A computer’s random number generator produces random integers from 1 to 50. What is the probability that at least one of the first 4 generated numbers is in the 20s?
0.0016
0.1024
0.4096
0.5904
Answers
Answer:
0.5904
Step-by-step explanation:
For each number, there are only two possible outcomes. Either it is in the 20s, or it is not. The probability of a number being in the 20s is independent of other numbers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
4 generated numbers:
This means that \(n = 4\)
Probability of a number in the 20s:
From 1 to 50, there are 50 numbers. Of those(from 20 to 29), there are 10 in the 20s. So \(p = \frac{10}{50} = 0.2\)
What is the probability that at least one of the first 4 generated numbers is in the 20s?
Either none is, or at least one is. The sum of the probabilities of these events is 1. So
\(P(X = 0) + P(X \geq 1) = 1\)
We want \(P(X \geq 1)\). So
\(P(X \geq 1) = 1 - P(X = 0)\)
In which
\(P(X = 0) = C_{4,0}.(0.2)^{0}.(0.8)^{4} = 0.4096\)
\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.4096 = 0.5904\)
Related Questions
7 grade math hellp me
Answers
Answer:
32
Step-by-step explanation:
180 - 148 = 32
I hope this helps!
It is claimed that 55% of marriages in the state of California end in divorce within the first 15 years. A large study was started 15 years ago and has been tracking hundreds of marriages in the state of California. Suppose 10 marriages are randomly selected. What is the probability that less than two of them ended in a divorce
Answers
Answer:
0.0045 = 0.45% probability that less than two of them ended in a divorce
Step-by-step explanation:
For each marriage, there are only two possible outcomes. Either it ended in divorce, or it did not. The probability of a marriage ending in divorce is independent of any other marriage. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
55% of marriages in the state of California end in divorce within the first 15 years.
This means that \(p = 0.55\)
Suppose 10 marriages are randomly selected.
This means that \(n = 10\)
What is the probability that less than two of them ended in a divorce?
This is
\(P(X < 2) = P(X = 0) + P(X = 1)\)
In which
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{10,0}.(0.55)^{0}.(0.45)^{10} = 0.0003\)
\(P(X = 1) = C_{10,1}.(0.55)^{1}.(0.45)^{9} = 0.0042\)
\(P(X < 2) = P(X = 0) + P(X = 1) = 0.0003 + 0.0042 = 0.0045\)
0.0045 = 0.45% probability that less than two of them ended in a divorce
Maria went to see a baseball game. The game started at 8:39 PM and ended at 11:54 PM. How long was the game?
Answers
The duration of the game was 3¹/₄ hours
How to convert minutes into hours vice versa?To convert, multiply your number of hours by 60 to get time in minutes. Whenever we have given conversion from higher unit to lower unit then always use multiply and divide the number of minutes by 60 to get the number of hours.
Given here, game started at 8:39 PM and ended at 11:54 PM.
Therefore the duration of the game is in minutes = 21+60+60+54
= 195 minutes
And thus duration of the game in hours is = 195/6
= 3¹/₄
Hence, The duration of the game was 3¹/₄ hours
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URGENT PLEASE HELP The perimeter of AJKL is 106. Find the length of
midsegment ST.
J
5x +7
S
3x +3
4x-1
(not drawn to scale)
K
A
17
B
15
16
D
18
Answers
Answer:
16
Step-by-step explanation:
3x+3+3x+3+5x+7+4x-1+4x-1=106
19x+11=106
19x=95
x=5
JL=5(5)+7=32
ST=1/2 of JL = 1/2 of 32 = 16
The length of midsegment ST will be 6. The perimeter of the triangle is given.
What is perimeter?It's the sum of length of the sides used to make the given figure.
The perimeter of AJKL is 106;
⇒KS+SJ+JL+LT+TK=106
⇒3x+3+3x+3+5x+7+4x-1+4x-1=106
⇒19x+11=106
⇒19x=95
⇒x=5
The side JL is obtained by,x=5
JL=5x+7
JL=5×(5)+7
JL=32
The side ST is obtained
ST=(1/2)×JL
ST= 1/2 of 32
ST = 16
Hence, the length of midsegment ST will be 16.
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Plz solve this problem for brainiest
Answers
Answer:
angle in a triangle is 180degree so you do Ais1+Bis1Cis 1+Dis1=4
Megan has $45.12 in her purse. She spends $7.89 for lunch and $21.25 for a pair of sunglasses.
What is the exact amount that Megan has left?
Answers
Answer:
15.98 dollars
Step-by-step explanation:
its really easy
we need to subtract the total amount that she has spent from the total amount that she had in her purse
the total amount in Megan's purse=$45.12
total amount that Megan spent=$7.89+$21.25 =$29.14
now,
the exact amount that Megan has left = $45.12-$29.14=$15.98
A person leaves home and walks 4 miles west, then 5 miles southwest.
How far from home is she?
miles
In what direction must she walk to head directly home?
degrees North of East
Answers
The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.
To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).
To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).
To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.
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HELPPPP
Using the following diagram, solve for x.
Answers
Answer:
x = 7.5
Step-by-step explanation:
8 6
10 x
3/4×8 = 6
3/4×10 = 7.5
hope it helps you
How tall is the tree?
5ft
35°
-20ft-
[?]ft
Round to the nearest foot.
Answers
Answer:
19
Step-by-step explanation:
tan35=x/20
20tan35=x
x=14.0041507641942
x+5=19.0041507641942
The nearest foot is 19
On a particular stretch of highway, the State Police know that the average speed is 62 mph with a standard deviation of 5 mph. On a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. Use central limit theorem to calculate
Answers
Using the normal distribution and the central limit theorem, it is found that there is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).In this problem:
Mean of 62 mph, hence \(\mu = 62\).Standard deviation of 5 mph, hence \(\sigma = 5\).Sample of 50 cards, hence \(n = 50, s = \frac{5}{\sqrt{50}} = 0.7071\)The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 1 subtracted by the p-value of Z when X = 66, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{66 - 62}{0.7071}\)
\(Z = 5.66\)
\(Z = 5.66\) has a p-value of 1.
1 - 1 = 0.
There is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
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Each month, Ellie spends 4 hours in tap class at her dance studio. If each month she spends 20% of her class time in tap class, what is the total number of hours she spends in dance classes each month? Show your work or explain how you found your answer in complete sentences.
Answers
Divide hours spent in tap class by the percentages:
4 / 0.20 = 20 hours
Her total number of hours for dance classes is 20 hours per month.
given ABCD ~ EFGH find the scale factor list all pairs of congruent angles write the ratios of the corresponding lengths in a statement of proportionality
Answers
Given
Graph
Procedure
\(\begin{gathered} \frac{EH}{BC}=\frac{3}{4}=\frac{3}{4} \\ \\ \frac{GH}{AB}=\frac{9}{12}=\frac{3}{4} \end{gathered}\)
The scale factor would be 3/4
if m 2 =6x+8 and m 6 = 8x-6, find the value of x so that l is parallel to m
Answers
Answer:
\(x = 7\)
Step-by-step explanation:
Given
\(m_2 = 6x + 8\)
\(m_6 = 8x - 6\)
Required
Determine x when both lines are parallel
For parallel lines, slopes must be equal.
i.e.
\(m_1 = m_2\)
In this case,
\(m_6 = m_2\)
Substitute values for m6 and m2
\(8x - 6 = 6x + 8\)
Collect Like Terms
\(8x - 6x = 8 + 6\)
\(2x = 14\)
Solve for x
\(x = 14/2\)
\(x = 7\)
Answer:7
Step-by-step explanation:
Solve for x: 1/4 (x-7) = 2x
A) x= 9
B) x= 1
C) x= -1
D) x= 15
Answers
Steps:
1/4 (x - 7) = 2x (distribute 1/4 with x and -7)
1/4x - 7/4 = 2x (distributed)
1/4x - 7/4 - 2x = 0 (put all values on 1 side)
1/4 x - 2x = 7/4 (put the x values together and 7/4 on the other side. *make sure you switch the signs (+ & -) when moving the values to the other side of the equal sign)
1/4x - 8/4x = 7/4 (multiply 2x by 4 on on top and bottom. *2x written as fraction is 2x/1)
-7/4 x = 7/4 (when you subtract 1/4x with 8/4x you get -7/4)
(-7/4)x / (-7/4) = 7/4 / (-7/4) (divide both sides by -7/4 to solve for x)
X = -1
Reminders when multiplying or dividing:
2 positives make a positive
2 negatives make a positive
A positive and a negative make a negative
A negative and a positive make a negative
Given that the polynomial f(x) has degree 8, which of the following most accurately describes the number of turning points of f(x)?
Answers
The x intercepts are the roots of the polynomial f(x) = 0.
The fundamental theorem of algebra says that the number of roots of this equation is 9, but not necessarily all of them are real; therefore the MAXIMUM number of x intercepts is 9.
However, since f(x) is of odd degree it must have at least one real root; therefore, the MINIMUM number of x intercepts is 1.
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial f(x) that has a degree of 8 will have 7 turning points.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
For any polynomial equation, the number of turning points is always less than or equal to the degree of the polynomial.
Generally, the number of turns is one less than the degree of the polynomial.
Hence, the polynomial f(x) that has a degree of 8 will have 7 turning points.
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Here are 2 points in the plane.
Using only a straightedge,can you find points in the plane that are the same distance from points A and B. Explain your reasoning
Answers
9514 1404 393
Answer:
no
Step-by-step explanation:
Using only a straightedge, you cannot measure distance, so cannot ensure that any two distances are the same.
__
The points of interest are on the perpendicular bisector of AB, which can be constructed using a compass and straightedge. The straightedge alone is insufficient.
If MK = 10 m, find the length of MKL.K52LMMRound the answer to 2 decimal places.meters
Answers
To find the Length of MKL, we need to find the length of JM and JL using the length of an arc formula
\(\begin{gathered} \text{Length of arc =}\frac{\theta}{360}\times2\pi r \\ \text{where r=MK/2 =5m} \end{gathered}\)STEP 1
Find the angle subtended at N and find the arc JM
N +52= 180 -------sum of angles on a straight line.
N= 180-52
N=128
\(\begin{gathered} JM=\frac{128}{360}\times2\times3.14\times5 \\ JM=11.164 \end{gathered}\)STEP 2
Find the length of JL
The angle subtended at Therefore,
\(\begin{gathered} JL=\frac{90}{360}\times2\times3.14\times5 \\ JL=7.85 \end{gathered}\)STEP 3
Find the lenght of MKL. MKL is the sum of JM and JL
\(\begin{gathered} \text{MKL}=11.164+7.85 \\ =19.01 \end{gathered}\)The answer is 19.01m
Distance from earth to the moon is 238,900 . From earth to the sun is 92935,700 ,about how many times the distance from earth to the moon is distance from earth to the sun
Answers
Answer: the sun is 389.015069067 times further away from earth to the moon
Step-by-step explanation: 92935700/238990=389.015069067
Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230. Find the probability that next year there will be no snowfall in that town on January 1.
1. 0.770
2. 4.348
3. 0.299
4. 1.230
Answers
The probability that next year there will be no snowfall in that town on January 1 is,
P (no snowfall) = 0.770
The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230.
Now, WE get;
the probability that next year there will be no snowfall in that town on January 1 is,
P (no snowfall) = 1 - P (snowfall)
P (no snowfall) = 1 - 0.230
P (no snowfall) = 0.770
Thus, The probability that next year there will be no snowfall in that town on January 1 is,
P (no snowfall) = 0.770
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Evaluate 10 - (x + 3) when 2 = 2.
Answers
Answer:
5
Step-by-step explanation:
Im asuming you meant " x = 2 ".
According to PEMDAS, parenthese come first so...
10 - ( 2 + 3 )
= 10 - 5
= 5
Answer:
its 50
Step-by-step explanation:
10 times (x+3) x=2
2 plus 3 is 5
10 time 5
=50
I need help with this one .
Answers
Answer:
32/9
Step-by-step explanation:
2 to the fifth power is 32. 3 to the second power is 9.
llan's family stays at a hotel and the room is $199 per night.
They stay for 4 nights and leave a 12% tip to housekeeping.
How much does their hotel cost total.
Answers
With a 12% housekeeping gratuity, the hotel bill for 4 nights comes to $891.52.
What is unitary method?
"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
Total cost = Bill before tip + Tip
Total cost = $796 + $95.52
Total cost = $891.52
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What is the perimeter of each of the figures?
Answers
Answer:
x=16
Step-by-step explanation:
(x-8)+2x+2x=4(x+2)
x-8+4x=4x+8
x=16
Answer:
x=16
Step-by-step explanation:
perimeter of triangle=a+b+c =perimeter of Square =L²
2x+2x+x-8=4(x+2)
5x-8=4x+8
C.L.T
5x-4x=8+8
x=16
What is the solution to -2(8x - 4) < 2x + 5?
O x
7/10 7/10
6
O
0 x < 1/1/201
O x > 6
O x < 6
Answers
The solution for the inequality -2(8x - 4) < 2x + 5 is x > 1/6.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
Let's simplify the inequality -
-2(8x - 4) < 2x + 5
Distribute the -2 -
-16x + 8 < 2x + 5
Subtract 2x from both sides -
-18x + 8 < 5
Subtract 8 from both sides -
-18x < -3
Divide both sides by -18, remembering to reverse the inequality because we're dividing by a negative number -
x > 3/18
Simplifying, we get -
x > 1/6
Therefore, the solution to the inequality is -
x > 1/6
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PLEASE HELP IM SO LOST
Answers
Answer: f(x) has an axis of symmetry at x = 4 and h(x) has an axis of symmetry at x = -2
Step-by-step explanation:
You can easily find the axis of symmetry by investigating around which line the functions are symmetrical about
for instance, in h(x), the graph is symmetrical on either side of x = -2, meaning that the line x = -2 cuts the parabola in 'half'
in f(x), this is a little harder to think about, but if you know how the graph will be shifted on the x-axis you can figure it out! In this case (x-4)^2 means that the graph will be shifted on the x-axis 4 units to the right (or from the origin to +4 on the X axis)
as such the line x = 4 will cut the function f(x) in 'half'
Determine whether descriptive or inferential statistics were used in the statement. in 2008, the average credit card debt for college students was $3173. (source: newser)
Answers
The collection, description, analysis, and drawing of conclusions from quantitative data are all included in the area of statistics, which is a branch of applied mathematics. Probability theory, linear algebra, and calculus of differential and integrals are some of the core mathematical concepts in statistics.
Descriptive statistics were used in the statement.
Descriptive statistics is a branch of statistics that deals with the collection, presentation, and summary of data. It is used to describe and summarize the main features of a data set, such as measures of central tendency (e.g., mean, median, mode) and measures of dispersion (e.g., range, variance, standard deviation).
In this case, the statement is simply reporting a single value, the average credit card debt for college students in 2008. This is an example of a descriptive statistic because it is a summary measure that describes a characteristic of the population or sample under study.
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Descriptive statistics were used in the statement.
What is descriptive statistics?Descriptive statistics is a branch οf statistics that deals with the analysis, descriptiοn, and summarizatiοn οf data. It invοlves the use οf variοus statistical measures, such as measures οf central tendency (mean, median, and mοde), measures οf dispersiοn (standard deviatiοn, variance, range), and graphical representatiοns (histοgrams, bοx plοts, scatter plοts, etc.) tο describe the features οf a dataset.
Descriptive statistics were used in the statement. The statement is simply describing the average credit card debt fοr cοllege students in 2008. Descriptive statistics are used tο describe οr summarize a dataset οr pοpulatiοn, while inferential statistics are used tο draw cοnclusiοns οr make predictiοns abοut a larger pοpulatiοn based οn a sample οf data. Since the statement οnly prοvides infοrmatiοn abοut a specific grοup οf cοllege students in 2008, it dοes nοt invοlve making any inferences οr predictiοns beyοnd this grοup.
Hence, Descriptive statistics were used in the statement.
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ASAP
3(– 2а - 4) + За
Answers
Answer:
3a -12
Step-by-step explanation:
3(– 2а - 4) + За → -6a - 12 + 3a → -3a -12
HELP 100 POINTS ANSWER IT PLEASE
Answers
Answer:
\(\boxed{\text{\large $ y=96.1\sqrt{x} $}}\)
Step-by-step explanation:
Using a graphing calculator, plot (x,y) points
x = no. of jobsy = no. of workers neededand plot the functions from the options to know which function fits the data
Answer:
Step-by-step explanation:
Using a graphing calculator, plot (x,y) points
x = no. of jobs
y = no. of workers needed
and plot the functions from the options to know which function fits the data
help meeee again ¾÷⅕ =
Answers
Answer:
decimal: 2.25
fraction: 9/4
Step-by-step explanation:
Answer:
Fraction: 15/4
Decimal: 3.75
To practice for a competition, Barry swam 730 meters in the pool each day for 4 weeks. How many kilometers did Barry swim in those 4 weeks? 1 m = 0.001 km
Answers
Answer:
20.44 km
Step-by-step explanation:
The values are,
→ 730 m = 0.730 km
→ 4 weeks = 28 days
Now Barry swam in 28 days is,
→ 0.730 × 28
→ 20.44 km
Hence, answer is 20.44 km.