simplify each of the following.
5.1.
[tex]2 sin(90 - x ) - cos(360 - x)[/tex]
​

a) There are no solutions to the equation.

To find all solutions to the equation 34 - 38 = 3, we can simplify the equation:

34 - 38 = 3

-4 = 3

However, this equation is not true, as -4 is not equal to 3. Therefore, there are no solutions to the equation.

b) Now, let's consider the diophantine equation 1/x + 1/y = 1/5, where x and y are integers. To find all solutions, we can follow these steps:

1: Multiply both sides of the equation by 5xy to eliminate the denominators:

5y + 5x = xy

2: Rearrange the equation:

xy - 5x - 5y = 0

3: Apply Simon's Favorite Factoring Trick:

Add 25 to both sides to complete the square:

xy - 5x - 5y + 25 = 25

xy - 5x - 5y + 25 = 25

(xy - 5x - 5y + 25) + 25 = 25 + 25

(x - 5)(y - 5) = 50

4: List all possible factor pairs of 50:

(1, 50), (2, 25), (5, 10), (-1, -50), (-2, -25), (-5, -10)

5: Solve for x and y in each factor pair:

For (x - 5)(y - 5) = 50:

If x - 5 = 1 and y - 5 = 50, then x = 6 and y = 55.

If x - 5 = 2 and y - 5 = 25, then x = 7 and y = 30.

If x - 5 = 5 and y - 5 = 10, then x = 10 and y = 15.

If x - 5 = -1 and y - 5 = -50, then x = 4 and y = -45.

If x - 5 = -2 and y - 5 = -25, then x = 3 and y = -20.

If x - 5 = -5 and y - 5 = -10, then x = 0 and y = -5.

Therefore, the solutions to the diophantine equation 1/x + 1/y = 1/5, where x and y are integers, are:

(x, y) = (6, 55), (7, 30), (10, 15), (4, -45), (3, -20), (0, -5).

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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

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 height of the vertical walls is 10 ft=480 sq ft. The triangles that make up the roof are isosceles triangle 80 sq ft. The greenhouse uses 504 square feet of glass to construct.

To calculate the amount of glass used to make the greenhouse, to determine the total surface area of the glass panels.

The greenhouse consists of four vertical rectangular walls and two triangular roof sections.

The total surface area of the vertical walls calculated by adding the areas of each wall. Since the greenhouse is rectangular, the height of the walls is 10 ft, and the total width of the walls (including the door) is 16 ft + 8 ft = 24 ft.

Area of each wall = height x width

Area of vertical walls = 2 x (height x width) = 2 x (10 ft x 24 ft) = 480 sq ft

Each roof section forms an isosceles triangle. The base of each triangle is the width of the greenhouse, which is 16 ft. The height of the triangle is the difference between the total height of the greenhouse (15 ft) and the height of the vertical walls (10 ft), which is 5 ft.

Area of each triangular roof section = 0.5 x base x height

Area of triangular roof = 2 x (0.5 x 16 ft x 5 ft) = 80 sq ft

The door is not made of glass, so we need to subtract its area from the total.

Area of the door = width x height = 8 ft x 7 ft = 56 sq ft

calculate the total glass surface area by subtracting the area of the door from the sum of the vertical walls and triangular roof sections.

Total glass surface area = (Area of vertical walls + Area of triangular roof) - Area of the door

Total glass surface area = (480 sq ft + 80 sq ft) - 56 sq ft

Total glass surface area = 504 sq ft

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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

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:

Step-by-step explanation:

The easiest way is to graph both functions and see where they intersect.  The intersection is where f(x) = g(x).

f(x) = -x² - 3x + 6

g(x) = 2x² + 5x + 3

Answer:

the pyramid is 80 ft² and the rectangular prism is 240 ft²

Step-by-step explanation:

Answer:

It's A don't listen to the other guy

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

edg 22

A tax of 7.5 percent was added to the product to make it equal to 27.95.

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:

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 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:

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:

[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:

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:

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:

27/49

plz mark me as brainliest

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:

$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

(a) There can be a maximum of 18 teams.

(b) The largest possible number of teams is 18, and there will be a total of 19 players on each team.

Given information:

In a local, recreational soccer league there are 252 men and 90 women signed up to play. The organizers need to make sure that everyone is on a team, the teams are the same size, each team has the same number of males; and each team has the same number of females.

(a) To find the largest possible number of teams, we need to divide the players (252 men and 90 women) into teams, where each team has the same number of males and females. Let's find the GCD (greatest common divisor) of 252 and 90:

GCD of 252 and 90 = GCD (252,90) = 18.

Therefore, there can be a maximum of 18 teams.

(b) Since the number of teams is 18, and we have 252 men and 90 women, there will be a total of 342 players.

Now, we need to divide these 342 players into 18 teams. Each team must have an equal number of males and females. Number of males = 252, Number of females = 90.

To divide the players equally into teams, we need to find the number of males and females that can be in one team.

Number of males in one team = 252/18 = 14

Number of females in one team = 90/18 = 5

Therefore, each team will have 14 males and 5 females, and there will be a total of 19 players on each team (14 + 5).

Thus, the largest possible number of teams is 18, and there will be a total of 19 players on each team.

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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:

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:

for 100: 14,800

for 10: 14,780

for 1: 14,780

for 1000: 15,000

Step-by-step explanation:

ok so just go for like if its

18 its going to be 20 if its 11 its going to be 10

Hope this helps!!

PLEASE CROWN TYY

Answer:

Rounding Rules:

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40. ...

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30.

Step-by-step explanation:

100: 14,800

10: 14,780

1: 14,780

1000: 15,000

Answer:

690.50

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A: Not A. It can be graphed. It is a vertical line where x = 3. Every point must have an x value of 3. (3,4), (3,0), (3.- 6) are all on x = 4. It can be graphed, but it is not a function.

B:  Not B. It is not a function at all. To be a function, it can only have 1 y value associated with it.

C: It's not a linear function because it is not a function.

D is your answer

Answer:

20 people participated in the survey.