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3 years ago

Solve: x^2-x-12÷x+5 ≥ 0

Mathematics

1 answer:

pav-90 [236]3 years ago

5 0

Answer:

Step-by-step explanation:

x3−x2+5x−12

≥0

Let's find the critical points of the inequality.

x3−x2+5x−12

x3−x2+5x−12=0(Multiply both sides by x)

(Use cubic formula)

x=1.836169

Check possible critical points.

x=1.836169(Works in original equation)

Critical points:

x=1.836169(Makes both sides equal)

x=0(Makes left denominator equal to 0)

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<0(Works in original inequality)

0<x≤1.836169(Doesn't work in original inequality)

x≥1.836169(Works in original inequality)

Answer:

x<0 or x≥1.836169

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You take the repeating group of digits and divide it by the same number of digits but formed only by 9s.

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Let's say you have 0.111111111111...., your repeating pattern is 1, that consists of one digit (1). You take that digit and you divide it by 9:

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Let's say you have 0.12121212121212...., the repeating pattern is 12, that consists of 2 digits (12). You take those 2 digits and divide them by 99:

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4 years ago

Ten young adults living in California rated the taste of a newly developed sushi pizza topped with tuna, rice, and kelp on a sca

timurjin [86]

Answer: For California: μ = 33.1; σ² = 1120.50; Range = 32;

For Iowa: μ = 24.5; σ² = 32.73; Range = 19

Step-by-step explanation:

Mean is the average of a population or a sample. It is defined as

μ = ∑x / n, where

x is each number of the set;

n is the total individuals in the sample.

Calculating the Mean for sample of taste of pizza in California:

μ₁ = $\frac{34+39+40+46+33+31+34+14+15+45}{10}$ = 33.1

Calculating the Mean for the sample in Iowa:

μ₂ = $\frac{28+25+35+16+25+29+24+26+17+20}{10}$ = 24.5

Variance measures how far the number in the set is from the mean. Its formula is

σ² = (∑x-μ)² / n -1

which means to find the variance, you have to get the difference between the number and the mean, square the result, add all of them and then divide by (n-1) individuals.

The Variance for the sample in California is

σ² = $\frac{(34 - 33.1)^{2}+(39-33.1)^{2}+(40-33.1)^{2}+(46-33.1)^{2}+(33-33.1)^{2}+(34-33.1)^{2}+(14-33.1)^{2}+(15-33.1)^{2}+(45-33.1)^{2}}{9}$ σ² = 120.50

The Variance for the sample in Iowa is

σ² = 32.73

Range is the difference between the highest and the lowest number of the set: range = highest - lowest

For the sample in California, the Range is

range = 46 - 14 = 32

For the sample in Iowa:

range = 35 - 16 = 19

For California:

Mean = 33.1;
Variance = 120.50;
Range = 32;

For Iowa:

Mean = 24.5;
Variance = 32.73;
Range = 19;

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3 years ago