The probability that in 5 flips, at least 3 tails will come will be 0.36.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.Given is that you flipped a weighted coin that comes up heads 40% of the time and tails 60%.
The coin shows up heads 40% of the time and tails 60%, this means that the probability of turning to tails would be 0.6 . For 5 flips that, the probability that at least 3 tails will come will be -
P{A} = (0.6 + 0.6 + 0.6)/5 = 1.8/5 = 0.36
P{A} = 0.36
Therefore, the probability that in 5 flips, at least 3 tails will come will be 0.36
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PLEASE HELP the question is in the picture
The required expression that can be simplified without the conversion of terms is 9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵. Option A is correct.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
In order to do, no needs to convert terms, so then expression with the same exponent of 10 is the required expression.
So,
= 9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵
= 10.00 × 10⁻⁵
= 10⁻⁴
Thus, the required expression that can be simplified without the conversion of terms is 9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵. Option A is correct.
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Answer:
9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵
Step-by-step explanation:
Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS
Answer:
56π/3 m³ or 58.64 m³------------------------------------------------
Find the sum of the volumes of the two given cones.
Cone volume:
V = 1/3 πr²hCone 1, d = 4m, h = 8m:
V = 1/3 π*(4/2)²*8 = 32π/3 m³Cone 2, r = 2m, h = 6 m:
V = 1/3 π*2²*6 = 8π m³Total volume:
V = 32π/3 + 8π = 56π/3 m³ = 58.64 m³ (rounded)Which of the following points would fall on the line produced by the point-slope form equation y + 12 = 3(x - 4) when graphed
Answer:
where r the points??
Step-by-step explanation:
give them atleast to find the ans.
The cross-country team had a fundraiser selling wreaths for $25 each. They made $15 for each wreath they sold. If they sold 114 wreaths, (a) how much money did they pay to make each wreath, (b) how much money did they collect, and (c) how much money did they make? If they made $180, (d) how many wreaths did they sell?
Answer:
(a) They paid $25-$15=$<<25-15=10>>10 to make each wreath.
(b) They collected $15114=$<<15114=1710>>1710.
(c) They made $1710-$10114=$<<1710-10114=180>>180.
(d) They sold $180/$15=<<180/15=12>>12 wreaths.
Step-by-step explanation:
Sure, here is a breakdown of the solution:
(a) The cross-country team paid $10 to make each wreath because they sold the wreaths for $25 and made $15 for each wreath they sold, so the cost to make each wreath was $25-$15=$10.
(b) They collected $1710 because they sold 114 wreaths and made $15 for each wreath they sold, so they collected a total of $15*114=$1710.
(c) They made $180 because they collected $1710 and it cost them $10 to make each wreath, and they sold 114 wreaths, so the total cost of making all the wreaths was $10*114=$1140. They made $180 because they collected $1710 and it cost them $1140 to make all the wreaths, so their profit was $1710-$1140=$180.
(d) They sold 12 wreaths because they made $180 and it cost them $15 to make each wreath, so they sold $180/$15=12 wreaths.
Match each data set with its range.
The range of the data set are
{10.2, 3.8, 21.9, 33.4, 31.8, 17.2} = 29.6
{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71} = 0.6
{6, 2, 14, 11, 28, 10, 19, 15, 11} = 26
The first data set is
{10.2, 3.8, 21.9, 33.4, 31.8, 17.2}
The range is the difference between the highest value and the smallest value
The highest value = 33.4
Lowest value = 3.8
The range = 33.4 - 3.8
= 29.6
The second data set is
{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71}
The highest value = 0.71
Lowest value = 0.11
The range = 0.71 - 0.11
= 0.6
The third data set is
{6, 2, 14, 11, 28, 10, 19, 15, 11}
Highest value = 28
Lowest value = 2
The range = 28 - 2
= 26
Therefore, the range of the each data set has been found
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A graphing calculator is recommended. Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) = e, a = 1 Graphſ and Tg on the same screen. y 3 2 -1 1 2 X -4 -3 -2 -1 -3 -2 - 1 1 2 6 -1 2 -3
Its Taylor polynomial T3(x) for function f with the number an as the center is T 3(x)=(x 2 + 61 x 2 ). 3
With an example, define a polynomial.Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered. A polynomial is a function that exclusively uses positive integer exponents or non-negative integer powers of a variable in an equation, such as a quadratic or cubic equation. A polynomial with an exponent of 1 is, for instance, 2x+5.
T 3 (x)=f(a) + 1!f ′ (a)(xa) + 2!f ′′(a)(xa) 2 plus 1 3!f ′′′(a)(x−a) 3=0plus 1!−1(x− 2π)+ 2!0(x− 2π) 2 plus 1 3!1 (x− 2π) 3=−(x− 2π)+ 61\s(x− 2π) 3
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Please be legible and thorough. please be detailed with your explanations. thank you very much.
Q: Solve the infinite potential well problem for a symmetric well. That is, the potential energy function is given by the following:
-a CO r I 2 -a 2 V(r)={ 0 .rs ss > a CO < 2 Or graphically: KV(x) 1 III a/2
your solution should give the following: (a) normalized eigenfunctions (b) eigenvalues hints: follow the same procedure as done in the text, section 2.2 of griffiths. the only significant difference is the boundary conditions. you should also note that unlike the version in the text(called the asymmetric well) this well is symmetric about the origin and hence shows reflection symmetry: V(.x)=V(-x). As a result, your eigenfunctions must be either even or odd under the same reflection operation. This means you should have two sets of eigenfunctions, one even and the other odd under x inversion. Make sure you see this. X
As per the given inversion, the time independent Schrödinger equation in one dimension is [tex]\frac{-hx^{2}}{2m} \times\frac{d^{2}(x)}{dx^{2} } + U(x)f(x)=Ef(x)[/tex]
The term inversion in math refers a concept in discrete mathematics to measure how much a sequence is out of its natural order.
Here we have given that the potential energy function is given by the following: -a CO r I 2 -a 2 V(r)={ 0, s > a CO < 2}
And we need to find the eigenfunctions must be either even or odd under the same reflection operation.
While we looking into the given question, let us consider E is the total energy of the particle, and U (x) the potential energy function and ψ (x) the spatial part of the wavefunction.
Based on the the function can be written as,
=> [tex]\frac{-hx^{2}}{2m} \times\frac{d^{2}(x)}{dx^{2} } + U(x)f(x)=Ef(x)[/tex]
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How many pounds are in 2,600 ounces? Enter only a number. Do not enter units.
Answer: 162.5 Pounds
1. Copy and complete: To multiply two powers with the same base, ? their exponents.
2. Give an example of an expression you could simplify using the quotient of powers property.
Find the product or quotient. Write your answer using exponents.
3. 4².4⁹ 4. 5³.5⁸ 5. 6₇.6 6. 7³.7⁴.7²
(1) To multiply two powers with the same base, add their exponents.
(2) An example of an expression you could simplify using the quotient of powers property is xᵃ / xᵇ
(3) The answer of following exponents are 4¹¹ , 5¹¹ , 6⁸ and 7⁹
A number's exponent indicates how many times the number has been multiplied by itself.
In general, xⁿ denotes that x has been multiplied by itself n times.
According to the question,
(1) Assuming two exponent having same base be xᵃ and xᵇ
Multiplying both the number => xᵃ . xᵇ
To Multiplying two exponent having same base , we add the power
=> x⁽ᵃ ⁺ᵇ⁾
Hence , To multiply two powers with the same base, add their exponents
(2) Simplifying using the quotient of powers property
Let xᵃ / xᵇ
Dividing exponent with same base , we subtract the powers
=> xᵃ⁻ᵇ
Simplifying the followings
3. 4².4⁹
=> 4⁽²⁺⁹⁾
=> 4¹¹
4. 5³.5⁸
=> 5 ⁽³⁺⁸⁾
=> 5¹¹
5. 6⁷.6
=> 6⁸
6. 7³.7⁴.7²
=> 7⁽³⁺⁴⁺²⁾
=> 7⁹
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young's modulus is a quantitative measure of stiffness of an elastic material. suppose that for metal sheets of a particular type, its mean value and standard deviation are 85 gpa and 2.3 gpa, respectively. suppose the distribution is normal. (round your answers to four decimal places.)
(a) Calculate P(79 x 81) when n = 25. (b) How likely is it that the sample mean diameter exceeds 81 when n = 36? You may need to use the appropriate table in the Appendix of Tables to answer this question
(a) Probability that sample mean lies between 79 and 81 is 0.9946.
(b) It is 0.04% likely is it that the sample mean diameter exceeds 81 when n = 36.
We are given that the metal sheets of a particular type, its mean value and standard deviation are 85 GPA and 2.3 GPA, respectively.
Suppose the distribution is normal.
Let X = sample mean diameter
The z-score probability distribution for sample mean is given by;
Z = (X - μ) / (σ / √n)
where,
μ = population mean = 85 GPA
σ = standard deviation = 2.3 GPA
n = sample size = 25
(a) Probability that sample mean lies between 79 and 81 is given by
= P(79<X<81) = P(X<81) - P(X≤79)
P(X<81) = P {(X - μ) / (σ / √n) < (81 - 85) / (2.3 / √25) = P(Z < 2.78) = 0.9973
P(X<79) = P {(X - μ) / (σ / √n) < (79 - 85) / (2.3 / √25) = P(Z < 2.78) = 0.0027
The above probability is calculated by looking at the value of x = 2.78 in the z table which has an area of 0.9973.
Here, P(79 < X < 81) = 0.9973 - 0.0027 = 0.9946
(b) Probability that the sample mean diameter exceeds 81 when n = 36 is given by = P(X > 81)
P(X<81) = P {(X - μ) / (σ / √n) < (81 - 85) / (2.3 / √25) = P(Z < 3.33) = 0.0004
The above probability is calculated by looking at the value of x = 3.33 in the z table which has an area of 0.9996.
Therefore, probability that sample mean lies between 79 and 81 is 0.9946 and it is 0.04% likely is it that the sample mean diameter exceeds 81 when n = 36.
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Which of the following sequences are convergent? Select all that apply (there are 2 answers).
a geometric sequence with r=3
an arithmetic sequence with d=2
a geometric sequence with r=3/5
an arithmetic sequence with d=-2/3
a geometric sequence with r=-1/6
The following sequences are convergent an arithmetic sequence with d=-2/3.
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers where each successive number is obtained by adding a constant value to the previous number. This constant value is referred to as the common difference. Arithmetic sequences are especially useful in mathematics, as they can be used to model real-world phenomena such as population growth and the depreciation of assets. By finding the common difference, one can solve a variety of problems involving the sequence. For example, given two terms of an arithmetic sequence, one can find the sum of the sequence, the nth term, and the number of terms in the sequence.
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Answer:
The other answer is actually wrong.
The answers are: r=3/5 and r=-1/6
Step-by-step explanation:
10:35 AM Sat Dec 10
Homework 6.2
:
ด
1.) Mr. Keith is paid semimonthly. His annual salary is $64,733. What is his semimonthly
salary rounded to the nearest cent?
3%
Sa
Mr. Keith's semimonthly salary is $16183.25.
What is rounded to the nearest cent?
If the number is five or higher and is to the right of the full cents, increase the cents by one. The cents should remain the same if the number is four or less.
For instance: $143.864. Consider the last digit, 4, since it is less than 5 and the cents should remain the same. Rounding up from $143.864 to $143.86.
Given that the annual salary of Mr. Keith is $64,733.
Semiannual means 4 times in yearly.
Thus divide whole salary by 4 to get semimonthly salary.
Therefore the semimonthly income is $64,733/4 = $16183.25 (rounded to the nearest cent)
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If the probability that a person will die in the next year is 452/100000
probability that the person will not die in the next year?
OA. 99%
B. 99548
C. 0.00452
OD. 0.99548
452
100,000
what is the
SUBMIT
Answer:
0.99548
Step-by-step explanation:
P(not die)=100000-452/100000
A rectangular solar panel is 84 cm by 35 cm. By adding the same amount to each dimension, the area is doubled. How
much is added?
Answer:
21
Step-by-step explanation:
84x35=2940
2940x2=5880
84+21=105
35+21=56
105*56=5880
HELP IM IN K12 PLEASE HELP
Step-by-step explanation:
p = a + 3
Three more a than p
a researcher would like to determine if relaxation training will affect the number of headaches for chronic headache sufferers. for a week prior to training, each participant records the number of headaches suffered. participants then receive relaxation training, and for the week following training the number of headaches is again measured. the change in number of headaches before and after training is as follows (minus signs indicate a reduction):
Regression analysis, regression, and immigration analyst analysis are the solutions.
What is Regression analysis?Regression analysis is a group of statistical procedures used in statistical modeling to determine the relationships between a dependent variable (often referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon), and one or more independent variables (often referred to as "predictors," "covariates," "explanatory variables," or "features").
In linear regression, the most typical type of regression analysis, the line (or a more complicated linear combination) that most closely matches the data in terms of a given mathematical criterion is found.
When using the ordinary least squares method, for instance, the specific line (or hyperplane) that minimizes the sum of squared differences between the genuine data and that line is computed (or hyperplane).
This enables the researcher to estimate the for precise mathematical reasons (see linear regression).
Hence, Regression analysis, regression, and immigration analyst analysis are the solutions.
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The following dot plot shows the number of songs on each album in Saiâs collection.
Each dot represents a different album. What is the total number of albums in Saiâs collection?
A. 10
B. 17
C. 7
Option B) 17
A simple kind of data visualization known as a "dot plot" involves the representation of data points as dots on a graph with x and y axes. Sai has 17 albums in his collection altogether.
Given data;
6 = 0; 7 = 1 ; 8 = 2; 9 = 2; 10 = 4; 11 = 1; 12 = 2; 13 = 2; 14 = 1; 15 = 0; 16 = 2
[tex]= 1+2+2+4+1+2+2+1+2[/tex]
[tex]=17[/tex]
The total number of albums in Sai collection is 17
A basic style of data visualization called a dot plot, often referred to as a strip plot or dot chart, shows data points as dots on a graph with x and y axes. The purpose of these graphs is to visually portray particular data patterns or groups.
Each dot in the provided dot plot represents an album. As a result, the total number of dots in the dot plot equals the total number of albums in Sai's collection.
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Brad reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation.
Brad recalls that correlation does not imply causation. In this example, Brad sees that increasing the number of cars per household would not cause members of his community to purchase health insurance. Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
Brad looks at a scatterplot that shows the correlation between the typical population's access to health insurance and the number of cars owned by each household in different parts of the country. A substantial positive association can be seen in the plot.
What are some examples of scatter plots?
The association between two sets of data is depicted by points on a scatter (XY) plot. Each dot in this illustration represents the weight and height of one individual. (The information is displayed as "Cartesian (x,y) Coordinates")
What is the purpose of a scatter plot?
Data points are plotted on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.
The values of the columns selected on the X and Y axes determine where each row in the data table is represented by a marker, whose position.
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I need help with this by tonight pls or I will not get an updated grade it's hard for me to understand this
Find the Sum, Difference, or Product
1. [tex]3x^2 + 4x -1 - 2x^2 -3x + 2 = x^2 + x + 1[/tex]
2. [tex]12x^5 - 3x^4 + 2x -5+8x^4-3x^3+4x+1 = 12x^5 +5x^4-3x^3+6x-4[/tex]
3. [tex]3x^3 - 2x^2 + 4x-8-5x^3-12x^2+3x+4 = -2x^3-14x^2+7x-4[/tex]
4. [tex]5x^6 - 2x^4 +9x^3+2x-4-7x^5+8x^4-2x+11 = 5x^6-7x^5+6x^4+9x^3+7[/tex]
5. [tex]x^3+3x^2-10x-24[/tex] (Multiply the first two factor, then multiply the product to the last factor)
6. [tex](7h+4)*(7h+4)= 49h^2+28h+28h+16 =49h^2+56h+16[/tex]
Factor the Sum or Difference of Cubes
Sum of Cubes Formula: [tex]a^3+b^3 = (a+b)(a^2-ab+b^2)\\[/tex]
Difference of Cubes Formula: [tex]a^3-b^3 = (a-b)(a^2+ab+b^2)\\[/tex]
Just apply it to the equations.
1. [tex]x^3 + 4^3 = (x+4) (x^2 - 4x+16)[/tex]
2. [tex]c^3 - 3^3 = (c-3) (c^2+3c+9)[/tex]
3. [tex](3d)^3 + 2^2 = (3d+2)((3d^)^2-(3d)(2)+4) = (3d+2)(9d^2-6d+4)[/tex]
4. [tex]5^3-(2b)^3= (5-2b)(5^2+(2b)(5)+(2b)^2) = (5-2b)(25+10b+4b^2)[/tex]
Factor the Polynomials Completely
Nt. I'm having a hard time with this one
1. [tex]x(x-6)(x+4)+24(x-1)[/tex]
2. [tex]2m^4 (m-4)(m-8)[/tex]
3. [tex](6v+7)(3v+2)[/tex]
4. [tex]4n^2(n^5-2)(n^5-6)[/tex]
5. [tex](9a^2-16b)(9a^2+16b)[/tex]
6. [tex](4z^2-25y)(4z^2+25y)[/tex]
select all that apply identify the steps involved in the six sigma approach. (check all that apply.)
the steps involved in the six sigma approach. -Define-Measure-Analyze-Improve-Control
-Define: Identify the problem and set objectives and goals
-Measure: Collect and analyze data related to the problem
-Analyze: Identify the root cause of the problem
-Improve: Develop and implement solutions to the problem
-Control: Monitor and maintain the improvements to ensure the problem does not recurrence are the steps involved in six sigma.
1. Define: Identify the problem, set objectives and goals, and develop a project plan.
2. Measure: Collect and analyze data related to the problem and determine the current process performance.
3. Analyze: Examine the data to identify the root cause of the problem.
4. Improve: Develop and implement solutions to improve the process.
5. Control: Monitor and maintain the improvements to ensure the problem does not recur.
6. Optimize: Continuously look for ways to make the process more efficient and effective.
the complete question is:
Select all that apply identify the steps involved in the six sigma approach. (check all that apply.)
-Define
-Measure
-Analyze
-Improve
-Control
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During a review game, Mr. Pai's class correctly answered 65 questions on the first try. If there were 75 questions in the game, at what rate were questions answered correctly on the first try? Express your answer as a decimal. Round to the nearest thousandth.
A. 0.087
B. 0.867
C. 0.133
D. 1.154
Using the concept of ratio, the rate at which questions were answered correctly is 0.867 which is option B
What is RateRate can be defined as comparing two or more ratio with a standard value.
The rate of correct answer can be calculated using the ratio between the number of correct answers to numbers of questions answered.
The rate is given as;
rate = 65 / 75
rate = 0.867
The rate of correct answers is 0.867
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TRUE OR FALSE the difference between timing diagrams and state diagrams is that timing diagrams show changes along the flow of time, whereas state diagrams show changes based on triggers received from other objects in or outside the system.
Therefore, the answer to this problem is that the statement is true.
What is state diagram?A state diagram is a particular kind of diagram used in computer science and related subjects to represent system behavior. A system must have a finite number of states in order to be represented by a state diagram; sometimes this is the case, and other times it is a valid abstraction.
Here,
Since,
Timing diagrams depict changes during the passage of time, whereas state diagrams depict changes as a result of triggers from other system objects or from external sources.
So ,the above statement is true
Therefore the answer to this problem is that the statement is true.
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Graph: y ≤ -2
Is (-2,-7) a solution? yes or no
Is ( 2,-1) a solution? yes or no
Answer:
(-2,-7) , yes
(2,-1) , no
Step-by-step explanation:
the question says y is less than or equal to -2 . In the first order pair (-2,-7) , x= -2 & y = -7 in the number line -2 comes first than -7 it means -2 is grater than -7 so the answer is yes but in the second order pair (2,-1) the value of x is 2 and the value of y is = -1 thus -1 is grater than -2 however the question says y should be less or equal but not greater than -2 so the answer is yes for the first order pair and no for the second one
This graph shows Jesemy's distance from home each hour he is on a car trip. How many miles will he be from home after 10 hours?
500 miles
550 miles
400 miles
350 miles
From the graph that shows Jeremy's distance from home each hour , then he will be 500 miles from home after 10 hours .
In the question ,
a graph is given ,
we have to find the distance that Jeremy's car will travel after 10 hours.
from the graph we can see that the points in the graph form a straight line .
we can see that ,
in 1 hour Jeremy's car travels a distance of 50 miles .
So , in 10 hours Jeremy's car will travel = 10×50 miles .
= 500 miles .
So , Jeremy's car will be 500 miles away from home after 10 hours .
Therefore , the correct option is (a) 500 miles .
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Find the value of the variable. The sum of angle measures is 180°. Then find the angle measures of the polygon
Answer:
28° + 112° + 40° = 180°
Step-by-step explanation:
A Triangle has 3 angles that adds up to 180°
You are given 3 angles already so they must add up to 180°
Equation: n + 4n + 40° = 180°
Simple the equation.
Add the variable n together.
5n + 40° = 180°
Subtract 40 to both sides.
5n = 140°
Divide 5 to both side to solve for n.
n = 28°
Now plug n into our angles to have our angles in degree.
n = 28°
4n = 4×28° = 112°
40°
28° + 112° + 40° = 180°
Answer:
Step-by-step explanation:
The internal angles of a triangle sum 180°
n + 4n + 40 = 180
5n = 180 - 40
5n = 140
n = 140/5
n = 28
Check:
28 + 4*28 + 40 = 180
28 + 112 + 40 = 180
Answer:
variable n = 28°
∡n = 28°
∡4n = 4*28 = 112°
Given P(A) = 0.6, P(B) = 0.79 and
P(A and B) = 0.544, find the value of P(B|A),
rounding to the nearest thousandth, if necessary.
[tex]P(B|A) = \frac{P(AandB)}{P(A)}[/tex]
Answer:
0.3324
Step-by-step explanation:
Darren kept track of the number of e-mails he received from one of his customers each day for 14 days on the dot plot. A number line goes from 1 to 12. 1 dot is above 2. 2 dots are above 7. 3 dots are above 8. 1 dot is above 9. 3 dots are above 11. 4 dots are above 12. Which statement must be true according to the dot plot?
The customer sent Darren more than 12 e-mails over the 14-day period. The maximum number of emails represented in the dot plot is 12 + 4 = 16
The dot plot provides information about the number of emails he received from one customer over a 14-day period.
The number line goes from 1 to 12, but there are 4 dots above 12 which means that the customer sent him more than 12 emails over the 14-day period.
Therefore, the statement "The customer sent Darren more than 12 e-mails over the 14-day period" must be true according to the dot plot.The maximum number of emails represented in the dot plot is 12 + 4 = 16. Therefore, the customer sent Darren more than 12 emails over the 14-day period.
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I want to know some example of a continuous function which is continuous at exactly one point. We know that f(x)=1x is continuous everywhere except at x=0. But i think this in reverse manner but i dont get any example. So please help me out!
Examples of a continuous function that is continuous at exactly one point are x=0,1,2,3,4.
In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter.
We know that the modulus function,
f(x)=∣x∣ is continuous but not differentiable at x=0.
So,
f(x)=∣x∣+∣x−1∣+∣x−2∣+∣x−3∣+∣x−4∣ is continuous but not differentiable at x=0,1,2,3,4.
Hence, this is the answer.
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10. Suppose a small library has five book shelves labeled A-E. In how many different ways can 30 books be placed on these shelves if the books are. (a) all different? (b) all identical?
All different: Since there are 30 books and 5 shelves, the books can be placed in 30!/(5!*25!) ways, which is 5,852,114,406 ways.
What is library?A library is a collection of books, periodicals, audio and visual materials, and other educational and informational resources that are made available for public use. Libraries typically provide a range of services and resources, such as access to computers, books, reading materials, reference assistance, classes, and programs.
A. (a) All different: Since there are 30 books and 5 shelves, the books can be placed in 30!/(5!*25!) ways, which is 5,852,114,406 ways. This is because the number of ways to arrange 30 different books across 5 shelves is the same as the number of permutations of 30 objects taken 5 at a time.
B. (b) All identical: Since there are 5 shelves and 30 books, the books can be placed in 5^30 ways, which is 922,337,203,685,477,439,232,000 ways. This is because there are 5 choices for each book, so the total number of possible arrangements is 5^30.
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As part of a study on the selection of grand juries in Alameda county, an educational level of grand jurors was compared with the county distribution:
Educational Level County # of Jurors
Elementary 28.4% 1
Seconday 48.5% 10
Some College 11.9% 16
College Degree 11.2% 35
Total 100% 62
Could a simple random sample of 62 people from the county show a distribution of educational level so different from the county-wide one? Chose one option and explain.
1) this is absolutley possible
2)this is possible, but fantastically unlikely
3)this is possible but unlikely-the chance is around 10% or so
4)this is nearly certain
This is possible but fantastically unlikely. A simple random sample of 62 people from the county would be unlikely to produce a distribution of educational levels so different from the county-wide one. The chances of this happening are extremely small.
A simple random sample is a sample drawn from a population in such a way that each member of the population has an equal chance of being selected. In this case, the population is the county, and the sample is the group of 62 grand jurors. When a simple random sample is drawn, it is possible for the sample to be different from the population in various ways.
For example, the sample may have a different distribution of educational levels than the population. However, the larger the sample size is, the more likely it is that the sample will be representative of the population. In this case, the sample size of 62 is relatively small, so it is possible that the sample will be different from the population in terms of educational level. However, the chance of this happening is not very high, since the sample size is not very large.
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