A certain element has a half life of 2.5 billion years. a. You find a rock containing a mixture of the element and lead. You determine that 45​% of the original element​ remains; the other 55​% decayed into lead. How old is the​ rock? b. Analysis of another rock shows that it contains 65​% of its original​ element; the other ​35% decayed into lead. How old is the​ rock?

Answers

Answer 1

Answer:

Step-by-step explanation:

For a first order decay, fraction remaining = 0.5n where n = number of half lives elapsed.

fraction remaining = 55% = 0.55

0.55 = 0.5n

log 0.55 = n log 0.5

-0.2596 = -0.301 n

n = 0.8625 = # of half lives elapsed

0.8625 half lives x 2.5 billion years/half live = 2.16 billion years have elapsed = age of the rock

b)  0.15 = 0.5n

log 0.15 = n log 0.5

-0.824 = -0.301 n

n = 2.74 half lives

2.5 billion years/half life x 2.74 half lives = 6.85 billion years = age of rock


Related Questions

-(x+2)+6. anyone know how to solve it?

Answers

idk

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{-x+4}[/tex]

Step-by-step explanation:

[tex]-(x+2)+6[/tex]

Distributing the negative sign to the terms in the bracket.

[tex]-x-2+6[/tex]

Combining like terms.

[tex]-x+4[/tex]

Scenario: You are headed to New Orleans to visit a friend. You
just got your driver's license and your parents are very strict -
they won't let you drive over 50 miles per hour. When you tell
your friend the bad news, they insist on getting on their bicycle
and coming to meet you somewhere in the middle.
They aren't
very fast on their bicycle, but your friend can travel a solid 10
miles per hour.


Question: Where will y'all meet up?

Answers

Answer:

you want a specific place as an answer? or the mileage?

7. Which of the following is true?
1. For a pair of functions to be inverses, their compositions must be equal to 1.

2. In an inverse relation, coordinates of the ordered pairs are multiplied by 2.

3. An inverse of a function is always a function.

4. The horizontal line test is used to determine if a function's inverse will be a function.

Answers

Answer:

The horizontal line test is used to determine if a functions inverse will be a function. You will compose the functions (that is, plug x into one function, plug that function into the inverse function, and then simplify) and verify that you end up with just "x". Here's what it looks like: Determine algebraically whether f (x) = 3x – 2 and g(x) = (x + 2)/3 are inverses of each other.

Use the horizontal line test to determine if a function is a one-to-one function.

If ANY horizontal line intersects your original function in ONLY ONE location, your function will be a one-to-one function and its inverse will also be a function.

hope this helps

The horizontal line test is used to determine if a function's inverse will be a function is true. Correct option is 4.

1. This statement is not true. For a pair of functions to be inverses, their compositions (f(g(x)) and g(f(x))) must result in the identity function (1) for all values of x, not just for a specific value.

2. This statement is not true. In an inverse relation, the coordinates of the ordered pairs are swapped (x becomes y and y becomes x), not multiplied by 2.

3. This statement is not true. While many functions have inverses that are also functions, it is not a universal rule. Some functions may not have an inverse that is a function.

4. This statement is true. The horizontal line test is used to determine if a function has an inverse that is also a function. If a horizontal line intersects the graph of the function at more than one point, then the function does not have an inverse that is a function. However, if every horizontal line intersects the graph at most once, then the function does have an inverse that is a function.

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Suppose an angle has a measure of x degrees. What is the measure of the angle that is five times as large as the first angle? If the two angles are supplementary, what equation can you write using the measures of the angles? What are the measures of the two angles?

Answers

Step-by-step explanation:

x+5x=180

6x=180

x=30

and 5x=150

Answer:

Solution given:

let angle be a and 5x

since sum of two angles are supplement

so

equation becomes

a+5a=180

now

solving it

6a=180

a=180/6

a=30

and 5a=5×30=150

required angles are 50 and 130.

PLEASE HELP ASAP
Jaime flipped a coin 20 times, and it landed on heads 15 out of the 20 times. Which would be the BEST way for Jaime to change his experiment so that his experimental probability of the coin landing on heads is closer to the theoretical probability?

Answers

Answer:

Step-by-step explanation:

Were you given answer choices?  If so, please share them when you post your question.

The best way to improve the experimental probability would be to flip the coin more than 20 times; the more this is done, the better the estimate will be.

find the probability of Rolling a number greater than or equal to 4 on a standard die

Answers

Answer:

P(E)=1/2

Step-by-step explanation:

Total numbers=6

Numbers greater than or equal to 4= 3(4,5,6)

P(E)= favourable outcomes/total outcomes

P(E)=3/6

     =1/2

Answer:

4/6

Step-by-step explanation:

probability of rolling a num greater than or equal to 4 = 4/6

=2/3

find sin60 A.1/2 B.2/2 C.3/2

Answers

Answer: [tex]\frac{\sqrt{3} }{2}[/tex]

Step-by-step explanation:

To find sin(60), you need to know the unit circle. Sin(60) is the same as sin(π/3). On the unit circle, sin(π/3) is √3/2. We know this because the coordinates are (cos, sin). Sin is the y coordinate.

Answer:

[tex]\huge\boxed{\sin60^o=\dfrac{\sqrt3}{2}}[/tex]

Step-by-step explanation:

Let's take a right triangle with acute angles 30° and 60°.

We know that the ratio of the sides of such a triangle is 2 : 1 : √3

(look at the picture)

We know:

[tex]sine=\dfrac{opposite}{hypotenuse}[/tex]

In this triangle we have:

[tex]opposite=a\sqrt3\\hypotenuse=2a[/tex]

Substitute:

[tex]\sin60^o=\dfrac{a\sqrt3}{2a}[/tex]         cancel a

[tex]\sin60^o=\dfrac{\sqrt3}{2}[/tex]

The base of o rectangle is triple the height
The height is 35 What is the base?
Write a algebraic expression and evaluate​

Answers

Answer:

105 units

Step-by-step explanation:

Height of rectangle = 35 units

Since, base of o rectangle is triple the height.

Therefore, base of rectangle = 3*35 = 105 units

Another way:

h = 35 (given)

b = 3h

b = 3*35 (Plug h = 35)

b = 105 units

ABCD has a perimeter of 27 units and is dilated by a scale factor of 1/3. What is the perimeter of A¹B¹C¹D¹?

Answers

Answer:

Perimeter of A'B'C'D' = 9 units

Step-by-step explanation:

Given:

Perimeter of ABCD = 27 units

Scale factor = 1 / 3

Find:

Perimeter of A'B'C'D'

Computation:

Perimeter of A'B'C'D' = 1/3[Perimeter of ABCD]

Perimeter of A'B'C'D' = 1/3[27]

Perimeter of A'B'C'D' = 9 units

-2-5 is equivalent (equal) to -2+(-5)
True
False

Answers

Answer:

  True

Step-by-step explanation:

Subtracting a number is identical to adding its opposite.

  -2 -5 = -2 +(-5)

The statement is True.

_____

If you doubt this, you can have your calculator tell you what the answers are.

(17-7)•6+2+56-8
Pemdas

Answers

I don’t even know the answer to be honest
(10)x6+2+56-8
60+2+56-8
62+56-8
118-8
110

Find the midpoint of the line segment from (1,-1) to (2,4)

Answers

Answer: (1.5, 1.5)

Step-by-step explanation:

If a dozen paper clips weighs 9.6 g, and a pile of paper clips weigh 14.4 g, how many paper clips are in the pile

Answers

Answer:

18 paperclips are in the pile!

Step-by-step explanation:

We know that a dozen paperclips are equal to 9.6g, so we are going to divide 9.6 by 12 to figure out how much each paperclip weighs (0.8g). So we then divide 14.4 by 0.8 to figure out how many paperclips are in the pile! Hope this helps!

the ratio of peanuts to raisins in a snack mix is 5:4. A bag of the snack mix contains 200 peanuts. How many raisins are in the bag?

Answers

Number of raisins in the bag is 160 raisins

Given that;

Ratio of peanuts to raisins = 5:4

Bag of the snack mix contains = 200 peanuts

Find:

Number of raisins in the bag

Computation:

Number of raisins in the bag = 4[200/5]

Number of raisins in the bag = 4[40]

Number of raisins in the bag = 160 raisins

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You go down 9 floors in an elevator. How would you write the integer?

Answers

Answer:

-9

Step-by-step explanation:

Going down= negative

Answer:

u write negative 9

Step-by-step explanation:

What is the solution for this inequality?

-10x < 40

Answers

Answer:

Step-by-step explanation:

-10x < 40

x > -4

Endpoints of segment MN have coordinates (0, 0), (5, 1). The endpoints of segment AB have coordinates (1 1/2 , 2 1/4 ) and (−2 1/4 , k). What value of k makes these segments parallel?

Answers

Answer:

k=21

Step-by-step explanation:

Find the slope of MN which is 1/5, (use the slope formula.)

Use the slope formula for AB using k as y_2

Substitute and you get k=21

21-2.25/-2.25-1.5=-5

The lines are perpendicular because the slopes are the negative reciprocal of one another.

For K = 5.3, the line segments are parallel.

We have endpoints of segment MN have coordinates (0, 0), (5, 1) and  endpoints of segment AB have coordinates (1 1/2 , 2 1/4 ) and (−2 1/4 , k).

We have to determine the value of k that makes these segments parallel.

What is the condition for the lines to be parallel?

For lines to be parallel - slope of line 1 should be equal to slope of line 2.

m(1) = m(2)

According to question, we have -

Coordinates of M = (0, 0)

Coordinates of N = (5, 1)

Therefore, the slope of line MN = [tex]\frac{1 -0}{5-0}[/tex] = 1/5

Coordinates of A = (11/2, 21/4)

Coordinates of B = (-21/4, k)

Therefore, the slope of line AB =

[tex]$\frac{k -\frac{21}{4} }{\frac{-21}{4} -\frac{11}{2} }[/tex]  =  [tex]$\frac{k - \frac{21}{4} }{\frac{1}{4} }[/tex]  =  [tex]$\frac{\frac{4k - 21}{4} }{\frac{1}{4} }[/tex]  = 4k -21

Now, for the lines to be parallel -

m(MN) = M(AB)

4k - 21 = [tex]\frac{1}{5}[/tex]

5(4k - 21) = 1

20k - 105 = 1

20k = 106

k = 5.3

Hence, for K = 5.3, the line segments are parallel.

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[tex]\frac{r}{2}+\frac{s}{r} -\frac{r}{4}+\frac{1}{5},r=-1,s=0[/tex]

Answers

Answer:

-1/20

Step-by-step explanation:

r/2 + s/r - r/4 + 1/5 =

= -1/2 + 0/(-1) - (-1)/4 + 1/5

= -1/2 + 1/4 + 1/5

= -10/20 + 5/20 + 4/20

= -5/20 + 4/20

= -1/20

Hi. I'm needing help with Graphing refelctions across the Y-Axis. f(x) = 1.5(0.5) ​

Answers

Answer:

g(x) is the reflection of f(x) over the y-axis.

hope it helps

Answer:

step 1:  g(x) = 1.5(0.5)^-x

step 2: g(0) = 1.5

step 3: plot points on graph

step 4: g(1) = 3    g(-1) = .75

step 5: Plot the points

step 6:  y=0

step 7:  The smooth curve includes these points

Step-by-step explanation:

Just took this on edge 2021

PLEASE ANSWER QUICK!Kierran is trying to find the circumference of a circle. He knows that the radius (r) of the circle is 6 feet and that the diameter, d=2r. Which formula should he use?
A) A=3.14(2r)^2
B) C=3.14(2r)
C) A=3.14d^3
D) C=3.14(2D)

Answers

Answer:

B) C=3.14(2r)

Step-by-step explanation:

Circumference of a circle= 2πr

radius=6 feet

Diameter= 2r

=2*6

=12 feet

π= 3.14

C= 2πr

= 2 * 3.14 * r

= 3.14 * 2 * r

C= 3.14 (2r)

Kierran should use the formula C= 3.14 (2r) to find the circumstance of the circle

Option B is the correct answer

C= 3.14 (2r)

= 3.14 * 2 * 6

= 37.68 eet

Classify the polygon. Then determine whether it appears to be regular or not regular. A. stargon; regular B. hexagon; not regular C. pentagon; not regular D. pentagon; regular

Answers

The answer to the question is c

Express the pair of fraction using the least common denominator of the two 3/8,7/10

Answers

Answer:

Step-by-step explanation:

3/8 x 5/5 = 15/40

7/10 x 4/4 = 28/40

15/40, 28/40

The least common denominator of the two pairs of fractions is 15/40 are 28/40. which is the correct answer would be an option (A).

What is LCD?

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

What is the fraction?

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

We have to determine the least common denominator of the two pairs of fractions.

The fractions are 3/8, and 7/10

⇒ 3/8

Multiply by 5/5 in the fraction,

⇒ 3/8 × 5/5 = 15/40

⇒ 7/10

Multiply by 4/4 in the fraction,

⇒ 7/10 × 4/4 = 28/40

Therefore, the least common denominator of the two pairs of fractions is 15/40 are 28/40

Learn more about the least common denominator here:

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The scores of players on a golf team are shown on the table Celia-3 Janine 3 Sami 1 Ted 4 Travis 0 The team combined score was 0. What was Travis score?

Answers

His score would have to be -5:

-3 + 3 = 0

0 + 1 = 1

1 + 4 = 5

5 + (-5) = 0

So you know that the su of all the scores is 0.

The scores in the table are cecilia -3, janine 3, sami 1 and ted 4 and travis x, where x is the number that we want to know.

if we sum those, we have : 3 - 3 + 4 + 1 + x = 0

and we get 5 + x = 0

then x= -5, so travis's score is -5 points.

Write 5 times x to the two thirds power in radical form.

Answers

(5 • x)^2/3

We know that the parentheses goes around 5 • x and that it also goes to the power of 2/3.

A geometric sequence is shown on the graph below. What is the formula for the nth term of the sequence?

Answers

Answer:

aₙ = 40*(1/2)ⁿ⁻¹

Step-by-step explanation:

As per graph we have:

a₁ = 40, a₂ = 20, a₃ = 10, a₄ = 5, a₅ = 2.5

So the first term is 40 and common ratio is

20/40= 10/20 = 5/10 = 2.5/5 = 1/2

Formula for nth term is:

aₙ = a₁rⁿ⁻¹aₙ = 40*(1/2)ⁿ⁻¹

( 5n 3 + n 4 - 5 ) - ( -5 - 6n 3 - 4n 4 )

Answers

( 5n 3 + n 4 - 5 ) - ( -5 - 6n 3 - 4n 4 )

Simplify the expression.

53 n

Answer:

The simplified solution to this expression is 5n⁴ + 11n³

Step-by-step explanation:

(5n³ + n⁴ - 5) - (-5 - 6n³ - 4n⁴)

Distribute the negative sign to (-5 - 6n³ - 4n⁴)

5n³ + n⁴ - 5 + 5 + 6n³ + 4n⁴

Group like terms.

(4n⁴ + n⁴) + (6n³ + 5n³) + (-5 + 5)

Combine like terms.

5n⁴ + 11n³

3. Ann wants to paste 18 posters on her bedroom wall. She wants to put the same
number of posters in each row. How many rows could Ann make, 4.5, 9 or 10?

Answers

Answer:

9

Step-by-step explanation:

18÷2=9

So, Ann could have 9 rows of posters with 2 posters in each row.

Describe the type of solution for the given system of linear equations.
x + 4y = 7
8y = 14 - 20

a. infinite solutions
b. two solutions
c. no solution
d. one solution

Answers

Answer:

B

Step-by-step explanation:

Question 1 of 10
Sam studied the effects of exercise on short-term memory. Which of these is
a response variable?
A. Exercise
B. Short-term memory
C. Neither exercise nor short-term memory
O D. Both exercise and short-term memory

Answers

Answer:

B. Short-term memory

Step-by-step explanation:

Response variable is a dependent variable. It is dependent on the explanatory variable that is referred to as the independent variable.

In research study, the response variable is what is usually measured by the researcher. In the case given above, short-term memory is the response variable, which is dependent on exercise.

Question 4 (1 point)
Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4, 5)
B = {1, 3, 5, 7}
How many elements are in A n B?

Answers

Answer:

pretty sure its A n B = {1,5}

Step-by-step explanation:

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