Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 121212 inches. He will make the "X" by stretching red ribbon diagonally from corner to corner.
How many inches of ribbon will Peter need to make the "X"?

To find x, we need to solve the quadratic equation 5x^2 - 100 = 0 using the quadratic formula.

To find x, we need to solve the quadratic equation 5x^2 - 100 = 0 using the quadratic formula. The formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 5, b = 0, and c = -100. Plugging these values into the quadratic formula, we get:

x = (-0 ± √(0^2 - 4 * 5 * -100)) / (2 * 5)

Simplifying further, we have:

x = (√2000) / 10

Therefore, x equals approximately ±14.14.

Answer:

8*6*6

Step-by-step explanation:

vote me

Answer:

11.25 cm2 would be your answer.

The simplified form of i^13 is -i.

The simplified form of i^13 is -i.

To find the simplified form, remember that i^4 = 1, so i^13 = i^(4*3+1) = i^(4*3) * i = (i^4)^3 * i = 1^3 * i = i.

Therefore, the simplified form of i^13 is -i.

The situation can be represented as three inequalities: g + p < 120, g < 45, p > 30, where g is the time spent in the gym and p is the time spent in the pool.

The situation you described can be represented as a system of inequalities. Let's denote gym time as g and pool time as p. Then, the system of inequalities would be the following:

These inequalities represent the constraints on how you can divide your time between the gym and the pool. Any solution to this system would be a pair of numbers (g, p) that satisfy all three inequalities, meaning it's a valid way for you to divide your time.

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The correct system of inequalities is Option 1: x + y < 120 (representing the total time constraint), x < 45 (reflecting the condition of spending less time in the gym), and y > 30 (representing the condition of spending more time in the pool). This corresponds to Option 1 in the given systems of inequalities.

The correct system of inequalities that represents your time allocation between the gym and the pool is Option 1. Let's define x as the time you spend in the gym and y as the time you spend in the pool. According to the given conditions and constraints, the total time, which is the sum of x and y, should be less than 120 minutes (x + y < 120). Furthermore, you want to spend less than 45 minutes in the gym (x < 45) and more than 30 minutes in the pool (y > 30). These three inequalities jointly form a system that accurately represents your situation at the gym and pool.

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The complete question is given below:

You have less than 120 minutes to spend in the gym and in the pool. You want to spend less than 45 minutes in the gym and more than 30 minutes in the pool. Which system represents the situation?

Option 1:

x + y < 120

x < 45

y > 30

Option 2:

x + y = 120

x = 45

y = 30

Option 3:

x + y <= 120

x < 45

y > 30

Option 4:

x + y < 120

x <= 45

y >= 30

Answer:

B

Step-by-step explanation:

TT two tails/no heads

TH one tail/one head

HT

HH two heads/no tails

The number of possible outcomes if two quarters are tossed and the total numbers of heads and tails are counted is 8.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Since there are number of possibility as;

TT two tails/no heads

TH one tail/one head

HTand HH two heads/no tails

Each quarter will come up heads or tails which is 2 possibilities.

Thus for three tosses the number of outcomes is 2 x 2 x 2 = 8.

Learn more about probability here;

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The probability of rolling exactly three 2s in five rolls of a six-sided die is 32.15%, calculated using the binomial probability formula. The correct answer from the provided options is C) 32.15%.

The student is asking about the probability of achieving a specific number of successes in a series of independent events, which is a problem that can be solved using the binomial probability formula. In this case, a success is defined as rolling a 2 on a six-sided die. The probability of rolling a 2 (success) on a single roll is \(\frac{1}{6}\), and the probability of not rolling a 2 (failure) is \(\frac{5}{6}\).

Therefore, the probability of rolling exactly three 2s in five rolls can be calculated by the formula:

\(P(X=k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}\)

where \(n\) is the number of trials, \(k\) is the number of desired successes, and \(p\) is the probability of a single success.

Substituting the values:

\(P(X=3) = \binom{5}{3} \cdot \left(\frac{1}{6}\right)^3 \cdot \left(\frac{5}{6}\right)^{5-3}\)

\(P(X=3) = 10 \cdot \left(\frac{1}{6}\right)^3 \cdot \left(\frac{5}{6}\right)^2\)

\(P(X=3) = 10 \cdot \frac{1}{216} \cdot \frac{25}{36}\)

\(P(X=3) = \frac{250}{7776}\)

\(P(X=3) \approx 0.03215 \text{ or } 3.215\%\)

So the correct answer from the provided options is C) 32.15%.

The chances of rolling exactly three successes when rolling a 6-sided die 5 times, where rolling a 2 is considered a success, is approximately 2.143%.

To find the chances of rolling exactly three successes, we need to use the concept of binomial probability. In this case, the probability of rolling a 2 (success) is 1/6, and the probability of not rolling a 2 (failure) is 5/6. We can use the formula for binomial probability: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success in one trial.

For this problem, n=5 (since the die is rolled 5 times), k=3 (we want exactly three successes), and p=1/6 (probability of rolling a 2). Plugging these values into the formula:

P(X=3) = (5 choose 3) * (1/6)^3 * (5/6)^(5-3)

Simplifying, we get:

P(X=3) = 10 * (1/6)^3 * (5/6)^2 = 10 * (1/216) * (25/36) = 250/11664 ≈ 0.02143 ≈ 2.143%

Answer:

the length of the hypotenuse = 32.45 centimeters

Step-by-step explanation:

A right triangle has legs that are 18 centimeters and 27 centimeters long

In a right angle triangle , to find hypotenuse we use Pythagorean theorem

[tex]c^2= a^2+b^2[/tex]

where a  and b are the length of two legs

Given a= 18  and b = 27

Lets find out C , plug in all the value in the formula

[tex]c^2= 18^2+27^2[/tex]

[tex]c^2=324 +729= 1053[/tex]

c^2 = 1053

now take square root on both sides

c= 32.45

So the length of the hypotenuse = 32.45 centimeters

To find the shortest distance from Robert's home to his office, we use the Pythagorean theorem with the distances traveled north and east to calculate the length of the hypotenuse, which is approximately 7.2 kilometers.

Robert leaves his home and drives 6 km due north and then 4 km due east. To determine the shortest distance from Robert's home to his office, we can use the Pythagorean theorem. This scenario forms a right-angled triangle where the two sides are the north-bound and east-bound legs of his journey, and the hypotenuse is the shortest distance.

Step 1: Label the lengths of the two sides adjacent to the right angle as 'a' and 'b', where 'a' is the 6 km north-bound leg and 'b' is the 4 km east-bound leg.

Step 2: Apply the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides:

c² = a² + b²

Step 3: Substitute the known values into the theorem:

c² = 6² + 4²

Step 4: Calculate the squares of the sides and sum them:

c² = 36 + 16

Step 5: Sum the squares gives us:

c² = 52

Step 6: Take the square root of both sides to find 'c':

c = √52

Step 7: Calculate the square root which approximately equals:

c = 7.2 km

Therefore, the shortest distance from Robert's home to his office is approximately 7.2 kilometers.

Given that csc θ = 14 and cot θ < 0, we find that sin θ = 1/14 and cos θ must be negative. We use the identity sin² θ + cos² θ = 1 to solve for the exact value of cos θ, selecting the negative solution. The remaining trigonometric functions are then found using these values.

Given that the cosecant of theta (csc θ) is 14 and cotangent of theta (cot θ) is less than zero, we can find the other trigonometric values. We begin by recalling that cosecant is the reciprocal of the sine function, so sin θ = 1/14. Subsequently, we are told cot θ < 0, which means either the cosine or the sine (or both) must be negative.

Since cot θ is negative and we know sin θ is positive (since csc θ is positive), then we can conclude that cos θ must be negative. However, the exact value of cos θ is not readily identifiable from these properties alone.

To find the trigonometric value of cos θ, we can utilize the identity sin² θ + cos² θ = 1. Substituting our known sin θ value, we solve for cos θ. This gives us two possible solutions for cos θ, either positive or negative. As previously deduced, we select the negative solution for cos θ. The remaining trigonometric functions can then be found given these values:

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Answer:

D). Y'= [tex]4x^{5}-12x^{4}+6x[/tex] and y'= [tex]5x^{3}-2x[/tex]

Step-by-step explanation:

We are given the equation [tex]4x^{5}-12x^{4}+6x=5x^{3}-2x[/tex].

On simplifying this equation, we get [tex]4x^{5}-12x^{4}-5x^{3}+8x=0[/tex]

i.e. Let, Y'= [tex]4x^{5}-12x^{4}+6x[/tex] and y'= [tex]5x^{3}-2x[/tex]

Now, according to the options,

A) Y =  [tex]-4x^{5}+12x^{4}-6x[/tex] = -Y' , that means the graph will be inverse of the required graph.

B) As the coefficient of 'x' in our given equation and the equation of option B are different, both will have different graphs.

C) As y =  [tex]-5x^{3}+2x[/tex] = -y', this means that the graph will be inverse of the required graph.

Hence, all above options are discarded and so option D is correct.

Final answer:

Among the options provided, only D.) 97 is a prime number because it only has two divisors: 1 and itself. All other options have more than two divisors and thus are not prime.

Explanation:

To determine which number is prime, we must recall that a prime number is a number that has only two distinct positive divisors: 1 and itself. Now, let's evaluate the options given:

A.) 49 is 7 times 7, so this is not a prime number.

B.) 27 is 3 times 9, hence this is not a prime number either.

C.) 14 is 2 times 7, which means it is not a prime number.

D.) 97 does not have any divisors other than 1 and itself, so it is a prime number.

So, the correct answer is D.) 97, since it fulfills the conditions for being a prime number.

By definition we have to:

Natural resources are all the material goods and services provided by nature without alteration by human beings; and that they are valuable for human societies because they contribute directly to their well-being and development (raw materials, minerals, food) or indirectly (essential ecological services for the continuity of life on the planet).

Therefore, the depletion of natural resources is considered an environmental cost because without these resources, life on planet Earth is difficult as we know it today.

Answer:

C. Resource depletion

Answer with explanation:

In the given right triangle

 [tex]\sin 60^{\circ}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\ \frac{\sqrt{3}}{2}=\frac{\text{Perpendicular}}{2\sqrt{3}}\\\\ \text{Perpendicular}}=2\sqrt{3} \times\frac{\sqrt{3}}{2}\\\\\text{Perpendicular}}=\sqrt{3} \times\sqrt{3} \\\\\text{Perpendicular}}=3[/tex]

→Side opposite to 60° angle = 3 units

Option C : 3 Units

Answer:  The other endpoint of the segment is (-1, -11).

Step-by-step explanation:  Given that the midpoint of a line segment is (6, -6) and one endpoint is (13, -1).

We are to find the co-ordinates of the other endpoint.

Let (a, b) be the co-ordinates of the other end-point.

Then, according to the given information, we have

[tex]\left(\dfrac{a+13}{2},\dfrac{b+(-1)}{2}\right)=(6,-6)\\\\\\\Rightarrow \left(\dfrac{a+13}{2},\dfrac{b-1}{2}\right)=(6,-6).[/tex]

Equating the x and y co-ordinates on both sides of the above, we get

[tex]\dfrac{a+13}{2}=6\\\\\\\Rightarrow a+13=12\\\\\Rightarrow a=12-13\\\\\Rightarrow a=-1[/tex]

and

[tex]\dfrac{b-1}{2}=-6\\\\\\\Rightarrow b-1=-12\\\\\Rightarrow b=-12+1\\\\\Righatrrow b=-11.[/tex]

Thus, the other endpoint of the segment is (-1, -11).