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3 years ago

What is the value of X?

Mathematics

2 answers:

SVEN [57.7K]3 years ago

8 0

Answer:

a) x=4 b) x=17.5

Step-by-step explanation:

a)5x/2+1=11 b)2x/7-3=2

5x/2=11-1 2x/7=2+3

5x/2= 10 2x/7=5

5x= 10x2 2x=35

5x=20 x=35/2

x=20/5 x=17.5

x=4

Eva8 [605]3 years ago

8 0

Answer:

Step-by-step explanation:

$a)\\\\\dfrac{5x}{2}+1=11\qquad\text{subtract 1 from both sides}\\\\\dfrac{5x}{2}+1-1=11-1\\\\\dfrac{5x}{2}=10\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot\dfrac{5x}{2\!\!\!\!\diagup_1}=(2)(10)\\\\5x=20\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{20}{5}\\\\\large\boxed{\boxed{x=4}}$

$b)\\\\\dfrac{2x}{7}-3=2\qquad\text{add 3 to both sides}\\\\\dfrac{2x}{7}-3+3=2+3\\\\\dfrac{2x}{7}=5\\\\\dfrac{2x}{7}=\dfrac{5}{1}\qquad\text{cross multiply}\\\\(2x)(1)=(7)(5)\\\\2x=35\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{35}{2}\\\\\large\boxed{\boxed{x=17.5}}$

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Suppose you have two urns with poker chips in them. Urn I contains two red chips and four white chips.Urn II contains three red

lorasvet [3.4K]

Answer:

$P(R_{2}) =\frac{10}{15} = 0.667$

Step-by-step explanation:

Step 1: Understanding the possible events

Selecting a chip from Urn I and then adding that chip to Urn II and then selecting a red chip from Urn II can be completed in two ways:

A. Selecting a red chip from Urn I and adding it to Urn II and then selecting a red chip from Urn II

B. Selecting a white chip from Urn I and adding it to Urn II and then selecting a red chip from Urn II

Therefore total probability is:

$P(R_{2}) = P(A) + P(B)$

Step 2: Probability of selecting either chip from Urn I

Urn I contains 2 reds and 4 white chips, that gives a total of 6 chips.

$P(R_{1}) = \frac{2}{6} =\frac{1}{3}$

$P(W_{1}) = \frac{4}{6} =\frac{2}{3}$

Step 3: Probability of selecting a red chip from Urn II

Urn II originally contains 3 reds and 1 white chip, that gives a total of 4 chips.

Remember: Once a chip is added from Urn I to Urn II the total number of chips will increase in the Urn II

Case 1: When a red chip is added from Urn I to Urn II

Red chips = 4

White chips = 1

Total Chips = 5

$P(R_{2_1}) = \frac{4}{5}$

Case 2: When a white chip is added from Urn I to Urn II

Red chips = 3

White chips = 2

Total Chips = 5

$P(R_{2_2}) = \frac{3}{5}$

Therefore the total Probability of selecting a chip from Urn I and then adding that chip to Urn II and then selecting a red chip from Urn II can be calculated as:

$P(R_{2}) = P(A) + P(B)$

$P(R_{2}) = P(R_{1}) . P(R_{2_1}) + P(W_{1}) . P(R_{2_2})$