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ziro4ka [17]
2 years ago
7

Given f(x)=-x-1, solve for x when f(x)=-10

Mathematics
1 answer:
Ilia_Sergeevich [38]2 years ago
3 0

f(x) = -10

set the equation equal to -10 and solve for x:

-10 = -x-1

Add 1 to both sides:

-9 = -x

Divide both sides by -1:

x = 9

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Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos
crimeas [40]

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
What is an interval scale and what is it used for?
koban [17]
An interval scale has measurements where the difference between values is meaningful. For example, the year 0 doesn’t imply that time didn’t exist. And similarly, a temperature of zero doesn’t mean that temperature doesn’t exist at that point. Arbitrary zeros (and the inability to calculate ratios because of it) are one reason why the ratio scale — which does have meaningful zeros — is sometimes preferred.
8 0
3 years ago
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Write three equivalent ratios to the given<br> ratios 4 to 8 and 5 to 10?
oee [108]

Answer:

1 to 2, 2 to 4, 3 to 6

Step-by-step explanation:

4s double is 8, 5s double is 10, so whichever you choose just double it.

In mathematically, 8/4 = 2, 10/5 = 2, so x to 2x

8 0
2 years ago
What is the annual wage for a person who works 2,000 hours and earns $12.00 an hour?
daser333 [38]
$24,000 per year!! Hope it helps :) goodluck
3 0
2 years ago
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The product of negative three and a number. Please translate.
ZanzabumX [31]

Answer:

-3n

Step-by-step explanation:

"The product of negative three and a number." can be written as -3n, or -3 * n, where n is "the number".

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