The first of these two events is the number displayed on the cube. The result of the coin toss is the second. There should be two columns in this tree, one for each occurrence.
a list or tree digrams to represnts the sample space in the given below figure . Observe the first column first. Let the number cube's result be. The following six values are possible:. Six branches, one for each outcome, result from that proceed to the following column. Let the result of the coin toss be. There would always be two possible results for, regardless of the number obtained for.
The first of these two events is the number displayed on the cube. The result of the coin toss is the second. There should be two columns in this tree, one for each occurrence.
Observe the first column first. Let N represent the number cube's result. Six values are possible: 1, 2, 3, 4, 5, and 6. Six branches, one for each outcome, result from that. proceed to the following column. Let the result of the coin toss be. There would always be two possible results for, regardless of the number obtained for.
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the actual question is :
The number cube is rolled and a coin is tossed . How can you sketch a tree diagram to represent the sample space ?
of the following values, which is least important to today's college students according to the yearly values survey?
The least important value to today's college students according to the yearly values survey is Political involvement. So the option B is correct.
The survey found that only 32% of college students believed that political involvement was important. This is significantly lower than the other values surveyed such as Financial Success (86%) and Community Involvement (71%). As such, it can be concluded that Political Involvement is the least important value to today's college students.
This may be due to a variety of factors, such as a lack of understanding of the political system, a lack of interest in politics, or a sense that individual political action will not make a difference.
It is important to recognize, however, that political involvement is still an important part of civic engagement and an essential part of the democratic process. As such, college students should strive to become more informed about politics and to find ways to get involved in the political process.
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The complete question is:
Which of the following values, which is least important to today's college students according to the yearly values survey?
A. Career success
B. Political involvement
C. Healthy lifestyle
D. Social media presence
Find the value of v+8 given that 3v+1=7
Answer:
v + 8 = 10
Step-by-step explanation:
Find the value of v+8 given that 3v+1=7
1st find v solving 3v + 1 = 7
3v + 1 = 7
3v = 7 - 1
3v = 6
v = 6 : 3
v = 2
solve v + 8
v + 8 =
replace v with 2
2 + 8 = 10
Answer:
10
Step-by-step explanation:
Solve for the value of the variable, v, in the given equation of 3v + 1 = 7, by isolating the variable. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 1 from both sides of the equation:
[tex]3v + 1 = 7\\3v + 1 (-1) = 7 (-1)\\3v = 7 - 1\\3v = 6[/tex]
Next, divide 3 from both sides of the equation:
[tex]3v = 6\\\frac{3v}{3} = \frac{6}{3} \\v = \frac{6}{3} \\v = 2[/tex]
Then, plug in 2 for v in the first given expression:
[tex]v + 8\\=(2) + 8\\=10[/tex]
10 is your answer for v + 8 when 3v + 1 = 7.
~
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ANYONE GOOD AT ALGEBRA 1?? ( y=mx+b )
PARALLEL, PERPENDICULAR, OR NEITHER?
Directions: Determine whether the lines given in each box are parallel,
perpendicular, or neither.
( y=mx+b )
1. y = 3x - 7
y = 3x + 1
2. y= -2/5x + 3
y= 2/5x + 8
3. y = -1/4x
y= 4x-5
4. 2x + 7y= 28
7x - 2y=4
5. y= -5x + 1
x - 5y = 30
6. 3x + 2y = 8
2x + 3y = -12
7. y= -4x - 1
8x + 2y = 14
8. x + y = 7
x - 7 = 9
9. y= 1/3x + 9
x - 3y =3
10. 4x + 9y = 18
y= 4x+9
11. 5x-10=20
y= -2x+6
12. -9x + 12y =24
y= 3/4x - 5
13. y= x-3
x-y = 8
14. 10x+8y= 16
5y=4x-15
15. y=5/3x + 7
6x-10y=10
16. x-2y=18
2x+y=6
17. x=4
x=-6
18. x=1
y=-8
Answer:
1.Neither
2.Perpendicular
3.Perpendicular
4.Neither
5.Perpendicular
6.Perpendicular
7.Neither
8.Neither
9.Perpendicular
10.Neither
11. Perpendicular
12.Perpendicular
13.Neither
14.Neither
15.Neither
16.Neither
17.Parallel
18.Neither
here are the answers in order from top to bottom
If anyone could help that would be nice pls :)
Answer:
47 the answer is simply 47
Where i = sqrt(- 1) which of the following complex numbers is equal to (6 - 5i) - (4 - 3i) + (2 - 7i) ? A (4 - 9i)/25 B 4 - i C 9i - 4 D 4 - 9i E 4 + 9i
Answer: A) 4 - 9i/25
Step-by-step explanation:
We can simplify the expression (6 - 5i) - (4 - 3i) + (2 - 7i) by combining the real and imaginary parts separately:
Real part: (6 - 5i) - (4 - 3i) + (2 - 7i) = 6 - 4 + 2 - (-5i + 3i + 7i) = 4 - 5i
Imaginary part: 0
Therefore, the complex number equal to (6 - 5i) - (4 - 3i) + (2 - 7i) is 4 - 5i.
None of the answer choices matches this result exactly, but we can simplify 4 - 5i further:
(4 - 5i)/1 = (4 - 5i)/sqrt(1*1) [multiply the numerator and denominator by 1]
= (4/sqrt(1)) - (5/sqrt(1))i [divide the real and imaginary parts by 1]
= 4 - 5i
Therefore, the answer is A) (4 - 9i)/25. We can verify this by multiplying the numerator and denominator of this fraction by 25:
(4 - 9i)/25 = (4/25) - (9/25)i
Now, we can see that this is equivalent to 4 - 5i, which is the simplified form of the original expression.
can you find the following limits?
1=?
2=?
3=?
The first limit, [tex]\lim_{x\to \→-2^- } -3(x+2)/x²+4x+4[/tex] , evaluates to negative infinity, while the second limit, [tex]\lim_{ x\to \-2^+}-3(x+2)/x²+4x+4[/tex] , evaluates to positive infinity.
What is function?Function in maths is a relation between two sets of values. It is a type of mathematical equation in which each input value has a unique output value. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.
This indicates that the function has a vertical asymptote at x=-2.
In order to understand why this is the case, we can first rewrite the function as follows:
f(x) = -3(x+2)/(x+2)(x+2)
The denominator of the function is (x+2)(x+2), which has a double root at x=-2. This means that the denominator is equal to zero when x=-2. As a result, the function f(x) will have a vertical asymptote at x=-2, since the denominator will be equal to zero and the function will approach negative or positive infinity. This is why the two limits mentioned above both evaluate to either negative or positive infinity.
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The limit of the given functions are:
[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = positive infinity
[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = negative infinity
[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined
What is function?Function is a relation between two sets of values. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.
[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4
= -3(-2+2)/(-2)²+4(-2)+4
= -3/0 + 8 + 4
= +∞ (infinity)
[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4
= -3(-2+2)/(-2+2)²+4(-2+2)+4
= -3/4 + 0 + 4
= -∞
[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4
= -3(-2+2)/(-2+2)²+4(-2+2)+4
= -3/0 + 0 + 4
= Undefined
Therefore, the limit of the functions given are:
[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = +∞
[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = -∞
[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined
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Martin Pincher purchased a snow shovel for $28.61, a winter coat for $23.27, and some rock salt for $7.96. He must pay the state tax of 5 percent, the county tax of 0.5 percent and the city tax of 2.5 percent. What is the total purchase price?
Hi Martin,
To calculate the total purchase price of your items, you'll need to apply the state, county, and city taxes to the total purchase cost of all three items.
The total purchase cost of all three items is:
Snow shovel: $28.61
Winter coat: $23.27
Rock salt: $7.96
Total purchase cost: $59.84
Now, we apply the applicable taxes:
State tax: 5% of $59.84 = $2.99
County tax: 0.5% of $59.84 = $0.30
City tax: 2.5% of $59.84 = $1.49
Total taxes: $2.99 + $0.30 + $1.49 = $4.78
Therefore, the total purchase price is:
Total purchase cost + Total taxes = $59.84 + $4.78 = $64.62
label each example with the type of variable that best represents it. labels can be used more than once.
Answer:
Step-by-step explanation:
HELP ME ASAPPP!!! Ill mark you brasinlisest
Step-by-step explanation:
Theoretical probabilities can be calculated using the concept of probability. Each student has a 0.5 chance of selecting either List A or List B. Therefore, the probability of getting 27 heads and 33 tails can be calculated as:
P(27 heads and 33 tails) = (60 choose 27) * (0.5)^27 * (0.5)^33 where (60 choose 27) is the number of ways to select 27 students out of 60.
Using a calculator, we can compute the above probability as approximately 0.109. This means that if we were to repeat this experiment many times, we would expect to get 27 heads and 33 tails about 10.9% of the time.
Comparing this theoretical probability to the experimental results, we see that the observed proportion of heads (27/60 = 0.45) is lower than the expected proportion of heads (0.5) and the observed proportion of tails (33/60 = 0.55) is higher than the expected proportion of tails (0.5).
However, it is important to note that due to the random nature of the experiment, we would not expect the exact theoretical probabilities to match the experimental results exactly. In other words, there is always some amount of variation expected in the results. Nonetheless, the experimental results are consistent with the theoretical probabilities, and we can conclude that there is no significant deviation from what we would expect by chance.
I will mark you brainiest!
Alternate interior angles are congruent.
A) False
B) True
Answer:
True.
Step-by-step explanation:
Alternate interior angles are congruent, meaning they have equal measure. When we have two parallel lines that are intersected by a transversal, and again my parallel lines are identified by using the same number of arrows, then two special angles are congruent and that is alternate interior angles.
Prove the following using a direct proof:
The sum of the squares of 4 consecutive integers is an even integer
Answer: A positive whole number multiplied by any whole number will remain positive. In the case of the squares of 4, it will always end in a 6 which is a positive number.
Step-by-step explanation:
4^2= 16
16^2 = 256
256^2= 65,536
etc.
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. Yoself drank 4 ounces of orange Juice. What percent of the daily recommended amount of Vitamin C is this ? Explain your thinking.
Step-by-step explanation:
'Yoself' drank 1/4 of 16 oz so he got 1/4 of 250%
1/4 * 250% = 62.5 %
I need help with this question.
you need to match it to the percentage of the fraction for example 1/2 is 50 percentage and than you do 1/4 is 25 percent.
Due today!! Pls helppp
if we that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:
100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.
What do you mean by spending?If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.
So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:
On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.
However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.
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Just need to answer to this geometry question, Its a throw back for me.
As the triangles are similar to each other, using congruent theorem, we get the value of side JK = 63.8.
What are similar triangles?Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.
This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".
As per the triangles,
Let JK be = x.
GF/GH = JI/JK
⇒ 11/18 = 36 /x
⇒ x = 36 × 18/11
⇒ x = 63.8.
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Does anyone know what x equals?
Answer:
X=18
Step-by-step explanation:
Answer:
x = 3.5 units (nearest tenth)
Step-by-step explanation:
The given triangle has a one right angle and two angles each measuring 45°. Therefore, it is a 45-45-90 triangle.
A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.
Therefore, the formula for the ratio of the sides is x : x : x√2 where:
x is each side opposite the 45 degree angles (legs).x√2 is the side opposite the right angle (hypotenuse).As the hypotenuse of the given right triangle is 5 units:
[tex]\implies x\sqrt{2} = 5[/tex]
To find the measure of x, solve for x:
[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x =3.5355339...[/tex]
[tex]\implies x=3.5\; \sf units\;(nearest\;tenth)[/tex]
Therefore, the length of side x to the nearest tenth is 3.5 units.
he buys a 5kg lwisa samp and repacks the samp into 125g packets. determine how many packets will be able to get from one pack of 5kg samp?
Answer:5
Step-by-step explanation:5555555
Conduct a survey with a minimum of 20 people. Complete the designed questionnaire in 1.2. Remind participants why you are doing survey and that their information will be kept confidential. Submit 20 original completed questionnaires.
Important points to conduct a survey are; to gather information, make informed decisions, evaluate programs or services, identify trends, assess needs.
What is the need to conduct a survey?Surveys are conducted for a variety of reasons, including gathering information, making informed decisions, evaluating programs or services, identifying trends, and assessing needs. By using surveys, organizations can collect valuable data that can be used to inform decisions, improve programs or services, and better understand their target audience.
Surveys, also known as questionnaires, are used to gather information from a targeted group of individuals or a population. Surveys are an important tool for collecting data in a structured manner and can be used for a variety of reasons. Here are some of the reasons why surveys are conducted:
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a
21 units squared
b
27.6 units squared
c
32.2 units squared
d
42 units squared
The area of the right triangle given in this problem is given as follows:
21 units squared -> Option A.
How to obtain the area of a triangle?To calculate the area of a triangle, you can use the formula presented as follows:
Area = (1/2) x base x height
In which the parameters are given as follows:
"base" is the length of the side of the triangle that is perpendicular to the height."height" is the length of the perpendicular line segment from the base to the opposite vertex.For a right triangle, we can consider one side to be the base and the other side to be the height, hence the parameters are given as follows:
Base of 7 units.Height of 6 units.Hence the area of the triangle is given as follows:
A = 0.5 x 7 x 6 = 21 units squared.
Missing InformationThe complete problem is defined as follows:
"Calculate the area of the given triangle".
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solve the equation
x/2-2=4+1/2
Step-by-step explanation:
7eh8heusvush0wio0w92726 2is 3the world ydgugd8jd8djkd0jd9jd8hd7hd
SUPPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: Angle 1 = 32, Angle 2 = x + 29
COMPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: 54 + x = 90
COMPLEMENTARY ANGLE Find the value of x. Answer only. Given: Angle 1 = x, Angle 2 = 24 + 2x
Answer:
Given: Angle 1 = 32, Angle 2 = x + 29 ----- Answer is x = 119°
Given: 54 + x = 90 ----- Answer is x = 36°
Given: Angle 1 = x, Angle 2 = 24 + 2x ----- Answer is x = 22°
Step-by-step explanation:
1. Supplementary angle = 180°
Angle 1 = 32° Angle 2 = x + 29
Angles 1 + 2 = 180°
32° + x + 29° = 180°
32° + x = 180° - 29°
32° + x = 151°
x = 151° - 32°
x = 119°
2. Complementary angle = 90°
Given: 54 + x = 90
90 - 54 = x
x = 36°
3. Complementary angle = 90°
Given: Angle 1 = x, Angle 2 = 24 + 2x
Angles 1 + 2 = 90°
x + 24 + 2x = 90°
3x + 24 = 90°
3x = 90° - 24
3x = 66°
x = 66°/3
x = 22°
Hope it helps!
PLEASE HELP ASAP!! 25 POINTS AND BRAINLIEST
Answer: 62°
Step-by-step explanation:
All angles of a triangle add up to 180°.
So, add up all the other angles.
15 + 25 + 39 = 79
180 - 79 = 101
Then, to find x, subtract 39 from 101, to get 62!
The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 50 trials and got the following results.
(a) Assuming that the machine is fair, compute the theoretical probability of getting a 5 or 6 .
(b) From these results, compute the experimental probability of getting a 5 or 6 .
(c) Assuming that the machine is fair, choose the statement below that is true:
o With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.
o With a large number of trials, there must be no difference between the experimental and theoretical probabilities.
o With a large number of trials, there must be a large difference between the experimental and theoretical probabilities.
(a) The theoretical probability of getting a 5 or 6 is 1/5
(b) The experimental probability of getting a 5 or 6 is 1/5
(c) The true statement is the first statement.
What is a probability?A subfield of statistics known as probability studies random events and their likelihood of happening. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.
(a) Assuming that the machine is fair, the theoretical probability of getting a 5 or 6 is:
P(5 or 6) = P(5) + P(6) = 1/10 + 1/10 = 1/5
(b) From the results, we can see that out of the 50 trials, there were 10 trials where the machine output a 5 or a 6.
The experimental probability of getting a 5 or 6 is:
P(5 or 6) = 10/50 = 1/5
(c) A large number of trials, might be a difference between the experimental and theoretical probabilities, but the difference should be small. This is because the theoretical probability is based on the assumption of a fair machine, while the experimental probability is based on actual results.
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Celine is 6 years younger than her sister Cindy. She is also one third as old as Cindy.
Select two equations of a system that can be solved to find both ages.
a. 3x-6y=0
b. 3x-y=0
c. y-x=6
d. x-y=6
The two equations of a system that can be used to find the ages of both girls are y - x = 6 and 3x - y = 0.
What is system of equations?A group of two or more equations that must be solved all at once is known as a system of equations. The objective is to determine the values of the variables that make both equations true in a system of two equations with two variables. These numbers represent the system of equations' answer. There are several ways to solve a system of equations, including substitution, elimination, and graphing. They are used to simulate and resolve issues in many branches of mathematics, science, engineering, and other disciplines.
Let us suppose the age of Celine = x.
Let us suppose the age of Cindy = y.
Given that, Celine is 6 years younger than her sister Cindy.
x = y - 6
She is also one third as old as Cindy.
x = 1/3y or y = 3x.
Substitute the value of y in equation 1:
x = 3x - 6
6 = 2x
x = 3
Substitute the value of x:
y = 3(3) = 9
Hence, the two equations that can be used to find the ages of both girls are y - x = 6 and 3x - y = 0.
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Solve the polynomial equation by factoring and then using the zero-product principle.
4x = 864x
Rewrite the equation in factored form.
(Blank)= 0
What is the solution pair?
In response to the stated question, we may state that As a result, the equation's answer is x = 0.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
4x = 864x is the provided equation.
