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2 years ago

I need to find Domain and Range but how do I know when to use brackets or parentheses

Mathematics

1 answer:

german2 years ago

3 0

Answer:

Square brackets [ or ] are used when the end point is included.
Parentheses ( or ) are used when the end point is not included.

Step-by-step explanation:

The domain is the horizontal extent of the graph. Here, it is from -2 to +3, with -2 included in the domain and +3 not included.

As an inequality, the domain is written ...

-2 ≤ x < 3

In interval notation, we use a square bracket for the "or equal to" case:

[-2, 3)

The range is the vertical extent of the function. Here, the range extends from -4 (not included) to +5 (included).

As an inequality, the range is written ...

-4 < y ≤ 5

In interval notation, the range is written using a square bracket for the "or equal to" case:

(-4, 5]

_____

<em>Comment on infinity</em>

There is no such thing as "equal to infinity" so an infinite limit is always represented in interval notation using a parenthesis.

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Grain is stored in cylindrical structures called silos. Find the volume of a silo with a diameter of 11.1 feet and a height of 2

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1.) Find the area of the circle at the top ( A= pi x radius squared )
2.) radius is 5.55 (half of 11.1)
3.) A= pi x 5.55 squared
4.) area of circle =96.77
5.) multiply area of circle(96.77) by height (20)
6.) answer = 1935.38

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3 years ago

Inez’s piggy bank has 10 quarters, 6 dimes, 3 nickels, and 2 pennies. What is the probability of Inez picking a nickel out of th

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The answer is 1/7 :)

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2 years ago

Read 2 more answers

Find the probability p(e or f) if e and f are mutually exclusive, p(e)equals 0.25, and p(f)equals 0.51.

Masteriza [31]

The definition of two events being mutually exclusive (or disjoint) only means that it is not possible for the two events to occur together. Given two events, E and F, they are mutually exclusive and also mean independent.

In this case, since events E and F are mutually exclusive, therefore the probability that either E or F will occur will simply be the sum of two events.

P (E or F) = P (E) + P (F)

P (E or F) = 0.25 + 0.51

P (E or F) = 0.76

Therefore this means that there is a 76% probability that either E or F will occur.

8 0

3 years ago

A right triangle has one vertex on the graph of y = 9 - x^2 , x > 0, at ( x , y ), another at the origin, and the third on th

jenyasd209 [6]

Answer:

a. A(x) = (1/2)x(9 -x^2)

b. x > 0 . . . or . . . 0 < x < 3 (see below)

c. A(2) = 5

d. x = √3; A(√3) = 3√3

Step-by-step explanation:

a. The area is computed in the usual way, as half the product of the base and height of the triangle. Here, the base is x, and the height is y, so the area is ...

A(x) = (1/2)(x)(y)

A(x) = (1/2)(x)(9-x^2)

b. The problem statement defines two of the triangle vertices only for x > 0. However, we note that for x > 3, the y-coordinate of one of the vertices is negative. Straightforward application of the area formula in Part A will result in negative areas for x > 3, so a reasonable domain might be (0, 3).

On the other hand, the geometrical concept of a line segment and of a triangle does not admit negative line lengths. Hence the area for a triangle with its vertex below the x-axis (green in the figure) will also be considered to be positive. In that event, the domain of A(x) = (1/2)(x)|9 -x^2| will be (0, ∞).

c. A(2) = (1/2)(2)(9 -2^2) = 5

The area is 5 when x=2.

d. On the interval (0, 3), the value of x that maximizes area is x=√3. If we consider the domain to be all positive real numbers, then there is no maximum area (blue dashed curve on the graph).

5 0

2 years ago

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estim

Alenkasestr [34]

Answer:

n = 400

Step-by-step explanation:

The formula for the error in our estimate is given by:

Standard Error : √ ( p(1-p)/ n)

Error = SE = Zα/2 √ ( p(1-p)/ n) where

Zα/2= critical value for 95% confidence level = 1.96

and we know our error is 3.5 %

But we do not the sample proportion p. Then what we can do is give an estimate of p in the absence of any other information.

In this case we will use p= 0.5 which is the value that maximizes the expression for the standard error :

if p = 0.8 then SE= 0.040

p = 0.3 then SE =0.036

p = 0.1 then SE = 0.030

p = 0.5 then SE = 0.050

Substituting

3.5/100 = 1.96 x √ (( 0.5 x 0.5 ) /n )

3.5/ (100 x 1.96 x 0.5 ) = 1/ √n

0.0357 = 1 /√n

n = 20²

n = 400

3 0

3 years ago