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3 years ago

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Mathematics

1 answer:

OLga [1]3 years ago

7 0

Answer:

d. x = 5

Step-by-step explanation:

Solve for x:

x - 3 = 7 - x

Hint: | Move terms with x to the left hand side.

Add x to both sides:

x + x - 3 = (x - x) + 7

Hint: | Look for the difference of two identical terms.

x - x = 0:

x + x - 3 = 7

Hint: | Add like terms in x + x - 3.

x + x = 2 x:

2 x - 3 = 7

Hint: | Isolate terms with x to the left hand side.

Add 3 to both sides:

2 x + (3 - 3) = 3 + 7

Hint: | Look for the difference of two identical terms.

3 - 3 = 0:

2 x = 7 + 3

Hint: | Evaluate 7 + 3.

7 + 3 = 10:

2 x = 10

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 2 x = 10 by 2:

(2 x)/2 = 10/2

Hint: | Any nonzero number divided by itself is one.

2/2 = 1:

x = 10/2

Hint: | Reduce 10/2 to lowest terms. Start by finding the GCD of 10 and 2.

The gcd of 10 and 2 is 2, so 10/2 = (2×5)/(2×1) = 2/2×5 = 5:

Answer: x = 5

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Let his original money is x

So, $\frac{x}{2}$ + $\frac{x}{3}$ + 2.25 = x
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Step-by-step explanation:

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Let f(x) = - 10x + 9 and g(x) = x2 + 12 <br>Find f( - 4)/g( - 4)

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Step-by-step explanation:

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A boat is carrying containers that weigh 4000 pounds each.

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4 = 16,000

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2 years ago

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

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Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago