Since we want it in the form: (x - a)², let's first expand (x - a)² and then equate for the coefficients.

(x - a)² = x² - 2ax + a²
x² + 4x - 15 = x² - 2ax + a²

Now, let's focus on the middle term.
4x = -2ax
4 = -2a
a = -2

Thus, we know that a = -2
Then, we can say (x + 2)² = x² + 4x - 15
x² + 4x + 4 = x² + 4x - 15
Thus, 19 units are needed in order to complete the square to produce:
(x + 2)²

6 0

3 years ago

A study conducted by the Center for Disease Control that asked 15,000 students about

BaLLatris [955]

Answer:

The sampling distribution of $\hat p$ is: $\hat p\sim N(p,\ \frac{p(1-p)}{n})$ .

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\mu_{\hat p}=p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$

The study was conducted using the data from 15,000 students.

Since the sample size is so large, i.e. <em>n</em> = 15000 > 30, the central limit theorem is applicable to approximate the sampling distribution of sample proportions.

So, the sampling distribution of $\hat p$ is: $\hat p\sim N(p,\ \frac{p(1-p)}{n})$ .

5 0

3 years ago

Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Suppose that the future populat

Salsk061 [2.6K]

Answer: In June 2097

Step-by-step explanation:

According to the model, to find how many years t should take for $P(t)=21100$ we must solve the equation $0.9t^2+6t+14000=21100$ . Substracting 21100 from both sides, this equation is equivalent to $0.9t^2+6t-7100=0$ .

Using the quadratic formula, the solutions are $t_1= \frac{-6-\sqrt{6^2 -4*0.9*(-7100)}}{2*0.9}=-92.21$ and $t_2=\frac{-6+\sqrt{6^2 -4*0.9*(-7100)}}{2*0.9}=85.54$ . The solution $t_1=-92.21$ can be neglected as the time t is a nonnegative number, therefore $t=t_2=85.54$ .

The value of t is approximately 85 and a half years and the initial time of this model is the January 1, 2012. Adding 85 years to the initial time gives the date January 2097, and finally adding the remaining half year (six months) we conclude that the date is June 2097.

6 0

3 years ago

Which list orders the numbers from least to greatest

DENIUS [597]

The second line
least to greatest: -3, -2.4, -21/4, -1.5, -11/8

5 0

3 years ago