Special angles type 1

The distance between the fountain and the playground is approximately 10.8 yards.

To find the distance between the fountain and the playground, we can use the Pythagorean theorem.

Given:

Coordinates of the center of the park: (0, 0)

Fountain is 4 yards north of the center: (0, 4)

Playground is 10 yards east of the center: (10, 0)

Let's consider the distance between the fountain and the playground as the hypotenuse of a right triangle formed by the fountain, playground, and the center of the park.

Using the Pythagorean theorem, the distance between the fountain and the playground (hypotenuse) can be calculated as follows:

Distance^2 = (Difference in x-coordinates)^2 + (Difference in y-coordinates)^2

Difference in x-coordinates = 10 - 0 = 10 yards

Difference in y-coordinates = 4 - 0 = 4 yards

Distance^2 = (10)^2 + (4)^2

Distance^2 = 100 + 16

Distance^2 = 116

Taking the square root of both sides to find the distance:

Distance = sqrt(116)

Distance ≈ 10.8 yards (rounded to the nearest tenth)

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To get the minimum value of f(x), we need to get the critical points of the function.

First, we need to set f'(x) equal to zero: e^-xcos(x^2) = 0
The exponential term e^-x can never be zero, so we can ignore it. This means that cos(x^2) = 0.
The solutions to this equation are x = sqrt((2n+1)pi/2) or x = sqrt(npi), where n is any integer. However, we are only interested in the solutions that lie between -1 and 1, since that is the domain of the function.
The only solution in this range is x = sqrt(pi/2), which is approximately 1.2533.
Next, we need to check whether this critical point is a minimum or a maximum. To do this, we can use the second derivative test. f''(x) = -e^-x(cos(x^2) + 2x^2sin(x^2))
At x = sqrt(pi/2), f''(x) is negative, which means that the critical point is a local maximum. Since there are no other critical points in the domain of the function, this is also the global maximum.
Therefore, there is no minimum value of f(x) for -1

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There are 120 different ways can the letters of the word words be rearranged to form a five-letter code word.

The number of different ways that the letters of the word "words" can be rearranged to form a five-letter code word can be found using the formula for permutations.

The formula for permutations is: n! / (n - r)!, where n is the number of items and r is the number of items chosen.

In this case, n = 5 (the number of letters in the word "words") and r = 5 (the number of letters chosen to form a code word).

So, the formula becomes: 5! / (5 - 5)! = 5! / 0! = 5! / 1 = 5! = 5 x 4 x 3 x 2 x 1 = 120

Therefore, there are 120 different ways that the letters of the word "words" can be rearranged to form a five-letter code word.

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Step-by-step explanation:

9. f(x) is x² so -4² will give you 16 under the f(x)

-4= 16

-2= 4

0= 0

1= 1

6 = 36

10. f(x) is x² -4 therefore f(x) is (-3)² -4= 5

-3= 5

-1= -3

0= -4

2= 0

5= 21

Answer:

k = -3.5

Step-by-step explanation:

6k ÷ 7 = -3

Multiply 7 to both sides

6k = -21

Divide both sides by 6

6k/6 = -21/6

k = -3.5

To check if the answer is correct or not, you can always plug in -3.5 for k in the equation.

6(-3.5) ÷ 7 = -3

-21 ÷ 7 = -3

-3 = -3

-3 equals -3 so it is correct that k = -3.5

Answer:

The value of k is 46°.

Step-by-step explanation:

Given that when 2 angles add up together, they will form 75°.

So in order to find the value of k, you have to subtract 29° from 75° :

\(k + 29 = 75\)

\(k = 75 - 29\)

\(k = 46\)

Answer:

46 degrees.

Step-by-step explanation:

The whole angle is 75 degrees. So you subtract the given value with the total angle. 75-29=46 degrees.

The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = \(^{52} C_{2}\)

And, the total number of ways of  getting exactly one face cards

= \(^{12} C_{1} \times ^{40} C_{1}\)  + \(^{40} C_{1} \times ^{12} C_{1}\)

= 2\(^{40} C_{1} \times ^{12} C_{1}\)

Therefore, the probability of getting exactly one face card

= \(\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }\)

\(= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }\)

\(= \frac{2(40\times 12)}{26\times 51}\)

\(=\frac{2\times 480}{1326}\)

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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Named constants are used rather than numbers for token codes because they make the code more readable and easier to understand.

Constants are also used to avoid any errors that may occur if a number is mistyped. By using named constants, it is easier to update the value of the constant if it needs to be changed in the future. Additionally, using named constants can help prevent mistakes, such as accidentally using the wrong number in a calculation. Overall, named constants provide a more organized and efficient way of coding.

For example, consider the following code:

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Answer:

1200

Step-by-step explanation:

15/18 * 1000/x

x = 1200

Answer:

1200 minute / 20 hour

Step-by-step explanation:

\(1000 \times 18 = 18000\)

\(18000 \div 15 = 1200\)

Answer:

the answer is a

Answer:

Density (ρ) = 20000 kilogram/cubic meter

Step-by-step explanation:

Answer:

5 is added to the product of 4 and 3

Answer:

Slope is -2/3

y-intercept is 8

Step-by-step explanation:

Y = mx + b

m = slope

b = y-intercept

Hope this helps. Pls give brainliest.

Answer:

b  11-2y

Step-by-step explanation:

Answer:

She would have woken up at 6:20 AM

Step-by-step explanation:

Answer:

6:20am

Step-by-step explanation:

Hope this helps!

Answer:

P= RS. 9000

R=7.6%

T= 9 months

Simple Interest (SI}=?

By using formula,

SI= PTR/100

= 9000* 7.6* 9/ 100* 12

= 615600/1200

= 513

The integral. 1 [*+1590 Joe (x15 + 15*)dx is  154/3.

Based on the information provided, I assume you want to evaluate the integral of a given function. Let me rewrite the function in a more standard format:

∫(x^15 + 15x) dx

Now, let's evaluate the integral step by step:

1. Identify the function within the integral: f(x) = x^15 + 15x

2. Apply the power rule for integration, which states that ∫x^n dx = (x^(n+1))/(n+1) + C, where n is a constant and C is the constant of integration.

3. Using the power rule for the first term: ∫x^15 dx = (x^(15+1))/(15+1) = (x^16)/16

4. Using the power rule for the second term: ∫15x dx = 15∫x dx = 15(x^2)/2

5. Combine both terms and add the constant of integration, C: (x^16)/16 + (15x^2)/2 + C

So, the evaluated integral of the given function is:
Putting these together, we have:

∫[1,5] (x^2 + 15) dx = [(1/3)x^3 + 15x] evaluated from x=1 to x=5

Plugging in these values, we get:

[(1/3)(5^3) + 15(5)] - [(1/3)(1^3) + 15(1)]

Simplifying, we get:

(125/3 + 75) - (1/3 + 15)

= (200/3) - (46/3)

= 154/3
= (x^16)/16 + (15x^2)/2 + C

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Answer:

Three or more points that lie on the same line are collinear points .

Step-by-step explanation:

The gravitational potential energy of the vacationers will decrease as they approach the end of the pier.

As the vacationers approach the end of the pier, their gravitational potential energy will decrease.

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It depends on the height of the object and the acceleration due to gravity.

In this scenario, as the vacationers walk out on the horizontal pier, their height above the ground remains constant. Since the height does not change, the gravitational potential energy also remains constant.

However, as they approach the end of the pier, their distance from the center of the Earth decreases. As a result, the gravitational potential energy decreases because it is directly proportional to the distance from the center of the Earth.

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Step-by-step explanation:

34666(8684x:#68095732)

The predicted gain (or loss) from a single trial is 53 cents per game on average.

A roulette wheel has the number 1 through 36, as well as 0 and 00. If you wager $1 that an odd number would show up, you will win or lose $1 depending on whether or not that occurrence occurs. If random variable X represents your net benefit, X=1 with probability 18/38 and X=-1 with probability 20/38.

E(X) = 1(18/38) – 1 (20/38) = -$.053

On average, the casino wins  5 cents for each game.

If the stakes are raised, the casino makes even more money:

E(X) = 10(18/38) – 10 (20/38) = -$.53

If the cost is $10 for each game, the casino wins an averaged of 53 cents per game. If 10,000 games are played in a single night, that's a cool $5300.

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The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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Answer:

Given that the garden is a right triangle with base 25m start and height 30 m The length of the hypothenus can be achieved by using pythagorean theorem. Please find the attached file for the diagram. I made a large unit for the sake of clarity.

Answer:

6.0 on the left side 5.0 at the bottom 7.8 on the right side

Step-by-step explanation:

It could also discuss the importance of conducting a test drive and negotiating the price based on any issues found during the inspection.

Given that the 2014 used Honda Accord Sedan LX has 143k miles and costs $12k, the asking price is reasonable.

However, whether or not it is a scam depends on the condition of the car.

If the car is in good condition with no major mechanical issues,

then the price is reasonable for its age and mileage.In terms of how long the car would last, it depends on several factors such as how well the car was maintained and how it was driven.

With proper maintenance, the car could last for several more years and miles. It is recommended to have a trusted mechanic inspect the car before making a purchase to ensure that it is in good condition.

A 250-word response may include more details about the factors to consider when purchasing a used car, such as the car's history, the availability of spare parts, and the reliability of the manufacturer.

It could also discuss the importance of conducting a test drive and negotiating the price based on any issues found during the inspection.

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Answer:

the watch is Rs 175

the radio is Rs 325

Step-by-step explanation:

x = price of the watch

y = price of the radio

x+y = 500

x + 150 = y

=>

x + (x+150) = 500

2x + 150 = 500

2x = 350

x = 175

=>

y = 175 + 150 = 325

The geometric mean return of the given data set is 0.02.

The geometric mean return measures the compound rate of return over a period of time. It is calculated by taking the product of all the returns and then taking the nth root of the product, where n is the number of returns.

Formula: GMR = ((1+r1)(1+r2)…(1+rn))^1/n – 1

In this case, the data set is as follows:

r1 = 0.05

r2 = 0.03

r3 = -0.02

Using the formula above, the geometric mean return is calculated as:

GMR = ((1+0.05)(1+0.03)(1-0.02))^1/3 - 1

GMR = ((1.05)(1.03)(0.98))^1/3 - 1

GMR = (1.1394)^1/3 - 1

GMR = 0.0204

Therefore, the geometric mean return of the given data set is 0.02.

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Answer:

7r² - 6r + 9

Step-by-step explanation:

Simply combine like terms to find our final polynomial:

8r² - 7r - 9 - r² + r

7r² - 6r + 9

Answer:

7r^2-6r-9

Step-by-step explanation:

8r^2-7r-9-r^2+r

(8r^2-r^2)+(-7r+r)-9

bring to standard form

7r^2-6r-9

Answer:

hello some parts of your question is missing attached below is the missing part

answer: the sum Given it can seen that according to the closure property of Rational numbers  the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x

Step-by-step explanation:

using the closure property and based on the sum given :

From the sum Given it can seen that according to the closure property of Rational numbers  the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x

I've seen a few comments about the answer so the answer the person above me answered is:

"The sum given can seen according to the closure property of rational numbers. The addition of two rational numbers will sum up to a rational number, provided that the rational numbers are ≠ 0 and a set of rational number is closed under the closures property rule, in other words: x + y = y + x."

Answer:

The 3rd option

Step-by-step explanation:

The pattern is every 2 hours is $15 so 4 hours would be equal to $30

Since 4 hours would equal 30 and we need 12 hours multiplying both numbers by 3 would get you the answer

4x3=12

30x3=90

Making it equal