The probability of getting two consecutive ones in a string of 1s and 0s of length n can be calculated as (n-1) / (2n).
Explanation:The probability of getting two consecutive ones in a string of 1s and 0s of length n can be calculated by considering the number of possible outcomes and the number of favorable outcomes.
Let's assume that the probability of getting a one is p and the probability of getting a zero is q. The favorable outcomes are when two consecutive ones occur, which can be represented as (1,1).
To calculate the probability, we need to determine the number of ways we can arrange the numbers in the string. Since we are only interested in the position of the ones, we can ignore the zeros.
Therefore, the number of favorable outcomes is n-1, because we have n-1 places where two consecutive ones can occur in a string of length n.
The number of possible outcomes is 2n, because each digit in the string can be either a one or a zero. Therefore, the probability of getting two consecutive ones is:
p = (n-1) / (2n)
Raina is putting 13 colored light bulbs into a string of lights. There are 5 white light bulbs, 6 orange light bulbs, and 2 blue light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
Answer: The number of ways would be 36,036.
Step-by-step explanation:
Since we have given that
Number of white light bulbs = 5
Number of orange light bulbs = 6
Number of blue light bulbs = 2
Total number of light bulbs = 13
So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.
[tex]N=\dfrac{n!}{r!}\\\\N=\dfrac{13!}{5!\times 6!\times 2!}\\\\N=36036[/tex]
Hence, the number of ways would be 36,036.
The number of different orders in which Raina can put the colored light bulbs into a string is 1,324, calculated using the formula of permutations with indistinguishable items.
Explanation:The question is about the number of different possible arrangements, or combinations, of the colored light bulbs. Since all light bulbs of the same color are identical, this is a problem of permutations with indistinguishable items. The formula to calculate this is n!/(r1!*r2!*...*rn!), where n is the total number of items, and r1, r2,...,rn are the number of each type of identical items.
So in this case, there are 13 colored light bulbs in total (n=13), with 5 white light bulbs (r1=5), 6 orange light bulbs (r2=6), and 2 blue light bulbs (r3=2).
The total different orders of light bulbs can be found by calculating 13!/(5!*6!*2!) = 1,324 possibilities.
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Twenty different video games showing alcohol use were observed. The duration times of alcohol use (in seconds) were recorded.
1. When using this sample for a t-test of the claim that the population mean is greater than 89 sec, what does df denote?
A. The sample standard deviation
B. The number of degrees of freedom
C. The sample size
D. The test statistic
2. What is its value?
Answer:
Degree of freedom = 19
Step-by-step explanation:
We are given the following information in the question:
Sample size, n = 20
For a t-test hypothesis it was claimed that the population mean is greater than 89 second.
1) df
Df denotes the degree of freedom.
The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary.2) Degree of freedom = n - 1
where n is the sample size
Degree of freedom = 20 - 1 = 19
If an integer n is to be selected at random from the integers 1 to 100, inclusive, what is the probability that n(n 1) will be divisible by 4
Answer:
Step-by-step explanation:
total integers=100 (1,2,3,...,98,99,100)
numbers divisible by 4 =25 (4,8,12,...,96,100)
P=25/100=1/4
an agent of a broker-dealer wishes to create a website to solicit securities business from customers. based on each customer's reponses to questions asked, appropriate investment recommendations will be made. which statement are true?
Answer:
The following statements are true:
The broker-dealer must review and approve the content of the website The broker-dealer must be registered in each State where a customer responds to the website The agent must be registered in each State where a customer responds to the websiteStep-by-step explanation:
An agent of a broker-dealer wishes to create a website to solicit securities business from customers based on each customer's response to questions asked, appropriate investment recommendation will be made. The statement which is not true under the given conditions is: "The Administrator must review and approve the content of the website." because the broker-dealer has to approve the content of the website.These recommendations which are discussed above are for the benefit and will ensure the safety and prevent the damage.please answer soon Which expression is equivalent to − 7 x + 6 ( x − 8 2 ) − 2 ( x + 3 ) + 10 ? A. − 3 x + 40 B. − 15 x − 20 C. − 3 x − 20 D. 15 x + 40
Multiply the parenthesis by 6:
-7x+6x-492-2(x+3)+10
Multiply the parenthesis by -2:
-7x+6x-492-2x-6+10
Calculate the sum of similar terms:
-3x-492-6+10
Calculate the sum or difference:
-3x-488
Sammy is making a bacon wrapped pizza for dinner. She is wrapping 47.1 inches of bacon around the outside edge of the pizza. What is the area of the pizza?
Answer:
Approx. 1.8 in.²
Step-by-step explanation:
Circumference of a circle (the pizza) = 2πr
Area of a circle = πr²
Set 2πr = 4.71 (because that's the length of bacon around the pizza) and solve for the radius "r". Then plug that "r" into the area equation πr² to find the area. You should get 1.8 square inches if I plugged them in correctly.
HELPPPPP
(Attaching the pic now)
Explanation:
1. BF bisects ∠CBA. Given
2. ∠CBF ≅ ∠ABF. Definition of angle bisector
3. BF ≅ BF. Reflexive property
4. ∠CFB ≅ ∠AFB. Given
5. ΔCBF ≅ ∆ABF. ASA congruence postulate
6. CF ≅ FA. Corresponding parts of congruent triangles are congruent (CPCTC)
_____
Comment on the problem
It appears as though all of the congruence symbols have gone missing.
Prove that if f is one-to-one, then f(X) ∩ f(Y ) = f(X ∩ Y ) for all X, Y ⊆ A. Is the converse true?
Answer:
See proof below, the converse is true
Step-by-step explanation:
Let f be a function whose domain is the set A, and X,Y be arbitrary subsets of A. One way to prove the equality of sets f(X)∩f(Y)=f(X∩Y) is, by definition, to prove the inclusions f(X)∩f(Y) ⊆ f(X∩Y) and f(X)∩f(Y )⊇f(X∩Y).
First, let a∈f(X)∩f(Y). Then a∈f(X) and a∈f(Y) by definition of intersection. Thus, a=f(t) for some t∈X (because a is an element of the direct image of X) and a=f(s) for some s∈Y. Then a=f(t)=f(s). We know that f is 1-1, so the previous equality implies that t=s. Now, t∈X and t=s∈Y, thus t∈X∩Y. Therefore, a=f(t) for some t∈X∩Y, which means that a is an element of the direct image of X∩Y, that is, a∈f(X∩Y). This holds for all a, thus f(X)∩f(Y) ⊆ f(X∩Y).
For the second inclusion, let b∈f(X∩Y), then there exists some z∈X∩Y such that b=f(z). Since z∈X∩Y, we have that z∈X and z∈Y. Thus, b=f(z) for some z∈X, that is, b∈f(X). Similarly, b∈f(Y) because b=f(z) and z∈Y. Therefore b∈f(X)∩f(Y) for all b∈f(X∩Y), then f(X)∩f(Y )⊇f(X∩Y). Note that this holds for any function f, as we did not use that f is 1-1.
To prove the converse, suppose that f(X)∩f(Y)=f(X∩Y) for all X, Y⊆ A. We will prove that f is 1-1, that is, for all a,b∈A if f(a)=f(b) then a=b.
Define the sets X:={a} and Y:={b}. Then f(X)={f(a)} and f(Y)={f(b)}. Assuming that f(a)=f(b), we obtain f(X)=f(Y). We know that f(X)∩f(Y)=f(X∩Y), which means {f(a)}=f(X∩Y). Then, there exists some s∈X∩Y such that f(s)=f(a), thus X∩Y is a non-empty set, which implies that a∈Y. But Y has only one element, b, therefore a=b which shows that f is 1-1.
Match the key aspect of a function's graph with its meaning.
