of 3 from 3 to99. Tony lists all the multiples of 5 from 5 to100. What is the first number that is on both lists? The second.
Answer:
Multiples of 3 = 3, 9Multiples of 5 = 5, 10Step-by-step explanation:
In a list of 3 to 99, the first multiple of 3 will be none other than 3 itself because when multiplied by 1, you get three.
The second number will be: 3 * 2 = 6
In a list from 5 to 100, the first multiple will be 5 with 5 being a multiple of itself when multiplied by 1.
Second number = 5 * 2 = 10
Consider the problem
Min 2X2 – 14X + 2XY + Y2 – 18Y + 50
s.t. X + 4Y ≤ 8
ANSWER A, B, AND C
Find the minimum solution to this problem. If required, round your answers to two decimal places.
Optimal solution is X = ______, Y = ________, for an optimal solution value of _________
If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change? If required, round your answer to two decimal places.
Increase/Decrease by ___________.
Resolve the problem with a new right-hand side of 9. How does the actual change compare with your estimate? If required, round your answers to two decimal places.
Objective function value is ___________ so the actual increase/decrease
is only __________ rather than __________.
The final solution of the given problem is X = 2.82, Y = 1.04 for an Optimal solution Value of -16.93.
Given the optimization problem in 2X2 – 14X + 2XY + Y2 – 18Y + 50s.t. X + 4Y ≤ 8, we have to find the minimum solution to the given problem.
Solution To find the solution to the given optimization problem, we need to use the Lagrange multiplier method. Using this method, we have the following system of equations: 2x - 14 + 2y = λ4y - λ = 0x + 4y ≤ 8Solving the above equations, we get the following solutions:x = 3, y = 1, λ = 6
The optimal solution is X = 3, Y = 1, for an optimal solution value of -17. If the right-hand side of the constraint is increased from 8 to 9, the objective function would change by -2.29. (Decrease by 2.29)Now, we have to resolve the problem with a new right-hand side of 9.
The new optimization problem will be in 2X2 – 14X + 2XY + Y2 – 18Y + 50s.t. X + 4Y ≤ 9
Using the same method as above, we have the following system of equations:2x - 14 + 2y = λ4y - λ = 0x + 4y ≤ 9Solving the above equations, we get the following solutions:x = 2.82, y = 1.04, λ = 6.07
The objective function value is -16.93 so the actual increase/decrease is only -0.07 rather than -2.29. Hence, the actual change is very different from the estimated change.
Therefore, the final solution of the given problem is X = 2.82, Y = 1.04 for an optimal solution value of -16.93.
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. SCULPTURE An artist creates two metal sculptures in the shape of regular octagons. A side of the larger sculpture is 3.5 times longer than a side of the smaller octagon. The area of the smaller octagon is 19.28 square inches.
a. What is the area of the larger octagon?
b. The artist is going to pack the sculptures in a cylindrical box to take them to an art show. To the nearest inch, what is the diameter of the smallest box he can use? Explain your reasoning. (Hint: Find the radius of the larger octagon.)
By using what we know about octagons, we will see that:
a) The area is 244.89 in^2b) The diameter is 18.58 inWhat is the area of the larger octagon?
For an octagon of side length S, the area is:
A = 2*(1 + √2)*S^2
In this case, the area of the smaller octagon is:
19.28 in^2 = 2*(1 + √2)*S^2
Solving for S we get:
S = √( 19.28 in^2/(2*(1 + √2))) = 2.03 in
If we apply an enlargement of a factor 3.5, the new side length is:
S' = 3.5*2.03 in = 7.11 in
Then the area of the larger octagon is:
A' = 2*(1 + √2)*(7.11 in)^2 = 244.89 in^2
b) For an octagon of side length S, the radius is:
R = S*√(1 + 1/√2)
Then the radius of the larger octagon is:
R' = (7.11 in)*√(1 + 1/√2) = 9.29 in
Then the diameter of the box must be:
D = 2*R' = 2*9.29 in = 18.58 in
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PLEASE HELLPPP MEEEEE
Answer:
2x - 3y = 24
Step-by-step explanation:
You use the formula Ax ± By = C.
This is the standard linear equation form.
Help! I’m awful at graphs and stuff
Answer: for b: function one has a greater rate of change
Step-by-step explanation: sorry i don't know the first one
Answer:
a) -2 and 4, b) function 2
Step-by-step explanation:
Rate of change is the same thing as slope. For the first function, the table, we can use two of the points and the slope formula. I'll use (-1,3) and (-2,5). Remember the slope formula:
\(m=\frac{y2-y1}{x2-x1}\)
Plug the points in:
\(m=\frac{5-3}{-2-(-1)}\\m=\frac{2}{-1}\\m=-2\)
(Remember that subtracting a negative = adding. I look at it like the two 'minus' signs form one plus sign, if that helps)
So the slope of function 1 is -2.
We can do the same thing with the second function. Two points that I notice on the graph are (-1,0) and (0,4). Let's use the same slope formula.
\(m=\frac{4-0}{0-(-1)}\\m=\frac{4}{1}\\m=4\)
And the slope of function 2 is 4. That answers the first part. The second part asks about rate of change.
Function 2 has a greater rate of change, since 4>-2.
Hope this helps!
pls send the correct answer its a quiz
An expansion has a scale factor of x > 1 (greater than 1). A reduction is a scale factor that is 0 x 1 (higher than 0 but less than 1).
What scale factor best describes the dilating effect?The scale factor of dilation explains how the size of the figure has changed. An expansion has a scale factor of x > 1 (greater than 1). A reduction is a scale factor that is 0 x 1 (higher than 0 but less than 1).A dilation is a transformation that increases or decreases a figure's size. As a result, despite having different sizes, the picture and preimage will have the same form. Additionally, dilations scale a figure's edges by the same amount. Dilations maintain angle measurements and the ratio between related portions as a result.To learn more about dilation refer to
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A drawer contains 2 Red Socks, 7 White Socks, and 9 blue sock Without looking, you draw out a sock and then draw out a second sock without returning the first sock. What is the probability that the first sock and the second sock are both red?
Answer:
1/153
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one ids attached to the event. If it doesn't a value of zero is attached to the event.
probability that the first sock and the second sock are both red = (number of red socks /total number of socks) x (number of red socks /total number of socks)
At the first pick, the probability = 2/18
At the second pick because there is no replacement, there would be 1 red socks and 17 socks = 1/17
2/18 x 1/17 = 1/153
A company produces very unusual CD's for which the variable cost is $ 20 per CD and the fixed costs are $
50000. They will sell the CD's for $ 44 each. Let u be the number of CD's produced.
Write the total cost C as a function of the number of CD's produced.
C=$
Write the total revenue R as a function of the number of CD's produced.
R= $
Write the total profit P as a function of the number of CD's produced.
P= $
Find the number of CD's which must be produced to break even.
The number of CD's which must be produced to break even is
Answer:
1) $30,000 + $12x
(2) $50x
(3) $38x - $30,000
(4) 790 CD's to break even
Given that,
Variable cost = $12 per CD
Fixed cost = $30,000
Selling price = $50 each
Let x be the number of CD's produced,
(1) Total cost function:
C(x) = Fixed cost + Variable cost
= $30,000 + $12x
(2) Total revenue:
R(x) = Units produced × selling price of each unit
= $50x
(3) Total profit:
P(x) = R(x) - C(x)
= $50x - ($30,000 + $12x)
= $50x - $30,000 - $12x
= $38x - $30,000
(4) Number of CD's which must be produced to break even:
Total profit = 0
$38x - $30,000 = 0
x = $30,000 ÷ $38
= 789.47 or 790 CD's to break even.
Hope this helps! :)
PLEASE HELP ASAP LIKE PLEASE
Answer:
40
Step-by-step explanation:
60-20=40
Bern has 60. Delhi has 20. Subtracting those =40
Bobo and the Bouncing Ball Math Problem
Please help me solve it. There are 3 questions, question 1, 2, and the Einstein problem.
WORTH 20 POINTS!
This doesn’t include the Einstein problem cause I didn’t have that one.
Answer:
1)0.125
2)127.825
Step-by-step explanation:
A certain 300-term geometric sequence has first term 1337 and common ratio $-\frac12$. How many terms of this sequence are greater than 1
There are 6 terms in the sequence greater than 1.
What is a geometric series ?A geometric series is sum of infinite numbers which has a common ratio between its successive terms.
The missing common ratio value is -1/2
It is given in the question that
the number of terms in the sequence = 300
Sum = a₁ (1-rⁿ)/(1-r)
nth term is given by
aₙ = a₁r⁽ⁿ⁻ ¹⁾
1337(1/2)^(n - 1) = 1
(1/2)^(n - 1) = 1/1337
Applying log on both sides
log (1/2)^(n - 1) = log (1/1337)
(n - 1) log(1/2) = log(1/1337)
n = log (1/1337)/ log (1/2) + 1 ≈ 11.384
the 11th term is 1337(-1/2)^(10) ≈ 1.305
and
And the 12th term is 1337(-1/2)^11 = -.653
As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.
Therefore there are 6 terms in the sequence greater than 1.
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Solve the differential equations 2xy(dy/dx)=1 y^2. y(2)=3
The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).
To solve the given differential equation
2xy(dy/dx) = y²
We will use separation of variables and integrate to find the solution.
Start with the given equation
2xy(dy/dx) = y²
Divide both sides by y²:
(2x/y) dy = dx
Integrate both sides:
∫(2x/y) dy = ∫dx
Integrating the left side requires a substitution. Let u = y², then du = 2y dy:
∫(2x/u) du = ∫dx
2∫(x/u) du = ∫dx
2 ln|u| = x + C
Replacing u with y²:
2 ln|y²| = x + C
Using the properties of logarithms:
ln|y⁴| = x + C
Exponentiating both sides:
|y⁴| = \(e^{x + C}\)
Since the absolute value is taken, we can remove it and incorporate the constant of integration
y⁴ = \(e^{x + C}\)
Simplifying, let A = \(e^C:\)
y^4 = A * eˣ
Taking the fourth root of both sides:
y = (A * eˣ\()^{1/4}\)
Now we can incorporate the initial condition y(2) = 3
3 = (A * e²\()^{1/4}\)
Cubing both sides:
27 = A * e²
Solving for A:
A = 27 / e²
Finally, substituting A back into the solution
y = ((27 / e²) * eˣ\()^{1/4}\)
Simplifying further
y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)
Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is
y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)
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what is this polygon called and is it a regular polygon or irregular polygon
Answer:
hexagon because it have 6 sides
Step-by-step explanation:
it is irregular because it sides are not equal
THIS POLYGON IS IRREGULAR BECAUSE THIS IS HEXAGON AND IT IS IRREGULAR
an hexagon is a six sided irregular polygon
What is polygon?
a simple closed curve which does not interest itself made up if only line system is called a polygon
REGULAR POLYGON- polygon whose all side are of equal length and all angles are of equal measure
are called regular polygon
EX - SQUARE
IRREGULAR POLYGON- polygon which are not regular are called a regular polygon quadrilateral and Isosceles triangle is an example
14. There are 12 marbles in a bag. Of these, Four of them are blue and the rest are green. You reach into the bag and take out two marbles without looking. What is the probability that both marbles are blue? Round to the nearest whole percent.
Answer:1/4
Step-by-step explanation: im sry if im wrong
The probability that both marbles are blue is 9 percent.
It is given that 12 marbles in a bag, four of them are blue and the rest are green.
To find the probability that both marbles are blue.
What is probability?The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
Let both the marble be blue for event A.
P(A)=2C4/2C12 (combination formula)
=6/66
=1/11
≅0.09
=9percent.
So ,the probability that both marbles are blue is 9 percent.
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use the given conditions to write an equation for the line. passing through (−9,2) and parallel to the line whose equation is
The given conditions to write an equation for the line passing through (−9,2) and parallel to the line whose equation is y = −3x+ 2.
What is an equation?There are many different methods to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically include one or more variables.
More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
\($$We have the equation of a parallel line and a point which it passes through. To write the equation of the line in point-slope form, we will use the following formula:y−y1=m(x−x1)We know that the slope of parallel lines are same and we are given the equation for parallel line, y=−3x+2$$\)
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an insurance company offers policy holders two plans. the customer can make one annual payment of $1127.58 or 12 payments of $98.99 each year. how much is saved in one year by paying the full amount?
The customer can pay
1 time anually: $1127.58
12 payments of $98.99
To determine how much he will pay if the chooses the monthly plan, multiply the monthly fee by 12
\(98.99\cdot12=1187.88\)If he chooses the monthly plan he will pay $1187.88 in a year.
Subtract both fees to determine how much he'll save if the chooses to pay the full amount:
\(1187.88-1121.58=60.3\)He will save $60.3
Solve the system of linear equations by graphing. need help on these 2
The solution is at (-5, 0)
see the graph below
Explanation:9) To graph the equatios, we would assign values to x and get corresponding values of y
x + y = -5 ...equation 1
-x + 2y = 5 ...equation 2
when x = -6, -5, -4
when x = -6
-6 + y = -5
y = -5 + 6 = 1
when x = -5
-5 + y = -5
y = -5 + 5
y = 0
when x = -4
-4 + y = -5
y = -5 + 4
y = -1
when x = -6
-(-6) + 2y = 5
6 + 2y = 5
2y = 5 - 6
y = -1/2
when x = -5
-(-5) + 2y = 5
5 + 2y = 5
2y = 5-5
2y = 0
y = 0
when x = -4
-(-4) + 2y = 5
4 + 2y = 5
2y = 5-4
y = 1/2
plotting the graph:
The solution of the graph is at the intersection of both lines.
The solution is at (-5, 0)
A fair 10-sided die is rolled.
What is the probability that the number is even or greater than 7?
Give your answer as a fraction in its simplest form.
PLEASE HELP
Answer:
2 fifths 2/5
Step-by-step explanation:
10 sided dice has 10 possibilities so 7 8 9 10 are even or greater than 7 that's 4 out of 10 numbers but in simplest form would be 2/5 (2 fifths)
Question 38.
Write the first six terms of the arithmetic sequence with the first term, a1 = 240, and common difference, d= 24.
The first six terms are a1 = ,a3= , a4= ,a5= , and a6= .
\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)
the surface area of a cube is increasing at the rate of 240 sq. inches per second. at the instant when the side has length 10 inches, how fast is the volume of the cube increasing?
The volume of the cube is increasing at the rate of 600 cubic inches per second.
We know that, the surface area of a cube is given by 6\(a^{2}\) where a is the side of the cube.
Differentiating the surface area w.r.t. time, we get 12a\(\frac{da}{dt}\) = 240 sq. inches per second (Given!)
Now, when the side i.e. a= 10 inches, 12(10)\(\frac{da}{dt}\)=240 sq. inches per second .
So, {da}/{dt} = 2 inches per second.
Now, volume of a cube is given by a^3 . Differentiating again w.r.t. time, we get dV/dt where V is the volume of the cube.
3a^2 (da/dt) . putting the values of a = 10 inches and da/dt = 2 inches per second we get
dV/dt = 3a^2 (da/dt) =3(10)^2 (2)= 600 cubic inches per second.
So, rate of increasing of volume is 600 cubic inches per second when the side has length 10 inches.
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There are children in a play the ratio of 1;1 the ratio of girls who csan sing to girls who cant sing is 1;1 8 girls can sing
Answer:
8 girsl can sing
8 girls cannot sing
Total number of girls = 16
Step-by-step explanation:
The ratio of girls who csan sing to girls who cant sing is 1:1
Which means the number of girls who can sing and cannot sing are equal .
IF the number of girls who can sing is 8 then the number of girls who cant sing is also 8.
8:8
Dividing both sides by 8 gives
1:1
The total number of girls would be (8+8= )16.
Use Pythagoras' theorem to work out the length of the hypotenuse in the triangle on the right, below.
Give your answer in centimetres (cm) and give any decimal answers to 1 d.p.
This is an exercise of the Pythagorean Theorem, which establishes that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, called legs.
This can be expressed mathematically as:
c = √(a² + b²) ⇔ a² + b² = c²Where "a" and "b" are the lengths of the legs and "c" is the length of the hypotenuse. This theorem is one of the fundamental bases of geometry and has many applications in physics, engineering, and other areas of science.
The Pythagorean Theorem formula is used to calculate the length of an unknown side of a right triangle, as long as the lengths of the other two sides are known. It can also be used to determine if a triangle is right if the lengths of its sides are known.
To calculate the hypotenuse, we will apply the formula:
c = √(a² + b²)
Knowing that:
a = 8cm
b = 15cm
Now we just substitute the data in the formula, and calculate the hypotenuse, then
c = √(a² + b²)c = √((8 cm)² + (15 cm)²)c = √(64 cm² + 225 cm²c = √(289 cm²)c = 17 cmThe hypotenuse C of the triangle is 17 cm.
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PLEASEEE help me solve this problem
Step-by-step explanation:
The scale factor is 2 because the original PQR triangle is of 1 by 2 while the image is of 2 by 4, which is multiplied by 2.