The cardinality of a set refers to the number of elements in the set. It is found by counting the elements in the set.
What is cardinality of a set?The cardinality of a set refers to the number of elements in the set. To obtain the cardinality, we have to count the elements in the set.
a) There are 6 elements in this set hence the cardinality is 6.
b) There is only one element in the set hence its cardinality is 1.
c) There are two elements in the set hence the cardinality is 2.
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Simplify the expression (7 + 9i)(8 - 10i)
The simplified expression of (7 + 9i)(8 - 10i) is 146 + 2i
How to simplify the expression?The expression is given as:
(7 + 9i)(8 - 10i)
Expand the bracket
7 * 8 + 9i * 8 -7 * 10i - 9i * 10i
Evaluate the products
56 + 72i -70i - 90(i²)
Evaluate the difference
56 + 2i - 90(i²)
In complex numbers;
i² = -1
So, we have:
56 + 2i - 90(-1)
Evaluate
56 + 2i + 90
Add the like terms
146 + 2i
Hence, the simplified expression of (7 + 9i)(8 - 10i) is 146 + 2i
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I don’t know how to solve
Answer:
line it, then try to add each number going from the top, my mother gave me that advice before, it works (:
Step-by-step explanation:
Answer:
X go's first then Y
Step-by-step explanation:
I did this before and got 100% promise and mark me brainiest
Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below:
A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 1 meter.
What is the maximum length of the seesaw?
Using the slope concept, it is found that the maximum length of the seesaw is of 1.73 meters.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The vertical change is of 1 m.The horizontal change is the length l.The angle is of 30º.Hence:
tan(30º) = 1/l
l = 1/tan(30º)
l = 1.73.
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if a person paid rs 32 as VAT to buy an article of cost Rs 2750 then how much money he /she pay? find it
The total amount paid for the article is Rs2782
How to determine the amount paid?The given parameters are:
Article = Rs 2750
VAT = Rs 32
The amount paid is calculated using:
Amount = Article + VAT
This gives
Amount = 2750 + 32
Evaluate
Amount = 2782
Hence, the total amount paid for the article is Rs2782
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Does the equation xy + 6y = 9 define y as a function of x?
O Yes
O No
Answer:
no. a function doesnt contain an = sign
Step-by-step explanation:
Answer:
Yes, it is a function.
Explanation:
xy + 6y = 9
y(x + 6) = 9
y = 9/(x + 6)
It is a inverse variation function.
Where equation: xy = k ["k" is constant]
Each value of x corresponds to a single value of y.Can someone explain how to get the answer I’m confused on how to solve
Answer:
x=29
Step-by-step explanation:
The square notation indicates 90 degrees.
90=(x+3)+(x-1)+(x+1)
90=3x+3
87=3x
x=29
Answer:
x = 29
(x + 3)° = 32°
(x - 1)° = 28°
(x + 1)° = 30°
Step-by-step explanation:
(x + 3)° + (x - 1)° + (x + 1)° = 90°-> (x + x + x +3 -1 + 1)° = 90°-> (3x + 3)° = 90°-> 3x + 3= 90-> 3x = 90 - 3-> 3x = 87-> x = 87/3-> x = 29-> (x + 3)° = (29 + 3)° = 32°-> (x - 1)° = (29 - 1)° = 28°-> (x + 1)° = (29 + 1)° = 30°1. Sue made a cookie cake for her friend's birthday. The diameter is 8 inches. The area of the cake is
inches² (round to the nearest hundredths place)
Answer:
50.24 inches^2
Step-by-step explanation:
D=8 inches, r=D/2, r=8/2=4 inches
Area of circle= πr^2
=3.14×4×4
=3.14×16
=50.24
This figure represents a small collectible box. Vicki wants to cover 45 of the surface with glitter.
How much of the total surface will be covered with glitter?
