Please help!!! How do I go about solving the cardinality of the Venn Diagram shown below?

The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.

Firstly, we'll graph the equations and find the points of intersection:

y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u

(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u

)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.

The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$

We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$

Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.

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Answer:

Length of a Road

Step-by-step explanation: No man that has ever lived (Well unless they're a nephilim or smth) is over a mile tall. Swimming pools and buildings aren't usually big enough to be measured in miles unless they're either a skyscraper or a Wisconsin water park attraction.

Answer:

Below

Step-by-step explanation:

The equation to use for CONTINUOUS compounding is :

FV = PV e^(it)

18532.08 = 8327 * e^( i*10)        where i is the interest in decimal form

18532.08/8327  = e^(10i)

2.225541 = e^(10i)             now take natural log  (ln) of both sides to get

.8000 = 10i

i = .08     or 8% interest

A. Ram spent $18 on six pens and six books. The grand total is $72.

B. The cost of each pen is $9.

C. The variable is called x.

What is an equation?

A set of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division balanced by the equal sign is known as an equation. The equation's left-hand side (LHS) is on the left side, and its right-hand side (RHS) is on the right side (RHS).

Here, we have

Given: the equation 6x + 18 = 72:

A. The issue is that Ram spent $18 on six pens and six books. The total amount he paid is $72.

B. The following equation will be used to demonstrate this:

6x + 18 = 72

Compile similar terms.

6x = 72 - 18

6x = 54

On dividing,

x = 54 / 6.

x = $9

Hence, each pen will set you back $9.

C. The variable's value is x = 9.

Hence, the pen's price is 9.

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By using Percentage , Profit distributed to Charity A is £ 624 and Charity B is £ 336

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Total ticket sold = 800

Cost of each ticket is £ 2

Total fund raised (raw) = 2 * 800 = £1600

4% of the ticket won a prize of £20 each

so total number of tickets winning a prize = 4 % of 800 = 32

Total prize money distributed = 32 * 20 = £ 640

Total amount to distribute to charity = 1600 - 640 = £ 960

Total profit that goes to Charity A is = 65 % of 960 = £624

And rest to charity B is = £ 336

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Answer:

0

Step-by-step explanation:

forgotten sorry

Answer:

39.74 %

Step-by-step explanation:

12 years - 11.5  = .5 years

.5 / 1.9 = .2631 S.D   above the mean

  From z-score table this corresponds to .6026

          60.26 are BELOW this life span

             39.74 % are above 12 years

Step-by-step explanation:

The margin of error is a statistical tool used to describe how a set off sample data that is being analyzed will accurately correspond with the overall data.

Basically, the margin of error explains how accurate and effective the result from the analysis or a survey is.

This means that the large the margin of error the less accurate the result will be.

An acceptable margin of error typically falls between 4% and 8% at the 95% confidence level.

The margin of error for this sample was 5.7% this means that

49.3% (= 55% – 5.7%) and

60.7% (= 55% + 5.7%)

of cell phone users  will prefer to be contacted by text message

Answer:

q = 4

Step-by-step explanation:

4q + 4 = 20

or, 4q = 20 - 4

or, q = 16/4

or, q = 4

Answer:

----------------------------

Find the composition of the functions f(x) and g(x), which is written as f(g(x)).

Given functions:

Find f(g(x)):

Evaluate f(g(2)):

So, (f·g)(2) = 14.

The two factors such that their product is the first number and their sum is the second number are 8 and 5.

A factor is defined as the number that divides another number, leaving no remainder.

In other words, if multiplying two numbers gives us a product, then the number we multiply is a factor of the product and divided by the product.

The factors of 40 and 13 such that their product is the first number and their sum is the second number = 8 and 5.

That is, 8×5 = 40

8+5 = 13

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Check the picture below.

so the picture has a rectangle that is 8 units high and 12 units wide, and it has a couple of "empty" trapezoids, with a height of 5 and "bases" of 9 and 3.

now, if we just take the whole area of the rectangle and then subtract the area of those two trapezoids, what's leftover is the blue area.

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ h=5\\ a=9\\ b=3 \end{cases}\implies \begin{array}{llll} A=\cfrac{5(9+3)}{2}\implies A=30 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\large Areas}}{\stackrel{rectangle}{(12\cdot 8)}~~ -~~\stackrel{\textit{two trapezoids}}{2(30)}}\implies 96-60\implies 36\)

Answer:

Let us assume the total number of students surveyed = x

Then

Number of students preferring red = x/4

Number of students preferring blue = x/8

Then

Number of students remaining = x - [(x/4) + (x/8)]

                                                  =x - [(2x + x)/8)

                                                  = x - (3x/8)

                                                  = (8x - 3x)/8

                                                  = 5x/8

Number of students preferring the color green = (3/5) * (5x/8)

                                                                          = 3x/8

We also know that the total number of students preferring the color green is 15

So

3x/8 = 15

3x = 15 * 8

x = (15 * 8)/3

  = 5 * 8

  = 40

So in total 40 students were surveyed. I hope the procedure is clear to you.

Step-by-step explanation:

Answer:

23/4

Step-by-step explanation:

5 x 4 = 20

20 + 3 = 23

23/4

The inverse function of f(x) = 3x + 5 is given as follows:

C. p(x) = 1/3x - 5/3.

The function in the context of this problem is defined as follows:

f(x) = 3x + 5.

To obtain the inverse function, first we must exchange the variables x and y, hence:

y = 3x + 5

x = 3y + 5.

Now we must isolate the variable y, hence:

3y = x - 5

y = (x - 5)/3.

p(x) = 1/3x - 5/3.

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Answer:

x- intercept = - 8 , y- intercept = 4

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

x - 2(0) = - 8

x - 0 = - 8

x = - 8 ← y- intercept

to find the y- intercept let x = 0 in the equation and solve for y

0 - 2y = - 8

- 2y = - 8 ( divide both sides by - 2 )

y = 4 ← y- intercept

Answer:

\(\boxed {\tt 20 \ movies}\)

Step-by-step explanation:

The equation given represents the number of movies, \(r\), that must be rented to spend the same amount at each store.

We want to find the number of movies, so we should solve for \(r\). To solve for \(r\)we must isolate it on one side of the equation.

\(1.5r+15=2.25r\)

First, let's get all the terms with a variable on one side. Subtract 1.5r from both sides of the equation.

\(1.5r-1.5r+15=2.25r-1.5r\)

\(15=2.25r-1.5r\)

\(15=0.75r\)

0.75 and \(r\) are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 0.75

\(\frac{15}{0.75}=\frac{0.75r}{0.75}\)

\(\frac{15}{0.75} =r\)

\(20=r\)

20 movies must be rented to spend the same amount at each store.

Answer:

Permutation:

The number of ways Jake can join the field trip with his classmates can be represented as a permutation since the order in which they join the field trip matters. Assuming that Jake and his classmates are the only ones who will join the field trip, the number of ways Jake can join the field trip is:

1 * 1 = 1

Therefore, there is only one way for Jake to join the field trip.

Combination:

The number of ways to sell the pens can be represented as a combination since the order in which the pens are sold does not matter.

There are two boxes of red pens and two boxes of black pens, so there are a total of four boxes of pens. Each box contains 15 pens, so there are a total of 60 pens. We can choose the number of red pens we want to sell from the two boxes of red pens, and the number of black pens we want to sell from the two boxes of black pens. The number of ways to choose the number of red and black pens can be calculated using a combination:

Number of ways to sell pens = C(2,1) * C(2,1) = 2 * 2 = 4

Therefore, there are 4 ways to sell the pens.

Answer:

So let the hypotenuse be

x

:

sin

(

47

°

)

=

opposite side

x

sin

(

47

°

)

=

12

x

To solve for

x

, divide

sin

(

47

°

)

by

12

:

x

=

12

sin

(

47

°

)

x

≈

16

Step-by-step explanation:

Answer: 16

Reason: bc it just is

The function notation of 9x + 3y = 12 is given as follows:

f(x) = 4 - 3x.

The function in the context of this problem is given as follows:

9x + 3y = 12.

The format for the function notation is given as follows:

Hence we must isolate the variable y, as follows:

3y = 12 - 9x

y = 4 - 3x (each term of the expression is divided by 3).

f(x) = 4 - 3x.

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Answer:

\(\tan T \approx 1.28\)

Step-by-step explanation:

\(\tan T=\frac{7}{\sqrt{30}} \approx 1.28\)

Answer:

3600

Step-by-step explanation:

If she has 800 her teacher gives her 3000= 3800 and she gave 100 to both of her friends - 200 then she will have 3600.

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Answer:

(-1,2)

Step-by-step explanation:

Write out the system in a matrix

3  5     7

2(6  -1    -8 ) Multiply row two by five and add to row one.

1  0  -1 Multiply row 1 by -6 and add it to row two.

6  -1  -8

1 0 -1

0 -1 -2 Multiply bottom row by -1

1 0 -1

0 1 2

x=-1, y=2

Answer:

Jeffery because the other dude go the 2 numbers wrong (he put the x coordinates on y and y on x)

The common size value for licensed content is 0.0848.

To calculate the common size value for licensed content, first, we need to find the total revenue of the company. We can get this information from the company's financial statements.

Let's assume the total revenue of the company is $100,000.

Next, we need to find the amount of money spent on licensed content. Let's assume that the amount spent on licensed content is $8,500.

Now, to calculate the common size value for licensed content, we need to divide the amount spent on licensed content by the total revenue, and multiply the result by 100.

So, the common size value for licensed content is:

Common size value = (8,500/100,000) x 100 = 0.0848

Therefore, the common size value for licensed content is 0.0848 (rounded to 4 decimals).

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Answer:

15u+15x-20

Step-by-step explanation:

* = multiply or times

We have to multiply everything in the parenthesis by -5, meaning:

-5*-3u = 15u

-5*-3x = 15x

-5*4 = -20

Put it all together: 15u+15x-20

\(\huge\text{Hey there!}\)

\(\huge\textbf{What is the distributive formula?}\)

\(\mathsf{a(b + c)}\\\\\mathsf{= a(b) + a(c)}\\\\\mathsf{= ab + ac}\)

\(\large\textbf{Extended distributive property formula:}\)

\(\mathsf{a(b + c + d)}\\\\\mathsf{= a(b) + a(c) + a(d)}\\\\\mathsf{= ab + ac + ad}\)

\(\huge\textbf{What are we solving for?}\)

\(\large\textbf{It seems like you have the extended distributive property}\)

\(\mathsf{-5(-3u - 3x + 4)}\)

\(\huge\textbf{What are the steps to solving for the}\\\\\huge\textbf{given equation?}\)

\(\mathsf{-5(-3u - 3x + 4)}\\\\\mathsf{= -5(-3u) - 5(-3x) - 5(4)}\\\\\mathsf{= 15u + 15x - 20}\)

\(\huge\textbf{What is the answer to the equation?}\)

\(\huge\boxed{\frak{{= 15\mathsf{u} + 15\mathsf{x} - 20}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

(x,y) ==> (x+2, y-1)

Step-by-step explanation: