A man who is two metres tall walks directly away from a light on top of a pole that is 8 m high rate of 1.8 m/s. at what rate is his shadow lengthening by?

Dispersion is a measure of how spread out a set of data values is. For the given data, I'll calculate three common measures of dispersion: range, variance, and standard deviation.

Sorted data: 0, 0, 1, 1, 3, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 12, 12, 13, 14, 14, 15, 17, 18, 19, 20

1. Range: The range is the difference between the highest and lowest values in the dataset. In this case, the range is 20 (highest value) - 0 (lowest value) = 20.

2. Variance: Variance is the average of the squared differences between each data point and the mean of the dataset. First, calculate the mean (sum of values / number of values) which is 233/25 = 9.32. Next, find the squared differences between each data point and the mean, and then average these squared differences. The variance for this dataset is approximately 34.93.

3. Standard Deviation: The standard deviation is the square root of the variance. In this case, the standard deviation is approximately √34.93 ≈ 5.91.

In summary, the range for the given data is 20, the variance is approximately 34.93, and the standard deviation is approximately 5.91. These measures of dispersion provide insights into the variability of the data.

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Answer:

Airplane

Step-by-step explanation:

Answer:

Airplane

Step-by-step explanation:

Volume is the amount of mass an object has. Using common sense you can easily identify an airplane as the largest,

Answer:

x-4y=-13

Step-by-step explanation:

Answer:

19.025

Step-by-step explanation:

( (4x3) + (13x2) + 5% ) divided by  1 + 1

4 x 3 = 12

13 x 2 = 26

5% = 1/20 or 0.05

so

   (12 + 26 + 0.05) ÷ 2

   (38 + 0.05) ÷ 2

   38.05 ÷ 2 = 19.025

(⌐■_■)

Answer:

37 dollars

Step-by-step explanation:

Subtract 12 from 308 to get the amount he spent on the books. Then divide by 8 to get the cost per book. 308-12 = 296 296/8=37

To find all subgame perfect Nash equilibria (SPNE), we need to analyze each decision node in the game tree and determine the best response for each player at that node.

Starting from the final round (bottom of the tree) and working our way up:

At the node labeled "N", Player 1 has two options: "H" and "S". Player 2 has only one option: "h". The payoffs associated with each combination of choices are as follows:

(H, h): Player 1 gets a payoff of 3, Player 2 gets a payoff of 0.

(S, h): Player 1 gets a payoff of 2, Player 2 gets a payoff of 3.

Since Player 1's payoff is higher when choosing "H" rather than "S" and Player 2's payoff is higher when choosing "h" rather than "H", the subgame perfect Nash equilibrium for this node is (H, h).

Moving up to the next round, we have a decision node labeled "a". Player 1 has two options: "C" and "T". Player 2 has only one option: "h". The payoffs associated with each combination of choices are as follows:

(C, h): Player 1 gets a payoff of 4, Player 2 gets a payoff of 0.

(T, h): Player 1 gets a payoff of 5, Player 2 gets a payoff of 5.

Since Player 1's payoff is higher when choosing "T" rather than "C" and Player 2's payoff is higher when choosing "h" rather than "C", the subgame perfect Nash equilibrium for this node is (T, h).

Finally, at the topmost decision node labeled "S", Player 1 has only one option: "S". Player 2 has two options: "C" and "T". The payoffs associated with each combination of choices are as follows:

(S, C): Player 1 gets a payoff of 0, Player 2 gets a payoff of 2.

(S, T): Player 1 gets a payoff of 3, Player 2 gets a payoff of 3.

Since Player 1's payoff is higher when choosing "S" rather than "N" and Player 2's payoff is higher when choosing "C" rather than "T", the subgame perfect Nash equilibrium for this node is (S, C).

In summary, the subgame perfect Nash equilibria for this game are (H, h), (T, h), and (S, C).

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Answer:

24

Step-by-step explanation:

The question is saying, how many three digit numbers can be made from the digits 3, 4, 6, and 7 but there can't be two of the same digit in them. For example 346 fits the requirements, but 776 doesn't, because it has two 7s.

Okay, on to the problem:

We can do one digit at a time.

First digit:

There are 4 digits that we can choose from. (3, 4, 6, and 7)

Second digit:

No matter which digit we chose for the first digit, there is only going to be 3 of them left, because we already chose one, and you can't repeat that same digit. So there are 3 options.

Third digit:

Using the same logic, there are only 2 options left.

We have 4 choices for the first digit, 3 choices for the second, and 2 for the third.

Hence, this is 4 * 3 * 2 = 24 three-digit numbers that can be made.

Answer:

Step-by-step explanation:

\(A=6\cdot7-\frac12\cdot4\cdot4-2\cdot(\frac12\cdot3\cdot3)=42-8-9=25\)

Answer:

Adults = 300

Step-by-step explanation:

Answer:

(x+6)(x-2)

Step-by-step explanation:

Answer:

1.11/39

Step-by-step explanation:

the answer is b x< 0

Answer:

Answer: F. 5

\({ \tt{ \frac{ {7}^{x} - \sqrt[3]{y} }{2z} }} \\ \\ = { \tt{ \frac{ {7}^{2} - \sqrt[3]{729} }{(2 \times 4)} }} \\ \\ = { \tt{ \frac{40}{8} }} \\ \\ = { \tt{5}}\)

Answer:

F. 5

Step-by-step explanation:

7^2 - 3√729 / 2(4)

=49-9/ 8

=40/8

=5

Answer:

y=-4

Step-by-step explanation:

2y-18=-26

    2y=-26+18

        =-8

      y=-8÷2

        =-4

Answer:

-3x^3+8x-6

step

p-q=5x^4+4x-3-(5x^4+3x^3-4x+3)=5x^4+4x-3-5x^4-3x^3+4x-3

=5x^4-5x^4-3x^3+4x+4x-3-3

=-3x^3+8x-6

The length of the line from P to the centre of the circle is 16.22 cm.

Given: Angle between the tangent from point P to a circle and the line from P to the centre of the circle is 23º.Radius of the circle = 4 cm

Formula used:In right triangle ABC with angle A, the tangent of A is the ratio of the side opposite to A and the side adjacent to A.Let PQ be the tangent from point P to a circle with centre O.Let PO be the line from P to the centre of the circle.Therefore, ∠POQ = 90º (Tangent to a circle is perpendicular to the radius through the point of contact.)

Let ∠QOP = x.∠OQP = 23º∠QPO = x

Using the sum of angles in triangle POQ, we have:x + 23º + x = 180º2x = 157ºx = 78.5º

Now, in triangle OPQ,∠OPQ + ∠OQP + ∠QPO = 180º∠OPQ + 23º + 78.5º = 180º∠OPQ = 78.5º

Side opposite to angle OPQ = OQ = 4 cm (Radius of the circle)

Side adjacent to angle OPQ = OP (Let)Tangent 78.5º = $\frac{O P}{O Q}$OP = OQ * Tan 78.5ºOP = 4 * Tan 78.5ºOP = 16.22 cm

Therefore, the length of the line from P to the centre of the circle is 16.22 cm.

Note: The answer should be in 3 significant figures, as the radius is given in 1 significant figure.

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Answer:

No statements are included in the question.  Several observations are noted.

Step-by-step explanation:

y = 6x + 2

y = 6x + 1

y=mx+b is the equation for a straight line, where m is the slope and b the y-intercept.  

Observations

1.  These are both straight lines.

2.  The slopes are both the same:  +6.  The lines are parallel.

3.  Since they are parallel, they will never intersect (within the solar system)

4.  The second line is one unit lower than the first:  it's y-intercept is +1, comapared to +2 for the first.

5.  Since they do not intercept, there is no solution for this system of equations.

These will likely match some of the statements.

226 integers are present between 100 and 999, inclusive, and have the property that some permutation of its digits is a multiple of 11 between 100 and 999. Hence, option A is the correct option.

The problem statement is to find the number of multiples of 11 between 100 and 999 inclusive, where some multiples may have digits repeated twice and some may not.

To solve this problem, we can first count the number of multiples of 11 between 100 and 999 inclusive, which is 81. Some of these multiples may have digits repeated twice, and each of these can be arranged in 3 permutations. Other multiples of 11 have no repeated digits, and each of these can be arranged in 6 permutations. However, we must account for the fact that switching the hundreds and units digits of these multiples also yields a multiple of 11, so we must divide by 2, giving us 3 permutations for each of these multiples.

Thus, we have a total of 81 × 3 = 243 permutations. However, we have overcounted because some multiples of 11 have 0 as a digit. Since 0 cannot be the digit of the hundreds place, we must subtract a permutation for each of these multiples. There are 9 such multiples (110, 220, 330, ..., 990), yielding 9 extra permutations. Additionally, there are 8 multiples (209, 308, 407, ..., 902) that also have 0 as a digit, yielding 8 more permutations.

Therefore, we must subtract these 17 extra permutations from the total of 243, giving us 226 permutations in total. Hence, option A is the correct option.

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\(3.5b + 4.5 + 0.5b - 0.5 - 1.5b\)

Combine Like Terms:

\((3.5b+0.5b-1.5b)+(4.5-0.5)\)

\(\boxed{2.5b+4}\)

Answer:

39.99 + 0.45a = 44.99 + 0.40a you're welcome (:

Answer:

The sum of two non-zero even numbers is even and greater than the addends

Step-by-step explanation:

The solution to the whole number equation is sum of two non-zero even numbers is even and greater than the addends

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the first number be p

Let the second number be q

Now , the values of p and q are even

So , when p = 2 and q = 4

The sum of two non-zero even numbers is even and greater than the addends

p + q > q   be equation (1)

p + q > p   be equation (2)

2 + 4 > 4

2 + 4 > 2

6 > 4 and 6 > 2

Hence , the equation is true and sum of two non-zero even numbers is even and greater than the addends

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Answer:

13

Step-by-step explanation:

5 + 4 x 2

5 + 8

13

The maximum number of non-overlapping regions into which a circle can be divided by 9 chords is 46.

The maximum number of non-overlapping regions that a circle can be divided into by n chords is given by the formula:

N = (n^2 + n + 2) / 2

Substituting n = 9 into the formula, we get:

N = (9^2 + 9 + 2) / 2

N = (81 + 9 + 2) / 2

N = 92 / 2

N = 46

Therefore, the maximum number of non-overlapping regions into which a circle can be divided by 9 chords is 46.

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The measure of angle S = 29 degrees, angle T= 29 degrees, and angle U = 122 degrees.

A triangle is a straightforward closed curve made up of three-line segments. An angle inside the form is known as an interior angle. The inner angles add up to a constant 180 degrees.

The sum of internal angle of the triangle is 180 degrees.

(x + 4) + (x + 4) + (5x - 3) = 180

7x + 5 = 180

7x = 175

x = 25

Substitute the value of x in each of the angle to find the measure of each angle as follows:

The value of angle S = x + 4 = 25 + 4 = 29 degrees.

The value of angle T = x + 4 = 25 + 4 = 29 degrees.

The value of angle U = 5x - 3 = 125 - 3= 122 degrees.

Hence, the measure of angle S = 29 degrees, angle T= 29 degrees, and angle U = 122 degrees.

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Answer:

Step-by-step explanation:

A = h(a+b)/2 for h

2A = h(a + b)

h(a+b) = 2A

h = 2A/(a+b)

The measure of side GF is solved to be

Too side GF we use trigonometry tan, in the formula

tan x = opposite / adjacent

Where x is the given angle and opposite and adjacent are the legs of the right triangle

In this case, opposite = EF = 3, and adjacent = GF, x = 60 degrees

tan 60 = 3 / GF

Isolating GF results to

GF = 3 / tan 60

GF = 1.73205080757

GF = 1.73

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Answer:

-32

Step-by-step explanation:

=(-2)^5

=-2*-2*-2*-2*-2-2

-2*-2=4

-2*-2=4

-2

4*4=16

16*-2=-32

Hope this helps :) ❤❤❤

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Answer:

Data collected shows that the more you water, the larger your plant will grow. If you use the following Equation, y = 1/2x + 2 How tall will a plant be at 25 weeks if x is the number of weeks watered and y represents the height of the plant? Show your work.

Step-by-step explanation:

The solution to -3 ≤ x ≤ 1 is represented by graph A.

aph A.

'In math, a

'In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.'

According to the given problem,

we know,

-3 ≤ x < 1 means, the values of x will lie between -3 and less than 1 because x is less than 1. The darkened region of the number line signifies that the value of x includes all real numbers between -3 and less than 1.

Hence, we can conclude graph A represents the solution to the given problem.https://brainly.com/question/16191404?referrer=searchResults

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