Question 1. If X= {prime numbers less than 13} Y = {odd numbers less than 21} (i). List the members of X and Y (ii). List the members of XnY (iii). List the members of XUY Question 2. If Q = {1, 3, 5, 7, 10, 11,15} and T={1,2,3,5,6,7,12}find Q U T
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Expreion have a quotient of 6 is 0. 48 ÷ 0. 08.

What is quotient?

In mathematics, the quotient is the result of performing division operations on two integers. It is essentially the outcome of the division procedure. In arithmetic division, the terms divisor, dividend, quotient, and remainder are employed in four different ways.Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

0. 48 ÷ 0. 8

=0.06

The solution for Long Division of \($\frac{4.8}{8}$\) is 0.6

The solution for Long Division of \($\frac{0.48}{0.08}$\) is 6.

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Answer:

A 1

Step-by-step explanation:

8x11=88

1x11=11

Answer:

∠ABD = 32

Step-by-step explanation:

Since ∠ABC is the total angle, subtract ∠DBC from ∠ABC to get ∠ABD.

145 - 113 = 32

Answer:

a)   Number of laundry he can do with this box  = 78 laundries.

b)   Price he paying for each load =  0.256 $

Explanation:

Total scoop contained in detergent box = 195 scoops.

Scoops used by each load of laundry =  scoops = 2.5 scoops

Number of laundry he can do with this box = 195/2.5 = 78 laundries.

Price of detergent box = 19.99 $

Price he paying for each load = Total price/ Number of loads

                                                  = 19.99/78

                                                  = 0.256 $

Answer:

$315

Step-by-step explanation:

600-600=0

0+315=315

The expression that represent the area of the cabin for rectangular floor plan is 2w² + 5w.

What is the area of rectangular shape?

In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter.

Given that the length of a cabin is equal to 5 feet more than twice the width.

Assume that the width of the cabin be w.

Then the mathematical expression of twice the width is 2w.

Then the mathematical expression of 5 feet more than twice the width is 2w + 5.The length of the cabin is 2w + 5 feet.

The area of rectangular shape is product of length and width.

The area of the cabin is (2w + 5)w

Apply distributive property:

= 2w × w + 5 × w

= 2w² + 5w

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The mean exam score of student 2 for all four exams is 87.5.  Based on the information provided, you have a spreadsheet containing the scores of 50 students on 4 different exams. To calculate the mean exam score for Student 2 across all four exams, you need to follow these steps:

1. Locate the scores for Student 2 on all four exams. They should be on the first sheet of the spreadsheet and likely in a row or column corresponding to Student 2.

2. Add the scores of Student 2 for all four exams together. For example, if their scores were 80, 85, 90, and 95, the total would be 80 + 85 + 90 + 95 = 350.

3. To calculate the mean, divide the total score (from step 2) by the number of exams (which is 4 in this case). Using the example scores above, the mean would be 350 / 4 = 87.5.

So, the mean exam score for Student 2 for all four exams is 87.5. Keep in mind that this example assumes hypothetical exam scores; you will need to replace them with the actual scores found in the spreadsheet to obtain the correct mean score for Student 2.

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To find the probability of either event occurring, we can use the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Given that P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.25, we can substitute these values into the formula.

\(P(A or B) = P(A) + P(B) - P(A and B)\)
\(P(A or B) = 0.6 + 0.5 - 0.25\)
\(P(A or B) = 0.85 - 0.25\)
\(P(A or B) = 0.60\)
The probability of either event occurring is 0.60 or 60%.

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The probability of either event occurring can be found by adding the probabilities of the individual events and subtracting the probability of both events happening together. In this case, the probability of either event A or event B occurring is 0.6.

The probability of either event occurring can be calculated using the principle of addition. To find the probability of either event happening, we need to sum the individual probabilities of the events and subtract the probability of both events happening together.

Given:

p(a) = 0.6 (probability of event A occurring)
p(b) = 0.5 (probability of event B occurring)
p(a and b) = 0.25 (probability of both events happening together)

To calculate the probability of either event occurring, we can use the formula:

p(a or b) = p(a) + p(b) - p(a and b)

Substituting the given values into the formula:

p(a or b) = 0.6 + 0.5 - 0.25

p(a or b) = 0.85 - 0.25

p(a or b) = 0.6

Therefore, the probability of either event A or event B occurring is 0.6.

To understand this concept better, let's consider an example. Suppose event A represents rolling a fair six-sided die and getting an even number (2, 4, or 6). The probability of event A occurring would be 0.5. Now, let event B represent flipping a fair coin and getting heads. The probability of event B occurring would be 0.5.

If we want to find the probability of either rolling an even number or flipping heads, we can use the formula mentioned earlier. The probability of rolling an even number is 0.5, the probability of flipping heads is 0.5, and the probability of both happening together is 0.25. Plugging these values into the formula, we get:

p(A or B) = 0.5 + 0.5 - 0.25

              = 0.75

Therefore, the probability of either rolling an even number or flipping heads is 0.75.

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Answer:

4m + 6

Step-by-step explanation:

Since the length is twice as long your equation should look like this

2(2m + 3) = L

which would be 4m + 6 as the length of the rectangle

Answer:

1/20

Step-by-step explanation:

3/10 - 1/4

First, convert the fractions to a common denominator:

3/10 *2/2 = 6/20

1/4 * 5/5 = 5/20

Now put them back into the equation and solve:

6/20 - 5/20 = 1/20

Another way to do this:

3/10 - 1/4

Convert the fractions into decimals:

3/10 = 0.3

1/4 = 0.25

substitute back into the equation and solve:

0.3 - 0.25 = 0.05

convert back into fractions:

0.05 = 1/20

196 children's tickets and 328 adult tickets were sold.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: One night a theater sold 524 movie tickets. An adult's ticket costs $6.50 and a child's ticket cost $3.50. In all, $2881 was taken in.

Let the amount of the child's ticket be x

Let the amount of adults tickets be y

If the total number of tickets sold is 524 movie tickets, then;

x + y  = 524

x = 524 - y...(1)

If an adult ticket cost $6.50 and a child’s ticket cost $3.5 with a total of $2881 in all, then;

3.5x +  6.5 y = 2881

35x + 65y = 28810 ...(2)

Substitute equation 1 into 2:

35x + 65y = 2881

35(542-y) + 65y = 28810

18970 - 35y + 65y = 28810

30y = 9840

y = 328

Put the value of y in equation (1) and we get

x = 524 - 328

x = 196

Hence,  196 children's tickets and 328 adult tickets were sold.

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If S, T be sets, then we have proved that  S = T if and only if S \ T = T \ S.

Assume S = T. Then, S \ T = T \ S = {}.

This is because if S = T, then there are no elements in S that are not in T, and vice versa.

Therefore, the difference between the sets is the empty set.

Hence, S \ T = T \ S = {} and we have shown that S = T implies S \ T = T \ S.

Assume S \ T = T \ S.

We will show that S is a subset of T and T is a subset of S, which will imply that S = T.

Let x be an arbitrary element of S.

If x is also in T, then x is not in S \ T = T \ S, which contradicts the assumption S \ T = T \ S.

Therefore, x is not in T.

This means that x is in S \ T, which implies that x is also in T \ S (by the assumption S \ T = T \ S).

But this means that x is in T, which is a contradiction.

Therefore, there are no elements in S that are not in T, so S is a subset of T.

Similarly, let y be an arbitrary element of T.

If y is also in S, then y is not in T \ S = S \ T, which contradicts the assumption S \ T = T \ S.

Therefore, y is not in S.

This means that y is in T \ S, which implies that y is also in S \ T (by the assumption S \ T = T \ S).

But this means that y is in S, which is a contradiction.

Therefore, there are no elements in T that are not in S, so T is a subset of S.

Since S is a subset of T and T is a subset of S, S = T.

Therefore, we have shown that S \ T = T \ S implies S = T.

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The given question is incomplete, the complete question is:

let S, T be sets. prove that S = T if and only if S \ T = T \ S.

Answer:

x = 9/2

Step-by-step explanation:

Answer:

x = \(\frac{9}{2}\)

Step-by-step explanation:

Given

5(2x + 1) = 50 ( divide both sides by 5 )

2x + 1 = 10 ( subtract 1 from both sides )

2x = 9 ( divide both sides by 2 )

x = \(\frac{9}{2}\)

Answer:

g = 1/2

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

9 + 3.5g = 11 - 0.5g

Step 2: Solve for g

Step 3: Check

Plug in g into the original equation to verify it's a solution.

Here we see that 10.75 does indeed equal 10.75.

∴ g = 1/2 is a solution of the equation.

Answer: g= 0.5

Step-by-step explanation:

Add

3.5g and 0.5g. to get

9+4g=11

then subtract 9 from the 11 and you should get 4g=2.

then divide 4 from 2 and you should get the answer of 2/4.

simplify it and you should get the answer g=0.5

The value of GH in the rectangle is 60 units.

A rectangle is quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

Therefore, the diagonal of the rectangle divides the rectangle into congruent triangles.

Therefore,

DH = GH

4w + 20 = 6w

subtract 4w from both sides of the equation

4w  - 4w + 20 = 6w - 4w

20 = 2w

divide both sides of the equation by 2

w  =20 / 2

w = 10

Therefore,

GH  = 6(10)

GH = 60 units

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Answer:

y=2x+4

Step-by-step explanation:

From(0,4)

Equation in slope intercept form

The solution to the given initial value problem given below.

To solve the given initial value problem, we'll use the method of matrix exponentials. Let's begin the process.

Step 1: Compute the matrix exponential
We need to find the matrix exponential of the coefficient matrix. The matrix exponential is given by the formula:

\(\[ e^{At} = I + At + \frac{{A^2 t^2}}{2!} + \frac{{A^3 t^3}}{3!} + \ldots \]\)

where A is the coefficient matrix, t is the independent variable, and I is the identity matrix.

In our case, the coefficient matrix A is:

\(\[ A = \begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \]\)

To compute the matrix exponential, we'll use the power series expansion. Let's compute the terms:

\(\[ A^2 = A \cdot A = \begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} = \begin{bmatrix} 13 & 12 \\ 12 & 13 \end{bmatrix} \]\)



Now, let's substitute these values in the formula for the matrix exponential:

\(\[ e^{At} = I + At + \frac{{A^2 t^2}}{2!} + \frac{{A^3 t^3}}{3!} + \ldots \]\[ e^{At} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} + \begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} t + \frac{1}{2!} \begin{bmatrix} 13 & 12 \\ 12 & 13 \end{bmatrix} t^2 + \frac{1}{3!} \begin{bmatrix} 69 & 66 \\ 66 & 69 \end{bmatrix} t^3 + \ldots \]\)

Simplifying further, we have:

\(\[ e^{At} = \begin{bmatrix} 1 + 3t + \frac{13}{2} t^2 + \frac{69}{6} t^3 + \ldots & 2t + 2t^2 + 11t^3 + \ldots \\ 2t + 2t^2 + 11t^3 + \ldots & 1 + 3t + \frac{13}{2} t^2 + \frac{69}{6} t^3 + \ldots \end{bmatrix} \]\)

Step 2: Compute the solution vector
Now, we can compute the solution vector x(t) using the formula:

\(\[ x(t) = e^{At} x(0) \]\)

where x(0) is the initial condition vector.

Substituting the values, we have:

\(\[ x(t) = \begin{bmatrix} 1 + 3t + \frac{13}{2} t^2 + \frac{69\)\(\[ A^3 = A \cdot A^2 = \begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 13 & 12 \\ 12 & 13 \end{bmatrix} = \begin{bmatrix} 69 & 66 \\ 66 & 69 \end{bmatrix} \]\)}{6} t^

\(3 + \ldots & 2t + 2t^2 + 11t^3 + \ldots \\ 2t + 2t^2 + 11t^3 + \ldots & 1 + 3t + \frac{13}{2} t^2 + \frac{69}{6} t^3 + \ldots \end{bmatrix} \begin{bmatrix} 8 \\ -2 \end{bmatrix} \]\\\)
Simplifying further, we get:

\(\[ x(t) = \begin{bmatrix} (1 + 3t + \frac{13}{2} t^2 + \frac{69}{6} t^3 + \ldots) \cdot 8 + (2t + 2t^2 + 11t^3 + \ldots) \cdot (-2) \\ (2t + 2t^2 + 11t^3 + \ldots) \cdot 8 + (1 + 3t + \frac{13}{2} t^2 + \frac{69}{6} t^3 + \ldots) \cdot (-2) \end{bmatrix} \]\)

This is the solution to the given initial value problem.

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Answer: 12.5 pounds

Step-by-step explanation:

How many times greater, 75=6x

divide by 6

Answer:

The graph of the function is positive on (negative infinity, –7)

Step-by-step explanation:

Reason: f(-8)= 840,000a

840,000a is a positive number

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Answer:

$3.75

Step-by-step explanation:

This is the answer! Just trust me!

Answer: 3.75

Step-by-step explanation: 15% times $25 equals $3.75

If the company earned a total of $37,500 in interest last year, how much cash did they keep in the bank is; $937,500.

This is about the concept of compound interest which is defined as the interest on savings that is calculated on both the initial principal and the accumulated interest from previous periods.

From the question, let us make x to represent the amount of cash.

Now, we are told that one portion of it pays 0.5%and as such this will be 0.005x.

Now, the other portion pays 3.5% and as such this is 0.035x.

Combining both knowing that the total the company earned in the last year was $37,500 and we have;

0.005x + 0.035x = 37500

0.040x = 37500

Solve for x to get;

x = (37500)/(0.04)

x = 937500

Therefore, the company started with $937,500.

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The best response for a person handling biohazards with an open wound on their hands is to not  work with biohazards until the cut is healed or cleared by a healthcare professional to work with the use of waterproof bandages and double gloves.

Biohazards are extremely dangerous because they can get into the human body and cause a lot of damage.

This is why a person with an open would or existing cut should not handle a biohazard until they are cleared to to so by a trained healthcare professional.

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Hi

1) f(x)= 0.9 x

2) g(x) = x-100

3) f °g. is first apply g then f. so :

f°g = 0.9 ( x-100) = 0.9x-90

4) g°f. is first apply f then g

so g°f = (0.9x) -100 = 0.9x-100

I let you conclude which is the best deal :)

Answer:

350 + 15x = 275 + 20x where x = 15

Step-by-step explanation:

350 + 15x = 275 + 20x

350 - 275 = 20x - 15x

75 = 5x

75/5 = 5x/5

15 = x

350 + 15(15) = 275 + 20(15)

350+225 = 275+300

575 = 575

The work done is 3750 Joules on the box.

To quantitatively express this concept, the work W is equal to the force f times the distance d, or W = fd. If the force is applied at an angle to the displacement, the work is W = fd cos.t.

The equation W = F * d * cos(theta), where W is the work done, F is the force applied, d is the displacement of the item, and theta is the angle between the force and displacement vectors, can be used to solve this problem.

The force in this instance is 500 N, and the distance is provided as 15 m, and the 60 degree angle between the vectors of force and displacement.

So, by changing these numbers in the equation, we obtain:

W = 500 N x 15 m x cos (60 degrees)

We can simplify this to: Applying the trigonometric identity cos(60 degrees) = 1/2

W = (500 N) * (15 m) * (1/2)

W = 3750 J.

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Answer:

C=24

Step-by-step explanations:

Answer:

6/90

Step-by-step explanation:

The probability that the first partner will be a marketing major is 0.10 or 10%.


If 10% of the class are marketing majors, the probability that the first partner will be a marketing major is 0.10 or 10%. This is because the probability of an event happening is the number of ways the event can happen divided by the total number of outcomes. In this case, the event is choosing a marketing major as the first partner, and the total number of outcomes is the total number of students in the class.

Since we know that 10% of the class are marketing majors, we can divide the number of marketing majors by the total number of students to get the probability. For example, if there are 100 students in the class, 10 of them would be marketing majors, so the probability of choosing a marketing major as the first partner would be 10/100 or 0.10.

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