Let A={1,{2,3},2},B={1,2,4},C={3,4,{2}},D=∅, E={∅}, where the universal set is U=A∪B∪C∪D∪E. Determine (write out members of the set explicitly, that is do not use set builder notation): (a) A∪B (e) A−C (b) C∪E (c) A∩B (d) C∩B (i) E×A (f) C−A (g)
A
ˉ
(h) (A∪C)−D (m) ∣C∣ (j) A×B (n) ∣E∪A∣ (k) P(B) (1) P(D) (o) (A∩U)∪
U
ˉ

Hey there mate :)

When a number is multiplied by a fraction equal to 1, the value of the number remains the same.

Using this, we can find the values:-

Image 1 answers :

\( \frac{4}{5} \times \frac{4}{4} = \frac{4}{5} \)

When we cancel the same 4 of LHS remaining we get as 4/5. By doing the same method, we can find the remaining answers.

\(\frac{2}{3} \times \frac{7}{7} = \frac{2}{3} \\ \\ \frac{5}{6} \times \frac{8}{8} = \frac{5}{6} \\ \\ \frac{3}{4} \times \frac{5}{5} \)

Image 2 answers :

\( \frac{2}{3} \times \frac{4}{2} = \frac{4}{3}\)

Here, cancel the common numbers in LHS and write back the remaining uncancelled numbers to get 4/3 in RHS.

Using same method,

\( \frac{3}{4} \times \frac{5}{3} = \frac{5}{4} \)

Next, Now in last two questions, we have to do a little differently. Till this much time we did by cancelling the common numbers. So, multiply the numerator and denominator.

\( \frac{1}{4} \times \frac{3}{2} \\ = > \frac{1 \times 3}{4 \times 2} \\ = > \frac{3}{8} \)

So, above question's answer is 3/8.

Likewise, using the same method, find the next question :-

\( \frac{2}{5} \times \frac{4}{3} \\ = > \frac{2 \times 4}{5 \times 3} \\ = > \frac{8}{15}\)

So, next answer is 8/15.

Hope this Helps...

\(Benjemin360 :)\)

Answer:

? = 114

Step-by-step explanation:

Angle Formed by Two Chords  =  1/2 ( sum of Intercepted Arcs)

? = 1/2 ( 53+ 175)

? = 1/2 ( 228)

? = 114

Answer:

56.4 pounds

Step-by-step explanation:

Multiply 12 (kittens) by 4.7(pounds) and you get 56.4 pounds, the total weight of the kittens combined.

(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].

(b) The 99% confidence interval has the widest interval.

(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.

Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.

Plugging in the values, we can calculate the confidence intervals:

90% confidence interval:

Lower bound = 436.5 - (1.645 * (11.9 / √20))

Upper bound = 436.5 + (1.645 * (11.9 / √20))

95% confidence interval:

Lower bound = 436.5 - (1.96 * (11.9 / √20))

Upper bound = 436.5 + (1.96 * (11.9 / √20))

99% confidence interval:

Lower bound = 436.5 - (2.576 * (11.9 / √20))

Upper bound = 436.5 + (2.576 * (11.9 / √20))

(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.

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Answer:

C= 0.1234567891011...  such as …123456787 _ft. 123456788

Step-by-step explanation: i hope this helps have a uwu or great day!  Oh here's a cute extra picture its my  2nd fav!

Answer:

C= 0.1234567891011...  or …123456787   ft. 123456788

Step-by-step explanation:

Answer:

$6,984.60 per year.

Step-by-step explanation:

Using a normal and very common budget, you should divide your monthly/annual salary into 3 main tiers, which are the following

If we go by this budget then we would need to turn the 20% into a decimal by dividing it by 100 and then multiply that decimal by the person's annual salary.

20% / 100 = 0.20

$34,923 * 0.20 = $6,984.60

Finally, we can see that the individual should be saving roughly $6,984.60 per year.

The percentage increase in average commute times between these years = 2.25%

In 2010, the average commute time for wake county workers = 23.9 mins

In 2016, the average commute time for wake county workers = 25 mins.

The increase is = 25- 23.9 = 1.1

The average commute time between the two years,

23.9+25 = 48.9 mins

Therefore, the percentage,

= 1.1/48.9×100

= 110/48.9

= 2.249%

= 2.25% to the nearest two decimal places.

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Answer:

a

Step-by-step explanation:

Answer:

6 onuces per serving

Step-by-step explanation:

To find the probability distribution for Y, the number of errors detected by the auditor, we can use the binomial distribution formula. The binomial distribution is used when there are only two possible outcomes, success or failure, and each trial is independent.

In this case, the probability of success (detecting an error) is 5% or 0.05, and the probability of failure (not detecting an error) is 1 - 0.05 = 0.95.

a. To find the probability distribution for Y, we can use the formula for the binomial distribution:

P(Y = y) = (nCk) * p^k * (1-p)^(n-k)

where n is the number of trials (3 in this case), k is the number of successes (errors detected), p is the probability of success (0.05), and (nCk) is the combination formula.

For y = 0:
P(Y = 0) = (3C0) * (0.05)^0 * (0.95)^(3-0) = (1) * (1) * (0.95)^3 = 0.857375

For y = 1:
P(Y = 1) = (3C1) * (0.05)^1 * (0.95)^(3-1) = (3) * (0.05) * (0.95)^2 = 0.135375

For y = 2:
P(Y = 2) = (3C2) * (0.05)^2 * (0.95)^(3-2) = (3) * (0.05)^2 * (0.95)^1 = 0.007125

For y = 3:
P(Y = 3) = (3C3) * (0.05)^3 * (0.95)^(3-3) = (1) * (0.05)^3 * (0.95)^0 = 0.000125

So the probability distribution for Y is:
Y = 0 with probability 0.857375
Y = 1 with probability 0.135375
Y = 2 with probability 0.007125
Y = 3 with probability 0.000125

b. To construct a probability histogram for p(y), you can create a bar graph where the x-axis represents the number of errors detected (Y) and the y-axis represents the probability (P(Y = y)). Each bar will have a height corresponding to the probability.

c. To find the probability that the auditor will detect more than one error, we need to calculate the sum of the probabilities for Y = 2 and Y = 3:

P(Y > 1) = P(Y = 2) + P(Y = 3) = 0.007125 + 0.000125 = 0.00725

Therefore, the probability that the auditor will detect more than one error is 0.00725.

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Answer:

Step-by-step explanation:

∠A and ∠B are complementary because they are the two non-right angles of a right triangle. This means that sinA=cosB and sinB=cosA.

Therefore,

Answer:

The interest calculated is 3.96%.

Step-by-step explanation:

I hope this helps you :)

Start by noting that <2 is the same as the angle formed by three line segments of equal length. Therefore, <2 = 60°.Therefore, <2 ≅ <3.

Length is a measurement of distance or space between two points, usually denoted by the letter ‘l’. It is a fundamental concept in geometry, physics and many other fields, and is generally expressed in terms of the meter, centimeter, kilometer, mile, foot, yard, and so on. A length can be measured in a straight line, along a curved line, or over a surface. It can also refer to the size or dimension of an object in one, two, or three dimensions. Length can also be used to measure time, as in the phrase “the length of a day” or “the length of a year”.

2. Similarly, <3 is the same as the angle formed by four line segments of equal length. Therefore, <3 = 90°.
3. Since both angles are formed by the same type of line segment, it can be assumed that they are proportional.
4. To prove this, we can use the ratio of the angles to show that <2 = <3.
5. The ratio of the angles can be found by dividing the measure of <2 by the measure of <3. This gives us 60°/90° = 2/3.
6. This shows that the angles are inversely proportional, since the ratio of the angles is 2/3.
7. Therefore, <2 ≅ <3.

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Answer:

3.92 x \(10^{12}\)

Step-by-step explanation:

The first factor needs to be a number greater than 0, but less than 10.  That would be 3.92.  Next count how many places you moved the decimal.  In standard notation the decimal should be 12 spaces to the right.  This is the exponent.

Helping in the name of Jesus.

Answer:

7 /10  0.7

Step-by-step explanation:

To add fractions, find the LCD and then combine.

Answer:

7/10

Step-by-step explanation:

First, find the smallest possible denominator between the two fractions. The smallest one is 20.

Now, both denominators need to become 20. To get the 5 in 1/5 to become 20, it needs to be multiplied by 4. Whatever you do to the denominator, you must do to the numerator.

1 x 4 = 4

The first fraction is now 4/20.

To get the 4 in 2/4 to become 20, you must multiply it by 5. Whatever you do to the denominator, you must do to the numerator.

2 x 5 = 10

The second fraction is now 10/20.

Add the fractions. Keep the denominators the same and add the numerators.

4/20 + 10/20 = 14/20

Simplify by dividing both numbers by 2

7/10

not sure but i thibj the second one

We are required to find the equivalent fraction here. When simplifying 16/64, we divide both sides by 16:

16 ÷ 16 = 1

64 ÷ 16 = 4

16/64 in its simplest form is 1/4. When we multiply both the numerator and denominator by 2, we will find that:

1/4 = 2/8

To verify this, we can multiply both parts of the fraction by 8:

2 × 8 = 16

8 × 8 = 64

Hence, we know our answer is correct.

The degrees of freedom are equal to the number of categories minus 1. As a result, df = 3-1 = 2. Hence, the given statement is true, and the df value is 2.

The statement "A chi-square test for goodness of fit is used with a sample of n = 30 subjects to determine preferences among 3 different kinds of exercise. The df value is 2." is a true statement.

What is chi-square test?

The chi-square goodness of fit test is a statistical hypothesis test that is used to evaluate whether a set of observed data follows a specific probability distribution or not. A chi-square test for goodness of fit compares an observed frequency distribution with an expected frequency distribution.

What is the meaning of df value in the chi-square test?

df (degree of freedom) represents the number of observations in the data that can vary without changing the overall outcome or conclusion of the test. It is determined by subtracting one from the number of categories being analyzed.

Let us apply the given values to the chi-square test: In the chi-square goodness of fit test, the expected frequency of each category is the same. Therefore, there will be only one expected frequency value for each category. We have three categories here.

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A chi-square test for goodness of fit is used with a sample of n= 30 subjects to determine preferences among 3 different kinds of exercise and df value is 2. The given statement is True.

It is a statistical hypothesis test that determines if there is a significant difference between the observed and expected frequencies in one or more categories of a contingency table.

The chi-square test of goodness of fit is used to determine how well the sample data fits a distribution or a specific theoretical probability.

The df value specifies the degrees of freedom that is calculated by subtracting one from the number of classes in the data.

To summarize, a chi-square test for goodness of fit is used with a sample of n= 30 subjects to determine preferences among 3 different kinds of exercise.

The df value is 2 is a true statement.

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Using the binomial distribution, it is found that there is a 0.16 = 16% probability of choosing a gray button, replacing it, and choosing gray again.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability of two gray buttons is:

P(X = 2) = (0.4)² = 0.16.

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Answer:

$680

Step-by-step explanation:

Capacity of the truck: 4200 pounds and 480 cubic feet of cargo.

Small package: 25 pounds and 3 cubic feet each.

Large package: 50 pounds and 5 cubic feet each.

For x number of small packages:

25x pounds and 3x cubic feet

Let x = 8,

200 pounds and 24 cubic feet.

For y number of large packages:

50y pounds and 5y cubic feet

Let y = 80,

4000 pounds and 400 cubic feet.

Since delivery service charges $5 for each small package and $8 for each large package.

The maximum revenue per truck = ($5x + $8y)

                                                       = ( $5 x 8) + ($8 x 80)

                                                       = $680

One key difference between Cousteau's argument and Kennedy's argument about space is that Cousteau believed that space exploration should not come at the expense of protecting and preserving our planet's oceans,

While Kennedy saw space exploration as a necessary and important component of national security and technological advancement. Jacques Cousteau and John F. Kennedy had different perspectives on the importance and priority of space exploration. While Kennedy argued that space exploration was crucial for national security and technological advancement, Cousteau believed that protecting and preserving the oceans on our planet should be the top priority. For Cousteau, the exploration of space should not come at the expense of neglecting our own planet and its natural resources. In contrast, Kennedy saw space exploration as a way to demonstrate American strength and leadership in the world and to gain a strategic advantage over other nations. Despite their different perspectives, both Cousteau and Kennedy recognized the importance of science and exploration in pushing the boundaries of human knowledge and achievement.

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Answer:

y = -15

Step-by-step explanation:

All you have to do is 51 divided by -3.4 and it equals -15. Inverse operations in short terms. And if you substitute -15 for y it will fir.

Answer:

-3.4y = 51

y = 51/-3.4

y = 510/-34

y = -15

Answer:

B

Step-by-step explanation:

Logically and if you observe the graph closely ┐( ∵ )┌

The answer is yes, there appears to be an association between grade level and prom theme based on the segmented bar graph. The Option B is correct

The graph shows that 12th-grade students prefer the 1920s theme more than the 11th-grade students do, and they also have a lower preference for the beach party theme. This indicates a difference in preferences between the two grade levels for these specific prom themes.

This graph provide information on whether both distributions have the same four categories or whether they have the same preference for each of the prom themes, so, its indicate whether the number of students in each class is the same or not.

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Anna has $540 to spend at the bicycle shop → this means that she can spend the $540 or less, you can symbolize this as ≤ $540

Her costs include:

• A bicycle for ,$402.87

• 3 bicycle reflectors for $10.97/each, the total will be 3*10.97=,$32.91

• A pair of bike gloves for ,$14.42

• With the remaining money, she wants to buy as many biking outfits as possible. Let "o" represent the number of outfits she can buy, considering each one costs $44.90, then the total cost for the outfits can be symbolized as ,$44.90o

The calculation for her total expenses is the sum of everything she buys:

"Bicycle"+"Reflectors"+"Gloves"+"Outfits"≤$540

Using the costs listed above the expression is

Simplify the like terms, i.e. add the alone numbers together

Therefore, the values that satisfy the given system are:
x = 11.36
y = -1
z = -1.82

To use Cramer's Rule to find values for x, y, and z that satisfy the given system, we need to first find the determinant of the coefficient matrix, A. The coefficient matrix is formed by taking the coefficients of x, y, and z from the system of equations:
A =
1  0  4
0 -5  3
-1  2  0
The determinant of A, denoted as |A|, is calculated as follows:
|A| = 1((-5)(0) - (2)(3)) - 0((1)(0) - (-1)(3)) + 4((1)(2) - (-1)(-5))
   = -15 - 0 + 26
   = 11
Next, we need to find the determinants of the matrices obtained by replacing the first column of A with the constants on the right-hand side of the equations. These determinants are denoted as Dx, Dy, and Dz.
Dx =
-5  0  4
-1 -5  3
-5  2  0
= (-5)((-5)(0) - (2)(3)) - 0((-1)(0) - (-5)(3)) + 4((-1)(2) - (-5)(-5))
= 125
Dy =
1  -5  4
0  -1  3
-1  -5  0
= 1((-1)(-1) - (-5)(3)) - (-5)((1)(-1) - (-1)(3)) + 4((1)(-5) - (-1)(-5))
= -11
Dz =
1  0  -5
0  -5  -1
-1  2  -5
= 1((-5)(-5) - (2)(-1)) - 0((1)(-5) - (-1)(-1)) + (-5)((1)(2) - (-1)(-5))
= -20
Finally, we can find the values of x, y, and z using the formulas:
x = Dx / |A|
 = 125 / 11
 = 11.36 (rounded to two decimal places)
y = Dy / |A|
 = -11 / 11
 = -1
z = Dz / |A|
 = -20 / 11
 = -1.82 (rounded to two decimal places)
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Answer:

The answer to the question is 5:3:4

The z-value of 85 in this normal distribution is 2. Therefore, the z-value of 85 in this normal distribution is 2.

To find the z-value of 85 in a normal distribution with a mean of 75 and a standard deviation of 5, we can use the formula: z = (x - μ) / σ

where:
x = the score we're interested in (in this case, x = 85)
μ = the mean of the distribution (μ = 75)
σ = the standard deviation of the distribution (σ = 5)

Plugging in the values, we get:

z = (85 - 75) / 5
z = 2

Therefore, the z-value of 85 in this normal distribution is 2.

To find the z-value of 85 in a normal distribution with an average score of 75 and a standard deviation of 5, you'll need to use the z-score formula:

Z = (X - μ) / σ

Where Z is the z-value, X is the raw score (85), μ is the average (75), and σ is the standard deviation (5).

Z = (85 - 75) / 5
Z = 10 / 5
Z = 2

The z-value of 85 in this normal distribution is 2.

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