Enter your answer as a decimal or mixed number in simplest form in the box.
cm²
Right trapezoidal prism. The height of the trapezoid base is labeled 4 centimeters. The larger base is labeled 6 and 1 half centimeters, and the shorter base is 5 and 1 fourth centimeters. The two legs of the trapezoid are labeled 4 centimeters and 4 and 1 fifth centimeters. The height of the prism is labeled 9 centimeters.
PLease helpppp!! only have 2 minutesd
Answer:
181.24
Step-by-step explanation:
The total surface area of the Trapezoidal Prism to be covered is: 181.24 cm².
What is the Surface Area of a Trapezoidal Prism?Surface Area = 2(area of trapezoid) + area of the 4 rectangular faces.
Area of Rectangle 1 = length × width = 9 × 4 = 36 cm²
Area of Rectangle 2 = length × width = 9 × 5 1/4 = 47.25 cm²
Area of Rectangle 3 = length × width = 9 × 4 1/5 = 37.8 cm²
Area of Rectangle 2 = length × width = 9 × 6 1/2 = 58.5 cm²
Area of the two trapezoids = 2[1/2(a + b)h] = 2[1/2(6½ + 5¼)4] = 47 cm²
Surface area = 36 + 47.25 + 37.8 + 58.5 + 47 = 226.55 cm²
Total surface that will be covered = 4/5(226.55) = 181.24 cm²
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Point G is on line segment FH. Given FG = 10 and GH =
10 and GH = 5, determine the
length FH.
Answer:
FH = 15
Step-by-step explanation:
G is lying between the point F & H on the line FH.
So, the distance of FH will be given by the sum of distance of FG and GH.
FH = FG + GH
= 10 + 5
= 15
find the length of the third side round to the nearest tenth if needed . 24 10
Answer:
the length of the third side is 26
Step-by-step explanation:
By Pythagoras theorem
AC² = AB² + BC²
AC² = 10² + 24²
AC² = 100 + 576
AC² = 676
AC = √676
AC = 26
ASAP! HELP!!!
2. Quadrilateral PQRS is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show all your work.
The measure of each of the angles ∠P,∠Q,∠R, ∠S are 45°,72°,135° and 98° respectively.
What is quadrilateral ?A quadrilateral is a polygon having four sides. The measure of the opposite angle of quadrilateral inside circle is 180°.
From the figure:
∠P=x+15
∠Q=3x-8
∠R=?
∠S=3x+8
∠Q+∠S=180
3x-8+3x+8=180
6x=180
x=30°
∠P+∠R=180°
x+15+∠R=180
30+15+∠R=180
∠R=180-45
∠R=135°
∠P=30+15=45
∠Q=3x-8=3(30)-8=72
=135
∠S=3x+8=3(30)+8=98
Hence,the measure of each of the angles ∠P,∠Q,∠R, ∠S are 45°
,72°,135° and 98°.
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Pls help me with my math
Answer:a
Step-by-step explanation:Bottom line includes the end point so should be less than or equal. Top line does not so should be greater than
Kurt and Courtney are playing basketball. Kurt makes 2 baskets in the first game and 4 baskets in each game after that. Courtney makes 4 baskets in the first game and 2 baskets in each game after that. The table below shows the number of baskets each made in the first 4 games. Which graph shows the ordered pairs of the total number of baskets each has made after each game?
Answer:
Kurt 10 Courtney 10 Mark brainiest
Step-by-step explanation:
I did this too
Answer:
they each have 10 if you count mark me brainiest, please
Step-by-step explanation:
A car and a motor bike are priced at $33090. If the value of the car is three times the value of the motor bike, how much is the car worth?
Please Help
Use the probability distribution table to answer the question.
X / P
0 / 0.03
1 / 0.13
2 / 0.70
3 / 0.10
4 / 0.04
What is P(2
Considering the given discrete probability distribution, it is found that [tex]P(2 < X \leq 4) = 0.14[/tex].
What does the discrete probability distribution gives?It give the probability of each outcome, and each outcome is represented by a countable number.
The desired probability is:
[tex]P(2 < X \leq 4) = P(X = 3) + P(X = 4)[/tex]
As there is an open interval at X = 2, it does not enter the calculation. The values are:
P(X = 3) = 0.1.P(X = 4) = 0.04.Hence:
[tex]P(2 < X \leq 4) = P(X = 3) + P(X = 4) = 0.1 + 0.04 = 0.14[/tex]
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I have 23 hundredths and 12 tenths. Who am I? Convince by using Base 10 Blocks
Answer:
1.43
Step-by-step explanation:
12 tenths ⇒ 1.2
23 hundredths ⇒ 0.23
0.23 + 1.2 = 1.43
name the marked angle two different ways
tbh I have no Idea ask your mother
NEED HELP
(8.02-8.05)
Solve the systems of equations below using the method indicated in each part of the table. Be sure to show ALL your work for each method in order to get full points! (15 points)
The solutions to the systems of equations are:
1. (2, 3) (see attachment below). [one solution]
2. no solution
3. (3, 13) [one solution]
Solution to a System of Equations?The solution to a system of equations is the x-value and y-value that will make both equations true. It can be found either using a graph, by elimination method, or substitution method as explained below.
1. Using graph to solve y = 2x - 1 and y = 4x - 5:
The solution is the point where both lines intersect which is: (2, 3) (see attachment below). [one solution]
2. Solving using substitution method:
x = -5y + 4 ---> eqn. 1
3x + 15y = -1 ---> eqn. 2
Substitute x = -5y + 4 into eqn. 2
3(-5y + 4) + 15y = -1
-15y + 12 + 15y = -1
-15y + 15y = -1 - 12
0 = -13 (this shows that there is no solution)
3. Using elimination method:
14x = 2y + 16 ---> eqn. 1
5x = y + 2 ---> eqn. 2
1(14x = 2y + 16)
2(5x = y + 2)
14x = 2y + 16 ----> eqn. 3
10x = 2y + 4 -----> eqn. 4
Subtract
4x = 12
x = 12/4
x = 3
Substitute x = 3 into eqn. 2
5(3) = y + 2
15 = y + 2
15 - 2 = y
13 = y
y = 13
The solution is: (3, 13).
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círculo de diámetro de 9 cm calcular radio perímetro y area doy corona
Answer:
Radio
r=4.5cm
Area
63.62cm2
Perímetro
C≈28.27cm
Help PLS ASAP!!!!!!!!!!!!
Answer:
The answer is
" THe middle triangle is scalene"
and "the right and left triangle are isosceles"
Step-by-step explanation:
This is because B, and D are wrong.
B is wrong because all three sides are different lengths
D is wrong because the right and left triangles are not equalateral
give brainliest please!
hope this helps :)
The White Russian cocktail contains vodka, Tia Maria and milk in the ratio of 5:2:3. To make the cocktail for a party the barman used 180ml of milk. What was the total volume of the cocktail? If this was served in 60ml glasses, how many glasses would it serve?
Answer:
1) 600cm^3 2) 10 glasses
Step-by-step explanation:
x = total amount in ml
(3/10)x = 180ml (MILK)
x = 600ml
(2/10)600 = 120ml (TIA MARIA)
(1/2)600 = 300ml (VODKA)
1) 600cm^3
2) 600ml : 60ml = 10 (GLASSES)
7. What are the x- and y-intercepts for -x + 2y = 8?
O
A. x-intercept =-8; y-intercept = 4
O
B. x-intercept = 4; y-intercept = 8
O
C. x-intercept = 4; y-intercept = -8
O D. x-intercept = 8; y-intercept = -4
Answer:
the answer
Step-by-step explanation:
the answer is A
• (4,0)
•(0,4)
•(1,3)
•(3,1)
Answer:
The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Step-by-step explanation:
If 5 apples cost $1.15, find the cost of 16 apples
Answer:
3.68$Step-by-step explanation:
If 5 apples cost $1.15, find the cost of 16 apples
we can solve with an equation5 : 1.15 = 16 : x
x = 1.15 * 16 : 5
x = 18.04 : 5
x = 3.68
check
5 : 1.15 = 16 : 3.68
4.34 = 4.34
the answer is good
A multiple-choice examination has 10 questions, each with four possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least six questions correctly?
Answer:
[tex]0.0197277[/tex]
Step-by-step explanation:
Consider the random variable X
Where X denotes the number of (success/having a correct answer)
in 10 identical and independent trials .
then
X follows the Binomial distribution with parameters
10 and p = p(success) = 1/4
[tex]p\left( X\geq 6\right) =\sum^{10}_{k=6} p\left( X=k\right)[/tex]
[tex]=\sum^{10}_{k=6} C^{k}_{10}\left( \frac{1}{4} \right)^{k} \left( \frac{3}{4} \right)^{10-k}[/tex]
[tex]=\frac{20686}{2^{20}} \\= 0.0197277[/tex]
To verify the associative property of addition, begin
by finding the sum of the polynomials:
(3x + 4) + ((5x²-1) + (2x + 6))
x² +
X +
DONE
The sum of the given polynomial is 5x²- 5x +9
Sum of polynomialPolynomials are expressions with a degree of 3 and above. Given the equation shown;
(3x + 4) + ((5x²-1) + (2x + 6))
Expand
(3x + 4) + ((5x²-1) + (2x + 6))
3x + 4 + 5x²-1 + 2x + 6
Collect the like terms
5x² + 5x + 4 - 1 + 6
5x²- 5x +9
Hence the sum of the given polynomial is 5x²- 5x +9
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These equations represent the number of bacteria in four different dishes as a function of time, t, in days. Which equation represents the population with the greatest growth factor (also called common factor)?
SOMEONE ANSWER THIS ANS YOU’LL EARN FREE EASY POINTS FOR GIVING ME THE RIGHT ANSWER!!
The growth factor:
⇒ is the base in the exponent:
⇒ the larger it is ⇒ the greater the growth factor is!
Let's Analyze our choices:
c(t)'s growth factor: 5/2a(t)'s growth factor: 5/6d(t)'s growth factor: 3b(t)'s growth factor: 1/50The greatest growth factor is 3
Answer: d(t)
Hope that helps!
what is common ratio? 1,-1.5,2.25,-3.375
The common ratio of the sequence is -1.5
How to determine the common ratio?The sequence is given as:
1,-1.5,2.25,-3.375
Divide the second term by the first to determine the common ratio (r)
r = T2/T1
This gives
r = -1.5/1
Evaluate
r = -1.5
Hence, the common ratio of the sequence is -1.5
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Find the 9th term of the geometric sequence 8,32,128,
[tex]\text{First term,}~ a = 8\\\\\text{Common ratio,}~ r= \dfrac{32}8 = 4\\\\\text{nth term} = ar^{n-1} \\\\\text{9th term} = 8\cdot 4^{9-1}\\\\\\~~~~~~~~~~~~~=8 \cdot 4^8\\\\\\~~~~~~~~~~~~~=524288\\\\\text{The 9th of the geometric sequence is 525288.}[/tex]
What do you think are the biggest advantages & disadvantages regarding the kind of technology we have access to in the early 21st century?
The advantages and disadvantages of the kind of technology we have access to in the early 21st century include:
Advantages:
The improvement of productivity.
Better and easier communication between people.
Disadvantages:
Can be bad for the environment.
Technology might be able to replace humans in jobs.
What is technology?Technology is the result of accumulated knowledge and the application of skills, and processes used in industrial production and scientific research.
Technology is embedded in the operation of all machines for the intended purpose of an organization.
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