The circular area covered by a lawn sprinkler has a 24.25-foot diameter. What is the area of the space covered by the sprinkler? Use 3.14 for π
. Round to the nearest hundredth if necessary.

To find the probability of getting at least 4 fives, we sum up the probabilities of these two cases:

P(at least 4 fives) = P(4 fives and 1 non-five) + P(5 fives)

To calculate the probability of getting at least 4 fives when rolling a fair die 5 times, we need to consider the different possible outcomes.

The probability of rolling a five on a fair die is 1/6, and the probability of not rolling a five is 5/6.

To determine the probability of getting exactly 4 fives and 1 non-five, we use the binomial probability formula:

P(4 fives and 1 non-five) = (5 choose 4) * (1/6)^4 * (5/6)^1

Similarly, for getting exactly 5 fives, we have:

P(5 fives) = (5 choose 5) * (1/6)^5 * (5/6)^0

Rounding the result to the nearest thousandth, we get the probability of getting at least 4 fives when rolling a fair die 5 times.

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1/4 - 1/2 = -1/4. Don't forget to include the negative sign in your answer, which indicates that the result is less than 0.  it's important to find a common denominator so that you can add or subtract them easily.

To subtract unit fractions like 1/4 and 1/2, you need to find a common denominator. A common denominator is a number that both denominators can divide into evenly. In this case, the smallest common denominator is 4, since 4 can be divided evenly by both 4 and 2.

To get both fractions to have a denominator of 4, you need to multiply 1/4 by 1 and 1/2 by 2/2, which equals 2/4.

Now that both fractions have the same denominator, you can subtract the numerators:

1/4 - 2/4 = -1/4


Overall, when working with unit fractions,

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Answer:

87

Step-by-step explanation:

beause

To determine the fair amount the player should win, we need to calculate the probability of drawing a diamond from a standard 52-card deck. There are 13 diamonds in a deck, and 52 total cards, so the probability of drawing a diamond is 13/52, or 1/4. This means that there is a 25% chance of winning the game.
To make the game fair, the expected value of the game must be zero. The expected value is calculated by multiplying the amount won by the probability of winning, and subtracting the amount lost by the probability of losing. In this case, the amount lost is $52, and the probability of losing is 75%, or 3/4.
So, the expected value equation would be:
0 = (amount won)(1/4) - ($52)(3/4)
Solving for the amount won, we get:
Amount won = $208/1 = $208
Therefore, in order for this game to be fair, the player should win $208 when they draw a diamond. This makes the expected value of the game zero, ensuring that it is a fair game for both the player and the house.
Answer more than 100 words: To summarize, the amount the player should win in order for the game to be fair is $208. This calculation is based on the probability of drawing a diamond from a standard 52-card deck, which is 1/4 or 25%. By calculating the expected value of the game, we can determine the amount the player should win in order for the game to be fair. The expected value equation takes into account both the probability of winning and the amount lost when losing. By setting the expected value equal to zero and solving for the amount won, we can determine the fair amount the player should win. This ensures that the game is fair for both the player and the house, as the expected value is zero.
In a fair game, the expected value of the game should be zero, meaning the player neither wins nor loses money on average. To determine the winning amount, let's analyze the probabilities and outcomes of the game.
A standard 52-card deck has 13 diamonds and 39 non-diamond cards. The probability of drawing a diamond is 13/52 or 1/4, and the probability of drawing a non-diamond is 39/52 or 3/4. If the player loses, they lose $52.
Let X be the winning amount if the player draws a diamond. The expected value (EV) is given by:
EV = (probability of winning) * (winning amount) + (probability of losing) * (losing amount)
Since the game is fair, EV = 0. Therefore:
0 = (1/4) * X + (3/4) * (-52)
To solve for X, multiply both sides by 4:
0 = X - 3 * 52
Now, add 3 * 52 to both sides to find the winning amount:
X = 3 * 52
X = $156
In order for this game to be fair, the player should win $156 when they draw a diamond.

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The solution to the equation -7x - 3 = -31 is x = 4.

To solve the equation -7x - 3 = -31, we will isolate the variable x.

Step 1: Begin by moving the constant term to the other side of the equation.

-7x - 3 + 3 = -31 + 3

Simplifying, we get:

-7x = -28

Divide both sides of the equation by -7 to solve for x.

(-7x) / -7 = (-28) / -7

Simplifying, we have:

x = 4

Therefore, the solution to the equation -7x - 3 = -31 is x = 4.

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The amount of wrapping paper that is needed to cover the package is 1625 sq cm.

To determine the amount of wrapping paper that is required to cover the package, we will be determining the surface area of a triangle with the formula: A = 1/2 × b × h.

To find this surface area, we will go around the triangle while considering the bases and heights as follows:

((20 + 5) * 5 /2) * 2 + (20 * 30) + (17 * 30) + (5 * 30) + (8 * 30)

125 + 600 + 510 + 150 + 240

1625 sq cm

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Answer:

the answer is B 6t and t are like terms

Learning statistics is essential for students as it helps them make sense of data and draw meaningful conclusions. It enables students to understand and analyze complex data, make informed decisions, and solve real-world problems.

Explanation:

Statistics is used in many fields of study, including business, economics, psychology, and social sciences. As a student, learning statistics can help you make sense of the vast amounts of data you encounter, whether it's in research papers, surveys, or experiments. Statistics enables you to analyze and interpret data, identify trends and patterns, and draw meaningful conclusions.

This can be useful in making informed decisions, solving problems, and developing new theories. Moreover, knowledge of statistics can also be valuable in your future career, as many professions require an understanding of data analysis and statistical methods. In short, learning statistics is an essential skill that can help you succeed academically and professionally.

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The trigonometric identity 1 + cot⁴θ = cosec⁴θ - 2cot²θ

Trigonometric identities are mathematical equations that contain trigonometric ratios in which one side is equal to the other.

Given the trigonometric identity

1 + cot⁴θ = cosec⁴θ - 2cot²θ, we need to show that the Left hand side L.H.S equals the Right Hand side R.H.S. we proceed as follows.

So, L.H.S = 1 + cot⁴θ

Now using the trigonometric identity

1 + cot²θ = cosec²θ

Making cot²θ subject of the formula, we have that

cot²θ = cosec²θ - 1

So, substituting this into the equation, we have that

1 + cot⁴θ =  1 + (cot²θ)²

= 1 + (cosec²θ - 1)²

Expanding the bracket, we have that

= 1 + cosec⁴θ - 2cosec²θ + 1

=  cosec⁴θ - 2cosec²θ + 1 + 1

=  cosec⁴θ - 2cosec²θ + 2

=  cosec⁴θ + 2 - 2cosec²θ

= cosec⁴θ + 2(1 - cosec²θ)

= cosec⁴θ + 2cot²θ

= R.H.S

Since L.H.S = R.H.S

1 + cot⁴θ = cosec⁴θ - 2cot²θ

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The correct answer is: In a random sample of 144 observations, with a sample proportion of 0.6, the 95% confidence interval for the true population proportion is estimated to be between 0.52 and 0.68.

This means that if we were to repeat this sampling process many times and construct a confidence interval each time, we would expect 95% of those intervals to contain the true population proportion. The other options given are not correct as they do not accurately reflect the information given in the question.

In a random sample of 144 observations, with P = 0.6, the 95% confidence interval for P can be calculated using the following steps:

1. Identify the sample proportion (p) and the sample size (n): p = 0.6 and n = 144.

2. Calculate the standard error (SE) of the sample proportion using the formula: SE = sqrt[(p * (1 - p))/n]. In this case, SE = sqrt[(0.6 * (1 - 0.6))/144] = sqrt[(0.6 * 0.4)/144] = sqrt[0.24/144] = 0.04.

3. Find the critical value (z) for the 95% confidence interval using a z-table or a calculator. For a 95% confidence interval, the critical value is approximately 1.96.

4. Calculate the margin of error (ME) using the formula: ME = z * SE. In this case, ME = 1.96 * 0.04 = 0.0784.

5. Determine the lower and upper bounds of the 95% confidence interval by adding and subtracting the margin of error from the sample proportion: Lower Bound = p - ME = 0.6 - 0.0784 = 0.5216; Upper Bound = p + ME = 0.6 + 0.0784 = 0.6784.

So, the 95% confidence interval for P is approximately 0.52 to 0.68.

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Answer:

Step-by-step explanation:

The distribution of the mean of random samples of size 4 can be approximated by a normal distribution with a mean of 154 Ibs (same as the population means) and a standard deviation of 11.5 Ibs (which is the population standard deviation divided by the square root of the sample size, i.e. 23 Ibs/ sqrt (4)= 11.5 Ibs). This is known as the Central Limit Theorem.

Use an Explicit formula to calculate how much it will cost Jiya to rent the truck for 7 hours .The correct answer is option (d) a7=55+(7-1)10

The rental company charges $55 for the first hour and then $10 per hour after that, we can use an explicit formula to calculate how much it will cost Jiya to rent the truck for 7 hours.

The explicit formula for the total cost of renting the truck for a given number of hours can be written as:

a(n) = c + (n-1)d

where a(n) is the total cost of renting the truck for n hours, c is the cost of the first hour, and d is the additional cost per hour.

Using this formula, we can find the cost of renting the truck for 7 hours:

a(7) = 55 + (7-1)*10

Simplifying the expression in the parentheses, we get:

a(7) = 55 + 6*10

Multiplying 6 by 10, we get:

a(7) = 55 + 60

Adding 55 and 60, we get:

a(7) = 115

Therefore, the explicit formula that describes how much it will cost Jiya to rent the truck for 7 hours is:

a7=55+(7-1)10

Simplifying the expression, we get:

a7 = 55 + 6*10

a7 = 55 + 60

a7 = 115

Therefore, the correct answer is option (d) a7=55+(7-1)10.

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The central angle formed by the Self Help slice is 86.4°.

A circle is formed when you draw a point and connect it from end to end forming a complete revolution.

We have to find the central angle formed by the Self Help slice

One revolution equals 360°.

Therefore, each piece of pie for each type of book is a fraction of one revolution.

The fraction can be determined by dividing the number for a specific type of book to the total number of books.

Specifically, the fraction for the Self Help slice would be 90/375 which is equal to 0.24 or 24%.

Then, 24% of 360 is 86.4.

Therefore, the central angle formed by the Self Help slice is 86.4°.

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There are 375 books sold at Sid's Bookstore. The table below summarizes these books by genre. This info is presented in circle graph. Find the central angle measure for Self Help slice in graph. Mystery 99, romance 81, self help 90, cooking 57, biography 48.

The Fahrenheit temperature of the cup of water, after 4.5 minutes, is given as follows:

155ºF.

The temperature function is defined as follows:

[tex]T(t) = T_a + (T_0 - T_a)e^{-kt}[/tex]

Considering the surrounding and initial temperature, we have that the function is given as follows:

[tex]T(t) = 69 + 135e^{-kt}[/tex]

The temperature after 1.5 minutes is of 185ºF, hence the coefficient k is obtained as follows:

[tex]185 = 69 + 135e^{-1.5k}[/tex]

[tex]e^{-1.5k} = \frac{116}{135}[/tex]

[tex]k = -\frac{\ln{\left(\frac{116}{135}\right)}}{1.5}[/tex]

k = 0.1011.

Hence:

[tex]T(t) = 69 + 135e^{-0.1011t}[/tex]

Hence the temperature after 4.5 minutes is given as follows:

[tex]T(4.5) = 69 + 135e^{-0.1011 \times 4.5}[/tex]

T(4.5) = 155ºF.

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The hotel should overbook enough rooms to maximize revenue without incurring expensive costs due to last-minute cancellations. To determine the optimal number of rooms to overbook, consider the following:

1. The average number of cancellations is 5 with a standard deviation of 3.
2. The average room rate is $80.
3. The cost of accommodating overbooked customers in a nearby hotel is $200.

Using these figures, the hotel can calculate the expected revenue for each room overbooked, while considering the risk of cancellations. The best approach is to use a probabilistic model, such as the normal distribution, to estimate the optimal number of rooms to overbook based on these statistics.

A detailed analysis would require further calculations and simulations, which are beyond the scope of this answer. However, a basic guideline for the hotel would be to overbook only a few rooms (e.g., 1-3) to minimize the risk of incurring the high cost of accommodating customers in nearby hotels while still maximizing the revenue from potential cancellations.

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Answer: I think the answer is A

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

12x + 5 = 65

subtract 5 from both sides

12x + 5 - 5 = 65 - 5

12x = 60

divide by 12

x = 5

Coressponding angles in parallel lines are equal and for u and v to be parallel,

So we have,

[tex]12x + 5 = 65[/tex]

[tex]12x = 65 - 5[/tex]

[tex]12x = 60[/tex]

[tex]x = \frac{60}{12} [/tex]

[tex]x = 5[/tex]

Hence the value of x must be 5° to make the lines u and v parallel

The mean distance thrown is approximately 37.31 feet. the Average distance thrown by the heavy ball.

To find the mean of the distances thrown from the stem-and-leaf plot, we need to add up all the distances and divide by the total number of throws.

From the stem-and-leaf plot, we can see that there are 13 throws in total.

To add up the distances, we can use the key to interpret the plot: for example, the number "31" means that one throw went 3.1 feet. Using this method, we can find the following distances:

20, 22, 25, 31, 33, 34, 41, 41, 45, 50, 56, 67, 71

Adding up these distances, we get a total of 485.

To find the mean, we divide by the total number of throws:

mean = 485/13 ≈ 37.31

Therefore, the mean distance thrown is approximately 37.31 feet.  the average distance thrown by the heavy ball.

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the statement "if you always test whether the number is positive or negative, big endian is more easy to use than little endian" is incorrect.

Endianness refers to the way in which a computer stores data in memory. In big endian, the most significant byte is stored at the smallest address and the least significant byte is stored at the largest address. In little endian, the least significant byte is stored at the smallest address and the most significant byte is stored at the largest address.

The choice between big endian and little endian has no impact on testing whether a number is positive or negative. Both endianness formats can store positive and negative numbers in the same way.

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Answer:option c is the answer

Step-by-step explanation:

The asked probabilities are 1/3, 6/7 and 50/71.

Given that are events we need to find the required probability,

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability (Event) = Favorable Outcomes/Total Outcomes = x/n

There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

The probability is classified into theoretical probability and experimental probability.

so,

Probability = favorable outcomes / total outcomes

1) P(Morgan is a vocalist) = 9/27 = 1/3

2) P(Angela is not a guitarist) = 18/21 = 6/7

3) P(Gina is a vocalist) = 50/71

Hence the probabilities are 1/3, 6/7 and 50/71.

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The measure of the angles m∠1 and m∠2 for the polygon are 72° and 54° respectively.

To calculate the sum of interior angles of a polygon, you can use the following formula:

Sum of interior angles = (n-2) x 180 degrees

Where "n" represents the number of sides (or vertices) of the polygon.

Given the 5 sided polygon;

(5 - 2) × 180 = 540

one interior angle = 540/5 = 108°

m∠2 = 108°/2

m∠2 = 54°

m∠1 = 180 - [2(54°)]

m∠1 = 180 - 108

m∠1 = 72°

Therefore, the measure of the angles m∠1 and m∠2 are 72° for the polygon and 54° respectively.

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The equation which is equivalent to 3x - 12 = -9 is 3(x - 4) { -9

3x - 12 = -9

The equation is divided into two parts; right part and left part

From the left part; find the common factor of 3x and 12 which is 3

So,

3(x - 4) = -9

3x - 12 = -9

Add 12 to both sides

3x = -9 + 12

3x = 3

divide both sides by 3

x = 3/3

x = 1

Hence, the value of x based on the given equation is 2

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The number of children are there in the given scenario are 400.

Given that, the ratio of children to adults on a school trip is initially 10:1.

Here, the given ratio can be written as 10x:1x

5 more children and 5 more adults join the trip so that the ratio is now 9:1

10x+5:1x+5

The new ratio is (10x+5)/(x+5) = 9/1

10x+5=9(x+5)

10x+5=9x+45

10x-9x=45-5

x=40

So, the number of children =10x=400

Therefore, the number of children are there in the given scenario are 400.

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Answer:

A. 72

Step-by-step explanation:

63/x = 87.5/100

x = 6300 divided by 87.5

x = 72

There are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.

For each play date, you have 3 options for the show time.

Since the events are independent and all options are equally likely, you can multiply the number of options together to find the total number of possible outcomes.

Number of possible outcomes

= Number of play dates × Number of show times

= 4 × 3

= 12

Therefore, there are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.

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Therefore, the angle between the biker's line of sight and the trail is changing at a rate of approximately 0.039 radians per second when she is 25 feet away from the tree.

To solve this problem, we need to use trigonometry and calculus. Let's call the angle between the biker's line of sight and the trail θ, and let's call the distance from the traffic cone to the aspen tree x. Then we can use the tangent function to relate θ and x:

tan(θ) = x/15

We can also use the Pythagorean theorem to relate x and the distance d between the biker and the tree:

d^2 = x^2 + 25^2

Taking the derivative of both sides with respect to time t, we get:

2d (dd/dt) = 2x (dx/dt)

Now we can substitute the equation for x in terms of θ and solve for (dθ/dt):

tan(θ) = x/15

sec^2(θ) (dθ/dt) = (1/15) (dx/dt)

(dθ/dt) = (1/15) (dx/dt) sec^2(θ)

We can use the equation for d to solve for x:

x^2 = d^2 - 25^2

2x (dx/dt) = 2d (dd/dt)

(dx/dt) = (d/dd) (sqrt(d^2 - 25^2)) (dd/dt)

(dx/dt) = (d/ sqrt(d^2 - 25^2)) (dd/dt)

Now we can substitute this expression for (dx/dt) into the previous equation and evaluate it when d = 25 and θ = arctan(15/25):

(dθ/dt) = (1/15) [(d/ sqrt(d^2 - 25^2)) (dd/dt)] sec^2(arctan(15/25))

(dθ/dt) = (1/15) [(25/ sqrt(25^2 - 25^2)) (13)] sec^2(arctan(15/25))

(dθ/dt) = (13/375) sec^2(arctan(15/25))

(dθ/dt) ≈ 0.039 radians per second

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Answer:

Measure the distance between those 2 points, A and B. Then when you get your answer, round it to the second number after your decimal. (The hundredth place) It is explained more below:

Step-by-step explanation:

After measuring, you should get a decimal number. With that number, you need to round to the nearest hundredth.

-Meaning you need to check the 2nd number right after the decimal. The second number right after the decimal will be 2 in this example.

I hope this helped. <3