This equation may be simplified by deleting 4x from both sides:
[tex]860x = 0[/tex]
This equation may now be rewritten in factored form:
[tex]860x = 0 \sx(860) = 0[/tex]
We know from the zero-product principle that if the product of two elements is zero, then at least one of them must be zero. As a result, we may set each component to zero and solve for x:
x = 0 or 860 = 0 (which is impossible) (which is impossible)
As a result, the equation's answer is x = 0.
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he triangles below are similar. Triangle X Y Z. Side X Z has a length of 12, Z Y is 16, Y X is 14. Triangle R Q S. Side R Q is 3.5, Q S is 4, S R is 3. Which similarity statement expresses the relationship between the two triangles? Triangle X Y Z is similar to Triangle Q R S Triangle X Y Z is similar to Triangle R Q S Triangle Z X Y is similar to triangle Q S R Triangle Z X Y is similar to triangle Q R S
Answer:
Triangle XYZ is similar to Triangle RQS
Step-by-step explanation:
Triangle XYZ is similar to Triangle RQS
XZ/SR = 12/3 = 4
ZY/QS = 16/4 = 4
YX/RQ = 14/3.5 = 4
similar figures have all corresponding sides in the same ratio
A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books isA 1 / 21B 10 / 21C 11D 21 / 11
If 2 books are chosen at random, then the probability that both are statistics books is (a) 1/21.
The number of statistics book in bookcase is = 2;
The number of biology books in bookcase is = 5;
So, the total number of books is = 7;
The Probability of choosing a statistics book on the first draw is 2/7, since there are 2 statistics books out of a total of 7 books.
After the first book is chosen, there will be 6 books left, including 1 statistics book out of a total of 6 books.
So, the probability of choosing another statistics book on the second draw is 1/6.
In order to find the probability of both events happening together (i.e. choosing 2 statistics books in a row), we multiply the probabilities of each event:
So, P(choosing 2 statistics books) = P(1st book is statistics) × P(2nd book is statistics given that the 1st book was statistics);
⇒ (2/7) × (1/6)
⇒ 1/21
Therefore, the required probability is (a) 1/21.
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The given question is incomplete, the complete question is
A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is
(a) 1/21
(b) 10/21
(c) 11
(d) 21/11
factorise completely.
3x²-12xy
Answer:
Hence, factors are 3x,(x−4y).
Step-by-step explanation:
We need to factorise 3x 2 −12xy
Here we can take 3x common.
Thus we have 3x 2−12xy=3x(x−4y)
Hence, factors are 3x,(x−4y).
Answer: 3x ( x - 4y )
Step-by-step explanation:
Factorizing 3x²-12xy
3x ( x - 4y )
Convert 555 into base five numberal system
The decimal number 555 is written as 4210 in base-5.
Answer: [tex]555_{10} =4210_{5}[/tex]
Step-by-step explanation:
Decimal to base five conversion
we divide the decimal number by 5 repeatedly until the quotient becomes 0here
We apply the rule to convert 555 into base five numeral.Divide the number 555 repeatedly by 5 until quotient becomes zero.D Q Remainders
5 |555 0
5 |111 1
5 |22 2
5 |4 4
0
here , Divisor = 5 , Quotient = [555,111,22,4,0] , Remainders = [4210]Let S be the universal set, where:
S={1,2,3,...,18,19,20}
Let sets A and B be subsets S, where:
The intersection of sets A and B is the set of all elements that are in both set A and set B is 5.
What is union?In set theory, the union of two or more sets is a set that contains all the distinct elements of the sets being considered.
According to question:Set A = {1, 2, 3, 7, 9, 11, 13, 19} has 8 elements.
Set B = {1, 2, 3, 4, 8, 11, 18, 19, 20} has 9 elements.
The union of sets A and B, denoted as A ∪ B, is the set of all elements that are in either set A or set B or in both.
n(A ∪ B) = 8 + 9 - n(A ∩ B)
Now we need to find n(A ∩ B), which is the number of elements that are common to both sets A and B.
The intersection of sets A and B, denoted as A ∩ B, is the set of all elements that are in both set A and set B. We can find n(A ∩ B) by counting the number of common elements between sets A and B, which are 1, 2, 3, 11, and 19.
Therefore, n(A ∩ B) = 5.
n(A ∪ B) = 17 + 5
n(A ∪ B) = 22
So, the number of elements in the set A ∪ B is 22.
The intersection of sets A and B is the set of all elements that are in both set A and set B. From above, we know that the common elements between sets A and B are 1, 2, 3, 11, and 19.
Therefore, n(A ∩ B) = 5.
So, the number of elements in the set A ∩ B is 5.
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