the ratios of the sides of a triangle are 3:2:4. if the shortest side is 26cm, what is the length of the longest side?

The relation S={(a,b)∈R×R:a²+b²=1} is not an equivalence relation on the set of real numbers R.

To show that S is not an equivalence relation, we need to demonstrate that it fails to satisfy one or more of the properties of an equivalence relation: reflexivity, symmetry, and transitivity.

Reflexivity: For a relation to be reflexive, every element of the set should be related to itself. However, in the case of S, there are no real numbers (a, b) that satisfy the equation a² + b² = 1 for both a and b being the same number. Therefore, S is not reflexive.

Symmetry: For a relation to be symmetric, if (a, b) is related to (c, d), then (c, d) must also be related to (a, b). However, in S, if (a, b) satisfies a² + b² = 1, it does not necessarily mean that (b, a) also satisfies the equation. Thus, S is not symmetric.

Transitivity: For a relation to be transitive, if (a, b) is related to (c, d), and (c, d) is related to (e, f), then (a, b) must also be related to (e, f). However, in S, it is not true that if (a, b) and (c, d) satisfy a² + b² = 1 and c² + d² = 1 respectively, then (a, b) and (e, f) satisfy a² + b² = 1. Hence, S is not transitive.

Since S fails to satisfy the properties of reflexivity, symmetry, and transitivity, it is not an equivalence relation on the set of real numbers R.

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Answer: 6,192 paperclips, 3,826 paperclips

Step-by-step explanation:

a) To find the sum of all the children's paperclips, you must find each of them.

First, to start off, create some equations that represent this information:

k = j * \(\frac{6}{7}\)

m = 3k

m = j + 2552

Then, for starts you can use the equation m = 3k and plug in for the variables

m = 3k

(j+2552) = 3(j * 6/7)

j + 2552 = 3j + 2.57

2549.43 = 2j

j = 1274.715

j = 1274 (round down because you can't have a fraction of a paper clip)

Next, use j to solve the other equations

m = j + 2552

m = 1274 + 2552

m = 3826

k = j * 6/7

k = 1274 * 6/7

k = 1092

sum = k + j  + m

sum = 1092 + 1274 + 3826

sum = 6,192 paperclips

b) We already know m, which is 3826.

3,826 paperclips

ANSWER:

1. translation: 3 units right and 1 unit down

2. 130°

Answer:

244,321

Step-by-step explanation:

So its asking what number could be possible for being more then 214,626(water park) but less then 248,368(state park)

201,369 is less then the water park so that isnt it

212,729 is also less then the water park

244,321 is more then the water park but less then the state park so theis is the answer

263,023 is greater then the state park so its not the answer

Yes, this statement is true. If x and y are both odd integers, then both x and y are of the form 2n + 1 for some integer n. The product of two odd numbers is still odd because (2n + 1)(2m + 1) = 4nm + 2(n + m) + 1, which is an odd integer.

Some examples would be

3*5 = 15

7*9 = 63

11*11 = 121

The template is odd*odd = odd.

----------

Here is the proof as to why this is the case.

x = 2k+1 where k is some integer

y = 2m+1 where m is some integer

Both x and y are odd since we added 1 to an even number.

Multiply out x and y

xy = (2k+1)*(2m+1)

xy = 2k(2m+1) + 1*(2m+1)

xy = 4km+2k + 2m+1

xy = 2*(2km+k+m) + 1

xy = 2n + 1 where n = 2km+k+m is an integer

The result is of the form 2*(integer)+1 which is odd. This concludes the proof.

In a cross-country race with 30 runners, there are 4,060 different groups that can finish in the top 3 positions.

Use the concept of combination defined as:

Combinations are made by choosing elements from a collection of options without regard to their sequence.

Contrary to permutations, which are concerned with putting those things/objects in a certain sequence.

Given that,

There are 30 runners in a cross-country race.

The objective is to determine the number of different groups of runners that can finish in the top 3 positions.

To determine the number of different groups of runners that can finish in the top 3 positions:

Use combinations instead of permutations.

In this case:

Calculate the number of different groups,

Use the combination formula:

\(^nC_r = \frac{n!} { (r!(n - r)!)}\)

Here

we have 30 runners and want to select 3 for the top 3 positions.

Put the values into this formula:

\(^{30}C_3 = \frac{30!}{ (3!(30 - 3)!)}\)

Simplifying this expression, we get:

\(^{30}C_3 = \frac{30!}{ (3! \times 27!)}\)

Calculate the value:

\(^{30}C_3 = 4060\)

Hence,

There are 4,060 different groups of runners that can finish in the top 3 positions.

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Answer:To find the number of students who want to be both a doctor and a social worker, we can use the Principle of Inclusion-Exclusion (PIE). This principle states that the total number of elements in the union of two sets is equal to the sum of the number of elements in each set minus the number of elements in their intersection.

So, the number of students who want to be both a doctor and a social worker can be calculated as:

|Doctor ∩ Social worker| = |Doctor| + |Social worker| - |Doctor U Social worker|

|Doctor ∩ Social worker| = 40 + 20 - 65

|Doctor ∩ Social worker| = -5

However, this result is negative which is not possible, therefore, no students want to be both a doctor and a social worker.

To find the number of students who want to be both, we have to find the number of students who want to be both a doctor and a social worker which is 0 in this case.

Step-by-step explanation:

Answer:

XYN is a right angle

explanation:

The total prize is $854. and in order to split the amount of money equally we divide the total price in 5 equal parts(You should identigy the word "split" to let you know you need to divide):

So, every member will get $170.8

Carl pays his broker a total of $200 in fees for the 40 trades he made during the year.

To calculate how much Carl pays his broker, we need to first determine how many trades he made in a year. Looking at the table, we can see that Carl made a total of 40 trades - 20 buys and 20 sells. Since each trade incurs a $5 charge, we can multiply the number of trades by the cost per trade to get the total amount paid to the broker.

40 trades x $5 per trade = $200 paid to the broker in a year

It's important to note that transaction costs can have a significant impact on investment returns, especially for small accounts, so it's important to consider these costs when making investment decisions. Some brokers may offer lower transaction fees or other incentives to attract clients, so it's worth shopping around and comparing fees before choosing a broker. Additionally, it may be more cost-effective to use a robo-advisor or invest in index funds or exchange-traded funds (ETFs) that have lower fees compared to actively managed funds.

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Answer:

it is 42 pounds of beans that Malcolm has

Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

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Answer:

y= -2 and x= 2.

Step-by-step explanation:

(y=-3x+4)4

(y=4x-10)3

make the x's cancel out.

you get 7y=-14.

y=-2.

-2=-3x+4

x=2

ANSWER :

The height of the prism is h = 7 ft

The are of the base is B = 12 ft^2

The perimeter of the base is P = 18 ft

Fill in the formula. S = 2x12 + 18x7

The surface area of the triangular prism is 150 ft^2

EXPLANATION :

The given formula for the surface area is :

where B = Base area

P = perimeter of the bases

h = height of the prism

The height of the prism is h = 7 ft

The base is a triangle with dimensions of b = 8 ft and a height h = 3 ft

The area of a triangle is :

The are of the base is B = 12 ft^2

The perimeter of the base is 5 + 5 + 8 = 18 ft, so P = 18 ft

Substitute the results in the formula :

Answer:

4%

Step-by-step explanation:

commission rate = (amount earned on sales / total cost of items sold) x 100

\(\frac{378}{9000}\) × 100 = 4.2%

To convert to the nearest whole number, look at the first number after the decimal,

two is less than 5, thus we would add zero to 4.

4.2% becomes 4%

Step-by-step explanation:

In the picture I solve all

Answer:

1: 40 hours

2: $100

3: A and D

4: 40 meals an hour

5: 25 presents

Answer:

(x+2+2y)(x+2-2y)

Step-by-step explanation:

Start with the given expression: x^2 + 4x + 4 - 4y^2.

Group the first three terms together and leave the last term separate:

x^2 + 4x + 4 - 4y^2.

Notice that the first three terms form a perfect square trinomial: (x + 2)^2.

Rewrite the expression using the perfect square trinomial:

(x + 2)^2 - 4y^2.

Recognize that this is now the difference of squares: (a^2 - b^2) = (a + b)(a - b).

In our case, a = (x + 2) and b = 2y.

Apply the difference of squares formula:

(x + 2 + 2y)(x + 2 - 2y).

Therefore, the fully factored form of the expression x^2 + 4x + 4 - 4y^2 is:

(x + 2 + 2y)(x + 2 - 2y).

The internal rate of return (IRR) is a financial metric used to evaluate the profitability of an investment project. It is the discount rate that makes the net present value (NPV) of the project equal to zero. In other words, it is the rate at which the present value of the cash inflows equals the present value of the cash outflows.

To determine whether Nadia should accept the investment in the new factory, we need to compare the IRR of the project with the required rate of return, which is 14.25 percent in this case.

If the IRR is greater than or equal to the required rate of return, then Nadia should accept the investment. This means that the project is expected to generate a return that is at least as high as the required rate of return.

If the IRR is less than the required rate of return, then Nadia should reject the investment. This suggests that the project is not expected to generate a return that is high enough to meet the required rate of return.

So, to determine whether Nadia should accept the investment, we need to calculate the IRR of the project and compare it with the required rate of return. If the IRR is greater than or equal to 14.25 percent, then Nadia should accept the investment. If the IRR is less than 14.25 percent, then Nadia should reject the investment.

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The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by the function P(x) = 31 + 2.6x.

What is the percentage function?

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100. Percentage formula = (Value/Total value) × 100. Example: 2/5 × 100 = 0.4 × 100 = 40 per cent.

The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by the function:

P(x) = 31 + 2.6x

Where P(x) is the percentage of adults who viewed college education as essential for success x years after the first year, and x is the number of years after the first year.

The function shows that the percentage increase by 2.6 every year for x years after the first year, and the initial percentage is 31%.

This function is representing a linear trend since the coefficient of x is constant.

Hence, The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by the function P(x) = 31 + 2.6x.

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Answer:

1.

a.) 24in

b.)75.36in

c.)452.16in

Step-by-step explanation:

1a. The radius is half of the diameter, so all you have to do is add 12 + 12 which is 24.

1b. the circumfrence of a circle is C (Circumfrence)=\(2\pi r\) so replace radius for 12 and then do 3.14(pi) x 2 which will get you 6.28 times 6.28 by 12 and you will get 75.36.

1c. Area=\(\pi r^{2}\) so first do the radius by the second power, or \(r * r\), susitute r for 12 and you will get 144, times 144 by pi and you will get 452.16in

Sorry I could not answer every question but hope this helps!

Answer:(-7, -8), (-7,5), (-6,0),(-1,8)

Step-by-step explanation:

Functions are relations with one output (y) for any unique input (x).

The first set has two values of y when x = -7:  -8 and 5.

The other sets have unique values for each x.

Answer:

Step-by-step explanation:

negative 5 is less then -3 is the statement. so saying that -3 is less than five, is false.

remember your number line.

-5_-4_-3_-2_-1_0_1_2_3_4_5_6

five sure is to the left of three, and saying that three is to the right of five is the exact same thing.

Answer:

\(\boxed{\mbox{\large{\quad 54\quad }}} \quad\text{ 25\% of last year's attendance}\\\\\boxed{\mbox{\large{\quad 216\quad }}}\quad\text{100\% of last year's attendance}\\\\\)  

Step-by-step explanation:

If we let x be the number of attendees last year then since this year's attendees 270 is 125% of x we get

125% of x = 270

125% as a decimal = 125/100 = 1.25

So we get the equation
1.25x = 270

Divide by 1.25 to get

1.25x/1.25 = 270/1.25

x = 216

So there were a total of 216 attendees last year

25% of last year attendees = 0.25 x 216 = 54

Answer:

C = 7.72 ~ 7.7

Step-by-step explanation:

So when you solve this equetion you must 1st find x then c

we can find x by using cos(60)

cos(60) = x/14

x = cos(60) × 14

x = 1/2 ×14

x = 7

so after we find x we are going to solve c by using cos (25)

cos (25) = X/C = 7/c

cos(25) × C = 7

C = 7/cos (25)

C = 7.72 ~ 7.7

so the solution is 7.7

thx my man i appreciate it

my days been fine. i been doin math. wbu?

Step-by-step explanation:

first find distance between ab

then between bc

then ac

in isosceles triangle 2 sides are equal

so if two sides means the distance we find are same

the givan triangle is isosceles

Answer:

the coordinates of vertices triangle ABC are (4,-1), B(5,6) and C (1,3) prove that triangle ABC is an isosceles right triangle.

Answer:

A, 0.13 mph.

Step-by-step explanation:

To get that, divide the cm/sec by 44.704.

6/44.704 ≈ 0.13