what is this?? i’ve been stuck on this for so long.

There are 39 elements in the intersection of the two sets.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Union: -

If set A and set B are two sets, then A union B is the set that contains all the elements of set A and set B. It is denoted as A ∪ B.

Example: Set A = {1,2,3} and B = {4,5,6}, then A union B is:

A ∪ B = {1,2,3,4,5,6}

Intersection:-

If set A and set B are two sets, then A intersection B is the set that contains only the common elements between set A and set B. It is denoted as A ∩ B.

Example: Set A = {1,2,3} and B = {4,5,6}, then A intersection B is:

A ∩ B = { } or Ø

Since A and B do not have any elements in common, so their intersection will give null set.

P(AUB) = P(A) + P(B) - P(A∩B)

Here, P (A) = the number of elements in the set A and so on.

We know that:

                     P (A)= 67

                     P (B)= 72

and                P (AUB) = 100

So, we can solve for the number in the intersection i.e.                     P(A∩B) = P(A) + P(B) - P(AUB)

P(A∩B) = 67 + 72 - 100

P(A∩B) = 139 - 100

P(A∩B) = 39.

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Answer:

2 m/s

Step-by-step explanation:

To find the speed of the ball, we can use the formula:

Speed = Distance / Time

Given that the distance the ball moves is 3 m and the time it takes is 1.5 s, we can substitute those values into the formula to get:

Speed = 3 m / 1.5 s

Simplifying the expression by dividing 3 by 1.5, we get:

Speed = 2 m/s

Therefore, the speed of the ball is 2 m/s.

Answer:

5.2 or 5.2O

Step-by-step explanation:

add 2.6m + 2.60 which means add 2.60 + 2.60

2.60

+2.60

______

5.2 (the zero is optional)

Answer:

66.9

Step-by-step explanation:

Answer:

\(\boxed {\tt 66.9 \ inches}\)

Step-by-step explanation:

We are given the formula:

\(c=2.54n\)

where \(c\) is centimeters and \(n\) is inches.

We know that Henry is 170 centimeters tall. Therefore, we can substitute 170 in for \(c\)

\(170=2.54n\)

We want to find out how tall Henry is, in inches. We must isolate the variable for inches, \(n\), on one side of the equation.

\(n\) is being multiplied by 2.54. The inverse of multiplication is division. Divide both sides of the equation by 2.54

\(\frac{170}{2.54} =\frac{2.54n}{2.54}\)

\(\frac{170}{2.54}=n\)

\(66.9291339=n\)

Round to the nearest tenth. The 2 in the hundredth place tells us to leave the 9 in the tenth place.

\(66.9 \approx n\)

\(n \approx 66.9 \ inches\)

Henry is about 66.9 inches tall.

Answer:

Infinite amount of solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = -2x + 4

2x + y = 4

Step 2: Solve for x

Substitution

Here we see that 4 does indeed equal 4.

∴ the systems of equations has an infinite amount of solutions.

Answer:

Infinite amount of solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Left to Right  

Equality Properties

Multiplication Property of Equality

Division Property of Equality

Addition Property of Equality

Subtraction Property of Equality

Algebra I

Terms/Coefficients

Coordinates (x, y)

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

y = -2x + 4

2x + y = 4

Step 2: Solve for x

Substitution

Substitute in y:                                                                                                  2x + (-2x + 4) = 4

Combine like terms:                                                                                         4 = 4

Here we see that 4 does indeed equal 4.

∴ the systems of equations has an infinite amount of solutions.

\(\boxed{\sf (-3, -1)}\boxed\)

Answer:

9 miles

Step-by-step explanation:

1/4 of an hour is 15 minutes. So 2 and 1/4 times multiplied by 4 would be the answer beacsue 15 minutes times 4 is an hour.

Answer:

9 mph.

Step-by-step explanation:

We multiply the distance by 4 because there are 4 lots  of a 1/4 in one hour:

That is 2 1/4 * 4

= (9/4) * 4

= 36/4

= 9 m ph.

Answer:

4 5/8

Step-by-step explanation:

Answer:

37 /56

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

2³ + 3² - 3(4) - 5²/5 + 7(4)

8 + 9 - 12 -25/5 + 28

17 - 12 - 5 + 28

5 - 5 + 28

28

Easiest and fastest way to is plug it into the calc and calculate. If not, use BPEMDAS.

Answer:

15 DEGREES

Step-by-step explanation:

OK SO BASICALLY,  USING THE EXTERIOR ANGLES THEOREM, YOU FIND THAT 9x = 5x + something. That something is 4x so:

9x = 5x + 4x

THEN YOU FIND THAT 8x = 5x + something. That something is 3x so:

8x = 5x + 3x

4x and 3x and 5x are the interior angles of the triangle (ABC)

Then you use triangle theorem and get 4x + 3x + 5x = 180

Then: 12x = 180 and so you get x = 15

The probability of choosing a full professor or a TA is 15/29 or 0.517

The probability of choosing a particular object is the number of ways that object can be chosen divided by the total number of objects in the group.

The total number of mathematics faculty members is:

4 (full professors) + 10 (associate professors) + 4 (assistant professors) + 11 (teaching assistants) = 29

The probability of choosing a full professor or a TA can be found by adding the probabilities of choosing a full professor and choosing a TA. The probability of selecting full professor is:

P(full professor) = 4/29

The probability of choosing a TA is:

P(TA) = 11/29

Therefore, the probability of choosing a full professor or a TA is:

P(full professor or TA) = P(full professor) + P(TA) = 4/29 + 11/29 = 15/29

So the probability of choosing a full professor or a TA is 15/29 or 0.517, which cannot be simplified any further.

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A unique triangle can be constructed if it satisfies the angle and length conditions. In the given options:

A) Angle measures: 30°, 60°, 90° - This forms a unique triangle because the sum of the angles equals 180°.

B) Angle measures: 50°, 50°, 80° - This also forms a unique triangle because the sum of the angles equals 180°.

C) Side lengths: 2 in., 7 in., 8 in. - This forms a unique triangle because it satisfies the Triangle Inequality Theorem (sum of any two sides is greater than the third side: 2+7 > 8, 2+8 > 7, 7+8 > 2).

D) Side lengths: 5 ft., 6 ft., 12 ft. - This does not form a unique triangle because it fails the Triangle Inequality Theorem (5+6 ≤ 12).

E) Side lengths: 11 cm, 15 cm, 17 cm - This forms a unique triangle because it satisfies the Triangle Inequality Theorem (11+15 > 17, 11+17 > 15, 15+17 > 11).

So, the conditions A, B, C, and E will result in the construction of a unique triangle.

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The confidence interval in both cases has been constructed as:

a) (26.02, 29.98)

b) (120.17, 127.83)

The formula to calculate the confidence interval is:

CI = xˉ ± z(σ/√n)

where:

xˉ is sample mean

σ is standard deviation

n is sample size

z is z-score at confidence level

a) xˉ = 28

σ = 4

n = 11

90 percentage confidence.

z at 90% CL = 1.645

Thus:

CI = 28 ± 1.645(4/√11)

CI = 28 ± 1.98

CI = (26.02, 29.98)

b) xˉ = 124

σ = 8

n = 29

90 percentage confidence.

z at 99% CL = 2.576

Thus:

CI = 124 ± 2.576(8/√29)

CI = 124 ± 3.83

CI = (120.17, 127.83)

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Answer:

Step-by-step explanation:

The product of a negative two and a positive three is equal to negative six (-6).

The correct decision rule for a test hypothesis with a significance level of 0.02, with two tails, is given as follows:

C. Reject H0 if Zstat< -2.33 or Zstat > +2.33.

The decision regarding the null hypothesis depends on if the p-value is less or more than the significance level:

For a two-tailed test with a significance level of 0.02, the critical value is given as follows:

z = 2.33.

Hence the decision rule is given as follows:

Hence option C is the correct option for this problem.

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John's wages are proportional to time as the hourly wage is same for all values of time given.

Proportional means that two quantities vary in direct proportion to each other. When the value of one quantity doubles, the value of the other also doubles.

In order to determine if John's wages are proportional to time, we need to find the ratio of the two quantities, wages and time.

We can calculate John's hourly wage (proportionality constant) by dividing his total wages by the number of hours worked:

Hourly wage = Total wages / Time

For example, the hourly wage for 2 hours is:

Hourly wage = 18 / 2

Hourly wage = 9

Similarly, we can calculate the hourly wages for the other times and we'll find that the proportionality constant is the same 9 for all number of hours.

Since the hourly wage is constant for all values of time, we can say that John's wages are proportional to time.

Complete Question: content loaded

John and amber work at an ice cream shop the hours worked and wages earned are given for each person:

John's wages

Time (in hours)          Wages (in dollars)

2                                      18

3                                      27

4                                      36

Determine if John's wages are proportional to time

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Answer:

Can i see the full answer so I can help you?

Step-by-step explanation:

Part A: The respondents in the population are a voluntary response sample.

Part B: The responses may not reflect the opinions of the general population

The total number of internet users in those is 1072 people.

The percentage of the total number of people that chose to respond is 38%

We can note that this survey does not compel the population to respond to the survey. These responses are given by the voluntary respondents.

Another point is that a voluntary response sample is a sample that consists of participants who are interested to participate in a sample group voluntarily.

In this type of survey, the people who are supposed to decide to provide voluntary responses to the survey are called voluntary response samples.

The percentage of those that chose to respond to this survey which is 38% is less than half of the total population. This result shows that the responses may not reflect the opinions of the general population.

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True, the links in the blockchain are created using an algorithm.

What is blockchain?                                                                                                                                                                                                                       Blockchain is a decentralized ledger technology that enables the secure exchange of digital assets across a network of participants without the need for a centralized authority or intermediary. The blockchain is created using an algorithm to secure the network and ensure that all transactions are transparent and verifiable.

In a blockchain, each block contains a cryptographic hash of the previous block, forming a chain of blocks (hence the name "blockchain"). The algorithm used to create the blockchain is a consensus algorithm, which ensures that all participants on the network agree on the same state of the ledger.

This consensus algorithm also ensures that no single participant can manipulate the ledger or change the contents of a block without being detected.

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The correct answer is (b) fraction numerator cos squared x over denominator 2 end fraction minus fraction numerator cos cubed x over denominator 3 end fraction plus C.

To evaluate the integral, we can use the identity sin²(x) + cos²(x) = 1 to write sin³(x) = sin²(x) × sin(x) = (1 - cos²(x)) × sin(x). Then, we can use u-substitution with u = cos(x) and du = -sin(x) dx to get:

integral sin³(x) cos²(x) dx = -integral (1 - u²) u² du
= integral (u⁴ - u²) du
= (1/5)u⁵ - (1/3)u³ + C
= (1/5)cos⁵(x) - (1/3)cos³(x) + C

Using the identity cos²(x) = 1 - sin²(x), we can also write the answer as:

(1/2)cos²(x) - (1/3)cos³(x) + C

Therefore, the correct answer is (b) fraction numerator cos squared x over denominator 2 end fraction minus fraction numerator cos cubed x over denominator 3 end fraction plus C.

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Answer:

-1764

Step-by-step explanation:

use BODMAS rule

⇒7{-7+8[5-3(4+6)]-9(9-4)}

solve round brackets

⇒7{-7+8[5-3(10)]-9()}

multiply 3 by 10 within the square bracket

⇒7{-7+8[5-30]-9(5)}

solve square bracket

⇒7{-7+8[-25]-9(5)}

move to curly brackets and multiply first

⇒{-7-200-45}

subtract

⇒7{-252}

multiply

⇒-1764 Answer

hope that helps...

The solution to the given initial-value problem is:

y(x) = e^(-2x) * (3e^(2x) - 2e^(-x) + 4e^(-2x)).

To solve the given initial-value problem, we can start by finding the complementary solution, which is the solution to the homogeneous equation y'' + 4y' + 5y = 0. The characteristic equation associated with this homogeneous equation is r^2 + 4r + 5 = 0, which yields complex roots: r = -2 ± i.

The complementary solution is then given by

y_c(x) = e^(-2x) * (C₁cos(x) + C₂sin(x))

, where C₁ and C₂ are constants to be determined.

Next, we find a particular solution to the nonhomogeneous equation

y'' + 4y' + 5y = 35e^(-4x)

. Since the right-hand side is of the form Ae^(kx), where A and k are constants, we can guess a particular solution of the form y_p(x) = Be^(-4x), where B is a constant to be determined.

By substituting this guess into the equation, we find B = 3. Therefore, the particular solution is y_p(x) =

3e^(-4x)

.

Finally, we combine the complementary solution and the particular solution to obtain the general solution: y(x) = y_c(x) + y_p(x). Applying the initial conditions y(0) = -2 and y'(0) = 1 allows us to determine the values of C₁ and C₂. After solving for C₁ and C₂, we arrive at the final solution:

y(x) =

e^(-2x) * (3e^(2x) - 2e^(-x) + 4e^(-2x)).

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Answer:

  (a)  x² +(y -3)² = 36

  (e)  x² +(y +8)² = 36

Step-by-step explanation:

You want to identify the equations for a circle with center on the y-axis and diameter 12 units.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

If the center is on the y-axis, then h = 0. If the diameter is 12 units, then the radius is 6 units and r² = 36. This means the desired equation will be of the form ...

  (x -0)² +(y -k)² = 36

  x² +(y -k)² = 36 . . . . . . . for some value of k

The relevant answer choices have k = 3 or -8:

  x² +(y -3)² = 36

  x² +(y +8)² = 36

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For all values of x greater than or equal to -2, the function f(x) = √(x + 2) + 2 will yield real outputs. So, x = -2.

To determine the input value at which the function f(x) = √(x + 2) + 2 begins to have real outputs, we need to find the values of x for which the expression inside the square root is non-negative. In other words, we need to solve the inequality x + 2 ≥ 0.

Subtracting 2 from both sides of the inequality, we get:

x ≥ -2

Therefore, the function f(x) = √(x + 2) + 2 will have real outputs for all values of x greater than or equal to -2.

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If 78 apples are in the tub, there are 6 apples in each bag

A division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 40 members into 4 groups of 10 members each or 10 groups of 4 members each, Or creating 2 groups of 20 members or 20 groups of 2 members.

This means that when dividing 40 by 10 we get 4 and when dividing 40 by 4 we get 10.

Emily sets up a tub by buying 13 bags of apple. The total apple in the tub when the 13 bags were poured are 78 apples.

Therefore to find the number of apple in each bad, we divide the total number of apple in the tub by the number of bags.

= 78/13 = 6 apples per bag

Therefore the number of apple in each bag is 6.

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The number of shots attempted by the player until he misses is considered a binomial equation because the probability of success is always constant.

Therefore, the particular criteria for forming a binomial equation is

Therefore, for the given case, the hockey player uses 21% of his shots and is requested to make his shots until he misses. The total number of shots attempted is observed.

Since each shot has only dual possible outcomes (success or failure), and probability of success is constant then this experiment meets all the  four characteristics of forming a  binomial experiment.

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Step-by-step explanation:

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