You made a profit of $382.50 from selling the 45 shares of the telecommunications company.
How to calculate the profit you made from selling the 45 shares of the telecommunications companyFirst we need to determine the total cost of purchasing those shares, and then subtract that from the total revenue from selling them.
The total cost of purchasing the 45 shares at a price of $63.00 per share is:
45 shares x $63.00 per share = $2,835.00
The total revenue from selling the 45 shares at a price of $71.50 per share is:
45 shares x $71.50 per share = $3,217.50
To calculate the profit, we subtract the cost from the revenue:
Profit = Revenue - Cost
Profit = $3,217.50 - $2,835.00
Profit = $382.50
Therefore, you made a profit of $382.50 from selling the 45 shares of the telecommunications company.
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Joan’s finishing time for the Bolder Boulder 10K race was 1.66 standard deviations faster than the women’s average for her age group. There were 410 women who ran in her age group. Assuming a normal distribution, how many women ran faster than Joan? (Round down your answer to the nearest whole number.)
Joan completed the race 1.66 standard deviations faster than the typical female of her age group. The standard deviation will be denoted by the symbol “” and the women's average finish time by the symbol “”. Then, Joan's remaining time was plus 1.66.
What is the assuming of normal distribution?The proportion of women who finished the race sooner than Joan. In this case, it is possible to apply the normal distribution.
The percentage of values to the left of z = 1.66 can then be calculated or found using a standard normal distribution table. The number of women who finished the race ahead of Joan is represented by the percentage in the table below.
According to a normal distribution table or calculator, there are approximately 0.9525 numbers to the left of the value z = 1.66.
Therefore, This means that out of the 410 female runners in Joan's age group, about 0.9525 × 410 = 391.23 of them beat her. The final count is 391 women, rounded to the next whole number.
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Q.Find the mistake made in the steps and justifications for solving the equation below.
Picture attached?
A. The justification for step 1 is incorrect and should be the multiplication property of equality.
B. The justification for step 3 is incorrect and should be the addition property of equality.
C. Step 5 is incorrect and should show be x=10/16.
D. Step 4 is incorrect and should be 10x = 24.
Answer:
The correct answer is D. Step 4 is incorrect and should be 10x = 24.
Ismail tried to prove that
sin
(
�
)
=
cos
(
90
°
−
�
)
sin(θ)=cos(90°−θ)sine, left parenthesis, theta, right parenthesis, equals, cosine, left parenthesis, 90, degree, minus, theta, right parenthesis using the following diagram. His proof is not correct.
The first mistake in Ismail's proof is that (3) cos(90 - Ф) = AC/BC
How to determine Ismail's mistakeThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The two column proof
In the two column proof, we have
cos(90 - Ф) = AC/BC
This equation is incorrect because by the definition of cosine, we have
cos(90 - Ф) = AB/BC
i.e. cos(x) = adjacent/hypotenuse
Hence, the mistake in his proof is cos(90 - Ф) = AC/BC
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In ΔVWX, x = 6.4 inches, w = 8.8 inches and ∠W=85°. Find all possible values of ∠X, to the nearest 10th of a degree.
What is the value of f(3) in the function below?
f(x) = 1/4 • 2*
A. 4
B. 2
C. 8
D. 3/2
The value of f(3) is 2.
Option B is the correct answer.
What is a function?A function has an input and an output with a relationship between them.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 1/4 x [tex]2^x[/tex]
Substitute x = 3.
f(3) = 1/4 x 2³
f(3) = 1/4 x 8
f(3) = 2
Thus,
The value of f(3) is 2.
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Suppose X is a random variable with mean X and standard deviation oXSuppose Y is a random variable with mean Y and standard deviation oY. The mean of X + Y is:a. MX+MYb.uX/oX) + (Y /oY). c. 1X+uY, but only if X and Y are independent. d (uX/oX) + (Y/oY), but only if X and Y are independent.
The answer is (a) MX + MY. Whether or not X and Y are independent, we cannot simplify (a) or (b) further.
The mean of X + Y is:
E(X + Y) = E(X) + E(Y)
So the answer is not (a) or (b).
(c) is incorrect because the formula given is only true if X and Y are independent, but no such assumption is given in the problem.
(d) is also incorrect because we cannot simply divide the means by the standard deviations to get the standard normal variables, especially when the variables X and Y have different means.
Therefore, the answer is (a) MX + MY.
Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
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Simplify: 3√28 + 4√7 + 2√32
HELP!!!
Answer:
[tex]10\sqrt{7}+8\sqrt{2}[/tex]
Step-by-step explanation:
Lets simplify.
[tex]3\sqrt{28}+4\sqrt{7} +2\sqrt{32}[/tex]
Rewrite [tex]28[/tex] as [tex]2^2*7[/tex]
[tex]3\sqrt{2^2*7}+4\sqrt{7} +2\sqrt{32}[/tex]
Pull terms out from under the radical.
[tex]3\left(2\sqrt{7} \right)+4\sqrt{7} +2\sqrt{32}[/tex]
[tex]6\sqrt{7} \right)+4\sqrt{7} +2\sqrt{32}[/tex]
Add [tex]6\sqrt{7}[/tex] and [tex]4\sqrt{7}[/tex].
[tex]10\sqrt{7} +2\sqrt{32}[/tex]
Rewrite [tex]32[/tex] as [tex]4^2*2[/tex].
[tex]10\sqrt{7} +2\sqrt{4^2*2}[/tex]
Pull terms out from under the radical.
[tex]10\sqrt{7}+2\left(4\sqrt{2}\right)[/tex]
[tex]10\sqrt{7}+8\sqrt{2}[/tex]
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Let f(x) = x2 − 2x + 1. Find the inverse function of f by identifying an appropriate restriction of its domain.
Answer: [tex]f^{-1} (x) = \sqrt{x} +1[/tex]
Step-by-step explanation:
[tex]y = x^2 - 2x + 1[/tex]
We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).
So, to find the inverse, first we'll switch the x and y and solve for y:
[tex]x = y^2 - 2y +1[/tex]
[tex]x = (y-1)^2[/tex], (factor!)
±[tex]\sqrt{x} = y - 1[/tex]
So, the inverse "function" is:
[tex]f^-1(x)[/tex] = ±[tex]\sqrt{x} +1[/tex]
But theres an issue here!
If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!
We need to restrict the domain to only include the values that are above the x axis.
So our final inverse function is:
[tex]f^{-1} (x) = \sqrt{x} +1[/tex]
Help me, please!!!!!!!!!
Answer: D, 3x+12
Step-by-step explanation: Distributing a number means that you have to multiply the number by all of the numbers inside the parentheses. 3*x is 3x, and 3*4 is 12. 3x+12 is 3x+12.
area of triangle۔ab =154،bc=346،ac=349
Therefore, the area of the triangle ABC is approximately 18096.3 square units.
What is the area of the triangle?
To calculate the area of a triangle, use the formula area = 1/2 * base * height.
We can use Heron's formula to find the area of the triangle ABC when the lengths of its three sides are known:
[tex]Area = {\sqrt{(s(s-a)(s-b)(s-c))}[/tex]
where "s" is the semiperimeter of the triangle, which is half the sum of the lengths of its three sides:
s = (a + b + c)/2
In this case, we have:
a = AB = 154
b = BC = 346
c = AC = 349
So the semiperimeter is:
s = (a + b + c)/2 = (154 + 346 + 349)/2 = 424.5
Now we can use Heron's formula to find the area of the triangle
[tex]Area = \sqrt{(s(s-a)(s-b)(s-c))}\\\\Area = \sqrt{(424.5(424.5-154)(424.5-346)(424.5-349))}\\\\Area= 18096.3[/tex]
Therefore, the area of the triangle ABC is approximately 18096.3 square units.
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Which relation is also a function?
Domain Range
A
V
11
C. Domain Range
X
Domain Range
B.
X
D. Domain Range
V
P
The relation is a function only if for element x in Set X, there is only one element in Set Y so, the choice B shows the relation.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).
When a relation will be called as a function .
Consider there be a relation R from a set X to a set Y .
Since the relation will be called a function if each element of set X is related to exactly one element in set Y.
which is, an element x in X, there is only one element in Y that x is related to.
Therefore , the correct option is B.
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Which equation could represent a proportional relationship?
A)h = p +27
B)h=38p
C) h= 47.3/p
D)hp = 29.50
B) h = 38p
An equation represents a proportional relationship if the ratio of the dependent variable to the independent variable is constant. In this equation, h is directly proportional to p, meaning that if p increases, h increases, and if p decreases, h decreases. The constant of proportionality is 38.
In other words, the equation h = 38p can be written as h/p = 38, which shows that the ratio of h to p is always equal to 38. This means that the equation represents a proportional relationship.
The other equations listed do not represent a proportional relationship because the ratio of the dependent variable to the independent variable is not constant. For example, in equation A, h is not directly proportional to p because the constant of proportionality changes as p changes. In equation C, h and p are inversely proportional because h decreases as p increases, and h increases as p decrease. And in equation D, the equation is not in the form of a proportion because there is an additional constant term on the right-hand side.
Algebra: let f(x)= 3x+7 f^-1 (x)=
Answer:
Step-by-step explanation:
To find the inverse of a function, we need to switch the x and y values and solve for y (or x, depending on how the original function is written). The inverse of the function f(x) = 3x + 7 is written as f^-1(x). To find f^-1(x), we can follow these steps:
Replace the function f(x) with y to make it easier to manipulate: y = 3x + 7.
Swap the x and y variables: x = 3y + 7.
Solve for y:
Subtract 7 from both sides to get x - 7 = 3y.
Divide both sides by 3 to get (x - 7) / 3 = y.
Write the inverse function using f^-1(x) instead of y:
f^-1(x) = (x - 7) / 3
So, the inverse of the function f(x) = 3x + 7 is f^-1(x) = (x - 7) / 3.
I need help with this problem
The estimate of the number 7th grader who play in the school band will be 120.
How to calculate the valueIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The estimate of the number 7th grader who play in the school band will be:
= 60 / 200 × 400
= 120
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its (3,-2) i did the test
Analyze the function f(x) = - tan 4x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes
For the function f(x) = -tan 4x,
Domain = π[(2n+1)/8] < x < π[(2n+3)/8] Range = set of all real numbers The period = π /4Two vertical asymptotes = π/8 and -π/8Given the function
f(x) = -tan 4x
The domain of the function is the set of all possible inputs of the function
The range is set of all possible outputs of the function
Here the function is
f(x) = -tan 4x
Domain of the function will be
π[(2n+1)/8] < x < π[(2n+3)/8]
The range of the given function is set of all real numbers
The period = π /4
Two vertical asymptotes are π/8 and -π/8
Therefore, the domain, range period and the two vertical asymptotes of the function has been found
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$10000 is deposited in an account earning 8% interest compounded continuously. Use the continuous interest formula below to determine how long it takes for the amount in the account to double. Round answer to 2 decimal places.
A=Pe^rt
____Years?
By using the continuous interest formula, we get 8.54 years that the amount will take to double itself.
What is continuous interest formula?The continuous interest formula is used to calculate the future value of a compound interest investment. It is written as follows:
Future Value = Principal × [tex](1 + r)^{n}[/tex]
where Principal is the original investment, r denotes the yearly interest rate, and n denotes the number of compounding periods.
The continuous interest formula is used to compute the future worth of an investment given its current value, yearly interest rate, number of times the interest is compounded each year, and number of years held.
In the given question,
A = A_0[tex]e^{rt}[/tex]
2A_0 = A_0[tex]e^{rt}[/tex]
2 = [tex]e^{rt}[/tex]
ln(2) = rt
t = [tex]\frac{2}{r}[/tex]
t = [tex]\frac{2}{0.08}[/tex]
t = 8.54 years
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According to Wikipedia, the following are the lengths of terms of the US Presidents that preceded Joe Biden. There is a total of 44. You may have expected to see a total of 45, as Biden is the 46th us President, but Grover Cleveland was considered the 22nd and the 24th President, but is only counted once in this list The 2922 is the length of two full terms and the 1461 is the length of one full term FDR, the 4422 in the table, had actually started his FOURTH term before dying in office The 31 is William Henry Harrison who became ill shortly after his inauguration. His death may have been due to pneumonia Number of US Presidents 12 1 1 Term in Days 4422 2922 2865 2.840 2.728 2.041 2.027 1.886 1,654 1.503 1,461 1.460 1.430 1.419 1 1 12 1 1 1.419 1.262 1,036 969 895 881 492 199 31 TOTAL: 1 1 1 1 1 1 1 1 1 44 Determine the mean, median and mode for this set of data Give each to the nearest whole day Mean = Median = Mode = and With one of the modes being a high value as well as the term of FDR being much higher than all others, was pulled up to a higher value than another of hte measures of central tendency the
The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.
To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:
Mean:
To find the mean, we add up all of the term lengths and divide by the total number of terms:
Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44
Mean = 1743.77 days
Median:
To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:
31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422
Median = (1460 + 1461) / 2
Median = 1460.5 days
Mode:
The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.
Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.
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For students majoring in Hospitality Management, it was determined that 5% have visited 1–10 states, 16% have visited 11–20 states, 45% have visited 21–30 states, 19% have visited 31–40 states, and 15% have visited 41–50 states. Suppose a Hospitality Management student is randomly selected. What is the probability that the student has visited 21 or more states?
A . 0.15
B. 0.21
C. 0.45
D. 0.79
Answer:
D. 0.79
Step-by-step explanation:
To find the probability that a Hospitality Management student has visited 21 or more states, we need to sum up the probabilities of the categories that represent students who have visited 21 states or more.
The probabilities of the categories are as follows:
Visited 21–30 states: 45% = 0.45
Visited 31–40 states: 19% = 0.19
Visited 41–50 states: 15% = 0.15
So, the total probability of a student having visited 21 or more states is:
0.45 + 0.19 + 0.15 = 0.79.
Therefore, the probability that a Hospitality Management student has visited 21 or more states is 0.79 or 79%.
Please help me with this question: Find the limit
Answer:
1/5
Step-by-step explanation:
Answer:
The solution is 1/5 or 0,2
Step-by-step explanation:
[tex] \displaystyle \sf\lim_{x \to 3} \frac{ {x}^{2} - 5x + 6 }{2 {x}^{2} - 7x + 3} \: \: \: \: \: \: \: \: \: \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)(x - 3)}{(2x - 1)(x - 3)} \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)\cancel{(x - 3)}}{(2x - 1)\cancel{(x - 3)}} \\\\ = \displaystyle \sf \lim_{x \to 3} \frac{(x - 2)}{(2x - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf = \frac{(3 - 2)}{(2(3) - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ = \boxed{\sf \frac{1}{5} \: or \: 0.2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
-9 3/8 as an improper fraction
Answer:the answer is -69/8
Step-by-step explanation:
first you plug -9 into 3/8 and it gives you -72/8+3/8 if you add those together you get -69/8
Write the dual of following problems: Maximize Z = 7X1 + 5X2 Subject to: X1 + 2X2 ≤ 6 4X1 + 3X2 ≤ 12 X1 , X2 ≥ 0 brainly
The dual problem of the primal problem "Maximize Z = 7X1 + 5X2, Subject to X1 + 2X2 ≤ 6, 4X1 + 3X2 ≤ 12, X1, X2 ≥ 0" is:
What are inequalities?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Greater than (or greater than or equal to), less than (or less than or equal to), or not equal to signs are used in place of the equal sign.
Minimize Z = 6Y1 + 12Y2
Here
Y1 + 4Y2 ≥ 7
2Y1 + 3Y2 ≥ 5
Y1, Y2 ≥ 0
(b) The dual problem of the primal problem "Maximize Z = 3X1 + 4X2, Subject to 5X1 + 4X2 ≤ 200, 3X1 + 5X2 ≤ 150, 8X1 + 4X2 ≥ 80, X1, X2 ≥ 0" is:
Minimize Z = 200Y1 + 150Y2
Subject to:
4Y1 + 5Y2 ≥ 3
5Y1 + 3Y2 ≥ 4
4Y1 + 8Y2 ≤ -80
Y1, Y2 ≥ 0
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"Your question is incomplete, probably the complete question/missing part is:"
Write the dual of following problems:
(a) Maximize Z = 7X1 + 5X2
Subject to:
X1 + 2X2 ≤ 6
4X1 + 3X2 ≤ 12
X1, X2 ≥ 0
(b) Maximize Z= 3X1 + 4X2
Subject to:
5X1 + 4X2 ≤ 200
3X1 + 5X2 ≤ 150
8X1 + 4X2 ≥ 80
X1, X2 ≥ 0
Compare to greatest or least 7/8 14/16
Answer:
The fraction 14/16 is greater than 7/8.
Step-by-step explanation:
A local coffee shop is testing out new flavors of coffee: Caramel Apple Latte and Salted Minty Mocha. A poll conducted by the
coffee shop determined that 46 customers preferred only the Caramel Apple Latte, 61 customers chose only the Salted Minty
Mocha, 27 customers chose both flavors, but 18 liked neither flavor. What is the probability that a randomly selected
customer would only like the Caramel Apple Latte?
The probability that a customer selected randomly would only like Carmel apple is 23/76
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space/ total outcome
sample space is the number of customers that like caramel apple latte only = 46
The total number of customers = 46+61+27+18 = 152
Therefore The probability that a customer selected randomly would only like Carmel apple = 46/152 = 23/76
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A. 600 square inches
B. 768 square inches
C. 648 square inches
D. 792 square inches
Answer:
Step-by-step explanation:
area of pole=75×8=600 square inch
area if sign=12×12+1/2×12×4
=144+24
=168 square inches
total area=600+168
=768 square inches
What is the answer to the problem 8(w+3)=_w+_ ?
Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total is made up of Planes?
There are 33% of the total is made up of Planes.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The table is given in the question, as follows:
Car Plane Train Total
Green: 120 250 500 870
Blue: 150 350 750 1250
Yellow: 170 200 450 820
Red: 200 300 300 800
Brown: 220 450 320 990
Total: 860 1550 2320 4730
Total number of planes = 1550
The total number of all vehicles = 4730
The percent of planes = (number of planes/number of all vehicles) x 100
The percent of planes = (1550/4730) x 100
The percent of planes = 0.3276 x 100
The percent of planes = 32.76
Round to the nearest percent, and we get
The percent of planes = 33%
Thus, 33% of the total is made up of Planes.
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Factorise (i) 4y²-6yz+9z²
Answer please
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The identity to be used here is [ (a - b)² = a² - 2ab + b² ]
First, try to get the given expression in form of terms on the RHS of the above identity
[tex]\qquad \sf \dashrightarrow \: 4y {}^{2} - 6yz + 9 {z}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: (2 {}^{2})( {y}^{2}) - 2(3)(y)(z) + (3 {}^{2} ) {z}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (3z) {}^{2} [/tex]
[ it's in form of a² - ab + b² now, add and deduct ab here ]
[tex]\qquad \sf \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (9z) {}^{2} - (2y)(3z) + (2y)(3z)[/tex]
[tex]\qquad \sf \dashrightarrow \: (2y) {}^{2} - 2(2y)(3z) + (3z) {}^{2} + (2y)(3z)[/tex]
[ Apply the identity ]
[tex]\qquad \sf \dashrightarrow \: (2y - 3z) {}^{2} + (2y)(3z)[/tex]
[tex]\qquad \sf \dashrightarrow \: (2y - 3z) {}^{2} + 6yz[/tex]
[ That's probably the answer, it can't be simplified more ]
To factorize the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex], we can use the quadratic formula.
We have the quadratic expression [tex]\sf\:ax^2 + bx + c \\[/tex], where $$\sf\:a = 4$$, $$\sf\:b = -6y $$, and $$\sf\:c = 9z^2 $$.
The quadratic formula states that for any quadratic equation of the form [tex]\sf\:ax^2 + bx + c = 0 \\[/tex], the solutions for $$\sf\:x $$ can be found using the formula:
[tex]\sf\:x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]
Applying this formula to our quadratic expression, we get:
[tex]\begin{align}\sf\:x &= \frac{-(-6y) \pm \sqrt{(-6y)^2 - 4(4)(9z^2)}}{2(4)} \\ &= \frac{6y \pm \sqrt{36y^2 - 144z^2}}{8} \\ &= \frac{6y \pm \sqrt{36(y^2 - 4z^2)}}{8} \\ &= \frac{6y \pm 6\sqrt{y^2 - 4z^2}}{8} \\ &= \frac{3}{4}y \pm \frac{3}{4}\sqrt{y^2 - 4z^2}\end{align} \\[/tex]
Thus, the factored form of the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex] is [tex]\sf\:(\frac{3}{4}y + \frac{3}{4}\sqrt{y^2 - 4z^2})(\frac{3}{4}y - \frac{3}{4}\sqrt{y^2 - 4z^2}) \\[/tex].
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
✨[tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
For a fishing trip, Henry is going to choose lures to put in his tackle box. He has 4 lures that are crankbaits and 9 that are Jigs. In how many ways can he choose
7 lures if more than 5 must be jigs?
The number of ways for which he can choose 7 lures if more than 5 must be jigs is of:
372 ways.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The possible combinations are given as follows:
Six jigs from a set of 9 and one crankbait from a set of 4.Seven jigs from a set of 9.Hence the number of ways is given as follows:
n = 9!/(6! x 3!) x 4!/(1! x 3!) + 9!/(7! x 2!)
n = 372 ways.
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The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:
4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1
11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5
7.5 6.2 5.8 2.8 3.4 10.4 9.8 6.6 3.7 6.4
8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.9 6.2
5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3
7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.3 7.2
5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2
8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7
5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6
10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6
7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3
9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2
8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
Stems Leaves
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 (b) What is a typical, or representative, flow rate?
L/min
(c) Does the display appear to be highly concentrated or spread out?
highly concentrated, except for a few values on the positive sidehighly concentrated in the middle highly concentrated, except for a few values on the negative sidespread out
(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?
Yes, the distribution appears to be reasonably symmetric.No, the data are skewed to the right, or positively skewed. No, the data are skewed to the left, or negatively skewed.No, the distribution of the values appears to be bimodal.
(e) Would you describe any observation as being far from the rest of the data (an outlier)?
Yes, the value 2.2 appears to be an outlier.Yes, the value 15.5 appears to be an outlier. Yes, the value 18.3 appears to be an outlier.No, none of the observations appear to be an outlier.
a ) Construction of stem and leaf display of the data is:
For n = 129 and with splint unit = 0.1, the stem and splint map of the given data on Shower- inflow rate( L/ min) is as follows
a stem-and-leaf display of the data.
Stems Leaves
2 28
3 1344567789
4 01356889
5 00001114455666789
6 0000122223344456667789999
7 00012233455555668
8 02233448
9 012233335666788
10 2344455688
11 2335999
12 17
13 9
14 36
15 0035
16 None
17 None
18 3
b) From brume and splint map we note that minimal Shower inflow rate is2.2 whereas outside is18.3 L/ mim. farther typical or representative rate is7.0 L/min.
c) The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.
d) Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.
e) From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.
A stem and splint plot, also known as a stem and splint illustration, is a way to arrange data so that it's simple to see how constantly colorful feathers of values do. It's a graph that displays ordered numerical data. A stem and a splint are divided into each piece of data.
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Complete question:
The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:
4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1
11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5
7.5 6.2 5.8 2.8 3.4 10.4 9.8 6.6 3.7 6.4
8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.9 6.2
5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3
7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.3 7.2
5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2
8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7
5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6
10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6
7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3
9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2
8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0
(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
Stems Leaves
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
(b) What is a typical, or representative, flow rate?
L/min
(c) Does the display appear to be highly concentrated or spread out?
highly concentrated, except for a few values on the positive sidehighly concentrated in the middle highly concentrated, except for a few values on the negative sidespread out
(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?
Yes, the distribution appears to be reasonably symmetric.No, the data are skewed to the right, or positively skewed. No, the data are skewed to the left, or negatively skewed.No, the distribution of the values appears to be bimodal.
(e) Would you describe any observation as being far from the rest of the data (an outlier)?
Yes, the value 2.2 appears to be an outlier.Yes, the value 15.5 appears to be an outlier. Yes, the value 18.3 appears to be an outlier.No, none of the observations appear to be an outlier.
