WILL NAME BRAINLIST! The point of a square pyramid is cut off, making each lateral face of the pyramid a trapezoid with the dimensions shown. 1 in 1 in. 3 in. What is ine area of one trapezoidal face of the figure? ___ in. 2​

If m and n are relatively prime, the numerator (an + bm) and denominator (mn) have no common factors other than 1, and therefore, (an + bm)/(mn) is in lowest terms.

To prove that (an + bm)/(mn) is in lowest terms if and only if m and n are relatively prime, we will need to establish two separate claims:

Claim 1: If (an + bm)/(mn) is in lowest terms, then m and n are relatively prime.

Claim 2: If m and n are relatively prime, then (an + bm)/(mn) is in lowest terms.

Proof of Claim 1:

Let's assume that (an + bm)/(mn) is in lowest terms. This means that the numerator (an + bm) and the denominator (mn) have no common factors other than 1.

Suppose m and n are not relatively prime, which means they have a common factor greater than 1.

Let's say that factor is d, where d > 1. Then we can express m and n as follows: m = dx and n = dy, where x and y are integers.

Now, we rewrite the numerator (an + bm) as follows:

an + bm = an + b(dx) = n(a + bx/d)

Since m = dx and n = dy, we have (an + bm)/(mn) = (n(a + bx/d))/(dx * dy) = (a + bx/d)/(xy).

We can see that both the numerator (a + bx/d) and the denominator (xy) have the factor d.

This contradicts our assumption that (an + bm)/(mn) is in lowest terms, as they have a common factor greater than 1.

Therefore, m and n must be relatively prime.

Proof of Claim 2:

Now, let's assume that m and n are relatively prime, which means they have no common factors other than 1.

To show that (an + bm)/(mn) is in lowest terms, we need to demonstrate that its numerator and denominator have no common factors other than 1.

Let's suppose that the numerator (an + bm) and the denominator (mn) have a common factor d, where d > 1.

This implies that d divides both an + bm and mn.

Since d divides mn, we can express m and n as follows: m = dx and n = dy, where x and y are integers.

Now, let's rewrite the numerator (an + bm) as follows:

an + bm = an + b(dx) = n(a + bx/d)

We can see that d divides both n and the expression (a + bx/d). Therefore, d also divides the numerator (an + bm).

However, we initially assumed that (an + bm)/(mn) is in lowest terms, which means the numerator and denominator have no common factors other than 1. This contradicts the assumption that they have a common factor d > 1.

Thus, if m and n are relatively prime, the numerator (an + bm) and denominator (mn) have no common factors other than 1, and therefore, (an + bm)/(mn) is in lowest terms.

By proving both Claim 1 and Claim 2, we have established that (an + bm)/(mn) is in lowest terms if and only if m and n are relatively prime.

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Answer:

Percent- 30

decimal-0.3

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

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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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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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:

[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]

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:

Natural selection is a mechanism, or cause, of evolution. Adaptations are physical or behavioral traits that make an organism better suited to its environment. Heritable variation comes from random mutations. Random mutations are the initial cause of new heritable traits.

Answer:

Darwin's theory of evolution

Charles Darwin developed a theory of evolution to explain the unity and diversity of life, based on the idea of shared common ancestors.

Natural selection

Darwin's theory was based on the mechanism of natural selection, which explains how populations can evolve in such a way that they become better suited to their environments over time.

Light colored mice are more easily seen by predators and are therefore preyed upon more. Dark mice are better adapted to their environment and better able to survive and reproduce.

Light colored mice are more easily seen by predators and are therefore preyed upon more. Dark mice are better adapted to their environment and better able to survive and reproduce.

Natural selection acting on mice population over time.

Individuals have variations within their heritable traits. Some variations make an individual better suited to survive and reproduce in their environment.

If this continues over generations, these favorable adaptations (the heritable features that aid survival and reproduction) will become more and more common in the population.

The population will not only evolve (change in its genetic makeup and inherited traits), but will evolve in such a way that it becomes adapted, or better-suited, to its environment.

Artificial selection

There are other types of selection, in addition to natural selection, that are out there in the world.

Artificial selection, also called "selective breeding”, is where humans select for desirable traits in agricultural products or animals, rather than leaving the species to evolve and change gradually without human interference, like in natural selection.

A timeline showing how dogs became domesticated over a long period of time due to artificial selection.

A timeline showing how dogs became domesticated over a long period of time due to artificial selection.

Dog breeding is a perfect example of how humans select for desirable or fashionable traits. Breeders deliberately mate parents with the hope of producing offspring with specific traits (such as color, size, ear shape, snout length, and so on).

Common mistakes and misconceptions

Evolution is not the same as adaptation or natural selection. Natural selection is a mechanism, or cause, of evolution. Adaptations are physical or behavioral traits that make an organism better suited to its environment.

Heritable variation comes from random mutations. Random mutations are the initial cause of new heritable traits. For example, a rabbit can't choose to have a different fur color. Rather, a genetic mutation causes a difference in fur color, which may help that rabbit hide better in its environment.

Natural selection acts on existing heritable variation. Natural selection needs some starting material, and that starting material is heritable variation. For natural selection to act on a feature, there must already be variation, and that variation must be able to be passed on to offspring.

Natural selection depends on the environment. Natural selection doesn't favor traits that are somehow inherently superior. Instead, it favors traits that are beneficial in a specific environment. Traits that are helpful in one environment might actually be harmful in another.

Step-by-step explanation:

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:

12x - 8y

Step-by-step explanation:

9x - 5y + 3x + 2y - 4y - y​

9x + 3x - 5y + 2y - 4y - y

12x - 8y

Answer:

12x - 8y would be the simplified version of this equation if this is not the type of answer your looking for please lmk

Step-by-step explanation:

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

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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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:

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.

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:

£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:

[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

1/4 or .75

6 divided by 4 equal 1/4 or .75

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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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:

690.50

Step-by-step explanation:

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:

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

Answer:

309.8 mm

Step-by-step explanation:

17.6 x 17.6= 309.76

309.76 rounded is 309.8

Answer:

309.8

Step-by-step explanation:

The formula for area of square is one of its sides times another (or its side squared).

So if one of the side is 17.6, it would be 17.6^2 which is 309.76.

You then round one decimal place and get 309.8

Have a good day

Answer:

27/49

plz mark me as brainliest

Answer:

Car M:

50.4/2 = 25.2

car M uses up 1 gallon every 25.2 miles

Car P:

Just from the graph, you can see that it uses up 1 gallon every 30 miles

The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.

Answer:

Step-by-step explanation:

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:

$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

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:

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