suppose you are playing poker with a non-standard deck of cards. the deck has 5 suits, each of which contains 12 values (so the deck has 60 cards total). how many 6-card hands are there, where you have at least one card from each suit?

The representativeness of a sample depends on how it is selected and whether it accurately reflects the characteristics of the larger population. Without more information about the sampling method used, it is difficult to determine if the sample of 16 politicians is likely to be representative of the citizens of the state.

If the sample was selected randomly from a diverse pool of politicians that accurately represents the political landscape of the state, there is a higher likelihood that the sample would be representative. However, if the sample was obtained through convenience sampling or if it disproportionately represents certain political affiliations or demographics, it may not be representative of the entire population of citizens in the state.

To assess the representativeness of the sample, it is important to consider factors such as the sampling method, sample size, diversity of the sample, and the specific characteristics being studied.

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The directional derivative of the function f(x,y) in the direction of the vector v at the point (0,1/3) is:

Duf(0,1/3) = ∇f(0,1/3) · u = [0, 3e/2] · [-5/13, 12/13] = (3e/2)(12/13) ≈ 1.38

To find the directional derivative of the function f(x, y) = 3e^x sin(y) at the point (0, 1/3) in the direction of the vector v = (-5, 12), we first need to calculate the gradient of the function, which is a vector containing the partial derivatives with respect to x and y.

The partial derivative with respect to x:
∂f/∂x = 3eˣ sin(y)

At point (0, 1/3), ∂f/∂x = 3e⁰ sin(1/3) = 3 sin(1/3)

The partial derivative with respect to y:
∂f/∂y = 3eˣ cos(y)

we first need to find the gradient of f at that point:
∇f = [∂f/∂x, ∂f/∂y] = [3ex sin(y), 3ex cos(y)]

Evaluated at (0,1/3), we get:
∇f(0,1/3) = [0, 3e/2

At point (0, 1/3), ∂f/∂y = 3e⁰ cos(1/3) = 3 cos(1/3)
So the gradient vector is ∇f = (3 sin(1/3), 3 cos(1/3)).

Next, we need to normalize the direction vector v:
|v| = √((-5)² + (12)²) = 13

Normalized vector v: (-5/13, 12/13)

Finally, we calculate the directional derivative (D_vf) as the dot product of the gradient vector and the normalized direction vector:
D(vf)= ∇f • (-5/13, 12/13) = (3 sin(1/3) × (-5/13)) + (3 cos(1/3) × (12/13))
D(vf) = (-15/13) sin(1/3) + (36/13) cos(1/3)
That is the directional derivative of the function at the given point in the direction of the vector v

Duf(0,1/3) = ∇f(0,1/3) · u = [0, 3e/2] · [-5/13, 12/13] = (3e/2)(12/13) ≈ 1.38

Therefore, the directional derivative of f(x, y) in the direction of v at the point (0,1/3) is approximately 1.38.

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The number of calories in the 3 ounce bar is 480.

To solve this problem, we can use a proportion. If the 2-ounce protein bar has 320 calories, then we can set up the following proportion:

2 oz / 320 cal = 3 oz / x cal

where x is the number of calories in the 3-ounce protein bar.

We can solve for x by cross-multiplying and simplifying:

2 oz * x cal = 3 oz * 320 cal

2x = 960x = 480

Therefore, the 3-ounce protein bar has 480 calories.

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The independent variable in the study is the  temperature of the water

The variable that the experimenter consciously modifies or changes is known as the independent variable.

The variable that is supposed to have an impact on the dependent variable is this one. After then, the dependent variable is assessed and recorded to see if it changes as a result of the independent variable's manipulation.

The temperature was changed before each trial hence the temperature was manipulated and that is the independent variable.

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False. Cultural traits that are diffused from one group are not always changed or adopted over time by the people in the receiving culture.

This is because different cultures have their own unique values, beliefs, and practices that may not align with the diffused cultural trait. Additionally, some cultural traits may be seen as a threat to the receiving culture and therefore not adopted.
Moreover, not all diffused elements of culture are successfully integrated into other cultures. Some may be rejected outright, while others may only be partially integrated or adapted to fit the receiving culture. It's important to note that cultural diffusion is a complex and ongoing process that involves a multitude of factors, including social, economic, and political influences, as well as individual attitudes and beliefs.

Therefore, the success of cultural diffusion and integration can vary greatly from one context to another.

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It will take 6 years for the enrollment at both schools to be equal.

To solve this problem, we need to set up an equation to represent the enrollment at both schools over time.

From the problem it can be deduced that

For Central Middle School:

Nichols Middle School

set these two equations equal to each other and solve for x:

800 + 75x = 890 + 60x

Simplifying the equation

15x = 90

Dividing both sides by 15, we get:

x = 6

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If 1/6 of the boys joined the basketball team, there are 160 boys in the soccer team.

If 1/6 of the boys joined the basketball team, then 5/6 of the boys did not join the basketball team. Similarly, if 2/9 of the boys joined the soccer team, then 7/9 of the boys did not join the soccer team.

Let's first find out how many boys did not join the soccer team:

7/9 x 540 = 380

Therefore, 380 boys did not join the soccer team.

To find out how many boys did join the soccer team, we can subtract the boys who did not join from the total number of boys:

540 - 380 = 160

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No, quadrilaterals ABCD and EFGH are not similar because the ratio of their corresponding sides is not proportional.

In Geometry, two (2) quadrilaterals are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Additionally, two (2) geometric figures such as quadrilaterals are considered to be congruent only when their corresponding side lengths are congruent (proportional) and the magnitude of their angles are congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probability that the selected person is a teaching assistant or a female is 29.

What is the probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, we have

Given: The physics department of a college has 10 male professors, 7 female professors, 13 male teaching assistants, and 9 female teaching assistants.

We have to find the probability that the selected person is a teaching assistant or a female.

N(A OR B) = N(A) + N(B) - N(A AND B)

N(teaching assistant) = 13 + 9 = 22

N(females) = 7 + 9 = 16

N(teaching assistant and female) = 9

N(teaching assistant OR female) = N(teaching assistant) + N(females) - N(teaching assistant AND female)

N(teaching assistant OR female) = 22 + 16 - 9

N(teaching assistant OR female) =  29

Hence, the probability that the selected person is a teaching assistant or a female is 29.

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The ∠EBC and ∠FCD are corresponding angles.Option(C) is Crrect.

Corresponding angles are angles that are in matching or corresponding positions when two parallel lines are intersected by a transversal. In other words, corresponding angles are pairs of angles that occupy the same relative position at each intersection of a transversal and parallel lines.

More specifically, if two parallel lines, line AB and line CD, are intersected by a transversal, line EF, at point G, then the angles that are opposite each other (one on each line) are corresponding angles. The corresponding angles are denoted by the same letter or symbol.

So, ∠EBC and ∠FCD are corresponding angles.Option(C) is Correct.

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The amount of cardboard  needed to make just one of the larger faces of the carton is 62.72 square inches.

To find out the amount of cardboard  needed to make just one of the larger faces of the carton, we need to first determine the dimensions of the face. Since we know the height of the carton is 7 inches, we need to figure out the length and width of the face.

Assuming the carton is rectangular, we can use the formula for the surface area of a rectangular prism to find the total amount of specialized cardboard needed for the entire carton. The formula is:

Surface area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively.

We know that the carton requires approximately 349 square inches of specialized cardboard to make, so we can set up the equation:

349 = 2lw + 2lh + 2wh

Since we are only interested in finding the amount of cardboard needed for one of the larger faces, we can assume that one of the dimensions (either length or width) is equal to the height of the carton (7 inches). Let's say that the other dimension is the length (l). Then we can rewrite the equation as:

349 = 2(7)(l) + 2(7)(h) + 2wh
349 = 14l + 14h + 2wh

Now we can substitute the value of h (7) into the equation:

349 = 14l + 14(7) + 2w(7)
349 = 14l + 98 + 14w
251 = 14l + 14w
251/14 = l + w

We don't know the exact dimensions of the face, but we do know that the sum of the length and width is 251/14 inches. Since the face is rectangular, we can assume that the length and width are equal (otherwise it would be a different shape). Therefore, each dimension would be half of 251/14 inches:

l = w = (251/14)/2 = 8.96 inches (rounded to two decimal places)

Now we can use the formula for the area of a rectangle to find the amount of specialized cardboard needed for one face:

Area = length x width
Area = 8.96 x 7
Area = 62.72 square inches

Therefore, approximately 62.72 square inches of specialized cardboard will be needed to make just one of the larger faces of the carton.

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Hi! To solve for the unknown value in the equation "x + 61 + 42 = degrees", follow these steps:

1. Combine the known values (61 and 42) by adding them together: 61 + 42 = 103.
2. Rewrite the equation with the combined values: x + 103 = degrees.
3. To isolate the unknown value (x), subtract 103 from both sides of the equation: x = degrees - 103.

So, the unknown value x can be found by subtracting 103 from the given degrees value.

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a. The two companies charge the same for 14 tons of sugar.

b. The cost when the two companies charge the same is $7953.50.

a. Let's represent the amount of sugar as x, and the total cost as C. Then we can set up the following equations for each company:

Company 1: C = 5143 + 200.75x

Company 2: C = 5500 + 175.25x

To find the amount of sugar for which the two companies charge the same, we can set the two equations equal to each other and solve for x:

5143 + 200.75x = 5500 + 175.25x

25.5x = 357

x = 14

So the two companies charge the same for 14 tons of sugar.

b. To find the cost when the two companies charge the same, we can plug in x = 14 into either equation. Let's use Company 1's equation:

C = 5143 + 200.75x

C = 5143 + 200.75(14)

C = 5143 + 2810.50

C = 7953.50

Therefore, the cost when the two companies charge the same is $7953.50.

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The limit of sec(y sec²y - tan²y - 1) as y approaches 1 is undefined. The function is not continuous at the point being approached.

Explanation: To evaluate the limit, we can first simplify the expression inside the secant function using the trigonometric identity:sec²θ - tan²θ = 1/cos²θ - sin²θ/cos²θ = (1 - sin²θ)/cos²θ = cos²θ / cos²θ = 1Substituting this expression back into the limit, we get:lim sec(y sec²y - tan²y - 1)y→1= lim sec(y - 1)y→1As y approaches 1, the argument of the secant function approaches 0, which means that the secant function approaches infinity. Therefore, the limit is undefined.Since the limit is not defined, the function is not continuous at the point being approached. A function is continuous at a point if and only if the limit of the function as x approaches that point exists and is equal to the value of the function at that point. In this case, since the limit does not exist, the function is not continuous at y = 1.

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Correct answer is: b) 5v3

In order to simplify the expression v75, you need to find the largest perfect square that is a factor of 75. In this case, the largest perfect square is 25, which is 5². So, you can rewrite v75 as v(25*3) or v(5²*3). Now, you can apply the property √(a*b) = √a * √b.

Your answer: v75 = 5v3 (option b).

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The maximum profit is $1,892,250.

The profit function is given by[tex]P(x) = -x^2 + 15x + 72x - 300 = -x^2 + 87x - 300.[/tex]

To find the number of hundred thousands of tires that must be sold to maximize profit, we need to find the value of x that maximizes P(x).

We can do this by finding the critical point of P(x) and then checking whether it corresponds to a maximum or a minimum.

The derivative of P(x) is:

P'(x) = -2x + 87

Setting this equal to zero to find critical points, we get:

-2x + 87 = 0

Solving for x, we get:

x = 43.5

Since the problem specifies that x must be at least 5, we know that the critical point x = 43.5 corresponds to a maximum.

Therefore, the number of hundred thousands of tires that must be sold to maximize profit is 43.5.

To find the maximum profit, we substitute x = 43.5 into the profit function:

[tex]P(43.5) = -43.5^2 + 87(43.5) - 300 = 1892.25[/tex]

Therefore, the maximum profit is $1,892,250.

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The final step when solving the given math problem is:

Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5)[/tex]

To solve √19x^5 for x, follow these steps:

Isolate the square root term: [tex]\sqrt{19x^5}[/tex] = y (Let y be the other side of the equation)

Square both sides: [tex](y^2) = 19x^5[/tex]

Divide both sides by 19: [tex](y^2)/19 = x^5[/tex]

Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5^)[/tex]

The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and can be found using mathematical operations.

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Note that the light is about 9.17 x 10³ times faster than sound. See the explanation below.

To arrive a the above, we only need to simplify Jakes observation as follows

[tex]\frac{1.1 * 10^{9} km/h }{1.2 * 10^{3}km/h }[/tex]

dividing the coefficients

1.1/1.2 = 0.91666666666

0.91666666666 x 10 ⁹⁻³

= 9.1666667 x 10 ⁵

further simplified, we have
9.17 x 10³

Thus, we can summarize that light is about 9.17 x 10³ faster than the speed of sound going by Jake observation.

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Full Question:

Jake noted that speed of light is approximately 1.1 × 10⁹ km/h;

the speed of sound is approximately 1.2 x 10³ km/h; and

11 + 12 = 0.916.

Using Jake's figures how many times faster is light than speed?

Write your answer in standard form.

Answer:

Step-by-step explanation:

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The area of ΔSTU is approximately 6.7 square centimeters.

To find the area of a triangle, we can use the formula A = (1/2)bh, where b is the base of the triangle and h is the height. In this case, we know that u is the base of the triangle, so we need to find the height.

To do this, we can use the sine function, which tells us that sin(6°) = h/u. Rearranging this equation, we get h = usin(6°). We can then substitute u and sin(6°) into the formula for the area to get

A = (1/2)(3.4)(3.4sin(6°)) ≈ 6.7 square centimeters.

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Answer:

Step-by-step explanation:

f(x) = ax² + bx + c      a= -8

f(x) = -8x² + bx + c     that a controls the direction and the stretch.

So the function will be stretched by 8.  The negative represents the direction because, it's negative, it will be facing down.  

Not sure how your class describes it but it could be facing down, concaved down, or expands downward.  

Answer: C = 14

Step-by-step explanation:

4c - 3c —> 4 - 3 = 1c

1c = 14

Divide both sides by one which gives you c = 14

Answer:

Step-by-step explanation:

1. The value of d is 10

2. measure of angle BSR is 120°

3. measure of angle RSM is 60°

The sum of angles on a straight line is 180°. This angles are adjascent angles.

angle BSR and RSM are on a straight line, therefore;

10d+20+6d = 180

16d = 180-20

16d = 160

d = 160/16

d = 10

therefore the value of d is 10

angle BSR = 10d+20 = 10×10+20

= 100+20 = 120°

angle RSM = 6d = 6 × 10

= 60°

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The minimum number of dots that could lie on the whole surface of four standard dice glued together is 56.

This can be achieved by placing the faces with 1 dot opposite the faces with 6 dots, the faces with 2 dots opposite the faces with 5 dots, and the faces with 3 dots opposite the faces with 4 dots on all four dice. Since the sum of the numbers on opposite faces of each individual die is always 7, the sum of the numbers on opposite faces of the four glued-together dice is also always 7. Therefore, the minimum number of dots on the whole surface is 7 times the number of faces, which is 7 x 8 = 56.

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In ΔRST, the overline{RT} RT is extended through point T to point U, Therefore the value of x = 10.

The sum of angles in a triangle is 180 degrees, we have:

m∠RST + m∠STU + m∠TRS = 180

We substitute the given values, and have:

(3x + 17) + (8x + 1) + (3x + 18) = 180

We simplify  and solve  for x, we get:

14x + 36 = 180

14x = 144

x = 10.

A triangle in geometry is descried a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most important  characteristic.

This characteristic is known as the triangle's angle sum property.

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Answer:

E. 10

Step-by-step explanation:

To solve the equation x + 50 = 60, we need to isolate x on one side of the equation. Subtracting 50 from both sides, we get:

x + 50 - 50 = 60 - 50

x = 10

Therefore, the solution to the equation is x = 10. Checking the answer choices, we see that E. 10 is the only number that belongs to the solution set. Therefore, the answer is:

E. 10

The dimensions of the square are 6 inches by 6 inches.

Let's assume that the side of the square is equal to x inches. Then, the area of the square can be expressed as x^2 square inches. The perimeter of the square is equal to 4 times the length of the side, or 4x inches.

According to the problem, the area of the square is 12 more than its perimeter, so we can write:

x^2 = 4x + 12

This is the equation we can use to find the dimensions of the square. To solve for x, we can rearrange the equation:

x^2 - 4x - 12 = 0

Then, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -4, and c = -12.

Plugging in these values, we get:

x = (-(-4) ± √((-4)^2 - 4(1)(-12))) / 2(1)

x = (4 ± √64) / 2

x = (4 ± 8) / 2

Therefore, the two possible solutions are:

x = 6 or x = -2

Since the side of a square cannot be negative, the only valid solution is x = 6.

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The transformation of the triangle is reflection over the x-axis

Given data ,

Let the transformation be represented as A

Now , the triangle is given as XYZ

where the coordinates are X ( 6 , 1 ) , Y ( 2 , 4 ) and Z ( -2 , 0 )

Now , the coordinates of the transformed triangle is

X' ( 6 , -1 ) , Y' ( 3 , -4 ) and Z' ( -2 , 0 )

The reflection of point (x, y) across the x-axis is (x, -y)

Hence , the transformation is reflection over x-axis

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