The area of a circle is 36π centimeters. What is the circumference of a circle in terms of π.

The correct sequence to model the given scenario is (b) f(n) = 1.12f(n-1)(1- f(n-1/6000)), and we can use this formula to calculate the oxygen released by the tree in each year, option (b) is correct.

The amount of oxygen released by the tree increases at a rate of 12% per year, which is represented by the factor 1.12f(n-1).

However, the tree cannot generate more than 6000 pounds of oxygen per year, which is represented by the limiting factor:

(1- f(n-1/6000)).

To understand this better, let's calculate the oxygen released by the tree in the second year using the formula

f(n) = 1.12f(n-1)(1- f(n-1/6000)).

f(2) = 1.12f(1)(1- f(1)/6000)

= 1.12(250)(1- 250/6000)

= 295.67 pounds of oxygen

Hence, option (b) is correct.

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The correct question is:

Which sequence below would best model the following description? A newly planted tree releases 250 pounds of oxygen over the period of its first year. The amount of oxygen released by the tree grows at a rate of 12% per year, but the tree cannot generate more than 6000 pounds of oxygen per year.

a. f(n) = 1.12f(n-1)(1+ f(n-1/6000)

b. f(n) = 1.12f(n-1)(1- f(n-1/6000)

c. f(n) = 1.12f(n-1) {6000/f(n-1)}

d. f(n) = 1.12f(n-1)(f(n-1) -6000)

Therefore , the solution of the given problem of trigonometry comes out to be approximately 21.424 metres long when the sun is 35 degrees above the horizon.

Some people assert that the growth of astrophysics was influenced by the merging of various fields. Many metric problems can be solved or the result of a calculation can be ascertained with the use of exact mathematical techniques. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They go by many other names and acronyms, including sine, variance, direction, and others. (csc).

Here,

When the sun is at a 35° elevation angle and the structure is 15 metres tall, we want to determine the length of the shadow (on the next side).

Let x represent the desired shadow's length. Next, we have

=> tan 35° = 15/x

When we multiply both sides by x, we obtain:

=> x tan 35° = 15

By dividing both sides by 35° of tan, we obtain:

=> x = 15 / tan 35°

We may calculate the value of the tangent of 35 degrees using a calculator:

=> tan 35° ≈ 0.7002

Next, we have

=> 15x/0.702x=21.424 metres

Consequently, a building 15 metres high will create a shadow that is approximately 21.424 metres long when the sun is 35 degrees above the horizon.

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The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine.

Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time?

The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine with the x-axis labeled time in seconds going from 0 to 28 and the y-axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16.

A scatter plot is a useful way to show the relationship between two variables, in this case, the amount of hot chocolate and time. Each point on the scatter plot represents a pair of values for time and hot chocolate amount. A line graph with line segments connecting each point to the next would not be appropriate because the data is not continuous, and there is no reason to assume that the relationship between time and hot chocolate amount is linear.

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Answer:

C. Luisa is incorrect, it's not 0. It's only zero when you get "x=0" as an answer but the variable x got canceled here. And as 3=3, it is a true statement so it includes all real numbers. If you had gotten 3=8 for example, it would be a fake statement, so then no solution.

And for the second part,

1. No solution

5x+24=5x+25

24=25

It's false

2. One solution

12p-7=-3p+8

15p=15

P=1

3. One solution.

3x+20=5x

20 = 2x

X = 10

Note that  the following probability as a simplified fraction and as a decimal is:  0.88617886178 and 109/123

Note that the key phrase here is “given that this person is a man.”

This means that all we are interested in is the row labeled Male.

           Married      Never      Div       Widowed    Total

Male    69                  40       11                   3           123    

We are asked to find the probability that the person was either Married or Never. So the fraction you want is (69 + 40) / 123.

⇒ (69 + 40) / 123.

⇒ 109/123

or 0.886179

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Express the following probability as a simplified fraction and a decimal.

if one person is selected from the population described in the table, find the probability that the person has never been married or is married, given that this person is a man.

  Married  Never Married  Divorced   Widowed   Total

Male    69    40     11     3     123

Female  67    33     20     5     125

Total    136    73     31     8     248

Question 1.Express the probability as a simplified fraction

The value of side length c is 13.55 units.

The length of side c is calculated by applying sine rule as shown below;

The formula for sine rule is given as;

a/sinC = b/sinA

For the given question, we will have the following equation,

c/sin (34) = 11 / sin (27)

The value of c in the triangle is calculated as follows;

c = (sin 34 / sin 27 ) x 11

c = 13.55 units

Thus, the value of side length c is determined by applying sine rules.

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The exponential value decay equation is solved and the value of the vehicle after 11 years is A = $ 13,413

Given data ,

Let the initial cost of the vehicle be = $ 29,800

Now , the rate of depreciation be r = 7 %

Let the number of years be n = 11 years

And , the exponential decay is given by the equation ,

x ( t ) = x₀ × ( 1 + r )ⁿ

On simplifying , we get

x ( 11 ) = 29800 ( 1 - 0.07 )¹¹

x ( 11 ) = 29800 ( 0.93 )¹¹

x ( 11 ) = 13,413.085

Hence , the cost of the vehicle after 11 years is A = $ 13,413

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Answer:

128 servings

Step-by-step explanation:

It takes 1 1/4 cups to make 10 servings

1 1/4 as a mixed fraction = 5/4  

So 5/4 cups makes 10 servings

1 cup makes 10 ÷ 5/4

Use the fraction rule for division
a/b ÷ c/d = a/b x c/d

10 ÷ 5/4 = 10 x 4/5 = 8 servings from 1 cup

1 gallon = 16 cups

At 8 servings per cup, total number of servings for 16 cups
= 8 x 16 = 128 servings ANSWER

If a candle having diameter as 9 cm, height as 12 cm is placed in a cylindrical box, then the height of the cylindrical box will be 13cm.

The "cylindrical-candle" diameter is given as = 9 cm;

The "cylindrical-candle" height is given as = 12 cm;

The candle is placed in a box which has a space of 0.5 cm between the candle and the box for packaging material;

which means that, there will an additional 0.5 cm in the top and bottom of the candle,

So, the height of the "cylindrical-box" is written as : 0.5 + 12 + 0.5;

Therefore, the "cylindrical-box" has a height of 13 cm.

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The table for the function y = f(x) - 5 is

x    f(x) - 5

5   -33

-3    -5

-2     2

0    21

From the question, we have the following parameters that can be used in our computation:

x    f(x)

5   -28

-3    0

-2     7

0    26

To create a table for the function y = f(x) - 5, we subtract 5 from the values of f(x)

using the above as a guide, we have the following:

x    f(x) - 5

5   -28 - 5

-3    0 - 5

-2     7 - 5

0    26 - 5

Evaluate

x    f(x) - 5

5   -33

-3    -5

-2     2

0    21

This represents the table for the function y = f(x) - 5

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The loan will increase to $39599.29 in 5 years

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Amount = P * (1 + r)ᵗ

Where

P = Principal = 35000

r = Rate = 2.5%

t = time = 5

Substitute the known values in the above equation, so, we have the following representation

Amount = 35000 * (1 + 2.5%)⁵

Evaluate

Amount = 39599.29

Hence, the amount is 39599.29

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The median number of eggs laid in a year is 231 from the given data, option A is correct.

The data table shows the numbers of eggs laid by individual chickens in a year.

Now, We can arrange it into ascending order as;

⇒ 222, 229, 229, 231, 234, 235, 262

Since, There are 7 terms

Hence, Median = (7 + 1)/2

= 4th term

= 231

Hence, the median number of eggs laid in a year is 231, option A is correct.

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The correct function that models the balance B of Lily’s account as a function of time in months is option A, which is B(t) = 325(1 − 0.005)ᵗ.

To see why, we can start with the initial balance of $325 and note that each month, the bank charges a monthly fee of 0.5%, which is equivalent to a monthly interest rate of 0.005. This means that after one month, the balance will be reduced by 0.5% or 0.005 times the original balance, giving:

B(1) = 325 - 0.005(325)

Similarly, after two months, the balance will be reduced by another 0.5% of the new balance, giving:

B(2) = (325 - 0.005(325)) - 0.005(325 - 0.005(325))

We can simplify this expression by factoring out the common factor of 325(1 - 0.005) after each term, giving:

B(2) = 325(1 - 0.005)²

Generalizing this pattern, we can see that after t months, the balance will be:

B(t) = 325(1 - 0.005)ᵗ

Therefore, option A is the correct function that models the balance of Lily’s account.

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Answer:

2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.

Step-by-step explanation:

To divide 2 1/4 by 1 1/2, we first need to convert both mixed numbers to improper fractions:

2 1/4 = (2 × 4 + 1) / 4 = 9 / 4

1 1/2 = (1 × 2 + 1) / 2 = 3 / 2

Now we can divide by multiplying by the reciprocal of the second fraction:

(9/4) / (3/2) = (9/4) * (2/3)

We can simplify this multiplication by canceling the common factor of 3 in the numerator of the second fraction and the denominator of the first fraction:

(9/4) * (2/3) = (33/4) * (2/13) = 9/2

So 2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.

[tex]\boxed{\sf \dfrac{3}{2}}.[/tex]

[tex]\sf \dfrac{2\dfrac{1}{4} }{1\frac{1}{2} }[/tex]

[tex]\sf 2\dfrac{1}{4}\Longrightarrow\dfrac{4}{4} +\dfrac{4}{4} +\dfrac{1}{4} =\dfrac{4+4+1}{4} =\dfrac{9}{4}[/tex]

[tex]1\dfrac{1}{2} =\dfrac{2}{2} +\dfrac{1}{2} =\dfrac{2+1}{2} =\dfrac{3}{2}[/tex]

[tex]\sf \dfrac{\dfrac{9}{4} }{\dfrac{3}{2} }[/tex]

• Check the attached image.

[tex]\dfrac{9}{4} *\dfrac{2}{3}[/tex]

[tex]\dfrac{9*2}{4*3} =\dfrac{18}{12} \\ \\\dfrac{18/2}{12/2} =\dfrac{9/3}{6/3}=\boxed{\sf \dfrac{3}{2}} .[/tex]

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Answer

Construction Model Stats

User

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

ChatGPT

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

User

The angle of elevation to the top of a building is found to be 18 degrees from the ground at a distance of 510 feet from the base of the building. Using this information, find the height of the building to the nearest whole number.

ChatGPT

We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:

tan(18 degrees) = h / d

Solving for h, we get:

h = d * tan(18 degrees)

Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:

h = 510 feet * tan(18 degrees)

h ≈ 157.3 feet

Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.

User

The following regular polygon has 15 sides. This distance from its center to any given vertex is 12 inches.

Which of the following is the best approximation for its perimeter?

(1) 68 inches

(3) 84 inches

(2) 75 inches

(4) 180 inches

ChatGPT

To find the perimeter of a regular polygon with n sides, we can use the formula:

Perimeter = n * s

where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.

In a regular polygon with n sides, the interior angle at each vertex is given by:

Interior angle = (n - 2) * 180 degrees / n

In a 15-sided polygon, the interior angle at each vertex is:

(15 - 2) * 180 degrees / 15 = 156 degrees

If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:

sin(78 degrees) = 12 / (1/2 * s)

s = 2 * 12 / sin(78 degrees)

s ≈ 2.17 inches

Finally, we can find the perimeter of the polygon:

Perimeter = 15 * s

Perimeter ≈ 32.55 inches

Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.

Answer:

To find the percentage of Virginia's gross pay that she took home after deductions, we need to first calculate her gross pay and then subtract the total amount of deductions to find her net pay. Then, we can divide her net pay by her gross pay and multiply by 100 to find the percentage.

Virginia earns $69,500 per year, so her gross pay per paycheck (assuming she is paid every two weeks) is:

$69,500 / 26 = $2,673.08

Her total deductions from her most recent paycheck were:

$200.20 + $180.65 + $72.00 + $110.00 + $250.00 = $812.85

So her net pay was:

$2,673.08 - $812.85 = $1,860.23

To find the percentage of her gross pay that she took home, we can divide her net pay by her gross pay and multiply by 100:

($1,860.23 / $2,673.08) x 100 ≈ 69.59%

Therefore, the closest option is (3) 69.59%.

Answer:

1,3,5,7,9

Step-by-step explanation:

0 can't be, let's take 10 or 20 or 30 for example, not a prime number.

1 can be because let's take 11, 31 as example, they're prime numbers.

2, 4, 6, 8 can't be the answer because they have factors

The rest of off numbers, namely 3,5,7,9 can be. Let's take for example 23, 05, 67, 59

The amount it would cost to paint the wall, given the cost of paint and the area covered is $ 56 .

The surface area of the circular wall would be :

A = 2 x π x r x h

The area is therefore:

= 2 x π x r x h

= 2 x 3. 14 x 15 x 4

= 376. 8 square feet

The number of gallons needed is therefore:

= 376. 8 / 225

= 1. 674

= 2 gallons

The cost of two gallons is:

= 2 x 28

= $ 56

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You are on the right track! To find the equation of the parabola given by the equation x^2 + 6x + 8 = 0, you can use the standard form of a quadratic equation, which is:

where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the parabola.

To get the equation of your parabola, you first need to complete the square on the x terms of the given equation:

From this equation, you can see that the vertex of the parabola is at (-3, -1) and the value of a is positive. This means that the parabola opens upwards.

To find the value of a, you can compare the equation with the standard form of the quadratic equation:

where h = -3, k = -1, and a is the coefficient you need to find. Substituting these values into the equation gives:

So the equation of the parabola is:

To plot the parabola, you can use the vertex (-3, -1) as a starting point and then use the coefficient a to determine the shape of the parabola. Since a is positive, the parabola opens upwards.

Here, We provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.

To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:

25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22

The sum of the values is:

25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813

Dividing by the number of values (30), we get:

Mean = 813/30 = 27.1

To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.

To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:

20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34

There are 30 values, so the median is the 15th value, which is 28.

To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:

Range = 34 - 20 = 14

To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:

20-24, 25-29, 30-34

The frequency table would look like this:

Interval | Frequency

20-24 | 4

25-29 | 18

30-34 | 8

To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:

Proportion = Frequency/Total frequency = 18/30 = 0.6

Angle = Proportion x 360° = 0.6 x 360° = 216°

We can repeat this calculation for each interval to obtain the angles for the pie chart.

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Answer:

(x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25

Step-by-step explanation:

The equation of a circle can be written in the form (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Since the lines are tangent to the circle at points (0,5) and (6,5), we can use these points to find the center and radius of the circle.

First, let’s find the slope of each line. The slope of the line y = 3/4x+5 is 3/4. The slope of the line 3x + 4y = 38 can be found by rearranging it into slope-intercept form: y = (-3/4)x + 19/2. So the slope of this line is -3/4.

Since the lines are tangent to the circle, they are perpendicular to the radius at their point of tangency. This means that the center of the circle lies on the line that passes through (0,5) and has a slope of -4/3, and also on the line that passes through (6,5) and has a slope of 4/3.

Let’s find the equation of these two lines. The line passing through (0,5) with a slope of -4/3 has an equation y - 5 = (-4/3)(x - 0), or y = (-4/3)x + 5. The line passing through (6,5) with a slope of 4/3 has an equation y - 5 = (4/3)(x - 6), or y = (4/3)x - 3.

The center of the circle is at the intersection of these two lines. To find it, we can set their right-hand sides equal to each other and solve for x: (-4/3)x + 5 = (4/3)x - 3. Solving this equation gives us x = 24/5. Substituting this value into either equation for y gives us y = (4/3)(24/5) - 3 = 21/5.

So the center of the circle is at (24/5, 21/5). To find its radius, we can use either point of tangency. Let’s use (0,5). The distance between this point and the center is given by sqrt((0-24/5)^2 + (5-21/5)^2), which simplifies to sqrt(481)/5.

Therefore, the equation of the circle is (x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25.

Answer:

----------------------

See attached graph to help with answer choices.

Given function:

Answer choices:

The surface area of the rectangular prism is 24.62 square units

From the question, we have the following parameters that can be used in our computation:

2.5 by 2.14 by 1.5

The surface area of the rectangular prism is calculated as

Area = 2 * (Length * Width + Length * Height + Height  * Width )

substitute the known values in the above equation, so, we have the following representation

Area = 2 * (2.5 * 2.14 + 2.5 * 1.5 + 2.14 * 1.5)

Evaluate

Area = 24.62

Hence, the surface area is 24.62 square units

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Answer:1020 ft (squared)

Step-by-step explanation:

Base width 1 (28 ft) x Base width 2 (40 ft) x height (6 ft) = 1020 ft (squared)

Answer:

A) circle.

When a sphere is cut by a horizontal plane, the resulting cross section is a circle. This is because a sphere is a three-dimensional object that is perfectly symmetrical in all directions, so any plane that intersects it will create a circular cross section.

Answer:

Answer:

n(A U B) = n(A) + n(B) – n(A ∩ B)

putting values we get

50 = 2a + a - 20

solving eqn.

70 = 3a

a = 70 / 3

now n(a) = 2a

= 2 x 70/3

= 140/3

hence, n(a) = 140/3

In linear equation, 9 is the constant of variation k.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.

given x varies inversely with y then

xy = k ← k is the constant of variation

to find k use the condition x = - 4 when y = - 9, hence

k = -4 × -9 = 36

 x = 36/y

 when x = 4 , then  y = 36/4

                                  x = 9

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