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2 years ago

Simplify: -3(y + 2)^2– 5 + 6y What is the simplified product in standard form?

Mathematics

2 answers:

Ymorist [56]2 years ago

7 0

-3(y²+4y+4) - 5 +6y

-3y² - 12y - 12 -5 + 6y

-3y² -6y -17

-(3y²+6y+17)

VMariaS [17]2 years ago

4 0

Answer:

-3y^2 - 6y - 17

Step-by-step explanation:

-3(y + 2)^2 - 5 + 6y =

Expand the square of the binomial.

= -3(y + 2)(y + 2) - 5 + 6y

Use FOIL to multiply the binomials.

= -3(y^2 + 2y + 2y + 4) - 5 + 6y

Combine like terms inside the parentheses.

= -3(y^2 + 4y + 4) - 5 + 6y

Distribute the -3.

= -3y^2 - 12y - 12 - 5 + 6y

Combine like terms.

= -3y^2 - 6y - 17

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A car insurance company suspects that the younger the driver is, the more reckless a driver he/she is. They take a survey and gr

erastovalidia [21]

Answer:

The confidence interval for the difference in proportions is

$-0.028\leq p_1-p_2 \leq 0.096$

No. As the 95% CI include both negative and positive values, no proportion is significantly different from the other to conclude there is a difference between them.

Step-by-step explanation:

We have to construct a confidence interval for the difference of proportions.

The difference in the sample proportions is:

$p_1-p_2=x_1/n_1-x_2/n_2=(183/217)-(322/398)=0.843-0.809\\\\p_1-p_2=0.034$

The estimated standard error is:

$\sigma_{p_1-p_2}=\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2} } \\\\\sigma_{p_1-p_2}=\sqrt{\frac{0.843*0.157}{217}+\frac{0.809*0.191}{398} } \\\\\sigma_{p_1-p_2}=\sqrt{0.000609912+0.000388239}=\sqrt{0.000998151} \\\\ \sigma_{p_1-p_2}=0.0316$

The z-value for a 95% confidence interval is z=1.96.

Then, the lower and upper bounds are:

$LL=(p_1-p_2)-z*\sigma_p=0.034-1.96*0.0316=0.034-0.062=-0.028\\\\\\UL=(p_1-p_2)+z*\sigma_p=0.034+1.96*0.0316=0.034+0.062=0.096$

The confidence interval for the difference in proportions is

$-0.028\leq p_1-p_2 \leq 0.096$

Can it be concluded that there is a difference in the proportion of drivers who wear a seat belt at all times based on age group?

No. It can not be concluded that there is a difference in the proportion of drivers who wear a seat belt at all times based on age group, as the confidence interval include both positive and negative values.

This means that we are not confident that the actual difference of proportions is positive or negative. No proportion is significantly different from the other to conclude there is a difference.

8 0

1 year ago

Which of the following notations correctly describe the end behavior of the polynomial graphed below?

algol13

The right answer is C

Let me to explain. From the graph we know that the vertex of this parabola is $V(0,8)$ . This is a maximum y-value. We also know that the parabola opens downward, so the leading coefficient is negative. Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right. In a mathematical language this is: