How do you find the slope of the table below

The author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

The number of steps a runner takes in a specific length of time is referred to as stride rate and is commonly expressed in steps per second. You can figure it out by dividing the total number of steps you took during a certain amount of time by how long that time period lasted. Stride rate, which is frequently used as a gauge of running effectiveness, is impacted by a variety of variables, including running speed, terrain, and personal running form.

Hence, in the given section, the author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

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Answer:

$23,302.50

Step-by-step explanation:

Answer:

fog(x)= -4x+11

Step-by-step explanation:

Here,

f(x) = 2x - 3

g(x) = 2x - 4x +7 = -2x+7

fog(x)= f(-2x+7)

          = 2(-2x+7)-3

          = -4x+14-3

          = -4x+11

Answer:

$17.5 differnce

Step-by-step explanation:

20% tip on is $57.49

20% tip off is $39.99

tip on vs off when a tip is on means its

Answer:

A. it is true for both equations

Step-by-step explanation:

x = 4 and y = 1

sub these values into the equations

4 + 1 = 5

4 - 1 = 3

Answer:

1/2

Step-by-step explanation:

You put 5 as a numerator and then 10 as a denominator which is 5/10. But you can simplify it, so you change it to 1/2. Hope this helps!

Answer:

1/2

Step-by-step explanation:

The solution to Laplace's equation with the given boundary conditions is: u(x,y) = (f(y)/2)x + (1/π)∑[n=1 to ∞] [(f(y)-f(0))(1-cos(nπx/2))/\(n^2\)cos(nπ/2)]

The Laplace's equation uxx + uyy = 0 is a partial differential equation that describes a steady-state temperature distribution or electrostatic potential in a 2D region. The given boundary conditions specify that u(0,y) = 0 and u(2,y) = f(y), where f(y) is a given function. These conditions indicate that the solution is a function of x and y, and that the value of u is fixed on the boundaries.

To find the solution, we use separation of variables and assume that u(x,y) = X(x)Y(y). This leads to the equation X''/X = -Y''/Y = λ, where λ is a constant. The boundary conditions imply that X(0) = 0 and X(2) = 1, and the general solution is X(x) = (1/π)∑[n=1 to ∞] \(sin(nx\pi /2)cos(n\pi /2)ex^{-n^{2}\pi ^{2}y/4 }\)).To determine Y(y), we use the boundary condition u(2,y) = f(y), which gives Y(y) = f(y)/(2X(2)). Substituting X(x) and Y(y) into the general solution for u(x,y), we obtain:

u(x,y) = (f(y)/2)x + (1/π)∑[n=1 to ∞] [(f(y)-f(0))(1-cos(nπx/2))/\(n^2\)cos(nπ/2)]

This is the final solution to Laplace's equation with the given boundary conditions. It describes the temperature or potential distribution in the 2D region, and depends on the function f(y) and the Fourier series coefficients of X(x). The solution satisfies the Laplace's equation and the boundary conditions, and is unique up to a constant.

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The order in which the robot makes the turns does not matter for knowing the direction it is finally facing. The number of left turns and right turns determines the net effect on the direction, regardless of their order. Therefore, the final expression for the direction the robot is going after 21 left turns and 22 right turns is: \(d^(^2^1^+^2^2^) = d^4^3.\)

To determine the direction the robot is going after 21 left turns and 22 right turns, we can evaluate the expression:

Expression: \((d * -i)^2^1 * (d * i)^2^2\)

Simplifying this expression, we get:

Expression: \(d^2^1 * (-i)^2^1 * d^2^2 * (i)^2^2\)

Since \((-i)^2^1\) and \((i)^2^2\) are equal to 1, the expression simplifies further:

Expression: \(d^2^1 * d^2^2= d^4^3\)

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Answer: A rotation of 270° clockwise is equivalent to a rotation of 90° counterclockwise, because a full rotation is 360° and 270° clockwise is the same as 90° counterclockwise in terms of direction.

Therefore, the answer is: counterclockwise 90°.

Step-by-step explanation:

The value of the missing length is 48

Using the Pythagorean theorem, we have that;

a² = b² + c²

Given that the parameters are;

Substitute the values, we get;

80² = 64² + c²

Find the squares

6400 - 4096 = c²

substract the values

c² = 2304

find the square root

c = 48

Hence, the value is 48

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Therefore, there are 72 different orders in which the eight targets can be broken according to the given rules.

To find the number of different orders in which the eight targets can be broken, we can consider the arrangement of the columns and the targets within each column. Since there are three targets in each of the first two columns and two targets in the third column, we can focus on the relative order of breaking the targets within each column. Let's represent the columns as follows:

Column 1: T T T

Column 2: T T T

Column 3: T T

To calculate the number of different orders, we can count the permutations of breaking the targets within each column and then multiply them together.

For Column 1, there are 3 targets, so there are 3! = 3 × 2 × 1 = 6 possible orders.

For Column 2, there are also 3 targets, so there are 3! = 6 possible orders.

For Column 3, there are 2 targets, so there are 2! = 2 possible orders.

To find the total number of different orders, we multiply the number of orders for each column:

Total number of orders = 6 × 6 × 2

= 72

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The value of b in the expression is -2.

a + a + b = 14

b + b + c = 8

a + b + c = 18

Therefore,

2a + b = 14

2b + c = 8

c = 8 - 2b

Hence,

a + b + 8 - 2b = 18

a - b = 18 - 8

a - b = 10

2a + b = 14

a - b = 10

3a = 24

a = 8

8 - b = 10

b = 8 - 10

b = -2

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Answer:

a = 8

b = -2

c = 12

Step-by-step explanation:

a + a + b = 14

2a + b = 14 ⇒ ( 1 )

b + b + c = 8

2b + c = 8 ⇒ ( 2 )

a + b + c = 18 ⇒ ( 3 )

First, let us make a as the subject in equation 1.

2a + b = 14

2a = 14 - b

\(a=\frac{14-b}{2} \\a = 7-\frac{b}{2}\)   ⇒ ( 4 )

Let us make c as the subject in equation 2.

2b + c = 8

c = 8 - 2b ⇒ ( 5 )

Now it is clear for us that, we can replace a & c with ( 7 - b / 2 ) & ( 8 - 2b ) respectively.        

And now let us solve the equation 3 to find the value of b.

\(a+b+c=18\\\\7-\frac{b}{2} +b+8-2b=18\\\\Combine\: \:like\:\: terms.\\\\\)

\(15-\frac{b}{2} -b=18\\\\\frac{15*2}{1*2} -\frac{b}{2}-\frac{b*2}{1*2}=18\\\\\frac{30}{2} -\frac{b}{2}-\frac{2b}{2}=18\\\\\frac{30-3b}{2} =\frac{18}{1} \\\\Use\:\: cross\;\: multiplication\)

\(30-3b=18*2\\\\30-3b=36\\\\30-36=3b\\\\-6=3b\\\\-2 = b\)

And now let us find  the value of a

For that, let us use the equation 1. There, we can replace b with ( -2 ) to find the value of a.

\(2a+b=14\\\\2a-2=14\\\\2a = 14+2\\\\2a=16\\\\a=8\)

Now, let us find the value of c.

For that, let us take the equation 2. There also, we can replace b with -2 to find the value of c.

\(2b+c=8\\\\2*-2+c=8\\\\-4+c=8\\\\c=8+4\\\\c=12\)

It will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

First, we need to convert the dimensions of the tank from inches to feet:

68 inches diameter = 68/12 feet = 5.67 feet diameter

24 feet long = 24 feet long

Next, we can calculate the volume of the tank in cubic feet:

Since 1 cubic foot of water weighs 62.4 pounds, we can calculate the weight of the water in the tank in pounds:

To find out how long it will take to fill the tank, we can use the flow rate of the fire hydrant:

Finally, we can divide the volume of the tank by the flow rate to find out how long it will take to fill the tank:

Therefore, it will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

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Answer:

Let's use variables to represent the number of kittens each person has fostered.

Let x be the number of kittens Kim has fostered.

Then, according to the problem, Preston has fostered one less than one third as many kittens as Kim, so Preston has fostered:

(1/3)x - 1

We know that the total number of kittens fostered is 47. Therefore, we can write an equation:

x + (1/3)x - 1 = 47

Simplifying and solving for x:

(4/3)x = 48

x = 36

So Kim has fostered 36 kittens.

To find out how many kittens Preston has fostered, we can substitute x = 36 into the expression we found earlier:

(1/3)x - 1 = (1/3)(36) - 1 = 11

Therefore, Preston has fostered 11 kittens.

In summary, Kim has fostered 36 kittens and Preston has fostered 11 kittens.

Answer:

36, 11

Step-by-step explanation:

Preston and Kim 47 kittens

Kim has fostered X number of kittens

Preston has fostered X/3 - 1 ( 1/3 of Kim - 1)

Total number of kitten will be Preston +Kim

X +1/3X - 1 = 47

Add 1 to both sides

X + 1/3X = 48

If 4/3X is 48, X is 36

If Kim has 36kittens, Preston fostered 47- 36 =11

To check

1/3 of 36 = 12

Subract 1 = 11

The area under a Normal curve depends on the interval being considered and the parameters of the Normal distribution, such as its mean and standard deviation.

To determine which of the given intervals corresponds to the smallest area under a Normal curve, we need to consider the properties of the Normal distribution. The Normal distribution is a symmetric bell-shaped curve that is completely determined by its mean and standard deviation. The mean, denoted by µ, is the center of the curve, while the standard deviation, denoted by σ, determines the spread of the curve.

Option b) µ to µ + 3σ corresponds to the interval that covers almost all the area under a Normal curve, as about 99.7% of the area lies within three standard deviations of the mean. Therefore, this option cannot correspond to the smallest area under a Normal curve.

Option a) Q1 to Q3 and option d) µ - σ to Q3 both cover more area than option c) Q1 to µ + 2σ. The interval Q1 to Q3 covers the entire middle 50% of the distribution, while the interval µ - σ to Q3 covers at least 50% of the distribution, as almost all the area lies within three standard deviations of the mean. Therefore, option c) Q1 to µ + 2σ corresponds to the smallest area under a Normal curve.

In summary, the interval corresponding to the smallest area under a Normal curve is option c) Q1 to µ + 2σ.

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To identify the vertical asymptotes, we have to factor the denominator. For horizontal asymptotes, we compare the degrees of the numerator and denominator.

For rational functions, there are vertical and horizontal asymptotes. To identify the vertical asymptotes, we first have to factor the denominator. After that, we should look for values that make the denominator zero. These values can be found by setting the denominator equal to zero and solving for x. The resulting x values would be the vertical asymptotes of the function.

The horizontal asymptote is the line that the function approaches as x goes towards infinity or negative infinity. For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and the denominator.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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Answer:

there is no question

Step-by-step explanation:

Answer:

same here my dude

Step-by-step explanation:

To solve this problem, we need to use the Laplace transform and the recursive relation (7) as follows:

(a) We know that T(1/2) = r2. Using the recursive relation (7), we can express T(s) in terms of T(s-1/2) as:

T(s) = sT(s-1/2)

Substituting s = 1 in the above equation, we get:
T(1) = 1 * T(1/2)
T(1) = T(1/2) = r2

Now, taking the Laplace transform of both sides of the recursive relation (7), we get:
L{tT(s)} = L{xT(s-1/2)}

Using the property of Laplace transform that L{t^n} = n!/s^(n+1), we can rewrite the left-hand side as:
L{tT(s)} = -d/ds L{T(s)}

Similarly, using the property of Laplace transform that L{x^n} = n!/s^(n+1), we can rewrite the right-hand side as:
L{xT(s-1/2)} = -d/ds L{T(s-1/2)}

Substituting these expressions in the Laplace transform equation, we get:
-d/ds L{T(s)} = -d/ds L{T(s-1/2)}

Simplifying the above equation, we get:
L{T(s)} = L{T(s-1/2)}

Now, using the initial condition T(1/2) = r2, we can rewrite the above equation as:
L{T(s)} = L{T(s-1/2)} = r2/s

Taking the Laplace transform of t-1/2, we get:
L{t-1/2} = 1/s^(3/2)

Multiplying this expression by L{T(s)} = r2/s, we get:
L{t-1/2} L{T(s)} = r2/s^(5/2)

The answer to part (a) is L{t-1/2} = r2/s^(5/2).

(b) To determine L{x7/2}, we can use the fact that L{x^n} = n!/s^(n+1). Thus, we have:
L{x7/2} = (7/2)!/s^(7/2+1)

Simplifying the above expression, we get:
L{x7/2} = 7!/2^7 s^(1/2)

Now, multiplying this expression by L{T(s)} = r2/s, we get:
L{x7/2} L{T(s)} = 7!/2^7 r2 s^(-3/2)

The answer to part (b) is L{x7/2} = 7!/2^7 r2 s^(-3/2).

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To find the Taylor polynomial of degree two approximating the function f(x) = cos(2x) centered at a, we'll follow these steps:

1. Find the first three derivatives of f(x).
2. Evaluate the derivatives at the given point a.
3. Use the Taylor polynomial formula.

Step 1: Find the first three derivatives of f(x).

f(x) = cos(2x)
f'(x) = -2*sin(2x)
f''(x) = -4*cos(2x)

Step 2: Evaluate the derivatives at the given point a.

f(a) = cos(2a)
f'(a) = -2*sin(2a)
f''(a) = -4*cos(2a)

Step 3: Use the Taylor polynomial formula.

The Taylor polynomial of degree two is given by:

P₂(x) = f(a) + f'(a)*(x-a) + (1/2)*f''(a)*(x-a)²

Substitute the values we found in Step 2:

P₂(x) = cos(2a) - 2*sin(2a)*(x-a) + (-2)*cos(2a)*(x-a)²

So, the Taylor polynomial of degree two approximating the function f(x) = cos(2x) centered at a is:

P₂(x) = cos(2a) - 2*sin(2a)*(x-a) - 2*cos(2a)*(x-a)²

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The sample is baised.

Since all the students who attended the football game will most likely want a football stadium to be built and those that do no want a stadium to be built are not proportionately represented in this sample

Answer:

  AD = 32

Step-by-step explanation:

You want the length of side AD of square ABCD, when CD = (x+15) and angle ABC is (6x-12)°.

The value of x can be found by recognizing that the measure of any angle in a square is 90°.

  (6x -12)° = 90°

  6x = 102 . . . . . . . . divide by °, add 12

  x = 17

The sides of a square are congruent, so ...

  AD = CD = (x +15) = 17 +15 = 32

The length of AD is 32 units.

Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

Answer:

please see answers below

Step-by-step explanation:

a) if length, L, is 8 inches more than the width, W, then we can say

L = W + 8.

b) L X W = 65

(W + 8) X W = 65

W² + 8W = 65

subtract 65 from both sides:

W² + 8W - 65 = 0.

we can use completing the square, quadratic formula or factorisation to solve.

I will use completing the square.

1) put the W, not W ², in parenthesis.

2) half the coefficient (8) of W. that is 4. Put that into same parenthesis. Square the parenthesis.

3) we have (W + 4)²

4) Subtract (+4) ²  = 16 from this.

5)[(W + 4) ² - 16] – 65 = 0

6) now we have (W + 4) ² – 81 =0

7) (W + 4) ² = 81

8) (W + 4) = ± √81

9) W = ± √81  - 4

10) W = ±9 - 4. W = -13 or W = 5.

lengths are widths are positive, so W must be positive. So we choose 5.

L = W + 8 = 5 + 8 = 13.

check if it works for the area of 65.

L X W = 13 X 5 = 65.

so length is 13 inches and width is 5 inches

Rewrite the fractions as decimals by dividing:

7/8 = 0.7777

3/4 = 0.75

1/2 = 0.5

2/3 = 0.666

0.777 is the largest number so 7/9 is the largest fraction.

Answer: 7/9

Answer:

2/3

Step-by-step explanation:

L.C.M:36

7/9:28/36

3/4:27/36

1/2:1836

2/3:36/36

This chart does not represent a function, as the input of -3 is mapped to two different outputs.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

For a point in the standard format (x,y), we have that:

From the table, we have points (-3, 11) and (-3,12), meaning that the input of -3 is mapped to outputs of 11 and 12, hence the relation does not represent a function.

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Answer:

3. x=14° y=7

4. x=29° y=3

Step-by-step explanation:

3. this is a 45 - 45- 90 triangle

so the side is a-a-a√2 ( two sides are the same)

4y-3=10+2y+1 -- collect like terms

4y-2y=10+1+3

2y=14

y=7

find the angle of the inside triangle

180-59-90 =

31°

we know the big triangle was a 45-45-90 angle

so x+31=45

x=45-31

x=14°

4. this is a square, all sides are same

5y+3y=24

8y=24

y=3

angle is 90°

x+x+9y+5=90

we know y=3 --substitute

x+x+9(3)+5=90

2x+27+5=90

2x=90-27-5

2x=58

x=58/2

x=29

Answer:

7

Step-by-step explanation:

13 exceeds - 1 by - 1 + 13 = 12, then

- 5 + 12 = 7

Answer:

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

13 exceeds - 1 by - 1 + 13 = 12, then

- 5 + 12 = 7

Answer: TRUE

Step-by-step explanation:

12g+21 equals to 3(4g+7) because you have to multiply 3 and 4g which will equal 12g and then multiply 3 and 7 which will equal 21.

So your final answer would be 12g+21 equals to 12g+21.

Hope it helps!!

Answer:

4= -4         97= -97

Step-by-step explanation:

Answer:

4 , 97

Step-by-step explanation:

4 is 4 numbers away from 0

97 is 97 numbers away from 0

Answer:

4.51 ⁰ simplified would be 1 :)

It is 1 because anything to the 0 power is 1.

Answer:

try 2.32 trust me

Step-by-step explanation: