find the area of the following regions. the region inside the lemniscate r^2=42cos20 and outside the circle r=sqrt(21)

Answer:

2x - 8 = 12  has the same solution as 12/x-4 = 2

Step-by-step explanation:

They both equal 10

Answer:

21

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

3y = ax + 7

3(4) = a(3) + 7

12 = 3a + 7

5 = 3a

3/5 = a

Best of Luck!

x = 3

y = 4

3y = ax + 7

By putting the values of x and y, we get

3(4) = a(3) + 7

or, 12 = 3a + 7

or, 12 - 7 = 3a

or, 5/3 = a

a = 5/3

12 = 5/3(3) + 7

or, 12 = 12

LHS = RHS

Hence, Verified.

Answer: 2000

Step-by-step explanation:

Answer:

To find the area of a parallelogram, we need to multiply the base by the height.In this case, we have a parallelogram with a 45-degree angle, a width of 22 cm, and a height of 10 cm.Since the opposite sides of a parallelogram are parallel, we can use the height as one of the sides and the width as the base.To find the other side (which is also the height), we need to use the fact that the opposite sides of a parallelogram are equal in length. We can use the Pythagorean theorem to find the length of the other side:a^2 + b^2 = c^2where a = b = 10 cm (the height) and c is the length of the other side.c^2 = 10^2 + 10^2c^2 = 200c = sqrt(200) ≈ 14.14 cmNow we can find the area:Area = base x heightArea = 22 cm x 10 cmArea = 220 cm^2Therefore, the area of the parallelogram is 220 square centimeters.

Answer:

k= -1/3

Step-by-step explanation:

hope this helps :)

(a) The number of ways to choose 5 colors without replacement from 15 distinct colors, where the order of the choices is not relevant, is given by the combination formula. This is denoted as "15 choose 5," or 15C5, which is equal to 3,003.

(b) If the order of the choices is relevant, then the number of ways to choose 5 colors without replacement from 15 distinct colors is given by the permutation formula. This is denoted as "15 permute 5," or 15P5, which is equal to 3,003,600.

In part (a), we use the combination formula because we want to know the number of ways to choose 5 colors from 15 distinct colors without regard to the order of the choices. This formula is given by nCr = n!/(r!(n-r)!), where n is the number of items to choose from, and r is the number of items to choose. In this case, n = 15 and r = 5, so we have 15C5 = 15!/(5!(15-5)!) = 3,003.

In part (b), we use the permutation formula because we want to know the number of ways to choose 5 colors from 15 distinct colors, where the order of the choices matters. This formula is given by nPr = n!/(n-r)!, where n is the number of items to choose from, and r is the number of items to choose. In this case, n = 15 and r = 5, so we have 15P5 = 15!/10! = 3,003,600.

Overall, the key difference between part (a) and part (b) is whether or not the order of the choices matters. If the order doesn't matter, we use the combination formula (nCr), and if the order does matter, we use the permutation formula (nPr).

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The standard deviation of the sampling distribution is 177

From the question, the given parameters are

Population standard deviation = 5 cm

Toy cars = 1250

Mean = 10.5

These can be represented as

σ = 5

n = 1250

μ = 10.5

The sampling standard deviation is calculated as

σₓ = σ√n

So, we have

σₓ = 5 * √1250

Evaluate

σₓ = 177

Hence, the sampling standard deviation is 177

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The intersection of two sets is the set of elements that are common to both sets. In this case, Set A = {5, 6, 7, 8} and Set B = {7, 8, 9, 10}. Therefore, the intersection of Set A and Set B is {7, 8}.

Therefore, the number that is in the intersection of sets A and B is D: 7

It's important to note that both numbers 7 and 8 are in the intersection of the sets, but the question is asking for only one number.

The correct statement regarding the linear functions is given by:

Both plans cost the same when 50 texts are sent.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we consider the flat fee as the intercept and the cost per message as the slope, hence the functions are given by:

Initially, Hiroto costs are higher, then after the threshold, Emilia's costs are higher. The threshold is given by:

E(x) = H(x)

10 + 0.25x = 20 + 0.05x

0.2x = 10.

x = 100/2

x = 50.

Hence the correct statement is given by:

Both plans cost the same when 50 texts are sent.

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Answer:

-3, -2, or -1

To transform the standard form of a quadratic function into vertex form, we need to complete the square. The vertex form of a quadratic function is f(x) = a(x-h)^2 + k, where (h,k) is the vertex.

First, we factor out the coefficient of x^2, which is -3 in this case:
f(x) = -3(x^2 + 2x - 8)
Next, we complete the square by adding and subtracting the square of half the coefficient of x, which is 1:
f(x) = -3(x^2 + 2x + 1 - 1 - 8)
Simplifying, we get:
f(x) = -3(x + 1)^2 + 27
Therefore, the vertex of the quadratic function is (-1,27).
To transform the standard form into intercept form, we can factor the quadratic expression:
f(x) = -3(x - 2)(x + 4)
Therefore, the x-intercepts of the quadratic function are x = 2 and x = -4.
In summary, we can transform the standard form of a quadratic function into vertex form by completing the square, and into intercept form by factoring the quadratic expression. So the intercept form of the quadratic function is f(x) = -3(x + 4)(x - 2).

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Answer:

a =10148

Step-by-step explanation:

A = P (1 + rt)

a= 8600(1+0.06*3)

a = 10148

Answer:

Step-by-step explanation:

Equation

3x + 9 + 2x = x - 2x - 3              

Solution

Combine all the like terms.

3x+2x+9 =  x - 2x - 3

5x + 9 = -x - 3                            Add x to both sides of the equation

5x+x +9 = -x+x -3                      Combine

6x + 9 = - 3                                Subtract 9 from both sides of the equation

6x+9-9 = - 3-9                           Combine

6x = -12                                      Divide both sides by 6

6x/6 = -12/6

x = - 2

Answer x = - 2

Answer:

44

yes. the total cost is 68 which is less than 70

Step-by-step explanation:

There is positive proportionality is two variables are positively related to each other.

The equation for direct proportionality =

y = bx

where y = dependent variable

b = constant

x = independent variable

amount of gasoline = b x length of the trip  

16 = b x 145

b = 16/145 = 0.110345

a. 400 x 0.110345 = 44

total litres used for the trip = 44 + 16 = 60

total cost of the trip = 60 x 1.13 = 67.8

total amount spent on gasoline is 67.8. this is less than the budget

Answer:

29,000

Step-by-step explanation:

this is the answer

Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

Answer:

96

Step-by-step explanation:

Given

- 8 × - 6 × 2 ( the product of 2 negatives is a positive )

= 48 × 2

= 96

The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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The solution of each of the following systems of linear equations using augmented matrices are below:

(a) x = -2 and y = -1

(b) x = -1/2 and y = 1

(c) x = -7 and y = 2

(d) Either \(S = \frac{16}{3}\) and there are infinite solutions or\(S \neq \frac{16}{3}\) and there are no solutions

a. x - 3y = 1, 2x - 7y = 3 Putting the above linear equation in augmented matrices form we get:

\(\left[\begin{array}{ccc}1&-3&|1\\2&-7&|3\\\end{array}\right]\)

Performing row operations to solve the above matrix we get:

\(\left[\begin{array}{ccc}1&-3&|1\\0&-1&|1\\\end{array}\right]\) therefore y = -1

and \(\left[\begin{array}{ccc}1&0&|-2\\0&1&|-1\\\end{array}\right]\) therefore x = -2.

b. x + 2y = 1, 3x + 4y = 1 Putting the above linear equation in augmented matrices form we get:\(\left[\begin{array}{ccc}1&2&|1\\3&4&|1\\\end{array}\right]\)

Performing row operations to solve the above matrix we get: \(\left[\begin{array}{ccc}1&2&|1\\0&-2&|-2\\\end{array}\right]\) so y = 1

and \(\left[\begin{array}{ccc}1&0&|\frac{-1}{2} \\0&1&|1\\\end{array}\right]\) so x = \frac{-1}{2}

c. 2x + 3y = -1, 3x + 4y = 2 Putting the above equation in matrix form we get: \(\left[\begin{array}{ccc}2&3&|-1\\3&4&|2\\\end{array}\right]\)

Performing row operations to solve the above matrix we get: \left[\begin{array}{ccc}2&3&|-1\\0&1&|2\\\end{array}\right] therefore y = 2

and \(\left[\begin{array}{ccc}1&0&|-7\\0&1&|2\\\end{array}\right]\) therefore x = -7

d. 3x + 4y = 1, 4x + Sy = -3 Putting the above equation in matrix form we get: \(\left[\begin{array}{ccc}3&4&|1\\4&S&|-3\\\end{array}\right]\)

As the above matrix is not in the echelon form, therefore we perform row operations to convert the matrix into echelon form: \\([\begin{array}{ccc}3&4&|1\\4&S&|-3\\\end{array}\right}]\)

Performing row operation R_{2}→ R_{2}-\frac{4}{3}R_{1}

We get: \(\left[\begin{array}{ccc}3&4&|1\\0&S-\fract{16}{3}&|\frac{-7}{3}\\\end{array}\right]\)

Therefore, either \(S = \frac{16}{3}\) and there are infinite solutions or S ≠ 16/3 and there are no solutions.

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Answer:

The answer would be D

Step-by-step explanation:

3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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Answer:

Independent Variable:  Jazz music

Dependent Variable: Sleeping Time

Experimental Group: people sleeping with jazz music

Control Group: people sleeping without jazz music

3 constants:

No of people in group

Jazz music

Sleep

Step-by-step explanation:

The independent variable is the one which is not altered by any outer influence. For example the jazz music will not be interrupted by the sleeping habits of people.

The dependent variable is the one which is affected by external changes such as sleeping time is afffected by external music or noises.

Experimental group on which experiment is being carried out.

Control group is which determines the changes in experimental group.

Constants which do not change for the number of experiment, could be number of people, type of jazz music, volume of jazz music also sleep is a constant .

Answer: f(x) = -cos(x) + 4.584

Step-by-step explanation:

we know that f'(x) = sin(x)

if we integrate that, we get:

f(x) = -cos(x) + C

Where C is a constant of integration.

And we also want that:

f(2) = 5

with that relationship we can find the value of C.

f(2) = 5 =  -cos(2) + C

(The calculation is done in radians)

        5 = -(-0.416) + C

       5 - 0.416 = C = 4.584

Then the function is:

f(x) = -cos(x) + 4.584

Answer:

I am pretty sure it is 56 because all you have to do is dvided and it comes out to 56.25 but you cant have .25 because that is not an equal peice so yeah I think it is 56

Answer:56.25

Step-by-step explanation:I had same problem it was correct

Answer: 806.5

Step-by-step explanation: you can split it into 3 different shapes: a triangle, rectangle, and a trapezoid. Then, find the area of each individual figure and add them all together and you get 806.5!!

Answer:

I can help you dude if any trouble (:

The maximum and minimum percents are  58% and 66%. respectively.

What is the maximum and minimum percents?

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

We have,

A margin of error

900 voters

62% favored raising the driving age.

The margin of error was ±4%. Give the maximum and minimum percent

so,

62% - 4%. = 58%

62% + 4%. = 66%

minimum 58%,

maximum 66%.

Hence, the maximum and minimum percents are  58% and 66%. respectively.

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