a sample from a mummified bull was taken from a certain place. The sample shows that 71% of the carbon-14 still remains. how old is the sample

Answers

Answer 1

Answer:

Step-by-step explanation:

Decay of carbon - 14 is exponential in nature . It decays as follows .

[tex]N=N_0e^{-\lambda t}[/tex]  λ is called decay constant .

λ = .693 / T where T is half life .

Half life of carbon-14 is 5700 years

λ = .693 / T

= .693 / 5700

= 12.158 x 10⁻⁵ year⁻¹

[tex]N=N_0e^{-\lambda t}[/tex]

N = .71 N₀

[tex].71 N_0 =N_0e^{-\lambda t}[/tex]

[tex].71 =e^{-\lambda t}[/tex]

Taking ln on both sides

ln .71 = - λ t

ln .71 = - 12.158 x 10⁻⁵  t

-0.3425 =  - 12.158 x 10⁻⁵  t

t = .3425 / 12.158 x 10⁻⁵

2817  years .


Related Questions

Find the sum of the first 12 terms of the sequence 512, 256, 128, … This is infinite series notation, the answer is NOT 896...

Answers

Answer:

1023.75

Step-by-step explanation:

The sum of a geometric sequence is

sum = a( 1 - r^n) / (1-r)

where a is the first term  r is the common ratio and  r^n is the nth term

We need to find the common ratio

r = 256/512 = 1/2

sum = 512 ( 1 - 1/2^12) / ( 1-1/2)

       =512( 1-.000244141) / (.5)

       =512(.999755859) /.5

     =1023.75

Answer:

1023.75

Step-by-step explanation:

sum = a( 1 - r^n) / (1-r)

a1 = 512

n = 12

r = 256 / 512 = 1/2

                              512 (1 - 1/2¹²)

therefore.. sum =  ------------------ = 1023.75

                                   1 - 1/2

Please answer this correctly without making mistakes

Answers

Answer:

10 9/20

Step-by-step explanation:

Hey there!

If Hillsboro to Campbell is 16 2/20 and Hillsboro to Oxford is 5 13/20,

we’ll do

16 2/20 - 5 13/20

Imrpoper form

322/20 - 113/20

322 - 113

209/20

10 9/20 miles from Oxford to Campbell.

Hope this helps :)

The comment above me ^ help me too

PLZ HELP 55 POINTS Two quantities, x and y, are related proportionally such that 3x=2y . Which equation shows the same proportional relationship? A x/y=3/2 B x/2=y/3 C x/3=y/2 D x/2=3/y

Answers

Answer:

B

Step-by-step explanation:

3x = 2y

One way to solve this is to simply plug in values. If we say the following:

x = 2

y = 3

Then, we can start testing.

A: [tex]x/y = 3/2[/tex]

by plugging 2 and 3 in, we see that A doesn't work.

B: x/2 = y/3

This works! First we should look at the other equations.

C: x/3 = y/2

Nope.

D: x/2 = 3/y

This also works, but only with certain numbers. If we were to make x = 4, and y = 6, this wouldn't work.

You could also find out all of this using algebra. so, our anwser is B.

Please help soon as possible! This is urgent! Match each expression with the correct description.

Answers

Answer:

Hey there!

q is 1, and n=-2.

q-n=1-(-2), which is 3.

n-q=-2=1, which is -3.

q is 1.

Thus, the least value is n-q, and the greatest value is q-n. Closest to zero would be q.

Let me know if this helps :)

Answer:

Least: n-q

Greatest: q-n

Closest to zero: q

in the diagram, POS and UOR are straight lines. OQ is the bisector of angle POR . angle POU and angle UOT are complementary angles.Find the values ofx abd y.​

Answers

Answer:

x = 34° and y = 62°

Step-by-step explanation:

Complementary angles sum to 90°, therefore 90 = 56 + x which means that x = 34°. The angles formed by an angle bisector are congruent and so are vertical angles; this means that ∠SOR = ∠POU = 56° and ∠POQ = ∠QOR = y. Since POS is a straight line, straight lines have a measure of 180° and because ∠POS = ∠POQ + ∠QOR + ∠SOR, we know that 180 = y + y + 56 → 180 = 2y + 56 → 180 → 2y = 124 → y = 62°.

F
19) The points (6,5), (7,2), (9,6), and (10,3) are vertices of an inscribed square.
A)(x - 8)2-(y - 4)2 = 5
B) (x – 8)2 + (y - 4)2 = 15
C) (X + 8)2 + (y + 4)2 = 5
D) (x - 8)2 + (y - 4)2 = 5
Find an equation for the circle

Answers

Answer:

The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]

(D) is correct option.

Step-by-step explanation:

Given that,

Points (6,5), (7,2), (9,6) and (10,3) are vertices of an inscribed square.

We need to calculate the distance between (7,2) and (9,6)

Using formula of distance

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

Put the value into the formula

[tex]d^2=(9-7)^2+(6-2)^2[/tex]

[tex]d^2=20\ m[/tex]

The radius will be

[tex]r^2=\dfrac{20}{4}[/tex]

[tex]r^2=5[/tex]

We need to calculate the center of the point (7,2) and (9,6)

Using formula of center point

For x axis,

[tex]h=\dfrac{x_{2}+x_{1}}{2}[/tex]

Put the value into the formula

[tex]h=\dfrac{9+7}{2}[/tex]

[tex]h=\dfrac{16}{2}[/tex]

[tex]h=8[/tex]

For y axis,

[tex]k=\dfrac{y_{2}+y_{1}}{2}[/tex]

Put the value into the formula

[tex]k=\dfrac{6+2}{2}[/tex]

[tex]k=\dfrac{8}{2}[/tex]

[tex]k=4[/tex]

We need to find the equation for the circle

Using formula of equation of circle

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Put the value into the formula

[tex](x-8)^2+(y-4)^2=5[/tex]

Hence, The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]

(D) is correct option.

Little bit more math hw

Answers

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

For these kind of problems, simply take the denominator and compare it to zero. Then solve the equation.

[tex]x+2=0\\\\\Rightarrow x=-2[/tex]       By subtracting 2 from both sides!

Best Regards!

Show all work to solve 3x2 − x − 2 = 0.

Answers

Answer:

x=-2/3 and 1

Step-by-step explanation:

3x^2-x-2=0

(3x+2)(x-1)

3x=-2

x=-2/3

x=1

the city of James town is 2 meters below sea level. Takoradi, a city in western region, is 7 meters below sea level . How much higher is James town than Takoradi​

Answers

Answer:

James town is 5 meters higher than Takoradi​ .

Step-by-step explanation:

Given:

Height of James town = 2 meters below sea level

Height of Takoradi town = 7 meters below sea level

To find:

How much higher is James town that Takoradi = ?

Solution:

As we can see the standard of height is how much the town is below the sea level.

So, the height of town having lesser value will be at a higher level.

Value of Height of James town is lesser than that of Takoradi town.

Therefore, James town is at a higher level.

Difference of height = 7 meters - 2 meters = 5 meters

So, the answer is:

James town is 5 meters higher than Takoradi.

A football field has the shape of a rectangle with dimensions of 300 feet long and 160 feet wide. If a fan was to run diagonally from one end zone to the opposite end zone, how far would she run to the nearest foot? Enter only the number.

Answers

Answer: 340

Explanation:

In order to find the length of the diagonal of a rectangle you need to cut the rectangle in diagonal then you have 2 right triangle:

We can take one right triangle to work with:

We can use Pythagorean’s theorem to find the hypotenuse of the right triangle (also the diagonal of the rectangle):

a^2 + b^2 = c^2
300^2 + 160^2 = c^2
90000 + 25600 = c^2
115600 = c^2
Sqrt 115600 = c
340 = c

Where c is the hypotenuse of the right triangle and also the diagonal of the rectangle

Answer:

340 feet

Step-by-step explanation:

we use Pythagora

d² = l² + w²

d = √300ft)² + 160ft)²

= √90000ft² + 25600ft²

= √115600ft²

= √(2⁴ₓ5²ₓ17²)ft²

= √(2²ₓ5ₓ17)ftₓ(2²ₓ5ₓ17)ft

= √340ftₓ340ft

= 340 feet

Anand needs to hire a plumber. He's considering a plumber that charges an initia
hourly rate of $28. The plumber only charges for a whole number of hours. Anar
more than $250, and he wonders how many hours of work he can afford.
Let H represent the whole number of hours that the plumber works.
1) Which inequality describes this scenario?
Choose 1 answer:
28 - 65H <250

Answers

Complete question :

Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an

hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.

Let H represent the whole number of hours that the plumber works.

1) Which inequality describes this scenario?

Choose 1 answer:

A. 28 + 65H < 250

B. 28 + 65H > 250

C. 65 + 28H < 250

D. 65 +28H > 250

2) What is the largest whole number of hours that Anand can afford?​

Answer:

65 + 28H < 250

Number of hours Anand can afford = 6 hours

Step-by-step explanation:

Given the following information :

Initial hourly rate = $65

Hourly rate = $28

Number of hours worked (whole number) = H

Maximum budgeted amount to spend = $250

Therefore ;

(Initial charge + total charge in hours) should not be more than $250

$65 + ($28*H) < $250

65 + 28H < 250

Number of hours Anand can afford :

65 + 28H < 250

28H < 250 - 65

28H < 185

H < (185 / 28)

H < 6.61

Sinve H is a whole number, the number of hours he can afford is 6 hours

Answer:

65 + 28H < 250

6
Step-by-step explanation:

tried it, it worked.
the other answer is correct but hard to understand so give them thanks and 4 star :)

What is the number of square units in the area of the triangle whose vertices are points A(2,0), B(6,0), and C(8,5)?

Answers

10 units squared. Hope this helped.

The area of the triangle is 10 square units.

The given coordinates are A(2,0), B(6,0), and C(8,5).

What is the formula to find the area of a triangle?

The formula of area of triangle formula in coordinate geometry is the area of the triangle in the coordinate geometry is:  [tex]A=\frac{1}{2} |x_{1} (y_{2}-y_{3})+x_{2} (y_{3}-y_{1})+x_{3} (y_{1}-y_{2})|[/tex]

Now, Area=1/2|2(0-5)+6(5-0)+8(0-0)|=0.5|20|

=10 square units

Therefore, the area of the triangle is 10 square units.

To learn more about the area of the triangle visit:

https://brainly.com/question/11952845.

#SPJ2

Please help me how to do no 5

Answers

Answer:

  -864

Step-by-step explanation:

The determinant of a matrix product is the product of the determinants. The determinant of a transpose is the same as the determinant of the original. Hence ...

  [tex]|AB^5C^T|=(4)(-2)^5(\frac{1}{4})=-32[/tex]

The multiplication of an n×n matrix by a scalar 'a' multiplies its determinant by a^n, so the desired determinant is ...

  [tex]|3AB^5C^T|=3^3(-32) = \boxed{-864}[/tex]

How many adults must be randomly selected to estimate the mean FICO​ (credit rating) score of working adults in a​ country? We want ​% confidence that the sample mean is within points of the population​ mean, and the population standard deviation is .

Answers

Answer: hello below is the complete question

How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number

answer : 737 adults

Step-by-step explanation:

confidence interval = 90% = 0.9

( E ) = 4

standard deviation = 66

first we have to calculate the value of a

a = 1 - confidence interval

  = 1 - 0.9 = 0.10      hence  a / 2 = 0.05

next find the value of Z a/2 from table

Z[tex]_{0.05}[/tex]  = 1.645

The number of Adults selected can be determined using this relation

N = [tex](Z_{a/2} * (s/E))^2[/tex]

   = [tex](Z_{0.05} * ( 66/4))^2[/tex]

   = 737

Laura is bowling 5 games. Her first 4 scores were 135, 144, 116, and 132.

To end up with an average score of at least 136.8, what is the lowest score Laura will need in the fifth game?

Answers

Answer:

157

Step-by-step explanation:

135+144+116+132=527

527+136.8=762.8

762.8÷5= 157

Joe drove 315 miles on 15 gallons of gas. What is his mileage in miles/gallon?
miles/gallon

Answers

Answer:

21 miles/gallon

Step-by-step explanation:

To find his mileage in miles/gallon, divide the number of miles by the number of gallons.

315/15

= 21

= 21 miles/gallon

Answer:

21 miles / gallon

Step-by-step explanation:

Take the miles and divide by the gallons

315 miles / 15 gallons

21 miles / gallon

Evaluate the expresión 6c-d when c=2 and d=10 I need help?

Answers

Answer:

the answer is 18

Step-by-step explanation:

8 is the answer

Find the length S of the spiral (t cos(t), t sin(t)) for 0 ≤ t ≤ 3π. (Round your answer to three decimal places.) S =

Answers

The arc length is

[tex]S=\displaystyle\int_C\mathrm ds[/tex]

where C is the given curve and ds is the line element. C is defined on 0 ≤ t ≤ 3π by the vector function,

[tex]\mathbf r(t)=(t\cos t,t\sin t)[/tex]

so the line element is

[tex]\mathrm ds=\left\|\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}\right\|\,\mathrm dt[/tex]

[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm d(t\cos t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm d(t\sin t)}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

[tex]\mathrm ds=\sqrt{1+t^2}\,\mathrm dt[/tex]

So we have

[tex]S=\displaystyle\int_0^{3\pi}\sqrt{1+t^2}\,\mathrm dt\approx46.132[/tex]

Select the correct answer. If , which statement is true? if g(x) = f(1/3x)
A. The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
C. The graph of function f is compressed horizontally by a scale factor of to create the graph of function g.
D. The graph of function f is compressed vertically by a scale factor of to create the graph of function g.

Answers

Answer:

B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.

Step-by-step explanation:

The rules for linear transformations are that

 g(x) = a·f(b·(x-c)) +d

stretches the graph vertically by a factor of "a" (before the shift)

compresses the graph horizontally by a factor of "b" (before the shift)

shifts it to the right by amount "c"

shifts it up by amount "d".

Your equation has b=1/3, so the graph is compressed by a factor of 1/3, which is equivalent to a stretch by a factor of 3.

The appropriate choice of description is ...

 b) the graph of g(x) is horizontally stretched by a factor of 3

Answer:

B

Step-by-step explanation:

Correct on Plato

PLEASE HELP Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes betweenh
$250 and $300.

Answers

Answer: 0.0215 .

Step-by-step explanation:

Let X denotes the weekly wages at a certain factory .

It is normally distributed , such that

[tex]X\sim N(\mu=400,\ \sigma= 50)[/tex]

Then, the probability that a worker  selected at random makes between

$250 and $300:

[tex]P(250<X<300)=P(\dfrac{250-400}{50}<\dfrac{x-\mu}{\sigma}<\dfrac{300-400}{50})\\\\=P(\dfrac{-150}{50}<z<\dfrac{-100}{50})\ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=P(-3<z<-2)\\\\=P(z<-2)-P(z<-3)\\\\=1-P(z<2)-(1-P(z<3))\\\\=P(z<3)-P(z<2)\\\\=0.9987-0.9772\\\\=0.0215[/tex]

Hence,the required probability = 0.0215 .

General solution of equation sin x + sin 5x = sin 2x + sin 4x is

Answers

Answer:

x=nπ3, n∈I

Step-by-step explanation:

sin x + sin 5x = sin 2x + sin 4x

⇒⇒   2 sin 3x cos 2x = 2 sin 3x cos x

⇒⇒   2 sin 3x(cos 2x - cos x) = 0

⇒    sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3⇒    sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3 , n∈I, n∈I

or    cos 2x−cos x=0 ⇒ cos 2x=cos xcos 2x-cos x=0 ⇒ cos 2x=cos x

⇒   2x=2nπ±x  ⇒  x=2nπ, 2nπ3⇒   2x=2nπ±x  ⇒  x=2nπ, 2nπ3 , n∈I, n∈I

But solutions obtained by x=2nπx=2nπ , n∈I, n∈I or x=2nπ3x=2nπ3 , n∈I, n∈I are all involved in x=nπ3x=nπ3 , n∈I

Olcquations
Week 5 Assignment: Mixture Problems and Systems of Equations
Due Sunday by 11:59pm
Points 10
Submitting an external tool
Solve interest applications using a system of equations
Question
Matthew invested $3,000 into two accounts. One account paid 3% interest and the other paid 8% interest. He earned 4%
interest on the total investment. How much money did he put in each account?
Sorry, that's incorrect. Try again?
3% amount: S 600
8% amount: S 2400
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Answers

Answer:

$600 at 8%$2400 at 3%

Step-by-step explanation:

You have the right numbers, but the wrong accounts.

__

Let x represent the amount invested at 8% (the highest rate). Then the total interest is ...

  .08x +.03(3000 -x) = .04(3000)

  .05x = .01(3000) . . . . subtract .03(3000)

  x = 3000/5 = 600

Matthew invested $600 at 8%, $2400 at 3%.

_____

Comment on checking your answer

You may notice that the overall interest rate is 4%, closer to 3% than to 8%. That means more of the money must be invested at 3% than at 8%.

If f(x)=4x-6 and g(x) vx+2 what is (f*g)(7)

Answers

Answer: The value of (f*g)(7) is 66.

Step-by-step explanation:

Given functions: [tex]f(x)= 4x-6\text{ and } g(x)=\sqrt{x+2}[/tex]

Since, product of two functions: [tex](u*v)(x)=u(x)\times v(x)[/tex]

[tex](f*g)(x)=f(x)\times g(x)\\\\=4x-6\times \sqrt{x+2}\\\\\Rightarrow\ (f*g)(x)=(4x-6) \sqrt{x+2}[/tex]

[tex](f*g)(7)=(4(7)-6)\sqrt{7+2}\\\\=(28-6)\sqrt{9}\\\\=22\times 3=66[/tex]

Hence, the value of (f*g)(7) is 66.

In a triangle ABC two points D,E are taken on BC so that angle BAD=angle DAE=angleCAE. Determine AE if AB=5,BC=10 angle BAC=90. PLEASE HELP I NEED HELP WITHIN TEN MINS PLEASE

Answers

Answer:

AE = 7.5

Step-by-step explanation:

Since <BAC = [tex]90^{0}[/tex], then;

<BAD = <DAE = <CAE = [tex]30^{0}[/tex] (complementary angles)

From ΔABC, applying the Pythagoras theorem to determine the length of side AC;

[tex]/BC/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/AB/^{2}[/tex]

[tex]/10/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/5/^{2}[/tex]

100 = [tex]/AC/^{2}[/tex] + 25

[tex]/AC/^{2}[/tex] = 100 - 25

[tex]/AC/^{2}[/tex] = 75

AC = [tex]\sqrt{75}[/tex]

Applying trigonometric function to ΔCAE,

Cos [tex]30^{0}[/tex] = [tex]\frac{AE}{\sqrt{75} }[/tex]

AE = [tex]\sqrt{75}[/tex] × Cos [tex]30^{0}[/tex]

    = 7.5

Therefore, AE = 7.5

You have worked these hours this week: 5 4/5, 6 1/3, 8 2/5, 4 2/3. How many hours did you work

Answers

1472 minutes

OR

24 hours and 32 minutes

OR

1 day and 32 minutes

OR

1 day, half an hour, and 2 minutes

Using the addition operator, the total number of hours worked this week would be 26.65 hours

Given the work hours thus :

Converting to improper fraction :

29/4 + 19/3 + 42/5 + 14/3

Taking the L. C. M ; = 60

(435 + 380 + 504 + 280) / 60

= 1599 / 60

= 26.65 hours.

Hence, total hours worked would be 26.65 hours.

Learn more : https://brainly.com/question/25686009

solve 3/4x+5=-9 please

Answers

Answer:

exact form: x=-56/3

mixed number form: -18 2/3

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=-56/3 or x= - 18.6

Log 1/10 how do you convert this without a calculator

Answers

Answer:

  log(1/10) = -1

Step-by-step explanation:

Use the law of exponents and the meaning of logarithm.

  1/10 = 10^-1

  log(10^x) = x

So, you have ...

  log(1/10) = log(10^-1)

  log(1/10) = -1

Calculate the surface area of this composite shape.

Answers

Answer:

1284 m^2

Step-by-step explanation:

Front face and back face:

2 * [28 m * 5 m + (22 m - 5 m) * 6 m] = 484 m^2

Left face and right face:

2 * 22 m * 8 m = 352 m^2

Bottom face and top face:

2 * 28 m * 8 m = 448 m^2

total surface area = 484 m^2 + 352 m^2 + 448 m^2 = 1284 m^2

The Brooklyn Burn is a small company that makes and sells hot sauces. The profit that The
Brooklyn Burn makes in a month from its “Buckingham Burn" hot sauce can be measured using
the following function:
y=6x - 200
where x is the number of bottles of "Buckingham Burn" hot
sauce sold, and y is the profit in dollars for the month.
Using this function and its context involving sales of hot
sauce), describe the meaning of the numbers shown in the
table at the right.

150
700

Answers

Answer:

I know the answer

Step-by-step explanation:

If we use 150 the answer would be 6(150) - 200 = 700. The answer is 200.

Brooklyn Burn sold 150 bottles of hot sauce every month, 700 is the profit they make eachmonth.

The miss Petra psychic hotline charges 5$ For the first minute and 2$ for each additional minute. Give an equation the describes the situation

Answers

Answer:

y=2(x-1)+5

Step-by-step explanation:

We know that it is 5 dollars for the first minute so we know the equation will start off with +5.

Than for the rest of the minutes, we have to make sure to subtract one from them, because the first number is worth 3 dollars more. Which is why it is x-1.

Then we multiply the new value times 2, because each additional minute is 2 dollars more.

Other Questions
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