1. The probability distribution of the number of cartoons watched by a nursery class on Saturday morning is shown below. What is the standard deviation of this distribution? 0 1 2 3 4 f(x) 0.15 0.25 0
Answers
The standard deviation of this distribution is approximately 1.09. The variance is the average of the squared differences between each value and the mean, weighted by their respective probabilities.
To calculate the standard deviation of the probability distribution, we first need to calculate the mean of the distribution. The mean is calculated by multiplying each value by its corresponding probability and summing them up. Here's how we can calculate it:
Mean (μ) = (0 * 0.15) + (1 * 0.25) + (2 * 0.35) + (3 * 0.2) + (4 * 0.05) = 0 + 0.25 + 0.7 + 0.6 + 0.2 = 1.75
Next, we calculate the variance of the distribution. The variance is the average of the squared differences between each value and the mean, weighted by their respective probabilities. The formula for variance is:
Variance (σ²) = [(0 - 1.75)² * 0.15] + [(1 - 1.75)² * 0.25] + [(2 - 1.75)² * 0.35] + [(3 - 1.75)² * 0.2] + [(4 - 1.75)² * 0.05]
= [(-1.75)² * 0.15] + [(-0.75)² * 0.25] + [(0.25)² * 0.35] + [(1.25)² * 0.2] + [(2.25)² * 0.05]
= 0.459375 + 0.140625 + 0.021875 + 0.3125 + 0.253125
= 1.1875
Finally, the standard deviation is the square root of the variance:
Standard Deviation (σ) = √(1.1875) ≈ 1.09
Therefore, the standard deviation of this distribution is approximately 1.09.
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Related Questions
Consider the discrete probability distribution to the right when answering the following question. Find the probability that x = 5.
X 2 5 6 8
P(X) 0.25 ? 0.16 0.08
Answers
The probability that X=5 is 0.16. This is calculated by looking at the probability distribution table, which shows that the probability of X=5 is 0.16.
To find the probability of X=5, we first look at the discrete probability distribution given. This tells us the probability of each of the possible values that X can take on. In this case, there are four possible values (0, 1, 2, and 5). We can see that the probability of X=5 is 0.16.
In general, when given a discrete probability distribution, we can calculate the probability of any event (such as X=5) by looking at the probabilities listed in the table. All we need to do is find the value we are looking for (in this case, 5) and then look at the corresponding probability listed in the table.
It is important to note that when dealing with discrete probability distributions, the probabilities must always add up to 1. In this example, we can verify that the probabilities add up to 1 (0.25 + 0.16 + 0.08 = 0.49, which is equal to 1).
In conclusion, the probability that X=5 is 0.16. This was found by looking at the given discrete probability distribution table.
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What is the slope of this graph?
Answers
at 2:40 p.m. a plane at an altitude of 30,000 feetbegins its descent. at 2:48 p.m., the plane is at25,000 feet. find the rate in change in thealtitude of the plane during this time.
Answers
The rate of change in altitude of the plane during the time is 625 ft/min.
Rate of changeGiven the Parameters:
Altitude at 2.40 pm = 30000 feets
Altitude at 2.48 pm = 25000 feets
Rate of change = change in altitude/change in time
change in time = 2.48 - 2.40 = 8 minutes
change in altitude = 30000 - 25000 = 5000 feets
Rate of change = 5000/8 = 625 feets per minute
Therefore, the rate of change in altitude of the plane is 625 ft/min.
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What is the equation of the line that is perpendicular two and has the same y-intercept as the line with (0,1) and (5,0)
Answers
Answer:
its all about reletives so if u take the number then multiply by five u get 56.3
Step-by-step explanation:
u know
Please help I will give brainliest and a lot of points :)
Answers
The inequality shaded in the graph is given as follows:
y ≥ 5x/2 + 3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:
b = 3.
When x increases by 2, y increases by 5, hence the slope m is given as follows:
m = 5/2.
Then the equation of the line is given as follows:
y = 5x/2 + 3.
The line is a solid line, and values above it are plotted, hence the inequality is given as follows:
y ≥ 5x/2 + 3.
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Find the surface area of a square based pyramid that has a base with 3m sides and a slant height of 4m.
Answers
The surface area of a square-based pyramid is 33 m².
What is the surface area of the pyramid?
A pyramid's surface area is calculated by summing the areas of all of its faces. A pyramid is a three-dimensional form with a polygonal base and triangle-shaped side faces that meet at a location known as the apex or vertex. The altitude or height of the pyramid is the perpendicular distance from the apex to the center of the base. The "slant height" is the length of the perpendicular traced from a triangle's apex to its base (side face).
Here, we have
Given: a square-based pyramid that has a base with 3m sides and a slant height of 4m.
The surface area of a square-based pyramid = a² + 2al
(where 'a' is the side length of the base and is the slant height)
a = 3m
l = 4m
SA = 3² + (2 x 3 x 4) = 33 m².
Hence, the surface area of a square-based pyramid is 33 m².
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suppose it is equally likely that a plane flight is 50%, 60%, 70%, 80%, or 90% full. a what fraction of seats on a typical flight are full? this is known as the flight load factor. b we are always complaining that there are never empty seats on our plane flights. given the previous information, what is the average load factor on a plane trip i take?
Answers
We can expect that on a typical flight, 70% of the seats will be full. We can expect the average load factor on a plane trip to be 70%, regardless of how many flights are taken.
(a) To find the fraction of seats on a typical flight that are full, we need to calculate the expected value of the flight load factor. Since each flight is equally likely to be 50%, 60%, 70%, 80%, or 90% full, we can use the formula for the expected value of a discrete uniform distribution:
expected value = (50% + 60% + 70% + 80% + 90%)/5 = 70%
(b) To find the average load factor on a plane trip, we need to consider multiple flights. Since each flight is equally likely to have a load factor of 50%, 60%, 70%, 80%, or 90%, we can use the formula for the expected value of a sample mean:
expected value of sample mean = population mean = 70%
However, it is important to note that the load factor can vary widely from flight to flight, and there may be some flights that are much more full or much less full than the average.
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is this table a function? explain how you know
Answers
a) Find constants A,B and C such that (x−1)(x−2)(x−3)
3x 2
−12x+11
≡ x−1
A
+ x−2
B
+ x−3
C
. (4) b) Express (x+1)(x 2
+1)
−2x
as a sum of partial fractions and hence write (x+1)(x 2
+1)
x 4
+x 3
+x 2
−x
as a sum of partial fractions. (10)
Answers
A. The constants A, B, and C for the expression (x-1)(x-2)(x-3) / (3x² - 12x + 11) are A = -1, B = 5, and C = -3.
b. The partial fraction decomposition of (x+1)(x²+1) / -2x is (-1/2)/(x+1) + (3/2)x/(x²+1) + (5/2)/x.
A- To find the constants A, B, and C:
Expand the numerator of the rational function:
(x - 1)(x - 2)(x - 3) = x³ - 6x² + 11x - 6
Set up the equation:
x³ - 6x² + 11x - 6 = A(x - 2)(x - 3) + B(x - 1)(x - 3) + C(x - 1)(x - 2)
Expand the right side:
x³ - 6x² + 11x - 6 = (A(x² - 5x + 6)) + (B(x² - 4x + 3)) + (C(x² - 3x + 2))
Collect like terms:
x³ - 6x² + 11x - 6 = (A + B + C)x² + (-5A - 4B - 3C)x + (6A + 3B + 2C)
By comparing the coefficients of x², x, and the constant term, we get the following system of equations:
A + B + C = -6
-5A - 4B - 3C = 11
6A + 3B + 2C = -6
Solving this system of equations, we find A = -1, B = 5, and C = -3.
B- To express (x+1)(x²+1) / -2x as partial fractions:
Write the rational function as A/(x+1) + (Bx+C)/(x²+1) + D/x, where A, B, C, and D are constants.
Multiply through by -2x to get rid of the denominator:
(x+1)(x²+1) = A(-2x)(x²+1) + (-2x)(Bx+C) + D(x+1)(x²+1)
Expand and collect like terms:
x³ + x² + x + 1 = (-2A)x³ + (-A + -2B)x² + (-2C + D)x + (A + C)
Comparing coefficients, we get the following equations:
-2A = 1
-A - 2B = 1
-2C + D = 1
A + C = 1
Solving these equations, we find A = -1/2, B = 0, C = 3/2, and D = 5/2.
Therefore, (x+1)(x²+1) / -2x can be expressed as (-1/2)/(x+1) + (3/2)x/(x²+1) + (5/2)/x, and we can rewrite (x+1)(x²+1) / x⁴ + x³ + x² - x as (-1/2)/(x+1) + (3/2)x/(x²+1) + (5/2)/x.
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7. Mario made six batches of cookies. His friends asked him to
make an extra batch. He used 15 cups of sugar and needs
another cups for the extra batch. How many cups of sugar
will Mario use altogether?
Answers
Answer:
17.5 Cups of Sugar
Step-by-step explanation:
Divide 15 by 6, to get 2.5. then add 15 and 2.5 (for the extra batch) and get 17.5
the center for medicare and medical services reported that there were appeals for hospitalization and other part a medicare service. for this group, of first round appeals were successful (the wall street journal). suppose first-round appeals have just been received by a medicare appeals office. refer to binomial probability table. round your answers to four decimal places. a. compute the probability that none of the appeals will be successful. 0.0060 b. compute the probability that exactly one of the appeals will be successful. 0.0403 c. what is the probability that at least two of the appeals will be successful?
Answers
Therefore, the probability that at least two of the appeals will be successful is 0.9537.
The probability that none of the appeals will be successful is 0.0060, while the probability that exactly one of the appeals will be successful is 0.0403. The probability that at least two of the appeals will be successful is calculated by subtracting the probability that none or one of the appeals will be successful from 1. That is, the probability of at least two of the appeals being successful is 1 – (0.0060 + 0.0403) = 0.9537.
This probability can also be calculated using a binomial probability table. In this case, the sample size is n = 8, the probability of success is p = 0.25, and the number of successes is x ≥ 2. The probability of x ≥ 2 successes is then equal to \(1 - P(x ≤ 1) = 1 - (P(x = 0) + P(x = 1)) = 1 – (0.0060 + 0.0403) = 0.9537\),
which is the same result as previously obtained.
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Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 6 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover the exact distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
Answers
Answer:
Then 1/2 or 30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.
Two hours after Tom began Tom would cover 12 miles and three hours after Linda started Linda would be 6 miles far away from the starting point
Step-by-step explanation:
Linda walks in a straight line at 2 miles/hour
then after t ( hours time) she is 2 (m/h) * t = d (L)
for Tom running at 6 m/h starting one hour later to cover the same distance d(L)
d(L) = 6 m/h * ( t - 1 ) then:
2 (m/h) * t = 6 m/h * ( t - 1 )
2*t = 6*t - 6
4*t = 6
t = 6/4
t = 1,5 h
Checking that result.
we see that in 1,5 hours Linda has covered 2* 1,5 = 3 miles
and in 0.5 hours Tom covered the same distance 0,5 * 6 = 3 miles
NOTE: Remember that tom started one hour later.
Then 1/2 or 30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.
b) In this case
d(T) = 6* ( t - 1 ) must be equal to twice of the Linda distance
d(L) = 2 * 2 * t
6*t - 6 = 4*t
2*t = 6
t = 3
To check it
in 3 hours Linda had covered 3 * 2 = 6 miles
in 2 hours Tom had covered 2 * 6 = 12 miles
John's total pay including benefits is $20 an hour. He is supposed to work 40 hours each week for 50 weeks per year. John wastes approximately 3 hours a week by procrastinating , daydreaming, and checking social media during his scheduled work day. How many dollars in lost productivity does John cost his company ?
Answers
Answer: John costs him company $3000 in lost productivity
Step-by-step explanation:
hours lost- 50 times 3 = 150
money lost- 150 times 20 = 3000
we took a sample of 6 students from the classroom. the mean height of the 6 students is 70 inches, and the standard deviation of height of 6 students in the classroom is 2. what is the standard error of the mean?
Answers
If the standard deviation is 2 then the standard error of the mean is 0.8165 .
In the question ,
it is given that ,
the sample size of students taken from the classroom is(n) = 6 students ;
the mean height of students is = 70 inches ;
the standard deviation(S.D.) height of students is = 2 inches ;
the standard error of mean can be calculated using formula ;
S.E. = (S.D.)/√n
substituting the value of S.D. and sample size ,
we get ,
S.E. = 2/√6
= 0.816496
≈ 0.8165
Therefore , the Standard Error of the mean is 0.8165 .
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think about a density curve that consists of two line segments. the first goes from the point (0, 1) to the point (0.4, 1). the second goes from (0.4, 1) to (0.8, 2) in the xy-plane. what percent of observations fall below 0.40?
Answers
The percent of observations fall below 0.40 is 1.00
Since we are given the points we are (0, 1),(0.4, 1),(0.4, 1), and (0.8, 2), we got the graph for the points
Since a density curve may be a chart that represents probability. The region beneath the density curve is rise to 100 percent of all probabilities. As we ordinarily utilize decimals in probabilities you'll moreover say that the range breaks even with 1The region beneath the chart breaks even with 1 and we are told to discover the percent of the observation that drops underneath 0.40 what this implies is that we ought to discover the rate of the observation that drops inside 0.40 of 1 which is the entire area. So,
P(O) = 0.40 × 1 = 0.40 , where O is the observations
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A personal computer manufacturer buys 35% of its chips from Japan and the rest from the United States of the Japanese chips, 16% are defective, and 13% of the American chips are defec Find the probability that a chip is defective and made in Japan (Round your answer to four decimal places)
Answers
The probability that a chip is defective and made in Japan is 0.0560 (rounded to four decimal places).
To calculate this probability, we need to consider the percentages of chips bought from Japan and the defect rates for both Japanese and American chips.
Given that 35% of chips are purchased from Japan, and out of those, 16% are defective, we can calculate the probability of a chip being both from Japan and defective as follows:
Probability(Defective and Made in Japan) = Probability(Made in Japan) * Probability(Defective | Made in Japan)
Probability(Made in Japan) = 35% = 0.35
Probability(Defective | Made in Japan) = 16% = 0.16
Probability(Defective and Made in Japan) = 0.35 * 0.16 = 0.0560
Therefore, the probability that a chip is defective and made in Japan is 0.0560 (rounded to four decimal places).
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tyler reades 2/15 pages on monday 1/3 on tuesday and 2/9 on wendsday and 3/4 on thursday .and has 14 pages left on friday how many pages are in the book
Answers
The number of pages that are in the book is 1 31/45 pages.
How to illustrate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Tyler reads 2/15 pages on Monday 1/3 on Tuesday and 2/9 on Wednesday and 3/4 on thursday .and has 14 pages left on friday how many pages are in the book.
The fraction for pages will be:
= 2/15 + 2/9 + 1/3 + 3/4 + 1/4
= 2/15 + 5/9 + 1
= 6 / 45 + 25/45 + 1.
= 1 31/45
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Complete question
tyler reades 2/15 pages on monday 1/3 on tuesday and 2/9 on wendsday and 3/4 on thursday .and has 1/4 pages left on friday how many pages are in the book
Ryan invested \$4,800$4,800 in an account in the year 1990, and the value has been growing exponentially at a constant rate. The value of the account reached \$6,300$6,300 in the year 1998. Determine the value of the account, to the nearest dollar, in the year 2007.
Answers
well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.
\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)
\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)
now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?
\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)
I REALLY NEED HELP!!!
Answers
Answer:
Complementary angles
Step-by-step explanation:
Complementary angles are angles that add up to 90 degrees.
Answer:
complementary
Step-by-step explanation:
The angles are part of a right angle as shown by the square.
Complementary angles are angles that add up to 90˚
since x-15 and 2x are parts of the right angle, they add up to 90
‼️PLEASE HELP‼️
Rosita is writing an explicit function for the geometric sequence:
80, 40, 20, 10,...
She comes up with t(n) = 160(1/2)^n
What domain should Rosita use for T so it generates the sequence?
Choose 1 answer
A: n ≥ 0 where n is an integer
B: n ≥ 0 where n is any number
C: n ≥ 1 where n is an integer
D: n ≥ 1 where n is any number
Answers
Answer:
C- where n (greater than or equal to ) 1
Step-by-step explanation:
C- where n (greater than or equal to ) 1
Because in that sequence 0 doesn't make sense since 160 * 1/2 = 80 ^ 0 = 1. Doesn't make sense since there's no "1" in that sequence.
It's not "any number" because It can't be negative nor a decimal.
So, C.
:) hope this helps
Answer:
The answer is C
Step-by-step explanation:
(I had the same Khan Academy question)
Question 9 An S corporation is generally set up to: implement an expansion strategy attract capital reduce tax burdenseasy entry into an industry take advantage of limited liability
Answers
An S corporation is generally set up to C. reduce tax burdens.
What is a S corporation?For federal tax purposes, S corporations elect to pass through corporate income, losses, deductions, and credits to their shareholders.
An S corp operates in the same way that any other corporation does. It establishes a board of directors and corporate officers, bylaws, and a management structure under the laws of its home state. It distributes company stock. Its owners cannot be held personally or financially liable for creditor or company claims.
S corporations are distinguished by the fact that they are not federally taxed on the majority of their earnings and distributions, allowing more money to be passed on to shareholders.
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I need help with this someone very smart in math this is algebra 2
Answers
Answer:
D
Step-by-step explanation:
The interest is compounded annually, which means that interest from the previous year earns you even more money next year.
It should be obvious that after one year Alexis will have
$475 + $475 * 1.25% = $475 * 100% + $475 * 1.25% =
= 101.25% * $475 = 1.0125 * $475
Then, next year she would have
1.0125 * $475 + (1.0125 * $475) * 1.25% =
= (1.0125 * $475) * 1.0125 = 1.0125^2 * $475
See the pattern?
Alexis will have $475 * 1.0125^x after x years.
sin−1(sin/6)
cos−1(cos5/4)
tan−1(tan5/6) compute without using a calculator
Answers
Without using a calculator, the trigonometric expressions simplify to:
1. sin^(-1)(sin(θ/6)) = θ/6
2. cos^(-1)(cos(5/4)) = 5/4
3. tan^(-1)(tan(5/6)) = 5/6.
To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.
1. sin^(-1)(sin(θ/6)):
Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.
2. cos^(-1)(cos(5/4)):
Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.
3. tan^(-1)(tan(5/6)):
tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.
Hence, without using a calculator, we find that:
sin^(-1)(sin(θ/6)) = θ/6,
cos^(-1)(cos(5/4)) = 5/4,
tan^(-1)(tan(5/6)) = 5/6.
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What is the domain of f(x) + g(x)
Answers
Answer:
All real numbers except 6
Don’t answer unless positive about answer please :)
Answers
Answer:
the asnwer is postive
Step-by-step explanation:
Answer:
its c or 2n-3=-21
Step-by-step explanation:
What is the perimeter of a square with an area of 81 cm2
Answers
Answer:
36 cm
Step-by-step explanation:
Answer:
36cm
Step-by-step explanation:
A square has 4 equal sides so you can find the square root of 81 which is 9. Each side is 9cm, so just add the four sides and it gives you 36. Hope this helps^^
can someone tell me the answer to. 16 = 2(2x + 4)
Answers
Answer:
16= 4x+8
16-8=4x
x=8/4
x= 2
Step-by-step explanation:
16=2(2x+4) 16=(2×2x) + (4×2) 16= 4x+8. 16-8=4x+8-8. 8=4x. 8/4=4x/4. 2=x
assume that y varies inversely with x. if y = 8 when x = 1.55, find x when y = -0.62
Answers
Answer:
y varies inversely with x is written as
y = k /x
where k is the constant of variation
y = 8 x = 1.55
8 = k / 1.55
Multiply through by 1.55
k = 12.4
The formula is
y = 12.4 / x
when y = - 0.62
- 0.62 = 12.4/x
- 0.62x = 12.4
Divide both sides by - 0.62
x = 12.4/-0.62
x = - 20
When y = - 0.62 x = - 20
Hope this helps
The circle below is centered at the origin and has a radius of 7. What is its
equation?
A ²+2²=7
B. x²-y²=7
C. x²-²2²=49A
D. x² + y² = 49
Answers
Answer:
x² + y² = 49
Step-by-step explanation:
The equation for a circle is: x² + y² = r²
here, we know our circle's radius (r) to be 7
So, the equation for our circle is: {replace "r" with value}
x² + y² = 7²
which can be simplified to:
x² + y² = 49
hope this helps!! have a lovely day :)
Find the value of p that makes the linear graph y = p − 3x pass through the point
where the lines 4x − y = 6 and 2x − 5y = 12 intersect.
Answers
Answer: Hi
Step-by-step explanation:
The equation for the line y = p - 3x can be rearranged as y + 3x = p.
Substituting this into the system of equations, we get:
4x - (y + 3x) = 6
4x - y - 3x = 6
x = 6
2x - 5y = 12
2(6) - 5y = 12
12 - 5y = 12
-5y = 0
y = 0
So the point of intersection is (6, 0).
Substituting these values into y = p - 3x, we get:
0 = p - 3(6)
0 = p - 18
p = 18
Therefore, the value of p that makes the line y = p - 3x pass through the point of intersection of the lines 4x - y = 6 and 2x - 5y = 12 is 18.