It is observed that f is a subset of A×B
What is subset ?A subset is a subset (another set or the same set). It is expressed as A⊆ B in the set notation to indicate that set A is a subset of set B.Set 1 is a subset of Set 2 if all of its components are included in Set 2. A set, as far as we are aware, is a clearly defined grouping of letters, objects, numbers, or anything else. Set 1 is a subset of Set 2 if Set 1 = A, B, C, and Set 2 = A, B, C, D, E, and F. This is because all the items in Set 1 are also present in Set 2.
Given that :A={1,2,3},B={7,8,9,10}andf={(1,7),(2,9),(3,8)}
A={1,2,3}
B={7,8,9,10}
A×B ={(1,7)(1,8)(1,9)(1,10)(2,7)(2,8)(2,9)(2,10)(3,7)(3,8)(3,9)(3,10)}
f={(1,7),(2,9),(3,8)}
A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A×B
It is observed that f is a subset of A×B
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29) Tom solved the equation 6x-2(15-2x) = 10 and checked his solution as shown below
6x - 30- 4x = 10
6 (20) - 30-4 (20) = 10
120-30-80 = 10
90-80 = 10
10 = 10
Do you agree or disagree with his check? Explain.
Help me solve the first problem please
Question 14
[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]
Question 15
[tex]\binom{15}{6}=\frac{15!}{9!6!}=5005[/tex]
Simplify fully 12(x - 2)² /6(x-2)(x + 5) 4
3. In a video game for
every 5 levels you pass,
you earn 4 points. If you
earned 20 points, how
many levels would you
have passed?
Answer:
If you have earned 20 points, this means you have passed 25 levels.
Step-by-step explanation:
25 = 5 (20/4)
-1.4 repeating as a fraction in simplest form
1.4 repeating as a simple fraction is 13/9
Simple fraction is a fraction with whole number as the numerator and denominator. The top term is called numerator and the bottom term is called denominator.
Decimal number is a number that consist of one whole number and a fractional part and those are separated by a decimal point
The repeating decimal = 1.4444
Consider the value x = 1.4444
Then multiply 10 on both side of the equation
We get
10x = 14.444
Subtract x from the 10x
10x-x = 14.444-1.4444
Subtract the like terms in the equation
9x = 13
Move 9 to the right hand side
x = 13/9
Hence, 1.4 repeating as a simple fraction is 13/9
The complete question is
1.4 repeating as a fraction in simplest form
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Consider the function
y = 2x.
Complete the table of points for
x = −2, −1, 0, 1, 2.
Find the exact y-values.
The table representing the exact values of y from the function is attached below.
In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The sets X and Y are referred to as the function's domain and codomain, respectively.
Functions were initially the idealisation of how a changing quantity depends on another quantity, and they can be traced back to the works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. A planet's position, for instance, depends on time. The idea of a function was developed historically at the end of the 17th century with the infinitesimal calculus function, and until the 19th century, the functions that were taken into consideration were differentiable (that is, they could be divided into two parts).The given function is of the form y = 2x .
Now let us find the respective values of y for the given values of x.
At x = -2
y = 2x = 2 × (-2) = -4
At x = -1
y = 2x = 2 × (-1) = -2
At x = 0
y = 2x = 2 × (0) = 0
At x = 1
y = 2x = 2 × (1) = 2
At x = -2
y = 2x = 2 × (2) = 4
Therefore the table to represent this y-values of the function is [tex]\begin{table}[]\begin{tabular}{lllll} & & & & \\ & & & & \\ & & & & \\ & & & & \end{tabular}\end{table}[/tex][tex]\begin{table}[]\begin{tabular}{ll} & \\ & \\ & \\ & \\ & \end{tabular}\end{table}[/tex]attached below.
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What is the solution of the linear-quadratic system of equations?
y = r2 +52 _ 3
y = x=2
The value of x is 1 , -5 and y is 3 , -3
What is quadratic equation ?A[tex]x^{2}[/tex] + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilized in a wide variety of situations. You may be surprised to learn that a quadratic equation accurately predicts a rocket's trajectory after launch. Additionally, a quadratic equation is useful in many fields, including physics, engineering, astronomy, etc.
Given that : the linear-quadratic system of equations is y = [tex]x^{2}[/tex] +5x - 3 and y -x=2 .
y = [tex]x^{2}[/tex] +5x - 3 .....(i)
y = 2+ x.....(ii)
put the value of y in equation i
2 + x = [tex]x^{2}[/tex] +5x - 3
[tex]x^{2}[/tex] +4x - 5 = 0
[tex]x^{2}[/tex] +(5-1)x - 5 = 0
x(x + 5) -1(x + 5) = 0
(x -1)(x + 5)=0
x=1
x=-5
now put value of x in equation ii
y = 2+ x.....(ii)
y = 3 (when x = 1)
y = -3(when x = -5)
The value of x is 1 , -5 and y is 3 , -3
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A passenger train traveled 35 miles in 50 minutes. At this rate, how many miles can the train travel in one hour?
Given:
A passenger train traveled 35 miles in 50 minutes.
[tex]\begin{gathered} \text{Number of miles the train travelled in one hour=}\frac{35}{50}\times60 \\ \text{Number of miles the train travelled in one hour=}42\text{ miles} \end{gathered}[/tex]umber of miles that train can travel in one hour is 42 miles.
a company has learned that by pricing a newly-released toy at 6 Stars sales will reach 2,000 per day raising the price to $8 will cause the sales to fall thousand per day assume the ratio of change in price to change in daily sales is constant and let X be the price of the toy and Y be the number of sales.find the linear equation that models the price sales relationship for this toy. use this equation to predict the daily sales of the toy if the price is set at $6.50
Ek, this is the solution:
Step 1: Let's review the information provided to us to answer the problem correctly.
Sales of the new toy = 2,000 per day
Price of the toy when sales are 2,000 per day = $ 6
Ther
F (x) = x+1
——
x+8
F-1(-7) =
The value of [tex]f^{-1}(-7)[/tex] is given by -57/8.
Given that:-
f(x) = (x + 1)/(x + 8)
We have to find the value of [tex]f^{-1}(-7)[/tex].
Let f(x) = y
Hence,
[tex]f^{-1}(y) = x[/tex]
Now, we will find the inverse of the given function.
Hence, we can write,
y = (x + 1)/(x + 8)
We can rewrite it as:-
y = (x + 8 - 7)/(x + 8) = (x + 8)/(x + 8) - 7/(x + 8) = 1 - 7/(x + 8).
1 - y = 7/(x + 8)
x + 8 = 7/(1 - y)
x = 7/(1 - y) - 8
x = 7/(1 - y) - 8(1 - y)/(1 - y)
x = (7 - 8(1 - y))/(1 - y)
x = (7 - 8 + 8y)/(1 - y)
[tex]f^{-1}(y) = \frac{(8y - 1)}{( 1 - y)}[/tex]
Replacing y with x in the above equation, we can write,
[tex]f^{-1}(x) = \frac{(8x - 1)}{( 1 - x)}[/tex]
The above equation is the inverse of the function.
Putting x = -7 in the above equation, we get,
[tex]f^{-1}(-7) = \frac{(8(-7) - 1)}{( 1 - (-7))}[/tex]
= (-56 - 1)/ (1 + 7) = - 57/8
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I need help with this question
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Explain the graph of the solution?We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.
Any two ordered pairs can be used to create a solution set on a graph by connecting them with a straight line. Thus, any point along this graphed line would be included in the solution set.
There is only one solution that holds true for both equations if the equations' graphs cross. There are no solutions that hold for both equations if the equations' graphs do not meet (for instance, if they are parallel).
The answer for this graph is -4.
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Apollo Spas services 298 hot tubs. If each hot tub needs 175 mL of muriatic acid, how many liters of acid are needed for all of the hot tubs?
In a case whereby Apollo Spas services 298 hot tubs and each hot tub needs 175 mL of muriatic acid,number of liters of acid that are needed for all of the hot tubs is 52.15 litres.
What is unit conversion?The unit conversion can be described as the changing of bone unit to another.
We can calculate the number of liters of acid that are needed as (298 * 175)= 52150ml
This can be converted to liter by dividing 52150ml by 1000 which can be done as (52150ml/1000) = 52.15 litres of acid.
Therefore, the liters of acid are needed for all of the hot tubs can be expressed as the 52.15 litres
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A computer repair shop charges a flat fee of $10.95 and then $24.90 per hour.
A customer paid $147.90 for computer repairs.
How many hours did the shop work on the customer's computer?
Enter your answer as a decimal in the box.
Shop work on the customer's computer for 5.5 hours.
Given,
Charge is flat fee of $ 10.95
and, then $24.50 per hour.
And, to find the number of hours if customer paid $147.90.
Now, According to the question:
Let shop work on computer for x hours .
Then, Amount paid = 10.95 + 24.90x
So, if customer paid $147.90
then, 147.90 = 10.95 + 24.90x
24.90x = 147.90 - 10.95
24.90x = 136.95
x = 136.95/ 24.90
x = 5.5
Hence, Shop work on the customer's computer for 5.5 hours.
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the width of a rectangular field is 3 meters less than its length. Find the length and width is the perimeter is 58meters
Let the Length of the rectangle be l and the width of the rectangle be w
The width of a rectangular field is 3 meters less than its length, this can be represented as
w = l - 3
Given the perimeter = 58meters
Perimeter of the rectangle = 2(l + w)
58 = 2(l + l-3)
58 = 2(2l - 3)
58 = 4l - 6
58 + 6 = 4l
64 = 4l
4l = 64
l = 64/4
l = 16
w = l - 3
w = 16 - 3
w = 13
Hence, the length of the rectangle is 16 meters while the width is 13 meters.
Which of the following is equivalent to 2.76? 2.76%, 27.6%, two and nineteen twenty fifths, or twenty five over nineteen?
The equivalent value to 2.76 is C. two and nineteen twenty-fifths.
What is an equivalent value?An equivalent value is an amount or numerical expression possessing the same value as the other.
Equivalent values are expressed as equations, using the equation symbol (=).
Equations are a class of the properties of mathematical expressions, including numbers and variables.
Two and nineteen twenty-fifths = 2¹⁹/₂₅.
When expressed as a decimal, 2¹⁹/₂₅ = 2.76.
Thus, 2.76%, 27.6%, or twenty-five over nineteen are not equivalent values of 2.76 but 2¹⁹/₂₅.
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C
-
ZA and ZB are vertical angles. If mA = (2x +26)° and m/B = (3x − 29)
then find the measure of ZA.
The measure of the vertically opposite angle ∠A = 136°
What is defined as the vertically opposite angle?When two lines intersect at a point, vertical angles are formed. They are always on equal footing. In other words, four angles are formed only when two lines pass or intersect. We can see that two opposite angles are equal, and these are regarded to as vertical angles. They are also identified as'vertically opposite angles' due to their being perpendicular to each other.From the given question;
∠A and ∠B are vertical angles.
Thus, ∠A = ∠B
The values are given as;
∠A = (2x +26)°
∠B = (3x − 29)°
Equating both;
(2x +26)° = (3x − 29)°
Simplyfying;
2x + 26 = 3x − 29
3x - 2x = 26 + 29
x = 55
Put the value of x in ∠A = (2x +26)°
∠A = (2x +26)° = 2x55 +26
∠A = 136°
Thus, the measure of the vertical angle ∠A = 136°.
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cept 3) Which equation represents a pt for line that is parallel to the line y=-4x + 5? 1) y=-4x + 3 cept_ = + 5 5 cept for 3) y = 4x+3 ) 4) y = 4x + 5 2) y=-x+ ) "
y=-4x + 3
EXPLANATION
Given:
y = -4x + 5
To find the equation which represent a line that is parallel to the above, all we need to do is to oserve their slope.
Using a unique properties that states : slope of parallel lines are equal.
Observe that comparing the equation y =-4x + 5 with y=mx + b
slope = m= -4
From the option given, the only equation when compared with y=mx + b that has a slope of -4 is y=-4x + 3.
Therefore, the equation which represent a line that is parallel to y=-4x + 5 is y=-4x + 3
The line y=kx+4 goes through the point (2, -2)
K = -3
Sketch the graph of the line (need answer ASAP!!)
The graph of the linear equation:
y = -3x + 4
Can be seen in the image at the end.
How to sketch the graph of the line?
To draw a line, we just need to find two points that belong to the line, graph them, and then connect them with a line.
Here we know that we have the line:
y = k*x + 4
Where k = -3, then:
y = -3*x + 4
By evaluating this in a value of x, for example, x = 0, we will get:
y = -3*0 + 4 = 4
Then we also have the point (0, 4) (and the given one, (2, -2))
So we can draw these two points and then connect them with a line (just use a ruler and draw a line that passes through both points).
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Use the [tex]lim_{x-0} \frac{sinx}{x}=1[/tex] to determine [tex]lim_{x-0} \frac{xcos5x}{sin5x}[/tex].
Rewrite the limit as
[tex]\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = \lim_{x\to0} \frac{5x}{\sin(5x)} \cdot \lim_{x\to0} \frac{\cos(5x)}5[/tex]
Then using the known limit,
[tex]\displaystyle \lim_{x\to0} \frac{\sin(x)}x = 1 \implies \frac1{\lim\limits_{x\to0}\frac{\sin(x)}x} = \lim_{x\to0}\frac x{\sin(x)}=1[/tex]
it follows that
[tex]\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = 1 \cdot \frac{\cos(0)}5 = \boxed{\frac15}[/tex]
Let f(x) represent a function.
Which descriptions match the given transformations?
The interpretation of the transformation of the given functions are;
f([tex]x + \frac{1}{4}[/tex]) means translated by 1/4 units to the left.
f(x) + 1/4 means that f(x) is translated by 1/4 units upwards
How to Interpret Function Transformations?There are different ways of function transformations such as translation, reflection, dilation, compression e.t.c
Now, the function written can be said to translated by 1/4 units to the left . This is because when we translate a function by say "a" units to the left, we are simply going to add a units to the x - variable.
To translate a graph upwards, it simply means we will add the number of units to the function; for example, f (x) + 3 moves the graph of the function f (x) upward by 3 units.
Thus, the given function f(x) + 1/4 means f(x) is translated by 1/4 units upwards
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In an election, 112 votes were cast and the
winning candidate beat her opponent by a
4:3 ratio. How many more votes did the
winning candidate receive?
8
16
23
28
35
Answer:
16
Step-by-step explanation:
112/7=16, 16x4=64, 16x3=48, 64-48=16
can someone help me
Write the verbal sentence as an equation or an inequality:
Four is greater than six times a number t.
Answer:
I hope this helps. Four is greater than six times a number t in inequality form is 4 › 6 * t
Ms. Lantz recently participated in the Rocket Run 5k. The distribution of finishing time for females is approximately normal with a mean of 57 minutes with a standard deviation of 8 minutes. According to the Houston Chronicle, a healthy female person should be able to run a 5K in less than 50 minutes.
Part B: Ms. Lantz wanted to use her 5K time to qualify for the Houston Marathon. In order to qualify you need to be in the fastest 20% of times. What finishing time would she need in order to qualify for the Houston Marathon?
Answer =___ minutes
**Round to the 4th decimal**
The finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes in Rocket Run 5k.
What exactly is the z-score?A Z-Score is just a measurable statistic that represents a score's relationship to the mean across a set of scores.A Z-score can inform a trader why a value is typical for a particular set of data or out of the ordinary.A Z-score of the less than 1.8 indicates that a business is nearing bankruptcy, whereas a score closer to 3 indicates that what a company is in good financial status.The formula for calculating the z-score is;
z = (x - μ)/σ
x = sample size
μ = mean of the sample
σ = standard deviation of the sample
The given values are-
μ = 57 minutes
σ = 8 minutes
Probability = 20% = 0.20
Find the z-score from the negative z table for 0.20
z score = -0.84
Put the values in z formula and find x.
z = (x - μ)/σ
-0.84 = (x - 57)/8
Simplifying;
x = -6.72 + 57
x = 50.28 minutes
Thus, finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes Rocket Run 5k.
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n-13-25 OR 2 +9n > -43
Need help asap
Answer:
261
Step-by-step explanation:
A Short answer Question
Using multiplication of matrices, it is found that the values of a and b are given as follows:
a = 4.b = 6.How does multiplication of matrices work?To multiply matrices, we multiply the rows of the first matrix by the columns of the second matrix.
Hence, the element of the row 1 and column 1 of the product matrix is given by the multiplication of the row 1 of the first matrix by the column 1 of the second matrix, then:
3(-1) -2(2) + a(3) = 5
-3 - 4 + 3a = 5
3a = 12
a = 4.
The element of the row 2 and column 2 of the product matrix is given by the multiplication of the row 2 of the first matrix by the column 2 of the second matrix, then:
4(3) - 1(b) + 2(-2) = 2
12 - b - 4 = 2
8 - b = 2
b = 8 - 2
b = 6.
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you borrow $200,000.00 that charges you 6.3% interest, compounded monthly. You will make payments monthly in the amount of $1,300.00. How many payments will it take for you to pay off the loan?
The number of payments to pay off the loan of $200,000 at 6.3% interest, compounded monthly is 315 monthly payments.
How is the number of payments computed?Using the compounding format for determining the monthly payments, the number of periods for the periodic payments can be computed.
In this situation, we used the online finance calculator to determine the number of payments.
Compounding accumulates the interest on a loan and adds it to the principal for computing subsequent interest.
At the end of the period, the balance is made up of the principal and compounded interest.
I/Y (Interest per year) = 6.3%
PV (Present Value) = $200,000
PMT (Periodic Payment) = $-1300
FV (Future Value) = $0
Results:
N (# of periods) = 314.854
Sum of all periodic payments = $-409,309.97
Total Interest $209,309.97
Thus, you are likely to make 315 monthly payments to settle the loan.
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I can’t find the answer for this question
Answer:
[tex]x = \frac{20}{91}[/tex]
Step-by-step explanation:
Since this is a proportion, first you need to cross multiply.
[tex]\frac{20}{7}[/tex] × [tex]\frac{2}{25}[/tex] = [tex]\frac{40}{175}[/tex]
[tex]\frac{26}{25} x = \frac{40}{175}[/tex]
Now multiply both sides by the reciprocal of 26/25 which is 25/26.
[tex]\frac{25}{26} (\frac{26}{25} )x=\frac{40}{175} (\frac{25}{26} )\\[/tex]
Cancel on the right side, 25 and 175, by 25. Then cancel 40 and 26 by 2.
[tex]x = \frac{20}{7} (\frac{1}{13} )[/tex]
[tex]x = \frac{20}{91}[/tex]
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive, given that he or she did not have the disease.
The individual actually had the disease
No positive 9 negative 133
Yes
Positive 140
Negative 18
The probability is approximately.
The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985
What is probability ?Probability is what has the potential to happen. This area of math examines how random events happen. A value between 0 and 1 is used to express it. In order to anticipate the possibility of events, probability has been introduced to mathematics. The degree of likelihood that something will happen can be used to define probability. This fundamental theory of probability, which is also applied to the probability distribution, can be used to estimate the likelihood of the results of a random experiment. We must first determine the total number of alternatives in order to determine the likelihood that a specific event will occur.
Given that : He or she did not have the disease. The individual actually had the disease No positive 9 , negative 133 Yes Positive 140 ,Negative 18 .
Yes No
Positive : 140 9
negative : 18 133
P = [tex]\frac{Someone get positive }{he not had the disease}[/tex]
= [tex]\frac{140}{142}[/tex]
=0.985
The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985
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Y-intercept 9 and slop -2
The equation of the line that has the given features is y = -1/3x - 4
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the equation of the line?From the question, the given parameters are
Slope, m = -2
y-intercept, c = 9
As a general rule:
A linear equation is represented as
y = slope * x + y-intercept
This can be rewritten as
y = mx + c
Next, we substitute the known values in the above equation
So, we have the following equation
y = -2x + 9
The above equation cannot be further simplified
So, we have
y = -2x + 9
However, it can also be expressed as
y = 9 - 2x
Hence. the linear equation is y = -1/3x - 4
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Possible question
What is the equation of a linear equation that has the following features
Y-intercept 9 and slop -2
Evaluate the expression when c=-3 and x=3 and x-2c
⇒Plug in places the given values in the expression x-2c and simplify
given that x=3 and c =-3
⇒[tex]=(3)-2(-3)\\=3+6\\=9[/tex]
The expression evaluated at the given variables is equal to 9.