A paleontologist uncovers a fossil of a saber-toothed cat in California. He analyzes the fossil and concludes that the specimen contain 15% of its original carbon-14. Carbon-14 has a half-life of 5730 years. Use carbon-14 dating to determine the age of the fossil.

The markup is 60%.

Given that,

Based on the above information, the calculation is as follows:

[tex]= (\$200 - \$125)\div \$125[/tex]

= 60%

Therefore we can conclude that The markup is 60%.

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The fraction of a batch of trail mix consisting of peanuts is 43/6.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Number of cups for peanuts = 2(2/3)

Total number of cups in the trial mix.

= 2(2/3) + 3/4 + 2(1/2) + 1(1/4)

= 8/3 + 3/4 + 5/2 + 5/4

= (32 + 9 + 30 + 15)/12

= 86/12

= 43/6

= 7(1/6)

Thus,

The fraction of peanuts is 43/6.

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Answer:

IQR

Step-by-step explanation:

Interquartile range (IQR): it's the difference between the largest and smallest values in the middle 50% of a set of data. It is not affected by the long tail in the graph because its calculation only consider the central part of data.

Range: it’s the difference between the highest value and the lowest value in a data set. It is affected by long tails because consider the whole data

Median absolute deviation (MAD): it's the median of the absolute deviations from the data's median. It's moderate affected by long tails because atypical measures give greater absolute deviation that may cause a greater MAD.

Answer:

[tex]V=\frac{27}{64}yd^3[/tex]

Step-by-step explanation:

The edge length of the cube shaped bin is [tex]\frac{3}{4}\text{ yards}[/tex]

Hence, [tex]s=\frac{3}{4}\text{ yards}[/tex]

The volume of the cube is given by

[tex]V=s^3[/tex]

Plugging the value of s, we get

[tex]V=(\frac{3}{4})^3[/tex]

This can be further simplified as

[tex]V=\frac{3\times3\times3}{4\times4\times4}\\\\V=\frac{27}{64}[/tex]

Hence, the volume of the container is 27/64 cubic yards.

Answer:

[tex]\large\boxed{x=4\pm2\sqrt6}[/tex]

Step-by-step explanation:

[tex]x^2-6x+12=2x+20\qquad\text{subtract}\ 2x\ \text{and}\ 12\ \text{from both sides}\\\\x^2-8x=8\\\\x^2-2(x)(4)=8\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\x^2-2(x)(4)+4^2=8+4^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-4)^2=24\iff x-4=\pm\sqrt{24}\\\\x-4=\pm\sqrt{4\cdot6}\\\\x-4=\pm\sqrt4\cdot\sqrt6\\\\x-4=\pm2\sqrt6\qquad\text{add 4 to both sides}\\\\x=4\pm2\sqrt6[/tex]

Final answer:

The quadratic equation x² - 6x + 12 = 2x + 20 is solved by completing the square, resulting in the solution x = 4 ± √24.

Explanation:

To solve the quadratic equation x² - 6x + 12 = 2x + 20 by completing the square, we first need to rearrange the equation to get 0 on one side. We do this by subtracting 2x and 20 from both sides, which gives us:

x² - 8x - 8 = 0

Next, we find the value to complete the square for the x terms. We take half of the coefficient of x, which is 8/2 = 4, and then square it, getting 4² = 16. We add 16 to both sides of the equation to form a perfect square on the left:

x² - 8x + 16 = 8 + 16

This simplifies to:

(x - 4)² = 24

To find the value of x, we take the square root of both sides:

x - 4 = ±√24

Finally, we solve for x:

x = 4 ± √24

Final answer:

To find the number of games won and lost by the baseball team, use the given win to loss ratio of 4/3 and the total number of games played (147) to establish a system of equations and solve for the number of wins and losses. The team won 84 games and lost 63 games.

Explanation:

The student has asked how many games a baseball team won and lost given that they played 147 regular season games with a win to loss ratio of 4/3. To solve this, let w represent the number of games won and l represent the number of games lost. According to the ratio, we have w/l = 4/3. Because the total number of games is 147, we can express this as w + l = 147.

First, express the number of losses in terms of wins using the ratio: l = 3w/4.

Next, substitute l in the total games equation: w + 3w/4 = 147.

Solving for w gives w = 84 (number of games won).

To find l, substitute w back into l = 3w/4 to get l = 63 (number of games lost).

The baseball team won 84 games and lost 63 games.

For the given condition of lines to be parallel, slope of red line is same as green line which is equal to [tex]\frac{-3}{7}[/tex].

" Parallel lines are defined as the lines in the same plane with equal distance between them and do not intersect in the same plane."

" Slope is defined as the ratio of increment in the y-coordinates to the x-coordinates."

Condition of slope for two parallel lines

[tex]y = m_{1} x + c_{1}\\\\y = m_{2} x + c_{2}[/tex]

[tex]m_{1}[/tex] and [tex]m_{2}[/tex] represents the slope of parallel lines.

As slope of parallel lines always equal.

Therefore,

[tex]m_{1} = m_{2}[/tex]

According to the question,

Given,

The slope of the green line [tex]= \frac{-3}{7}[/tex]

Condition given,

Lines are parallel.

Using the condition of slope of parallel lines we have,

The slope of the parallel lines is always equal.

Therefore,

The slope of the red line [tex]= \frac{-3}{7}[/tex]

Hence, the slope of the red line [tex]= \frac{-3}{7}[/tex] as per the given lines is parallel.

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The area of circle of circumference 37.7 is 112.76 .

The area of a circle is pi times the radius squared (A = π r²)

where ,

A = Area of circle

r = radius of circle

The circumference of a circle is defined as the linear distance around it.

C=2πr

where ,

c = circumference of circle

r = radius of circle

According to question

Circumference = 37.7

2[tex]\pi r\\[/tex] = 37.7

[tex]\pi r[/tex] = 18.85

[tex]\frac{22}{7}r[/tex]=18.85   ([tex]\pi = 22/7[/tex])

r = 18.85 × [tex]\frac{7}{22}[/tex]

r = 5.99

Now area of circle = [tex]\pi r^{2}[/tex]

Area of circle = [tex]\frac{22}{7} * 5.99^{2}[/tex]

Area of circle = 112.76

Hence , the area of circle is 112.76 .

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Answer:

5 boxes

Step-by-step explanation:

Given that;

The total amount Ray has with him to buy masonary nails and finishing nails for his project is $36

If Masonry nails sell for $5.50 per box

Finishing nails cost $3.50 per box.

Now, Only full boxes are available for purchase.

If Ray buys 3 boxes of masonry nails

i.e 3 × $5.50 = $16.5

what is the maximum number of boxes of finishing boxes he can buy?

To determine the number of finishing nails boxes he can buy. we will subtract the expense spent on the prior 3 masonary nails from his total amount

i.e $36 - $16.5

= $19.5

Let's not forget that, only full boxes are available for purchase and not half or quarter.

SO since 1 finishing nail box cost $3.50

then let x finishing nail box cost $19.5

∴ (x) × $3.50 =1 × $19.5

(x) = [tex]\frac{1*19.5}{3.50}[/tex]

(x)  = 5.57 boxes

Since full boxes are available for purchase then   (x)  ≅ 5 boxes, then Ray will be left with $2 at his pocket.

Therefore, the maximum number of boxes of finishing boxes he can buy is 5 boxes

Answer:

The answer is -4

Step-by-step explanation:

-3x4+8 =-4

Final answer:

If an integer n, when divided by 7, leaves a remainder of 3, then multiplying n by 3 and dividing by 7 will leave a remainder of 2.

Explanation:

Let's solve the problem where n when divided by 7 leaves a remainder of 3 and find the remainder when 3n is divided by 7. According to the information, if n divided by 7 leaves a remainder of 3, we can express n as 7k + 3 for some integer k.

To find the remainder when 3n is divided by 7, substitute 7k + 3 for n: 3n = 3(7k + 3) = 21k + 9. We can further simplify this to 21k + 7 + 2, or 7(3k + 1) + 2. Here, it's evident that when 21k + 9 (or similarly 7(3k+1)+2) is divided by 7, it leaves a remainder of 2.

Step-by-step explanation:

Let's use this equation as an example - [tex]102=-7r+4[/tex]

The whole point of a linear equation is to find what the variable (which in our case is r ) equals to.

Our equation: [tex]102=-7r+4[/tex]

First step is to try to get r alone on one side.

First step: [tex]102-4=-7r[/tex] we wouldn't do [tex]102+4=-7r[/tex] (notice it's negative and not positive) since we're switching the positive 4 to the other side we'd switch the positive to a negative, making it [tex]102-4[/tex].

Know that everytime we switch a number or variable to the other side we must always switch the sign to the opposite of what it is. If it's dividing, we multiply, if we subtract, we add, etc. Same with the other way around.

Second step is to solve both sides of the equation.

Second step: [tex]98=-7r[/tex]

Third step is to divide the both sides by the number with the variable, making it 98 divided by -7r and -7r divided by -7

Third Step: [tex]\frac{98}{-7} =\frac{-7r}{-7}[/tex] = [tex]-14=r[/tex]

Now we've found our variable.

Answer: [tex]-14=r[/tex]