Find the GCF of the monomials: 18x² and 21x²y
A)3x
B)3x²
C)3xy
D)3x²y
PLEASE HELP MEEE

The area of the region that lies inside both the curves r = sin 2θ and r = sin θ is π/3 + (1/16)√3.

To find the area of the region that lies inside both the curves, we need to determine the limits of integration for the angle θ.

The curves r = sin 2θ and r = sin θ intersect at certain values of θ. To find these points of intersection, we can set the two equations equal to each other and solve for θ:

sin 2θ = sin θ

Using the trigonometric identity sin 2θ = 2sin θ cos θ, we can rewrite the equation as:

2sin θ cos θ = sin θ

Dividing both sides by sin θ (assuming sin θ ≠ 0), we have:

2cos θ = 1

cos θ = 1/2

θ = π/3, 5π/3

Now we have the limits of integration for θ, which are π/3 and 5π/3.

The formula for calculating the area in polar coordinates is given by:

A = (1/2) ∫[θ₁,θ₂] (r(θ))² dθ

In this case, the function r(θ) is given by r = sin 2θ. Therefore, the area is:

A = (1/2) ∫[π/3,5π/3] (sin 2θ)² dθ

To evaluate this integral, we can simplify the expression (sin 2θ)²:

(sin 2θ)² = sin² 2θ = (1/2)(1 - cos 4θ)

Now, the area formula becomes:

A = (1/2) ∫[π/3,5π/3] (1/2)(1 - cos 4θ) dθ

We can integrate term by term:

A = (1/4) ∫[π/3,5π/3] (1 - cos 4θ) dθ

Integrating, we get:

A = (1/4) [θ - (1/4)sin 4θ] |[π/3,5π/3]

Evaluating the integral limits:

A = (1/4) [(5π/3 - (1/4)sin (20π/3)) - (π/3 - (1/4)sin (4π/3))]

Simplifying the trigonometric terms:

A = (1/4) [(5π/3 + (1/4)sin (2π/3)) - (π/3 + (1/4)sin (4π/3))]

Finally, simplifying further:

A = (1/4) [(5π/3 + (1/4)√3) - (π/3 - (1/4)√3)]

A = (1/4) [(4π/3 + (1/4)√3)]

A = π/3 + (1/16)√3

Therefore, the area of the region that lies inside both the curves r = sin 2θ and r = sin θ is π/3 + (1/16)√3.

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Answer:

974

Step-by-step explanation:

Let assume that:

The set of student that took part in Calculus be = C

Those that took part in discrete mathematics be = D

Let those that took part in data structures be = DS; &

Those that took part in Programming language be = P

Thus;

{C} = 507

{D} = 292

{DS} = 312

{P} = 344

For intersections:

{C ∩ DS} = 14

{C ∩ P} = 213

{D ∩ DS} = 211

{D ∩ P}  =43

{C ∩ D} = 0

{DS ∩ P} = 0

{C ∩ D ∩ DS ∩ P} = 0

According to principle of inclusion-exclusion;

{C ∪ D ∪ DS ∪ P} = {C} + {D} + {DS} + {P} - {C ∩ D} - {C ∩ DS} - {C ∩ P} - {D ∩ DS} - {D ∩ P} - {DS ∩ P}

{C ∪ D ∪ DS ∪ P} = 507 + 292 + 312 + 344 - 14 - 213 - 211 - 43 - 0

{C ∪ D ∪ DS ∪ P} = 974

Hence, the no of students that took part in either course = 974

The height of the skyscraper is approximately 115.25 meters (rounded to the nearest hundredth of a meter).

To find the height of the skyscraper, we can use trigonometry and the information provided about the angle of elevation and the horizontal distance.

Let's denote the height of the skyscraper as h. We are given that Myesha's eye height above the ground is 1.75 meters, and she measures the angle of elevation to be 19 degrees.

In a right triangle formed by Myesha's eye, the top of the skyscraper, and a point on the ground directly below the top of the skyscraper, the angle of elevation (θ) is the angle between the line of sight from Myesha's eye to the top of the skyscraper and the horizontal ground.

The opposite side of the triangle is the height of the skyscraper (h), and the adjacent side is the horizontal distance from Myesha to the base of the skyscraper (337 meters).

Using the trigonometric function tangent (tan), we can set up the following equation:

tan(θ) = h / 337

Since we know the value of the angle of elevation (θ = 19 degrees), we can substitute it into the equation:

tan(19 degrees) = h / 337

Now we can solve for h:

h = tan(19 degrees) * 337

Using a calculator or trigonometric tables, we find that tan(19 degrees) is approximately 0.34202. Substituting this value into the equation:

h = 0.34202 * 337

h ≈ 115.25

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Answer:

[tex]Area = 1560ft^2[/tex]

Step-by-step explanation:

Given

See attachment for playground

Required

Determine the area

The playground is a trapezoid. So;

[tex]Area = \frac{1}{2}(Sum\ parallel\ sides) * Height[/tex]

From the attachment, the parallel sides are: 68ft and 36ft

The height is: 30ft

So, the area is:

[tex]Area = \frac{1}{2}(68ft + 36ft) * 30ft[/tex]

[tex]Area = \frac{1}{2}(104ft) * 30ft[/tex]

[tex]Area = 52ft * 30ft[/tex]

[tex]Area = 1560ft^2[/tex]

Answer:

[tex]\sqrt{968}[/tex]

Step-by-step explanation:

Since this is a right triangle, we are able to use pythagorean theorem, a^2+b^2=c^2. In this case x would be the "c", so 22^2+22^2=x^2. Isolate the variable and solve for x. 484+484=x^2

968=x^2

[tex]\sqrt{968\\}[/tex]=x

Answer:

D

Step-by-step explanation:

when it's a power of the power we multiply the powers to get a single value for the power.

(6^(1/4))^4=6^(4*(1/4)) (4*(1/4)=1)

=6^1=6

so the answer is D

Answer:

The answer is 71

Step-by-step explanation:

Why because

1 cm /31 mi = 2.3 cm / m

1 x m = 31 x 2.3

n = 71.3

71.3 rounded to nearest mile is 71.

Answer:

[tex](a)\ Area = 3765.32[/tex]

[tex](b)\ Area = 4773[/tex]

Step-by-step explanation:

Given

[tex]A_1 = 169in^2[/tex] --- area of each square

[tex]Shade = 4in[/tex]

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

[tex]L^2 = A_1[/tex]

[tex]L^2 = 169[/tex]

[tex]L = \sqrt{169[/tex]

[tex]L=13[/tex]

The length of two squares make up the radius of the semicircle.

So:

[tex]r = 2 * L[/tex]

[tex]r = 2*13[/tex]

[tex]r = 26[/tex]

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

[tex]A_2 = 16 * 169[/tex]

[tex]A_2 = 2704[/tex]

The area of the semicircle is:

[tex]A_3 = \frac{\pi r^2}{2}[/tex]

[tex]A_3 = \frac{3.14 * 26^2}{2}[/tex]

[tex]A_3 = 1061.32[/tex]

So, the area of the window is:

[tex]Area = A_2 + A_3[/tex]

[tex]Area = 2704 + 1061.32[/tex]

[tex]Area = 3765.32[/tex]

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

[tex]Length = 4 * 13 + 8[/tex]

[tex]Length = 60[/tex]

[tex]Height = 4*13 + 4[/tex]

[tex]Height = 56[/tex]

The area is:

[tex]A_1 = 60 * 56 = 3360[/tex]

The radius of the semicircle becomes initial radius + 4

[tex]r = 26 + 4 = 30[/tex]

The area is:

[tex]A_2 = \frac{3.14 * 30^2}{2} = 1413[/tex]

The area of the shade is:

[tex]Area = A_1 + A_2[/tex]

[tex]Area = 3360 + 1413[/tex]

[tex]Area = 4773[/tex]

1.) A=pi(r)^2

2.) V=Bh

3.) 3.1

4.) 20

5.)36

6.) 10

7.)18

Answer:

Step-by-step explanation:

1.) formula of circle =pi times r^2

2.)volume of cylinder =pi times r^2 times h

3.)value of pi rounded = 3.14

4.) diameter of can A =2r=2(10) = 20

diameter of Can A is 20

5.)diameter of can B =2r =2(18) =36

diameter of Can B is 36

6.)radius = 10

7.)radius =18

I did all of them.

Answer:

$250

Step-by-step explanation:

Calculation to determine the expected value per policy sold

Expected value​ per policy sold =$600-(1/50)*$5,000-(1/100)*$10,000-(1/200)*$30,000

Expected value​ per policy sold =$600-$100-$100-$150

Expected value​ per policy sold =$250

Therefore the expected value per policy sold will be $250

The normal sampling distribution can be used

The critical values at α = 0.05 are z₀ = -1.96 and z₀ = 1.96

The standardized test statistic is -11.652

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

In the above we can see that the sample sizes are greater than 30 as required by the central limit theorem

This means that the normal sampling distribution can be used and the parameters are

H₀: p₁ = p₂

H₁: p₁ > p₂

In (a), we have

α = 0.05

The critical values at α = 0.05 are z₀ = -1.96 and z₀ = 1.96

Start by calculating the pooled sample proportion using

p = (x₁ + x₂)/(n₁ + n₂)

So, we have

p = (32 + 183)/(119 + 203)

p = 0.67

So, we have

z = (x₁/n₁ - x₂/n₂)/√[p(1 - p)/n₁ + p(1 - p)/n₂)

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

z = (32/119 - 183/203)/√[0.67(1 - 0.67)/119 + 0.67(1 - 0.67)/203]

Evaluate

z = -11.652

Hence, the standardized test statistic is -11.652

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Answer:

27/49

plz mark me as brainliest

Answer:

$63

Step-by-step explanation:

The store is 20% off, Jessica has a coupon that is 5% off add that together and it's 25% off. $84 - 25% = $63

Answer:

Percent- 30

decimal-0.3

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

£2308.5 per day

Step-by-step explanation:

Since in one day they have to deliver 384 catalogues and 1890 leaflets and each student can deliver either 16 catalogues or 90 leaflets in hour, the amount of students required to deliver 384 catalogues in one hour is 384/16 =  24 students.

Also, the number of students required to deliver 1890 leaflets in one hour is 1890/90 = 21 students.

So the total number of students required to make the delivery is thus 24 + 21 = 45 students. This is the minimum number of students required for the delivery.

Since all students hired are paid £51.30 per day, even if they don't work a full day, so the amount of wage paid for this minimum amount of students is thus minimum amount × wage = 45 × £51.30 per day = £2308.5 per day

Answer:

£307.80

Step-by-step explanation:

Wow seems the verified answer is wrong.

Who would've thought?

16*384=24

90*1890=21

21+24=45

45/8=5.62500

5.625 rounds to 6

51.30*6=£307.80

Thats your working out

You have to divide 45 by 8 because there are 8 hours in a day in which they can work.

Then round the number as you cant have a fraction of a person

Which you would then multiply by 51.30

Brainliest would be appreciated <33

Hope it helps!

Answer:

35.

Step-by-step explanation:

can i get brainliesttt

jus solved it.

The value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9 is {0.2^2 p(1-p)}/{1.645^2}

Given a random variable X where X ~ N(p, p(1-p)/k) and 0<=p<=1, we need to find the value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9.

In general, if X ~ N(μ,σ²), then

P[|X-μ| < a] = 2Φ(a/σ) - 1

where Φ(z) is the standard normal cumulative distribution function.

Therefore, we can say that

P[|X-p| < 0.2] = 2Φ(0.2/√(p(1-p)/k)) - 1 ≥ 0.9

or 2Φ(0.2/√(p(1-p)/k)) ≥ 1.9

or Φ(0.2/√(p(1-p)/k)) ≥ 0.95

or 0.2/√(p(1-p)/k) ≥ Φ^(-1)(0.95)

where Φ^(-1)(z) is the inverse of the standard normal cumulative distribution function.

Therefore,  Φ^(-1)(0.95) = 1.6450.2/√(p(1-p)/k) ≥ 1.645

or k ≤ 0.2²p(1-p)/1.645²

From the above inequality, we get the maximum value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9 is given by the formula:

k ≤{0.2^2 p(1-p)}/{1.645^2}

Therefore, the value of k for which X will estimate to p within an accuracy of 0.2 with probability greater than 0.9 is {0.2^2 p(1-p)}/{1.645^2}

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1/4 or .75

6 divided by 4 equal 1/4 or .75

Answer:

I think the answer would be Y= -2X+5 .

Hope it helps u ^^♥️

To find the value of w that satisfies the equation 2u v - 3w = 0, where u = (-6, 0, 0, 2) and v = (-3, 5, 1, 0), we can substitute the given values into the equation and solve for w.

Substituting the given values of u and v into the equation 2u v - 3w = 0, we have:

2(-6, 0, 0, 2)(-3, 5, 1, 0) - 3w = 0.

Expanding the scalar multiplication and performing the dot product, we get:

(-12, 0, 0, 4)(-3, 5, 1, 0) - 3w = 0,

(36 + 0 + 0 + 0) - 3w = 0,

36 - 3w = 0.

Simplifying the equation, we have:

36 = 3w,

w = 12.

Therefore, the value of w that satisfies the equation is 12. By substituting w = 12 into the equation 2u v - 3w = 0, we get:

2(-6, 0, 0, 2)(-3, 5, 1, 0) - 3(12) = 0,

(-12, 0, 0, 4)(-3, 5, 1, 0) - 36 = 0,

36 - 36 = 0,

0 = 0.

Hence, the value of w = 12 makes the equation true, satisfying the given condition.

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Step-by-step explanation:

When performing operations on fractions, it is important to maintain the relationship between the numerator and the denominator. In general, if you do something to the numerator, you should also do the same to the denominator.

In your example, if you want to multiply the fraction 2/2 by 6/2, it is necessary to multiply both the numerator and the denominator by the same value. Here's why:

When you multiply fractions, you multiply the numerators together and the denominators together. So, in this case, the multiplication would be:

(2/2) * (6/2) = (2 * 6) / (2 * 2) = 12/4

If you had only multiplied the numerator (2) by 6, the result would have been:

(2 * 6) / 2 = 12/2

As you can see, these two results are different. The correct result is 12/4, which simplifies to 3/1 or simply 3. If you only multiplied the numerator, you would have obtained 12/2, which simplifies to 6.

So, it's necessary to apply the same operation (in this case, multiplication by 2) to both the numerator and the denominator in order to maintain the value of the fraction.

Answer:

The answer is 56.33 in decimal form but in fraction form the answer is 5633/

100

Step-by-step explanation:

6.55 x 8.6

Answer: 10

Step-by-step explanation:

Alexis Scored 4 more than twice the number of points Jessica scored.

Jessica scored 3

twice the number of 3 would be 3 x 2 which equals six

4 more than twice the number which is 6 would be 10, 4+6=10

Answer:

The correct answers are:

• Option 1,

• Option 3 and

• Option 4

Step-by-step explanation:

From the two-way table, it is true that;

1.) 5 students study both French and Spanish.

2.) 30 students study French but not Spanish.

3.) 2 students study neither French nor Spanish

4.) 35 students study French

5.) 68 students study Spanish

6.) 63 students study Spanish but not French

This makes the correct answers options 1, 3 and 4

P.S: I believe your question is from the attached image

Answer:

A. 5 students study both French and Spanish.

C. 2 students study neither French nor Spanish.

D. 30 students study French, but not Spanish.

:)

N = visitors

1030 = 1300 - 18(P - 30)

1030 - 1300 = -18(P - 30)

-270 = -18(P - 30)

-270/-18 = (P - 30)

15 = P - 30

45 = P

Answer:

1,534 inches squared

Step-by-step explanation:

To find surface area we just solve for the area of all the sides and add those together. A rectangular prism (a box like above) has 6 sides. There are...

2 sides each of the following dimensions:

2(13×26)=

2(338)=676

2(13×11)=

2(143)=286

2(26×11)=

2(286)=572

Add the area of all 6 sides...

676+286+572=1,534

Remember it is squared not cubed.

Answer:

Step-by-step explanation:

An arithmetic sequence is when the difference of the terms is same

F)2, 5, 9, 14, ...

5 ≠ 4 ≠ 3, no

G)100, 50, 12.5, 1.6, ...

-10.9 ≠ -37.5 ≠ -50, no

H)3, 10, 17, 24,...

7 is the common difference, yes

j) -2,-1,-1/2,-1/4

1/4 ≠ 1/2 ≠ 1, no

let $p$ and $q$ be the two distinct solutions to the equation$$\frac{4x-12}{x^2 2x-15}=x 2.$$if $p > q$. The value of $p - q$ is 4.

To find the value of $p - q$, we first need to solve the given equation and determine the values of $p$ and $q$.

The equation is:

$$\frac{4x-12}{x^2 - 2x - 15} = x^2.$$

Step 1: Factorize the denominator:

The denominator can be factored as $(x - 5)(x + 3)$.

Step 2: Simplify the equation:

$$\frac{4x-12}{(x - 5)(x + 3)} = x^2.$$

Step 3: Multiply both sides of the equation by $(x - 5)(x + 3)$ to eliminate the denominator:

$$(4x - 12) = x^2(x - 5)(x + 3).$$

Step 4: Expand and rearrange the equation:

$$4x - 12 = x^4 - 2x^3 - 15x^2 + 25x.$$

Step 5: Rearrange the equation and combine like terms:

$$x^4 - 2x^3 - 15x^2 + 21x - 12 = 0.$$

Step 6: Factorize the equation:

$$(x - 3)(x + 1)(x - 2)(x + 2) = 0.$$

From this, we get four possible solutions: $x = 3$, $x = -1$, $x = 2$, and $x = -2$.

However, we are interested in the two distinct solutions $p$ and $q$, where $p > q$. Therefore, the values of $p$ and $q$ are $p = 3$ and $q = -1$.

Finally, we can find the value of $p - q$:

$$p - q = 3 - (-1) = 3 + 1 = 4.$$

Hence, the value of $p - q$ is 4.

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