Answer:
(a)
[tex]A\ u\ (B\ n\ C) = \{a,b,c\}[/tex]
[tex](A\ u\ B)\ n\ C = \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ C = (A\ u\ B)\ n\ (A\ u\ C)[/tex]
(b)
[tex]A\ n\ (B\ u\ C) = \{b,c\}[/tex]
[tex](A\ n\ B)\ u\ C = \{b,c,e\}[/tex]
[tex](A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}[/tex]
[tex]A\ n\ (B\ u\ C) = (A\ n\ B)\ u\ (A\ n\ C)[/tex]
(c)
[tex](A - B) - C = \{a\}[/tex]
[tex]A - (B - C) = \{a,b,c\}[/tex]
They are not equal
Step-by-step explanation:
Given
[tex]A= \{a,b,c\}[/tex]
[tex]B =\{b,c,d\}[/tex]
[tex]C = \{b,c,e\}[/tex]
Solving (a):
[tex]A\ u\ (B\ n\ C)[/tex]
[tex](A\ u\ B)\ n\ C[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C)[/tex]
[tex]A\ u\ (B\ n\ C)[/tex]
B n C means common elements between B and C;
So:
[tex]B\ n\ C = \{b,c,d\}\ n\ \{b,c,e\}[/tex]
[tex]B\ n\ C = \{b,c\}[/tex]
So:
[tex]A\ u\ (B\ n\ C) = \{a,b,c\}\ u\ \{b,c\}[/tex]
u means union (without repetition)
So:
[tex]A\ u\ (B\ n\ C) = \{a,b,c\}[/tex]
Using the illustrations of u and n, we have:
[tex](A\ u\ B)\ n\ C[/tex]
[tex](A\ u\ B)\ n\ C = (\{a,b,c\}\ u\ \{b,c,d\})\ n\ C[/tex]
Solve the bracket
[tex](A\ u\ B)\ n\ C = (\{a,b,c,d\})\ n\ C[/tex]
Substitute the value of set C
[tex](A\ u\ B)\ n\ C = \{a,b,c,d\}\ n\ \{b,c,e\}[/tex]
Apply intersection rule
[tex](A\ u\ B)\ n\ C = \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C)[/tex]
In above:
[tex]A\ u\ B = \{a,b,c,d\}[/tex]
Solving A u C, we have:
[tex]A\ u\ C = \{a,b,c\}\ u\ \{b,c,e\}[/tex]
Apply union rule
[tex]A\ u\ C = \{b,c\}[/tex]
So:
[tex](A\ u\ B)\ n\ (A\ u\ C) = \{a,b,c,d\}\ n\ \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}[/tex]
The equal sets
We have:
[tex]A\ u\ (B\ n\ C) = \{a,b,c\}[/tex]
[tex](A\ u\ B)\ n\ C = \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}[/tex]
So, the equal sets are:
[tex](A\ u\ B)\ n\ C[/tex] and [tex](A\ u\ B)\ n\ (A\ u\ C)[/tex]
They both equal to [tex]\{b,c\}[/tex]
So:
[tex](A\ u\ B)\ n\ C = (A\ u\ B)\ n\ (A\ u\ C)[/tex]
Solving (b):
[tex]A\ n\ (B\ u\ C)[/tex]
[tex](A\ n\ B)\ u\ C[/tex]
[tex](A\ n\ B)\ u\ (A\ n\ C)[/tex]
So, we have:
[tex]A\ n\ (B\ u\ C) = \{a,b,c\}\ n\ (\{b,c,d\}\ u\ \{b,c,e\})[/tex]
Solve the bracket
[tex]A\ n\ (B\ u\ C) = \{a,b,c\}\ n\ (\{b,c,d,e\})[/tex]
Apply intersection rule
[tex]A\ n\ (B\ u\ C) = \{b,c\}[/tex]
[tex](A\ n\ B)\ u\ C = (\{a,b,c\}\ n\ \{b,c,d\})\ u\ \{b,c,e\}[/tex]
Solve the bracket
[tex](A\ n\ B)\ u\ C = \{b,c\}\ u\ \{b,c,e\}[/tex]
Apply union rule
[tex](A\ n\ B)\ u\ C = \{b,c,e\}[/tex]
[tex](A\ n\ B)\ u\ (A\ n\ C) = (\{a,b,c\}\ n\ \{b,c,d\})\ u\ (\{a,b,c\}\ n\ \{b,c,e\})[/tex]
Solve each bracket
[tex](A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}\ u\ \{b,c\}[/tex]
Apply union rule
[tex](A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}[/tex]
The equal set
We have:
[tex]A\ n\ (B\ u\ C) = \{b,c\}[/tex]
[tex](A\ n\ B)\ u\ C = \{b,c,e\}[/tex]
[tex](A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}[/tex]
So, the equal sets are:
[tex]A\ n\ (B\ u\ C)[/tex] and [tex](A\ n\ B)\ u\ (A\ n\ C)[/tex]
They both equal to [tex]\{b,c\}[/tex]
So:
[tex]A\ n\ (B\ u\ C) = (A\ n\ B)\ u\ (A\ n\ C)[/tex]
Solving (c):
[tex](A - B) - C[/tex]
[tex]A - (B - C)[/tex]
This illustrates difference.
[tex]A - B[/tex] returns the elements in A and not B
Using that illustration, we have:
[tex](A - B) - C = (\{a,b,c\} - \{b,c,d\}) - \{b,c,e\}[/tex]
Solve the bracket
[tex](A - B) - C = \{a\} - \{b,c,e\}[/tex]
[tex](A - B) - C = \{a\}[/tex]
Similarly:
[tex]A - (B - C) = \{a,b,c\} - (\{b,c,d\} - \{b,c,e\})[/tex]
[tex]A - (B - C) = \{a,b,c\} - \{d\}[/tex]
[tex]A - (B - C) = \{a,b,c\}[/tex]
They are not equal
these questions seem harder than usual im sorry for the bother
Answer:
A
Step-by-step explanation:
Is this the correct answer? Pls help me
Answer:
Yes
Step-by-step explanation:
Try to find this answer! Thank you!
Please help, will mark Brainly and if you need help with anything I’ll help with any work you send
Don’t tell me to go to a website, it doesn’t work at all. Stop spamming that.
Answer:
In the first one you are missing (a +7) so it's going to be 9(a +7) or when you factor that out it will be 9a 63
In the other one you are missing the (a +5) so it's going to be 7a(a + 5) or when you factor it out it will be 7a2 + 35a
Step-by-step explanation:
a2+ 9a + 20 = (a + 4) (a + 5)
a2 + 11a+ 28 = ( a + 7) ( a + 4 )
In 42 of the 64 years from 1950 through 2014,the S& P 500 finished higher after the first five days of trading (in 2011 there was virtually no change). In 37 out of 42 years, the S&P 500 finished higher for the year. Is a good first week a good omen for the upcoming year? The following table gives the first-week and annual performance over this 64-year period.
S&P 500's Annual Performance
First week Higher Lower Total
Higher 37 5 42
Lower 11 11 22
Total 48 16 64
a) If a year is selected at random,
what is the probability that the S&P 500 finished lower for the year?
b) Given that the S&P finished lower after the first five days of trading,
what is the probability that it finished lower for the year?
c) Are the two events "first week performance" and "annual performance"
independent or dependent? Explain why.
Answer:
what website or book is that?
Big chickens: A report from a poultry industry news Web site stated that the weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1376 grams and standard deviation 183 grams. Use the TI-84 PLUS calculator and round your answers to at least two decimal places. (a) Find the 24th percentile of the weights. (b) Find the 86th percentile of the weights. (c) Find the second quartile of the weights. (d) A chicken farmer wants to provide a money-back guarantee that his broilers will weigh at least a certain amount. What weight should he guarantee so that he will have to give his customers' money back only 1% of the time
Answer:
i think its b
Step-by-step explanation:
Jim takes out a mortgage for 30 years at an interest rate of 2.49% and his monthly repayments are $986.50. What is the principal loan amount? Round your answer to the nearest ten thousand dollars. Do NOT round until you have calculated the final answer.
Answer:
250000
Step-by-step explanation:
P=986.50(1-(1+.0249/12)^-(12)(30) Then divide the answer you get by (.0249/12)
Answer: 250,000
Step-by-step explanation:
We must apply the formula for P0, that is,
P0=986.50(1−(1+0.024912)−30⋅12)(0.024912),
which gives P0=$250,000 to the nearest $1.
Myles has a room that is 300 m². If he wants to tile the room using 5 cm x 5 cm tiles, how many whole tiles will he have to use?
Answer:
Number of whole tiles need = 120,000 tiles
Step-by-step explanation:
Given:
Area of room = 300 m²
Dimension of each tile = 5cm x 5cm
Find:
Number of whole tiles need
Computation:
Dimension of tile in meter = 5 /100 = 0.05 m
Area of each tile = 0.05 x 0.05
Area of each tile = 0.0025 m²
Number of whole tiles need = Area of room / Area of each tile
Number of whole tiles need = 300 / 0.0025
Number of whole tiles need = 120,000 tiles
Total 120,000 tiles need to cover 300 m² room.
Mountain officials want to build a new ski lift from B to C, as shown in the figure below. The distance from A to C is 1540 feet. They measure angle DAC to be 38º and angle DBC to be 25º. What is the distance from A to B ? Round your answer to the nearest tenth of a foot.
Answer:
there is a 13 degree difference from DBC and DAC
with that you divide 1540 by 13 as you get that 118.461 feet
that means that there is a 118.461 difference from B to C and A to B
so the answer is either 1658.461ft or 1421.539ft I am not sure if that is correct or not but best of luck mate
Is 53 or 63.38 correct pls help me
Answer:
Okay so A will equal 45 degrees
Step-by-step explanation:
When you have a right triangle the other angle measures will be 45 degrees. The interior sum of all the angles will always be 180 degrees. The other angle will be 45 degrees as well
What is X in this equation?
Answer:
B) 44
Step-by-step explanation:
x + 54 + 82 = 180
x + 136 = 180
x = 180 - 136
x = 44
Help me plssssss I suck at this
Answer: 7
Step-by-step explanation:
Answer:
35 more bottles than bags of popcorn
Step-by-step explanation:
Simply multiply both 14 and 21 by 5 and then subtract the larger number by the smaller one and you get your answer
x = 12 - 3y
3x + 9y = 24
Answer:
Cool
Step-by-step explanation:
Thanks !!!
12. Li drinks 1 liter of water each day after soccer practice. How many
milliliters of water does she drink after 5 practices?
F. 5,000 milliliters
H. 50 milliliters
G. 500 milliliters
L. 5 liters
Answer:
F. 5000militres
Step-by-step explanation:
1 litre= 1000ml
1 practice= 1000ml
therefore 5 practices= 5*1000ml
= 5000ml
Find the distance between the two points rounding to the nearest tenth (if necessary). (1,−7) and (4,−5)
Answer:
5
Step-by-step explanation:
distance formula [tex]\sqrt{(4-1)^{2} + (-5+7)^{2}[/tex]
29. The table shows the average annual salary in dollars based on the minimum level of education required for two occupations. Based on the average annual salaries in the table, how much more would an accountant eam than a tax preparer over a 30 year career? Occupations Occupation Average Annual Salary (dollars) Level of Education Required Accountant 71,040 41,700 Bachelor's degree High school diploma Tax preparer A $112,740 B. $3,382,200 C. $880,200 D. $1,251,000
Answer:
c. 880,200
Step-by-step explanation:
ur welcome
a plate moves at a sped of 45 mm/yr. How far will the plate move in 100 years?
Answer:
4,500 millimeters per year.
Step-by-step explanation:
brainliest?
Answer:
4500 mm or 4.5 m
Step-by-step explanation:
45 mm/yr x 100 yr = 4500 mm = 4.5 m
Evaluate the expression: –5 + 280 + 62.
Answer:
the answer is 337
Step-by-step explanation:
-5 + 280 + 62
= 337
Answer:
337
Step-by-step explanation:
-5 plus 280 is 275
275 + 62 is...
337
which expression is equivalent to m-4/m+4 + (m+2) ?
A. m-4/(m+4)(m+2)
B. (m+4)(m+2)/m-4
C. m-4)(m+2)/m+4
D. m+4/(m-4)(m+2)
Answer:
C.
Step-by-step explanation:
......................
The expression that is equivalent to the expression (m - 4)/(m + 4) + (m + 2) is {m + m² + 6m + 4}/{m + 4}.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is to find the expression is equivalent to -
(m - 4)/(m + 4) + (m + 2)
We have the following expression as -
(m - 4)/(m + 4) + (m + 2)
{(m - 4) + (m + 2)(m + 4)}/(m + 4)
{(m - 4) + m² + 4m + 2m + 8}/(m + 4)
{m + m² + 6m + 4}/{m + 4}
Therefore, the expression that is equivalent to the expression (m - 4)/(m + 4) + (m + 2) is {m + m² + 6m + 4}/{m + 4}.
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In hypothesis testing, the null hypothesis is the hypothesis that the researcher believes is true and wishes to prove. True or False
Answer:true
Step-by-step explanation:
Someone please answer this
Answer:
Answer what?
Step-by-step explanation:
What is the tangent ratio of angle within a right triangle?
9514 1404 393
Answer:
(d)
Step-by-step explanation:
The purpose of the mnemonic SOH CAH TOA is to help you remember that ...
Tan = Opposite/Adjacent
please answer asap NO SCAM LINKS.
If a dozen dozen candies cost a half-a-dozen dimes a dozen, how much will a half-a-dozen dozen candies cost?
Answer:
74
Step-by-step explanation:
The cost of half-a-dozeon dozen candies for this case will be $3.6
How much a dozen consists of ?A dozen of a thing means 12 of such thing is in consideration. If we say we have a dozen pencils, then twe mean we have 12 pencils.
For this case, it is given that:
Cost of a dozen dozen candies = half a dozen dimes a dozenCost of a half a dozen dozen candies = ? (to find)A dozen contains 12 quantities.
A dozen dozen candies means 12 times 12 = 144 candies
half a dozen dimes dozen cost = (12/2) × 12 dimes = 72 dimes
That means:
144 candies cost 72 dimes.
Dividing both quantities by 144 to get price of 1 candy:
144/144 = 1 candy's price = 72/144 dimes = 0.5 dimes = 0.05 dollars (1 dime = 0.1 dollars)
Half a dozen times dozen candies = 72 candies
1 candy costs 0.05 dollars
72 candies cost [tex]72 \times 0.05 = 3.6[/tex] dollars.
Thus, the cost of half-a-dozeon dozen candies for this case will be $3.6
Learn more about forming equations here:
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Can you help meeeeeee this is math and there have to be not one answer many like 3,2 and some time 1 ok Thankyou
Answer:m=134
Step-by-step explanation:
that's the only correct answer
Help me with this math assignment
Answer:
24 cubic feet
Step-by-step explanation:
brainliest or 5 stars and heart or BOTH
correct me if im wrong
PLEASE HELP ASAP
Find the missing side of this right
triangle,
Х
8
16
x = [?]
Answer:
its is 192 I just took this assignment
Suppose 10 tosses of a coin were all heads, and you switch to a new coin. What is the probability of tossing this new coin and getting another head?
Answer:
50% or 1/2 Could be 100% but i think it is 50%
Step-by-step explanation:
Because Changing the coin will make no difference.
The probability of getting heads is same as the probability of tails which is [tex]\frac{1}{2}[/tex].
What is the probability?
The concept of probability is used to assign a numerical description to the likelihood of occurrence of an event.
Probability can be defined as the number of favorable outcomes divided by the total number of possible outcomes of an event.
Here given that,
The [tex]10[/tex] tosses of a coin were all heads, and you switch to a new coin.
So, the probability of getting all heads is [tex]2^{-n}[/tex]
And we have [tex]n=10[/tex],
Then, the probability of getting the heads is
[tex](^{n}C_k)(\frac{1}{2})^k(\frac{1}{2})^{n-k}=2^{-n}(^nC_k)[/tex]
Hence, the probability of getting heads is same as the probability of tails which is [tex]\frac{1}{2}[/tex].
To know more about the probability
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what is the volume of a cereal box that is 2 inches thick, 12 inches high and 10 inches wide?
Answer:
240
Step-by-step explanation:
12 times 2 is 24
24 times 10 is 240
Have a nice day
Answer:
240 [tex]Inches^{3}[/tex]
Step-by-step explanation:
Find the area of the shape shown below. 2 4 1. 2 2 2 2 units
9514 1404 393
Answer:
10 square units
Step-by-step explanation:
The shape is a trapezoid with bases of 2 units and 8 units. Its height is 2 units, so its area is ...
A = 1/2(b1 +b2)h
A = (1/2)(2 +8)(2) = 10
The area of the shape is 10 square units.