The intersection of sets A and B has a cardinality of 8, the intersection of sets A and C has a cardinality of 17, and the intersection of sets B and C has a cardinality of 15. The union of sets A, B, and C has a cardinality of 4.
We are given the cardinalities of three sets: |A| = 96, |B| = 57, and |C| = 62. Additionally, we know the cardinality of the intersection of sets A and B, denoted as |A∩B|, is 8. The cardinality of the intersection of sets A and C, denoted as |A∩C|, is 17, and the cardinality of the intersection of sets B and C, denoted as |B∩C|, is 15.
To find the cardinality of the union of sets A, B, and C, denoted as |A∪B∪C|, we can use the principle of inclusion-exclusion. According to this principle, the formula for finding the cardinality of the union of three sets is:
|A∪B∪C| = |A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|
Plugging in the given values, we have:
|A∪B∪C| = 96 + 57 + 62 - 8 - 17 - 15 + |A∩B∩C|
We are also given that |A∪B∪C| = 4. Substituting this value into the equation, we get:
4 = 96 + 57 + 62 - 8 - 17 - 15 + |A∩B∩C|
Simplifying the equation, we find:
|A∩B∩C| = 9
Therefore, the cardinality of the intersection of sets A, B, and C is 9.
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A Swedish study examined gingival bleeding in 164 pairs of same-sex twins of which one twin had low exposure to smoking, while the other had high exposure to smoking. The reasons for using this co-twin control design include pair matching for sex, age, and genetic factors, and that confounding factors such as oral hygiene and food habits are also likely to be matched within a pair. The aim of the study is to test whether smoking is associated with higher risk of gingivitis. The study found that in 40 pairs the low-exposed twin had gingivitis while the high-exposed twin did not, in 23 pairs the high-exposed twin had gingivitis while the low-exposed twin did not, while in the remaining 101 pairs the twins had same status: in 15 pairs both had gingivitis and in 86 pairs both did not have gingivitis.
a. Which type of study design applies to this study: paired or independent samples?
b. Write the 2×2 table cross-tabulating the pairs of exposed and unexposed twins in terms of their gingivitis status (yes/no).
c. The research hypothesis is that smoking is associated with gingivitis. For the statistical analysis, what are the null and alternative hypotheses?
d. Perform a statistical test for the null hypothesis, using hand calculations. Interpret your results
a. The study design that applies to this study is paired design.
b. The 2×2 table:
Gingivitis (+) Gingivitis (-)
--------------------------------------------------
Exposed (+) 23 40
Exposed (-) 15 86
c. For the statistical analysis, the null and alternative hypotheses are as follows:
Null hypothesis: Smoking is not associated with gingivitis
Alternative hypothesis: Smoking is associated with gingivitis
d. Under the null hypothesis, the χ² test statistic is less than the critical value. Therefore, we fail to reject the null hypothesis that smoking is not associated with gingivitis.
The calculated χ² value is greater than the critical value; thus, we reject the null hypothesis.
a. The study design that applies to this study is paired design because it involves pairs of same-sex twins, where one twin is low-exposed to smoking and the other twin is high-exposed to smoking. The pairs are matched based on sex, age, and genetic factors..
b. The 2×2 table that cross-tabulating the pairs of exposed and unexposed twins in terms of their gingivitis status is as follows:
Gingivitis (+) Gingivitis (-)
--------------------------------------------------
Exposed (+) 23 40
Exposed (-) 15 86
c. For the statistical analysis, the null and alternative hypotheses are as follows:
Null hypothesis: Smoking is not associated with gingivitis
Alternative hypothesis: Smoking is associated with gingivitis
d. Perform a statistical test for the null hypothesis using hand calculations
To test the null hypothesis, we will use the McNemar's test. The formula for McNemar's test is given below:
χ² = [(b - c)²]/(b + c)
where b is the number of discordant pairs, and c is the number of discordant pairs.
The calculations are: b = 23, c = 40χ² = [(23 - 40)²]/(23 + 40) = 6.25
The calculated χ² value is 6.25.
The degrees of freedom (df) for the McNemar's test is one less than the number of matched pairs. In this study, there were 164 pairs; thus, df = 163.
The critical value of χ² with df = 163 and α = 0.05 is 1.736.
Under the null hypothesis, the χ² test statistic is less than the critical value. Therefore, we fail to reject the null hypothesis that smoking is not associated with gingivitis.
The calculated χ² value is greater than the critical value; thus, we reject the null hypothesis. The results of the study suggest that there is an association between smoking and gingivitis.
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PLSSSSSSSSSSSSSS HELPPP FOR REAL SOMEBODDYY REWARD BRAINLIEST!!!!!!!!!!!!!!!!!
Answer:
1. x = 3
2. (1, 0)
3. x = 3, -2
4. 144
5. -3 + 4√3
Step-by-step explanation:
PLEASE HELP!!
In a geometric sequence, a2=2, a3=12, and a4=72. Which equation can be used to find the nth term of the sequence, an?
an=2⋅10n−1
an=6⋅2n−1
an=13⋅6n−1
an=2n−1
Ik this is late, but people who are looking for the answer can see this.
Answer:
an =1/3*6^n-1
Step-by-step explanation:
You should plug in 2 for n in each equation, which, the correct one should give you 2. Then, to make sure, you plug in 3 in the equations that gave you 2.
Example:
an = 1/3 * 6 ^n-1
Plug in 2.
an = 1/3 * 6 ^2-1
an = 1/3 * 6 ^1
1/3 * 6 = 2
Step 2.
an = 1/3 * 6 ^3-1
an = 1/3 * 6 ^2
1/3 * 36 = 12
Hope this helps.
The correct equation which can be used to find the nth term of the sequence, an is,
⇒ a (n) = 1/3 × 6ⁿ⁻¹
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In a geometric sequence,
⇒ a₂ = 2, a₃ = 12 and a₄ = 72
Now, From option 3;
The equation is,
⇒ a (n) = 1/3 × 6ⁿ⁻¹
Put n = 2
⇒ a (2) = 1/3 × 6²⁻¹
⇒ a (2) = 1/3 × 6
⇒ a (2) = 2
Hence, This is the correct equation which can be used to find the nth term of the sequence, an.
Thus, The correct equation which can be used to find the nth term of the sequence, an is,
⇒ a (n) = 1/3 × 6ⁿ⁻¹
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What is the point-slope form of a line with slope
(-3, 6)?
nun
that contains the point
A. y- 3 = (x+3)
B. y+6 = {(x+3)
O C. y- 6 = - 3(x+ 3)
O D. y-6 = {(x+3)
Mr. Brown opened a new account with a deposit of $4,000.
- The account earned annual simple interest. - He did not make any additional deposits or withdrawals.
- At the end of 4 years, the balance was $4,400. What is the annual interest rate on this account? O 5%
O 2.5%
O 10%
O 7.5%
Pharoah Limited purchased a computer for $8,600 on January 1, 2020. Straight-line depreciation is used for the computer, based on a five-year life and a $900 residual value. In 2022, the estimates are revised. Pharoah now expects the computer will be used until December 31, 2023, when it can be sold for $700. Calculate the 2022 depreciation expense.
The depreciation expense for 2022, based on the purchase price for the computer of $8,600, the revised estimate in 2022, using the straight-line method is $2,410 per year
What is the straight line depreciation method?The straight-line depreciation method is method for calculating the depreciation of an asset in which the value of the asset is uniformly reduced within each period until the salvage value of asset is reached.
The depreciation on the computer = $8,600 - $900 = $7,700
The annual depreciation rate for the computer in the first two years, using the straight line depreciation method is; $7,700/5 = $1,540 per year
The depreciation of the computer by the end of 2021 = 2 × $1,540 = $3,080
Therefore, the net book value of the computer at the end of 2021 = $8,600 - $3,080 = $5520
The estimates are revised with Pharoah expecting to use the computer until December 2022, to sell for $700, therefore;
The revised depreciable amount for the computer = $5,520 - 700 = $4,820
The revised depreciation rate for the years, 2022 and 2023 is therefore;
Depreciation = $4,820/2 = $2,410 per year
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The ratio of carrots to potatoes in a garden was 1:2. The ratio of potatoes to tomatoes was 1:3. If there are 45 carrots in the garden, how many tomatoes are in the garden?
Answer:
270 tomatoes
Step-by-step explanation:
Lets organize the Info
Carrots to Potatoes is 1:2
Potatoes to Tomatoes is 1:3
There are 45 Carrots
So lets input it in the ratio Carrots : Potatoes
45 : 2(45)
45 : 90
There are 90 Potatoes in the garden
Lets input that info to the ratio Potatoes : Tomatoes
90: 3(90)
90 : 270
Summarize:
There are :
45 carrots
90 potatoes
270 tomatoes
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
270 tomatoes
Step-by-step explanation:
If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do
you know?
Answer:
Step-by-step explanation:
but is their any answer choices
24 + 8x + 10(2x)
Terms:
Constants:
Coefficients:
Find the area of the shaded region.
Answer:
69.53 ft
Step-by-step explanation:
area of a box: 18*18 = 324
area of a circle: (pi)*9^2 = 254.47
324-254.47 = 69.53 ft
The total weight of three kittens is 14 ounces kitten one weighs 1/4 pound kit in two weighs 5.5 ounces how many ounces does kitten three weigh?
