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2 years ago

What is the vertex of the quadratic function f(x)=(x-8)(x-2)

1 answer:

7 0

F(x)=(x−8)(x−2)

y=(x−5)2−9
(Pretend the 2 is an exponent)

Use the vertex form, y=a(x−h)2+ky=a(x-2+k, to determine the values of a,h, and k.

a=1
h=5
k=-9

Find the vertex (h, k).
(5, -9)

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An advertising agency that serves a major radio station wants to estimate the mean amount of time the station’s audience members

Flura [38]

Answer:

$n=(\frac{1.645(45)}{5})^2 =219.18 \approx 220$

So the answer for this case would be n=220 rounded up to the nearest integer

Step-by-step explanation:

Information given

$\sigma = 45$ represent the population deviation

$ME = 5$ represent the margin of error

The margin of error for the true mean is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (4) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 90% of confidence interval now can be founded using the normal distribution. The significance level is $\alpha=1-0.9=0.1$ and the critical value would be $z_{\alpha/2}=1.645$ , replacing into formula (b) we got:

$n=(\frac{1.645(45)}{5})^2 =219.18 \approx 220$

So the answer for this case would be n=220 rounded up to the nearest integer

5 0

3 years ago

Read 2 more answers

The doubling period of a bacterial population is 20 20 minutes. At time t = 100 t=100 minutes, the bacterial population was 9000

Nuetrik [128]

Answer:

The initial population was 2810

The bacterial population after 5 hours will be 92335548

Step-by-step explanation:

The bacterial population growth formula is:

$P = P_0 \times e^{rt}$

where P is the population after time t, $P_0$ is the starting population, i.e. when t = 0, r is the rate of growth in % and t is time in hours

Data: The doubling period of a bacterial population is 20 minutes (1/3 hour). Replacing this information in the formula we get:

$2 P_0 = P_0 \times e^{r 1/3}$

$2 = e^{r \; 1/3}$

$ln 2 = r \; 1/3$

$ln 2 \times 3 = r$

$2.08 \% = r$

Data: At time t = 100 minutes (5/3 hours), the bacterial population was 90000. Replacing this information in the formula we get:

$90000 = P_0 \times e^{2.08 \; 5/3}$

$\frac{9000}{e^{2.08 \; 5/3}} = P_0$

$2810 = P_0$

Data: the initial population got above and t = 5 hours. Replacing this information in the formula we get:

$P = 2810 \times e^{2.08 \; 5}$

$P = 92335548$

3 0

3 years ago

What is the difference between a factor of a number and a multiple of a number? use the number 25 has an example

Ne4ueva [31]

Answer:

factor: a submultiple; an integer value that gives an integer quotient when the number is divided by it.
multiple: the product of the number and another integer

Step-by-step explanation:

<h3>Factors</h3>

A set of factors of a number (N) is a set of integers {f1, f2, f3, ...} whose product is the number:

f1 × f2 × f3 × ... = N

Often the term "factors" is used to mean "prime factors," the set of prime numbers whose product is N.

When N = 25, the prime factors are {5, 5}. That is ...

5×5 = 25

<h3>Divisors</h3>

A "divisor" of a number is a sub-multiple of N. That is, the quotient N/k is an integer for some divisor k of N. Usually, we're interested in integer divisors. All prime factors will be integer divisors of N. The term "factor" is often used when the term "divisor" is meant.

Divisors of N = 25 include 1, 5, and 25. There will be an odd number of integer divisors (as here) if the number N is a perfect square.

<h3>Multiples</h3>

For an integer k, the value k×N is called a <em>multiple</em> of N, often, the <em>k-th multiple</em> of N.

Multiples of 25 include 25, 50, 75, 100, 125, and any other decimal number ending in 25, 50, 75, or 00.

<em>Another example</em>

When N=30, the prime factors are {2, 3, 5}. The divisors are {1, 2, 3, 5, 6, 10, 15, 30}. (Note there are an even number of divisors.) Multiples of 30 include 30, 60, 90, 120, ....

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2 years ago

Use the photo to answer

mr_godi [17]

The circumference is 113.04 and multiple that by 7.50 to get 847.8 and i believe that’s the answer.

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3 years ago

Use the parabola tool to graph the quadratic function.<br><br> f(x)=2x^2+12x+16

viva [34]

The first thing you should know is that you need three points to be able to graph a second degree equation.
You can create a table and plot several points to obtain the parabola
In this case we will use a computational tool called wolfram alpha
Answer:
See attached image.
The graph is shown for two different intervals of the domain.

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3 years ago