f(x) > 0
intervals of the domain where the
graph is above the x-axis
f(x) < 0
location on graph where input is zero
x-intercept
location on graph where output is
zero
y-intercept
intervals of the domain where the
graph is below the x-axis
Answer:
Part 1) Intervals of the domain where the graph is above the x-axis (f(x) > 0)
Part 2) location on graph where input is zero (y-intercept)
Part 3) location on graph where output is zero (x-intercept)
Part 4) Intervals of the domain where the graph is below the x-axis (f(x) < 0)
Step-by-step explanation:
Verify each case
Part 1) we have
Intervals of the domain where the graph is above the x-axis
we know that
If the graph is above the x-axis, then the value of f(x) is positive
therefore
f(x) > 0
Part 2) we have
location on graph where input is zero
Let
x ---> the independent variable or input value
f(x) ---> the dependent variable or output value
we know that
The y-intercept is the value of f(x) (output value) when the value of x (input value) is zero
therefore
y-intercept
Part 3) we have
location on graph where output is zero
Let
x ---> the independent variable or input value
f(x) ---> the dependent variable or output value
we know that
The x-intercept is the value of x (input value) when the value of the function f(x) (output value) is zero
therefore
x-intercept
Part 4) we have
Intervals of the domain where the graph is below the x-axis
we know that
If the graph is below the x-axis, then the value of f(x) is negative
therefore
f(x) < 0
Answer:
Intervals of the domain where the graph is above the x-axis (f(x) > 0)
location on graph where input is zero (y-intercept)
location on graph where output is zero (x-intercept)
Intervals of the domain where the graph is below the x-axis (f(x) < 0)
Step-by-step explanation:
answer edge 2020
7600 people were surveyed about their favorite type of milkshake what percentage of the people like vanilla how many of the people like chocolate how many of the total people like vanilla or strawberry
Answer:
Lack of information
Step-by-step explanation:
I can't find what percent or whatever information about the flavour,so I guess you need to give more information. If you give me more information, I will try to reply in the comments.
Hope this helps!!! ;)
Calculate the simple interest paid on a loan of $544 at 3% for three months.
$48.96
$4.80
$4.90
$4.08
Answer:
4.08
Step-by-step explanation:
Interest I =Pnr
3 months =3/12 year = n
r = 3%
and, P = 544$
Therefore,
[tex]i = 544 \times (3 \div 100) \times (3 \div 12) \\ \: \: \: = 4.08[/tex]
3(5j+2)=2(3j-6)(if there is no solution,type in ''no solution'')j= Answer
Answer:
j = -2
Step-by-step explanation:
It usually works well to start by eliminating parentheses.
15j +6 = 6j -12
Now you can subtract 6j from both sides to get the variable term on one side of the equation only:
9j +6 = -12
And you can subtract 6 from both sides to get the variable term by itself:
9j = -18
Now, dividing by the coefficient of the variable gives you the solution:
j = -2
The solution is j = -2.
Answer:
j = -2
Step-by-step explanation:
3 (5j + 2) = 2 (3j - 6)
15j + 6 = 6j - 12
15j - 6j = - 12 - 6
9j = - 18
j = - 18/9
j = - 2
What is the length of the midsegment of the trapezoid
Answer:
The length of the mid-segment of the trapezoid = 7
==================================================
Step-by-step explanation:
The mid-segment of a trapezoid is the segment that connecting the midpoints of the two non-parallel sides.
As shown in the figure the two non-parallel sides are AB and CD
∴ The mid-segment of the trapezoid = [tex]\frac{BC +AD}{2}[/tex]
From the figure: BC = 8 and AD = 6
∴ The mid-segment of the trapezoid = [tex]\frac{8+6}{2} = 7[/tex]
1/4 + 1/8= I know it should be easy but my teacher told me that we can't add fractions if they have different denominators. Now if you are going to explain the to me I am in 5th grade so please don't make it to complicated.Thank you.
Which events are independent?
Select each correct answer.
One ball is drawn from a bag of balls after another ball is drawn without replacement.
A coin is flipped and a spinner is spun.
White marbles are drawn from a bag of marbles without replacing the marbles.
Four number cubes are rolled at the same time.
----
I know I have asked this before but people have given me only one answer, which was C but I think I need to select more than one answer. Thanks so much for any help.
Answer:
Option B) and option D) are independent events. i.e. following events are independent events:
B) A coin is flipped and a spinner is spunD) Four number cubes are rolled at the same time.Step-by-step explanation:
Two events would be termed as Independent events if the occurrence of one event would not affect the occurrence of other event.
Let us first consider the options having independent events.
B) A coin is flipped and a spinner is spunD) Four number cubes are rolled at the same time.Option B) i.e. 'a coin is flipped and a spinner is spun' is treated as neither of the events is affecting the outcome of other event. For example, assuming a coin and spinner are kept isolated, the occurrence of event of a flipping coin is not affecting the outcome of the occurrence of spinner.
The same goes with the option D) i.e. 'four number cubes are rolled at the same time', as neither of the rolling is affecting the rolling of other coin.
Now, let us consider the options having dependent events
A) One ball is drawn from a bag of balls after another ball is drawn without replacement.C) White marbles are drawn from a bag of marbles without replacing the marbles.Let us suppose one ball is drawn from a bag of balls after another ball is drawn without replacement. If there is no replacement, it logically means, after every drawn event, total number of the balls are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event. Hence, the occurrence of every event depends upon the occurrence of other event, meaning the two events will keep affecting the outcome if no replacement is made before the next event.
The same logic goes with when white marbles are drawn from a bag of marbles without replacing the marbles. If there is no replacement, it logically means, after every drawn event, total number of the white marbles and marbles are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event.
So, after all the discussion, we can safely say make a conclusion that option B) and option D) are independent events. i.e. following events are independent events:
B) A coin is flipped and a spinner is spunD) Four number cubes are rolled at the same time.Keywords: dependent events, independent events
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What is the fiftieth term of the arithmetic sequence 3, 7, 11, 15, ... ?
199
151
53
203
Answer:
53
Step-by-step explanation:
if THE equation of a circle is (x + 5)2 + (y - 7)2 = 36, it’s center point is
Answer:
(-5,7) is the center
Step-by-step explanation:
Keys went to the grocery store on Monday and bought 5 apples and 2 oranges for a total of 3.45. On Thursday she bought 3 oranges and 7 apples for a total of $4.90
Answer:
Keys would have to spend $6.60 on apples for both days.
Step-by-step explanation:
Keys went to buy 5 apples and 2 oranges for $3.45 and 7 apples and 3 oranges for $4.90 .
We have to find how much money she spends on apples on both the days.
Let price of apples be x and oranges be y.
We have to make equations and solve them to find the price of oranges and apples.
5x + 2y = 3.45
7x + 3y = 4.90
Solve both these equations to find x and y.
We get x= $0.55 and y = $0.35
Key has bought 12 apples and it would cost = 12 [tex]\times[/tex] 0.55
= $6.60
Trey is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 54 feet and its width is 30 feet. Suppose each can of wood stain covers 135 square feet. How many cans will he need to cover the court?
Answer:
The number of cans that he will need to cover the court is 12 cans
Step-by-step explanation:
The court is in the shape of a rectangle. Its length is 54 feet and its width is 30 feet. The formula for the area of a rectangle is expressed as length × width. Therefore, the area of the wooden floor is
54×30 = 1620 square foot
Suppose each can of wood stain covers 135 square feet, the number of cans that would cover the rectangular floor of the court would be
1620/135 = 12
Find f(2) if f(x) = 2x + 1.
A) 3
B) 5
C) 7
D) 9
Answer:
The answer to your question is letter B
Step-by-step explanation:
Process
1.- Write the equation
f(x) = 2x + 1
find f(2)
2.- Substitute x for 2
f(2) = 2(2) + 1
3.- Simplify
f(2) = 4 + 1
f(2) = 5
Answer:
5
Step-by-step explanation:
2(2) + 1 = 5
A bakery wants to determine how many trays of doughnuts it should prepare each day. Demand is normal with a mean of 5 trays and standard deviation of 1 tray. If the owner wants a service level of at least 95%, how many trays should he prepare (rounded to the nearest whole tray)? Assume doughnuts have no salvage value after the day is complete. 6 5 4 7 unable to determine with the above information.
Answer:
4 trays should he prepared, if the owner wants a service level of at least 95%.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 5
Standard Deviation, σ = 1
We are given that the distribution of demand score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(X > x) = 0.95
We have to find the value of x such that the probability is 0.95
P(X > x)
[tex]P( X > x) = P( z > \displaystyle\frac{x - 5}{1})=0.95[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{x - 5}{1})=0.95 [/tex]
[tex]=P( z \leq \displaystyle\frac{x - 5}{1})=0.05 [/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 5}{1} = -1.645\\x = 3.355 \approx 4[/tex]
Hence, 4 trays should he prepared, if the owner wants a service level of at least 95%.
The family size bottle of sunscreen holds 12 fluid ounces (fl oz)left parenthesis, start text, f, l, space, o, z, end text, right parenthesis of sunscreen. The regular bottle holds 75%, percent less. How many fewer fluid ounces does the regular bottle of sunscreen hold?
Sebastian was in a hotel lobby and took the elevator up 7 floors to his room. Then he took the elevator down 9 floors to the parking garage. He described his movement with the expression below.
Answer:
7-9
Step-by-step explanation:
Sebastian goes up from 0 by 7 floors. Then, he goes down by 9.
Which of the following is the simple interest paid on a loan of $354 at 6% for six months?
$10.62
$10.26
$12.47
$12.74
Answer: interest at the end of 6 months is $10.62
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 6 months = 6/12 = 0.5 years
P = $354
R = 6%
Therefore
I = (354 × 6 × 0.5)/100
I = 1062/100
I = 10.62
Judy bought her tent on sale .The same price was $70 off the original price . Judy also used a coupon for an extra $15 off if Judy paid $125 for the tent , what was it's original price
Answer:210
Step-by-step explanation:
175+70+15=210
Answer:the original price is $210
Step-by-step explanation:
Let x represent the original price of the tent. She bought it at price that is $70 off the original price. This means that $70 was taken off the original price.The amount after the discount has been removed would be
x - 70
Judy also used a coupon for an extra $15 off. This means that the amount the Judy finally paid for the tent would be
x - 70 - 15
if Judy paid $125 for the tent, it means that
x - 70 - 15 = 125
x = 125 + 70 + 15
x = $210
please help asap please
Answer:
Step-by-step explanation:
The slope of the line needs to be determined first:
[tex]m=\frac{-9+-5}{-12+-8}=\frac{-14}{-20}=\frac{7}{10}[/tex]
Now let's use that and one of the coordinates to write an equation in point-slope form:
[tex]y-5=\frac{7}{10}(x-8)[/tex]
and, simplifying,
[tex]y-5=\frac{7}{10}x-\frac{56}{10}[/tex]
Now let's multiply everything by 10 to get rid of the fractions:
10y - 50 = 7x - 56
and
-7x + 10 y = -6
Apparently, they do not like to lead with negatives, which is not uncommon:
7x - 10y = 6
So his model is not correct.
At Delia’s company, the purchases are recorded at net amounts. On August 5, $40,000 worth of merchandise was purchased on account for terms of 2/10, n/30. $3,000 of this merchandise was returned, and the account was credited. As of August 31, the balance still had not been paid. What amount will be recorded as the purchase return?
Answer:
$2,940
Step-by-step explanation:
Data provided in the question:
Cost of merchandise purchased = $40,000
Cost of merchandise returned = $3,000
Terms = 2/10, n/30
Now,
The amount that will be recorded as the purchase return
= Cost of merchandise returned - Discount on cost of merchandise
= $3,000 - ( 2% of $3,000 )
= $3,000 - ( 0.02 × $3,000 )
= $3,000 - $60
= $2,940
Your grandmother always has a jar of cookies on her counter. One day while you are visiting, you eat 555 cookies from the jar. In the equation below, ccc is the number of cookies remaining in the jar and bbb is the number of cookies in the jar before your visit.
Answer:
For 1 How does grandma have so many cookies??? For 2 if i eat 555 cookies then imma have diabetes. and for 3 there really is no way to find this out. The only way to find out how many cookies there is now it to see how much cookies there were before and you cant do that without seeing how much is in there now. Its a catch 22.
Step-by-step explanation:
The residents of a city voted on whether to raise property taxes. The ratio of yes votes was 5 and no votes was 7.
If there were 3710 yes votes, what was the total number of votes?
Answer:
Step-by-step explanation:
Set this up as a proportion. The idea is that if we can find out the number of "no" votes based on the ratio of 5:7, then we can add the "no" votes to the number of "yes" votes to get the total number of votes.
[tex]\frac{yes}{no}:\frac{5}{7}=\frac{3710}{x}[/tex]
Cross multiply to get
5x = 25790 so
x = 5194 "no" votes.
5194 + 3710 = 8904 total votes
The scoring of modern IQ tests is such that IQs have a Normal distribution with mean
100 and standard deviation 15. What is the approximate IQ of someone with a z-score of 0.93?
Answer:
114
Step-by-step explanation:
z = (x − μ) / σ
0.93 = (x − 100) / 15
x ≈ 114