The solution for set B × A is {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
Given,
The sets,
A = {1, 2, 3}
B = {4, 6}
We have to find B × A.
Here,
Consider the Cartesian product:
The set of all ordered pairs (x, y) such that x belongs to A and y belongs to B is referred to as the Cartesian Product of sets A and B in mathematics. For instance, the Cartesian Product of A and B is (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), and (2, 5) if A = [1, 2] and B = [3, 4, 5].
The Cartesian product of B × A = {(b, a) | b € B, a € A}
So,
B × A = {4, 6} × {1, 2, 3}
B × A = {(4, 1), (4, 2), (4, 3), (6, 1), (6, 2), (6, 3)}
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Last week Forrest cut the grass exactly 3 times. It takes him between 55 and 75 minutes per cut.
CWrite an inequality to model all of the possible amounts of time (t) Forrest could have spent
cutting the lawn last week. Show or explain all your work.
Explanation:
If he mowed the lawn exactly once, then 55 ≤ t ≤ 75 describes all the possible values of t. Basically t is between 55 and 75 inclusive of both endpoints.
Multiply each value by 3
55*3 = 165
75*3 = 225
That's how we end up with 165 ≤ t ≤ 225 to represent the possible span of time values where he mowed the grass three times. His fastest possible time is 165 minutes (2 hr, 45 min) and his slowest possible time is 225 minutes (3 hr, 45 min).
Find the equaton of the line in point-slope form that passes through (-4,6) and (-2,5)
Instructions: Fill in the table of values for the exponential function. Insert all answers as fractions, when applicable.
Given,
The expression is:
[tex]y=-2(\frac{1}{2})^x[/tex]Required:
The value of y at x = -2, -1, 0, 1, 2.
The value of y at x = -2.
[tex]y=-2(\frac{1}{2})^{-2}=-2\times(2)^2=-2\times4=-8[/tex]The value of y at x = -1.
[tex]y=-2(\frac{1}{2})^{-1}=-2\times(2)^1=-2\times2=-4[/tex]The value of y at x = 0.
[tex]y=-2(\frac{1}{2})^0=-2\times(2)^0=-2\times1=-2[/tex]The value of y at x = 1.
[tex]y=-2(\frac{1}{2})^1=-2\times\frac{1}{2}=-1[/tex]The value of y at x = 2.
[tex]y=-2(\frac{1}{2})^2=-2\times\frac{1}{4}=-\frac{1}{2}=-0.5[/tex]The table for the different value of the function:
x y
-2
[tex](3 {s}^{2} +9s + 3) - ( {6}s + 1)[/tex]Add and subtract polynomialsFor this one we're doin subtract!!!!
Given data:
The given expression is (3 s^2 +9s + 3) - ( 6s + 1).
The given expression can be written as,
[tex](3s^2+9s+3)-(6s+1)=3s^2+3s+2[/tex]Thus, the simplification of the given expression is 3s^2 +3s +2.
A side of the triangle below has been extended to form an exterior angle of 133º. Find the value of x. 133° 21° xo
In order to find the value of x, we need to remember that the sum of the interior angles of a triangle is 180°
so we have the next equation
21+x+(180-133)=180
21+x+47=180
x=180-21-47
x=112°
Jordan’s of Boston sold Lee Company of New York computer equipment with a $7,000 list price. Sale terms were 4/10, n/30 FOB Boston. Jordan’s agreed to pay the $400 freight. Lee pays the invoice within the discount period. What does Lee pay Jordan’s?
How many different 3 digit combinations can there be for a combination lock that has a six digit wheel?
The number of 3 digit combinations possible for the six digit wheel combination lock is; 216 combinations.
Combinations and selections.It follows from the task content that the number of possible 3 digit combinations for the six digit wheel as required is to be determined.
The number of possible selections in a given sample space is defined by the combination which defines the situation.
On this note, each digit from the 3 digit combinations could be any of the six digits on the wheel.
Therefore, the number of possible combinations is; 6 × 6 × 6 = 216 combinations.
Ultimately, the number of possible combinations is; 216 combinations.
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Why did I get this wrong I did 4/3 times 3.14 times 7 to the next power I did all what my teacher told me
Given the figure of a sphere
The radius = r = 7
We need to find the volume of the sphere
The volume =
[tex]\frac{4}{3}\cdot\pi\cdot r^3=\frac{4}{3}\cdot3.14\cdot7^3=1436.0267[/tex]Rounding the answer to the nearest hundredth
So, the volume = 1436.03
If ten people shake hands with each other exactly once, how many handshakes take place?
Apply the formula:
n(n+1)/2
Where n is the number of shake hands of the first person (9)
9 (9+1) /2
9 (10)/2
90/2
45 shakes
Paolo noticed that Channel 8 devoted 1/6 hour to news story and Channel 12 devoted 1/8 to the same story. Which channel devoted more time? How much more time?
the channel that devoted more time was channel 8, because since 6<8 then it follows thay 1/6>1/8 (the inequiality changes), channel 8 devoted
[tex]\frac{1}{6}-\frac{1}{8}=\frac{8-6}{6(8)}=\frac{2}{48}=\frac{1}{24}\text{more time}[/tex]A decrease in smoking in the United States has resulted in lower death rates caused bylung cancer. The number of death rates per 100,000 people y can be expressed byy = - 26x2 - .55x + 91.81, where x represents the number of year after 2000.
Given the equation:
[tex]y=-0.26x^2-0.55x+91.81[/tex]Where x represents the number of years after 2000.
Let's solve for the following:
a.) Calculate the number of deaths per 100,000 for 2015 and 2017.
• For 2015, we have:
Number of years between 2015 and 2000 = 2015 - 2000 = 15
Substitute 15 for x and solve for y:
[tex]\begin{gathered} y=-0.26(15)^2-0.55(15)+91.81 \\ \\ y=-0.26(225)-8.25+91.81 \\ \\ y=-58.5-8.25+91.81 \\ \\ y=25.06\approx25 \end{gathered}[/tex]The number of deaths per 100,000 for 2015 is 25.
• For 2017:
Number of years between 2017 and 2000 = 2017 - 2000 = 17 years
Subustitute 17 for x and solve for y:
[tex]\begin{gathered} y=-0.25(17)^2-0.55(17)+91.81 \\ \\ y=7.32\approx7 \end{gathered}[/tex]The number of deaths oer 100,000 for 2017 is 7.
• b.) Let's solve for x when y = 50 using the quadratic formula.
Apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{(b^2-4ac)}}{2a}[/tex]Now, subsitute 50 for y and equate to zero:
[tex]50=-0.26x^2-0.55x+91.81[/tex]Subtract 50 from both sides:
[tex]\begin{gathered} 50-50=-0.26x^2-0.55x+91.81-50 \\ \\ 0=-0.26x^2-0.55+41.81 \\ \\ -0.26x^2-0.55+41.81=0 \end{gathered}[/tex]Apply the general quadractic equation to get the values of a, b and c:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ -0.26x^2-0.55+41.81=0 \end{gathered}[/tex]Hence, we have:
a = -0.26
b = -0.55
c = 41.81
Thus, we have:
[tex]\begin{gathered} x=\frac{-(-0.55)\pm\sqrt[]{-0.55^2-4(-0.26\ast41.81)}}{2(-0.26)} \\ \\ x=\frac{0.55\pm\sqrt[]{0.3025+43.4824}}{-0.52} \\ \\ x=\frac{0.55\pm6.617}{-0.52} \\ \\ x=-13.78,\text{ 11.}67 \end{gathered}[/tex]Since the number of years cannot be a negative value, let's take the positive value 11.67
Therefore, the value of x is 11.67 when y = 50.
is 11.22497 a rational or irrational number
11.22497 is a rational number
First we need to undertsand what rational and irrational numbers are:
Rational numbers are numbers that can be written as a ratio of two numbers. it is the division of two integers.
Integers are numbers with no fraction.
irrational numbers cannot be written as a fraction of two integers.
The number 11.22497 can be written as a fraction of two ingers:
[tex]11.22497\text{ =}\frac{1122497}{100000}[/tex]Therefore, it is a rational number.
Complete the equation for the circle with center (6,2) and radius 8.
The equation of the circle is :-
[tex]\begin{gathered} (x-6)^2+(y-2)^2=8^2 \\ (x-6)^2+(y-2)^2=64 \end{gathered}[/tex]hi! im mia, and i need help with math!question: Write a statement that correctly describes the relationship between these two sequences: 6, 7, 8, 9, 10, and 18, 21, 24, 27, 30.
The Solution:
Given the pair of sequences below:
[tex]\begin{gathered} \text{ First sequence: 6,7,8,9,10} \\ \\ \text{ Second sequence: 18,21,24,27,30} \end{gathered}[/tex]We are asked to write a statement that correctly describes the relationship between the two sequences.
The two sequences are both linear sequences. Their common differences are:
[tex]\begin{gathered} \text{ First sequence: d=T}_3-T_2=\text{T}_2-T_1 \\ =8-7=7-6=1 \\ \text{ So, the co}mmon\text{ difference is 1} \end{gathered}[/tex]The general formula for the first sequence is
[tex]T_n=a+(n-1_{})d=6+(n_{}-1)1=6+n-1=5+n[/tex]Similarly,
[tex]\begin{gathered} \text{ Second sequence}\colon\text{ } \\ d=\text{T}_3-T_2=\text{T}_2-T_1 \\ d=24-21=21-18=3 \\ \text{ So, the co}mmon\text{ difference is 3} \end{gathered}[/tex]The general formula for the second sequence is
[tex]S_n=18+(n-1_{})3=18+3n_{}-3=15+3n=3(5+n)[/tex]Thus, the relationship between the two sequences is:
[tex]S_n=3T_n[/tex]Where
[tex]\begin{gathered} S_n=\text{ the second sequence} \\ T_n=\text{ the first sequence} \end{gathered}[/tex]Therefore, the correct answer is:
[tex]S_n=3T_n[/tex]can you help me? on this math problem. (in the pic)
Given:
(x, y) ==> (1, -6)
m = 5
To write the equation, use the slope intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
To solve for b, substitue 1 for x, -6 for y, and 5 for m in the equation.
Thus we have:
y = mx + b
-6 = 5(1) + b
-6 = 5 + b
Subtract 5 from both sides:
-6 - 5 = 5 - 5 + b
-11 = b
The y-intercept is -11.
Therefore, the equation of the line in slope-intercept form is:
y = 5x - 11
ANSWER:
y = 5x - 11
Graph the equation and find the x-coordinate of the x-intercept:1.5x - 3y = 7Round to the nearest hundredth
We can begin by finding the x-intercept. This is the point at which the graph crosses the horizontal axis. This point is given when the y-value of the function is 0, then, we can solve the equation for y = 0 and find the value for x:
[tex]\begin{gathered} 1.5x-3y=7\to y=0 \\ 1.5x-3\cdot(0)=7 \\ 1.5x=7 \\ x=\frac{7}{1.5} \\ x\approx4.67 \end{gathered}[/tex]The x value of the x-intercept of the equation is approximately 4.67.
This is a linear equation, to build the graph we just need 2 points and join them with the line.
The x-intercept is the point (4.67, 0). Another easy point to find and build the graph can be the y-intercept, which is given when x = 0. Replacing in the equation:
[tex]\begin{gathered} 1.5x-3y=7\to x=0 \\ 1.5\cdot(0)-3y=7 \\ -3y=7 \\ y=\frac{-7}{3} \\ y\approx-2.33 \end{gathered}[/tex]With this, the other point we can use to graph the equation is (0, -2.33).
Drawing both points on a cartesian plane:
Both points (x and y-intercepts) are drawn in red.
I don't need Jimmy wants a game for him and his son Jimmy Jr. The game he wants is $79.93 and he only has $100 in his wallet. he found a discount for 60% off for the game. how much will he save?
Answer:
$47.96
Explanation:
The cost of the game = $79.93
He found a discount for 60% off for the game.
Therefore, the amount he will save will be:
[tex]=60\%\text{ of 79.93}[/tex]We simplify our result:
[tex]\begin{gathered} =\frac{60}{100}\times79.93 \\ =\$47.96 \end{gathered}[/tex]Jimmy will save $47.96.
Pattern Exercise Mins Components Fitnes 0 5 1 9 2 25 3 89 4 ? What do you notice about the pattern of components from minute to minute? 2. State the value for the question mark. I E O BI
We can calculate how much each component increases, this is shown in the following image:
So we can see that the pattern in which the components increase from minute to mites is that starts by adding 4, then they add 4x4=16, then they add 16x4=64, and so on:
So the rule is that the next increase is the previous increase multiplied by 4.
Thus, the next increase in components (the question mark) should be:
The previous one +256, which gives:
[tex]?=89+256=345[/tex]Answer: 345
Why can the big candy makers produce candy that is less expensive per piece
Answer:
Step-by-step explanation:
The reason behind the big candy makers producing candy that is less expensive per price is that the cost that they have to bear for production will be less in comparison to small candy makers.
bc a lot of people buy their products, so they have enough money to make a profit even if they sell it at a lower cost.
Suppose that you earn $15
Answer: 800 hours
Step-by-step explanation:
Describe it and decide if normal curve could be used as model
Answer:
The symmetric is symmetric
The distribution is unimodal
The mean, median, and mode are equal
A normal distribution is appropriate
Explanation:
The normal distribution is symmetric and unimodal, where the mode, the median, and the mean are equal. This distribution has the following shape
Therefore, the normal curve can be used as a model for the distribution.
So, the answers are:
The symmetric is symmetric
The distribution is unimodal
The mean, median, and mode are equal
A normal distribution is appropriate
if the population of a city is 158,000 and isdecreasing by 8% every year, what will thepopulation be in 5 years?
Solution:
From the question, we use the population decay formula expressed as
[tex]\begin{gathered} P(t)=P(1-r)^t \\ where \\ P\Rightarrow initial\text{ population} \\ r\Rightarrow decay\text{ rate} \\ t\Rightarrow time \\ P(t)\Rightarrow population\text{ at time t} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} P=158000 \\ r=8\%=\frac{8}{100}=0.08 \\ t=5 \end{gathered}[/tex]By substituting these values into the population decay formula, we have
[tex]\begin{gathered} P(t)=158000(1-0.08)^5 \\ =104134.88066 \end{gathered}[/tex]Hence, the population in 5 years will be
[tex]104134.88066[/tex]Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
Which number sentence can be used to find the difference between five times three and two times six?
x= 5x3-2x6
x = 5x2+3x6
x = 5(3+2x6)
x = 5x3+2x6
the following augmented matrix is in row-echelon form and represents a linear system. solve the system by using back-substitution if possible.
Given the matrix:
Given that it represents a linear system, we have the set of equations:
(1)x + 3y = 6
0x + (1)y = -1
x + 3y = 6..................equation 1
y = -1.........................equation 2.
Let's solve the system using substitution method.
Substitute -1 for y in equation 1:
x + 3(-1) = 6
x + (-3) = 6
x - 3 = 6
Add 3 to both sides:
x - 3 + 3 = 6 + 3
x = 9
From equation 2, we have the value of y:
y = -1
Therefore, the solution to the system is:
x = 9, y = -1
In point form:
(x, y) ==> (9, -1)
ANSWER:
x = 9, y = -1
i need help please help
Answer:
I think d)
Step-by-step explanation:
if A (0, 2) and B (2, 0) dilation is a transformation, which is used to resize the object, so it can only mean that both are bigger and like the same number, hope that makes sense
I need help on this
To answer this question, we need to evaluate each function in x=66, this way:
[tex]\begin{gathered} y=7(66) \\ y=462 \\ y=(66)^2-12(66)+84 \\ y=3648 \\ y=1.1317^{66} \\ y=3517.76 \end{gathered}[/tex]In this case, the function that has a greater value at x=66 is the one in the second option:
[tex]y=x^2-12x+84[/tex]Hello am just trying to see if I did this right
Answer
Variable
c = Cost of one bag of chips
Equation
2.50 + 3c = 5.05
Solution
c = Cost of one bag of chips = 0.85 dollars
Explanation
Cost of one juice pouch = 1.25 dollars
Cost of 2 juice pouches = 2(1.25) = 2.50 dollars
Cost of a bag of chips = c dollars
Cost of 3 bags of chips = (3)(c) = (3c) dollars
(Cost of two juice pouches) + (Cost of three bags of chips) = Total Cost
2(1.25) + 3c = 5.05
2.50 + 3c = 5.05
Subtract 2.50 from both sides
2.50 + 3c - 2.50 = 5.05 - 2.50
3c = 2.55
Divide both sides by 3
(3c/3) = (2.55/3)
c = 0.85 dollars
Hope this Helps!!!
find the solution of this system of equations-7y=-34-2x2x+4y=10
we have the system
-7y=-34-2x ------> equation A
2x+4y=10 ------> equation B
In the equation A
Multiply by -1
-2x+7y=34------> new equation A
Adds new equation A and equation B
-2x+7y=34
2x+4y=10
------------------
7y+4y=34+10
11y=44
y=4
Find the value of x
Substitute the value of y in equation A or equation B
2x+4(4)=10
solve for x
2x+16=10
2x=10-16
2x=-6
x=-3
therefore
the solution is the point (-3,4)In a class of 36 students, 25
study Chemistry, 22 study
Maths and 25 study Physics, 17
study Physics and Maths,18
study Physics and Chemistry
and 15 study only one of the
three subjects. Find the;
a) number of students who
study all three subject?
b) number of students who
study only Maths and
Chemistry?
c) Probability that a student
selected at random study only
two of the three subjects?
a) Number of students who study all three subject = 15
b) Number of students who study only Maths and Chemistry = 1
c) Probability that a student selected at random study only two of the three subjects = 1/36
Define Probability
Simply put, probability is the likelihood that something will occur.
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
As it is given total number of students is = 36
The subject are Physics, Maths, and Chemistry
Let, physics = p
maths = m
chemistry = c
The possible combination are,
p, c, m, pm, cp, cm, pcm (means 7 combination total)
Let x be the number of student who study all three subjects.
The students who study physics and maths = 17 - x
The students who study physics and chemistry = 18 - x
The number of student who study physics = 25
Now, with the expression we can find the students who study only physics
25 - ((x) + (18 -x) + (17- x))
⇒25 - (x + 18 - x + 17 - x)
⇒25 - (35 - x)
⇒25 - 35 + x
⇒x - 10
Let y be the number of student only chemistry and mathematics.
Now, with the expression we can find the students who study only chemistry
25-(x + (18- x)) + y
⇒25 - 18 + y
⇒ 7 - y
Now, with the expression we can find the students who study only maths
22 - (x + (17 - x)) + y
⇒ 22 - 17 + y
⇒ 5 - y
The possible combination and expression for each
pcm → x
cm → y
pc → 18 - x
pm → 17 - x
p → x - 10
c → 7 - y
m → 5 - y
____________
Total → 37 - y
But the number of students is 36 , so y = 1
That means,
The number of student who take only chemistry = 7 - y
= 7 - 1 = 6
The number of student who take only maths = 5 - y
= 5 - 1 = 4
The 15 students takes only one of the three subject
the number that take only physics is 5
so, x - 10 = 5
x = 15 (the student who takes all 3 subjects)
The student who takes only physics and chemistry = 18 - x
= 18 - 10 = 3
The student who takes only physics and Maths = 17 - x
= 17 - 15 = 2
To cross check put the values of x and y,
pcm → 15
cm → 1
pc → 3
pm → 2
p → 5
c → 6
m → 4
____________
Total → 36
Therefore, the answers :
a) Number of students who study all three subject = 15
b) Number of students who study only Maths and Chemistry = 1
c) Probability that a student selected at random study only two of the three subjects = ( 3 + 1 + 2) / 36 = 1/36
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y=x2 shifted down 2 units and to the right 4 units
Answer:
y=(x-4)^2 -2
Step-by-step explanation:
the negative four means move to the right if it is positive it moves to the left in a graph