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3 years ago

Solve for x 3 x − 8 ≤ 23 AND − 4 x + 26 ≥ 6 Please help thank you!!

Mathematics

1 answer:

MAXImum [283]3 years ago

8 0

To solve for x, you need to isolate/get the variable "x" by itself in the inequality:

3x - 8 ≤ 23 Add 8 on both sides

3x - 8 + 8 ≤ 23 + 8

3x ≤ 31 Divide 3 on both sides to get "x" by itself

$\frac{3x}{3} \leq \frac{31}{3}$

$x\leq \frac{31}{3}$ (x is any number less than or equal to 31/3)

-4x + 26 ≥ 6 Subtract 26 on both sides

-4x ≥ -20 Divide -4 on both sides [When you multiply/divide by a negative number to both sides of an inequality, you flip the sign </>]

$\frac{-4x}{-4} \geq \frac{-20}{-4}$ (two negative signs cancel each other out and become positive)

x ≤ 5 (x is any number less than or equal to 5)

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Hello! Can you please help me with this? I will give the first correct answer brainliest if you help + 5 stars and a like and a

WARRIOR [948]

Answer:

Step-by-step explanation:

First, substitute in 12 for x

2.4(12 ÷ 1/4)

Distribute 2.4 within the parenthesis

2.4 x 12 = 28.8

2.4 x 1/4 or 2.4 x 0.25 = 0.6

28.8 ÷ 0.6

Divide to get your answer:

I Hope That This Helps! :)

5 0

2 years ago

A machine has 12 identical components which function independently. The probability that a component will fail is 0.2. The machi

iogann1982 [59]

Answer:

$P(X>3) =1- P(X\leq 3) = 1-[P(X=0)+P(X=1) +P(X=2) +P(X=3)]$

And if we find the individual probabilities we got:

$P(X=0)=(12C0)(0.2)^0 (1-0.2)^{12-0}=0.0687$

$P(X=1)=(12C1)(0.2)^1 (1-0.2)^{12-1}=0.2062$

$P(X=2)=(12C2)(0.2)^2 (1-0.2)^{12-2}=0.2835$

$P(X=3)=(12C3)(0.2)^3 (1-0.2)^{12-3}=0.2362$

And if we replace we got:

$P(X>3) =1- P(X\leq 3) = 1-[0.0687+0.2062 +0.2835 +0.2362]=0.20543$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$