The cardinality of the set (A − C) n B is 35 .
Cardinality of a set is defined as the number of elements in the mathematical set. It can be finite or infinite. For example, the set A = {1, 2, 3, 4, 5, 6} has cardinality 6. Because the set A has 6 elements. Set cardinality is also known as set size. A real number can be defined as a combination of rational and irrational numbers. They can be both positive and negative, denoted by the symbol "R". Natural number all count numbers starting at 1. N = {1 ,2 , 3 ,4, .....}We have given three sets A = {x | x ≤ N} where N is a natural number .
Then , set A will get values [tex]A= \{1,2,3,4,5......\}[/tex]
B = {x-5 < x < 105, x ≤ R} where R is a real number whose values is in domain of (- ∞ ,∞)
Then , set B will get values [tex]B=(-5,105)[/tex]
C = {x|x is a rational number, 10 < x < 80} rational number which can expressed in [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex] .
Then , set C will get values [tex]=(10,80][/tex]
According to the question
(A − C) n B [tex]=(\{1,2,3,4,5 ........\}-(10,80] \sqcap (-5,105)[/tex]
[tex]=\{1,2,3,4,5,6,7,8,9,10,81,82,83 .......\} \sqcap (-5,105)\\[/tex]
={1,2,3,4,5,6,7,8,9,10,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103, 104 ,105}
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Need helpppp!!!!!!!!!!
Answer:
When x approaches -∞, y approaches ∞ and when x approaches ∞, y approaches ∞.
Step-by-step explanation:
In a warehouse, there are 2 robots that work together. They move in the same direction concurrently, so if one moves North, they both North. The robots will follow any instructions they’re given and will collect any objects they find along the way. They only take instructions by the points of the compass and can only move in 4 directions (N, E, S, W).
For example, if the 2 robots are given the directions: “N, E, S”, then Robot A will collect a ball and Robot B will collect a hat.
Write the directions the robots would need to follow to collect the following objects, remembering that both robots get the same directions, and assuming that for each question they start off in the same (pictured above) positions:
1. Robot A: ball Robot B: ball
2. Robot A: hat, ball Robot B: box, hat
3. Robot A: ball, ball Robot B: hat, ball
1. For collecting balls by both Robot A and B the direction will be N->E->E
2. For collecting hat and ball by Robot A and box and hat by Robot B, the direction will be N->N->S->E->E
3. For collecting both the balls by Robot A and a hat and ball by Robot B, the direction will be E->E->N
The direction that both Robot A and Robot B can take are N, E, S and W
For Part 1:
Robot A and Robot B need to collect the ball which is in the 2nd row 5th column for Robot A and 4th row 3rd column for Robot B, therefore the direction will be:
=N->E->E
For Part 2:
Robot A needs to collect a hat and ball which are in the 1st-row third column and 2nd row 5th column respectively. Robot B needs to collect a box and a hat which are in the 3rd row 1st column and 4th row 3rd column respectively. Therefore, the direction will be:
= N->N->S->E->E
For Part 3:
Robot A needs to collect both the balls which are in the 3rd-row 4th column and 2nd row 5th column respectively. Robot B needs to collect a hat and a ball which are in the 5th row and 2nd column & 4th row 3rd column respectively. Therefore, the directions will be:
= E->E->N
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How do you solve absolute value inequalities on both sides
The median number of pools installed by 9 construction teams in a certain summer is 11. The
range of the number of pools installed by those teams that summer is 14.
Determine if the following statement is true, is false, or does not contain enough information.
At least one team installed 11 pools
Answer: False. If this were true, then the range would have been 18 - 6 = 12.
Step-by-step explanation:
1 Find all possible square roots (1 point)
√400=
20 or -20
15 or -18
16 or -16
14 or -14
Answer:
20 or - 20 is the answer
Step-by-step explanation:
20×20 = 400
or
-20 × -20 = 400
Cm^2-g/cm^4
Does cm become cm^2. How to I subtract it?
Answer:
[tex]\frac{cm^{6} - g}{cm^{4} }[/tex]
Step-by-step explanation:
Write 1/cm^2 - g/cm^4 to visualize it better, then distribute using the fraction rule ([tex]\:a-\frac{b}{c}=\frac{ac-b}{c}[/tex]): [tex]\frac{cm^2cm^4-g}{cm^4}[/tex]
Combine like terms to get: [tex]\frac{cm^6-g}{cm^4}[/tex]
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Adam invests 16,000 in an investment certificate (GIC) that pays 3 percent, compounded annually.
How much interest will he have earned after two years?
$867.40
$960.00
$974.40
$1,031.40
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}[/tex]
[tex]A=16000\left(1+\frac{0.03}{1}\right)^{1\cdot 2} \implies A = 16974.4~\hfill \underset{earned~interest}{\stackrel{16974.4~~ - ~~16000}{ 974.40}}[/tex]
Monica sold 3 pairs of her old Slick Sprinter sneakers at the Re-Laced secondhand store. Before she left, Monica spent $13 of her earnings on a used pair of boots. She had $8 remaining. How much did Monica receive for each pair of sneakers?
Monica received $ 7 amount of money for each pair of sneakers she sold.
We are given that:
Remaining amount with Monica = $ 8
She spent on earing = $ 13
The total amount she had = $ 13 + $ 8
The total amount she had = $ 21
Now, she sold 3 pairs of sneakers and gained $ 21
So, the price of each snicker will be calculated by using division.
So, we get that:
Monica receive for each pair of sneakers = $ 21 / 3 = $ 7
Therefore, Monica received $ 7 amount of money for each pair of sneakers she sold.
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Dana has driven her car 95,598 miles. She estimates she can
drive the car another 5000 miles before the mileage reaches
100,000 miles. Use the rules for estimating differences to
explain if Dana is correct.
Answer: Dana estimation is incorrect because difference = 598 miles
Step-by-step explanation:
Given data,
Dana has driven her car 95,598 miles.
She estimates she can
drive the car another 5000 miles.
she can,
drive the car another 5000 miles before the mileage reaches
100,000 miles.
Estimated Mileage of the car is equal to 100,000 miles.
That is,
Estimated Mileage of the car is = 100,000 miles.
So,
We can write,
Total distance Dana has to travel = already driven + additional miles to cover
Total distance Dana has to travel = 95,598 + 5,000 miles
Total distance Dana has to travel = 1,00,598 miles.
As per mileage of car is 100,000 miles.
So, Dana has to travel = 1,00,598 miles.
So, Dana estimation is incorrect because difference is = 100,598 - 100,000
Therefore,
Dana estimation is incorrect because difference = 598 miles
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Write a ratio that forms a proportion with 2/9
The ratio that forms a proportion with 2/9 in the question is 14/63.
What is ratio?
Ratio can be described as the term that is been used in mathematics which is been used in the indication of how many times one number contains another.
From the given figure, which is 2/9 , the ratio that form the proportion can be found as
[(2*7) / (9*7) ]= 14/63
In conclusion we can see that the ratio that forms a proportion with 2/9 in the question is 14/63 because if we follow the way the ratio is been calculated , we can see that 14/63is the correct answer, which is option D.
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The missing options are:
10/40
12/63
12/45
14/63
Plot the ordered pair -5,3
1/2
A graph of the given ordered pair (-5 3 1/2) has been plotted as shown in the image attached below.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is an ordered pair?An ordered pair can be defined as a pair of two elements that are typically written in a fixed order within parentheses as (x, y), which represents the x-axis (abscissa) and the y-axis (ordinate) on a coordinate plane.
In conclusion, the point (-5) would be plotted on the x-axis (abscissa) while point (3 1/2) would be plotted on the y-axis (ordinate) of a coordinate plane as shown in the image attached below.
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Evan has an even number of shells he has more than 10 shells and less than 15
Answer:
It can ither be 12 or 14
Step-by-step explanation:
The numbers have to be even and must be greater than 10 but less than 15 and the only numbers that are greater than 10 but less than 15 are 12 and 14.
Hope this helps.
on the same axes draw the graphs of y=2x and y=2xt5(tables for y=2x and y=2xt5)
The graph for y=2x and y=2x + 5 is drawn at bottom.
Why are graphs used by mathematicians?A common technique for graphically showing data linkages is the graph. While taking up less space, a graph accomplishes the goal of conveying information that are either too many or complicated to be completely stated in the text.
A graph is a diagram or graphical representation that organizes the display of facts or values. The points on a graph are typically used to depict the relationships between two or more things.
For the given question,
y = 2x
The coordinates are -
(1,2), (2,4), (3,6), (4,8)
y=2x + 5
The coordinates are -
(1,7), (2,9), (3,11), (4,13)
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Eula needs to buy binders that cost $4 each and notebooks that cost $2 each. She has $20. The graph of the inequality 4x + 2y ≤ 20, which represents the situation, is shown. What is the greatest number of binders Eula can buy? What is the greatest number of notebooks Eula can buy? If Eula buys 7 notebooks, what is the greatest number of binders she can buy?
The required answers are,
The greatest number of binders Eula can buy is 5.
The greatest number of notebooks Eula can buy is 10.
If 7 notebooks are ordered, one binder may also be bought, costing $2 more for Eula.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now the given inequality is,
4x + 2y ≤ 20
here x is the number of binders and y is number of notebooks.
Cost of 1 binder = $4
Cost of 1 notebook = $2
Now for maximum number of binders put y = 0 in the given inequality we get,
4x + 2*0 ≤ 20
Solving we get,
4x ≤ 20
Dividing both the side by 4 we get,
x ≤ 5
Thus, Eula is permitted to acquire 5 binders in the absence of notebook purchases.
Now for maximum number of notebooks,
Putting x = 0 in the given inequality we get,
4*0 + 2y ≤ 20
Solving we get,
2y ≤ 20
Dividing both the side by 2 we get,
y ≤ 10
Thus, Eula is permitted to purchase 10 notebooks if no binders are purchased.
Now if Eula buys 7 notebooks, putting y = 7 in the given inequality we get,
4x + 2*7 ≤ 20
Solving we get,
4x + 14 ≤ 20
Subtracting both the side by 14 we get,
4x ≤ 6
Dividing both the side by 4 we get,
x ≤ 3/2
⇒ x ≤ 1.5 ≈ 2
Thus, If 7 notebooks are ordered, one binder may also be bought, costing $2 more for Eula.
Hence,If 7 notebooks are ordered, one binder may also be bought, costing $2 more for Eula.
Thus, the required answers are,
The greatest number of binders Eula can buy is 5.
The greatest number of notebooks Eula can buy is 10.
If 7 notebooks are ordered, one binder may also be bought, costing $2 more for Eula.
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Answer: 1) 5 2)10 3) 1
Step-by-step explanation:
on edge its correct
Rewrite the slope intercept equation into point slope form
Y=-1/3x+9
The point slope form of the given slope intercept form is:
y ₋ 9 = ₋1/3 (x ₋ 0)
Given, we have the slope intercept form as :
y = ₋1/3x ₊ 9
To convert the given form into point slope form we first need to determine the slope and the point.
A straight line is represented as a point on the line and its slope in point slope form. That means using the point slope form, one may find the equation of a line passing through the points (x ₁, y ₁) and having a slope of "m".
from the given equation y = ₋1/3x ₊ 9
the above equation is in the form of: y = mx ₊ b
slope (m) = ₋1/3
y intercept (b) = 9
x intercept = 0
Therefore, the points are: (0,9) = (x₁ , y₁)
hence the point slope form is:
y - y₁ = m(x ₋ x₁)
y ₋ 9 = -1/3(x ₋ 0)
hence we get the required point slope form.
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Please help ASAP
Which Venn diagram has shading that represents the given set?
[tex]S^{C}[/tex] ∩ T sets is the option C.
How to represent sets in Venn diagram?Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
A set is a collection of items.
S is a set and T is also a set.
[tex]S^{C}[/tex] simply means S complement.
Complement of S simply means not in S. It means everything not in S.
∩ simply means intersection
Therefore,
[tex]S^{C}[/tex] ∩ T implies not in S intersection T sets.
Hence, [tex]S^{C}[/tex] ∩ T is the option C.
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the swimming pool. The result are Time, / (min) 0-10 11-20 21-30 31-40 Number of people 6 8 4 2 20 16.9
a Use the mid-interval values to calculate an estimate for the mean time spent in the pool.
What is the modal class?
The modal class of the given frequency distribution table is found as: 0-10.
The mean found for the frequencies of swimming pool is 36.5.
What is defined as the frequency distribution table?A frequency distribution table is a graph that summarizes all data into two columns: variables/categories and frequency. It consists of either two or three columns. Depending on the size of the data set, the first column will typically list all of the outcomes as particular values or as class intervals.The given grouped class interval is-
Time(min): 0-10 11-20 21-30 31-40
Number of people: 68 42 20 16
Modal class: The modal class is indeed the class interval within such a set of data that has the greatest number of data points, also known as the highest frequency.
Thus, from the given frequencies, the maximum frequency that is 68 occurred for the class of 0-10.
Thus, the modal class is: 0 - 10.
For the calculation of mean;
mean = sum of all frequencies/number of frequencies
mean = (68 + 42 + 20 + 16)4
mean = 146/4
mean = 36.5
Therefore, the mean of the frequency for the swimming pool is 36.5.
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The product of 10 and a number p
Answer:
10p, assuming p is a variable
need help math worklkkk
IM GIVING BRAINLIEST! PLEASE I NEED HELP! Ava had $28.50 to spend at the farmer's market. After buying 3 pumpkins Ava, has $12 left. Which equation could you use to find the price of one pumpkin (x)?
28.50/3=x
3x-12=28.50
x+12=28.50
3x+12=28.50
The midpoint of \overline{\text{AB}} AB is M(7, 0)M(7,0). If the coordinates of AA are (8, -3)(8,−3), what are the coordinates of BB?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{8}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +8}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(7~~,~~0)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +8}{2}=7\implies x+8=14\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3}{2}=0\implies y-3=0\implies \boxed{y=3}[/tex]
For each value of x, determine whether it is a solution to 15< x.
Based on the information provided, we have the following:
15 < 10; No, it is not a solution.15 < 16; Yes, it is not a solution.15 < 13; No, it is not a solution.15 < 20; Yes, it is not a solution.What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Next, we would determine whether or not the given values of variable x are solutions to the given inequality by evaluating as follows:
When x = 10, we have:
15 < 10; No, it is not a solution.
When x = 16, we have:
15 < 16; Yes, it is not a solution.
When x = 13, we have:
15 < 13; No, it is not a solution.
When x = 20, we have:
15 < 20; Yes, it is not a solution.
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Complete Question:
For each value of x, determine whether it is a solution to 15 < x.
Is it a solution?
10: yes or no
16: yes or no
13: yes or no
20: yes or no
Define sets U, A, B, and C as shown below. Find A'n (BUC').
U= ({a,b,c,d,e,f.g.h}
A = {f,g,h}
B={a,g,h}
C={a,b,c,d,e)
Answer:
{a}
Step-by-step explanation:
You want the set A'∩(B∪C') given the definitions of each of the sets U, A, B, C.
Inverse setsThe inverse of a set is the set of elements of the universal set that are NOT in the given set.
A' = {a, b, c, d, e, f, g, h} - {f, g, h} = {a, b, c, d, e}
C' = {a, b, c, d, e, f, g, h} - {a, b, c, d, e} = {f, g, h}
UnionThe union of two sets is the list of elements in either of the two sets.
B∪C' = {a, g, h} +{f, g, h} = {a, f, g, h}
IntersectionThe intersection of two sets is the list of elements common to both:
A'∩(B∪C') = {a, b, c, d, e} ∩ {a, f, g, h} = {a}
1 foot is 12 inches. 5 cm is approximately 2 inches. Work out an approximation for the number of cm in 4 feet.
4 Feet = 121.92 cm.
Step-by-step explanation:The formula is to multiply the length value by 30.48.
Feet (ft) Centimeters (cm)
1 ft 30.48 cm
2 ft 60.96 cm
3 ft 91.44 cm
4 ft 121.92 cm
Jane has a pre-paid cell phone with Splint. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 320 minutes and the cost was $143.00. In July she used 710 minutes and the cost was $279.50.
The cost function expressed as the number of times spent calling is cost function = c(x) = 31 + 0.35x
How to solve for the cost functionThe cost function that can be written as per the number of units that she used is given as
c(x) = a + bx
x = 320
a + 320b = 143
When x = 710
we would have
a + 710b = 279
subtract the equations
710 b - 320 b = 279 - 143
390b = 136
b = 136/390
= 0.35
Put the value of b in equation 1
a + 320 x 0.35 = 143
a + 112 = 143
a = 31
cost function =
c(x) = 31 + 0.35x
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complete questionA) Express the monthly cost C as a function of a, the number of minutes of calling time she used.
what could be the volume of a rectangle box? A. 24 square meters. B 24 meters C. 24 cubic meters. D.24 grams C.24 centimeters
Answer: C
Step-by-step explanation:
Area de una pared 42 ²/3 yardas cuadradas Angela usa 1 galon y 1/3 de pintura. i Cuál es la tasa de cobertura de Angela en yardas cuadradas por galón y 1/3 de pintura?
Responder:
Parte A: 32 yardas cuadradas por galón
Parte B: 13 pies cuadrados por galón de diferencia
Explicación paso a paso:
Parte A:
Para saber cuántas yardas cuadradas cubre cada galón, tienes que dividir 42 2/3 entre 1 1/3, lo que equivale a 32. Eso significa que cada galón de pintura cubre 32 yardas cuadradas.
Parte B:
Primero, tienes que convertir cuánto cubrió Ángela en yardas cuadradas a pies cuadrados. Como una yarda cuadrada equivale a 9 pies cuadrados, tenemos que multiplicar 32 por 9, lo que equivale a 288. Para encontrar la diferencia, debes restar 288 - 275, lo que equivale a 13.
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Your cousin renews his apartment lease and pays a new monthly rent his new rent is a calculated by applying a discount of $50 to his original rent and then applying at 10% increase to the discounted amount what was your cousins original monthly rent when his new rent is 5% greater
Answer:
10000000$
Step-by-step explanation:
gu kha le bhosadike duck you
she sold 12 cupcakes for 42 dollars what is the constant of proportionality
The table of values shows the output values of three different equations for the same input values, x.
Drag the correct expression to each row to complete each equation.
An equation is a formula that expresses the equality of two expressions, by connecting them with the equal sign. The relations are: x+3, 3x², 3ˣ
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equal sign.
Finding the relations:
Relationship 1:
The y-values have a common difference of 1, so the relationship is linear with as slope of 1. The only matching choice is (x+3), which matches the values of y1.
Relationship 2:
The y-values have differences that increase with a common difference. They are (3-0) = 3, (12-3) = 9, (27-12) = 15, (48 -27) = 21. The second differences are (9-3) = 6, (15-9) = 6, and so on with all second differences being 6. This tells you that a second-degree polynomial can model this sequence. The only matching choice is 3x² which matches the values of y².
Relationship 3:
The y-values have increasing differences that also have increasing differences. The values have a common ratio of 3, indicating an exponential function will model this sequence. The only matching choice is (3ˣ), which matches the values of y³.
Therefore the relations are: x+3, 3x² and 3ˣ
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Answer: Hope you guys can see it
Step-by-step explanation: