45 x 60 / 45 = ______ <br><br> pleasee help

An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount o

Lubov Fominskaja [6]

An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of $^{14}\text{C}$ . Estimate the minimum age of the charcoal, noting that $2^{10} = 1024$

Answer:

57300 years

Step-by-step explanation:

Using the relation of an half-life time in relation to fraction which can be expressed as:

$\dfrac{N}{N_o} = (\dfrac{1}{2})^{\frac{t}{t_{1/2}}$

here;

N represents the present atom

$N_o$ represents the initial atom

t represents the time

$t_{1/2}$ represents the half - life

Given that:

Its charcoal is found to contain less than 1/1000 the normal amount of $^{14}\text{C}$ .

Then ;

$\dfrac{N}{N_o} = \dfrac{1}{1000}$

However; we are to estimate the minimum age of the charcoal, noting that $2^{10} = 1024$

so noting that $2^{10} = 1024$ , then:

$\dfrac{1}{1000}> \dfrac{1}{1024}$

$\dfrac{1}{1000}> \dfrac{1}{2^{10}}$

$\dfrac{1}{1000}> (\dfrac{1}{2})^{10}$

If

$\dfrac{N}{N_o} = \dfrac{1}{1000}$

Then

$\dfrac{N}{N_o} > (\dfrac{1}{2})^{10}$

Therefore, the estimate of the minimum time needed is 10 half-life time.

For $^{14}\text{C}$ , the normal half-life time = 5730 years

As such , the estimate of the minimum age of the charcoal = 5730 years × 10

= 57300 years

5 0

2 years ago

In a sample of 60 diners at a restaurant, 12 had ordered an appetizer. If the restaurant serves 800 diners each day, how many ar

san4es73 [151]

If im correct i think it should be 160 because i divided 60 by 12 and got 5 the divided 800 by 5 and got 160.

5 0

2 years ago

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Evaluate the following expression: 12 – 10 + 5 - 11. Remember to show your work

MatroZZZ [7]

Answer:

-4

Step-by-step explanation:

3 0

2 years ago

A vector is in standard position, with its terminal point in the second quadrant and an x-coordinate of –5. The vector has a mag

joja [24]

a.

The y-coordinate of the vector with its terminal point in the second quadrant is 6.

The magnitude of the vector, r = √(x² + y²) where x = x-coorcinate of vector = -5 and y = y-coordinate of vector.

Since r = √61 and r = √(x² + y²)

Making y subject of the formula, we have

y = √(r² - x²)

Substituting the values of the variables into the equation, we have

y = √((√61)² - (-5)²)

y = √(61 - 25)

y = ±√36

y = ±6

Since r is in the second quadrant, its y-coordinate is positive.

So, y = 6

So, the y-coordinate of the vector with its terminal point in the second quadrant is 6.

b.

The direction angle of the vector with its terminal point in the second quadrant is 130°

The direction angle of the vector is gotten from tanФ = y/x

Subsstituting x and y into the equation, we have

tanФ = y/x

tanФ = 6/-5

tanФ = -1.2

tan(180° - Ф) = 1.2

Taking inverse tan of both sides, we have

180° - Ф = tan⁻¹(1.2)

180° - Ф = 50.2°

Ф = 180° - 50.2°

Ф = 129.8°

Ф ≅ 130° to the neares whole number

The direction angle of the vector with its terminal point in the second quadrant is 130°.

Learn more about vectors here:

brainly.com/question/18478651

3 0

2 years ago

Which graph shows a set of ordered pairs that represent a function?<br><br>Need help

Sveta_85 [38]

Answer:

The third graph, the top right graph

Step-by-step explanation:

A function when determined graphically is a graph that passes the straight line test, which means if there is any two points on the graph which you can plot a vertical straight line going through both of them it is not a function. If 1 x value is equal to 2 y values, it is not a function.

8 0

2 years ago

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45 x 60 / 45 = ______ pleasee help