In a dice game you win $1 if you roll a 1,2,3, or 4. If you roll a 5 or 6 you lose $2. What is the expected value of the game?

The number of residents Town A used to have is 1400, and the number of residents Town B used to have is 3600, as shown by the simple equation below.

Let x be the number of residents Town A used to have. The number of residents in Town B is:

5000 - x

We know that Town A had 12% whites and Town B had 10% whites. After the merge, the percentage of whites is 10.56%. With that in mind:

12%x+10%(5000-x) = 10.56%(5000)

0,12x + 500 - 0,1x = 528

0.02x = 28

x = 1400

Therefore, the number of residents Town A used to have is 1400. Now, the number of residents town B used to have is:

5000 - 1400 = 3600

With that in mind, we can conclude our answer is correct.

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The expanded form of 12³ is given as follows:

12³ = 12 x 12 x 12 = 1728 cubic feet.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V(a) = a³.

This expression is equivalent to multiplying the side length of the object by itself twice, as follows:

V(a) = a x a x a.

The side length for this problem is given as follows:

a = 12 feet.

Hence the volume of the cube is given as follows:

V = 12³ = 1728 feet³.

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The ordered pair that would best represent the location of point E' is (8z, 4z).

A graph of the vertices of the dilated image is shown in the image below.

The rule that best represent the dilation of quadrilateral WXYZ to quadrilateral W'X'Y'Z'.

In Mathematics and Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 5/2 centered at the origin as follows:

Ordered pair W (-2, 1) → Ordered pair W' (-2 × 5/2, 1 × 5/2) = W' (-5, 5/2).

Ordered pair X (2, 2) → Ordered pair X' (2 × 5/2, 2 × 5/2) = X' (10, 10).

Ordered pair Y (1, -1) → Ordered pair Y' (1 × 5/2, -1 × 5/2) = Y' (5/2, -5/2).

Ordered pair Z (-2, -2) → Ordered pair Z' (-2 × 5/2, -2 × 5/2) = Z' (-5, -5).

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Answer: x = -5, 5 y= 0

Step-by-step explanation:

vertical asymptotes = x= -5, 5

horizontal asymptotes = y= 0

Answer: option b

Step-by-step explanation:

The value of the function f(1/2) for the f(x) = 2 / 5 x- 5 / 2 is equal to -2.3.

Function is equal to,

f(x) = 2 / 5 x- 5 / 2

To get the value of f ( 1 / 2 ) .

Substitute the value of x equals to ( 1 / 2 ) we get,

f(x) = (2 / 5 ) x- ( 5 / 2 )

This implies,

f ( 1 / 2 ) = ( 2 /5 ) × ( 1 / 2 ) - ( 5 / 2 )

⇒ f ( 1 / 2 ) = ( 1 / 5 ) - ( 5 / 2 )

Take the least common multiple of 5 and 2 we get,

least common multiple of 5 and 2 is 10.

⇒ f ( 1 / 2 ) = ( 2  - 25 ) / 10

⇒ f ( 1 / 2 ) = -23 /10

⇒ f ( 1 / 2 ) = -2.3

Therefore, the value of f(1/2) for the given function is equal to -2.3.

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The above question is incomplete, the complete question is:

Consider the function: ƒ(x) = 2/5 x- 5/2 find the value of f( 1/2)?

Don would take 1500 minutes to fill the 1000-gallon water tank using the 2-gallon bucket.

If the capacity of the water tank is 1000 gallons and Don uses a bucket that can hold 2 gallons to fill the tank, we can calculate the number of buckets Don needs to fill the tank.

Let's assume the number of buckets Don needs to fill the tank is represented by 'n'.

Capacity of the tank = 1000 gallons

Capacity of each bucket = 2 gallons

Number of buckets needed to fill the tank, n = Capacity of the tank / Capacity of each bucket

n = 1000 gallons / 2 gallons

n = 500

So, Don needs 500 buckets, each holding 2 gallons, to fill the 1000-gallon water tank.

Given that it takes Don 3 minutes to fill the bucket with water and pour it into the tank, the total time taken by Don to fill the tank would be the product of the number of buckets (500) and the time taken to fill each bucket (3 minutes).

Total time taken to fill the tank = Number of buckets × Time taken to fill each bucket

Total time taken = 500 × 3 minutes

Total time taken = 1500 minutes

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The translation is of 5 units to the right and 3 units down, it can also be written as:

(x, y) ---> (x + 5, y - 3)

To study the translation, just look at some vertex in both figures.

The top left vertex of F is at (2, 7)

And the top left vertex at G is (7, 4)

Taking the difference between these, we will get:

(7, 4) - (2, 7) = (5,, - 3)

Then the translation from F to G can be defined as:

(x, y) ---> (x + 5, y - 3)

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The new mixture contains 34% peanuts. The correct option is A

The idea of weighted averages can be applied.

First, let's determine the mixture's entire weight:

Total weight = 4 kg + 12 kg = 16 kg

We can now calculate how many peanuts there are overall in the mixture:

Total weight in kilograms is =  (4 kg) (0.16) + (12 kg) (0.40)

= 0.64 kg + 4.80 kg

= 5.44 kg.

Finally, we can find the percentage of peanuts in the mixture:

Percent of peanuts = (Total amount of peanuts / Total weight) x 100%

= (5.44 kg / 16 kg) x 100

   = 34%

Therefore, the new mixture contains 34% peanuts, which is option A.

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The contrapositive statement is option D

If the hypothesis and conclusion of an earlier conditional statement are reversed, a contrapositive statement is produced.

Technically speaking, the contrapositive of a conditional statement that starts with "If p, then q" is "If not q, then not p." The initial assertion and its contrapositive, then, are both true because they are logically equivalent.

Thus the contrapositive statement as shown is the statement ~q ~p

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Answer:

18q + 27

Step-by-step explanation:

9(2q + 3)

9 x 2q = 18q

9 x 3 = 27

18q + 27

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