A wooden artifact is found in an ancient tomb. Its carbon-14 14 6 C activity is measured to be 65.0% of that in a fresh sample of wood from the same region. Assuming the same amount of 14C was initially present in the artifact as is now contained in the fresh sample, determine the age of the artifact.

Answer:

0.0157

Step-by-step explanation:

From the information given:

The sample size  = 70

The expected no. of days of year that are birthday of exactly 4 people is:[tex]P = \bigg [ \dfrac{1}{365} \bigg]^4[/tex]

The expected number of days with 4 birthdays = [tex]\sum \limits ^{365}_{i=1} E(x_i)[/tex]

[tex]\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ ^{70}C_{4} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{70-4} \bigg][/tex]

[tex]\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ \dfrac{70!}{4!(70-4)!} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{66} \bigg][/tex]

[tex]\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ 916895 \times 5.6342 \times 10^{-11} \times 0.8343768898 \bigg][/tex]

= 0.0157

Therefore, the required probability = 0.0157

Answer:

Step-by-step explanation:

y = 10/4 x

y = 2.5 x

Answer:

(1,1)

Step-by-step explanation:

Answer: I would say (1,1) or (0,1)

sorry if I got it wrong or couldn’t help

Answer:

5/12

Step-by-step explanation:

im finding answers for hegarty maths and i got it wrong and it said 5/12 was the answers

thank me later

Answer:

2/36

Step-by-step explanation:

i found it on another website

Answer:

y = 4 x - 7

The slope is the number multiplied by x, 4

Step-by-step explanation:

;-;

Answer:

The answer is C

Step-by-step explanation:

Less than = <

Quotient= Division

4 divided by X(unknown) will be LESS than -1

Answer---> X divided by 4 < -1

9514 1404 393

Answer:

  89.1 liters

Step-by-step explanation:

"At the same rate" means miles and liters are proportional. The unknown is liters, so we can write the proportion with liters in the numerator:

  liters/miles = x/672 = 49/369.6

Multiplying by 672, we have ...

  x = 672(49/369.6) ≈ 89.09091

It will take 89.1 liters of gas to go 672 miles.

Answer:

the answer is

x=8

Step-by-step explanation:

3x = 24

divide

Answer: x=8

Step-by-step explanation:

Answer:

3/5

First you would need to find the greatest common factor of 15 and 25

which is 5

Then divide the numerator and denominator by the GCF

15 divided by 5

25 divided by 5

Then simplify your answer is

3/5

Answer:

1/5 or 0.2 of the whole pizza

but it says that theres only 3/4 of the pizza there. so 3/4 of a pizza eaten by 5 people each person would get 0.15 of the pizza

Step-by-step explanation:

Answer:

Break-even point = $19,123 (Approx)

Step-by-step explanation:

Given:

Fixed cost = $62,150

Selling price = $9.50

Variable cost = $6.25

Find:

Break-even point

Computation:

Break-even point = Fixed cost / [Selling price - Variable cost]

Break-even point = 62150/[9.50-6.25]

Break-even point = 62150/3.25

Break-even point = $19,123 (Approx)

Answer:

No Solution.

X cannot equal anything in order for these to be equal.

Step-by-step explanation:

Answer:

X = 9

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

Move all terms that don't contain x to the right side and solve.

Answer:

alternative interior

Answer:

C multiply by 3, then subtract 5      

B

C m<7

Step-by-step explanation:

Answer: 11. D 12.d 13. A

Step-by-step explanation:

Answer:

Evern though this isn’t a math question, I’ll still help you :)

11. Option D

12. Option D

13. Option B

Hope this helps! :)

Answer:

x = 11

y = 8

z = 42

Step-by-step explanation:

From the given figure

∵ l[tex]_{1}[/tex] and l[tex]_{2}[/tex] intersected at a point

∴ ∠1 and ∠4 are vertically opposite angles

→ Vertically opposite angles are equal in measures

∴ m∠1 = m∠4

∵ m∠1 = 4(3y - 12)°

∵ m∠4 = (8y - 16)°

→ Equate their measures

∵ 4(3y - 12) = 8y - 16

∴ 4(3y) - 4(12) = 8y - 16

∴ 12y - 48 = 8y - 16

→ Subtract 8y from both sides

∵ 12y - 8y - 48 = 8y - 8y - 16

∴ 4y - 48 = -16

→ Add 48 to both sides

∴ 4y - 48 + 48 = -16 + 48

∴ 4y = 32

→ Divide both sides by 4

∴ y = 8

∵ ∠4 and ∠5 formed a pair of linear angles

→ The sum of the measures of the linear angles is 180°

∴ m∠4 + m∠5 = 180°

∵ m∠5 = (12x)°

∵ m∠4 = 8(8) - 16 = 64 - 16 = 48°

→ Add them and equate the sum by 180

∵ 48 + 12x = 180

→ Subtract 48 from both sides

∴ 48 - 48 + 12x = 180 - 48

∴ 12x = 132

→ Divide both sides by 12

∴ x = 11

∵ ∠4, ∠3, and ∠2 formed a line

∴ ∠4, ∠3, and ∠2 are linear angles

→ The sum of the measure of the linear angles is 180°

∴ m∠4 + m∠3 + m∠2 = 180°

∵ m∠4 = 48°

∵ m∠3 = 3(11) + 9 = 33 + 9 = 42°

∵ m∠2 = (2z + 6)

→ Add them and equate the sum by 180

∵ 48 + 42 + 2z + 6 = 180

→ Add the like terms in the left side

∴ 96 + 2z = 180

→ Subtract 96 from both sides

∵ 96 - 96 + 2z = 180 - 96

∴ 2z = 84

→ Divide both sides by 2

∴ z = 42

Answer:

y=20/7 or y=2.85

Step-by-step explanation:

Answer:

y=3

Step-by-step explanation:

2y-4=-5y+16

2y+5y-4=16

7y-4=16

7y=16+4

7y=20

y=[tex]\frac{20}{7}[/tex]

y=3

Answer:

the answer is approximately 28.28

Step-by-step explanation:

you use the pythagorean theorem to find the last length. I could explain it further, but you can take my word for it, its correct. I double checked.

Answer:

[tex]C. \frac{1}{2} \times \frac{5}{4} [/tex]

Answer:

confidence interval:

This tells us the degree of certainty or uncertainty that is existent in a sampling method. It gives us a range of values, telling us we are fairly sure that our true value or parameter lies within the range.

Degree of confidence:

This tells us that the confidence interval has captured the true/exact population parameter.

If we have 95% degree of confidence, we are 95% sure that that the exact/true parameter are in the confidence interval

31.286 i think that its 31.286 bc welp me smart

Answer:

A

Step-by-step explanation:

Using the symbols in the Venn diagram, we want to find A given that

B = 16

C = 15

D = 30

and given that 25 students don't take any of these courses.

There are 200 students total, so we need to have A plus the total number of students given in the diagram sum to 200. This means

(math only) + (English only) + (biology only) + (math and English, no biology) + (math and biology, no English) + (English and biology, no math) + (all three) + (none of the three) = 200

or

12 + 11 + 16 + 30 + A + 16 + 15 + 25 = 200

Solve for A to get A = 75, making the answer C.

Answer: x =5

Step-by-step explanation:

[tex]x + 3 + 3(x + 2) = - 24[/tex]

[tex]x + 3 + 3x + 6 = - 24[/tex]

[tex]4x + 9 = - 24[/tex]

[tex]4x = - 24 - 9[/tex]

[tex]4x = - 33[/tex]

[tex]x = \frac{ - 33}{4} [/tex]

Answer:

The similar one are 1 and 5

A. Triangle DEF where ∠D is 35° and ∠E is 20°.

C. Triangle JKL where ∠J is 35° and ∠L is 125°.

D. Triangle MNO where ∠N is 20° and ∠O is 125°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles of a triangle is equal to 180°.

Given, A triangle ABC has ∠A = 35° and ∠B = 20°.

∴ ∠C = 180° - 35° - 20°.

∠C = 125°.

Triangle will be similar if every corresponding angle of different triangles has the same measure.

So, Triangles that are similar to triangle ABC is triangle DEF where ∠D is 35° and ∠E is 20°.

Triangle JKL where ∠J is 35° and ∠L is 125°.

Triangle MNO where ∠N is 20° and ∠O is 125°.

learn more about triangles here :

https://brainly.com/question/2773823

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