Answer:
The maximum number of possible extreme values for a fourth-degree polynomial function like f(x) = x^4 + x^3 - 7x^2 - x + 6 is 3.
To determine the number of extreme values, we can find the derivative of the function f(x) and set it equal to zero to solve for critical points.
f(x) = x^4 + x^3 - 7x^2 - x + 6
f'(x) = 4x^3 + 3x^2 - 14x - 1
Setting f'(x) = 0, we can solve for critical points:
4x^3 + 3x^2 - 14x - 1 = 0
Using numerical methods like the cubic formula or numerical approximation techniques, we can find that there are three real roots for this equation, which correspond to the critical points of f(x).
Since f(x) is a fourth-degree polynomial, we know that it has at most four critical points. Therefore, the maximum number of extreme values for f(x) is three, which can be achieved if the function has two local maxima and one local minimum or one local maximum and two local minima.
What is the total surface area of the gift box in in2?
The total surface area of the gift box in discuss as required to be determined in the task content is; 416 in².
Surface area of a cuboidAs evident in the task content; the gift box in discuss can be likened to a cuboid with dimensions; 12 by 10 by 4.
Hence, since the total surface area of a cuboid is given by;
Area = 2 (lw + lh + wh)
Therefore, for the given gift box;
Area = 2 ( (12×10) + (12 × 4) + (10 × 4) )
= 2 ( 120 + 48 + 40 )
= 2 (208)
= 416.
Ultimately, the total surface area of the gift box in discuss is; 416 in².
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Bridgette just went down the slide at the playground. She walks 1 meter to get from the end of the slide back to the ladder. Then she climbs 3 meters to the top of the slide again. How long is the slide? If necessary, round to the nearest tenth.
Please respond.
Thank you!
Answer:
2.14 (rounded to the nearest tenth)
Step-by-step explanation:
Let's assume that the length of the slide is represented by the variable "x".
Based on the information provided in the question, Bridgette walks 1 meter from the end of the slide back to the ladder and climbs 3 meters to reach the top of the slide again. Therefore, the total vertical distance Bridgette covers in one trip down and up the slide is 1 + x + 3 = x + 4 meters.
The length of the slide is the hypotenuse of a right triangle formed by the slide and the total vertical distance Bridgette covers in one trip down and up the slide. Using the Pythagorean theorem, we can write: x^2 = (x + 4)^2 - 1^2
Simplifying this equation, we get: x^2 = x^2 + 8x + 16 - 1
7x = 15
x = 2.14 (rounded to the nearest tenth)
Therefore, the length of the slide is approximately 2.1 meters.
Answer:
The slide is 3.2 m long---------------------------------
The slide and ladder form a right triangle with:
Horizontal leg (distance from slide to ladder) = 1 m,Vertical leg (ladder) = 3 m.Let the length of the slide be s, this is a hypotenuse.
Find s using Pythagorean:
[tex]s=\sqrt{1^2+3^2} =\sqrt{1+9}=\sqrt{10}=3.2\ m \ rounded[/tex]100 points please help
Answer:
(x + 1) (3x + 5)
Step-by-step explanation:
Let's check
(x + 1) (3x + 5)
3x² + 5x + 3x + 5
3x² + 8x + 5
So, (x + 1) (3x + 5) is the correct answer.
The number 0.08 is 1/10 of which value.
Answer: 0.008
Step-by-step explanation:
1/10 of 0.08
of is the same as multiplying
1/10 x 0.08= 1/10 x 8/100= 8/1000
8 divided by 1000= 0.008
what is the perimeter for a rectangle diagonal of 29 feet and a width of 14 feet?
Answer: We can use the Pythagorean theorem to find the length of the rectangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the diagonal is the hypotenuse and the width and length of the rectangle are the other two sides.
Let's use "l" to represent the length of the rectangle:
l^2 + 14^2 = 29^2
l^2 = 29^2 - 14^2
l^2 = 561
l = sqrt(561)
l ≈ 23.67 feet
Now that we know the length and width of the rectangle, we can use the formula for the perimeter, which is the sum of all four sides:
Perimeter = 2 * length + 2 * width
Perimeter = 2 * 23.67 + 2 * 14
Perimeter = 47.34 + 28
Perimeter = 75.34 feet
Therefore, the perimeter of the rectangle is approximately 75.34 feet.
Step-by-step explanation:
The number of houses in Central Village, New York, grows every year at a rate of 3.9%. In 2015, the local
government counted 540 houses. Using this data, how many houses can the local government of Central Village
predict there will be in 2035? (Round your answer to the nearest whole.)
Answer:
We can use the formula for exponential growth:
A = P(1 + r)^t
where:
A = final amount
P = initial amount
r = annual growth rate (as a decimal)
t = time (in years)
Let's plug in the values:
P = 540
r = 0.039
t = 2035 - 2015 = 20
A = 540(1 + 0.039)^20
A ≈ 891
Therefore, the local government of Central Village can predict there will be approximately 891 houses in 2035.
Answer:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r)^n
where:
A = the final amount
P = the initial amount
r = the annual interest rate (as a decimal)
n = the number of years
In this case, we want to find the final amount (the number of houses in 2035), given the initial amount (540 houses in 2015), the annual interest rate (3.9%), and the number of years (20 years from 2015 to 2035).
So, we can plug in the values and solve for A:
A = 540(1 + 0.039)^20
A = 540(1.039)^20
A = 540(2.011)
A = 1086.54
Rounding to the nearest whole number, we get:
A ≈ 1087
Therefore, the local government of Central Village can predict there will be about 1087 houses in 2035.
Brian wants to exchange South African rands for British pound if one is were 30 commerce 07519 9 lb how many pounds will he get for 2100 if he must pay an agency commission of 1.5%
Answer:
We can approach this problem using the following steps:
Calculate the exchange rate after factoring in the agency commission. Since the agency commission is 1.5%, the effective exchange rate will be:
Effective exchange rate = Exchange rate - (Exchange rate * Commission rate)
= 30.075199 - (30.075199 * 0.015)
= 29.6185968
Multiply the amount of South African rands by the effective exchange rate to get the amount in British pounds.
Amount in pounds = Amount in rands / Exchange rate
So, for an amount of 2100 South African rands, the calculation would be:
Amount in pounds = 2100 / 29.6185968
= 70.815 pounds (rounded to three decimal places)
Therefore, Brian will get 70.815 pounds for 2100 South African rands after factoring in the agency commission.
the average bmi (body mass index) value of children 9 years old is 18.4 with a standard deviation of 4.5. if it is known that the distribution is approximately normal, what is the probability that a randomly selected 9-year-old has a bmi greater than 26.8? give your answer to three decimal places.
The probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.
What is the formula to calculate standard deviation?
The formula to calculate standard deviation is:
SD = sqrt [(Σ(xi - μ)²) / N]
Where, SD = standard deviation
x = individual data points
μ = mean of the sample
N = sample size
What is the formula for z-score?
The formula for z-score is:
z = (x - μ) / σ
Where,
z = z-score
x = raw score
μ = mean of the population
σ = standard deviation of the population
Given that, The average BMI (body mass index) value of children 9 years old is 18.4 with a standard deviation of 4.5.
To find the probability that a randomly selected 9-year-old has a BMI greater than 26.8, we have to find the z-score.
z = (x - μ) / σz = (26.8 - 18.4) / 4.5z = 1.86
Now, we have to find the probability from the z-table, which is 0.9686. But we have to find the probability greater than 26.8, so we have to subtract it from 1.1 - 0.9686 = 0.0314 ≈ 0.031
Therefore, the probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.
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At the bakery where Isaac works, one of the cups in a cupcake tray has a radius of 3 centimeters. What is the cup's diameter? centimeters
The diameter οf the cup is 6 centimeters.
What is the diameter οf a circle?A circle's diameter is defined as a line thrοugh the centre that jοins the circumference at bοth ends. It is twice as lοng as the circle's radius. In οther wοrds, the line that splits a circle in half evenly at its centre is the diameter οf the circle.
The diameter οf a circle is equal tο twice its radius.
Therefοre, tο find the diameter οf the cup, we need tο multiply the radius by 2:
Diameter = 2 x Radius
Diameter = 2 x 3 cm = 6 cm
Hence, the diameter οf the cup is 6 centimetres.
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Calculate the mode of the data set {5, 8, 2, 5, 11, 2, 5, 13}
PLS HELP
Answer:
5
Step-by-step explanation:
The mode is the most commonly occurring number in a set of numbers. In this one it is 5.
This is part of a bus timetable between Birmingham and Coventry,
Birmingham 07 02 07 30 08 05 | 08 35 09 02 09 31 a) How many minutes
should the 07 02 bus
Yardley
07 21 07 4908 2408 5409 21 09 50
take to go from
Solihull 07 43 08 11 08 4609 16 09 43 10 12 Birmingham to
Coventry?
Meriden 07 59 08 27|09 0209 32 09 5910 28
92
minutes (1)
Coventry 08 34 09 02 09 3710 07 10 34 | 11 03
b) Steve goes from Birmingham to Coventry by bus,
He takes 9 minutes to walk from his house to the bus stop in Birmingham,
He takes 12 minutes to walk from the bus stop in Coventry to work,
Steve has to get to work by 10 am,
What is the latest time Steve should
leave his house to get to work on time?
(3)
Total marks: 4
The minutes that it would take for the 0702 bus to go from Birmingham to Coventry is 92 minutes.
The latest time that Steve should leave his house so as to get to work on time is 07 56 hours .
How to find the time taken ?If the bus from Birmingham leaves at 07 02 hours, it would reach Coventry at 08 34. The time taken is therefore :
= 08 34 - 07 02
= 1 hour 32 minutes
In minutes, this is:
= 60 minutes in an hour + 32
= 92 minutes
The total time it would take Steve to reach Coventry from Birmingham would be:
= Time to Coventry + Time spent walking from house + Time spent walking in Coventry
= 92 minutes + 9 + 12
= 113 minutes
The time Steve should leave his house at the latest is:
= 10 am - 113 minutes
= 08 07 hours
However, he would miss the 08 35 bus if he did this so he needs to leave in time for the 08 05 bus which is:
= 08 05 - 9 minutes walking
= 07 56 hours
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Note: Round intermediate calculations to at least 4 decimal places and your final answers to 2 decimal places. c-2. Based on the z-score standardized Manhattan distance values, identify the pair of the first three employees that are most simiar. Empioyees 1 and 3 Employeos 1 and 2 Employees 2 and 3 Undetermined, because the Manhattan distance values give inconclusive results.
The pair οf emplοyees 1 and 3 have the smallest Manhattan distance, indicating that they are the mοst similar based οn the z-scοre standardized Manhattan distance values. Therefοre, the answer is Emplοyees 1 and 3
What Is Z-Scοre?The relatiοnship between a value and a set οf values' mean is described by the statistical measurement knοwn as the Z-scοre.
Manhattan distance = [tex]|z^1 - z^2| + |z^3 - z^4| + ... + |zn-1 - zn|[/tex]
The z-scοres fοr each variable are calculated as fοllοws:
z-scοre = (x - mean) / standard deviatiοn
Emplοyee 1:
Age z-scοre = (25 - 27.33) / 1.2472 = -1.8616
Salary z-scοre = (48000 - 51666.67) / 9930.77 = -3.6915
Emplοyee 2:
Age z-scοre = (35 - 27.33) / 1.2472 = 6.1420
Salary z-scοre = (72000 - 51666.67) / 9930.77 = 2.0505
Emplοyee 3:
Age z-scοre = (27 - 27.33) / 1.2472 = -0.2645
Salary z-scοre = (53000 - 51666.67) / 9930.77 = 1.4256
Distance between emplοyees 1 and 2: |(-1.8616) - 6.1420| + [(-3.6915) - 2.0505] = 13.3956
Distance between emplοyees 1 and 3: |(-1.8616) - (-0.2645)| + [(-3.6915) - 1.4256] = 4.7236
Distance between emplοyees 2 and 3: |(6.1420) - (-0.2645)| + [(2.0505) - 1.4256] = 8.5020
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Whose work is correct?
Elise’s work
Jake’s work
Malik’s work
Xiao’s work
Answer: Without further context, it is impossible to determine whose work is correct. (Elise, Jake, Malik, and Xiao) Please post each person's work first so that I can post a proper answer.
Answer:
Maliks
Step-by-step explanation:
how many 6-letter names are possible, assume that the first
letter has to be a capital letter?
The 308915776 6-letter names that are possible, assuming that the first letter has to be a capital letter.
Given that the first letter in the name has to be a capital letter and the number of letters in the name is 6, find how many 6-letter names are possible.There are 26 capital letters in the English alphabet. Since the first letter must be a capital letter, we have 26 choices for the first letter.There are 26 lowercase letters in the English alphabet. We have 26 choices for each of the 5 remaining letters of the name.Using the multiplication principle of counting, the total number of possible 6-letter names with a capital first letter is:26 × 26 × 26 × 26 × 26 × 26=26⁶= 26 * 26 * 26 * 26 * 26 * 26 = 308915776 Therefore, there are 308915776 6-letter names that are possible, assuming that the first letter has to be a capital letter.
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For annually compounded interest, what rate would result in a single investment doubling in 3 years?
Work Shown:
[tex]A = P*(1+r/n)^{n*t}\\\\2P = P*(1+r/1)^{1*3}\\\\2 = (1+r)^{3}\\\\(1+r)^{3} = 2\\\\1+r = \sqrt[3]{2}\\\\r = -1+\sqrt[3]{2}\\\\r \approx 0.25992\\\\[/tex]
That converts to 25.992% after moving the decimal point two spots to the right. Round this value however your teacher instructs.
A line has a slope of –12 and passes through the point (6,–9). Write its equation in slope-intercept form.
Answer: y = -12x + 63
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope of the line, which is -12, and a point that the line passes through, which is (6,-9).
Using the point-slope form of a linear equation, we have:
y - (-9) = -12(x - 6)
Simplifying this equation, we get:
y + 9 = -12x + 72
Subtracting 9 from both sides, we get:
y = -12x + 63
Therefore, the equation of the line in slope-intercept form is y = -12x + 63.
The endpoints of PQ on the real number line are −14 and 2 . What is the coordinate of the midpoint of PQ ? F. −8 G. −6 H. −2 J. 0 K. 8
The midpoint of PQ is -6. The line PQ have endpoints on the real number line at −14 and 2
How to solve a midpoint equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
The midpoint O between two points A and B on the number line is:
O = (A + B)/2
The endpoints of PQ on the real number line are −14 and 2, hence:
Midpoint = (-14 + 2) / 2 = -12/2 = -6
The midpoint of PQ is -6
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the circumference of a circle is 38.8km find the length of the radius give your answer rounded to 3 SF
Answer:
6.18km
Step-by-step explanation:
circumference= diameter×π
38.8km÷π=12.350423583931.... this is the diameter
12.3504...÷2=6.1752117919655..... is the radius
radius rounded to 3sf= 6.18km i think
Help pls! There is a part b it says “predict the population of the city in 30 years to the nearest whole number”
The function that represents the estimated population after t years with an annual rate of decrease of 0.25% is y = [tex]358,000(0.9975)^{t}[/tex]. So correct option is D) .
Describe Annual rate?Annual rate can also be used to describe growth rates or changes in other types of measurements, such as population growth or inflation. For example, if the population of a city grows by 2% per year, the annual rate of population growth is 2%.
It is important to note that when annual rates are used to describe financial products or investments, they may be compounded over time. Compounding refers to the process of earning interest on interest, which can significantly increase the total amount of interest owed or earned over time. Therefore, it is important to carefully consider the effects of compounding when evaluating financial products or investments.
The function that represents the estimated population after t years with an annual rate of decrease of 0.25% is:
y = [tex]358,000(0.9975)^{t}[/tex]
Therefore, the correct option is D) y = [tex]358,000(0.9975)^{t}[/tex].
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Units of Capacity
Customary
System Units
1 gallon
1 quart
1 cup
Metric System Units
3.79 liters
0.95 liters
0.237 liters
How many centiliters are in 5 quarts?
quarts → liters → centiliters
->
a=
b=
C=
d=
5 quarts a C
1
-x-x=475 cL
=475
b d
After answering the provided question, we can conclude that As a result, expression 5 quarts contain 473.176473 centilitres. It is 473 cL rounded to the nearest centilitre
what is expression ?An expression in mathematics is a collection of manifestations, digits, and transnational corporations that resemble a significant correlation or regimen. A square root, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, pervasiveness, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
To convert 5 quarts to centilitres, first convert it to litres, then to centilitres.
1 gallon = 0.946352946 litres (conversion factor from customary system)
5 quarts equals 5 x 0.946352946 litres equals 4.73176473 litres
100 centilitres = 1 litre (conversion factor from metric system)
4.73176473 litres = 4.73176473 multiplied by 100 centilitres per litre = 473.176473 centilitres
As a result, 5 quarts contain 473.176473 centilitres. It is 473 cL rounded to the nearest centilitre.
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Find h(1.1) if
h(t) = -4.9t² +8.
Answer:i got u :uuuuuuuuuuuuuu
Farud had 4 ⅓ bags of M&Ms left after Halloween. Jackson had ¹³⁄₃ bags of M&Ms left. Farud said that he had more because he had 4 whole bags and Jackson had no whole bags. Is he correct? Explain how you know on the lines below.
Answer:
he is incorrect because Jackson also has 4 whole bags because 13/3 is a mixed number therefore jackson really has 4 13/3 or 4 1/3 which would be the amount as Fraud
Step-by-step explanation:
Helpppppp meeeeeeeeeeeee
Answer:
16
Step-by-step explanation:
Call the 3n+3 angle x. Call the 2n+7 angle y. The right angle, x, and y all lie in a straight line, meaning that the three angles added together equal 180. Adding, 5n + 100=180, so n=16.
A motorcycle decelerates steadily from 108 km/h to 36 km/h, covering a distance of 160m. For how long was the motorcycle decelerating?
Answer:
5760
Step-by-step explanation:
The hexagonal prism below has a base area of 36 units² and a height of 5.9 units.
Find its volume.
The volume of the hexagonal prism is the amount of space in the prism
The volume of the hexagonal prism is 212.4 cubic units
How to determine the volume?The given parameters are:
Base area = 36 square units
Height = 5.9 units
The volume is then calculated as:
Volume = Base area x Height
So, we have:
Volume = 36 x 5.9
Evaluate the product
Volume = 212.4
Hence, the volume of the hexagonal prism is 212.4 cubic units
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You want to determine the total amount of data stored on a server.
User A has 3550 GB of data stored on the server.
User B stores 4000 GB of data.
User C stores 2450 GB.
User D stores 1010 GB of data.
User E stores 7000 GB of data on the server.
Without using a calculator, use the properties of operations to determine the total amount of data stored on the server.
A
1801 GB
B
18,010 GB
C
19,010 GB
D
1901 GB
One way to approach this problem without using a calculator is to group the numbers by their place value (i.e., thousands, hundreds, tens, and ones), and then add them together.
For example,
For thousands:
User A has 3 thousands,
User B has 4 thousands,
User C has 2 thousands,
User E has 7 thousands.
There are no thousands for User D.
So the total number of thousands is 3+4+2+7 = 16 thousands.
For hundreds:
User A has 550 hundreds (since 3550 = 3 x 1000 + 550),
User B has 0 hundreds (since 4000 is a multiple of 1000),
User C has 450 hundreds (since 2450 = 2 x 1000 + 450),
User D has 10 hundreds,
User E has 0 hundreds (since 7000 is a multiple of 1000).
So the total number of hundreds is 550+0+450+10+0 = 1010 hundreds.
For tens and ones:
Since all the numbers are in thousands or hundreds, there are no tens or ones to add.
Therefore, the total amount of data stored on the server is:
16 thousands + 1010 hundreds = 16,100 GB
which ordered pairs is the solution to this set of linear inequalities?
y < 2x +2 and y ≥ -x -1
a.(-1,0)
b(0,3)
c(2,0)
d(-1,-4)
Answer:
c (2,0)
Step-by-step explanation:
One way to solve this system of inequalities is to graph the inequalities and see which ordered pair lies in the shaded region that is common to both inequalities
See the graph and each of the ordered pairs. Only (2, 0) lies entirely within the shaded region
(-1, 0) lies on the intersection of the two lines so it will satisfy the >= inequality but not the < inequality
Answer (2, 0)
However if you cannot use graphing then a brute force method must be used to see which ordered pair satisfies both inequalities
a. (-1, 0)
Check y < 2x + 2 ?
=> 0 < 2(-1) + 2 ?
=> 0 < -2 + 2
0 < 0 ? False
Eliminate option a
b. (0, 3)
y < 2x + 2?
=> 3 < 2(0) + 2?
3 < 2? False
Eliminate option b
c. (2, 0)
y < 2x + 2?
=> 0 < 2(2) + 2 ?
=> 0 < 4 + 2
=> 0 < 6 True
Move to the second inequality
y ≥ -x - 1?
0 ≥ -2 - 1
0 ≥ -3 True
So option c is the correct choice
While it is not necessary to check option d, let's do it anyway
d. (-1, -4)
y < 2x + 2 ?
-4 < 2(-1) + 2 ?
-4 < -2 + 2 ?
-4 < 0 ? True
Move to the second inequality
y > -x - 1 ?
-4 > -(-1) - 1
-4 > -2? False
Option d is eliminated
Correct answer: (2, 0) which is option c
Answer this ASAP will give the brainliest answer
Given that y = 8 cm and θ = 25°, work out x rounded to 1 DP.
The diagram is not drawn accurately.
Answer: x = 18.9 to 1dp
Step-by-step explanation: Using SOH CAH TOA,
Sin 25 = 8/x
Making x subject of the formula:
x = 8/Sin 25
x = 18.92961267
x = 18.9 to 1dp
The Central Limit Theorem states that The sampling distribution of the sample standard deviation will be approximately normal as long as the sample size is large enough. The sampling distribution of the sample mean will be approximately normal as long as the original population is normal. The distribution of the sample will be approximately normal as long as the sample size is large enough. The sampling distribution of the sample mean will be approximately normal as long as the sample size is large enough regradless of the underlying population distribution. QUESTION 14 Assume that the time spent on social media daily by ZU students has a mean of 130 minutes and a standard deviation of 43 minutes. If random samples of 246 students are selected, find the standard error of the mean? Round your answer to 2 decimal places. QUESTION 15 Assume that the speed of vehicles traveling on MBZ Highway is normally distributed with a mean of 108 km/h with a standard deviation of 5.5 km/h. According to the empirical rule, 95.44% of the speeds of vehichles traveling on MBZ Highway will be between 97 and 119 km/h 86 and 130 km/h 102.5 and 113.5 km/h 91.5 and 124.5 km/h
14: 2.38 minutes
15: lower bound is 97 km/h and the upper bound is 119 km/h
Question 14: The standard error of the mean (SE) can be calculated using the following formula: SE = s/√n, where s is the standard deviation of the population (43 minutes) and n is the sample size (246 students). Plugging in the values, SE = 43/√246 ≈ 2.38. Therefore, the standard error of the mean is 2.38 minutes and it should be rounded to 2 decimal places, giving us 2.38 minutes.
Question 15: According to the empirical rule, 95.44% of the speeds of vehicles traveling on MBZ Highway will be between 97 and 119 km/h. Therefore, the lower bound is 97 km/h and the upper bound is 119 km/h.
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in a group of 23 people, what is the probability at least 2 have the same birthday? you may assume no one was born on a leap year and that each of the 365 days is equally likely. (suggestion: use the rule for complements)
The probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.
The probability of at least 2 people having the same birthday in a group of 23 people can be calculated using the rule for complements. The complement of this event is that all 23 people have different birthdays. We can calculate the probability of this event and then subtract it from 1 to find the probability of at least 2 people having the same birthday.
The probability of the first person having a different birthday from the others is 1. The probability of the second person having a different birthday from the first is 364/365, since there are 364 days left that are not the first person's birthday. The probability of the third person having a different birthday from the first two is 363/365, and so on.
The probability of all 23 people having different birthdays is:
1 * (364/365) * (363/365) * ... * (343/365)
This simplifies to:
364! / (36522 * 341!)
Using a calculator, we find that this is approximately 0.4927.
Therefore, the probability of at least 2 people having the same birthday is:
1 - 0.4927 = 0.5073
So, the probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.
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In a group of 23 persons, the probability that at least two of them share the same birthday is around 0.5073, or 50.73%.
The probability that at least 2 people in a group of 23 have the same birthday, can be calculated by using the rule for compliments. First, we can calculate the probability that no two people share a birthday in a group of 23.
The first individual will have any birthday, however the 2nd individual have to have a distinct birthday, which has a probability of 364/365 (since there are 365 days in a year and one day has already been "used" by the first person). The probability that the third individual will have a different birthdate from the previous two is 363/365. Continuing in this way,
The probability that all 23 people have different birthdays is:
(365/365) x (364/365) x (363/365) x ...
Since the probabilities of all conceivable outcomes must sum up to 1, subtract the likelihood that at least two persons will have the same birthdate from one:
P(at least 2 people have the same birthday) = 1 - (365/365) x (364/365) x (363/365) x ... x (344/365)
P(at least 2 people have the same birthday) = 0.5073
Therefore, the probability that at least 2 people in a group of 23 have the same birthday is approximately 0.5073 or 50.73%
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