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2 years ago

Solve inequality. t+8 ≥ 19

Mathematics

1 answer:

jeka942 years ago

5 0

To solve the inequality, subtract 8 from both sides. The solution is t ≥ 11 or [11, ∞)

Tips to solve linear inequalities:

Isolate the variable on one side by using subtraction or addition. Subtraction and addition will not change the inequality.
Use division or multiplication to find the solution. Multiplication and division by a positive number will not the inequality. However, if we multiply or divide both sides with a negative number, we need to flip the inequality direction.

Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis ( or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.

Example: x ≥ 2 can be written as [2, ∞), while

x > 0 is written as (2, ∞)

The given problem:

t+8 ≥ 19

Subtract 8 from both sides. Subtracting a number from both sides will not change the inequality. Hence,

t+8 - 8 ≥ 19 - 8

t ≥ 11

Using the interval notation, the solution is [11, ∞)

Learn more about solving inequalities here:

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Please help!!!!! thank u!!

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Read 2 more answers

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .