The probability of three people who share the same birthday is 0.6459.
Let us consider that A₀ be the event that everyone in the room has a distinct birthday. Let Ai be the event that pairs of people share a birthday. Then the probability we are interested in is
P(at lest three people share a birthday) = 1 - P(A₀) - ∑ P(Ai)
where there are n people in the lecture hall.
First we note that P(A₀) is in the book and is
P(A₀) = (365Cn)n!/365^n.
Now we will compute P(Ai).
For i = 1,
P(A₁) = (365) × [tex]\frac{(nC2)(365-1Cn-2)(n-2)!}{365^{n} }[/tex]
For i = 2,
P(A₂) = [tex]\frac{(365C2)(nC2)(n-2C2)(365-2Cn-4)(n-4)!}{365^{n} }[/tex]
This generalizes for i pairs of people sharing i distinct birthdays
P(Ai) = (365Ci)πj=1toi(n-2j+2C2)(365-iCn-2i)(n-2i)!/([tex]365^{n}[/tex])
Substituting all values into the equation and putting in n = 100, we can compute a value for this probability.
Therefore we get,
P(at least 3 people share a birthday)0.6459.
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(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
The ratio of the measures of two complementary angles 7:8 what is the measure of the smallest angle?
Answer: 84
Step-by-step explanation: so 7:8 increased by some number is 180 degrees. add 7 and 8 to get 15. 180/15 is 12 so x = 12 7*12 is 84.
(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
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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
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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]
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Researchers at the Washington University School of Medicine randomly placed 480 rats into one of three
chambers containing radio antennas. one group was exposed to digital cell phone radio waves the second
to analog cell phone waves and the third group to no waves. two years later the rats were examined for
signs of brain tumors. in June 2002 the scientist said that differences among the three groups were not
statistically significant.
a) is this a study or an experiment? explain
b) explain in this context what "not statistically significant" means.
c) comment on the fact that this research was funded by Motorola, a manufacturer of cell phones.
The answer to following questions are as follows:-A)experiment
B)meaning “statistically non significant” C)explained below
What is a wave?A wave is a dynamic disturbance that propagates over one or more quantities in the domains of physics, mathematics, and allied sciences. When waves are periodic, those parameters repeatedly oscillate around an equilibrium value at a certain frequency.
The answers are: a) It is an experiment since some claims are not supported by evidence.
b) When the analysis reveals that there are substantial variations between the observed, "not statistically significant" refers to "statistically non significant." And we are unable to analyse any of the statistics' results.
c) The fact that Motorola, a cell phone company, funded this research reveals to us that this claim is untrue because Motorola conducts this research to boost their sales.
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The city council voted on a new tax. 63 council members voted in favor of the tax. The
council has 90 members. What percentage of the council members voted in favor of the tax?
Write your answer using a percent sign (%).
Answer: 70%
Step-by-step explanation:
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.
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Find the radius of the cirlce
Answer:
R= 2sqrt(13) = about 7.2
Step-by-step explanation:
D^2= 12^2 + 8^2
= 144+64=208
D=4sqrt(13)
R= D/2= 2sqrt(13)
y is five times X +15
Select the price per unit in blanks a. And b, and choose which is the best buy. A. Tomato juice, 46 oz. Can for $2. 53 would = b. Tomato juice, 6-pack of 10 oz. Cans for $4. 50 would = c. The best buy would be.
The first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.
Given, A Tomato juice 46 oz. Cans cost $2. 53
B Tomato juice 6-pack of 10 oz. Cans costs $4. 50
we have to find the best buy between the given two.
In first case,
46 cans cost $2.53
46 cans = $2.53
1 can = 2.53/46
1 can costs $0.055
In second case,
60 cans cost $4.50
60 cans = $4.50
1 can = 4.50/60
1 can costs $0.075
So, it is clear that first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.
Hence, the first deal in which 1 can costs $0.055, is the best buy as it costs $0.020 less than the second deal in which 1 can costs $0.075.
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Which expression is equal to (3x − 4)(2x − 5)?
-
O 3x²
-
23x - 20
O 6x² - 7x+20
O 6x²-23x+20
O 6x² - 23x - 20
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.
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A function is represented by the graph.
Complete the statement by selecting from the drop-down menu.
The y-intercept of the function y = 3x + 2 is
Choose...
the y-intercept of the function represented in the graph.
A graph with a line through point (0, 2) and point (2, 6)
We want to finish each statement by analyzing the graph provided.
The function's y-intercept is y =2.
y = 3x+2 is the equation.
The line connects (0, 2) and (2, 6).
What is meant by a function?The earliest known attempt to the concept of function may be traced back to the works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were initially the idealization of how a variable quantity depended on another quantity. The position of a planet, for example, is a function of time.
So, first, we need to find the y-intercept. We know that the y-intercept is the y-value at which the function intersects the y-axis, and we can see from the graph that the y-intercept is y = 2.
Then we'd like to see the line's equation.
Remember that y = ax + b is a generic line.
Where a denotes the slope and b the y-intercept, we may deduce:
y = ax + 2
We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a=(y₂-y₁)/(x₂-x₁)
Given that the line passes through (0, 2) and (-2/3, 0), the slope is as follows:
a=(-2/3)/(-2)
a=1/3
The equation of the line is:
y =3x+2
And using that equation, we can show that the line does indeed pass through the points (0, 2) and (2, 6)
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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:
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.
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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]
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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.
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The wholesale cost of a dining room table at a fumiture store is $1,215.80. The markup for the table is 30%. What is the selling price of the dining room table?
Answer
$1,580.54
1215.80×(1+0.3)= 1580.54
select the first correct reason why the given series converges. a. convergent geometric series b. convergent p series c. comparison (or limit comparison) with a geometric or p series d. alternating series test e. ratio test
Because it diverges using a comparison test, the correct answer is an option (E).
What is a comparison test?The comparison test, also known as the direct comparison test to distinguish it from other closely related tests, offers a method for determining whether an infinite series or an improper integral will converge or diverge.
The test is effective in both situations by contrasting the given series or integral with one whose convergence characteristics are known.
So, refer to the image attached below.
According to the image which has the reason for convergence and divergence, we know that the correct answer would be option (E).
The reason is the comparison test.
Therefore, because it diverges using a comparison test, the correct answer is an option (E).
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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
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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.
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A store manager would like to set the three-digit code of the store's new safety vault. How many possible 3-digit code choices does he have if he can pick digits from 0 to 9 with repetition allowed?.
Answer: 270 I think
Step-by-step explanation:
try it you can get this right
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
Describe the relationship between the lines.
1. The lines intersect to form an angle that is 180°
2. The lines intersect to form an angle that is 90°
3. The lines do not intersect.
4. The lines intersect to form an angle that is not 90°
a study of 1000 randomly selected flights of a major airline showed that 798 of the flights arrived on time.what is the probability of a flight arriving on time?
By using the concept of probability, it can be calculated that
Probability that the flight arrives on time = [tex]\frac{399}{500}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Total number of flights = 1000
Number of flights arriving on time = 798
Probability that the flight arrives on time = [tex]\frac{798}{1000}[/tex]
= [tex]\frac{399}{500}[/tex]
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Evaluate the expression for n = 2 and p = –6.
np + n =
Answer: -10
Step-by-step explanation:
Substitute the numbers in for the variables.
np + n = (2)(-6) + 2
-12 + 2
-10
E. Realiza las divisiones de polinomio
a) (15a²-a-28)÷(3a + 4) =
Given that the dividend is 15a²-a-28 and the divisor is 3a+4, the quotient will be 5a-7 and the remainder will be 0.
What is polynomial?A multi-term algebraic statement is referred to as a polynomial. It contains exponents, coefficients, variables, constants, and arithmetic operators. It uses a polynomial long division algorithm to divide the polynomials. It is the long division technique in a more generalized form. In this method, a polynomial is divided by other polynomials of the same degree or lower. Synthetic division method is a simple and quick technique that is occasionally employed as well.
Here,
dividend=15a²-a-28
divisor=3a+4
remainder=0
15a²-a-28=(3a+4)(5a-7)
quotient=5a-7
The quotient will be 5a-7 and remainder will be 0 as dividend is 15a²-a-28 and divisor is 3a+4.
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The question is below! Will mark brainliest! Best answer!
Answer: 315 children and 15 adults
Step-by-step explanation:
15 x 21 = 315
315 + 15 = 330
c = 315
a = 15
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