4. (9 pts) Draw an example of sets that meet the following descriptions, Malwe sure to include and label the univenal set U. a. A and B are disjoint sets b. A is a proper subset of B c. A∪B∪C=U, but A,B, and C are all mutually disjoint

Answer:

A

Step-by-step explanation:

Hope this helps :)

Answer:

A

Step-by-step explanation:

By using the concept of Probability, 0.771 is the probability by which worker 1 will outproduce worker 2

Let Xi be the random variable representing the number of units the first worker produces in day i.

Define X = X₁+ X₂ + X₃ + X₄ + X₅ as the random variable representing the number of units the first worker produces during the entire week.

We know that Mean =(Sum of all quantities)/(Number of quantities)

Mean=75 and number of quantities =5(given)

Therefore, from the formula

=>Sum of all quantities=75×5

or We can Say that X₁+ X₂ + X₃ + X₄ + X₅=375--------------------------------(eq1)

Now, talking about the standard deviation of first worker

We know that standard deviation = \(\frac{\sqrt{(Each quantity - Mean)^{2} } }{\sqrt{Total Number of quantities} }\)

We are given standard deviation of first worker as 20,

Therefore 20×\(\sqrt{Total Number of quantities}\) = \(\sqrt{(Eachquantity -Mean)^{2} }\)

20√5 = √[(X₁ - Mean)²+(X₂ - Mean)²+(X₃ - Mean)²+(X₄ - Mean)²+(X₅ - Mean)²]-(eq2)

Therefore, from eq1 and eq2,

we get Mean(µx) =375 and standard deviation(σ\(x\)) =20√5

Similarly, define random variables Y₁, Y₂, . . . , Y₅ representing the number of units produces by the second worker during each of the five days and define Y = Y₁ + Y₂ + Y₃ + Y₄ + Y₅.

From the Mean formula,

we get  Y₁ + Y₂ + Y₃ + Y₄ + Y₅=(65×5)--------------------------------(eq3)

Standard deviation of second worker = 21(given),

So using the standard deviation formula, we get

Therefore 21×\(\sqrt{Total Number of quantities}\)=\(\sqrt{(Eachquantity -Mean)^{2} }\)

21√5=√[(Y₁ - Mean)²+(Y₂ - Mean)²+(Y₃ - Mean)²+(Y₄ - Mean)²+(Y₅ - Mean)²]-(eq4)

Therefore, from eq3 and eq4,

we get Mean(µy) =325 and standard deviation(σy) =21√5

Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X − Y > 0).

It is a quite surprising fact that the random variable U = X −Y , the difference between X and Y ,is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σu ,where σ\(u^{2}\) = σ\(x^{2}\)+σ\(y^{2}\) =400·5+441·5 = 841·5 = 4205

It follows that  σu=√4205.

Now probability of first worker(P₁)=375/√4205

probability of second worker(P₂) =325/√4205

We can clearly see P₁>P₂

Difference in Probability of both workers(P)=P₁-P₂

=>P=[(375/√4205)-(325/√4205)]

=>P=50/√4205

=>P=50/64.84

=>P=0.771

Hence, probability by which worker 1 will outproduce worker 2 is 0.771.

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Answer:

The shorter side of pentagon is 6cm long

Step-by-step explanation:

Given two equations are:

\(y = x + 2\\2x + 3y = 36\)

We can use any one of the methods to solve the simultaneous linear equations

As it is also given that x is the length of shorter side, we have to find the value of x

Using the substitution method

We will put the value of y i.e. x+2 in the 2nd equation

So,

\(2x+3(x+2) = 36\)

Simplification gives us:

\(2x+3x+6 = 36\\5x+6 = 36\\5x = 36-6\\5x = 30\\x = \frac{30}{5}\\x =6\)

Hence,

The shorter side of pentagon is 6cm long

Answer:

Sorry

Step-by-step explanation:

Sorry I don't know the answer because I haven't learned this yet. Hope you get your answer!

Answer:

x = 11

Step-by-step explanation:

The 2 angles are alternate exterior angles and congruent, thus

6x - 2 = 5x + 9 ( subtract 5x from both sides )

x - 2 = 9 ( add 2 to both sides )

x = 11

Answer:

n=130 is the answer because you habe to subtract it from 360

Answer:

volume is 9847.04 \(m^{3}\)

Step-by-step explanation:

V = π * \(r^{2}\)  * h

V = 3.14 * \(14^{2}\) * 16

=9847.04 \(m^{3}\)

Hope you could understand.

If you have any query, feel free to ask.

Answer:

There are infinite numbers between -2 and -3

Step-by-step explanation:

First off these numbers:

-2.1 or this number as any equivilant fraction.

-2.2 or this number as any equivilant fraction

-2.3 or this number as any equivilant fraction

-2.4 or this number as any equivilant fraction

-2.5 or this number as any equivilant fraction

-2.6 or this number as any equivilant fraction

-2.7 or this number as any equivilant fraction

-2.8 or this number as any equivilant fraction

-2.9 or this number as any equivilant fraction

any numbers that are reepeating like : -2.3333333333.....

and any numbers that end and don't go on forever without a single repeating number. -2.485485485485485485485485..... is not rationally repeating. -2.444444444444 is rational.

Answer: σ: 2.76

Step-by-step explanation:

Count, N: 5

Sum, Σx: 125

Mean, μ: 25

Variance, σ2:  7.6

Steps

look at attached pic for formula

σ^2 = \(\frac{Σ(xi - μ)^{2} }{N}\)

\(\frac{(21 - 25)2 + ... + (29 - 25)2}{5}\)

⇒ \(\frac{38}{5}\)

⇒ 7.6

σ =  \(\sqrt{7.6}\)

⇒   2.756809750418

⇒ or 2.76

Answer:

36

Step-by-step explanation:

if 17.7 million = 49%, then 17.7 / 49 = 1% or .361 million. Times 100 = 36.1 million rounded to 36 million.

Answer:

one solution

Step-by-step explanation:

3x-1=3

Add 1 to each side

3x-1+1=3+1

3x = 4

Divide by 3

3x/3 = 4/3

x = 4/3

There is one solution

Answer:

One solution

Step-by-step explanation:

3x=4

x=4/3

no other answer

Answer:

-49/15

Step-by-step explanation:

To determine the position of point A on the number line, we need to subtract the length of segment AB from the position of point B.

Given that the position of point B is 2/5, we can subtract the length of AB, which is 3 2/3, from 2/5.

To subtract fractions, we need to find a common denominator. The least common denominator for 3/3 and 5 is 15.

Converting 3 2/3 to an improper fraction:

3 2/3 = (3 * 3 + 2)/3 = 11/3

Subtracting the fractions:

2/5 - 11/3 = (2 * 3 - 11 * 5)/(5 * 3) = (6 - 55)/15 = -49/15

The position of point A is -49/15 on the number line.

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Answer: 9.2

Step-by-step explanation:

You devide 15 in the number of ounces in the pitcher

There are 10 servings in one pitcher.

Comparing quantities is the qualitative relation between two quantities which reflects the relative size of both the quantities

Now it is given that,

Number pitcher of lemonade in 147 ounces = 1 Pitcher

Now, if 1 serving is 15 ounces

Therefore, Number of servings in 15 ounces = 147/15

⇒ Number of servings in 15 ounces = 9.8

⇒ Number of servings in 15 ounces ≈ 10

So, Number of servings in 1 Pitcher =  10

Thus, there are 10 servings in one pitcher.

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Answer:

96.6

Step-by-step explanation:

120.5 subtracted by 23.90 give you how much the gold nugget weight.

Answer:

hello it is so

Step-by-step explanation:

simple simply do the division if don't I can

Answer:

Vertex: (-2, 0)

Axis of symmetry: x = -2

Direction of opening: Upwards

Min: 0

Y-intercept: 4

Step-by-step explanation:

    Let us graph this line, and then pull out the details we need. See attached.

    What do all of these different things mean?

Vertex: This is where the graph intercepts the axis of symmetry (x = -2, see below) and is at point (-2, 0) for this graph.

Axis of Symmetry: This is the line that the graph is symmetrical across. The "center" of the graph. Here, it is x = -2.

Direction of Opening: The direction that the graph is going/opening towards. In this case, it is upwards.

Min: The minimum (in this case) value, the lowest y-coordinate. This is 0 here.

Y-intercept: The point at which the line intercepts the y-axis. This is 4 here.

The value of p+q = 403,For the given complex number a+bi and \(b^{2} =\frac{p}{q}\)

where p and q are co-primes

F(z)= (a+ib)z⇒this is equidistant from "0" and "z"

Given  modulus of complex number (a+ib) = 10 ; \(b^{2} =\frac{p}{q}\) p and q ∈Z

G.C.D of ( p and q)=1

(a+ib)z equidistant from "0" and "z"

\(&\Rightarrow|(a+i b) z-z|=|(a+i b) \bar{z}-0|\\&|z(a+i b-1)|=|(a+i b) \bar{z}|\\&[\bar{z}||(a-1)+i b|=| z|(a+i b)|\\&|a-1+i b|=|a+i b|\\&\sqrt{(a-1)^2+b^2}=\sqrt{a^2+b^2}\\&|a+i b|=10 \quad a^2+1-2 a+b^2=x^2+b^2\\&\sqrt{a^2+b^2}=10\\&a=1 / 2\\&a^2+b^2=100\\&b^2=100-\frac{1}{4}\\\)

\(b^{2} =\frac{399}{4}\)

p = 399 and q= 4

p+q= 399+4

p+q=403

Hence the value of p+q = 403

Complete question:A function f is defined on the complex number by f (z) = (a + bi)z, where 'a' and 'b' are positive numbers. This function has the property that the image of each point in the complex plane is equidistant from that point and the origin. Given that |a+bi|=8 and that\(b^{2} =\frac{p}{q}\)  where p and q are coprime. Find the value of (p+q)

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Step 1

Write the expression for the current value of the vehicle in any given year

Step 2

Substitute and get the price of the vehicle after 10 years

To the nearest whole number the cost of the vehicle after 10 years = $10,860

Answer:

Between 9 and 10.

Step-by-step explanation:

We know that √81 = 9 and that √100 = 10.

Since √95 is between √81 and √100, we know it will be between 9 and 10.

√95 = 9.74679

Step-by-step explanation:

Let x = the number of years since the first year and let y = the total number of plants.

Roses: y = 5 + 2x

Tulips: y = 20 – 3x

You can use elimination to solve.

y = 5 + 2x

(-)y = 20 – 3x

0 = -15 + 5x

15 = 5x

3 = x

This means that 3 years after the first year, the number of rose bushes equals the number of tulip plants.

The graphs appear to

intersect at (3, 11) which verifies that x=3

The number of rose bushes will equal the number of tulip plants after 3 years

The given parameters are:

Rose bushes

Tulip bushes

So, the number of rose bushes and tulip bushes each year is:

y = 5 + 2x

y = 20 - 3x

From the graph of both equations, we have:

(x,y) = (3,11)

Hence, the number of rose bushes will equal the number of tulip plants after 3 years

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Matched design A/B tests are usually analyzed using the paired sample t-test.  Hence, the answer is option B (Paired sample t-test).

The paired sample t-test is used to compare the mean differences between two related groups. The test is used to analyze before and after results of an experiment, the two groups of subjects are matched according to age, sex, or other factors.

It is used to compare the mean difference between the two groups after they have been treated with different interventions.The other options of the independent samples t-test, logistic regression analysis, and analysis of variance (ANOVA) are not appropriate statistical tests for matched design A/B tests.

Therefore, the correct option is Paired sample t-test. Hence, the answer is option B (Paired sample t-test).

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Answer:

\( \frac{596}{125} \)

should be it

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Answer:

The price of one pretzel is $-10.75

Step-by-step explanation:

I'm not really sure why the pretzel would be negative dollars, but I checked my answer multiple times and it's right. For this problem you need a system of equations. The system will be 3d+2p=16 (since 3 drinks and 2 pretzels is 16 dollars) and 6d+5p=21.25 (since 6 drinks and 5 pretzels is 21.25 dollars). To solve this system, the first thing we're going to do is multiply the first system by -2 so that we can cancel the d variable. This will leave you with

-6d-4p=-32. Now, you can add this to the other equation. Since the -6 and 6 cancel, we only have the p variable now (that's why we multiplied by -2, to cancel out the d variable when we added later). Now we have -4p=-32 and 5p=21.25. Add these two equations together and you'll get 1p=-10.75, or p=-10.75. If you needed to solve for the drinks, you could plug -10.75 back into one of the first two equations, but for this problem we don't so -10.75 is your answer.

Answer:

my answer is A

Step-by-step explanation:

if you work out the equation where you know that at the x intercept y=0 you will find A to be true

The correct interpretation of the interval is:

B. We are 95 percent confident that the difference in population means for miles traveled by the two companies is between 1.86 miles and 2.15 miles.

The conditions for inference that have been met are: D. I and III only.

For the first question, the correct interpretation of the confidence interval is:

B. We are 95 percent confident that the difference in population means for miles traveled by the two companies is between 1.86 miles and 2.15 miles.

This interpretation reflects the fact that the confidence interval was constructed based on the sample means, but it provides an inference about the population means of the two companies.

For the second question, the conditions for inference that have been met are:

D. I and III only

I. The data were collected using a random method.

This ensures that the samples are representative of the population.

III. Each sample size is large enough to assume normality of the sampling distribution of the difference in sample means.

This condition implies that the sample sizes are sufficiently large to rely on the central limit theorem, which states that the sampling distribution approaches a normal distribution as the sample size increases.

Condition II, which states that each sample size is less than 10 percent of the population size, is not explicitly mentioned in the question. Therefore, we cannot assume that this condition has been met.

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Answer:

I. First number, a = 40.

II. Second number, b = 50.

III. Third number, c = 120.

Step-by-step explanation:

Let the three numbers be a, b and c respectively.

Given the following data;

Translating the word problem into an algebraic equation, we have;

a + b + c = 210

b = a + 10

c = 3a

Substituting the value of b and c into the equation, we have;

a + a + 10 + 3a = 210

5a + 10 = 210

5a = 210 - 10

5a = 200

a = 200/5

a = 40

To find the value of b;

b = a + 10

b = 40 + 10

b = 50

To find c

c = 3a

c = 3*40

c = 120

Step-by-step explanation:

\( = 1 - ( \frac{1}{6} + \frac{1}{5} )\)

\( = 1 - ( \frac{5}{30} + \frac{6}{30} )\)

\( = 1 - \frac{11}{30} \)

\( = \frac{30}{30} - \frac{11}{30} \)

\( = \frac{19}{30} \)

So, he keeps \( \frac{19}{30}\)

Answer:

Sanjeev kept 19/30 of his cake.

Step-by-step explanation:

So, if Sanjeev ate 1/6 of the cake there will be 5/6 of the cake left over.

He gave 1/5 of this 5/6 to his friend.

He did not give 1/5 of the entire cake, he gave 1/5 of the remainder of his cake, which was 5/6.

To solve this, we must first convert both fractions to the same denominator.

1/5 and 5/6 becomes 6/30 and 25/30

He gave away 6/30 of this 25/30

It is now clear that we must take away how much he gave away from the remainder of the cake.

25/30 subtract 6/30 becomes 19/30

We cannot simplify this.

Therefore, Sanjeev kept 19/30 of his cake.

Answer:

  swap the middle two steps to put them in order

Step-by-step explanation:

The steps in order would be ...

a) To determine the speed at which the large truck is approaching the stopped bus, we need to find the derivative of the distance function with respect to time.

1. Taking the derivative of d(t) with respect to t, we have:

d'(t) = d(t) / dt = (1/2) * (0.22 + (1.2 - 100t)^2)^(-1/2) * (-2) * (1.2 - 100t) * (-100)

2. Simplifying this expression, we get: d'(t) = 100 * (1.2 - 100t) / √(0.22 + (1.2 - 100t)^2)

3. Substituting the given values (t = 0), we can calculate the speed at which the truck is approaching the bus:

d'(0) = 100 * (1.2 - 100 * 0) / √(0.22 + (1.2 - 100 * 0)^2)

     = 100 * 1.2 / √(0.22 + 1.2^2)

     ≈ 100 * 1.2 / √(0.22 + 1.44)

     ≈ 100 * 1.2 / √1.66

     ≈ 100 * 1.2 / 1.288

     ≈ 93.17 km/h

Therefore, the speed at which the large truck is approaching the stopped bus is approximately 93.17 km/h.

b) To determine when the truck stops approaching the bus, we need to find the time at which the derivative of the distance function becomes zero.

1. Setting d'(t) = 0, we can solve for t: 100 * (1.2 - 100t) / √(0.22 + (1.2 - 100t)^2) = 0

Simplifying the equation, we have: 1.2 - 100t = 0

2.Since time is measured in hours, we convert this to minutes:

0.012 hours * 60 minutes/hour = 0.72 minutes

Therefore, the truck will stop approaching the bus after approximately 0.72 minutes.

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