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astra-53 [7]
3 years ago
13

A certain element has a half-life of 69 years. An experiment starts with 1,500 grams of the element. The amount of the element r

emaining x years after the experiment began can be modeled with the function f(x) = 1,500(2)–x/69. The mathematical domain of the function is all real numbers.
Which statement describes how the reasonable domain compares to the mathematical domain?

1The reasonable domain is restricted to integers.
2The reasonable domain is restricted to positive real numbers.
3The reasonable domain has a minimum value of 1,500.
4The reasonable domain has a maximum value of 1,500.
Mathematics
1 answer:
igor_vitrenko [27]3 years ago
7 0

Answer:

2. The reasonable domain is restricted to positive real numbers.

Step-by-step explanation:

The variable "x" is time in years from when the experiment began. It makes no sense to have negative values of x, as the experiment had not yet begun in negative time.

___

I would include x=0 in the domain, too, though you already know the amount of remaining element at x=0 and don't have to use the function to calculate it.

__

x might be restricted to integers if you're only measuring the remaining amount once a year.

The maximum value of 1500 applies to the *range* of the function, not its domain.

The minimum value of 1500 has nothing to do with anything.

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During a sale at the bookstore​, books sold for ​$4 and magazines sold for ​$3.50. Jan spent ​$22 and bought a total of 6 books
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Answer:

four magazines and two books

Step-by-step explanation:

3.50*4= 14

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Step-by-step explanation:

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3 years ago
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are sum
s344n2d4d5 [400]

The contingency tables serve to record the frequencies with which an object appears according to the measured variables, in this case two variables, each with two scales, the scratch resistance and the shock resistance, both measured as high and low.

The information is organized in such a way that the value of each box represents the total number of objects that meet the characteristics measured for each variable, for example in this case we have 70 discs with <em>high shock resistance and high scratch resistance</em>, 9 with <em>high scratch resistance and low shock resistance</em>, 16 with <em>high shock resistance and low scratch resistance</em> and finally 5 discs with <em>low scratch and shock resistance</em>.

We complete the table like this to obtain other total values:

\qquad\qquad\qquad\qquad\qquad\text{Shock resistance}\\\text{Scratch resistence}\left[\begin{array}{cccc}&\text{high}&\text{low}&\text{total}\\\text{high}&70&9&79\\\text{low}&16&5&21\\\text{total}&86&14&100\end{array}\right]

With this information, and taking into account that the values ​​presented are frequencies, to obtain the probability, each one must be divided into the total number of objects and multiply by 100, for this case as 100 objects, the frequency is the same percentage or probability .

Answer

a) The probability that, when selecting a random disk, its scratch resistance is high and its shock resistance is high is 70%, since this is the value that corresponds to the intersection of both variables in the table.

b) the probability that, when selecting a random disk, its resistance to scratches is high or that its resistance to impacts is high is 95% because the probability that its resistance to scratches is high is 79 % and the probability that its impact resistance is high is 86%, as one or the other requests, this is the sum of both minus the intersection, that is 79% + 86% -70% = 95%

c) the two events described are not mutually exclusive, that is, they cannot pass through, since the table informs us that of the analyzed discs 70, these two characteristics possessed, high shock resistance and high scratch resistance

8 0
3 years ago
The range of the data: 7, 10, 30, 16, 8, 5, 3, 18, 35, and 1 tell the answer only
Nikitich [7]
It is 32 because highest number subtracted by lowest
3 0
3 years ago
Read 2 more answers
The Distributive Property allows you to say that 3(x − 1) = 3x −
Serga [27]

Answer:

3x - 3

Step-by-step explanation:

In the distributive property each value inside the parenthesis will be multiplied by the value outside the parenthesis.

In the expression 3(x - 1) it will look like:

(3 . x) - (3 . 1)

Then we multiply both value separately giving us:

3x - 3

So in conclusion it would be right to assume that.

3(x - 1) = 3x - 3

8 0
3 years ago
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