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Step2247 [10]
3 years ago
5

Choose the product. (3x 2 + 2x - 3)(x - 1)

Mathematics
1 answer:
Andrews [41]3 years ago
6 0
(3x² + 2x - 3) (x-1),

The product of the above factors is: 3x³ - x² - 5x + 3

Distributive property of multiplication

x(3x² + 2x - 3) - 1(3x² + 2x - 3) 
3x³ + 2x² - 3x - 3x² - 2x + 3

Group like terms:
3x³ + 2x² - 3x² - 3x - 2x + 3
3x³ - x² - 5x + 3

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A billing company that collects bills for​ doctors' offices in the area is concerned that the percentage of bills being paid by
omeli [17]

Answer:

1) A. H0: p = 0.30

HA: p not equal to 0.30

2) A. The Independence Assumption is met.

C. The Randomization Condition is met.

D. The Success/Failure Condition is met.

3) Test statistic z = 2.089

P-value = 0.0367

4) C. Reject H0. There is sufficient evidence to suggest that the percentage of bills paid by medical insurance has changed.

Step-by-step explanation:

1) This is a hypothesis test for a proportion.

The claim is that there is a significant change in the percent of bills being paid by medical​ insurance.

As we are looking for evidence of a difference, no matter if it is higher or lower than the null hypothesis proportion, the alternative hypothesis is defined by a unequal sign.

Then, the null and alternative hypothesis are:

H_0: \pi=0.3\\\\H_a:\pi\neq 0.3

2) Cheking the conditions:

The independence assumption and the randomization condition are met as the bills were selected randomly from the population.

The 10% condition can not be checked, as we do not know the size of the population.

The success/failure condition is met as the products np and n(1-p) are bigger than 10 (the number of successes and failures are both bigger than 10).

3) The significance level is assumed to be 0.05.

The sample has a size n=9260.

The sample proportion is p=0.31.

 

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.3*0.7}{9260}}\\\\\\ \sigma_p=\sqrt{0.000023}=0.005

Then, we can calculate the z-statistic as:

z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.31-0.3-0.5/9260}{0.005}=\dfrac{0.01}{0.005}=2.089

This test is a two-tailed test, so the P-value for this test is calculated as:

\text{P-value}=2\cdot P(z>2.089)=0.0367

As the P-value (0.0184) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant change in the percent of bills being paid by medical​ insurance.

5 0
3 years ago
What are the slope and y-intercept of the line described by the equation<br> y= 4x - 7?
Verdich [7]

Answer:

A. Slope: 4; y-intercept: (0-7)

Step-by-step explanation:

The equation given is in slope-intercept form, y =mx+b, where m is the slope and b is the y-intercept.

Our equation is y=4x -7,

Where m = 4 b = -7

If m = to the slope and b = to the y-intercept, our slope would be 4/1 or 4, and our y-intercept would be (0,-7).

The answer, A would be the best for the question.

Hope it helps!

8 0
2 years ago
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