What’s the equation in vertex form?

Mathematics

1 answer:

pshichka [43]2 years ago

8 0

Answer:

$\large\boxed{y=(x+5)^2-64}$

Step-by-step explanation:

$\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\h=\dfrac{-b}{2a},\ k=f(h)\\\\\text{We have the equation:}\ y=x^2+10x-39\to x=1,\ b=10,\ c=-39.\\\\\text{Substitute:}\\\\h=\dfrac{-10}{2(1)}=\dfrac{-10}{2}=-5\\\\k=f(-5)=(-5)^2+10(-5)-39=25-50-39=-64\\\\\text{Finally:}\\\\y=1(x-(-5))^2-64=(x+5)^2-64$

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One of the questions in the Pew Internet & American Life Project asked adults if they used the Internet, at least occasional

Marizza181 [45]

Answer:

Part (a) The point estimate of the proportion of adults aged 18 to 29 who use the Internet is 0.9498.

Part (b) The point estimate of the proportion of adults aged 30 to 49 who use the Internet is 0.8896.

Part (b) Estimate of the proportion of population who use the Internet is 0.7624.

Step-by-step explanation:

Consider the provided information.

Part (a) point estimate of the proportion of adults aged 18 – 29 who use the Internet

The results showed that 454 out of 478 adults aged 18-29 answered yes;

$\hat p=\frac{454}{478}=0.9498$

The point estimate of the proportion of adults aged 18 to 29 who use the Internet is 0.9498.

Part (b) Develop a point estimate of the proportion of adults aged 30-49

741 out of 833 adults aged 30-49 answered yes;

$\hat p=\frac{741}{833}=0.8896$

The point estimate of the proportion of adults aged 30 to 49 who use the Internet is 0.8896.

Part (c) Suppose your target population of interest is that of all adults (18 years of age and over). Develop an estimate of the proportion of that population who use the Internet.

$\hat p=\frac{454+741+1058}{478+833+1644}$