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3 years ago

Three kinds of mathematical statements

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

6 0

Answer:

Universal Statements, Conditional Statements,And Existential Statements.

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(1 point) Carbon dating is often used to determine the age of a fossil. For example, a humanoid skull was found in a cave in Sou

Aleksandr [31]

Answer:

The estimated age of the skull is 39118 years.

Step-by-step explanation:

The amount of the substance after t years is given by:

$A(t) = A(0)(1-r)^t$

In which A(0) is the initial amount, and r is the decay rate.

The half-life of carbon-14 is about 5600 years.

This means that $A(5600) = 0.5A(0)$ . We use this to find r, or 1 - r, to replace in the equation. So

$A(t) = A(0)(1-r)^t$

$0.5A(0) = A(0)(1-r)^{5600}$

$(1-r)^{5600} = 0.5$

$\sqrt[5600]{(1-r)^{5600}} = \sqrt[5600]{0.5}$

$1 - r = (0.5)^{\frac{1}{5600}}$

$1 - r = 0.9999$

$A(t) = A(0)(0.9999)^t$

Only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire.

This is t for which $A(t) = 0.02A(0)$ . So

$A(t) = A(0)(0.9999)^t$

$0.02A(0) = A(0)(0.9999)^t$

$(0.9999)^t = 0.02$

$\log{(0.9999)^t} = \log{0.02}$

$t\log{0.9999} = \log{0.02}$

$t = \frac{\log{0.02}}{\log{0.9999}}$

$t = 39118$

The estimated age of the skull is 39118 years.

6 0

3 years ago

Christopher is thinking of two positive integers. The sum of the integers is 27. When twice the first integer is added to half o

LenKa [72]

Answer:

Let x and y be the two positive integers the Christopher is thinking.

x is equal to 7

and y =20

8 0

3 years ago

5x + 10+5(x+2) distributive property <br> (Just simply)

viva [34]

Answer:

10x + 20

Step-by-step explanation:

5x + 10 +5(x) + 5(2)

= 5x+10 +5x +10

= 10x +20

7 0

3 years ago

You are currently earning £14,600 per year. At your annual review, you are awarded a wage rise of 1.5%. What is your new rate of

Anna71 [15]

Answer:

14819

Step-by-step explanation:

14 600 x 0.015 = 219

14600 plus 219 = 14819

7 0

3 years ago

Simplify 14 to the fifteenth power over 14 to the fifth power.

podryga [215]

Answer:

4^10

subtract 15-5 and leave the 14 be

8 0

3 years ago

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