what is the fraction equivalent of the ratio of boys to girls in a class if there are 12 boys and 18 girls ?

The area inside the polar curve R = 2cos(3θ) for three full rotations is 6π.

The polar curve R = 2cos(3θ) is symmetric about the x-axis, with three petals that extend from θ = 0 to θ = π/3, π to 4π/3, and 5π/3 to 2π. To find the area inside the curve, we need to integrate the expression for the area element in polar coordinates over the desired region:

dA = (1/2) [tex]R^{2}[/tex] dθ

The limits of integration for θ are from α = -6π to β = 6π, since we want to find the total area inside the curve for three full rotations. Thus, the integral for the area is:

A = ∫(β=6π, α=-6π) (1/2) [tex]R^{2}[/tex]dθ

= ∫(β=6π, α=-6π) (1/2) (2cos(3θ))^2 dθ

= 2∫(β=6π/3, α=-6π/3) cos^2(3θ) d(3θ) (using the identity cos^2(3θ) = (1 +    cos(6θ))/2)

= ∫(β=6π/3, α=-6π/3) (1/2 + (1/2)cos(6θ)) d(3θ)

= (1/2)θ + (1/12)sin(6θ) ∣(β=6π/3, α=-6π/3)

= (1/2)(6π - (-6π)) + (1/12)(sin(36π) - sin(-36π))

= 6π

Correct Question :

Find The Area Inside R=2cos(3θ) (Tip: Use Α=−6π And Β=6π )

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The solution is, the measure of angle C is 52.

Here, we have,

If AC = BC

and, given that,

.A =(8x-40)

B =(5x - 1)

so, we have,

AC = BC i.e. ABC  is isosceles triangle.

so, the angle A & B are equal .

so, we get,

(8x-40)  = (5x - 1)

or, x = 39/3

        = 13

so, angle A = angle B = 64

so, m<C = 180 - 2*64

              = 52

Hence, The solution is, the measure of angle C is 52.

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Answer:

We can use the binomial probability formula to find the probability of getting exactly 3 blue marbles in two draws:

P(X=3) = (2 choose 3) * (0.6)^3 * (0.4)^(-1) = 0.288

However, since we are asked for the probability of the random variable having an outcome of 3 (i.e. getting exactly 3 blue marbles), we can simply use this probability:

P(X=3) = 28.8%

Therefore, the answer is (a) 24%.

The acceleration of the car at that time was 3 m/s².

We have,

From the kinematic equation to find the acceleration:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Initial velocity u = 15 m/s

Final velocity v = 45 m/s,

Time t = 10 s

We can rearrange the equation to solve for acceleration:

a = (v - u) / t

Substituting the values, we get:

a = (45 m/s - 15 m/s) / 10 s

a = 3 m/s^2

Therefore,

The acceleration of the car at that time was 3 m/s².

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The complete question in English.

A car moving on a straight track increases its speed from 15 m/s to 45 m/s using a po of 10 seconds.

Assuming that the acceleration was uniform, calculate:

acceleration at that time.

Answer:1.112,121, 124,137,147,156,173,189

2.the median is 242

Step-by-step explanation:

Note that the table of budget is attached accordingly, and steps 1-4 have been completed. See the table.

4) Since the emergency fund for that month was $200, it means that they are in the short for $105. They can only affod it if they take from their savings.

5) they had a balance of $800 for the month. This is miscellaneous funds. They can make use of this for the trip to NASA. This way, they won't have to touch the savings or entertainment.

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Full Question:
See attached image.

Reflect

4. Analyze Relationships One month, the family must make an

emergency car repair for $305. Are they able to pay for it out of the

fixed emergency fund for that month? If not, how can they afford it?

5. The family wants to make a trip to Houston to visit the NASA Space

Center. What are some ways they can save without using all of the

allotted $160 for entertainment

Answer:

I did the math in my head but please please trust me

It’s below

Step-by-step explanation:

C = 1 1/2

B = 2

A = 5

I’m going to try to explain as best as I can

First solve for C by subtracting the other numbers in its line going up to down from 9:

9 - 3 1/2 + 4 = C

9 - 7 1/2 = C

1 1/2 = C

now that w have C we can solve for b doing same steps:

9 - 5 1/2 + 1 1/2 = b

9 - 7 = b

2 = b

now we do A:

9 - 2 + 2 = a

9 - 4 = a

5 = a

Answer

A should be 5

B should be 2

c should be

[tex] 1\frac{1}{2 \\ } [/tex]

all should add up to 9

2+A(5)+b(2)= 9

a(5)+3 1/2+ 1/2=9

5 1/2+ b(2)+ 1 1/2= 9

3 1/2+ 1 1/2+ 4= 9

Answer:1,000

Step-by-step explanation:

So we add 25 million to 5 million which is 30 million. Then we divide 30 million to 30 thousand and get 1 thousand.

The mass of the trunk of the sequoia tree is 141443.1 kg.

The volume of a cylinder, using the formula:

V = πr²h

π is pi (approximately 3.14)

r is the radius of the trunk (which is half the diameter)

h is the height of the trunk

1 meter = 3.28084 feet

we can convert the given measurements from feet to meters to ensure consistent units.

The base diameter of the tree is 12.2 meters / 3.28084 = 3.719 meters,

so the radius is 3.719 / 2 = 1.8595 meters.

The height of the tree is 95 meters / 3.28084 = 28.9568 meters.

Therefore, the volume of the trunk is:

V = π(1.8595)²(28.9568) = 314.318 cubic meters

Now calculate the mass of the trunk by multiplying the volume by the density of the wood:

M = V × ρ

=  314.318  × 450

= 141443.1 kg

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The expression 7/12x - y/6x² in its simplest form is (7x - 2y)/(12x²).

We have,

To simplify the expression 7/12x - y/6x², we need to find a common denominator for the two terms.

The common denominator is 12x^2.

Multiplying the first term by x/x and the second term by 2/2, we get:

(7x)/(12x²) - (2y)/(12x²)

Combining the two terms, we get:

(7x - 2y)/(12x²)

Therefore,

7/12x - y/6x² in its simplest form is (7x - 2y)/(12x^2).

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If Farmer Johnson's minimum AVC is, for example, $1.50 per dozen eggs, then any price below $1.50 would result in losses that he could not sustain in the long run.

To determine the lowest price a dozen eggs could reach before Farmer Johnson would be forced to shut down in the short run, we need to know his minimum average variable cost (AVC) of producing eggs.

The average variable cost is the variable cost per unit of output, and it includes costs that vary with the level of production, such as labour, feed, and utilities.

If the price of a dozen eggs falls below the minimum AVC, Farmer Johnson will not be able to cover his variable costs and will incur losses. In the short run, he may continue to produce as long as he can cover his variable costs, but he will eventually be forced to shut down if he cannot cover his fixed costs as well.

Without information on Farmer Johnson's specific costs, we cannot determine the exact minimum AVC or the lowest price at which he would shut down. However, we can say that the lowest price a dozen eggs could reach before he would be forced to shut down is equal to his minimum AVC.

If Farmer Johnson's minimum AVC is, for example, $1.50 per dozen eggs, then any price below $1.50 would result in losses that he could not sustain in the long run.

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The table can be complete based on the function given by substituting as:

When s = 0, M(s) = -3

When s = 4, M(s) = 7

When s = 9, M(s) = 12

Given a function,

M(s) = 5√s - 3

Substitute each of the value of s to find the corresponding value of M(s).

When s = 0,

M(s) = 5√0 - 3 = 0 - 3 = -3

When s = 4,

M(s) = 5√4 - 3 = 10 - 3 = 7

When s = 9,

M(s) = 5√9 - 3 = 15 - 3 = 12

Hence the blank spaces are -3, 7 and 12.

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The possible sum of Kiran adding 4.7x10 √4 and 1.2 x 10 √5 is 94 + 1.2 x 10 √5

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

Kiran added 4.7x10 √4 and 1.2 x 10 √5

This means that we have

4.7 * 10√4 + 1.2 x 10 √5

Evaluate the square root of 4

So, we have

4.7 * 10 * 2 + 1.2 x 10 √5

When the products are evaluated, we have

94 + 1.2 x 10 √5

Hence, the possible result of the summation is 94 + 1.2 x 10 √5

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The value of Y is givan as y = 2 * 3^x

The general form is of

y = ab^x

where we have to define the terms as

'a' is the initial value, 'b' is the base, and 'x' is the exponent

Point (0, 2):

y = ab^x

2 = a * b^0

Since any non-zero number raised to the power of 0 is 1, we have:

2 = a * 1

a = 2

Point (1, 6):

y = ab^x

6 = 2 * b^1

6 = 2 * b

b = 6 / 2

b = 3

From the values that we have solve we would have

y = 2 * 3^x

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The statement that is not true on the cube - shaped box is C. The volume of the box is 1 square foot.

The possible dimensions for the bottom layer would be :

In answer to the rectangular prism inquiry, we know that the prism is made of 36 cubic units and has a height of 3 units. To discover all potential bottom layer dimensions, divide the total number of cubic units (36) by the height (3 units):

36 / 3 = 12

The possible dimensions of the bottom layer:

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

This means that the possible dimensions would be:

Length = 1 unit , Width = 12 units

Length = 2 units , Width = 6 units

Length = 3 units , Width = 4 units

A square foot is a unit of area, not volume. The volume should be measured in cubic feet.

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The volume of the cylinder of radius 3 m and height 8 m is given as follows:

V = 72π cubic meters.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The parameters for this problem are given as follows:

r = 3 m and h = 8 m.

Hence the volume of the cylinder is obtained as follows:

V = π x 3² x 8

V = 72π cubic meters.

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Answer:

y = - [tex]\frac{1}{2}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 8 ) and (x₂, y₂ ) = (6, 3 )

m = [tex]\frac{3-8}{6-(-4)}[/tex] = [tex]\frac{-5}{6+4}[/tex] = [tex]\frac{-5}{10}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 4, 8 )

8 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )

6 = c

y = - [tex]\frac{1}{2}[/tex] x + 6 ← equation of line

The linear function with the greatest rate of change is f(x) = 2x

The general linear function can be written in the following way.

y = ax + b

a is the slope or rate of change, and b is the y-intercept.

From the given options, the line with the greatest rate of change is the one that grows the fastest, and we can see that the equation for that line is:

y = 2x

So that is the correct option.

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Answer:

1(.1) + 2(.2) + 3(.3) + 4(.4)

= .1 + .4 + .9 + 1.6 = 3.0

Answer:

Step-by-step explanation:

To calculate the weighted mean, first multiply each number by its corresponding weight, then add-up the products and divide by the sum of the weights-

weighted mean = (1 x 0.1 + 2 x 0.2 + 3 x 0.3 + 4 x 0.4) / (0.1 + 0.2 + 0.3 + 0.4)

Then simplifying the numerator:-

weighted mean = (0.1 + 0.4 + 0.9 + 1.6) / (0.1 + 0.2 + 0.3 + 0.4)

Then adding up the numerator:-

So the weighted mean of the numbers 1, 2, 3, and 4 with weights 0.1, 0.2, 0.3, and 0.4 respectively is 3.

Step-by-step explanation:

in what form do you need the equation ?

I assume it is the slope-intercept form :

y = ax + b

"a" being the slope of the line, "b" being the y-intercept of the line.

the slope of a line is the ratio

y-coordinate difference / x-coordinate difference

when going from one point on the line to another.

and the y-intercept (y-axis intercept, to be precise) is the y-value when x = 0.

so, starting with the slope, we go for example from (1, 6) to (6, 1) :

x changes by +5 (from 1 to 6).

y changes by -5 (from 6 to 1).

so, the slope is

-5/+5 = -1

so, we know, our equation looks like

y = -x + b

to get "b" we use one of the points, e.g. (1, 6) :

6 = -1 + b

b = 7

and our final equation is

y = -x + 7

The distance from (-18, -5) and (-18, 24) is 29 units which is calculated with  the formula of shortest distance between two coordinates.

Hence option d is the correct option.

The coordinates are given as, say P is (-18, -5) and Q is (-18, 24).

The distance between P and Q can be calculated with the formula of shortest distance between two coordinates as,

Shortest distance between P and Q, PQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }[/tex]  units

⇒ PQ = [tex]\sqrt{((-18) - (-18))^2 + ((24) - (-5))^2 }[/tex]  units

⇒ PQ = [tex]\sqrt{(-18 +18)^2 + (24 +5)^2 }[/tex]  units

⇒ PQ = [tex]\sqrt{(0)^2 + (29)^2 }[/tex]  units

⇒ PQ = [tex]\sqrt{29^2}[/tex] units

⇒ PQ = 29 units

Hence option d 29 units is the correct option.

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The solution is, the simplification of the expression is:

{16 - 9x^2 + 14x}

Here, we have,

given that,

the expression:

{√49 + [√81 - x (9x - 14)]}

now, we have to simplify this expression:

{√49 + [√81 - x (9x - 14)]}

={7 + [9 - x (9x - 14)]}

={7 + [9 - 9x^2 + 14x]}

={7 +9 - 9x^2 + 14x}

={16 - 9x^2 + 14x}

Hence, The solution is, the simplification of the expression is:

{16 - 9x^2 + 14x}

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The value of c in the given diagram would be 10. 83.

From the diagram we see that when C is subtracted by 5 and then multiplied with this value 6 times, we get the value of 35.

In other words:

6 ( C - 5 ) = 35

Showing that when C - 5 is multiplied by 6, we get the value of 35.

Therefore, solving gives:

6 C - 30 = 35

6 C = 35 + 30

6 C = 65

C = 65 / 6

C = 10. 83

In conclusion, the value of C is 10. 83.

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The solution of the expression is 3.659

First, we will start with the expression inside the brackets, i.e., [(3 1/3 * 1.9) + (19.5 / (4 1/2)]. Here, we have two operations - multiplication and division. According to PEMDAS, we need to perform multiplication before division.

To simplify this expression, we will first convert 3 1/3 to an improper fraction. 3 1/3 is the same as 10/3. Therefore, the expression inside the brackets becomes

=> [(10/3 * 1.9) + (19.5 / (9/2)].

Next, we will simplify the multiplication first -

=> 10/3 * 1.9 = 19/3.

Now, let's simplify the division operation

=>  19.5 / (9/2) = 4.33

Therefore, the expression inside the brackets becomes

=>  [(19/3) + 4.33] = 8.99

Moving on to the denominator of the given expression

=> [62/75 - 0.16]. Here, we need to perform subtraction first as it comes before division in PEMDAS.

62/75 =  0.8266

Therefore, the denominator of the given expression becomes

=> [0.8266 - 0.16] = 0.6666

Now, let's simplify the numerator of the given expression. We have

=> [(3.5 + 4 2/3 + 2 2/15) / (0.5 * (1 1/20 + 4.1))].

Let's first convert all the mixed fractions to improper fractions.

3.5 can be written as 7/2, 4 2/3 can be written as 14/3, and 2 2/15 can be written as 32/15.

Therefore, the numerator becomes

=>  [(7/2 + 14/3 + 32/15) / (0.5 * (21/20 + 4.1))].

Let's first simplify the expression inside the brackets

=>  21/20 + 4.1 = 5.15.

Therefore, the numerator becomes

=>  [(7/2 + 14/3 + 32/15) / (0.5 * 5.15)].

Now, let's simplify the addition operation in the numerator. We need to find a common denominator to add the fractions.

The common denominator for 2, 3, and 15 is 30.

Therefore, (7/2 + 14/3 + 32/15) can be written as

=> (105/30 + 140/30 + 64/30).

Adding the fractions, we get (309/30).

Therefore, the numerator becomes [(309// (0.5 * 5.15)].

Next, let's simplify the expression inside the brackets - 0.5 * 5.15 = 2.575.

Therefore, the numerator becomes

[(309/30) / 2.575] = 3.68

Now that we have simplified the numerator and denominator of the given expression separately, we can simplify the entire expression.

[(8.99) / (0.6666)] / [3.68]

Let's first simplify the expression inside the first set of brackets.

(8.99) / (0.6666) = 13.486

Therefore, the given expression becomes 13.486 / 3.68 = 3.659

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The transformed fuction shifted 4 units to the right of the parent function is g(x)= x + 2

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

Parent function, f(x)= x+6,

Transformation: shifted 4 units to the right

The rule of the above transformation is

g(x) = f(x - 4)

Substitute the known values in the above equation, so, we have the following representation

g(x)= x - 4 + 6,

Evaluate the terms

g(x)= x + 2

Hence, the transformed fuction is g(x)= x + 2

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Answer:

Step-by-step explanation:

I’m sorry but I don’t know how I can solve you question

Answer:

8 people bought economy and 2 bought first class

Step-by-step explanation:

there are 10 person and total is 1580 so 250+ 9(135)=1460 which is wrong so we gonna try adding 2(250) and 8(135) which got us 1580

The mass of a piece of metal that has a volume of 12.4 cubic centimeters.

We can set up a proportion with the given masses and volumes:

Mass ₁ / Volume ₁ = Mass ₂ / Volume ₂

We can choose any two sets of masses and volumes from the table to use in the proportion. Let's use the first set of masses and volumes:

2.5 / 2.5 = Mass₂  / 12.4

We can solve for Mass 2 by cross-multiplying and simplifying:

2.5 x 12.4 = 2.5 Mass ₂

31 = Mass ₂

Therefore, the mass of a piece of metal with a volume of 12.4 cubic centimeters is 31 grams. We can round this answer to the nearest tenth of a gram, which gives us 31.0 grams.

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