The volume of a sphere is 1372π/3 cubic inches. What is the diameter of the great circle? (Recall that the formula for the volume for a sphere is v=4/3πr^3.)

volume of the center sphere = 4/3*PI*r^3

r = 3 ( given in the picture)

 so 4/3 * 3.14 *3^3 = 113.04 cubic feet

 volume of 1 cone: pi *r^2 *h/3

r = 3 and h=3 ( given in the picture)

so 3.14 * 3^2 * 3/3 = 28.26 cubic feet

 there are 4 cones so 28.26* 4 = 113.04 cubic feet

113.04 + 113.04 = 226.08 cubic feet

 rounded to nearest cubic foot = 226 cubic feet

The estimated age of the parchment is approximately 4,086.17 years.

To estimate the age of the parchment, we can use the concept of carbon dating.

Carbon-14 (14C) is a radioactive isotope of carbon that is commonly used for dating archaeological artifacts.

The amount of 14C in an organism remains relatively constant while the organism is alive because it continuously takes in carbon from the atmosphere and food.

However, after the organism dies, it no longer takes in new carbon, and the 14C begins to decay at a known rate.

The half-life of carbon-14 is approximately 5,730 years. This means that after 5,730 years, half of the original amount of carbon-14 in a sample would have decayed.

Let's use the information provided: the parchment fragment had about 61% as much 14C radioactivity as does plant material on Earth today.

This means that the remaining 14C in the parchment is 61% of the original amount. The remaining 14C is the amount that has not yet decayed, and the rest has decayed over time.

Now, we can set up an equation:

[tex]0.61 = (1/2)^{(t/5730)[/tex]

Where:

t = time in years since the parchment was alive.

Now, we need to solve for 't.' Taking the logarithm of both sides to isolate 't':

[tex]\log(0.61) = (t/5730) \times \log(1/2)[/tex]

Now, solving for 't':

[tex]t = (5730 \times \log(0.61)) / \log(1/2)[/tex]

Using a calculator, we find:

t ≈ 4,086.17 years

So, the estimated age of the parchment is approximately 4,086.17 years.

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Using the concept of radiocarbon dating and the fact that the parchment has 61% as much 14C radioactivity as present plant material, the calculated estimate for the parchment's age is approximately 2,200 years, rounded to the nearest hundred years.

To estimate the age of the parchment based on the information that it had about 61% as much 14C radioactivity as does plant material on Earth today, we use the concept of radiocarbon dating. The half-life of carbon-14 (14C) is 5,730 years, which means after every 5,730 years, the amount of 14C decreases by half. Given that the parchment retains 61% of its original 14C, we can formulate the decay equation to solve for the parchment's age.

The decay equation is given by: \(N_t = N_0(1/2)^{t/T}\), where \(N_t\) is the remaining amount of 14C, \(N_0\) is the original amount of 14C, \(t\) is time, and \(T\) is the half-life of 14C. In this case, \(N_t/N_0 = 0.61\), and we know \(T = 5730\) years.

By substituting the given values into the decay equation and solving for \(t\), we find that the parchment is approximately 2,200 years old, rounded to the nearest hundred years. This estimation assumes the natural 14C to 12C ratio in the atmosphere has been constant over the time period in question.

Answer:  

[tex]\displaystyle\frac{35}{45}, \frac{49}{63}[/tex] are two equivalent fractions of the given fraction.

Step-by-step explanation:

We are given the following information in the question:

We are given the fraction:

[tex]\displaystyle\frac{7}{9}[/tex]

We have to find an equivalent fraction. This could be done by multiplying both the numerator and the denominator by the same number.

Equivalent fraction:

Multiplying both numerator and denominator by 5

[tex]\displaystyle\frac{7\times 5}{9\times 5} = \frac{35}{45}[/tex]

Multiplying both numerator and denominator by 7

[tex]\displaystyle\frac{7\times 7}{9\times 7} = \frac{49}{63}[/tex]

Hence, [tex]\displaystyle\frac{35}{45}, \frac{49}{63}[/tex] are two equivalent fractions of the given fraction.

The equation 10x+5y=5 can be rewritten in slope-intercept form as y = -2x + 1. This equation's slope is -2 and the y-intercept is 1. The line intercepts the y-axis at (0,1) and for every 1 unit increase in x, y decreases by 2 units.

To write the equation 10x+5y=5 in slope-intercept form, you need to solve for y. The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

First, divide the entire equation by 5 to simplify it:

(10x+5y)/5 = 5/5 becomes 2x + y = 1.

Then, solve the equation for y:

y = -2x + 1

The slope (m) of the equation is -2 and the y-intercept (b) is 1. Therefore, the line intercepts the y-axis at the point (0,1) and for every 1 unit increase in x, y decreases by 2 units due to the negative slope.

To graph this line, first plot the y-intercept at the point (0,1). Next, from this point, move right 1 unit (increase in x) and down 2 units (decrease in y) to get the point (1,-1). Draw a straight line through these points to represent the equation y = -2x + 1.

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The expression 15/3x-6 evaluates to -4.75 when x=4. The solution involves substitution followed by the order of operations: first multiplication, then division, and finally subtraction.

The student asked to evaluate the expression 15/3x-6 when x=4. To do this, we first substitute the value of x into the expression, which then becomes 15/(3*4)-6.

Now we simplify the expression step by step:

So, when x equals 4, the value of the expression 15/3x-6 is -4.75.

Answer:

Option C - Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.

Step-by-step explanation:

Given : A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations.

One flower is chosen at random and given to a woman for her to keep.

Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose.

To find : Are these events independent or dependent?

Solution :

According to the statements,

The probability that the second woman receives a pink rose is dependent upon what the first woman receives.

Total flowers = 5+4+6=15

If the first woman does not receive a pink rose,

Then, the probability of the second woman receiving one is [tex]\frac{4}{15}[/tex]

If the first woman does receive a pink rose

Then, the probability of the second woman receiving one is  [tex]\frac{3}{15}=\frac{1}{5}[/tex]

Therefore, Option C is correct.

Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.

Lisa can either sell 100 hard candies or 50 chocolate to make $300.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Lisa wants to make at least $300.00 selling candy. Hard candy cost $3.00 per piece and chocolates cost $6.00 per piece.

Establishing the equation for this problem.

Let,

Hard candy = x

Chocolate = y

Therefore,

3x+6y=300

To find y, let x=0

3(0)+6y =300

6y = 300

y = 50

Similarly,

To find x, put y=0

3x+6(0)=300

3x=300

x=100

Hence, Lisa can sell 100 hard candies or 50 chocolate to make $300.

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Answer:

FOR ALL THOSE LAZY PPL, HERE'S THE ANSWER....

22 units.

Have a nice day mates.

Answer:

The x intercepts are -4, -1 and 5 or (-4,0), (-1,0) and (5,0).

Step-by-step explanation:

Consider the provided graph.

Here we need to find the x intercepts of the function.

The x-intercepts are where the graph crosses the x-axis.

Here, the  provided graph crosses the x axis 3 times.

Thus there must be 3 x intercepts of the function.

Now label the points on which graph intersect the x axis as shown in figure 1.

Thus the labeled points are (-4,0), (-1,0) and (5,0)

Hence, the x intercepts are (-4,0), (-1,0) and (5,0) or -4, -1 and 5.

They take 3 hours to complete the work together.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

An experienced bricklayer can construct a small wall in 4 hours.

And, An apprentice can complete the job in 12 hours.

Now,

Since, An experienced bricklayer can construct a small wall in 4 hours.

Hence, In 1 hour it will be completed 1/4 work.

And, An apprentice can complete the job in 12 hours.

So, In 1 hour it will be completed 1/12 work.

Let number of hour to complete the work together = x

in 1 hour both together completed 1/x work.

So, we can formulate;

1/4 + 1/12 = 1/x

Solve for x;

3/12 + 1/12 = 1/x

4/12 = 1/x

1/3 = 1/x

x = 3 hours.

Thus, They take 3 hours to complete the work together.

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The game which is 2.2 GB will need 170 minutes to download at a rate of 0.01 GB per minute. But the computer has only 120 minutes of battery life which is insufficient.

The total size of the game is 2.2 GB. The part that is already downloaded is 0.5 GB, so the remaining size of the game to be downloaded is 2.2 GB - 0.5 GB = 1.7 GB. Now, since the downloading speed is 0.01 GB/minute, we extrapolate the remaining time as (1.7 GB) / (0.01 GB/min) which equals 170 minutes.

(a) So, the inequality representing at least how many minutes it will take to download the rest of the game is x ≥ 170, where x is the required time in minutes.

(b) Two hours of battery life is equivalent to 2*60 = 120 minutes. Since 170 minutes is required to download the game and the available battery life is only 120 minutes, the battery will not be enough to download the game.

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With a diameter of 12mm and using π as 3.14, the circumference is calculated as 37.68mm.

The circumference of a circle can be calculated using the formula:

Circumference = π x diameter

Given: Diameter = 12mm

Using π = 3.14:

Circumference = 3.14 x 12mm = 37.68mm

Therefore, the circumference of the circle is 37.68mm.

Answer:

3(3+4a)(1-2a)

Step-by-step explanation:

Answer:

y = 2

Step-by-step explanation:

When we have graph is given also one value from x and y is given then for finding the other value, We simply see the line where x = -2 is graphed and then we will see what is the value of y there.

Here at x = -2, y = 2 this is clearly apparent from the graph.

The tip for the cab is close to 10 percent is around $2.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A cab ride from the airport to your home costs $19.50.

Now, The tip given is 10% of the fare so,

= (10/100)×19.50.

= 0.1×19.50.

= 1.95.

So, The exact tip would be $1.95 which is approximately $2.

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Using formula:

Using the first image to calculate the area:

[tex]\to \bold{ x\times 12 = 12x }[/tex]

Using the second image to calculate the area:

[tex]\to \bold{16\times (x-2) = 16x -32 }[/tex]

equalling both the area:

[tex]\to \bold{12x = 16x -32}\\\\\to \bold{32 = 16x -12x}\\\\\to \bold{32 = 4x }\\\\\to \bold{4x=32 }\\\\\to \bold{x=\frac{32}{4}}\\\\\to \bold{x=8}\\\\[/tex]

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4(50) +3r = 365

200+3r = 365

3r =165

r = 165/3

r = 55