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Strike441 [17]
1 year ago
12

Plot the axis of symmetry and the point where the maximum value occurs for this function: h(x) = -(x 2)2 8.

Mathematics
1 answer:
Tpy6a [65]1 year ago
8 0

See attachment for the axis of symmetry and maximum point.

<h3>What is a function?</h3>
  • A function from a set X to a set Y allocates exactly one element of Y to each element of X.
  • The set X is known as the function's domain, while the set Y is known as the function's codomain.
  • Originally, functions were the idealization of how a variable quantity depends on another quantity.

To plot the axis of symmetry:

  • The given function is: h(x) = -(x+2)^{2}  +8
  • This function is in the form: g(x) = a(x-h)^{2} +k
  • Where the axis of symmetry is given by, x = h.
  • y comparison, we have -h=2.
  • This implies h=-2
  • Therefore the axis of symmetry is x = -2.

Therefore, the maximum value occurs at the vertex, given by (h,k)=(-2,8).

So, see attachment for the axis of symmetry and maximum point.

Know more about functions here:

brainly.com/question/25638609

#SPJ4

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A football team gained 9 yards on one play and then lost 22 yards on the next.Write a sum of integers to find theoverral change
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Answer:

-13 yards

Step-by-step explanation:

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22 - 9 = 13

But, we already know that since the answer is to the left of zero, it will be a negative number. So we flip the sign to get -13 yards.

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Step-by-step explanation:

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Which statement comparing ​|−12|​ and ​|8|​ is true?Which statement comparing ​|−12|​ and ​|8|​ is true?
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An e-mail filter is planned to separate valid e-mails from spam. The word free occurs in 60% of the spam messages and only 4% of
ANEK [815]

Answer:

(a) 0.152

(b) 0.789

(c) 0.906

Step-by-step explanation:

Let's denote the events as follows:

<em>F</em> = The word free occurs in an email

<em>S</em> = The email is spam

<em>V</em> = The email is valid.

The information provided to us are:

  • The probability of the word free occurring in a spam message is,             P(F|S)=0.60
  • The probability of the word free occurring in a valid message is,             P(F|V)=0.04
  • The probability of spam messages is,

        P(S)=0.20

First let's compute the probability of valid messages:

P (V) = 1 - P(S)\\=1-0.20\\=0.80

(a)

To compute the probability of messages that contains the word free use the rule of total probability.

The rule of total probability is:

P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})

The probability that a message contains the word free is:

P(F)=P(F|S)P(S)+P(F|V)P(V)\\=(0.60*0.20)+(0.04*0.80)\\=0.152\\

The probability of a message containing the word free is 0.152

(b)

To compute the probability of messages that are spam given that they contain the word free use the Bayes' Theorem.

The Bayes' theorem is used to determine the probability of an event based on the fact that another event has already occurred. That is,

P(A|B)=\frac{P(B|A)P(A)}{P(B)}

The probability that a message is spam provided that it contains free is:

P(S|F)=\frac{P(F|S)P(S)}{P(F)}\\=\frac{0.60*0.20}{0.152} \\=0.78947\\

The probability that a message is spam provided that it contains free is approximately 0.789.

(c)

To compute the probability of messages that are valid given that they do not contain the word free use the Bayes' Theorem. That is,

P(A|B)=\frac{P(B|A)P(A)}{P(B)}

The probability that a message is valid provided that it does not contain free is:

P(V|F^{c})=\frac{P(F^{c}|V)P(V)}{P(F^{c})} \\=\frac{(1-P(F|V))P(V)}{1-P(F)}\\=\frac{(1-0.04)*0.80}{1-0.152} \\=0.90566

The probability that a message is valid provided that it does not contain free is approximately 0.906.

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