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kicyunya [14]
3 years ago
10

The heights of the pine trees in a certain forest are normally distributed, with a mean of 86 feet and a standard deviation of 8

feet.
Approximately what percentage of the pine trees in this forest are taller than 100 feet?
Mathematics
1 answer:
laiz [17]3 years ago
6 0

Answer:

4%

Step-by-step explanation:

We solve this question using z score formula

z = (x-μ)/σ,

where

x is the raw score = 100 feet

μ is the population mean = 86 feet

σ is the population standard deviation = 8 feet

Hence,

x > 100 feet

z = (100 - 86)/8

z = 1.75

Probability value from Z-Table:

P(x<100) = 0.95994

P(x>100) = 1 - P(x<100) = 0.040059

Converting to Percentage

= 0.040059 × 100

= 4.0059%

Approximately = 4%

Therefore, the percentage of the pine trees in this forest are taller than 100 feet is 4%

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A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time perio
MAXImum [283]

Rate of change of profit for this period is $2750 per month

<em><u>Solution:</u></em>

Given that,

Profit of $6500 in January and $17,500 in May

<em><u>To find: Rate of change</u></em>

Since,

January is the first month of the year (1) while May is the fifth month (5)

<em><u>Therefore, we get two points</u></em>

(1, 6500) and (5, 17500)

Using these points we can find the rate of change in profit for this time period

<em><u>The rate of change using the following formula:</u></em>

m = \frac{y_2-y_1}{x_2-x_1}

Here from the points,

(x_1, y_1) = (1, 6500)\\\\(x_2, y_2) = (5, 17500)

<em><u>Therefore, rate of change is given as:</u></em>

m = \frac{17500-6500}{5-1}\\\\m = \frac{11000}{4}\\\\m = 2750

Thus rate of change of profit for this period = $2750 per month

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Answer:

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Explanation:

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A function is a relation that maps an input to a single output. Common representations are ...

  • list of ordered pairs
  • table
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Functions sometimes take multiple inputs to generate a given output.

Often, one of the first things you're concerned with is whether a given relation <em>is</em> a function. It <u><em>is not</em></u> a function if a given input maps to more than one output.

We say a relation <em>passes the vertical line test</em> when a vertical line through its graph cannot intersect the graph in more than one point. Such a relation <em>is a function</em>.

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When a function is written in equation form, it is often given a name (usually from the (early) middle of the alphabet. Common function names are f, g, h. Any name can be used.

When a function is defined by an equation, the variables that are inputs to the function are usually listed in parentheses after the function name:

  f(x), g(a, b), h(m)

These variables show up in the function definition that follows the equal sign:

  f(x) = 3x -4

  g(a, b) = (1/2)a·b

  h(m) = 1/(m^3 +3) +5

The listed variable is called the "argument" of the function.

This sort of form of an equation is sometimes called "functional form." That is, a dependent variable, such as y, can be defined by ...

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or the same relation can be written in functional form as ...

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Sometimes students are confused by this notation, thinking that f(x) means the product of f and x. Yes it looks like that, but no, that's not what it means.

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If we want to evaluate the above f(x) for x=2, we put 2 (every)where x is:

  f(x) = 3·x -4

  f(2) = 3·2 -4 = 6 -4 = 2

We can evaluate the function for literals, also.

  f(a) = 3a -4

  f(x+h) = 3(x+h) -4 = 3x +3h -4 . . . here, h is a variable, not the function name

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We can add, subtract, multiply, divide functions, and we can compute functions of functions. The latter is called a "composition", and is signified by a centered circle between the function names.

<u>Add functions</u>: f(x) +h(x) = (3x +4) +(1/(x^3 +3) +5)

  also written as (f+h)(x)

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  also written as (f-h)(x)

<u>Multiply functions</u>: f(x)·h(x) = (3x +4)(1/(x^3 +3) +5)

  also written as (f·h)(x) or (fh)(x)

<u>Divide functions</u>: h(x)/f(x) = (1/(x^3 +3) +5)/(3x +4)

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Because a function name can stand for an algebraic expression of arbitrary complexity, we often use a function name to talk about the properties of expressions in general.

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