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3 years ago

What value of x makes the equation 8(1.5x - 6) = 2x - 0.5(24 - 16x? true?

Mathematics

1 answer:

nydimaria [60]3 years ago

3 0

Answer:

x=18

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

8(1.5x−6)=2x−0.5(24−16x)

(8)(1.5x)+(8)(−6)=2x+(−0.5)(24)+(−0.5)(−16x)(Distribute)

12x+−48=2x+−12+8x

12x−48=(2x+8x)+(−12)(Combine Like Terms)

12x−48=10x+−12

12x−48=10x−12

Step 2: Subtract 10x from both sides.

12x−48−10x=10x−12−10x

2x−48=−12

Step 3: Add 48 to both sides.

2x−48+48=−12+48

2x=36

Step 4: Divide both sides by 2.

2x/2=36/2

x=18

Answer:

x=18

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1 year ago

A scale for a scale drawing is 10cm:1mm. which is larger the actual object or drawing explain

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3 years ago

If you bet $1 that a sum of 5 will turn up, what should the house pay (plus returning your $1 bet) if a sum of 5 turns up in ord

erma4kov [3.2K]

Here is the complete question.

1). What are the odds for rolling a sum of 5 in a single roll of two fair dice?

2). If you bet $1 that a sum of 5 will turn up, what should the house pay (plus returning your $1 bet) if a sum of 5 turns up in order for the game to be fair?

Answer:

1). $\frac{1}{8}$

2). $8.

Step-by-step explanation:

1).

The sample space (S) for rolling two fair dice is given as the following parameters illustrated below:

$\left[\begin{array}{cccccc}(1,2)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\(2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\(3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6)\end{array}\right] \left[\begin{array}{cccccc}(4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6)\\(5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6)\\(6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6)\end{array}\right]$

Let F represent the event that the sum of both dice turns up is 5.

F = [(1,4),(2,3),(3,2),(4,1)}

∴ The probability for an event F is illustrated below as:

$\frac{P(F)}{P(F')}$ $=\frac{\frac{4}{36} }{1-\frac{4}{36} }$

$=\frac{\frac{4}{36} }{\frac{32}{36} }$

$={\frac{4}{36}}*\frac{36}{32}$

= $\frac{1}{8}$

2). From above, we can see that the probability for rolling a sum of 5 are 1 to 8. Therefore, if you roll a sum of 5, in order for the game to be fair, the house is required to pay $8.

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