MODELING REAL LIFE There are a total of 64 students in a filmmaking club and a yearbook club. The filmmaking club has 14 more students than the yearbook club.
a. Write a system of linear equations that represents this situation. Let x represent the number of students in the filmmaking club and y represent the number of students in the yearbook club.
System of equations: x=?
?x+?y=64

b. How many students are in the filmmaking club? the yearbook club?
There are . students in the filmmaking club and students in the yearbook club.

The class had cleaned x × A square miles before lunch.

Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).

If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:

Area cleaned before lunch = x × A

Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.

Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).

If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:

Before lunch, the area was cleaned = x A

We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.

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Answer: Option B.

Step-by-step explanation:

A recursive formula is written as:

aₙ = aₙ₋₁*13

Now, if the first term is 7, then:

a₁ = 7

This means that:

a₂ = 7*13

a₃ = (7*13)*13 = 7*(13)^2

a₄ = (7*13^2)*13 = 7*(13)^3

You already can see the pattern here, the n-th term will be written as:

aₙ = 7*(13)^(n - 1)

Then the correct option is B

Answer: 13,600.

Step-by-step explanation: every hour is 400 bacteria produced. 400x19= 7600. 7600+6000=13600

Answer:

$230

Step-by-step explanation:

Answer:

$230

Step-by-step explanation:

Divide 60 by 12 and get 5.

Then multiply 5 × 46 and get $230 dollars.

Answer:

IMAGE 1: positively skewed because it is skewed more to the right

IMAGE 2: symmetric because, well, it's symmetric.

IMAGE 3: negatively skewed because it is skewed to the left.

Answer:

1. It is Skewed rightwards (Positively skewed)

2. Bell shaped (Symmetric)

3.Skewed Left (Negatively Skewed)

didn't realize the diagrams were three.... Hehe

POSITIVELY SKEWED

The value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

The equation is given as:

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000

From the question, we understand that the expression is to be solved from left to right (without using the pemdas mathematical rule)

So, we start by multiplying 2 and 4

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 8 + 48000 / 8 - 1 x 30 x 2 + 40000

Add 8 and 48000

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 48008 / 8 - 1 x 30 x 2 + 40000

Divide 48008 by 8

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6001 - 1 x 30 x 2 + 40000

Subtract 1 from 6001

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 6000 x 30 x 2 + 40000

Multiply 6000 and 30

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 180000 x 2 + 40000

Multiply 180000 by 2

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 360000 + 40000

Evaluate the sum

2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 = 400000

Hence, the value of the expression 2 x 4 + 48000 / 8 - 1 x 30 x 2 + 40000 is 400000

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The result is 16, which matches the information given in the problem. Thus, our solution is correct. Thao originally had 30 coins.

Let's solve this problem step by step.

Let's assume the number of coins Thao originally had is x.

According to the problem, Thao gives two fifths of her coins to her sister. Two fifths of x can be represented as (2/5)x.

After giving away two fifths of her coins, Thao receives 4 coins for her birthday. So, the number of coins she has now is (2/5)x + 4.

The problem states that she now has 16 coins. Therefore, we can set up the following equation:

(2/5)x + 4 = 16

To solve for x, we need to isolate x on one side of the equation. We can start by subtracting 4 from both sides:

(2/5)x = 16 - 4

(2/5)x = 12

To get rid of the fraction, we can multiply both sides of the equation by 5:

5 * (2/5)x = 5 * 12

2x = 60

Next, divide both sides of the equation by 2 to solve for x:

(2x)/2 = 60/2

x = 30

Therefore, Thao originally had 30 coins.

To verify our answer, we can substitute x = 30 back into the equation (2/5)x + 4 and see if it equals 16:

(2/5) * 30 + 4 = 12 + 4 = 16

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The simplified expression of \(\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}\) is \(\frac{8a}{a^8 - 1}\)

The expression is given as:

\(\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}\)

Add the first two terms

\(\frac{a - 1 + a + 1}{(a + 1)(a - 1)} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}\)

Evaluate

\(\frac{2a}{a^2 - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}\)

Evaluate the first two terms

\(\frac{2a^3 + 2a - 2a^3 + 2a}{(a^2 - 1)(a^2 + 1)} - \frac{4a}{a^4 + 1}\)

Evaluate

\(\frac{4a }{a^4 - 1} - \frac{4a}{a^4 + 1}\)

Take the LCM

\(\frac{4a^5 + 4a - 4a^5 + 4a }{(a^4 - 1)(a^4 + 1)}\)

Evaluate the like terms

\(\frac{8a}{a^8 - 1}\)

Hence, the simplified expression is \(\frac{8a}{a^8 - 1}\)

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Step-by-step explanation:

It is important to know that the diagonals of a rhombus are PERPINDICUALR bisectors of each other .   Opposite angles are equal and adjacen angles sum to 180 degrees .

Then remember alternate angles are equal  and there are 180 degrees inside of a triangle .....then you should be able to solve these...here is the first one

Answer:

36, 72, 108, 144

Step-by-step explanation:

The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.

The set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.

The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.

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47.17 feet is the height of the building.

We can use the Pythagorean theorem to solve the problem:

Let h be the height of the building.

Then we have a right triangle with legs 20 and h, and a hypotenuse 50.

Using the Pythagorean theorem, we have:

\(50^2 = 20^2 + h^2\)

Simplifying and solving for h, we get:

\(h = \sqrt{(50^2 - 20^2)\)

h ≈ 47.17 feet (rounded to two decimal places)

Therefore, the height of the building is approximately 47.17 feet.

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Answer:

y=-1/3x+6 .Hope this helps

Answer:

3y = -x + 18

Step-by-step explanation:

Given the equation y = 3x + 2;

By comparison with the general equation

y = mx + C ; where m is the slope

We see that m = 3

Now for a perpendicular line and it's slope is -1/m = -1/3 and let it be M2

But the new slope cuts across points (3,5) .

It means M2 = y - 5/ x-3

-1/3 = y-5/ x-3

-1(x-3) = 3(y-5)

-x +3 = 3y -15

3y = -x + 18

Step-by-step explanation:

Given equation is:-

Dividing both sides by 4, we get

By doing simply, we get

Hence, the value of c will be ¾.

Answer:

sin( 3pi/4 ) = -√2/2

So, B.

Answer:

feeling good

Step-by-step explanation:

I am just happy

Transferring ownership of real property (land and buildings) can happen in a variety of ways, and it is not necessarily consensual.

A transfer can occur, for example, through eminent domain, in which the government takes private property for public use and compensates the owner for its worth. Transfers can also occur through foreclosure, which occurs when a borrower fails on a loan and the lender takes control of the property.

Regardless of the conditions, the legal steps for transferring ownership usually include execution, delivery, acceptance, and recording. The signing of a legal instrument that transfers ownership is referred to as execution. The transfer of custody or control of the property to the new owner is referred to as delivery. The new owner's agreement to accept the transfer is referred to as acceptance.

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Answer:

The Perimeter of a rectangle will be:

P = 252 in

Hence, option (E) is true.

Step-by-step explanation:

Given the rectangle with the sides

We know that the Perimeter of a rectangle can be calculated using the formula

where l is the length, and w is the width

substituting  \(l\) = 14-5, \(w\) = 7×4

P = (14-5) × (7×4)

P = 9 × 28

P = 252 in

Therefore, the Perimeter of a rectangle will be:

P = 252 in

Hence, option (E) is true.

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

On a number line, 7.05 would be located

From the question, we have the following parameters that can be used in our computation:

Number = 7.05

The analysis of its position s as follows:

So, the true statements are B and C.

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