Which of the following is the difference of two squares ?

The speed of the passenger train is 80 mph.

Let's call the speed of the passenger train "p" and the speed of the freight train "f". We know that "p" = "f" + 14, and that the time it takes for the two trains to cover their respective distances is the same.

Therefore, we can write the equation:

400/p = 330/f

Expanding the second term and substituting "p" for "f" + 14:

400/p = 330/(p - 14)

Cross multiplying and simplifying:

400 * (p - 14) = 330 * p

Expanding both sides:

400p - 5600 = 330p

Subtracting 330p from both sides:

70p = 5600

Dividing both sides by 70:

p = 80 mph

So the speed of the passenger train is 80 mph.

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The speed of the passenger train is 80 mph.

Let's call the speed of the passenger train "p" and the speed of the freight train "f". We know that "p" = "f" + 14, and that the time it takes for the two trains to cover their respective distances is the same.

Therefore, we can write the equation:

400/p = 330/f

Expanding the second term and substituting "p" for "f" + 14:

400/p = 330/(p - 14)

Cross multiplying and simplifying:

400 * (p - 14) = 330 * p

Expanding both sides:

400p - 5600 = 330p

Subtracting 330p from both sides:

70p = 5600

Dividing both sides by 70:

p = 80 mph

So the speed of the passenger train is 80 mph.

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The interest rate required to end up with $251,000 is 6.9% to the nearest hundredth of a percent.

Compound interest is computed on the principal as well as the interest accumulated over the preceding period. It differs from simple interest in that interest is not added to the principal when computing interest for the next month.

The formula to calculate the compound interest is:

A = P * (1 + r/n)^(nt),

where:

A = final amount

P = principal amount ($95,000)

r = interest rate

n = number of compounding periods per year

t = time in years (18)

Rearranging the formula to solve for r:

r = (A/P)^(1/nt) - 1

Plugging in the given values:

r = ($251,000/$95,000)^(1/18*12) - 1

= 0.069 or 6.9%

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The value of p is obtained as follows:

p = 18%.

The value of p is obtained applying the proportions in the context of this problem.

A proportion is applied as a percentage is given by the division of the number of desired outcomes by the number of total outcomes, which is then multiplied by 100%.

The outcomes for this problem are given as follows:

Hence the percentage is given as follows:

p = 137/750 x 100%

p = 18%.

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Sharon completed a walkathon by walking a total of 9. 52 miles. Sharon would need 3.4 hours to complete the walk if she urinated on average 2. 8 times each hour.

Detailed explanation:

The distance that Shareen must travel is 9.52 miles.

Shareen travels at a mean speed of 2.8 mph.

We need to determine how long it took Shareen to finish the walk.

the average speed formula,

v = length/duration

[tex]$t & =\frac{d}{v} \\[/tex]

[tex]$t & =\frac{9.52}{2.8} \\[/tex]

[tex]$t & =3.4 \text { hour }[/tex]

As a result, the walk will take 3.4 hours to complete.

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The unit vector orthogonal to both A and B is u = (0.23, -0.92, 0.15).

Given vectors:

A = (2, 3, 4)

B = (1, -1, 4)

A unit vector is a vector with a magnitude of 1. Two vectors are orthogonal if the angle between them is 90 degrees. In order to find unit vectors orthogonal to both A and B, we must first compute the cross product of A and B. The cross product of two vectors is a vector perpendicular to both of the given vectors and can be denoted by A × B.

The cross product of A and B is given by:

A × B = (3, -12, 2)

To normalize this vector and find the unit vector, we must divide the vector by its magnitude. The magnitude of the vector A × B is equal to the square root of the sum of the squares of its components. We can write this as:

|A × B| = √(3^2 + (-12)^2 + 2^2) = √(169) = 13

Therefore, the unit vector orthogonal to both A and B is given by:

A × B/|A × B| = (3/13, -12/13, 2/13)

This vector can also be written in terms of its unit components, as:

u = (0.23, -0.92, 0.15)

Therefore, the unit vector orthogonal to both A and B is u = (0.23, -0.92, 0.15).

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The solution of (x^2 + 4x + 8)(2x - 1) is, 2x^3+7x^2+12x-8.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

(x^2 + 4x + 8)(2x - 1)

now, we know,

(a+c)*b = ab+cb

so, we get,

⇒2x^3+8x^2+16x-x^2-4x-8

⇒2x^3+7x^2+12x-8

Hence, The solution of (x^2 + 4x + 8)(2x - 1) is, 2x^3+7x^2+12x-8.

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The cost of Japan and Switzerland tickets are 17.15 dollars and 13.15 dollars respectively.

it would cost $77.75 to buy three tickets in Japan plus 2 tickets in Switzerland. Three tickets in Switzerland plus two tickets in japan would cost $73.75.

Using system of equation,

let

x = cost of each ticket in Japan

y = cost of each ticket in Switzerland

Therefore,

3x + 2y = 77.75

2x + 3y = 73.75

Multiply equation(ii) by 1.5

3x + 2y = 77.75

3x + 4.5y = 110.625

subtract the equations

2.5y = 32.875

y = 32.875 / 2.5

y = 13.15 dollars

Hence,

3x + 2y = 77.75

3x = 77.75 - 2y

3x = 77.75 - 2(13.15)

3x = 77.75 - 26.3

x = 51.45 / 3

x = 17.15 dollars

Therefore,

cost of Japan ticket = 17.15 dollars

cost of Switzerland ticket = 13.15 dollar

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Answer:

8

Step-by-step explanation:

Since the two horizontal lines are parallel, we have that triangle CDG and triangle CEF are similar (corresponding points in that order). Therefore, using similarity, CD/CG = CE/CF. Therefore 3/4 = 9/(4+x).

So 12 = 4+x, and x = 8.

The minimum sample size required will be 231.

What is Sample Size?

The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study whose purpose is to draw conclusions about a population from a sample.

The sample size(n) is 2558.

p = 46%

= 0.46 sample fraction of US adults who had experienced with substance misuse in their relatives

1) Where, 0.05/2 (n is the crucial value of z for two tailed test at 0.05 level of significance = 1.96) is the 95% CI for the population proportion of adults in the United States who had dealt with substance misuse in their family (P). (This can be acquired from the z table by locating the z that corresponds to an area close to 0.05/2).

Hence, the confidence interval is given by

= [0.46 ± 0.02]

= [0.44, 0.48]

As a result, we are 95% confident that the population share of US individuals who have experienced substance misuse in their relatives will fall between 0.44 and 0.48

2) Margin of error = E

= 0.02

3) Null hypothesis  0.4 percent of US people have dealt with substance misuse in their families.

P = 4/10

= 0.4

Alternative hypothesis  More than 0.5 percent of US individuals have dealt with substance misuse in their relatives.

P > 0.4

95% confidence interval is - [0.44, 0] 48]

We may reject the null hypothesis since the confidence interval does not include the null value of population proportion (0.4)

As a result, we have enough evidence that more than four out of every ten US adults have dealt with substance misuse in their families.

As a result, the newspaper could make the assertion.

4) According to the Gallop Poll poll of 2558 US individuals, more than four out of ten US citizens have dealt with substance misuse in their families.

5) The required minimum sample size is given by:

P is the specified value of population proportion under the null hypothesis = 0.4

= (1.96/0.02)²  (0.4) (1 - 0.4)

= [tex]98^{2}[/tex] (0.4) 0.6

= 230.5

So, the minimum sample size required will be 231.

Since, the sample size taken in survey (2558) is more than 231, the sample size taken is not too small.

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The minimum sample size required will be 231.

What is Sample Size?

The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study whose purpose is to draw conclusions about a population from a sample.

The sample size(n) is 2558.

p = 46%

= 0.46 sample fraction of US adults who had experienced with substance misuse in their relatives

1) Where, 0.05/2 (n is the crucial value of z for two tailed test at 0.05 level of significance = 1.96) is the 95% CI for the population proportion of adults in the United States who had dealt with substance misuse in their family (P). (This can be acquired from the z table by locating the z that corresponds to an area close to 0.05/2).

Hence, the confidence interval is given by

= [0.46 ± 0.02]

= [0.44, 0.48]

As a result, we are 95% confident that the population share of US individuals who have experienced substance misuse in their relatives will fall between 0.44 and 0.48

2) Margin of error = E

= 0.02

3) Null hypothesis 0.4 percent of US people have dealt with substance misuse in their families.

P = 4/10

= 0.4

Alternative hypothesis  More than 0.5 percent of US individuals have dealt with substance misuse in their relatives.

P > 0.4

95% confidence interval is - [0.44, 0] 48]

We may reject the null hypothesis since the confidence interval does not include the null value of population proportion (0.4)

As a result, we have enough evidence that more than four out of every ten US adults have dealt with substance misuse in their families.

As a result, the newspaper could make the assertion.

4) According to the Gallop Poll poll of 2558 US individuals, more than four out of ten US citizens have dealt with substance misuse in their families.

5) The required minimum sample size is given by:

P is the specified value of population proportion under the null hypothesis = 0.4

= (1.96/0.02)²  (0.4) (1 - 0.4)

=  (0.4) 0.6

= 230.5

So, the minimum sample size required will be 231.

Since, the sample size taken in survey (2558) is more than 231, the sample size taken is not too small.

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The length of each piece to the nearest inch is 16 inches.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that,

Total length of the board = 2 meters

Gillian cuts the board into 5 equal pieces.

Length of each piece of the board in meters = 2 / 5 = 0.4 meter

We know that,

1 meter = 39.37 inches

0.4 meter = 39.37 × 0.4

                = 15.748 inches

                ≈ 16 inches

Hence the length of each piece of the board is approximately 16 inches.

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None of the statements is true, as they all refer average to the false statement that exactly one, two, three, or four of the statements is false. This statement itself is false, and so none of the other statements can be true.

None of the statements is true because they all refer to the false statement that exactly one, two, three, or four of the statements is false. This statement itself is false, and so none of the other statements can be true. The statement that exactly one of the statements is false is false because it is referring to itself as the false statement, which means that it is not actually false. Similarly, the statement that exactly two of the statements are false is false because it is referring to itself as one of the two false statements, which means that it is not actually false. The statement that exactly three of the statements are false is also false because it is referring to itself as one of the three false statements, and the statement that exactly four of the statements are false is false because it is referring to itself as one of the four false statements. Therefore, none of the statements is true.

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Answer:

this can be solved using trigonometry

Answer:

y = -2x-8

Step-by-step explanation:

1. (-8,8)

2. (1,-10)

first lets find the slope

m = y2-y1 / x2-x1

m = -10-8 / 1-(-8)

m = -18 / 9

m = -2

y = -2x+b

lets find b by plugging in point 2

-10 = -2(1)+b

-10 = -2+b

b = -8

our equation:

y = -2x-8

Answer:

b. stratosphere

Step-by-step explanation:

The ozone layer, located in the stratosphere is responsible for absorbing the most UV radiation. This is because the ozone molecule (O3) is able to absorb UV radiation due to its molecular structure, specifically the presence of three oxygen atoms which allows it to efficiently absorb the UV-C radiation (the most damaging to living organisms). This protects life on Earth from harmful effects of UV radiation, such as DNA damage, skin cancer and other harmful impacts on plants and marine life.

The correct option is C. Length = 24 feet, width = 18 feet

To measure a rectangular room, use a tape measure, pencil and paper to record the length and width of the room. Then multiply these numbers to get the total area of the room.

The calculation is as follows:

Since 2cm = 6 feet

So,

The length is = 4(6) = 24 feet

And, the width be = 3(6) = 18 feet

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A scale drawing of Julie's living room is shown below:

A rectangle is shown. The length of the rectangle is labeled as length equal to 8 cm, and the width is labeled as width equal to 6 cm.

If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room?

A)Length = 16 feet, width = 12 feet

B)Length = 10 feet, width = 8 feet

C)Length = 32 feet, width = 24 feet

D)Length = 14 feet, width = 12 feet

The lateral surface area of the pyramid is 4√5 square inches.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

We know the lateral surface area of a square pyramid when height is given is, [tex]\sqrt{\frac{a^2}{4} + h^2[/tex].

Given, A square pyramid has a height of 8 inches and the base is also 8 inches.

Therefore, the lateral surface area of the pyramid is,

= [tex]\sqrt{\frac{8^2}{4} + 8^2[/tex] square inches.

= [tex]\sqrt{\frac{64}{4} + 64[/tex] square inches.

= [tex]\sqrt{16 + 64[/tex] square inches.

= √80 square inches.

= 4√5 square inches.

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"He did not apply the order of operations correctly. He should have performance the subtraction before the division. The correct answer is 23, not 7."

Bob did not apply the order of operations correctly. He should have performed the subtraction (3 - 3) before the division (÷ 3). The correct order of operations is to perform any calculations inside parentheses first, then perform any exponents, then perform any multiplication or division (from left to right), and finally perform any addition or subtraction (from left to right).

Applying the correct order of operations to the expression 3m - 3 ÷ 3, we get:

Therefore, the correct answer is 23, not 7.

It is important to always apply the order of operations correctly in mathematical expressions to ensure that the correct answer is obtained. Failure to follow the correct order of operations can lead to incorrect answers and misunderstandings.

This question should be provided as:

Bob used these steps to evaluate 3m - 3 ÷ 3 for m = 8. Complete the explanation about his error.

He did not apply the order of operations correctly. He should have performance the _______ before the ______. The correct answer is _____, not 7.

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on july 1 a one year non interest bearing note for 110250 was accepted in exchange for an unpaid accounts receivable for 105000 time was5%

option:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:D

The probability of each possible outcome has been calculated and the most likely joe placed his pencil on point a of the hexagon below. is zero

The task provides a context to calculate discrete probabilities and represent them on a bar graph. It could also be used to create a class activity where students gather, represent, and analyze data, running simulations of the random walk and recording and then displaying their results.

If we denote by H an outcome of heads and by T and outcome of tails, then the possible outcomes for the four coin flips can be represented by a sequence of four letters, with each letter being either a T or an H. For example HHHH would represent the case where all four coin tosses come up heads. There are two choices for each letter and four letters so this gives 2^4=16possible outcomes.

To see more clearly why the two possibilities for the first toss need to be multiplied by the two possibilities for the second toss observe that each outcome, H or T for the first toss, leads to two possible outcomes when paired with the second toss: H leads to HH and HT while T leads to TH and TT. This reasoning for multiplying by two for each additional coin toss leads to 2^4 possibilities if the coin is tossed four times.

For f(6) to be zero, there need to be the same number of steps to the left as to the right. So there must be 3 heads and 3 tails. We can make a list of the possibilities. To simplify the list, we will list the possibilities for which tosses came up heads so that 123 will mean that the first, second, and third tosses were heads while the fourth

123,124,134,234.

There are four possibilities so the probability that f(4)=0 is 4/ 16.

A word is worthwhile regarding the way in which the possible ways three heads could occur was listed above. The list is long and so to avoid duplication and to make sure the list is complete a method is useful. The list above has been formed by choosing the smallest first number (this is why the first ten numbers in the list begin with a 1), then the smallest possible second number, and finally the smallest third number.

In order for f(4) to be one there would need to be one more occurrence of heads than tails. But this means that the total number of coin tosses would have to be odd: if n is any whole number then n+(n+1)=2n+1 is an odd number. Therefore the probability that f(4)=1 is 0. The argument for why f(4) can never equal 1 is essentially the same as the argument in ''Random Walk II'' for why it is not possible for f(5) to be equal to 2.

Finally for the probability that f(4)=4. This means that Scott must have moved in the positive direction after each of the six coin tosses so all six coin tosses must have been heads. So this can happen in only one way while there are 2^4=16 different possible outcomes for the four coin tosses so the probability that f(4)=4 is 1/16.

The probability of each possible outcome has been calculated and the most likely joe placed his pencil on point a of the hexagon below. is zero.

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The probability of each potential result has been evaluated, and the most likely result is zero, where Joe set his pencil on point an of the hexagon.

The assignment gives you a context for computing discrete probabilities and visualizing them as bars. It might also be used to develop a lesson plan where students acquire, depict, and evaluate data, simulate the random walk, then record, analyze, and present their findings. The four coin flips' various outcomes can be represented by a string of four letters, each of which can be either a T or an H. If we signify by H an outcome of heads and by T an outcome of tails. For instance, the circumstance when all four coin tosses result in heads would be represented by HHHH. Each letter and the four letter combination has two options. so this gives [tex]2^4=16[/tex] possible outcomes.

For a clearer understanding of why the two possibilities for the first toss must be multiplied by the two possibilities for the second toss, consider the fact that each of the two possible outcomes for the first toss, H or T, leads to two additional outcomes when paired with the second toss: H leads to HH and HT while T leads to TH and TT. This reasoning for multiplying by two for each additional coin toss leads to [tex]2^4[/tex] possibilities if the coin is tossed four times.

There must be exactly as many steps to the left as there are to the right in order for f(6) to be zero. The result is that there must be three heads and three tails. A list of the possibilities can be created. To make the list shorter, we will list the possibilities for which tosses resulted in heads. For example, 123 would indicate that the first, second, and third tosses were all heads, but the fourth

123,124,134,234.

There are four possibilities so the probability that f(4)=0 is 4/ 16.

An explanation of how the potential causes of three heads were given above is important. The list is lengthy, thus a method is helpful to prevent duplication and ensure the list is full. The first 10 digits on the list above start with a 1, which was chosen as the smallest first number, followed by the smallest second number and, ultimately, the smallest third number.

There would have to be one more head than tail occurrences for f(4) to be one. However, this necessitates that the total number of coin tosses be odd: if n is any whole integer, then [tex]n(n+1)=2n+1[/tex] is an odd number. Consequently, there is no chance that f(4)=1 at all. Similar to the justification in "Random Walk II" for why f(5) cannot equal 2, the justification for why f(4) can never equal 1 is basically the same.

Finally, we have the likelihood that f(4)=4. This implies that Scott must have walked in the right direction after each of the six coin flips, proving that all six flips resulted in heads. Given that there are [tex]2^4=16[/tex] possible outcomes for the four coin flips, there is only one way that this may happen, making the chance that f(4)=4 1/16. The likelihood of each potential result has been evaluated, and the most likely value is zero.

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The number of DVDs sold in any day is one-third the number of DVDs sold the previous day three times the number of DVDs sold the following day.

The exponential function D(t) = 729(1/3)^t models the number of DVDs sold where t is the number of days since the release date and D(t) is the number of DVDs sold.

The definition of an exponential function is given as follows:

y = ab^x.

In which:

For this problem, the parameter values are given as follows:

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The expressions by value from least to greatest are x-1, x, -2x, 1-x

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: The value of x is -1/4

Thus evaluating for each expression by substituting value of x we get

1) x=-1/4

2) 1-x= 1+1/4

         =5/4

3)x-1=-1/4-1

       =-5/4

4)-2x= -2×-1/4

       = 1/2

Hence,  The answers are 1/4,5/4,-5/4,1/2

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The length of the rectangular garden will be 13 feet.

Let x be the length of the rectangular garden.

If the length of the garden is to be 5 feet longer than the width, then the expression for the width should be "x - 5".

If the area of the garden will be 104 square feet, then the equation for the area will be:

A = x(x - 5) = 104 square feet

Simplify the equation and solve for the value of x.

x² - 5x - 104 = 0

(x + 8)(x - 13) = 0

x = -8 ; x = 13

(choose the positive value since dimensions should always be positive)

Therefore, the length of the rectangular garden is 13 feet.

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Answer:  

Step-by-step explanation:

4564.  2 75444214///4222.-112

The fully simplified form of the expression is [tex]\frac{3}{2x+12}-\frac{-3}{x-8} +\frac{4}{x+6}[/tex]

A quadratic equation is a type of polynomial equation that has the general form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is an unknown variable. The equation has two solutions, which can be found using the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, where the ± symbol indicates that there are two possible solutions.

Quadratic equations are used to model a variety of real-world phenomena, such as the motion of objects under the influence of gravity, the path of a projectile, and the growth of a population over time. They are also used to describe the parabolic shape of curves and to solve optimization problems, such as finding the maximum or minimum value of a function

We can simplify the expression as follows:

[tex]\frac{3}{2x+12} =\frac{x-15}{x^{2} -2x-48}[/tex]

First, we'll simplify the denominators. To do this, we can factor the quadratic expression x² - 2x - 48:

x² - 2x - 48 = (x - 8)(x + 6)

Now we can rewrite the denominators:

[tex]\frac{3}{2x+12}-\frac{x-15}{(x-8)(x+6)}[/tex]

Next, we'll simplify the fraction in the second term using partial fraction decomposition:

[tex]\frac{x-15}{(x-8)(x+6)} =\frac{A}{x-8}+\frac{B}{x+6}[/tex]

where A and B are constants that we can find by multiplying both sides by (x - 8)(x + 6) and equating the numerators:

x - 15 = A(x + 6) + B(x - 8)

Expanding both sides:

x - 15 = Ax + 6A + Bx - 8B

Comparing coefficients:

-15 = Ax + 6A + Bx - 8B

1 = A + B

8B = Ax + 6A + 15

-6A = -15 - Ax - 8B

-6A = -15 - (A + B)x - 8B

-6A = -15 - x + 7x

-6A = -15 - x + 7x

-6A = -15 + 6x

Solving for A and B, we have:

A = -3

B = 4

So, the second term can be written as:

[tex]\frac{x-15}{(x-8)(x+6)} =\frac{-3}{x-8}+\frac{4}{x+6}[/tex]

Putting everything together, we have:

[tex]\frac{3}{2x+12} -\frac{x-15}{(x-8)(x+6)} =\frac{3}{2x+12}-\frac{-3}{x-8} +\frac{4}{x+6}[/tex]

which is the fully simplified form of the expression.

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The team is predicted to win 56.2% of its games this season.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. The probability can also be expressed as in form of a percentage as we multiply it by 100.

It's the middle of a season, and Bill James has calculated the Pythagorean Winning Percentage (W%) of a team as .562.

To convert, the probability to percentage just multiply by 100 =.562*100

= 56.2%.

Hence The team is predicted to win 56.2% of their games this season.

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To add or subtract mixed numbers with like denominators, follow these steps:

For example, Add: 1 ¾ + 1 ½

Convert to improper fractions:

1 ¾ = 7/4

1 ½ = 3/2 = 6/4

Add the numerators and keep the denominator the same:

7/4 + 3/2 = (7 + 6) / 4 = 13/4

Convert the result back to a mixed number:

13/4 = 3 1/4

So the answer is 3 1/4.

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The value of θ is approximately equal to 0.92729522.

The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.

The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.

If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.

θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).

So, the value of θ is approximately equal to 0.92729522.

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The value of θ is approximately equal to 0.92729522.

The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.

The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.

If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.

θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).

Therefore, the value of θ is approximately equal to 0.92729522.

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The time that Nagma takes to complete five rounds is 0.4 hours or 24 minutes.

Travel time is the total time required to pass a certain length of road.

Given,

Length = 180m

Width = 120 m

Speed = 7.5 km/hr

Time of five rounds?

Steps,

The first step that must be done is to find the travel time for one round

Distance of one round = 2(length + width)

Distance of one round = 2(180 + 120)

Distance of one lap = 3 (300)

Distance of one round = 600 m = 0.6 km

Time needed to reach 5 rounds

Time = 5 (distance : speed)

Time = 5 (0.6 : 7.5)

Time = 0.4 hours = 24 minutes

So, the time needed to complete five rounds is 0.4 hours or 24 minutes.

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Answer:

x=2

Step-by-step explanation:

undefined slope means the line is vertical