For problems 1 and 2, use the set A = {factors of 45} = {1,3,5,9,15,45} 1. [ 15 points ] Show that the relation R defined by : x Ry iff x mod 5 = y mod 5 is an equivalence relation, and list the equivalence classes. 2. [15 points ] Show that the "divides" relation is a partial ordering, and draw the Hasse diagram.

The prices which the school would collect $0 revenue are $0 and $ 40 respectively.

Since the revenue R(p) = p(200 - 5p).

The price at which the school earn s $0 revenue from the raffle sales is when R(p) = 0.

So, p(200 - 5p) = 0

p = 0 or 200 - 5p = 0

p = 0 or 200 = 5p

p = 0 or p = 200/5 = 4

So, the prices which the school would collect $0 revenue are $0 and $ 40 respectively.

The two ticket prices that would produce a revenue of $500 are $2.68 and $ 37.32

We need to find the two ticket prices that would result in a revenue of $500. So, R(p) = 500.

So, p(200 - 5p) = 500

200p - 5p² = 500

Re-arranging, we have

5p² - 200p + 500 = 0

Dividing through by 5, we have

p² - 40p + 100 = 0

Using the quadratic formula, we find the value of p.

So,

\(p = \frac{-(-40) +/- \sqrt{(-40)^{2} - 4 X 1 X 100} }{2 X 1} \\p = \frac{40 +/- \sqrt{1600 - 400} }{2} \\p = \frac{40)+/- \sqrt{1200} }{2} \\p = \frac{40 +/- 34.64 }{2} \\p = \frac{40 - 34.64 }{2} or p = \frac{40 + 34.64 }{2} \\p = \frac{5.36}{2} or p = \frac{74.64 }{2} \\p = 2.68 or 37.32\)

So, the two ticket prices that would produce a revenue of $500 are $2.68 and $ 37.32

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Answer:

a. 45° and 135

The non-horizontal rays of ∠ and ∠ will not intersect to form a triangle; the rays will be parallel to each  other.

b. 45° and 45°

The non-horizontal rays of ∠ and ∠ will intersect to form a triangle

c. 45° and 145°

The non-horizontal rays of ∠ and ∠ will not intersect to form a triangle.

Step-by-step explanation:

Hope this helps

Answer:

1. 7x

2. x+15

3. 18/x

Step-by-step explanation:

Assume the number is x because we don’t know what it is.

1. Product means multiplication so x * 7 equals 7x.

2. More means addition so x+15.

3. This one is easy. 18 divided by x = 18/x

the amount of money in the account after 9 years is approximately $5982.09.

How to solve?

Using the formula for continuous compounding, the value of the investment account after t years is given by:

V = Pert

where P is the principal initially invested, e is the base of a natural logarithm, r is the annual interest rate, and t is the time period in years.

In this case, we have P = $2670, r = 8%, and t = 9 years. We can substitute these values into the formula to find the value of the account after 9 years:

V = Pert

V = 2670e²(0.089)

V = 2670×e²0.72

V = $5982.09 (rounded to the nearest cent)

Therefore, the amount of money in the account after 9 years is approximately $5982.09.

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Probability of randomly selecting a tree or an insect = 3/5

Total number of flashcards, n(Total) = 30

Number of insects, n(Insects) = 10

Number of trees, n(Trees) = 8

Probability of randomly selecting a tree, P(tree) = 8/30

Probability of randomly selecting an insect, P(insect) = 10/30

Probability of randomly selecting a tree or an insect = P(tree) + P(insect)

Probability of randomly selecting a tree or an insect = 8/30 + 10/30

Probability of randomly selecting a tree or an insect = 18/30

Probability of randomly selecting a tree or an insect = 3/5

The items matched in the left column to the items in the right column are

Ratio is the number representing a comparison between two named things or quantities.

1. total to fish

= 8 : 3

2. starfish to fish

= 5 : 3

3. starfish to total

= 5 : 8

4. fish to starfish

3 : 5

In conclusion, the ratio of the total to fish to starfish is 8 : 3 : 5

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The critical z-value using a z-table or calculator:

Critical z-value = ±2.576.

What is null hypothesis's?

A null hypothesis is a statement or assumption that there is no significant difference or relationship between two or more variables or groups. In statistical hypothesis testing, the null hypothesis is usually denoted as H0 and is tested against an alternative hypothesis (Ha), which is the hypothesis that there is a significant difference or relationship between the variables or groups being studied.

According to the question:
(a) The null hypothesis is that there is no significant difference in the average amount of money spent per day between the two groups. The alternative hypothesis is that there is a significant difference in the average amount of money spent per day between the two groups.

Since we are not given any information about the direction of the difference, we will use a two-tailed test. The appropriate test to use in this situation is the two-sample t-test.

(b) To find the critical z-value, we first need to calculate the degrees of freedom for the test:

df = (n1 + n2 - 2) = (25 + 27 - 2) = 50

Using a significance level of 0.01, we find the critical z-value using a z-table or calculator:

Critical z-value = ±2.576

(c) To find the test value, we will first calculate the pooled standard deviation using the formula:

\(sp = \sqrt{((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2)}\)

where s1 and s2 are the sample standard deviations and n1 and n2 are the sample sizes. Substituting the given values, we get:

\(sp = \sqrt{((24 * 5.3^2) + (26 * 6.8^2)) / 50} = 6.083\)

Next, we calculate the t-value using the formula:

\(t = (x1 - x2) / (sp * \sqrt{1/n1 + 1/n2})\)

where x1 and x2 are the sample means. Substituting the given values, we get:

\(t = (38.6 - 37.4) / (6.083 * \sqrt{1/25 + 1/27}) = 1.213\)

Since the absolute value of the test value is less than the critical z-value, we fail to reject the null hypothesis. Therefore, we cannot conclude that there is a significant difference in the average amount of money spent per day between the two groups.

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for this case we have the folloeing information: In a class we have 17 flute players and 15 Clarinet Players for the Amy's Music Class.

The total of students are:

And then if we need to select one player (student) the probability would be given by:

And the best answer would be A) 1/32

Answer:

20

Step-by-step explanation:

if she has 13 flowers and adds 7 more that is 20 because 13+7=20

Answer:

answer of 4 nbr is 5 x=5 cointerior

156 pairs of consecutive integers in {1000,1001,1002,...,2000} is no carrying required when the two integers are added

You will need to consider four cases.

when _999 and _000 are the last three digits of consecutive numbers. Just possible cases are 1999, 2000

At the point when the last 2 digits of the continuous numbers are _ _ 9 9 and _ _ 0 0. 5 possible scenarios (corresponding to (0,1), (1,2), (2,3), (3,4), and (4,5) at the hundredth place) exist.

when the last digit of consecutive numbers is in the form ____ 9 and ____ 0. 5*5 = 25 possible scenarios.

when none fall into that category, possible case=. 5*5*5 = 125,

and the answer is 125+25+5+1 = 156.

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There are two cases of collisions : Key “23” and “27NLY” collide at slot “1”.

Key “27NLY” and “a” collide at slot “(9+L+Y) mod 11”.

Given a sequence of 5 element keys < 23, I 38, 27 >, for searching task: H(k) = 3, 26, 16, 38, 27 mod 11. The steps and calculations are shown in the table below:

Here are the steps to insert the keys into a hash table of 11 slots using the hash function H(k) = 3, 26, 16, 38, 27NLY mod 11:

Key                                  Hash Value                                             Slot

23                                    23 mod 11 = 1                                             1

38                                    38 mod 11 = 5                                     5

27NLY                    (3 + 26 + 16 + 38 + (27 * N)

                               + L + Y) mod 11 = (86 + N

                                     + L + Y) mod 11                       (86 + N + L + Y) mod 11

N = 13

-> (86 +

N + L +

Y) mod

11= (86

+ 13+ L

+ Y) mod

11 = (99+L

+Y) mod

11 = (9+

L+Y) mod

11 -> Slot:

(9+L+Y)

mod 11  

a                                              a mod 11 = a                                        a

The cases of collision are:

Key “23” and “27NLY” collide at slot “1”.

Key “27NLY” and “a” collide at slot “(9+L+Y) mod 11”.

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The test statistic of the proportion is given by z = 4.47, meaning that the first option is correct.

At the null hypothesis, it is tested if there is not enough evidence that the proportion is greater than 0.06, that is:

\(H_0: p \leq 0.06\)

At the alternative hypothesis, it is tested if there is enough evidence that the proportion is greater than 0.06, that is:

\(H_1: p > 0.06\)

The equation that gives the test statistic for a proportion is defined using the z-distribution as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

The parameters for the equation are defined as follows:

In the context of this problem, the values of these parameters are given as follows:

\(p = 0.06, n = 724, \overline{p} = \frac{72}{724} = 0.0994\)

Hence the test statistic for the proportion is calculated as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.0994 - 0.06}{\sqrt{\frac{0.06(0.94)}{724}}}\)

z = 4.47.

Meaning that the first option is correct.

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Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

Answer:

Step-by-step explanation:

"To find the four-year inflation rate from December 1973 to December 1977, you can use the formula:

Inflation rate = ((CPI in 1977 - CPI in 1973) / CPI in 1973) x 100%

From the CPI table, we can see that the CPI in December 1973 was 146.4, and the CPI in December 1977 was 207.9. So, the inflation rate is:

((207.9 - 146.4) / 146.4) x 100% = 41.9%

Therefore, the four-year inflation rate from December 1973 to December 1977 is 41.9%. Does that help?"

Answer:

2028

Step-by-step explanation:

2027 is a prime number, so a = 2027 and b = 1, then a + b  = 2028

Answer:

C= 5.4

Step-by-step explanation:

Rise: 5

Run: 2

a²+b²=c²

c=√a²+b²

c=√rise²+run²

c=√5²+2²

c=√25+4

c=√29

c=5.385164807

c=5.4

*c=hypothesis

To solve the given problem using the simplex method, we need to follow the steps outlined. Let's go through each step:

(a) Reformulating the problem with non-negativity constraints:

We introduce non-negativity constraints by adding slack variables. The problem becomes:

Maximize: z = -11 + 2x2 + 13s1

subject to:

3x2 + x3 + s2 = 120

r1 - 12 - 4x3 + s3 = 80

-3 + 1x1 + 12x2 + 243x3 + s4 = 100

(b) Applying the simplex method step by step:

Create the initial tableau by representing the objective function and constraints in a tabular form.

Choose the pivot column, which is the column with the most negative coefficient in the objective function row.

Choose the pivot row, which is determined by the minimum non-negative ratios of the right-hand side values divided by the pivot column values.

Perform row operations to make the pivot element 1 and all other elements in the pivot column 0.

Repeat steps 2-4 until no negative coefficients exist in the objective function row.

(c) Once the simplex method is completed, we obtain the values of the decision variables (x1, x2, x3) in the optimal solution, as well as the objective function value (z).

Unfortunately, without the specific values and calculations, it is not possible to provide the exact values of the decision variables and the objective function in the optimal solution.

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Answer:

(-400, infinity)

Step-by-step explanation:

The probability that Utah beats BYU in 3 of the 4 football games is 32/81.

The probability that Utah beats BYU in 3 of the 4 football games can be calculated using the binomial probability formula, which considers the number of trials, successes, and individual probabilities. Here's a step-by-step explanation:
Identify the parameters:
  Number of games (n): 4
  Number of wins for Utah (k): 3
  Probability of Utah winning a single game (p): 2/3
  Probability of Utah losing a single game (q): 1 - p = 1/3
Use the binomial probability formula:
  P(X = k) = \(C(n, k) * p^k * q^(n-k)\)
Calculate C(n, k), which is the combination formula, representing the number of ways to choose k successes from n trials:
  C(n, k) = n! / (k!(n-k)!)
  C(4, 3) = 4! / (3!(4-3)!) = 4
Calculate the probability of Utah winning 3 games and losing 1 game:
  P(X = 3) = \(C(4, 3) * (2/3)^3 * (1/3)^(4-3)\)
  P(X = 3) = 4 * (8/27) * (1/3)
  P(X = 3) = 4 * (8/81)
  P(X = 3) = 32/81\
So, the probability that Utah beats BYU in 3 of the 4 football games is 32/81.

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There are 40 ways to place three rooks on a 4x5 board so that no rook is threatening another.

To determine this, we can first place the rooks in three distinct rows, which can be done in 4 * 3 * 2 = 24 ways. Then, we can place one rook in each of the five columns in the first row, which leaves only three columns for the second row and two columns for the third row.

Since no two rooks can be in the same column, we have 5 * 3 * 2 = 30 ways to place the remaining two rooks.

Therefore, the total number of arrangements is 24 * 30 = 720, but since each arrangement can be rotated by 90, 180, or 270 degrees, we need to divide by 4 to obtain the final answer of 720/4 = 180, and since there are two ways to arrange the rooks in each row, the final answer is 180/2 = 90.

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Answer:

y=1/3x-4

Step-by-step explanation:

The point where the line intercepts the y-axis is the y-intercept and where the digit -4 comes from

1/3 comes from how many times the line rises (1) and run (3)

Hope this helps!

1.242 ≤ d ≤ 1.305 is the corresponding interval for the diameter of the washer.

Given that,

Company A makes and sells a washer having a 4-centimeter outer radius. The corporation has decided on a washer with an actual radius in the range of 3.9 ≤ C ≤ 4.1.

Inequality is defined as the connection of an equation having the symbol ( ≤, ≥, <, >) in place of the assignment operator.

Here,

C = 3.14d

Given inequality,

3.9 ≤ C ≤ 4.1

3.9 ≤ 3.14d ≤ 4.1

dividing both sides of the inequality by 3.14,

1.242 ≤ d ≤ 1.305

As a result, the needed matching spacing for the washer's diameter is 1.242 ≤ d ≤ 1.305.

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Answer:

19 and 128

Step-by-step explanation:

19.3 is closer to 19 than 20 and 127.8 is closer to 128 than 127

Answer:

A- 19, when rounding up it's usually .5 and up since this is .3 you would round down

B- 128, since this one is above .5 you would round-up and get 128

Step-by-step explanation:

A- 19

B-128

Answer:

8/10

Step-by-step explanation:

The rise on the y axis is eight and the run on the x axis is 10

(Hope this helped)

Answer:

D

Step-by-step explanation:

from what I could tell, it sounds like D would be correct

The area of the triangle is 3 units^2. Since the area is equal to

hside * side/ 2.

Define area.

The measure of a region's size on a plane or curved surface is called area. While surface area refers to the area of an open surface or the boundary of a three-dimensional object, the area of a plane region or plane area refers to the area of a form or planar lamina.

Area is defined as the total amount of space occupied by a flat (2-D) surface or the shape of an object. On a sheet of paper, draw a square with a pencil. It is a two-dimensional figure. The area of a shape on paper is the area it occupies.

Solution Explained:
Given,

Length of Hypotenuse = 3units
One side = 2units

Area = (Length of Hypotenuse X Length one side) / 2
        = (3 X 2) / 2
        = 3units^2 (after calculation)

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Answer:

A. x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle \frac{x^2 - 25}{x - 5}\)

Step 2: Simplify

The value of the variables m and n are 3/2 and 4 respectively

Noe that quadratic functions are defined as functions having its degree as 2.

The general formula for a quadratic function is expressed as;

ax² + bx + c

Standard form

ax² + bx + c = 0

Given the illustration, we have that the two functions have similar roots.

Then, we have;

The value of n = 4

For the value of m, we represent it thus; (-b/a)

-5x/m = -10x/3

cross multiply the values, we get;

m = 3(-5x)/-10x

m = 3/2

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