Roslyn is an engineer. She is designing a part for a new engine. The length of the part is 16 centimeters (cm), the width is 6 cm, and the height of the cone top is 5 cm, as shown.
What is the volume?
Answers
The volume of the shape shown is 105π cm³
What is volume?
Volume is the amount of space occupied by a three dimensional shape and object.
Volume of the cone = (1/3) * π * (6/2)² * 5 = 15π cm³
Volume of the cylinder = π * (6/2)² * (16 - 5 - 6/2) = 72π cm³
Volume of the hemisphere = (2/3)π * (6/2)³ = 18π cm³
Volume of the shape = 15π cm³ + 72π cm³ + 18π cm³ = 105π cm³
The volume of the shape shown is 105π cm³
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Related Questions
A line segment has endpoints at (1,6) and (9,-10). The midpoint of the segment is located
Answers
Answer:
The answer is
( 5 , - 2 )Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
\(M = ( \frac{x_1 + x_2}{2} , \: \frac{y_1 + y_2}{2} ) \\\)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(1,6) and (9,-10)
The midpoint is
\(M = ( \frac{1 + 9}{2} \: , \: \frac{6 - 10}{2} ) \\ = ( \frac{10}{2} \: , \: - \frac{4}{2} )\)
We have the final answer as
( 5 , - 2)Hope this helps you
Please help, the question is in the picture.
Answers
Step-by-step explanation:
answer is first option,,,
Create an equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six.
1.3 squared over 1.5 cubed
1.3 to the twenty-fourth power over 1.5 to the eighteenth power
1.5 cubed over 1.3 squared
1.5 to the eighteenth power over 1.3 to the twenty-fourth power
Answers
The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.
How to explain the expressionHere are the steps to simplify the expression:
Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.
Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.
Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.
Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.
Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.
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what is the eccentricity of an infinitely long ellipse?
Answers
The eccentricity of an infinitely long ellipse will be less than 1.
What is the eccentricity of an ellipse?The ratio of the focus's distance from the ellipse's center and the ellipse's distance from one of its ends.
It is easy to comprehend how circular an ellipse is in relation to a circle when we consider its eccentricity. It also measures the ovalness of the ellipse and eccentricity close to one refers to the high degree of ovalness.
The eccentricity of an ellipse is always less than 1 i.e e < 1. The formula for the eccentricity of an ellipse is given by
Eccentricity = Distance from Focus/Distance from DirectrixWhich can be written as
=> e = c/a.Where
e = Eccentricity of the ellipse
c = Distance of the focus from the center of the ellipse
a = Distance of the end of the ellipse from the center
As we know the eccentricity of an ellipse is always less than 1, So we can conclude that the eccentricity of an infinitely long ellipse is less than 1.
Therefore,
The eccentricity of an infinitely long ellipse will be less than 1.
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z= -y + m/x
Solve for x
Please show work.
Answers
Jazmine can run 4 5/6 miles in 2/3 of an hour. How many miles can she run in 1 hour?
Answers
Answer: she can run \(6\dfrac54\) mile sin 1 hour.
Step-by-step explanation:
Given : Distance run by Jasmine in \(\dfrac23\) of an hour = \(4\dfrac56\text{ miles}=\dfrac{24+5}{6}\text{ miles}\)
\(=\dfrac{29}{6}\) miles
Distance run by Jasmine in 1 hour = \(\dfrac{29}{6}\times\dfrac{3}{2}=\dfrac{29}{4}\) miles.
\(=6\dfrac{5}{4}\) miles.
Hence, she can run \(6\dfrac54\) mile sin 1 hour.
When conducting an ANOVA, FDATA will always fall within what range? a. between negative infinity and infinity b. between 0 and 1 c. between 0 and infinity d. between 1 and infinity
Answers
The correct answer is (c) between 0 and infinity. This can be answered by the concept from F statistic.
The F statistic, which is used in ANOVA (Analysis of Variance), is calculated as the ratio of the variance between groups to the variance within groups. Since variance is always a positive value (it measures the spread or dispersion of data), the F statistic will always be greater than or equal to 0.
Furthermore, the F statistic follows an F-distribution, which is a continuous probability distribution that ranges from 0 to infinity. The F-distribution has a skewed shape, with most of the values clustered towards 0 and decreasing as the values get larger. This means that the F statistic can take on values anywhere between 0 and infinity, but it cannot be negative.
Therefore, when conducting an ANOVA, FDATA will always fall within the range of 0 to infinity.
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3,7,2,4,7,5,7,1,8,8
What is the mean
Answers
a) The mode of the list is 7
b) The median of the list is 7.
c) The mean is 5.4
d) The range is 7
What is the Mean, Mode and Median?
Mean: The mean is the average of a set of numbers, calculated by adding up all the numbers and dividing by the total number of numbers in the set.
Mode: The mode is the most frequently occurring number in a set of numbers.
Median: The median is the middle value in a set of numbers when the set is sorted in ascending or descending order.
a) Mode: The mode of the list is 7, as it is the number that occurs most frequently (3 times).
b) Median: To find the median, the list must first be sorted in ascending order:
1, 2, 3, 4, 5, 7, 7, 7, 8, 8
The median of the list is 7.
c) Mean: The mean is found by adding up all the numbers in the list and dividing by the total number of items:
(3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8)/10 = 54/10 = 5.4
d) Range: The range is the difference between the largest and smallest numbers in the list:
8 - 1 = 7
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The 40-hour work week is considered the standard in American society today. Imagine you wish to use data from the 2010 General Social Survey (GSS) to determine whether the mean number of hours worked per week by respondents in the sample differs from the 40- hour standard. a When 81 workers (n) were surveyed how many hours they worked in the previous week, the mean was 44.1 (x-bar) with a standard deviation of 12.8 (sx). Does this suggest that the population mean workweek for workers is different from 40 hours per week? Assume an a = .05. In answering this question, use the six steps below (copy and paste the steps in the space below, and fill in your answers to each question): 1. State the null and research hypotheses 2. State the level of significance, alpha (a) 3. Select a sampling distribution and state the test statistic 4. State the rejection region (critical test statistic) 5. Calculate the research test statistic and see if it falls in the rejection region 6. State your conclusion in terms of the problem
Answers
1. The null hypothesis is H₁: μ = 40 and the alternative hypothesis is H₁: μ ≠ 40
2. The level of significance, alpha (a), is 0.05
3. The test statistic is the z-statistic.
4. The rejection region consists of the values that fall outside the critical test statistic.
5. Tthe z-statistic is 2.88
6. We can reject the null hypothesis.
How to determine if the mean number of hours worked per week differs from the 40-hour standard?We are solving based on the provided steps:
Step 1. State the null and research hypotheses:
Null hypothesis (H0): The population mean workweek for workers is equal to 40 hours per week.Alternative hypothesis (Ha): The population mean workweek for workers is different from 40 hours per week.Step II. State the level of significance, alpha (a):
The level of significance, alpha (a), is 0.05, which relates to a 95% confidence level.
Step III. Select a sampling distribution and state the test statistic:
Since the sample size (n = 81) is greater than 30, we shall use the z-test.
The test statistic is the z-statistic.
Step IV. State the rejection region (critical test statistic):
Since we have a two-tailed test and an alpha level of 0.05, we divide the alpha value equally between the two tails, resulting in an alpha/2 (0.05/2 = 0.025).
To find the critical test statistic, we look up the z-value corresponding to the 0.025 significance level in the standard normal distribution table.
The rejection region consists of the values that fall outside the critical test statistic.
Step V. Then, we calculate the research test statistic to see if it falls in the rejection region:
The formula to calculate the z-statistic is:
z = (x-bar - μ) / (σ / √n)
Where:
x-bar = sample mean μ = population mean σ = population standard deviationn = sample size.Given:
x-bar = 44.1
μ = 40
σ = 12.8
n = 81.
Substitute the values:
z = (44.1 - 40) / (12.8 / √(81))
z = 4.1 / (12.8 / 9)
z = 4.1 / 1.422
z ≈ 2.88
Step VI: State your conclusion in terms of the problem:
After comparing the research test statistic to the critical test statistic from step 5, we find that the z-value of 2.88 falls in the rejection region.
In conclusion, we can reject the null hypothesis.
Hence,
a) Using the sample data from the 2010 GSS, there is evidence to suggest that the population mean workweek for workers is different from 40 hours per week.
b) The research test statistic, with a value of 2.88, falls within the rejection region when compared to the critical test statistic. So, the null hypothesis is rejected.
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HELP ASAP (100 POINTS)
The equation for the line of best fit for change in temperature, y, to amount of snow, s, is given by ŷ = − 2.6s + 1.1. On Friday, the observed amount of snow was 1.3 inches and the temperature change was 1.2 degrees. Find and interpret the residual.
1.08; The line of best fit underpredicts the temperature change.
−1.08; The line of best fit overpredicts the temperature change.
−3.48; The line of best fit overpredicts the temperature change.
3.48; The line of best fit underpredicts the temperature change.
Answers
Answer:
3.48; The line of best fit underpredicts the temperature change.Step-by-step explanation:
ŷ = − 2.6s + 1.1.
residual value = Measured value - Predicted value
Measured value = actual y-coordinate of the point, y
Predicted value = value of y from the equation, y1
residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)
residual value = y - y1
For s = 1.3
y = 1.2
value of y from the equation, y1:
y1 = -2.6*(1.3) + 1.1
y1 = -3.38 + 1.1
y1 = -2.28
residual value = y - y1
residual value = 1.2 - -2.28
residual value = 1.2 + 2.28
residual value = 3.48Interpretation:
Since the predicted value is far less than the observed value, the line of best fit underpredicts the temperature change.
Answer:
3.48; The line of best fit underpredicts the temperature change.
Step-by-step explanation:
i took the test :)
The algebraic representation of a transformation is (x,y) (3x,3y). This is an example of which type of transformation
Answers
To visualize this transformation, imagine a rectangle with vertices at and (0,2). Applying the transformation (x,y) → \((3x,3y)\) to each vertex, we get a new rectangle with vertices at \((0,0), (3,0), (3,6),\) and \((0,6)\), which is three times the size of the original rectangle.
What form can take Algebraic representations?Algebraic representations can take many forms, including equations, inequalities, functions, and matrices. These representations provide a powerful tool for analysing complex systems and deriving meaningful insights from them.
The algebraic representation \((x,y) (3x,3y)\) describes a dilation transformation, specifically an enlargement or stretch by a scale factor of 3 in both the x and y directions.
This means that every point in the original figure is multiplied by 3 in both the x and y directions, resulting in a larger, similar figure.
To visualize this transformation, imagine a rectangle with vertices at \((0,0), (1,0), (1,2),\) and \((0,2).\) Applying the transformation (x,y) → (3x,3y) to each vertex, we get a new rectangle with vertices at \((0,0), (3,0), (3,6),\) and (0,6), which is three times the size of the original rectangle.
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what is the surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 24 meters
Answers
The surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 24 meters is 1,670.5 square meters.
The surface area of a cone is calculated using the following formula:
Surface area = πr² + πrl, where π is approximately equal to 3.14, r is the radius of the base of the cone, and l is the slant height of the cone.
In this problem, we are given that the height of the cone is 42 meters and the diameter of the base is 24 meters. The radius of the base is half of the diameter, so the radius is 12 meters. The slant height of the cone can be calculated using the Pythagorean theorem.
l² = 12² + 42²
l² = 1764
l = 42.01 meters
The surface area of the cone is then calculated as follows:
Surface area = πr² + πrl
Surface area = 3.14 * 12² + 3.14 * 12 * 42.01
Surface area = 1,670.5 square meters
Here are some additional explanations:
The radius of a circle is the distance from the center of the circle to any point on the edge of the circle.The slant height of a cone is the distance from the vertex of the cone to any point on the edge of the base of the cone.The surface area of a cone is calculated by adding the area of the base of the cone and the area of the lateral surface of the cone.The area of the base of a cone is calculated using the formula πr².The area of the lateral surface of a cone is calculated using the formula πrl.To know more about area click here
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Compute the second-order partial derivative of the function h(u, v) = u/(u + 16v) (Use symbolic notation and fractions where needed.)hvv (u, v) =
Answers
The second-order partial derivative of the function h(u, v) = u/(u + 16v) with respect to v, denoted as hvv (u, v), is computed as 32u/(u + 16v)^3.
To find the second-order partial derivative of h(u, v) with respect to v (hvv), we need to differentiate the function with respect to v twice. Let's begin by finding the first-order partial derivative of h(u, v) with respect to v, denoted as hv (u, v).
To compute hv, we use the quotient rule. The numerator of h(u, v) is u, and the denominator is (u + 16v). Applying the quotient rule, we get:
hv (u, v) = (u)'(u + 16v) - u(u + 16v)' / (u + 16v)^2
= u - u = 0.
Since hv (u, v) is equal to 0, there are no v terms left when we differentiate again. Therefore, the second-order partial derivative hvv (u, v) is also 0.
In conclusion, the second-order partial derivative of h(u, v) = u/(u + 16v) with respect to v is hvv (u, v) = 0.
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Suppose the market is competitive. Sketch the supply and demand and state the equilibrium quantity.
Suppose the market is competitive. Sketch the supply and demand and state the equilibrium quantity. 1.) Using the multipoint drawing tool, graph the market demand from the four hospitals. Label your line 'Demand'. (Use the "Esc" key after you have placed your last point to exit the drawing tool.) 2.) Using the multipoint drawing tool, graph the market supply of the four producers. Label your line 'Supply'. (Use the "Esc" key after you have placed your last point to exit the drawing tool.) The equilibrium quantity of ventilators sold is units. Carefully follow the instructions above and only draw the required pbjects.
Answers
In a competitive market, we need to graph the market demand and supply curves and determine the equilibrium quantity. The equilibrium quantity represents the quantity at which the demand and supply curves intersect.
To sketch the supply and demand curves, we first need to gather information on the market demand and supply. The demand curve represents the quantity of ventilators that the four hospitals are willing to purchase at different prices, while the supply curve represents the quantity of ventilators that the four producers are willing to sell at different prices.
Using the multipoint drawing tool, we can plot the market demand curve based on the data provided for the hospitals. Label this line as 'Demand'. Next, using the same tool, we can plot the market supply curve based on the data provided for the producers. Label this line as 'Supply'.
The equilibrium quantity is determined at the point where the demand and supply curves intersect. It represents the quantity of ventilators that will be sold in the market. To find this point, we identify the quantity at which the demand and supply curves meet on the graph.
By following the instructions and accurately plotting the demand and supply curves, we can determine the equilibrium quantity of ventilators sold in the market.
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i need help please i’ll give u a brainliest for the correct answer
Answers
Answer:
75.4m²
Step-by-step explanation:
The shape shown is a cylinder
The volume of a cylinder can be calculated using this formula:
\(V=\pi r^2h\)
where r = radius and h = height
The cylinder shown has a radius of 2m and a height of 6m
Using this information we plug in the values into the formula
\(V=\pi 2^26\\2^2=4\\4\pi =12.56637\\12.56637*6=75.39822\)
So the area of the cylinder is 75.39822
Our final step is to round to the nearest hundredth
The final answer would be 75.4m²
Look at this set of 9 numbers:
30
59
44
58
30
69
89
30
44
By how much would the mode increase if the number 80 were added to the set?
Answers
Answer:
The mode would not increase or decrease.
Step-by-step explanation:
I say this because the mode is the value(s) in the data set that occur most frequently. 30 is the mode before adding 80 because 30 is in the set 3 times, more than the other values. Because 80 would be the only 80 in the set it would not become the mode once added. I hope this explained my reasoning and helped!
Drag the tiles to the correct boxes to complete the pairs.
Match each quadratic function to its graph.
A: f(x) = -2(x + 3)2 − 1
B: f(x) = -2(x + 3)2 + 1
C: f(x) = 2(x + 3)2 + 1
D: f(x) = 2(x − 3)2 + 1
Answers
Answer:
f(x) = 2(x + 3)² + 1 corresponds to graph C.
f(x) = -2(x + 3)² + 1 corresponds to graph D.
f(x) = 2(x - 3)² + 1 corresponds to graph A.
f(x) = -2(x + 3)² - 1 corresponds to graph B.
Step-by-step explanation: hope its right
Please help me !!!!!!!
Answers
If one student is chosen at random, the probability that the student was a female and got 'A' is 0.38
What is probability?Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is expressed. To forecast the likelihood of events, probability has been introduced in mathematics.
The likelihood that something will occur is essentially what is meant by probability. This is the fundamental theory of probability, which is also used to calculate the probability distribution, and it is from it that you will learn the likelihood of various outcomes in a random experiment.
The total number of outcomes that can occur should be known before calculating the likelihood that a specific event will occur.
Total numbers of students = 53
Total numbers of females = 34
Total numbers of females of A grades = 20
So probability = 20/53
= 0.38
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I am on a time crunch please answer fast!
Answers
Answer:
Step-by-step explanation:
Function 2 has a slope of 1.1 while function 1 has a slope of just 1.
May I have brainliest?
convert 350 cm into meters
Answers
Answer:
3.5 meters
Step-by-step explanation:
Felicia earns $800 a month. The table shows her monthly budget.
Monthly Budget
Expense Amount of Money
College savings $200
Car payment $275
Cell phone $125
Clothes $50
Food $100
Other $50
Which statement is supported by the information in the table?
F.Felicia spends 10% of her monthly budget on clothes and food.
G.Felicia spends 25% of her monthly budget on her car payment.
H.Felicia spends 20% of her monthly budget on college savings.
J.Felicia spends 50% of her monthly budget on her car payment and cell phone.
I'm not really good at math and I'm doing a test online right now and I am very confused.
Answers
Answer:
The answer is J.
Step-by-step explanation:
50% of 800 is 400.
125+275=400
Joe is a gardener. His hourly rate was £8 He increased his hourly rate by 10% Then he increased it by 10% again. What is his hourly rate after that?
Answers
Answer:
9.68
Step-by-step explanation:
8 x .1 = 0.8 (10% as a decimal is .1)
8 + 0.8 = 8.8
8.8 x .1 = .88
8.8 + .88 = 9.68
The Wooly Wonder Company makes t-shirts and hats. It makes a profit of $4 on t-shirts and $5 on hats. It takes 10 minutes to print a shirt and 15 minutes to dry it. It takes 16 minutes to print a hat and 12 minutes to dry it. There are 20 hours (1200 minutes) of time available for printing and 20 hours available to dry them. How many of each should be made to maximize profits, and what is that profit?
Answers
Answer:
To maximize profits;
96 t-shirts should be produced
85 hats should be produced
The profit from the t-shirts is $348
The profit from the hats is $425
Step-by-step explanation:
The given information are;
The amount of profit per t-shirt = $4
The amount of profit per t-shirt = $5
The time it takes to print a t-shirt = 10 minutes
The time it takes to dry the printed t-shirt = 15 minutes
The time it takes to print a hat = 16 minutes
The time it takes to dry the printed hat = 12 minutes
The amount of time available for printing = 20 hours = 1200 minutes
The amount of time available for drying = 20 hours = 1200 minutes
Therefore, we have;
The total number of t-shirts that can be printed in 20 hours = (The amount of time available for printing)/(The time it takes to print a t-shirt)
The total number of t-shirts that can be printed in 20 hours = (1200 minutes)/(10 minutes)
The total number of t-shirts that can be printed in 20 hours = 120 t-shirts can be printed
The total number of t-shirts that can be dried in 20 hours = (The amount of time available for drying the t-shirts)/(The time it takes to dry a t-shirt)
The total number of t-shirts that can be dried in 20 hours = (1200 minutes)/(15 minutes) = 80 t-shirts can be dried
The total number of hats that can be printed in 20 hours = (The amount of time available for printing)/(The time it takes to print a hat)
∴ The total number of hats that can be printed in 20 hours = (1200 minutes)/(16 minutes) = 75 hats can be printed
The total number of hats that can be dried in 20 hours = (The amount of time available for drying the hats)/(The time it takes to dry a hat)
∴ The total number of hats that can be dried in 20 hours = (1200 minutes)/(12 minutes) = 100 hats
Therefore, given that only 80 t-shirts can be dried in 20 hours, we have;
The total number of t-shirts to be produced = 80 t-shirts
The profit made from the shirts is 80 × $4 = $320
Also, given that only 75 hats can be dried in 20 hours, we have;
The total number of t-shirts to be produced = 75 hats
The profit made from the shirts is 75 × $5 = $375
However, to maximize profit, we have;
Total time to print and dry the t-shirts = 1200 + 1200 = 2,400 minutes
Therefore, whereby X number of t-shirts can be produced in the total time, we have;
10·x + 15·x = 2,400 minutes
25·x = 2,400 minutes
x = 2,400 minutes/25 = 96 t-shirts should be produced
Profit = $4 × 96 = $348
Similarly, for the hat, we have;
16·x + 12·x = 2,400 minutes
28·x = 2,400 minutes
x = 2,400 minutes/28 ≈ 85 hats should be produced (rounding down)
Profit = $5 × 85 = $425.
pls help need it pls pls
Answers
Answer:thats map testing
Step-by-step explanation:
Answer:
C. 17
Step-by-step explanation:
Subtract 3 from 6 first in the parenthesis, then multiply that by 5.
3 x 5 = 15
Now add 2 to 15.
15+2=17
Donuts4U has donuts on sale at 12 for $5.40. How many donuts can you buy for a dollar?
Answers
Answer:
2 donuts
Step-by-step explanation:
All we need to do to find the unit price is divide both values.
5.40 / 12 = $0.45 per donut
The question is asking how many donuts you can get for $1 so lets divide again.
1 / 0.45 = 2.22...
We know that the store won't cut the donut so we can only get 2 donates for a dollar. We can laos save the 10 cents we have over for taxes.
Best of Luck!
11.
19.4
x 5.37
Estimate. I don’t need the answer immediately.
Answers
Answer:
Approximately 95
Step-by-step explanation:
19 x 5 = 95
The graph of a function is shown:
which of the following correctly identifies the set of outputs?
a: {(5,-2), (1,-1), (-2,2), (2,5)}
b: {(-2,5), (-1,1), (2,-2), (5,2)}
c: {-2, -1, 2, 5}
d: {-2, 1, 2, 5}
Answers
Answer:
B.
Step-by-step explanation:
Use (X, Y)
X being the horizontal line
Y being the vertical line
how do I solve this complex expression-
(5+2i)+(6i^2-3i+2)
Answers
Answer:
1-i
Step-by-step explanation:
Hello,
you know that \(i^2=-1\), right?
so
\((5+2i)+(6i^2-3i+2)\\\\=5+2i-6-3i+2\\ \\=1-i\)
Thanks
A 9-pack of popsicles costs $4.77. What is the unit price?
Answers
Answer:$0.53
9 pack = $4.77
1 pack = $?
9÷1=9, $4.77÷9=$0.53
Answer: $0.53
Step-by-step explanation: 9 divided by 1 is 9 and 4.77 divided by 9 is 0.53. ;)
how many sets of 5 students can be selected out of 30 students?
Answers
Answer:
142 506
Step-by-step explanation:
here the order does not matter
Then
we the number of sets is equal to the number of combinations.
Using the formula :
the number of sets is 30C5
\(C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}\)
\(=142506\)
There are 142506 ways in which 5 students can be selected out of 30 students.
How can a certain number of individuals be selected using a combination?The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.
By using the formula:
\(\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}\)
where;
n = total number of individual in the set = 30r = number of chosing individuals to be selected = 5\(\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}\)
\(\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}\)
\(\mathbf{^nC_r = 142506}\)
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