The dimension of the cylindrical container that will minimize the cost of the container is a radius of 4.371 and a height of 25.85
since we know that the volume of a cylinder is :
355=πr²h, where r is the radius of the base and h is the height
So, we can say h=355/πr², here we have two circular components with the areas 2A=2πr² , for the cost of 0. 02 cents per cm² and a rectangular component of area A=2πrh , with cost of 0. 03 cents per cm².So the cost function will be :
C=0.02(2πr²)+0.03(2πrh)
C=0.04(πr²)+0.06(πrh), substuting the vale of h
C=0.04(πr²)+0.06(πr(350/πr²))
C=0.04(πr²)+(21/r), differentiating both sides we get .
C'=0
=>0.08(πr)-(21/r²)= 0, simplifying the equation we get
=>r= 3√525/2π =4.371
so for h, it will be: 355/π(3√(525/2π)) = 355/π(3√(83.55)) =350/π( 4.371) =25.85
To know more about cylinder refer to the link brainly.com/question/16134180
#SPJ4
Assume that the probability a child is a boy is 0.51 and that the sexes of children born into family are independent. What is the probability that a family of five children hasa. exactly three boys?b. all girls?c. at least one girl?
a) Probability of exactly three boys is 0.3185
b) Probability of at least one boy is 0.9717
c) Probability of at least one girl is 0.9655
d) Probability of all of same sex is 0.06275
What is probability?
Probability refers to potential. A random event's occurrence or the outcome is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.The potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.a) Probability of exactly three boys
Choose 3 out of 5 in C(5,3)=10 ways
So probability is:10*0.51^3*0.49^2
~0.3185
(b) Probability of at least one boy
p(at least one boy)=1-p( all girls)
=1-0.49^5
=0.9717
c) Probability of at least one girl
p(at least one girl)=1-p( all boys)
=1-0.51^5
=0.9655
d) Probability of all of same sex
p(all of same sex)=p(all boys)+p(all girls)=
0.51^5+0.49^5
=0.06275
To know more about probability check the below link:
https://brainly.com/question/13604758
#SPJ4
y is five times X +15
If a cyclist rides at an average speed of 18 miles per hour, how many miles does she ride in seven hours?.
If a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
A cyclist rides at an average speed of 18 miles per hour.
We have to find the number of miles she ride in seven hours
Assume x be the number of miles she ride
Let us form a proportional equation
18/1 = x/7
Apply cross multiplication
18×7=x
126=x
Hence, if a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
what fraction of seven number combinations formed used the numbers of the patter 3795523 will have the 2 3's always together
By using the concept of permutation, it can be calculated that
Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]
= [tex]\frac{2}{7}[/tex]
What is permutation?
Permutation is the arrangement technique that determines how many possible arrangement that can be made in a set where the order of arrangement matters.
Here, concept of permutation is used
Number of 7 number combinations that can be formed using the number 3795523 = [tex]\frac{7!}{2! \times 2!}[/tex] = 1260
The two 3's are always together
Number of 7 digit numbers formed = [tex]\frac{6!}{2!}[/tex] = 360
Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]
= [tex]\frac{2}{7}[/tex]
To learn more about permutation, refer to the link-
https://brainly.com/question/12468032
#SPJ4
Suppose that a monopolistically competitive firm must build a production facility in order to produce a product. The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost, MC = $3. Demand for the product that the firm produces is given by P = 27- 3Q.
Fill in the entire table below. All of the numbers you fill in will be integers (no decimals), some have been added.
Quantity of Output Price Total Cost Average Total Cost Total Revenue Profits
1 2 3 4 5 7.8 6 7 6.4 8 9 5.7 B. How many units of output will the firm produce if it maximizes its profit?
C. What price should this firm charge if it wants to maximize its profit?
The output firm will get maximum profits when the quantity is 4 units and the company will charge a price of $15 for maximum profit.
The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost, MC = $3
Demand for the product that the firm produces is given by P = 27- 3Q.
The total cost is calculated by adding fixed cost and variable cost.
TC = FC + VC
Average total cost = total cost / quantity
Quantity price (37 - 3Q) fixed cost variable cost total cost average cost
1 27 - 3(1) = 24 24 3 (1) 27 27
2 27 - 3(2) = 21 24 3(2) = 6 30 15
3 27 - 3(3) = 18 24 3(3) = 9 33 11
4 27 - 3(4) = 15 24 3(4) = 12 36 9
5 27 - 3(5) = 12 24 3(5) = 15 39 7.8
Upon analysing the table we can say that
B) the number of output units is 4
C) Maximum profit is when price is $15
Therefore, the maximum profit is when the output units is 4 and the company will charge a price of $15 for maximum profit.
To learn more about marginal cost refer here
https://brainly.com/question/12231343
#SPJ4
would it be unusual for a random sample of 500 adult americans to result in 210 or more who believe marriage is obsolete?
Yes, it would be unusual for a 500 adult Americans to result in 210 or more who believe marriage is obsolete. The probability value is 0.39 for adult Americans.
We know very well that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.
We have given that 39% american adults women believes that marriage is now obsolete.
So,39% of 500 adult American women is =[(39/100)×500]
=39×5=195
So,probability of adult women who believes marriage is obsolete is =(195/500)=0.39
Now, we need to check that whether 210 women believes marriage is obsolete or not.
So, number of favorable outcome is 210 and total number of outcomes=500.
Therefore, probability of adult women who believes marriage is obsolete is=(210/500)=0.42
Now,we can see that 195 women probability is lower than 210 women probability. It means that more number of women considered marriage is obsolete.
Hence, yes it is unusual and the probability value of adult Americans is 0.39
To know more about probability, visit here:
https://brainly.com/question/11234923
#SPJ4
(Complete question) is:
would it be unusual for a random sample of 500 adult americans to result in 210 or more who believe marriage is obsolete?If so determine the probability, otherwise type 0 for this result NOT to be unusual
Raise seven to the second power then find the sum of the result of Z
Answer: We write J raised to the 9th power as J9 (which means J multiplied by J a total of nine times). "Sum" means "add them" so J9 + K
Step-by-step explanation:
write a quadratic function in standard form whose graph passes through the given points (10,0), (1,0), and (4,3).
The quadratic function in standard form whose graph passes through the given points (10,0), (1,0), and (4,3) is; y = 0.2x² - 2.2x + 2
How to write the standard form of the quadratic equation?
The standard form of a quadratic equation is;
y = ax² + bx + c
where a, b and c are constants
Thus, for the coordinate (10,0), we have;
0 = a(10)² + b(10) + c
100a + 10b + c = 0 -----(1)
For the coordinate (1,0), we have;
0 = a(1)² + b(1) + c
a + b + c = 0 -----(2)
For the coordinate (4,3), we have;
3 = a(4)² + b(1) + c
16a + b + c = 3 ------(3)
Using online simultaneous equation, we have;
a = 0.2 and b = -2.2 and c = 2
The quadratic function is;
y = 0.2x² - 2.2x + 2
Read more about Quadratic Equations at; https://brainly.com/question/25841119
#SPJ1
The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table.
A 2-column table with 9 rows. Column 1 is labeled Weight (x) with entries 8, 12, 18, 24, 30, 32, 35, 37, 40. Column 2 is labeled Height (y) with entries 22, 23, 26, 30, 32, 33, 35, 36, 38.
Using technology, what is the correlation coefficient?
–0.997
–0.503
0.503
0.997
Using technology, the correlation coefficient is 0.997
How to calculate correlation coefficient?We should know that correlation coefficient is a statistical model which is used to determine or measure the relationship between two variables.
The table is
x y x² y² xy
8 22 64 484 176
12 23 144 529 276
18 26 324 676 468
24 30 567 900 720
30 32 900 1024 960
32 33 1024 1089 1056
35 35 1225 1225 1225
37 36 1369 1369 1332
40 38 1600 1444 1520
Total 236 275 7226 8740 7733
[tex]r= \frac{nExy)-(Ex)(Ey)}{\sqrt{[n(EX^{2}][nEy^{2}(Ey)^{2} } }[/tex]
applying the figures from the table we have
r=[tex]\frac{9*7733-(236)(275)}{\sqrt{[9*7226-55696][9*8740-75625]} }[/tex]
Simplifying the expression we have
r=[tex]\frac{4697}{\sqrt{28340830} }[/tex]
r=0.88
r=0.9 approximately
Therefore the correct answer is 0.997 which is the correlation coefficient.
Learn more about correlation coefficient on https://brainly.com/question/15577278
#SPJ1
a summer squash, spinach, and leek frittata recipe requires 6 ounces of spinach. if the ep unit cost of the ingredient is $2.25 per pound, what is the total cost of the ingredient?
The total cost of the ingredient is $0.84 for 6 ounces.
Define fixed cost.
The cost or expense known as fixed cost is unaffected by a short-term horizon's growth or reduction in the number of units produced or sold. To put it another way, it refers to a cost that is linked to a time period rather than a specific economic activity.
It can be viewed as costs that a business must pay regardless of the volume of business activity, such as the number of units produced or sales made. One of the two main parts of the overall manufacturing cost is the fixed cost.
Solution Explained:
Given,
1 pound = $2.25
Since 1 pound = 16 ounces
So, 16 ounces = 2.25
1 ounce = 2.25/16 = 0.14
Therefore, 6 ounces = 0.14 X 6 = 0.84
To learn more about fixed cost, use the link given
https://brainly.com/question/24868261
#SPJ4
If there are 39 students and 4 have blue eyes what is the fraction?
Answer:
4/39
Step-by-step explanation:
You want to know the fraction of 39 students represented by the 4 that have blue eyes.
FractionThe fraction is the ratio of the part of interest to the whole.
(students with blue eyes)/(total number of students) = 4/39
a number, y, is equal to twice the sum of a smaller number and 3. the larger number is also equal to 5 more than 3 times the smaller number. which equations represent the situation? 2 x minus y
The equations represent the given situation is:
2x - y = -6
3x - y = -5
where, x is the smaller number and y is the larger number.
Let the smaller number be x.
We have been given a number, y, is equal to twice the sum of a smaller number and 3
So, we get an equation,
y = 2(x + 3)
y = 2x + 6
2x - y = -6
The larger number is also equal to 5 more than 3 times the smaller number.
So, we get an equation,
y = 5 + 3x
3x - y = -5
Therefore, the equations represent the situation:
2x - y = -6
3x - y = -5
Learn more about equation here:
https://brainly.com/question/649785
#SPJ4
(7, 5) and (8, 7). What is its equation in slope-intercept form?
Answer:
y = 2x - 9
Step-by-step explanation:
The slope is the change in y over the change in x. From the 2 points, the y's are 7 and 5. The x's are 8 and 7.
[tex]\frac{7-5}{8-7}[/tex] = [tex]\frac{2}{1}[/tex] = 2
2 is the slope.
Now we need to find the y intercept (b). Use one of the points on the line. It does not matter which one. I am going to use (8,7)
slope (m) = 2
x = 8
y = 7
y=mx + b
7 = 2(8) + b Plug in what we know and solve for b
7 = 16 + b Subtract 16 from both sides
-9 = b
The y intercept (b) is -9
y = mx + b
y = 2x -9
pls help :( The table shows the sizes of Farmer Reuben's fields. Use the table and a separate sheet of paper to help you answer each question.
The areas of each of Reuben's fields are given as follows:
Corn Field: 24,000 square feet.Wheat Field: 140,000 square feet.Barley Field: 40,000 square feet.Hence the total area of all of Reuben's fields is given as follows:
204,000 square feet.
How to obtain the areas of the fields?The areas of the fields is given by the multiplication of each of the dimensions of the field, as the fields have a rectangular format.
Then the total area is obtained as the sum of the areas of each field.
The dimensions of each field are given as follows, from the table given by the image at the end of the answer:
Corn Field: 400 feet by 60 feet.Wheat Field: 700 feet by 200 feet.Barley Field: 200 feet by 200 feet.Hence the areas of each of the fields are given as follows:
Corn Field: 400 x 60 = 24,000 square feet.Wheat Field: 700 x 200 = 140,000 square feet.Barley Field: 200 x 200 = 40,000 square feet.Then the total area is given as follows:
24,000 + 140,000 + 40,000 = 204,000 square feet.
Missing InformationThe problem asks for the areas of each field and the total area.
The dimensions are given by the image shown at the end of the answer.
More can be learned about the areas of a rectangle at https://brainly.com/question/25292087
#SPJ1
A CBS News/New York Times poll found that 329 out of 763 randomly selected adults said they would travel to outer space in their lifetime, given the chance. Estimate the true proportion of adults who would like to travel to outer space with 88% accuracy. Round your answers to at least three decimal places.
The true proportion of adults is in the interval 0.4026< P< 0.4594.
Here we have to estimate the true population of adults who would like to travel to outer space with 88% accuracy.
Data provided:
selected (x) = 329
Total(n) = 763
Sample proportion (p') = x/n
= 329/ 763
= 0.431
Critical z-value = 1.59
margin of error(E) = z[tex]\sqrt{p'( 1-p')/n}[/tex]
= 1.59 [tex]\sqrt{0.431(1-0.431) / 763}[/tex]
= 1.59 × 0.0179
= 0.0284
88% confidence interval is:
(p' ± E) = ( 0.431 ± 0.0284)
= 0.4594 and 0.4026
Therefore the estimate is 0.4026< P< 0.4594.
To know more about critical z-value refer to the link given below:
https://brainly.com/question/16029738
#SPJ4
The Myer family purchased a bedroom set for $2,480. The sales tax rate is 7%. Find the total cost of the set and the tax.
The total cost of the set and the tax is 2653.6 dollars.
How to find the total cost of the set and the tax?The Myer family purchased a bedroom set for $2,480. The sales tax rate is 7 percent.
Therefore, the total cost of the set and the tax can be calculated as follows:
tax = 7% of 2480
tax = 7 / 100 × 2480
tax = 17360 / 100
tax = $173.6
Therefore, let's find the total cost of the set and tax.
total cost = 173.6 + 2480
total cost = 2653.6 dollars
learn more on sales tax rate here: https://brainly.com/question/24140373
#SPJ1
Answer please! I couldn’t figure it out.
By solving a system of equations we will see that she sold 80 phones and 240 accessories.
How many phones and accessories were sold?
Let's define the variables:
x = number of phones.
y = number of accessories.
We know that she makes $160 on commissions, and that she sold 3 times as many accessories as phones, so we can write the system of equations:
y = 3x
x*$8 + y*$4 = $160
To solve the system, we can replace the first equation into the second one.
x*$8 + (3x)*$4 = $160
x*$8 + x*$12 = $160
x*$20 = $160
x = $160/$20 = 80
She sold 80 phones, and the number of accessories is:
y = 3x
y = 3*80 = 240
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
rosie is driving from knoxvile, tennesse orlando, florida. she drives 317.88 miles before she stops for lunch and then another 203 4/5 miles before taking a break. rosie has driven 4/5 of the entire trip. how many total miles is her trip?
The total miles of the trip are 521.68 miles.
What is addition?Addition in maths, a process of combining two or more numbers.
Given that, Rosie drives 317.88 miles before lunch and then [tex]203\frac{4}{5}[/tex] miles before break,
Total miles = 317.88 + [tex]203\frac{4}{5}[/tex] miles = 521.68 miles
Hence, The total miles of the trip are 521.68 miles.
For more references on addition, click;
https://brainly.com/question/29560851
#SPJ1
Which ordered pair is a solution to the equation?
-4x + 7 = 2y - 3
Choose 1 answer:
A Only (2, 1)
B Only (5, -5)
C Both (2, 1) and (5,-5)
D Neither
Answer: Neither (5/2, 0)
Step-by-step explanation:
-4x + 7 = 2y - 3
+3 +3
2y = -4x + 10
(Divide both sides by 2)
y = -2x +5
—————————————————
-4x + 7 = 2(-4x + 10) - 3
-4x + 7 = -8x + 20 - 3
-4x + 7 = -8x + 17
+8x -7 +8x -7
8x - 4x = 17 - 7
4x = 10
(Divide both sides by 4)
x = 5/2
—————————————
y = -2(5/2) + 5
y = -5 + 5
y = 0
——————————
Check Work:
-4x + 7 = 2y - 3
-4(5/2) + 7 = 2(0) -3
-10 + 7 = 0 - 3
-3 = -3 ✔️
the ph of a solution is measured eight times by one operator using the same instrument. she obtains the following data: 7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.16 and 7.18. calculate the a. sample mean b. sample variance and standard deviation c. coefficient of variation
a. sample mean = 7.1838
b. sample variance = 0.0004 and standard deviation = 0.0207
c. coefficient of variation = 0.29%
What is sample variance?
The expectation of a random variable's squared deviation from its population mean or sample mean is known as variance in probability theory and statistics. Dispersion is a measure of how far apart a group of numbers is from their mean value, and variance is a measure of dispersion.
A probability distribution's variance is defined as the mean of the squared deviation from the distribution's mean. The expected value, commonly known as the mean, is the value you will obtain on average if you take several samples of a probability distribution.
Solution Explained:
a) Mean x=∑x/n
=7.15+7.2+7.18+7.19+7.21+7.2+7.16+7.18/8
=57.47/8
=7.1838
b) Sample Variance S2=∑x2-((∑x)^2/n)/n-1
=(412.8531-(57.47)^2/8)/7
=412.8531-412.8501/7
=0.003/7
=0.0004
Sample Standard deviation S=√∑x^2-((∑x)^2)/n)/n-1
=√(412.8531-((57.47)^2/8))/7
=√412.8531-412.8501/ 7
=√0.003/7
=√0.0004 =0.0207
c) Coefficient of Variation (Sample) =
S/x X100%
=(0.0207/7.1838) X 100%
=0.29%
To learn more about sample variance, use the link given
https://brainly.com/question/28542390
#SPJ4
What is the slope of the line that passes through the points (-5, 8) and (-5, 4)? Write your answer in simplest form.
exhibit 9-4 a random sample of 16 students selected from the student body of a large university had an average age of 25 years. we want to determine if the average age of all the students at the university is significantly different from 24. assume the distribution of the population of ages is normal with a standard deviation of 2 years. the test statistic is . a. 1.645 b. 2.00 c. 1.96 d. .05
It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.
If the average student age is not substantially different from 24 years, then the null hypothesis is tested, which is:
[tex]H_{0}[/tex] : μ = 24
If it differs from 24 years, the alternative premise is tested, so:
[tex]H_{1}[/tex] : μ ≠ 24
The z-distribution is utilized because we have the population's standard deviation. The test statistic comes from:
z = x - μ÷ σ/[tex]\sqrt{n}[/tex]
The parameters in this issue have the following values:
x(mean) = 25
μ = 24
σ = 2
n=16
As a result, the test statistic's value is:
z = 25-24÷ 2/[tex]\sqrt{16}[/tex]
z = 2
The probability of a sample mean older than 25 years determines the test's p-value, which is 1 less than the p-value of z = 2.
The p-value for z = 2 in the z-table is 0.9772; 1 - 0.9772 = 0.0228.
Given that the test's p-value is 0.0228 0.05, we may say that:
It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.
To learn more about probability:
https://brainly.com/question/11234923
6 3/ 4 divide by 4 1/2
The value of the equation A = ( 6 3/4 ) / ( 4 1/2 ) is 3/2 or 1 1/2
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first number be A = 6 3/4
A = 27/4
Let the second number be B = 4 1/2
B = 9/2
Now , the equation is C = A/B
The value of C = A / B
Substituting the values of A and B in the equation , we get
Value of C = ( 6 3/4 ) / ( 4 1/2 )
Value of C = ( 27/4 ) / ( 9/2 )
Value of C = ( 27 / 9 ) / 2
Value of C = 3 / 2
Therefore , the value of C is 3/2 or 1 1/2
Hence , The value of the equation A = ( 6 3/4 ) / ( 4 1/2 ) is 3/2 or 1 1/2
To learn more about equations click :
https://brainly.com/question/10413253
#SPJ1
(a) what was the average newspaper circulation from 1986 through 2000. (round your answer to three decimal places.) 557.680 incorrect: your answer is incorrect. million newspapers (b) in what year was the newspaper circulation closest to the average circulation from 1986 through 2000? (round your answer up to the nearest integer.)
The year becomes 1993, when the newspaper circulation is closest to the average circulation.
Part a:
The function is n(x)=0.00792x^3−0.37x^2+3.557x+51.588
The formula for the average of the function is 1b−a∫baf(x)dx
The year 1986 corresponds to 6 and 2000 corresponds to 20 as x is the number of years since 1980.
Obtain the average:
1b−a∫baf(x)dx==≈1/20−6∫20-6[0.00792x^3−0.37x^2+3.557x+51.588]dx
1/14[0.00792x^4/4−0.37x^3/3+3.557x^2/2+51.588x]20-6
51.70094
Therefore, the average newspaper circulation from 1986 to 2000 was 51.70094.
Part b:
Now, the equation is obtained as
0.00792x^3−0.37x^2+3.557x+51.588=51.70094
0.00792x^3−0.37x^2+3.557x−0.11294=0
Obtain the value of x using an online graphing calculator as follows:
Thus, the value of x becomes 13.481
Hence, 1993 is the year of the closest average circulation
Learn more about average:
https://brainly.com/question/2906096
#SPJ4
Given the algebraic expression (125x^7/3) ^-1/3 create an equivalent expression
The resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]
What is indices and exponents?A term's multiplicative history can be determined by an index, which is a discrete number. Indexes is the plural of index.
The exponentiation operator is the caret (). It is important to distinguish the exponent operator from the base-10 exponent sign. In a numeric literal, a base-10 exponent sign (scientific notation) can be represented by either an uppercase "E" or a lowercase "e."
[tex](125x^{7/3})^{-1/3}[/tex]
Using the indices law that states;
[tex](a^n)^m = a^{mn}[/tex]
Given,
[tex](125x^{7/3})^{-1/3}[/tex]
Since, [tex](125x^{7/3})^{-1/3}[/tex]= [tex][((5x)^3)^{7/3}]^{-1/3}[/tex]
= [tex][(5x)^7]^{-1/3}[/tex]
= [tex]5x^{-7/3}[/tex]
= [tex]\frac{1}{5x^{7/3}}[/tex]
Hence the resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]
To know more about indices refer to:
https://brainly.com/question/16933066
#SPJ1
PROBLEM SOLVING A train travels from Orlando to Miami, and then back to Orlando. The table shows the numbers of tickets purchased for each leg of the trip. The cost per ticket is the same for each leg of the trip. Is there enough information to determine the cost of one coach ticket?
Answer:
Step-by-step explanation: 10.75
nine tiles are numbered 1, 2, 3, . . . , 9, respectively. each of three players randomly selects and keeps three of the tiles, and sums those three values. the probability that all three players obtain an odd sum is m/n, where m and n are relatively prime positive integers. find m n.
The value of m and n from the obtained probability is equal to 3 and 14 respectively.
As given in the question,
Nine tiles numbered 1, 2, .....9
Number of odd numbered tiles are 1,3,5,7,9 = 5
Number of even numbered tiles are 2,4,6,8 = 4
Number of players =3
Possibility to choose 3 tiles by first player out of 9 tiles = ⁹C₃
= 84 ways
Possibility to choose 3 tiles by second player out of 6 tiles = ⁶C₃
=20 ways
Possibility to choose 3 tiles by third player out of 3 tiles = ³C₃
= 1 way
Total number of ways = 84× 20 ×1
= 1680
To have a sum of 3 tiles is odd number at least one tile should be odd.
Chances of first player all the 3 tiles are 0dd out of 5 = ⁵C₃
Next two players must 2 even tiles and 1 odd tile.= ²C₁
One player can be selected in ³C₁ way
Remaining 4 even tiles distributed equally = (4!)(2!)/ (2!)² ( 2!)
Number of favourable outcomes = ⁵C₃ × ²C₁ ׳C₁ × (4!)(2!)/ (2!)² ( 2!)
= 10 × 2 × 3 × 6
= 360
Probability (m/n) = 360 /1680
= 3/14
m = 3 and n = 14.
Therefore, from the probability that all three players obtain an odd sum is m/n , the value m = 3 and n = 14.
Learn more about probability here
brainly.com/question/11234923
#SPJ4
A bucket can hold a total of 5 gallons of water. If the bucket is 9/20 full, how much water is in the bucket?
Answer:2.25 gallons
Step-by-step explanation:
a rectangle has a length of 1 inches and a width of 6 inches whose sides are changing. the length is increasing by 4 in/sec and the width is shrinking at 2 in/sec. what is the rate of change of the perimeter?
The rate of change of the perimeter is 4 in/sec .
In the question ,
it is given that ,
the length of the rectangle is [tex]=[/tex] 1 inch
the width of the rectangle is = 6 inch
the rate of increasing length is (dL/dt) = 4 in/sec
rate of shrinking width is (dW/dt) = -22 in/sec ,
We know that the perimeter of the rectangle is = 2(L + W) ,
that is , P = 2L + 2W ,
Differentiating perimeter with respect to time "t" ,
we get ,
dP/dt = 2 × ( dL/dt) + 2 × (dW/dt )
Substituting the values from above ,
we get ,
= 2 × (4) + 2 × (-2)
= 8 - 4
= 4
Therefore , the required rate of change is = 4 in/sec .
Learn more about Rate Of Change here
https://brainly.com/question/29654834
#SPJ4
If the bond angle between two adjacent hybrid orbitals is 120°, which is the hybridization?.
If the bond angle between two adjacent hybrid orbitals is 120° the hybridization is Sp2 hybridization .
Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.
sp2 hybridization
There are other ways to combine the orbitals than sp3 hybridization when an excited state carbon atom is produced. As opposed to the three p orbitals in the sp3 hybridization, the s orbital only interacts with two p orbitals in the sp2 hybridization. As a result, three orbitals are combined to create three hybrid orbitals, also known as sp2 hybrid orbitals.
The sp2 hybridization occurs when the s orbital is mixed with only two p orbitals as opposed to the three p orbitals in the sp3 hybridization
To learn more about bond angles
https://brainly.com/question/29690391
#SPJ4