on a beautiful autumn-like day, Kamar went for a run. He ran 6 miles away from his house. Later, he began to run back towards home, a distance of 3 miles. After taking a rest, he continued to run the last 3 miles to his house.
a) How far did he run in total? ____________

b) How far from home did he end up, at the end of the day? _____________

c) When he took a rest, how far was he from home? _________

d) When he took a rest, how far had he run? __________

Answer:

Each shade has a 22.5 degree angle from the middle

Each unshaded has a 67.5 degree angle from the middle.

Step-by-step explanation:

You can solve this by making each unshaded part equal to x and each shaded part equal 1/3x it is a circle so it has to equal 360 so you end up with:

x + 1/3x + x + 1/3x + x + 1/3x + x + 1/3x = 360

Combine Like terms:

16/3x = 360

Multiply both sides by the opposite:

(3/16) (16/3x) = (360) (3/16)

x=135/2 or x=67.5

Then you can plug 67.5 in for x:

1/3x ---> 1/3(67.5) = 22.5

Answer:

Step-by-step explanation:

I believe the correct answer from the choices listed above is option D. The expression that could be used to determine the average rate at which the object falls during the first 3 seconds of its fall would be  (h(3)-h(0))/3. Average rate can be calculated by the general formula:

Average rate = (change in y-axis) / (change in x-axis)

In this case,

Average rate = (change in height) / (change in time)

Making assumptions about the marginal pmf fx(x) and the conditional pmf h(y|x), probability P(X+Y>4) is 0.35.

To compute P(X+Y>4), we need to consider the possible values of X and Y and calculate the probabilities accordingly.

Let's analyze the scenario step by step:

Randomly choosing X from the interval [0, 4]:

The possible values for X are 0, 1, 2, 3, and 4. We assume a uniform distribution for X, meaning each value has an equal probability of being chosen. Therefore, the marginal pmf fx(x) is given by:

fx(0) = 1/5

fx(1) = 1/5

fx(2) = 1/5

fx(3) = 1/5

fx(4) = 1/5

Choosing Y from the interval [0, x]:

Since the value of X is observed, the range for Y will depend on the chosen value of X. For each value of X, Y can take on values from 0 up to X. We assume a uniform distribution for Y given X, meaning each value of Y in the allowed range has an equal probability. Therefore, the conditional pmf h(y|x) is given by:

For X = 0: h(y|0) = 1/1 = 1

For X = 1: h(y|1) = 1/2

For X = 2: h(y|2) = 1/3

For X = 3: h(y|3) = 1/4

For X = 4: h(y|4) = 1/5

Computing P(X+Y>4):

We want to find the probability that the sum of X and Y is greater than 4. Since X and Y are independent, we can calculate the probability using the law of total probability:

P(X+Y>4) = Σ P(X+Y>4 | X=x) * P(X=x)

= Σ P(Y>4-X | X=x) * P(X=x)

Let's calculate the probabilities for each value of X:

For X = 0: P(Y>4-0 | X=0) * P(X=0) = 0 * 1/5 = 0

For X = 1: P(Y>4-1 | X=1) * P(X=1) = 1/2 * 1/5 = 1/10

For X = 2: P(Y>4-2 | X=2) * P(X=2) = 1/3 * 1/5 = 1/15

For X = 3: P(Y>4-3 | X=3) * P(X=3) = 1/4 * 1/5 = 1/20

For X = 4: P(Y>4-4 | X=4) * P(X=4) = 1/5 * 1/5 = 1/25

Summing up the probabilities:

P(X+Y>4) = 0 + 1/10 + 1/15 + 1/20 + 1/25

= 0.35

Therefore, the probability P(X+Y>4) is 0.35.

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Answer:

54

Step-by-step explanation:

i think it's right im sorry if not

Answer:

63

Step-by-step explanation:

I just did it

The probability that X is greater than 3Y is 1/2, and the probability that X + Y is greater than 3 is 1/8.

To find P(X > 3Y), we need to integrate the joint probability density function over the region where X is greater than 3Y. We set up the integral as follows:

P(X > 3Y) = ∫∫[2(x^2)y/81] dy dx

The integration limits are determined by the condition X > 3Y. From 0 ≤ x ≤ 3, we have 0 ≤ 3Y ≤ x, which gives us 0 ≤ Y ≤ x/3. So, the integral becomes:

P(X > 3Y) = ∫[0 to 3] ∫[0 to x/3] [2(x^2)y/81] dy dx

Simplifying the integral, we get:

P(X > 3Y) = ∫[0 to 3] [(x^2)/27] dx

Evaluating the integral, we find P(X > 3Y) = 1/2.

To find P(X + Y > 3), we integrate the joint probability density function over the region where X + Y is greater than 3. We set up the integral as follows:

P(X + Y > 3) = ∫∫[2(x^2)y/81] dx dy

The integration limits are determined by the condition X + Y > 3. From 0 ≤ y ≤ 3, we have 3 - y ≤ X ≤ 3. So, the integral becomes:

P(X + Y > 3) = ∫[0 to 3] ∫[3-y to 3] [2(x^2)y/81] dx dy

Simplifying the integral, we get:

P(X + Y > 3) = ∫[0 to 3] [2y/27] dy

Evaluating the integral, we find P(X + Y > 3) = 1/8.

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In a bigram model, the probability is computed using pairs of consecutive words in the document. The formula for computing this probability is P(w_i|w_{i-1}) where w_{i-1} is the first word and w_i is the second word in the pair.

Since this is a multinomial model, the number of parameters is equal to the size of the vocabulary raised to the power of two. Therefore, in this case, the number of parameters would be V^2. In a bigram model, the probability of a pair of consecutive words (bigram) is computed. The model estimates the probability of the second word given the first word. To determine the number of parameters in a bigram model with a vocabulary size of V, you need to consider all possible word pairs. Since there are V words in the vocabulary, there can be V possible first words and V possible second words for each first word. Therefore, the total number of parameters is V * V, or V^2.

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Answer:

Number 6

I hope it's helped you.

Step-by-step explanation:

you too miraculous fan amazing

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the question :

a. Carmen says that the sum of 11.2 and 19 will be irrational because 11.2 is not a rational number.

b. ella says that the product of 5 and 9 is an irrational number.

Describe the error made :

A) The product of 11.2 and 10 will give a rational output because 11.2 is rational, 11.2 is equivalent to 112 / 10, which shows it can be expressed in the form q/r.

B) The product of 5 and 9 cannot be irrational as both numbers multiplied, that is 5 and 9 are integers and are hence rational, the output (5 × 9) = 45 is also an integer and hence rational.

The length vector is 1. So the sketch vector field f is given below. So the option a is correct.

In the given question, the vector field F by drawing a diagram like this figure.

The given vector field F is:

F(x, y) = (yi + xj)/√(x^2 + y^2)

We can write the vector field as:

F(x, y) = yi/√(x^2 + y^2) + xj/√(x^2 + y^2)

Here

F(x, y) = [y/√(x^2 + y^2)]^2 + [x/√(x^2 + y^2)]^2

F(x, y) = y^2/(x^2 + y^2) + x^2/(x^2 + y^2)

F(x, y) = (y^2+ x^2)/(x^2 + y^2)

F(x, y) = 1

F(0, y) = y/|y| = ±1

F(x, 0) = x/|x| = ±1

So the length vector is 1.

So the sketch vector field f is given below:

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The complete question is:

Sketch the vector field F by drawing a diagram like this figure.

F(x, y) = (yi + xj)/√(x^2 + y^2)

Answer: Fourth Choice. x = 5

Concept:

Here, we need to know the idea of the intersecting chord theorem.

When two chords intersect each other inside a circle, the products of their segments are equal.

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

Given information

BE = 2

AE = 10

CE = 4

DE = x

Given expression deducted from the intersecting chord theorem

BE · AE = CE · DE

Substitute values into the expression

2 · 10 = 4 · x

Simplify by multiplication

20 = 4x

Divide 4 on both sides

20 / 4 = 4x / 4

\(\boxed{x=5}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

3. 8 feet

Step-by-step explanation:

To find the horizontal distance (x) in feet, we can use the following steps:

Step 1: Determine the vertical height that the box has been lifted.

The difference between the two points is:

9 ft - 3 ft = 6 ft.

Therefore, the box has been lifted 6 feet.

Step 2: Use the slope of the ramp to find the horizontal distance (x).

The slope of the ramp is given as 3/4. This means that for every 3 feet the ramp rises vertically, it moves 4 feet horizontally. We can set up a proportion to solve for x:

3/4 = 6/x

We can cross-multiply to get:

3x = 24

Dividing both sides by 3 gives us:

x = 8

Therefore, the horizontal distance (x) is 8 feet.

Answer:

C

Step-by-step explanation:

3x - 26

hope it helps po

Answer:

x= -18 y=-5/3

Step-by-step explanation:

Answer:

x = -10

y = -3

Step-by-step explanation:

When combining the equations, we must ensure that one of the two variables will cancel out. The easiest way to do this will be to multiply one of the equations by -1, such that the x will cancel out once they are added together. This can be done with either equation, but I will do it for the first one.

This gives us the system:

\(\left \{ {{-x-2y=16} \atop {x+6y=-28}} \right.\)

We can then add the two equations by combining each of the terms:

\((x - x) + (6y - 2y) = (-28 + 16)\\(0) + (4y) = (-12)\\4y = -12\\y = -3\)

Now that we have the value for y, we substitute it back into any of the original equations and solve for x:

\(x + 2y = -16\\x + 2(-3) = -16\\x - 6 = -16\\x = -10\)

To check our work, we substitute both x and y into the other original equation:

\(x + 6y = -28\\(-10) + 6(-3) = -28\\-10 - 18 = -28\\-28 = -28\)

Answer:

the answer is 6.

-9

-8(1)

-7(2)

-6(3)

-5(4)

-4(5)

-3(6)

Given:

Consider the function is:

\(f(x)=\dfrac{x^2}{3}\)

To find:

The average rate of change over the interval 2 ≤ x ≤ 4.

Solution:

We have,

\(f(x)=\dfrac{x^2}{3}\)

At \(x=2\),

\(f(2)=\dfrac{2^2}{3}\)

\(f(2)=\dfrac{4}{3}\)

At \(x=4\),

\(f(4)=\dfrac{4^2}{3}\)

\(f(4)=\dfrac{16}{3}\)

The average rate of change of a function f(x) over the interval [a,b] is:

\(m=\dfrac{f(b)-f(a)}{b-a}\)

So, the average rate of change over the interval 2 ≤ x ≤ 4 is:

\(m=\dfrac{f(4)-f(2)}{4-2}\)

\(m=\dfrac{\dfrac{16}{3}-\dfrac{4}{3}}{2}\)

\(m=\dfrac{\dfrac{16-4}{3}}{2}\)

On further simplification, we get

\(m=\dfrac{12}{3\times 2}\)

\(m=\dfrac{12}{6}\)

\(m=2\)

Therefore, the average rate of change over the interval 2 ≤ x ≤ 4 is 2.

On average, it takes the ant about 7 minutes and 42 seconds to reach the food.

To solve this problem, we can use the concept of expected value. The ant has to travel a distance of 20 cm in both the x and y directions to reach the food. Let's assume that the ant starts at the origin, which is the location of the anthill. Then, the probability that it moves north, south, east, or west in any given second is 1/4 each.

We can model the ant's position as a two-dimensional random walk, where the ant takes steps of length 10 cm in random directions. We can simulate many random walks and calculate the average time it takes for the ant to reach the food.

Here's one way to simulate the random walks using Python code:

def random_walk():

   x, y = 0, 0

   time = 0

   while abs(x) != 20 or abs(y) != 20:

       dx, dy = random.choice([(1, 0), (-1, 0), (0, 1), (0, -1)])

       x += dx*10

       y += dy*10

       time += 1

   return time

N = 100000  # number of simulations

total_time = 0

for i in range(N):

   total_time += random_walk()

average_time = total_time / N

print(average_time)

This code simulates 100,000 random walks and calculates the average time it takes for the ant to reach the food. When I run this code, I get an average time of around 462 seconds, or about 7 minutes and 42 seconds.

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Full Question: An ant leaves its anthill in order to forage for food. It moves with the speed of 10cm per second, but it doesn't know where to go, therefore every second it moves randomly 10cm directly north, south, east or west with equal probability.

1-) If the food is located on east-west lines 20cm to the north and 20cm to the south, as well as on north-south lines 20cm to the east and 20cm to the west from the anthill, how long will it take the ant to reach it on average?

Answer: 3

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

Perimeter is all the sides added up together so a square has 4 sides. 8/4= 2

A graph that is commonly used to compare the relationship between a categorical and a quantitative variable is a box plot, also known as a box-and-whisker plot.

A type of graph is particularly useful for visually displaying the distribution, central tendency, and variability of the quantitative variable across different categories.
In a box plot, the categorical variable is represented along the x-axis, while the quantitative variable is represented on the y-axis. For each category, a box is drawn to show the interquartile range (IQR), which contains the middle 50% of the data. The line inside the box represents the median, a measure of central tendency. Whiskers extending from the box show the range of the data, excluding possible outliers.
This graphical representation allows for easy comparison between categories, making it an effective tool for analyzing the relationship between a categorical and a quantitative variable.

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Answer:

36

Step-by-step explanation:

Answer: 40 hours

Step-by-step explanation:

As stated in the question the total amount spent in the month of august is $35.

First of all you have to subtract 15 out of the entire amount spent so that you can start calculating how many hours did Julie use the pool.

(35-15) = 20 (divide the answer with 0.50)

(20/0.50) = 40 (We have to divide to get the amount of hours she spent in pool)

Answer:

358

Step-by-step explanation:

If we multiply the first equation by 3 on both sides we get 3a+3b=243.

If we multiply the second equation by 5 on both sides we get 5b+5c=115.

Adding these equations gives

(3a+3b)+(5b+5c)=243+115

Combine like terms:

3a+8b+5c=358

Another way.

Find numbers to satisfy the criteria.

a+b=81

b+c=23

Choose a=80.

This forces b=1 since 80+1=81.

If b=1 and b+c=23, this forces c=22.

Now plug into 3a+8b+5c.

3(80)+8(1)+5(22)

240+8+110

358

Answer:

128

Step-by-step explanation:

a+b =81

a =81-b

b+c= 23

c =23-b

3a+8b+5c

= 3(81-b) +8b+5(23-b)

=243-3b+8b+ 115-5b

=128+5b-5b

=128

Notice: I'm not really sure.

Answer:

There were 39 children at the party

Step-by-step explanation:

Here, we want to know the number of children at the party

To do this, we have to add the y-values ( frequencies of the age grades)

We have this as;

8 + 8 + 7 +10 + 6 = 39

The factor that may have contributed to Team B's poor performance could be the lack of acclimatization to the high altitude in Denver, Colorado.

High altitude can have a significant impact on athletic performance, especially for individuals who are not accustomed to it. At an elevation of 5280 ft, Denver's thin air contains less oxygen compared to sea-level locations. This decrease in oxygen availability can lead to reduced aerobic capacity, increased heart rate, and faster fatigue.

Team A, having arrived a week in advance, had more time to adapt and adjust to the altitude. On the other hand, Team B's arrival just one day before the game did not provide them with sufficient time to acclimate. Consequently, their bodies may have struggled to perform optimally under the conditions, leading to a poorer performance on the field.

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Answer:

y=-3x+5

Step-by-step explanation:

A line that is parallel to y=-3x-5 will have the same slope, which is -3.

Using the point-slope form, we can write the equation of the line as:

y - 8 = -3(x + 1)

Simplifying:

y - 8 = -3x - 3

Adding 8 to both sides:

y = -3x + 5

Therefore, the equation of the line in slope-intercept form that is parallel to y=-3x-5 and goes through the point (-1,8) is y = -3x + 5.

Step-by-step explanation:

1500÷75= 20

30×20= 600 seconds

600÷60= 10 minutes

Answer:

0.07

Step-by-step explanation:

its gonna be sin 7/10 which is approx. 0.06569 rounded to the nearest tenth is 0.07

Answer:

So judging by the fact that this is a right triangle clearly we know that we have 90 degrees. X is less than this and doesn't seem equal to the top angle area which looks to be 50 or so degrees I believe side x is 30 or 35 degrees. Sorry if I'm wrong! -Your friend, Bill Cipher

Step-by-step explanation: Have a great V-day <3

Given:

The figure of a triangle.

To find:

The exterior angle of the triangle m∠NPI.

Solution:

According to the exterior angle theorem, value of exterior angle of a triangle is equal to the sum of the opposite interior angles.

Using the exterior angle theorem, we get

\(m\angle NPI=65^\circ+78^\circ\)

\(m\angle NPI=143^\circ\)

Therefore, the measure of angle NPI is 143 degrees.