Every rational number can be expressed in decimal form. This argument cannot be used to demonstrate that rational numbers between 0 and 1 are countable. We frequently use this fact to demonstrate that rationals are countable since every rational number has a decimal representation that terminates on a non-teminating repeating sequence.
Rational number:
P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals). The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
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Michael is 333 times as old as brandon. 181818 years ago, michael was 999 times as old as brandon. How old is brandon now?.
Bradon is 24 years old and Micheal is 72 years old.
Michael is 3 times as old as brandon. 18 years ago, michael was 9 times as old as brandon
Let m represent Michael
Let b represent Brandon
Then,
m = 3b <-----------"Michael is 3 times as old as Brandon."
m - 18 = 9(b - 18) <-----------"18 years ago, Michael was 9 times as old as Brandon."
3b - 18 = 9b - 162
-18 = 6b - 162
144 = 6b
b = 24 <-------This is Brandon's age.
3b = m
3(24) = 72 <------This is Michael's age.
Therefore, Michael is 3 times as old as Brandon. Also, 18 years ago, Brandon would have been 6 and Michael would have been 54
Now, Bradon is 24 years old and Micheal is 72 years old.
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Solve using substitution.
y = 6x + 2
y = 6x 10
Answer:
Step-by-step explanation:
1/27,20/9
If f(x) = -x^2 + 3, Find f(-3)
x^2 means x to the power of 2
Answer:
-6
Step-by-step explanation:
-(-3)²+3
-9 + 3
-6
a ship is off course. if the ship is traveling at 11 miles per hour, how far off course will it be after 3 hours?
Ship travels 33miles in 3 hours.
What is distance?
Distance is the actual distance that a body travels. Additionally known as path length. For instance, the path length for an item going from point O to point P will be distance OP = 360 m. It is a scalar quantity, the distance. It lacks direction and just possesses magnitude.
Ship travels in one hour = 11miles
Therefore, Ship travels in 3 hours = 11×3
= 33miles
Hence, Ship travels 33 miles in 3 hours.
*SHIP OFF COURSE IS NOT GIVEN IN THE QUESTION.
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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 125.2-cm and a standard deviation of 2.3-cm. For shipment, 25 steel rods are bundled together.
Find the probability that the average length of a randomly selected bundle of steel rods is less than 124.5-cm.
P(M < 124.5-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.
P(M < 124.5) = 0.0603.
P(M 169.3 cm 168.3 cm) = 0.7724
Given that,
Steel rods are produced by a firm. The lengths of the steel rods have a mean of 125.2 cm and a standard deviation of 2.3 cm, and they are regularly distributed. 25 steel rods are packaged together for shipping.
We have to determine the probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.
P(M < 124.5-cm) =
We know that,
Mean =μ= 125.2
Standard deviation=σ=2.3
n=25
P(M<124.5)= P[(M-μ)/σ< 124.5-125.2/0.46]
=P(z<-1.522)
Using the z-table,
=0.0603
Therefore, The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.
P(M < 124.5) = 0.0603.
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three factories produce light bulbs to supply the market. factory a produces 20%, 50% of the tools are produced in factory b and 30% in factory c. 2% of the bulbs produced in factory a, 1% of the bulbs produced in factory b and 3% of the bulbs produced in factory c are defective. a bulb is selected at random in the market and found to be defective. what is the probability that this bulb was produced by factory b?
0.27 = 0.0027% probability that this bulb was produced by factory B.
Given,
In the question:
Three factories produce light bulbs to supply the market. Factory a produces 20%, 50% of the tools are produced in factory B and 30% in factory C. 2% of the bulbs produced in factory A, 1% of the bulbs produced in factory b and 3% of the bulbs produced in factory C are defective.
We use the conditional probability formula to solve this question. It is
P(A|B) = P(A∩B) / P(A)
In which,
P(B|A) is the probability of event B happening, given that A happened.
P(A∩B) is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Bulb is defective.
Event B: Produced by factory A.
Probability of a bulb being defective.
2% of 20%(factory A)
1% of 50%(factory B)
3% of 30%(factory C). So
P(A) = 0.02 x 0.2 + 0.01 x 0.5 + 0.03 x 0.3
P(A) = 0.018
Defective and from factory B:
1% of 50%. So
P(A∩B) = 0.01 x 0.5 = 0.005
What is the probability that this bulb was produced by factory B?
P(A|B) = P(A∩B) / P(A)
P(A|B) = 0.005/ 0.018
P(A|B) = 0.27
Hence, 0.27 = 0.0027% probability that this bulb was produced by factory B.
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The dimensions of a room with one window and one door are shown. Ivan wants to have the four walls painted. The painter says the area is 542.2 square feet.
PLEASE HELP ASAPPP!!! THX (multi-answer)
A reasonable estimation of the total area of the room to be painted is:
A. 2[(30+40) x 8] = 2(70 x 8) = 2 x 560 = 1,120 ft²E. [2(40) x 8] + [2(30) x 8] = 640 + 480 = 1,120 ft².What is an estimation?Estimation involves the approximation of values with number rounding.
Estimates make it easier to do some mathematical operations involving fractions or decimals.
What is the area?The area is the space occupied by a two-dimensional object.
The area is always the product of the length and width (height or depth).
Given the dimensions of the room:
Length of one side = 29¹/₂ ft
Height of the four sides = 8 ft
Length of the second side = 38³/₈ ft
Based on estimation, the dimensional values are approximated to:
Length of one side of the rectangular room = 30 ft
Height of the four sides = 8 ft
Length of the second side of the rectangular room = 40 ft
There are four walls for the room, and we can deduct the areas of the door and window, but these are not given, so we ignore them.
The area of the four walls can be computed as follows:
Area of two sides with same dimensions = 480 ft² [2(30 x 8)]
Area of two sides with same dimensions = 640ft² [2(40 x 8)]
Total area = 1,120 ft² (480 ft² + 640 ft²)
Thus, the options that satisfy the estimated area of the four walls of the room are Options A and E.
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Which of the following graphs could represent a quartic function?
On the assumption that each curve has only real roots, the quartic function is the graph C.
What graph does represent a quartic equation?
In this question we have four choices of graphs of polynomials, that is algebraic expressions of the form:
p(x) = Σ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., m - 1, m}
Where m is the grade of the polynomial.
The factor form of the polynomial is described below:
p(x) = a · Π (x - rₙ), for n = {0, 1, 2, 3, ..., m - 1, m}
If we consider that each choice has real roots, then the grade of the polynomial coincides with the number of times that the curve pass through the x-axis. Then, the graph C represent a quartic function, that is, a polynomial with grade 4 with the special feature that is a function of the form f(x) = a · x² · (x - r₁) · (x - r₂).
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how many four-digit numbers greater than 2999 can be formed such that the product of the middle two digits exceeds 5?
The 3360 possible four-digit numbers are greater than 2999.
What is the combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
We know it has to be a four-digit number,
The first digit has to be between 3 and 9 (inclusive) so there are 7 options.
The unit digit can be any number so there are 10 options.
The answer will be 7 * (# of possible middle digit combos) * 10.
There are 7*48*10 = 3360 possible four-digit numbers.
Hence, the 3360 possible four-digit numbers are greater than 2999.
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A perfect square has length n if its last n digits (in base 10) are the same and non-zero. What is the longest possible length? What is the smallest square achieving this length?
The longest possible length is 3
The smallest square achieving this length : 38² = 1444.
Square:
A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. The complete length of a square's boundary is its perimeter. As a result, the length of each side can be added to determine the square's perimeter. Since a square has four sides, its perimeter may be calculated by adding all four of its sides. The space a square takes up is its area.
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-7/8 is greater than or equal to m - 13/8
Answer:
Step-by-step explanation:
greater than
Answer: Greater than
Here is an equation.
y = 3x + 5
a) When x = 10, what is the value of y?
b) When x = -10, what is the value of y?
Answer:
a) y = 35b) y = -25Step-by-step explanation:
Given equation,
→ y = 3x + 5
The value of y when x is 10,
→ y = 3x + 5
→ y = 3(10) + 5
→ y = 30 + 5
→ [ y = 35 ]
The value of y when x is -10,
→ y = 3x + 5
→ y = 3(-10) + 5
→ y = (-30) + 5
→ [ y = -25 ]
So, these are the values of y.
The population of city A is 23.5% of city B and the population of city B is 51% of city C. If city C has 9.89 million people, which of the following is the closest approximation of city A's population in millions?
0.95 million
1.2 million
1.25 million
1.3 million
1.42 million
The required closest approximation of city A's population is 1.185 million.
What is percent?Percentages are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, on the off chance that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.
According to question:We have, city A is 23.5% of city B
A/B = 235/1000 = 47/200 = (B)47/200-----------(1)
and, city B is 51% of city C.
B/C = 51/100
B = (51/100)×9.89 = 5.0439 million
As C = 9.89 million
Put the value of c in equation (1)
A = (5.0439)47/200 = 1.185 million
Thus, required population of city A is 1.185 million.
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PLEASE HELP
The variable y varies jointly with x and w when y = -42, x = 2, and w = -3.
1.) Find the constant of variation.
k =
2.) Find w when y = 3 and x = 1/14
w =
Answer:
1). The constant of variation is 7
2). w = 6 for the given values of x and y
Step-by-step explanation:
"Varies jointly" tells us that y is a direct result of a mathematic operation involving x and w. We will assume y is directly prorportional to x and w, in the sense that we can find a multiplicative relationship of the form y=Kxw, where K is the constant of variation.
We are given one data point: y=-42 where x is 2 and w is -3. Let's put those values into our trrial expression:
y=Kxw
-42=K(2)(-3)
-42 = -6K
K = 7
The expression becames y = 7xwThe constant of variation is 7.
The value of w for y=3 and x=(1/14) would be:
y=7xw
3 = 7*(1/14)*w
3 = (1/2)*w
w = 6Answer:
1) k = 7
2) w = 6
Step-by-step explanation:
Joint variation equation
If y varies jointly with x and w:
[tex]\boxed{y \propto xw \implies y=kxw}[/tex]
for some constant k.
Given:
y = -42x = 2w = -3Substitute the given values into the joint variation equation and solve for k:
[tex]\begin{aligned}y&=kxw\\\implies -42&=k \cdot 2 \cdot -3\\-42&=-6k\\k&=\dfrac{-42}{-6}\\k&=7\end{aligned}[/tex]
Therefore, the equation is:
[tex]\boxed{y=7xw}[/tex]
To find w when y = 3 and x = 1/14, substitute these values into the found equation and solve for w:
[tex]\begin{aligned}y&=7xw\\\implies 3&=7 \cdot \dfrac{1}{14} \cdot w\\3&=\dfrac{7}{14} \cdot w\\42&=7w\\w&=6\end{aligned}[/tex]
sampling on campus. you see a woman student standing in front of the student center, now and then stopping other students to ask them questions. she says that she is collecting student opinions for a class assignment. explain why this sampling method is almost certainly biased.
Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.
What do you mean by sampling?
Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.
According to the question,
A true sampling would be a mixed demographic group. A sampling from several like areas:
e.g. infront of the student store, infront of the regular store, infront if a food pantry, infront of ... or even better do a blind survey.
Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.
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do you know how to do this my niece is struggling?
the fracture strength of tempered glass averages 13.5 (measured in thousands of pounds per square inch) and has standard deviation 2. (a) what is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 13.8? (round your answer to four decimal places.)
The probability that the average fracture strength of 100 randomly selected pieces will be equal to 33.19%.
In order to find the probability first we find the Z score. The Z score related the standard deviation and the mean of any data as
Z = X - μ/σ where Z is the Z score, X is the random variable, μ is the mean and σ is the standard deviation.
The standard deviation of the randomly selected 100 variables will be given as
s = σ/√n where n = 100 and σ = 2
s = 2/√100
s = 0.2
Now, the Z score for this data will be
Z = X - μ/s where X = 13.8, and μ = 13.5 and the value of s = 0.2
Z = 13.8 - 13.5/0.2
Z = 1.5
Now, for Z = 1.5 the p value will be 0.66807
The probability will be P = 1 - 0.66807 = 0.33193 that is 33.19%
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An electric cooter company charge 1 to rent a cooter plu an additional 0. 15 per minute the cooter i rented. Which expreion repreent the cot, in dollar, for renting a cooter for m minute
Since the scooter is rented for $1 and the firm charges $0.15 per minute, the necessary expression is 1+0.15m.
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Here,
rent of scooter=$1
rent of scooter per minute=$0.15
The expression,
=1+0.15m
The required expression is 1+0.15m as rent of scooter is $1 and per minute rent charged by company is $0.15.
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Tim answered all the questions on the math test but got 10 wrong answers. He got 4 points for each correct answer, there were no penalty points for incorrect answers. His score was 76 points.
Write an equation to find the total number of questions (q) on Tim's math test
The equation to find the total number of questions (q) on Tim's math test is 76 = 4x + 0
How to write and solve equation?Number of wrong questions = 10
Points received for right question = 4 points
Points received for wrong question = 0 points
Total of Tim's score = 76%
Let
the number of questions right answered by Tim be x.
Total points gained by Tim for the right answer = number of questions right answered x Points received for a right answer
= x × 4
= 4x
Points gained by Tim for the wrong answer = number of questions wrong answered x Points received for a wrong answer
= 10 × 0
= 0
Total points scored by Tim = Points gained for the right answer + Points gained for the wrong answer
76 = 4x + 0
76 = 4x
divide both sides by 4
x = 76/4
x = 19
Hence, the number of question answered right by Tim are 19.
Total number of questions attempted by Tim
Total number of questions attempted by Tim
= number of questions answered right +number of questions answered Wrong
= 19 + 10
= 29
Hence, the total number of questions attempted by Tim is 29.
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the average hourly wage in the u.s. in october 2018 was $22.90. considering low unemployment and continued growth of the economy in 2019 it was expected that the hourly wage in october 2019 would increase. the p-value associated with the hypothesis test is .001. the correct conclusion is
The correct conclusion for "it was expected that the hourly wage in October 2019 would increase, and the p-value associated with the hypothesis test is .001" is "the average wage is not increased."
What is hypothesis?A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. A strong hypothesis outlines the predicted link between the dependent and independent variables and is succinct and straightforward. It is best to be as specific and testable as possible when describing this relationship.
The answer to the statement "it was predicted that the hourly wage in October 2019 would grow, and the p-value associated with the hypothesis test is.001" should be "the average wage is not raised."
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in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees. find the length of w, to the nearest centimeter
The length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.
Using cos law:
W = √(41² + 17² - 2×41×17 cos 134)
After solving:
W = 54.20 cm
Thus, the length of w, to the nearest centimeter is 54.20 cm if in triangle VWX, x=41 cm, v=17 cm and angle W =134 degrees.
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suppose that a coin is tossed three times and the side showing face up on each toss is noted. suppose also that on each toss heads and tails are equally likely. let hht indicate the outcome heads on the first two tosses and tails on the third, tht the outcome tails on the first and third tosses and heads on the second, and so forth. (a) use set-roster notation to describe the elements in the sample space whose outcomes are all the possible head-tail sequences obtained in the three tosses. (b) Write each of the following events as a set, in set-roster notation, and find its probability. (i) The event that exactly one toss results in a head. set probability (ii) The event that at least two tosses result in a head. set probability (ii) The event that no head is obtained. set probability
a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.
Suppose that a coin is tossed three times and the side showing face up on each toss is noted. Suppose also that on each toss heads and tails are equally likely. Let HHT indicate the outcome heads on the first two tosses and tails on the third, THT the outcome tails on the first and third tosses and heads on the second, and so forth.
Given that
a) A coin is tossed three times and the side showing face up on each toss is noted.
The total number of possible outcome are 2³ = 8
The sample space is given by
SS = {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT}
b) Write each of the following events as a set, in set-roster notation, and find its probability.
(i)The event that exactly one toss results in a head.
In this case we need to include only those outcomes where we have exactly on head,
E(1 head) = {THT, TTH, HTT}
So there are 3 such outcomes, the probability is
P(1 head) = no. of desired outcomes/total number of outcomes
P(1 head) = 3/8
P(1 head) = 0.375
(ii) The event that at least two tosses result in a head
In this case we need to include only those outcomes where we have at least two heads which means two or greater than two,
E(at least 2 heads) = {HHH, THH, HTH, HHT}
So there are 4 such outcomes, the probability is
P(at least 2 heads) = 4/8
P(at least 2 heads) = 0.5
(iii) The event that no head is obtained.
In this case we need to include only those outcomes where we have no heads at all.
E(no heads) = {TTT}
So there is only 1 such outcome, the probability is
P(no heads) = 1/8
P(no heads) = 0.125
Hence the answer is a) SS = {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT} i) P(1 head) = 0.375 ii) P(at least 2 heads) = 0.5 iii) P(no heads) = 0.125.
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41. which is not a type of comparison for which you would anticipate a two-sample test? a) before treatment versus after treatment. b) old method versus new method. c) sample mean versus desired mean. d) experimental group versus control group.
The sample mean versus desired mean is not a type of comparison one would anticipate for a two-sample test to be performed. Therefore, the option C holds true.
A sample test can be referred to or considered as the test that includes the conducting of an activity to determine the nearest possible outcome of a much larger set of observations. The purpose of conducting such a test is testing that two population means are the same in a set of observations. If the means are same, it means that the test is successful.
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Complete the following (use the straight-line method): Auto: $40,000 Residual: $4,000 Estimated life: 5 years Year Cost Depreciation Accumulated Book Expense Depreciation Value
After 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
Given,
Cost of auto =$40,000
Residual value =$4000
Estimated lifetime =5 years
Straight-line Method:-
Depreciation cost can be calculated by formula,
[tex]Depreciation=\frac{cost\ of\ assest-residual}{estimated\ lifetime}[/tex]
It is constant for every year.
Accumulated depreciation can be calculated by formula,
[tex]Accumulation\ Depreciation=\frac{cost\ of\ assets-residual}{estimated\ lifetime}*Number\ of\ years[/tex]
Book value at start of year is nothing the cost of asset at that year and Book value at end of year is difference between cost of asset at that year and depreciation cost.
Using the above formulas all the values for each year is caculated and formed into a table.
Year BookValue DepreciationCost Accumulation Book Value
Start End
1 $40,000 $7,200.00 $7,200 $32,800
2 $32,800 $7,200.00 $14,400 $25,600
3 $25,600 $7,200.00 $21,600 $18,400
4 $18,400 $7,200.00 $28,800 $11,200
5 $11,200 $7,200.00 $36,000 $4,000
Thus, after 5 years the depreciation cost is $7200; accumulated depreciation expense is $36000 and book value at the end of year is $4000.
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Charlie went to purchase a new pair of
boots that were originally marked $89.
When he checked out they rang up $62.50.
What percent discount did Charlie
receive on the new boots?
30% was the discount recived
Professor Very Busy needs to allocate time next week to include time for office hours. He needs to forecast the number of students who will seek appointments. He has gathered the following data:
Week #Students
6 Weeks ago 83
5 Weeks ago 110
4 Weeks ago 95
3 Weeks ago 80
2 Weeks ago 65
Last Year 50
What is this week's forecast using the naive approach? Assume that a decreasing trend in student appointments exists.
Other than the original data point 6 weeks ago, there is a clear trend over the last 5 weeks with continuously decreasing demand, so this week's forecast is last week's demand plus the difference between last week's demand and the demand two weeks ago. 50 + (50 - 65) = 35
Professor Very Busy needs to allocate time next week to include time for office hours then TAF(Week 7) = S(Week 6) + T(Week 6) = 57.5 + (-5.5) = 52.0
Smooth the pattern as well as the arrangement to get the outlook this year.
S(Week 5) = TAF(Week 5) + alpha*(Actual(Week 5) - TAF(Week 5))
= 75 + 0.5(65 - 75) = 70
S(Week 6) = TAF(Week 6) + alpha*(Actual(Week 6) - TAF(Week 6))
= 65 + 0.5(50 - 65) = 57.5
T(Week 6) = T(Week 5) + beta*(TAF(Week 6) - TAF(Week 5) - T(Week5))
= -5 + 0.1(65 - 75 - (-5)) = -5 + (-0.5) = -5.5
Therefore, TAF(Week 7) = S(Week 6) + T(Week 6) = 57.5 + (-5.5) = 52.0
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the height of seaweed of all plants in a body of water are normally distributed with a mean of 10 cm and a standard deviation of 2 cm.use excel to find which length separates the lowest 30% of the means of the plant heights in a sampling distribution of sample size 15 from the highest 70%? round your answer to the nearest hundredth.
The value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
A normal distribution has symmetrically distributed data that is skew-free. As one proceeds away from the center, values tend to decrease and tend to cluster more frequently in that area. The mean, mode, and median of a normal distribution are all equal measures of central tendency.
Given data:
X: height of seaweed.
X~N (μ;σ²)
μ= 10 cm
σ= 2 cm
We will calculate the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70
P(X ≤ x) = 0.30
P(X ≥ x) = 0.70
Now by using the standard normal distribution,
we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula
[tex]Z = \frac{X-\mu}{\sigma}[/tex]
translates the Z value to the corresponding X value.
P(Z ≤ z) = 0.30
In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.
z= -0.52
Now you have to clear the value of X:
[tex]Z = \frac{X-\mu}{\sigma}[/tex]
X= (Z * σ) + μ
X = (-0.52 * 2)
= 8.96
hence, the value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
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consider the following binomial experiment: a study in a certain community showed that 5% of the people suffer from insomnia. if there are 10,400 people in this community, what is the standard deviation of the number of people who suffer from insomnia? a) 520.00 b) 22.23 c) 50.99 d) 9880.00 e) 49400.00 f) none of the above.
The number of those who have insomnia has a standard deviation of 22.23.
Given,
People suffer from insomnia = 5%
Total number of people in the community = 10,400
We have to find the standard deviation of the number of people who suffer from insomnia;
Here,
p = 0.05
q = 0.95
n = 10,400
Then,
np = 10400 x 0.05 = 202
Now,
npq = 202 x 0.95 = 494
Standard deviation = √npq = √494 = 22.23
That is,
The standard deviation of the number of people who suffer from insomnia is 22.23
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3x+12=-5x+28 necesito ayuda para mi examen please
Answer:
x = 2
Step-by-step explanation:
3x + 12 = -5x + 28
3x + 12+ 5x = -5x + 28 + 5x
8x + 12 = 28
8x + 12 - 12 = 28 - 12
8x = 16
8x/8 = 16/8
x = 2
how many different 12-bit strings begin with 0101, end with 1100 or have 0110 as the four middle bits?
There are 4 different 12-bit strings possible that begin with 0101, end with 1100 or have 0110 as the four middle bits.
We have to find the number of 12-bit strings that are starting with 0101, end with 1100 or have 0110 in the middle bits.
So, the first four position are reserved for 0101 and we have two options for the middle four bits and the end four positions.
So, we can write here,
Total possible different positions for 1100 and 0110 is,
= 2 x 2
= 4
Because, the two combination can appear simultaneously or they can appear one by one.
So, the total different 12-bit strings possible that have 0101 in the start, 1100 in the end or 0101 in the middle are 4.
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