Answer:
4.5 ounces
Step-by-step explanation:
Given data
Total weight=14 ounces
1st kitten= 1/4pound = 4 ounces
2nd kitten= 5.5 ounces
3rd kitten = x ounces
Let the expression for the total weight be
4+5.5+x=14
solve for x
9.5+x=14
x= 14-9.5
x=4.5 ounces
Hence the 3rd kitten weighs 4.5 ounces
Ben's dad is making a large pot of pasta sauce that calls for 3.5 kilograms of tomatoes. If he triples the amount of tomatoes for the recipe, how many grams of tomatoes will he use? Enter your answer in the box.
Answer: 10,500 gm
Step-by-step explanation:
Given
Pasta requires 3.5 kg of tomatoes
we know, [tex]1\ kg=1000\ mL[/tex]
If the amount is triples, the quantity of tomatoes is [tex]3\times 3.5=10.5\ kg[/tex]
[tex]\Rightarrow 10.5\ kg\equiv 10.5\times 1000=10,500\ gm[/tex]
Thus, he uses 10,500 gm of tomatoes
Is j+j+j+j and j with the power of four equivalent?
Answer:
No, they are not equivalent.
Step-by-step explanation:
j + j + j + j = 4j
j^4
Let's say j = 2
4j = 8
j^4 = 16
Answer:
NO
Step-by-step explanation:
j+j+j+j
remember multiplication is repeated addition!
j+j+j+j = 4j
THIS IS DIFFERENT! powers are repeated MULTIPLICATION.
j^4 = j to the power of 4 = j * j * j * j, NOT j+j+j+j !!!!!
Jamal needs the order the four cards shown in increasing order .which would be the correct order of cards
Answer:
It's C, not D
Step-by-step explanation:
The solution is, Jamal needs the order the four cards shown in increasing order , D > A > B > C would be the correct order of cards.
option A.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
given that,
Jamal needs the order the four cards shown in increasing order
we have,
A. -2/9 = -0.22
B. -.25 = - 0.25
C. -29% = -0.29
D. -1/5 = -0.2
we know that,
-0.2> -0.22> -0.25 > -0.29
so, the correct order of cards is:
D > A > B > C
Hence, The solution is, Jamal needs the order the four cards shown in increasing order , D > A > B > C would be the correct order of cards.
option A.
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PLEASE ANSWER THIS ASAP
Answer:
Option D
is the correct....
у
80
The graph of quadratic function
is shown on the grid.
What is a solution to r(x) = 0?
60
40
A -50
20
B 4
х
-4
4
8
12
- 16 -12 -8
16
C 14
-20
D-60
vo
-60
-80
Answer:
C 14
Step-by-step explanation:
2,900 Written in scientific notation
The number 2,900 in scientific notation is 2.9 * 10³
How to write the number in scientific notationFrom the question, we have the following parameters that can be used in our computation:
Number = 2,900
Multiply the number by 1
So, we have
Number = 2,900 * 1
Express 1 as 1000/1000
So, we have
Number = 2,900 * 1000/1000
Divide
Number = 2.9 * 1000
Express 1000 as 10³
So, we have
Number = 2.9 * 10³
Hence, the number in scientific notation is 2.9 * 10³
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Name the decimal and fraction for R on the number line.
Click the icon to view the number lines.
The decimal is 1.
The fraction is
Find the area of the figure.
Step-by-step explanation:
Area of Rectangle at the top =
Length x Width
[tex] = 3.5 \times 3 \\ = 10.5 {mm}^{2} [/tex]
Area of Quarter- Circle = 1/4 x Area of Circle
[tex] = \frac{1}{4} \pi {r}^{2} \\ = \frac{1}{4} \pi( {3.5}^{2} ) \\ = 3 \frac{1}{16} \pi {mm}^{2} [/tex]
Area of Rectangle at the right = Length x Width
[tex] = 5.5 \times 3.5 \\ = 19.25 {mm}^{2} [/tex]
Total Area = Area of 2 Rectangles + Area of Quarter Circle
[tex] = 10.5 + 3 \frac{1}{16} \pi + 19.25 \\ = 29.75 + 3 \frac{1}{16}\pi \\ = 32 \frac{13}{16}\pi {mm}^{2} [/tex]
I will leave the answer in terms of pi as I'm not sure if you need to round off your answer.
Let X be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent from X). In case of Heads, we let Y=X. In case of Tails, we let Y=−X.
Is Y normal? Justify your answer.
yes
no
not enough information to determine
Compute Cov(X,Y).
Cov(X,Y)=
Are X and Y independent?
yes
no
not enough information to determine
Problem 3. Problem 1(c)
Find P(X+Y≤0).
P(X+Y≤0)=
Based on these considerations, it can be concluded that Y is not a normal random variable.
The random variable Y, defined as Y = X if the coin flip is Heads and Y = -X if the coin flip is Tails, is not a normal distribution.
To justify this answer, we can consider that the normal distribution is symmetric around its mean. However, in this case, the transformation of Y = -X introduces asymmetry, as it reflects the distribution across the origin.
Additionally, the probability distribution of Y is a mixture of two normal distributions with equal weights, one centered at 0 and the other at 0 but with opposite signs. This combination results in a distribution that is not normal.
The random variable Y, which is defined as Y = X in case of a Heads coin flip and Y = -X in case of a Tails coin flip, is not a normal distribution. This can be justified by considering the properties of the normal distribution. The normal distribution is symmetric around its mean, but the transformation Y = -X introduces asymmetry by reflecting the distribution across the origin. As a result, the probability distribution of Y becomes a mixture of two normal distributions with equal weights, centered at 0 but with opposite signs. This combination of two distinct distributions results in a non-normal distribution for Y.
Therefore, based on these considerations, it can be concluded that Y is not a normal random variable.
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Find: (6m^5 + 3 - m^3 - 4m) - (-m^5 + 2m^3 - 4m + 6)
Answer:
7m^5 - 3m^3 - 3
Step-by-step explanation:
If 3/4 of a cup of a snack food gives you your daily value of calcium, then what fraction of your daily value of calcium is in 1 cup of the snack food? (Enter a fraction in the form A/B, where A and B are whole numbers. Do not include any words or calculations.)
The fraction of your daily value of calcium in 1 cup of the snack food is 4/3.
Given information:
If 3/4 fraction of a cup of a snack food gives you your daily value of calcium
To find:
what fraction of your daily value of calcium is in 1 cup of the snack food?
Solution:
If 3/4 of a cup of a snack food gives you your daily value of calcium, then 1/4 of a cup of a snack food would give you 1/3 of the daily value of calcium.
Now, 1 cup of the snack food would give you four times that amount of 1/3 of the daily value of calcium.
Thus, the fraction of daily value of calcium in 1 cup of the snack food would be 4 x 1/3= 4/3
Answer: Therefore, the fraction of your daily value of calcium in 1 cup of the snack food is 4/3.
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another, these are tricky to me.
Answer:
It would be D ^^
Step-by-step explanation:
I learned this 2 years ago lol <3
Bernard works for a business that sells and repairs tires. He can repair tires in an hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Answer:
3 tires per hour
Step-by-step explanation:
Bernard works for a business that sells and repairs tires. He can repair 24 tires in an 8 hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Number of tires repaired per day = 24 tires
Number of time used to repair tire per day = 8 hours
What is Bernard's unit rate for the number of tires repaired in one hour?
Number of tires repaired in one hour = Number of tires repaired per day / Number of time used to repair tire per day
= 24 tires / 8 hours
= 3 tires per hour
The unit rate for the number of tires repaired in one hour is 3 tires per hour
Find the missing length
Answer:
15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
A² + B² = C²
9 • 9 = 81
12 • 12 = 144
81 + 144 = 225
Sqrt
√255 = 15
Express the following in form, where p and q are integers and q≠ . (0.1282828) find the answer please and thank you
Answer: [tex]\dfrac{127}{990}[/tex].
Step-by-step explanation:
Let x=0.1282828...
Multiply 10 on both sides , we get
10 x = 1.282828... (i)
Now multiply 100 on both sides , we get
1000x=128.2828... (ii)
Eliminate (i) from (ii), we get
[tex]990x=127\\x=\dfrac{127}{990}[/tex]
Hence, the required [tex]\dfrac{p}{q}[/tex] form: [tex]\dfrac{127}{990}[/tex].
The school band has 8 alto saxophones and 2 baritone saxophones. What is the ratio of baritone saxophones to alto saxophones?
Answer:
4:1
Step-by-step explanation:
8/2 = 4:1 cause 2 can go into 8, 4 times.
Okay, so I need the one step equation for this question: Lee drove 420 miles and used 15 gallons of gasoline. How many miles did Lee's car travel per gallon of gasoline. I really need the one step equation version, as I know the number is 28. Please help me!
What exponential has a value of 729?
Answer: There are infinitely many.
For example, 5314410.5 or 93. You are probably looking for (3)^6 tho
7(2x+3)-x(14-y)
[tex]7(2x + 3y) - x(14 - y)[/tex]
Answer:
[tex]y(x+21)[/tex]
Step-by-step explanation:
[tex]7(2x+3y)-x(14-y)\\=14x+21y-14x+xy\\= 21y+xy\\= y(x+21)[/tex]