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3 years ago

How do you do inequalities

Mathematics

1 answer:

sineoko [7]3 years ago

5 0

Answer:

See description below.

Step-by-step explanation:

An inequality is an equation with more than one solution and they use <, >, $\leq$ or $\geq$ . There are a number of ways to work with inequalities.

Solving: To solve inequalities in one variable, treat it just like an equation. Solve using inverse operations. If you divide or multiply by a -1 then be sure to flip the sign. For example, if you have > then it becomes <.

Graphing on a number line: To graph inequalities in one variable, use a number line. Plot a point on the number line with an open circle then an arrow pointing toward the solution set. If you have an equal to, you would shade in the open circle.

Solving: To solve inequalities in two variables, you need a system meaning more than one. You solve it like a system of equations by graphing.

Graphing: To graph inequalities with two variables, graph each in y=mx+b form using the y-intercept and slope. Connect the points with a dashed line unless equal to. Equal to inequalities have a solid line. To show the solution set, shade the side of the inequality which (x,y) points make it true. To find this, test a point by substituting into the inequalities.

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Construct the discrete probability distribution for the random variable described. Express the probabilities as simplified fract

lisov135 [29]

Answer:

$P(X = 0) = 0.03125$

$P(X = 1) = 0.15625$

$P(X = 2) = 0.3125$

$P(X = 3) = 0.3125$

$P(X = 4) = 0.15625$

$P(X = 5) = 0.03125$

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

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

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

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

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

And p is the probability of X happening.

Fair coin:

Equally as likely to be heads or tails, so $p = 0.5$

5 tosses:

This means that $n = 5$

Probability distribution:

Probability of each outcome, so:

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

$P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125$

$P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625$

$P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125$

$P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125$

$P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625$

$P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125$

5 0

3 years ago

Help me with this question

kaheart [24]

First combine like terms and put the expression in standard form. This expression is now in simplest form and cannot be simplified anymore.
3a + 10ab - 7a^2b - 10ab^2 + 12ab - (-4) + (-a^2b) - 5a
-10ab^2 - 8a^2b -2a + 24ab - (-4)

Hope this helps

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3 years ago

In 1980, the average monthly rate for basic able TV in the United States was

poizon [28]

The average rate of change in the monthly rate per year is -$0.056 i.e decreases by 0.056 every consecutive year.

Step-by-step explanation:

Step 1; The initial value is $7.69 in 1980 and the final value is $6.13 in 2008.

Difference in values = Final value - initial value = $6.13- $7.69 = -$1.56 (the negative symbol indicates that the cost has gone down with time)

Period between the values =Final year - initial year = 2008 - 1980 = 28 years.

Step 2; To find the rate of change per year, we divide the difference in values in that given period of time by the number of years in that period.

Rate of change per year = Difference in values in that period/ no of years.

= -$1.56 / 28 = -$0.056 (the negative symbol indicates that the cost has gone down with time)

So for every year between 1980 and 2008, the price of the monthly rate for basic able TV reduced by $0.056.

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4 years ago