My wife and I recently attended a party at which there were four other married couples. Various handshakes took place. No one shook hands with themselves or with their spouse, and no one shook hands with the same person more than once.
After all the handshakes were over, I asked each person, including my wife, how many hands he or she had shaken. To my surprise, they each gave a different answer!
How many hands did my wife shake?

The actual length of the living area is 134.4 feet if the length in the scale drawing is 16.8 in the scale.

To determine the actual length of the living space from a scale drawing, we need to use the scale factor, which is the ratio of the length in the drawing to the actual length. If the length in the scale drawing is 16.8 inches and the scale is given as a ratio of 1 inch in the drawing to 8 feet in actual size, we can set up a proportion:

1 inch (drawing) / 8 feet (actual)

= 16.8 inches (drawing) / x (actual)

We can cross-multiply and simplify to find x's value:

1 inch × x = 8 feet × 16.8 inches

x = (8 feet × 16.8 inches) / 1 inch

x = 134.4 feet.

Therefore, the actual length of the living space is 134.4 feet.

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The Mean Absolute Deviation (MAD) for the five-month moving average method, using the given patient data (749, 739, 779, 749, 546, 374, 610), is approximately [rounded MAD value with at least 4 decimal places].

To calculate the MAD using the five-month moving average method, we first need to calculate the moving averages for each group of five consecutive months. We start by taking the average of the first five months (749, 739, 779, 749, 546) and place the average as the first moving average. Then we shift the window by one month and calculate the average of the next five months (739, 779, 749, 546, 374) and continue this process until we reach the last group of five months (546, 374, 610).

Next, we calculate the absolute differences between each actual value and its corresponding moving average. For example, the absolute difference for the first month is |749 - moving average 1|, and so on. We sum up all these absolute differences and divide the total by the number of data points to obtain the MAD.

Performing these calculations using the given patient data will yield the MAD value, rounded to at least 4 decimal places. This MAD value represents the average absolute deviation from the moving averages and indicates the overall variability or dispersion of the data points around the moving averages.

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Answer:

$18

Step-by-step explanation:

Given statement solution is :- The value of the number is -1/9.

Let's solve the problem step by step.

Let's assume the number we're looking for is represented by the variable "x".

The problem states that the sum of 9 times the number (9x) and 7 is equal to 6. We can write this as an equation:

9x + 7 = 6

To isolate the variable "x," we need to move the constant term (7) to the other side of the equation. We can do this by subtracting 7 from both sides:

9x + 7 - 7 = 6 - 7

This simplifies to:

9x = -1

Finally, to solve for "x," we divide both sides of the equation by 9:

9x/9 = -1/9

This simplifies to:

x = -1/9

So, the value of the number is -1/9.

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a) The linear inequality: 2x + 2y ≤ 20.

b) Two possible sizes for the sandbox: 3 feet by 7 feet and 5 feet by 5 feet.

The graph  for the equation y + 2 = 3x + 3 is drawn below.

a) To write a linear inequality describing the situation, let's assume the length of one side of the rectangular sandbox is x feet and the width is y feet. The perimeter of the sandbox is given by the equation:

2x + 2y ≤ 20

This equation represents the constraint that the sum of the lengths of all sides of the sandbox should be less than or equal to 20 linear feet.

b) To find two possible sizes for the sandbox, we can choose different values for x and solve for y.

Let's consider two scenarios:

1) Setting x = 3 feet:

By substituting x = 3 into the inequality, we have:

2(3) + 2y ≤ 20

6 + 2y ≤ 20

2y ≤ 20 - 6

2y ≤ 14

y ≤ 7

So, one possible size for the sandbox is 3 feet by 7 feet.

2) Setting x = 5 feet:

By substituting x = 5 into the inequality, we have:

2(5) + 2y ≤ 20

10 + 2y ≤ 20

2y ≤ 20 - 10

2y ≤ 10

y ≤ 5

Thus, another possible size for the sandbox is 5 feet by 5 feet.

Therefore, two possible sizes for the sandbox are 3 feet by 7 feet and 5 feet by 5 feet.

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Therefore, the slope of the line passing through the points (0, 3) and (2, 6) is 3/2.

In mathematics, the slope refers to the measure of steepness or inclination of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between those points. In other words, the slope of a line is the change in y divided by the change in x between any two points on that line. The slope can be positive, negative, or zero, and it determines the direction and the steepness of the line. The slope is an important concept in algebra, geometry, and calculus, and it is used to describe many real-world phenomena, such as the velocity of an object, the rate of change of a function, and the growth or decline of a population.

Here,

To find the slope of the line passing through the points (0, 3) and (2, 6), we can use the formula:

slope = (change in y) / (change in x)

So, we have:

slope = (6 - 3) / (2 - 0)

slope = 3 / 2

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We will have the following:

We will calculate the total charge as follows:

So, the total charge will be:

So, the total charge is approximately $352.

The number of socks you pull out to have two black socks is 3 socks

Total number of pairs of socks in a drawer = 10

Number of black pairs of socks = 5

Number of blue pairs of socks  = 5

A. If you picked 2 socks [black] and [blue] 3rd pick guarantees you will have one pair of either blue or black

The number of socks you pull out to guarantee that you have a pair of one color is 3 socks

B. If you want to pick 2 good pairs and your 6 picks are the worst case, so 7th pick of the socks will give you good pair of two colors.

The number of socks you pull out to have two good pairs is 7 socks

C. If you want to have a pair of black socks your worst case will be you pick all 10 blue socks so another 2 socks must be black.

Therefore, the number of socks you pull out to have two black socks is 12 socks.

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Answer:

5 units

Step-by-step explanation:

Calculate the length using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (B(- 3, - 2) and (x₂, y₂ ) = C(0, 2)

BC = \(\sqrt{(0+3)^2+(2+2)^2}\)

     = \(\sqrt{3^2+4^2}\)

    = \(\sqrt{9+16}\)

    = \(\sqrt{25}\)

    = 5

Answer:

7

Step-by-step explanation:

if she got 30 from 6 cars then 30/6 is 5. $5 per car times 7 is $35

The values of x and y are 7 and 12 respectively

From the question, we are to determine the values of x and y

From the given information,

Line AB and Line CD bisect each other at point E

Then, we can conclude that

AE = BE

and

CE = DE

From the given information,

AE = 3x - 10y + 123

BE = -2x - 7y + 122

CE = 9x + 10y - 171

DE = 3x + 20y - 249

Then, we can write that

3x - 10y + 123 = -2x - 7y + 122

Simplifying

3x +2x -10y + 7y = 122 -123

5x -3y = -1 ----------- (1)

Also,

9x + 10y - 171 = 3x + 20y - 249

Simplifying

9x -3x +10y -20y = -249 + 171

6x -10y = -78 --------- (2)

Now, solve equations (1) and (2) simultaneously

5x -3y = -1 ----------- (1)

6x -10y = -78 --------- (2)

Multiply equation (1) by 10 and equation (2) by 3

10 × ( 5x -3y = -1

3 × ( 6x -10y = -78

50x -30y = -10 ----------- (3)

18x -30y = -234--------- (4)

Then, subtracting equation (4) from equation (3), we get

50x -18x -30y-(-30y) = -10-(-234)

32x -30y + 30y = -10 + 234

32x = 224

∴ x = 224/32

x = 7

Put the value of x into equation (1), to find y

5x -3y = -1

5(7) -3y = -1

35 -3y = -1

35 + 1 = 3y

36 = 3y

∴ y = 36/3

y = 12

Hence, the values of x and y are 7 and 12 respectively

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Answer:

His salory before Increse is 17250

Hope this helps:)

..............

The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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Answer:

E.24/7 tan(74) = opposite/advanced The length of the side opposite to the 74 degree angle is 24 units*The length of the side adjacent to the 74 degree angle is 7 units*If you substitute the value into the formula to obtain: tan(74) = 24/7 The correct answer is option E

Answer:

so67 =9

Step-by-step explanation:

Answer:

Step-by-step explanation:

2. 24^2+7^2 = 625

V 625 = 25

3. 6^2 + 5^2 = 25 +36 = 61

V 61  =7.81024967 =7.8

4. 4^2 +9^2 = 97

V 97= 9.84885780 = 9.8

5. 2^2 +3^2 = 13

V 13 =3.60555127 =3.6

and done!

Answer:

1. hypotenuse is 25

2. hypotenuse is 7.8

3. hypotenuse is 9.8

4. hypotenuse is 3.6

Step-by-step explanation:

To find the hypotenuse, just use the formula a^2 + b^2 = c^2

a and b are the sides with short lengths, while c is the one with the greatest line.

Let's try #1, and then you can do the rest by yourself, as it is very easy.

1) sides a and b are given, a = 7 and b = 24

hypotenuse = a^2 + b^2 = c^2

--> 7a^2 + 24b^2 = c^2

--> 49 + 576 = c^2

--> 625 = c^2

--> take the square root of 625

--> 25 = c

The volume of the block is increasing at a rate of \(6 ft^3/hour\) at this time.

Space in three dimensions is quantified by volume. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.  

The area occupied inside an object's three-dimensional bounds is referred to as its volume. The item's capacity is another name for it. A three-dimensional object's volume, which is expressed in cubic metres, is the quantity of space it takes up.

Let's start by finding the formula for the volume of a cube with side length s:

V = \(s^3\)

Now, let's differentiate both sides with respect to time (t):

dV/dt = \(3s^2(ds/dt)\)

We know that ds/dt = 2 ft/hour, and when s = 1 ft, we have:

dV/dt = \(3(1^2)(2) = 6 ft^3/hour\)

Therefore, the volume of the block is increasing at a rate of \(6 ft^3/hour\) at this time.

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Given

Solving, step-by-step

Answer:

3p - q = 3(2-5) - (8x3) = -9 - 24 = -33. Therefore, 3p-q=-33.

Answer:

600

Step-by-step explanation:

yw

Answer:

All Real Numbers

Step-by-step explanation:

I will be using x instead of θ as a variable:

1.) \(1+tan^2\)x is equal to \(sec^2\)x, so we can substitute \(sec^2\)x for \(1+ tan^2\)x.

2.) Now, since \(csc^2\)x is equal to \(\frac{1}{sin^2x}\), and \(sec^2\)x is equal to \(\frac{1}{cos^2x}\), we can just move \(cos^2x\) to the numerator and \(sin^2x\) to the denominator. \(\frac{cos^2x}{sin^2x}\) is equal to \(cot^2x\)

3.) Since we have \(cot^2x\) = \(cot^2x\) , the answer is All Real Numbers.

Answer:

x = 4 and y = 3.

Step-by-step explanation:

To solve the system of equations using elimination, we can eliminate one variable by multiplying one or both equations by appropriate constants so that the coefficients of either x or y will cancel out when added or subtracted. Let's use the second equation to eliminate y.

Multiply the second equation by -4 to make the coefficients of y in both equations the same:

-4(3x + y) = -4(15)

-12x - 4y = -60

Now, we have two equations:

4x + 4y = 28

-12x - 4y = -60

Add the two equations together:

(4x + 4y) + (-12x - 4y) = 28 + (-60)

-8x = -32

Divide both sides of the equation by -8 to solve for x:

x = (-32) / (-8)

x = 4

Substitute the value of x back into one of the original equations (let's use the second equation):

3x + y = 15

3(4) + y = 15

12 + y = 15

y = 15 - 12

y = 3

Therefore, the solution to the system of equations is x = 4 and y = 3.

Answer: 24

Step-by-step explanation:

1. Number Them

Elf and Dwarf = 1

Hobbit = 2

Wizard = 3

Man = 4

* Elf and Dwarf are put together so that they are always sitting together

2. Multiply

1 x 2 x 3 x 4 = 24

Answer:

3/8 shortening

1/4 salt

1 1/8 granulated sugar

1/4 baking soda (or 3/4 if that is 1 1/2 t from the original recipe)

1/8 eggs

1 c cake flour

1/4 vanilla extract

food coloring

1/8 butter flavoring

Answer:

163

Step-by-step explanation:

What's great about these problems is that when there is a line that is divided by another line, causing 2 angles, the 2 angles must equal 180 degrees.  That means the 163-degree angle + either the x or the z angle would equal 180 degrees.  The second best part about this is that if it is separated how yours is, with 2 lines, opposite angles are equal.  That means that angle x and angle z are equal, as well as the 163 angle is equal to the y angle.  Hope this helps with more than just this problem!

Answer:

Infinite Solution

Step-by-step explanation:

We know that there are no variables on either die of the equation so the answer would be infinite because when you put a number for the variable it will always be true.

Hope this helps :)

The probability that a student chose football given that they like watching sports is: c. 0.27.

Using this formula

P[Like (Football)/Like (Sport)]

Where:

P=Probability

Like (Football)=0.23

Like (Sport)=0.23+0.18+0.26+0.17=0.84

Let plug in the formula

P[Like (Football)/Like (Sport)]=0.23/0.84

P[Like (Football)/Like (Sport)]=0.27

Therefore the probability that a student chose football given that they like watching sports is: c. 0.27.

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Answer:

C.

Step-by-step explanation: