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Nookie1986 [14]
2 years ago
14

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

Mathematics
1 answer:
stich3 [128]2 years ago
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.
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7 0
3 years ago
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