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3 years ago

How would you factor 3x^2+6x

1 answer:

5 0

Factor 3x3x out of 3x2−6x3x2-6x.
3x(x−2)=03xx-2=0Set the single term factor on the left side of the equation equal to 00.3x=03x=0Divide each term by 33 and simplify.x=0x=0Set each of the factors of the left side of the equation equal to 00.x−2=0x-2=0Since −2-2 does not contain the variable to solve for, move it to the right side of the equation by adding 22 to both sides.x=2x=2Solve the equations for xx.x=0,2 your welcome

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3 years ago

Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In p

Olegator [25]

Answer:

Reject H₀. There is a significant difference in drug resistance between the two states.

Step-by-step explanation:

In this case we need to determine whether the data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states.

The significance level of the test is, α = 0.02.

(1)

The hypothesis can be defined as follows:

H₀: There is no difference between the proportions of drug-resistant cases in the two states, i.e. $p_{1} - p_{2}= 0$ .

Hₐ: There is a statistically significant difference between the proportions of drug-resistant cases in the two states, i.e. $p_{1} - p_{2}\neq 0$ .

(2)

Compute the sample proportions and total proportion as follows:

$\hat p_{1}=\frac{12}{189}=0.063\\\\\hat p_{2}=\frac{8}{429}=0.019\\\\\hat p=\frac{12+8}{189+429}=0.032\\$

Compute the test statistic value as follows:

$Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p(1-\hat p)\times [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}$

$=\frac{0.063-0.019}{\sqrt{0.032(1-0.032)\times [\frac{1}{189}+\frac{1}{429}]}}\\\\=2.86$

The test statistic value is 2.86.

(3)

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

$p-value=2\cdot P(Z>2.86)=2\times 0.00212=0.00424$

p-value = 0.00424 < α = 0.02.

The null hypothesis will be rejected at 0.02 significance level.

Reject H₀. There is a significant difference in drug resistance between the two states.

7 0

3 years ago

-8/9 - (2 1/3) show all your work

Sauron [17]

Answer:

1 8/9 - 1 2/3 = 2/

≅ 0.2222222

Step-by-step explanation:

How do you solve fractions step by step?

Conversion a mixed number 1 8/

to a improper fraction: 1 8/9 = 1 8/

= 1 · 9 + 8/

= 9 + 8/

= 17/

To find a new numerator:

a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/

= 9/

b) Add the answer from previous step 9 to the numerator 8. New numerator is 9 + 8 = 17

c) Write a previous answer (new numerator 17) over the denominator 9.

One and eight ninths is seventeen ninths

Conversion a mixed number 1 2/

to a improper fraction: 1 2/3 = 1 2/

= 1 · 3 + 2/

= 3 + 2/

= 5/

To find a new numerator:

a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/

= 3/

b) Add the answer from previous step 3 to the numerator 2. New numerator is 3 + 2 = 5

c) Write a previous answer (new numerator 5) over the denominator 3.

One and two thirds is five thirds

Subtract: 17/

- 5/

= 17/

- 5 · 3/

3 · 3

= 17/

- 15/

= 17 - 15/

= 2/

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(9, 3) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 3 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seventeen ninths minus five thirds = two ninths

8 0

3 years ago