On his trip to meet Clare, Kiran brought his dog with him. At the same time Kiran
and Clare started walking, the dog started running 6 miles per hour. When it got to
Clare it turned around and ran back to Kiran. When it got to Kiran, it turned around
and ran back to Clare, and continued running in this fashion until Kiran and Clare
met. How far did the dog run?

The probability that the student selected is 5/8.

According to the question,

We have the following information:

A class consists of 30 women and 18 men.

Now, total students in the class = Number of women + number of men

Total students = 30+18

Total students = 48

Now, the probability that the student is a woman:

Probability of an event = Number of women/total number of students

30/48

(More to know: probability of an event can not be greater than 1.)

Now, converting this into the simplest form by dividing both the numerator and denominator by 6:

5/8

Hence, the probability that the student selected is 5/8.

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Answer:

4/7

Step-by-step explanation:

(8-4)/(10-3) = 4/7

parallel = same slope

Answer:

The slope of line n is 4/7

Step-by-step explanation:

First find the slope of line m

m = ( y2-y1)/(x2-x1)

m = (8 - 4)/(10 -3)

m = 4/7

Parallel lines have the same slope

The slope of line n is the same as slope of line m

The slope of line n is 4/7

Answer:

a parallel to b

Step-by-step explanation:

A baker makes 90 cakes in a 60-hour week

A baker makes 18 cakes in a 12-hour day.

So, the number of cakes she makes in an hour would be,

18/12 = 1.5 cakes/hour

We need to find the number of cakes she make in a 60-hour week.

Using unitary method we find the required number of cakes,

1.5 * 60 = 90

Therefore, a baker makes 90 cakes in a 60-hour week

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The reduced or lowest form of 15 / 40 is 3 / 8. The given statement is true.

First, let us understand about the reducing a fraction:

To express a fraction in the lowest terms, divide the numerator and denominator by the greatest common factor of the numerator and denominator.

We are given:

15 / 40 = 3 / 8

Let the LHS; 15 / 40

We need to write the following fraction in the lowest terms:

15 / 40

To write 15 / 40 in the lowest terms, we divide the numerator and the denominator by the greatest common factor of 15 and 40.

Since the factors of 15 are 1, 2, 3, 5, and 15 and the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40, the greatest common factor of 15 and 40 will be 5.

So we will divide the numerator and the denominator of 15 / 40 by 5.

15 ÷ 5 = 3

40 ÷ 5 = 8

So, the reduced form of 15 / 40 is 3 / 8 which is 15 / 40 = 3 / 8.

Thus, the reduced or lowest form of 15 / 40 is 3 / 8. The given statement is true.

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The solution of the system of equations is , x= -16 - 10/2 = 13

According  to our question-

-2x + 5y = -16  (3) =       -6x + 15y = -48

 3x -  4y  = 17  (2) =         6x -   8y  =   34

7y =     -14

y= -14/7 = 2

-2x + 5(2) = -16

-2x + 10 = -16

x= -16 - 10/2 = 13

hence,The solution of the system of equations is , x= -16 - 10/2 = 13

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Answer:

d) -21

Step-by-step explanation:

Given problem,

→ -11 + |-5| - |-15|

Let's solve the given problem,

→ -11 + |-5| - |-15|

→ -11 + 5 - 15

→ -11 - 10 = -21

Hence, the answer is -21.

Answer:

D. −21

Step-by-step explanation:

The bars either side of an expression or a value are the absolute value symbol.  

"Absolute value" means how far a value is from zero.

Therefore, the absolute value of a number is its positive numerical value.

Given expression:

[tex]-11 + |-5| - |-15|[/tex]

Absolute values in the given expression:

Therefore:

[tex]\begin{aligned} \implies -11 + |-5| - |-15|&=-11+5-15\\&=-6-15\\&=-21 \end{aligned}[/tex]

Answer:

Slope (m) = -1/2 or -0.5

Hope that helps ! ^^

Answer:

m= - 1/2

The step-by-step explanation is in the screenshot below!

==================================================

Explanation:

The term wy^2 out front multiplies with each term inside the parenthesis (because of the distributive rule).

Let's multiply the outer term with the first term inside the parenthesis to get the following:

wy^2 times 8y^3 = 8wy^5

Compare 8wy^5 with 40y^5, and we see the coefficients 8w and 40 match up. Therefore, 8w = 40 solves to w = 5

The graph of the function f(x) = 1/4x + 3 is attached below and the point (-x, f(-4) ) is pointed on it.

Graph:

Graph refers the visual representation of the function of set of data.

Given,

Here we have the function f(x) = 1/4x + 3

Now, we have to plot the function into the graph and we also plot the point (-4, f(-4)) on it.

By using the graphing calculator, we have plot the function f(x) = 1/4x + 3, then we get the graph like the following.

In order to point the (-4, f(-4)),

We have to find the value of f(-4), by apply the value of x as -4 in the given function then we get the values of the function as,

=> f(-4) = 1/4 (-4) + 3

=> f(-4) = -1 + 3

=> f(-4) = 2

Therefore, the point is (-4, 2).

Now we have to plot this point on the graph, and the point is on the line of the given function.

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x = √(27/11) is the local minima of the function g(x) = x¹¹ - 3x⁹ +2

Given, a function g(x) = x¹¹ - 3x⁹ +2

we have to find the local minima using the second derivative test.

first we differentiate the function,

g(x) = x¹¹ - 3x⁹ +2

g'(x) = 11x^10 - 27x^8

Now, putting g'(x) = 0

11x^10 - 27x^8 = 0

x^8(11x² - 27) = 0

Now, x = 0 or x = √(27/11)

After again differentiating the function we get

x = √(27/11) as the local minima of the function.

Hence, x = √(27/11) is the local minima of the function g(x) = x¹¹ - 3x⁹ +2

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The measure of  the angle AEG = 92°

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles. These are formed in the matching corners or corresponding corners with the transversal.

∠CFH + ∠EFC = 180( angles on a straight line)

making ∠EFC subject and substituting ∠CFH = 2x + 20, we have

∠EFC = 180 - ( 2x + 20)

∠EFC = 180 - 2x -20

∠EFC = 160 - 2x

but ∠EFC = ∠BEF ( alternate angles are equal)

substituting their values

160 - 2x = 3x - 10

collect like terms

-2x - 3x = -10 - 160

-5x = -170

x = -170/-5

x = 34

Also ∠EFC = ∠AEG = 160 -2x ( corresponding angles are equal)

∠AEG = 160 -2X, but x = 34

∠AEG = 160 - 2(34)

∠AEG =160 - 68 = 92°

In conclusion, The value of the ∠AEG = 92°

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Answer:

10/21

Step-by-step explanation:

1/7+1/6=6/42+14/42

=(6+14)/42

=20/42

=10/21

The probability that the advertising firm chosen at random has less than $1 million in revenue is 0.56.

The probability that the advertising firm chosen at random has an income between $1 million and $20 million or over $20 million is 0.44.

The rule used is the rule of addition only.

Probability is used in statistics to calculate the likelihood that a random event would take place.  The likelihood that the random event occurs has a probability value that lies between 0 and 1.

The more likely it is that the event would occur, the closer the probability value would be to 1. The more unlikely it is that the event would not happen, the closer the probability value would be to 0.

The rules of addition is used to determine the probability that either of two events would occur.

Probability that the advertising firm chosen at random has less than $1 million in revenue = total number of firms that have a revenue that is less than 1 million / total number of firms surveyed

Probability that the advertising firm chosen at random has less than $1 million in revenue = 148 / 264 = 0.56

Probability that the advertising firm chosen at random has an income between $1 million and $20 million or over $20 million = (number of firms that have an income between $1 million and $20 million / total number of firms) + (number of firms that have an income over $20 million / total number of firms)

= (67 / 264) +  (49 / 264)

= 116 / 264 = 0.44

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The horizontal line passing through the point (2, -6) is y = -6 and the vertical line passing through the point (2, -6) is x = 2

We need to write equations for the horizontal and vertical lines passing through the point (2, -6)

For a vertical line the value of x will never change. This will be true for any value of y.

So, the equation for a vertical line passing through this point is:

x = 2

Similarly, for a horizontal line the value of y will never change. This is true for any value of x.

So, the equation for a horizontal line passing through this point is:

y = -6

Therefore, the horizontal line passing through the point (2, -6) is y = -6 and the vertical line passing through the point (2, -6) is x = 2

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Slope of the given equation is m = 1/3

intercept of the given equation = (0 , -2)

and the graph is attached below .

using slope intercept formula

y =  mx  + b

we get

slope of the given equation ( y = 1/3 x   - 2  )

is m = 1/3

if we put values either of x or y

we get intercepts as  ( 0 , -2 )

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There is not any chance of getting negative number in answer.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = 5

Here, f(x) = 5 shows that whatever is the value of x the result value will be 5.

As, there is no variable x in the defined function and only having a constant 5 which is positive in nature.

So, whatever be the value of x is we will get 5  only.

Thus, there is not any chance of getting negative number in answer.

For example, f(1)= 5, f(3)= 5, f(-5)= 5

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Answer: (-3,0)

Step-by-step explanation:

-1 - 2 = -3

1+2=3

3+2=5

2 is the common thing between 2 and 4, 4 and 6,  6 and 8 so from -2 + 2 = 0

Answer:

Step-by-step explanation:

You want the equation of the circle shown on the radar screen as having a radius of 8 miles, centered at the origin.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Your circle is shown as having a radius of 8 miles. It is centered at the same origin where the control tower is located. That means we have ...

  (h, k) = (0, 0)

  r = 8

Using these values in the circle equation gives ...

  (x -0)² +(y -0)² = 8²

We can simplify the inequality to:

-1/2 < -1/n < -1/5

The solutions are n = 3 and n =4, and the sum of these is equal to 7

We start with the inequality:

-3n < 7n - 20 < 3n

First, we need to solve this for n.

if we divide all the inequality by n, we will get:

-3 < 7 - 20/n < 3

Now we can subtract 7 in all the parts to get:

-3 - 7 < -20/n < 3 - 7

-10 < -20/n < -4

Fiinally, if we divide by 20 we get:

-10/20 < -1/n < -4/20

-1/2 < -1/n < -1/5

So if n is only an integer number, the values of n that make the inequality true are:

n = 3 and n = 4

Then the sum of these two values is:

sum = 3 + 4 =7

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The statement that best describes how to determine if the plane clears the tower is;

Use the Pythagoras Theorem where the distance to the tower is a leg of the right triangle and the distance in the air is the hypotenuse. Find the other leg. Convert to feet to compare to the tower height

Given,

The length the plane will travel before lifting = 1500 yards

The distance further the plane will travel after lifting off the ground = 603 yards

The horizontal distance from the point of lifting off the ground to control tower = 600 yards

The horizontal distance from the point of liftoff to the control tower, the height of the control tower, and the distance of the plane's path after takeoff create a right triangle with the following sides:

The distance of the path of the plane after lifting off the ground = The hypotenuse side of the triangle

The horizontal distance from the point of lifting off the ground to control tower and the height of the control tower = The two legs of the right triangle

Let h stand for the height of the control tower, x for the horizontal distance from the plane's liftoff point to the control tower, and R for the length of the plane's route after liftoff, and we obtain;

h = √(R² - x²)

We have;

R = 603 yards

x = 600 yards

∴ h = √(R² - x²) = h = √(603² - 600²) = 60.07 yards

The height of the control tower, h = 60.07 yards

1 yard = 3 feet

∴ 60.07 yards = 3 × 60.07 feet ≈ 180.22 feet

Therefore, given that the height of the control tower = 198 feet, the plane at the height of approximately 180.22 feet clears the tower.

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Answer:

Step-by-step explanation:

so I believe the question is

[tex]\frac{1}{4}[/tex]X - [tex]\frac{1}{3}[/tex]Y=1

and we want to know if that is linear, and what the standard form for the equation would be

let's move a few things around using our algebra skillz

[tex]\frac{1}{4}[/tex]X-1 = [tex]\frac{1}{3}[/tex]Y

[tex]\frac{3}{4}[/tex]X-3 = Y

y = [tex]\frac{3}{4}[/tex]x-3  (in standard form  y=mx+b)

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

we can see that this does make a line,  so it's linear, and it's in standard form now.  

The variables that the scatter plot at the right would  be most likely to represent is option C: The number of siblings a person has and the person's GPA.

To illustrate how much one variable affects another, scatter plots are tools that are often used to place data points on a horizontal as well as  vertical axis.

A marker is used to represent each row in the data table, and the position of the marker depends on the values of the columns that are set up on the X and Y axes.

From the graph above, the Independent variables (siblings) are typically plotted on the horizontal axis, and dependent variables (Person's GPA) are typically plotted on the vertical axis.

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The height of the tower that was supported with the wire is 132.29 feet.

The tower, the wire and the ground would form a right triangle. A right triangle is a polygon that has three sides. The longest side is the hypotenuse. The other two sides are the length and the base.

In this question, the wire is the hypotenuse, the tower is the length and the ground is the base. Pythagoras theorem would be used to determine the height of the tower.

The Pythagoras theorem: a² + b² = c²

where:

a = length

b = base

c = hypotenuse

a² + 150² = 200²

a² + 22,500 = 40,000

a² = 40,000 - 22,500

a² = 17,500

a = √17,500

a = 132.29 feet

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Answer:

Below

Step-by-step explanation:

m = x ( -12b+9)  - 3

m+ 3 = x (-12b+9)

x =   (m+3) / ( -12b+9)       0r     (m+3) / (9-12b)

Answer:

[tex]y=2x-1[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Step-by-step explanation:

that's a right answer u're working on sir appreciated