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3 years ago

Please show ALL YOUR WORK and how u came to the conclusion.

Mathematics

1 answer:

hichkok12 [17]3 years ago

4 0

Answer:

Step-by-step explanation:

clearly, the equation has to allow t=0, and for that point we need to get 100% (of carbon-14) as result.

and so we also see, that the function calculates the % of the remaining carbon-14.

so, we need the desired outcome 60(%),

because 60 = 100 - 40.

and again, we need a function that shows t=0.

the only answer option fulfilling both criteria is A.

B divides in the exponent by t, so t=0 is not in the domain of the function.

and C and D aim for the wrong remaining percentage.

You might be interested in

-2x^2+4x-1 from 6x^2+3x-9

kirza4 [7]

Answer:

$8{x}^{2} - x - 8$

Step-by-step explanation:

We want to subtract

$- 2 {x}^{2} + 4x - 1$

from

$6 {x}^{2} + 3x - 9$

We set up the subtracttion problem to get:

$6 {x}^{2} + 3x - 9 - ( - 2 {x}^{2} + 4x - 1)$

We expand the parenthesis to get:

$6 {x}^{2} + 3x - 9 + 2 {x}^{2} - 4x + 1$

Group similar terms:

$6 {x}^{2} + 2 {x}^{2} + 3x- 4x + 1 - 9$

We simplify to get:

$8{x}^{2} - x - 8$

4 0

3 years ago

In 1995, Orlando, Florida, was about 175,000. At the time, the population was growing at a rate of about 2000 per year. Write an

gladu [14]

Answer:

y= 2000 * x + 175000

Step-by-step explanation:

Given is Population is 175,000

Increase in rate = 2000/year

Let x be the population in 1995 which is C= 175,000

y= Population after per year

We know the formula for slope intercept form is

y= mx + C ............... (i)

Now from the suppose values and given

m= 2000

Now putting values in equation (i) gives

y= 2000 * x + 175000

Here x is the No of years

6 0

2 years ago

Find the unit rate. 6 2/5 revolutions in 2 2/3 seconds

Brums [2.3K]

The unit rate will be in revolutions per second. That means divide number of revolutions by number of seconds.

first convert from mixed fraction.
6 2/5 = 32/5 revolutions
2 2/3 = 8/3 seconds

32/5 ÷ 8/3
flip multiply
32/5 × 3/8 = 12/5 revolutions per second

12/5 = 2 2/5 revolutions per second

6 0

3 years ago

1. If the domain of a function f(x) is the set {10, 20, 30}. What does the information tell you about f-1(x)?

ziro4ka [17]

PART A (1 in diagram)

Each mapping diagram represents a function because none of the elements in the inputs maps on to two different elements in the outputs.

1. The domain of the given function f(x) is the set {10, 20, 30}.

All we can say about

${f}^{ - 1} (x)$

is that, it has a range of {10, 20, 30}.

This is because the domain of a function becomes the range of its inverse function.

2. If the graph of a function f(x) includes the point (3, 0), then the graph of the inverse function ,

${f}^{ - 1} (x)$

will contain the point (0,3).

Reason:The point on the graph of the inverse function is obtained by reflecting the corresponding point on the graph of the function in the line y=x. We just have to swap the coordinates.

In simple terms the domain of the function becomes the range of the inverse function and vice versa.

3. If the first term in an arithmetic sequence is 2.

Then we have a=2.

If the twelfth term is 211, then

$a + 11d = 211...(1)$

Put a=2 into this equation.

$2 + 11d = 211$

Solve for d.

$11d = 211 - 2$

$11d = 209$

$d = \frac{209}{11} = 19$

$a_n = 135$

then

$a + (n - 1)d = 135$

Substitute a=2 and d=19

$2 + (n - 1)19 = 135$

$19(n - 1) = 133$

$(n - 1) = \frac{133}{19}$

$n - 1 = 7$

$n = 7 + 1 = 8$

Therefore n=8

4 0

3 years ago

The length of a rectangle is 22 feet longer than the width. the perimeter is 1616 feet. find the dimensions of the rectangle.

NemiM [27]

So we can setup variable equations for this:
so we're given that the length is 22feet longer than the width!
so as an expression length is equal to 22+w
and width as an expression is just w
so the formula for the perimeter for a rectangle is 2l+2w=perimeter
so fill it in now!
1616=2(22+w)+2w
1616=44+2w+2w
1616=44+4w
1572=4w
divide by four..
w=393
and length is simply 22 more than that as stated in the question!
so length is 415
dimensions are: 415x393

7 0

3 years ago