Answer:
5 5/12 pounds of nails
Step-by-step explanation:
(3 1/3 boxes) × (1 5/8 pounds/box) = (10/3)(13/8) pounds = 65/12 pounds
= 5 5/12 pounds
Mark used approximately 5.41 pounds of nails to build the tree house. This is found by converting the given fractions to decimal and then multiplying the weight of one box of nails by the number of boxes use
Explanation:In the problem, we know that a box of 100 nails weighs 1 5/8 pounds. We are also told that Mark used 3 1/3 boxes of nails. Therefore, we first need to find out how much one box of nails weighs, and then multiply that weight by the number of boxes Mark used.
To convert 1 5/8 to a decimal, we know that 5/8 = 0.625, so 1 5/8 = 1.625 pounds. Mark used 3 1/3 boxes, and 1/3 converted to a decimal is approximately 0.33, so Mark used approximately 3.33 boxes. By multiplying 1.625 pounds by 3.33, we find that he used approximately 5.41 pounds of nails to build the tree house.
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ƒ(1) = 65,536, ƒ(n) = √ __ ƒ(n - 1)
Can any one answer this please
Answer: 10.6
Step-by-step explanation:
divide the number she spent (2.65) by the amount the store charges per ounce (.25)
2.65/ .25 = 10.6
A bag contains three red marbles, two green ones, one lavender one, four yellows, and five orange marbles. HINT [See Example 7. How many sets of four marbles include all the red ones?
Answer:
There are 12 sets of four marbles include all the red ones.
Step-by-step explanation:
Given : A bag contains three red marbles, two green ones, one lavender one, four yellows, and five orange marbles.
To find : How many sets of four marbles include all the red ones?
Solution :
Number of red marbles = 3
Number of green marbles = 2
Number of lavender marbles = 1
Number of yellow marbles = 4
Number of orange marbles = 5
We have to form sets of four marbles include all the red ones,
For position of getting red ones we have three red marbles i.e. [tex]^3C_3[/tex]
For the fourth one we have 12 choices i.e. [tex]^{12}C_1[/tex]
Total sets of four marbles include all the red ones is
[tex]=^3C_3\times ^{12}C_1[/tex]
[tex]=1\times 12[/tex]
[tex]=12[/tex]
Therefore, There are 12 sets of four marbles include all the red ones.
Select all of the answers below that are equal to B = {John, Paul, George, Ringo, Pete, Stuart}
Question 1 options: {flowers, computer monitor, flag, teddy bear, bread, thermostat}
{bookmark, needle, street lights, sock, greeting card, Ringo}
{The Monkees} {book, door, speakers, soap, toothpaste, pool stick}
{scotch tape, iPod, Sharpie, Street Lights, window, clock}
{Paul, Ringo, Pete, John, George, Stuart}
Answer:
The correct option is 5) {Paul, Ringo, Pete, John, George, Stuart}.
Step-by-step explanation:
Consider the provided sets:
B = {John, Paul, George, Ringo, Pete, Stuart}
Two sets are equal if all the elements of Sets are same.
Set B has the elements: John, Paul, George, Ringo, Pete and Stuart
Now consider the provided options of sets.
From the provided options of set only option 4 has all the elements of set B but the order is different.
Thus, the correct option is 5) {Paul, Ringo, Pete, John, George, Stuart}.
A bird flies from its nest 9 km in the direction of 60 degrees north of east, where it stops to rest on a tree. It then flies 20 km in the direction due southeast and lands atop a telephone pole. Place an xy-coordinate system so that the origin is the bird's nest, the x-axis points east, and the y-axis points north. a. At what point is the tree located? b. At what point is the telephone pole located?
Answer with explanation:
The motion of the bird is shown in the attached figure
part a)
In the ordinate axis as shown in the attached figure we can see that the tree is located at a point [tex](9cos(60),9sin(60)=(4.5km,7.794km)[/tex] with respect to origin O
Part b)
The location of the telephone pole as seen from the co-ordiante axis is at
[tex]x=4.5+20cos(45)=18.64km\\\\y=7.794-20sin(45)=-6.348km[/tex]
The points are located as shown in the figure
Given the three topics listed below, discuss a visual, verbal, and algebraic way of connecting the concepts:
1. The distance formula
2. The standard equation of a circle (not centered at the origin)
3.The Pythagorean Theorem
Can you think of other related mathematics topics that can be extended from these three? Write a 1/2 page not including diagrams.
Answer:
Lots of connections!
Step-by-step explanation:
I attached some images to make it more clear.
Visual and verbal discussion:
A good starting point is the circle. One can think of a circle as the set of points that are equidistant to a certain point. In that sense, one can define a circle using the distance. At the same time, given a point [tex](x_{0},y_{0})[/tex] in the plane, we can connect the point with the origin of the coordinates system forming a rectangle triangle! (See 2nd image)
Algebraic discussion:
1. The distance Formula:
Given two points in the plane [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] we can find the distance between both points with the distance formula:
[tex]d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
2. Equation of a circle centered at a point [tex](x_{0},y_{0})[/tex]
[tex]r = \sqrt{(x-x{_0}^2) + (y-y_{0})^2}[/tex]
3. The Pythagorean Theorem:
Given a triangle of sides [tex]a;b[/tex] and hypotenuse [tex]h[/tex] we have that
[tex]h^2 = a^2 + b^2[/tex]
Only by writing this equations we can already see the similarities between all three.
In fact, the most amazing thing about all three is that they are equivalents. That is, we can obtain every single one of them as an immediate result of another.
For instance, as I said before, one can think of a circle as the set of points equidistant to a certain origin or center point. So we could use the distance formula for each point on the circumference and we would obtain always the same value [tex]r[/tex] hence obtaining the equation of a circle.
Also as we discussed, any point on the plane form a rectangle triangle with its coordinates and calculating the distance of said point to the origin of the coordinate system would give us no other thing than the hypotenuse of said triangle!
300 ml over 15 min is what rate of ml per hour
Answer:
1200 ml per hour
Step-by-step explanation:
To compute what rate is 300 ml over 15 mins as a rate of ml per hour, we do a rule of 3, using a variable x as that amount of ml we don't know yet. We should have everything in the same units, so instead of writing 1 hour we write 60 minutes:
[tex] \frac{300~ml}{15~min}=\frac{x~ml}{60~mins}[/tex]
Now we solve for x:
[tex] \frac{300~ml}{15~min}\cdot 60~mins=x~ml[/tex]
[tex] \frac{18000~ml}{15} =x~ml[/tex]
[tex] 1200~ml =x~ml[/tex]
And so, now that we know the value of x, the rate we wanted to find is
[tex]\frac{1200~ml}{60~mins}[/tex]
Which is just 1200 ml per hour.
All butterflies are insects. A Morpho is a butterfly. Therefore, a Morpho is an insect. Deductive reasoning has three parts:
Answer:
Yes, a Morpho is an insect.
Step-by-step explanation:
As per the question,
We have been provided the information that
I. All butterflies are insects.
II. A Morpho is a butterfly.
By drawing the Venn-diagram of given conditions, drawn as below.
Now,
We can conclude that a Morpho comes in the circle of butterfly and the circle of butterflies comes under the circle of Insects.
All butterflies = Insects
A morpho = A butterfly
∴ A morpho = An insect
Therefore if a morpho is a butterfly than it is definitely an insect because all butterflies are insects.
Hence, the given statement is true.
A car has mass 1500 kg and is traveling at a speed of 35 miles/hour. what is its kinetic energy in joules? (Be sure to convert miles/hour to m/s). If the car increases its speed to 70 miles/hour, by what factor does its kinetic energy increase? show work
Answer:
The kinetic energy of car with mass 1500 kg and with speed of 35 miles/hour is KE=183598 J and when the car increases its speed to 70 miles/hour the kinetic energy changes by a factor of 4.
Step-by-step explanation:
The first step is to convert the speed miles/hour to m/s.
[tex]35\frac{miles}{hour} *\frac{1609.34 \>m}{1 \>miles}*\frac{1 \>hour}{3600 \> s}=15.646 \frac{m}{s}[/tex]
Next, the formula for the kinetic energy is
[tex]KE=\frac{1}{2} mv^{2}[/tex]
So input the values given:
[tex]KE=\frac{1}{2} (1500)(15.646)^{2}\\KE=750 \cdot (15.646)^{2}\\KE=183597.987 = 183598 \frac{kg \cdot \>m^{2}}{s^{2}} \\KE=183598 \>J[/tex]
Notice that the speed of 70 miles/hour is the double of 35 miles/hour so we can say that [tex]v_{2}=2v_{1}[/tex] and use the formula for the kinetic energy
[tex]KE_{2} =\frac{1}{2} m(v_{2}) ^{2}\\if \: v_{2}= 2v_{1}, then \:\\KE_{2} =\frac{1}{2} m(2v_{1}) ^{2}\\KE_{2} =\frac{1}{2} m4(v_{1})^{2}\\KE_{2} =4(\frac{1}{2} m(v_{1})^{2})\\We \:know \:that \:KE_{1} =\frac{1}{2} m(v_{1})^{2} so\\KE_{2} =4(KE_{1})[/tex]
We can see that when the car increases its speed to 70 miles/hour the kinetic energy changes by a factor of 4.
Show that the following argument with hypotheses on lines 1–2 and conclusion on line c is
valid, by supplementing steps using the rules of inference and/or logical equivalences. Clearly label which rule you used in each step.
1. p → q
2. ∼ (q ∨ r)
c. ∼ p
Answer:
Step-by-step explanation:
[tex] p \Rightarrow q \equiv (\neg p \vee q) [/tex] [logical equivalence]
[tex] \neg (q \vee r) \equiv (\neg q \wedge \neg r) [/tex] [morgan laws]
if [tex] (\neg q \wedge \neg r) [/tex] is true, then [tex] \neg q [/tex] is true and [tex] \neg r [/tex] is too.
with [tex] \neg q [/tex] true, then [tex] q [/tex] is false [double denial]
In the first equivalence it follows that [tex] \neg p [/tex] is true [identity law]
Then it can be concluded that [tex] \neg p [/tex]
Which of the following items would not be used for geometric probability? a. area of a rug c. length of time b. number of trees d. length of a field
Answer: b. number of trees
Step-by-step explanation:
The concept of geometric probability is basically use when we have continuous data .
Since it is impossible to count continuous data , but geometrically ( in form of length, area etc) we can count the outcomes in general to calculate the required probability.
Therefore, from the given options , Option b. "number of trees" would not be used for geometric probability because among all it is the only discrete case which is countable.
Rest of items ( a. area of a rug , c. length of time , d. length of a field) would be used for geometric probability,
Which of the statements is false?
(A) interesection of connected sets is connected
(B) union of two connected sets, having non-empty intersection, is connected
(C) interesection of any number of comapct sets is compact
(D) continuous image of a compact set is compact
(E) continuos image of a connected set is connected
I'm pretty sure b is your answer
Final answer:
The false statement is (A), which claims that the intersection of connected sets is connected. This is not always true, as connected sets can intersect in a way that creates disjoint, non-connected subsets. So the correct option is A.
Explanation:
The student is asked to identify which statement is false among those given related to the properties of connected and compact sets in the context of mathematical analysis. In these options, (A) claims that the intersection of connected sets is connected, (B) states that the union of two connected sets with a non-empty intersection is connected, (C) states that the intersection of any number of compact sets is compact, (D) asserts that the continuous image of a compact set is compact, and (E) maintains that the continuous image of a connected set is connected.
The false statement among those provided is (A). It is not true that the intersection of connected sets is necessarily connected. For example, consider two overlapping connected sets such that their intersection is not connected, like two overlapping annuli where the intersection creates separate disjoint areas. However, options (B), (C), (D), and (E) are correct under the definitions of connected and compact sets in topology.
On a True/False test, Amy answered the first three questions wrong but answered the rest of the questions correctly. On the same test, Scott answered exactly two questions wrong. He answered the last question wrong, the 26 questions before it correctly, and the question before that wrong. If Amy and Scott were both incorrect on the same question exactly once, what is the greatest possible percent of the total number of questions that Amy could have answered correctly?
Final answer:
Amy could have answered approximately 89.29% correctly, assuming the test had the minimum number of questions allowing for all conditions in the problem to be satisfied.
Explanation:
The question involves determining the greatest possible percent of questions Amy could have answered correctly on a true/false test, given specific details about how Amy and Scott answered their questions.
To find the maximum percentage Amy could have gotten correct, we must assume that the test had the smallest number of questions that fulfill all the given conditions. This would be when the question before the last question, which Scott got wrong, aligns with one of the first three questions that Amy got wrong. Since they were both incorrect only once on the same question, Amy's third question is the same as Scott's second-to-last question. Thus, the test would have a minimum of 28 questions (the 26 Scott got right, plus the two he got wrong).
Amy answered the first three questions wrong and all others correctly, so she got 25 out of 28 questions correct. To find the percentage, we divide 25 by 28 and multiply by 100. Therefore, Amy answered approximately 89.29% of the questions correctly. Amy could not have a higher percentage because having more questions on the test would only lower her score.
Greg is covering a wall with equal-sized tiles that cannot be cut
into smaller pieces. The wall is 66 inches high by 72 inches wide.
What is the largest square tile that simon can use?
A. 9 in.
B. 16 in.
C. 36 in.
D. 64 in.
Answer:
C. 36 in.
Step-by-step explanation:
The wall is 66 inches high by 72 inches wide.
The tiles are
a) 9 inch square = 3 by 3
b) 16 inch square = 4 by 4
c) 36 inch square = 6 by 6
d) 64 inch square = 8 by 8
Factors of 66 = 2 x 3 x 11
Factors of 72 = 2 x 2 x 2 x 3 x 3
Now, we can see that in both 66 and 72 , we have 2 x 3 common that is 6.
And square of 6 is 36.
So, the answer is option C.
two automobiles leave a city at the same time and travel along straight highways that differ in direction by 84 degrees. if their speeds are 60 mi/hr and 45 mi/hr, approximatly how far apart are the cars at the end of 20 minutes?
Answer:
D = 23.7 miles
Step-by-step explanation:
Given data:
[tex]\theta=84 degrees[/tex]
Time[tex] = 20 min = \frac{1}{3} hr[/tex]
Distance of A [tex]= (60 mi/hr)\times \frac{1}{3} hr =20 mi[/tex]
Distance of B =[tex] (45 mi/hr)\frac{1}{3} hr = 15 mi[/tex]
Draw a triangle.
By using cosine formula we can determine the distance between them
[tex]D^2 = 20^2 + 15^2 - 2\times 20\times 15\times cos(84)[/tex]
[tex]D^2 = 625 - 600 cos(84) [/tex]
[tex]D^2 = 625 - 63.2 [/tex]
[tex]D^2 = 561.8[/tex]
Thus D = 23.7 miles
Freedonia has 49 senators. Each senator is either honest or corrupt. Suppose you knowthat at least two of the Freedonian senators are honest and that, out of any threeFreedonian senators, at least one is corrupt. Based on these facts, can you determinehow many Freedonian senators are honest and how many are corrupt? if so, what is theanswer?
Answer:
There are 47 corrupt senators and 2 honest senators.
Step-by-step explanation:
Freedonia has 49 senators. Each senator is either honest or corrupt.
At least 2 of the Freedonian senators are honest and that, out of any 3 Freedonian senators, at least 1 is corrupt.
As we can see that there are no 3 senators where all of them are honest. So either there is one senator who is corrupt and 2 are honest.
Also it is given that at least two of the Freedonian senators are honest.
Hence, we can conclude there are 2 honest senators and 47 corrupt senators.
An aircraft seam requires 30 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 21% of all seams need reworking, what is the probability that a rivet is defective?
Answer:
[tex] 0.0078[/tex]
Step-by-step explanation:
To compute the probability of a rivet being defective we can do the following:
The seam won't need reworking if the 30 rivets are working as intended. Since there's a 21% chance of the seam needing reworking, we then know that there's a 79% chance of the seam not needing reworking, which means that there's a 79% chance of having the 30 rivets working as intended. Now, each rivet is either defective with a probability p, or NOT defective with a probability 1-p. Since rivets are defective independently from one another, the probability of the 30 rivets working as intended is [tex] (1-p)^{30}[/tex], and since we know this has a chance of happening of 79%, we get the equation:
[tex] 0.79=(1-p)^{30}[/tex]
Solving for p, we get:
[tex] 0.79^{1/30}=1-p[/tex]
[tex] p=1-0.79^{1/30}\approx 0.0078[/tex]
An opinion poll contacts 1101 adults and asks them, " Which political party do you think has better ideas for leading the country in the 21st century?" In all, 613 of the 1101 say, " The Democrats." The sample in this setting is
A. the 613 people who chose the Democrats.
B. the 1101 people interviewed.
C. all 235 million adults in the United States.
D. None of the above.
Answer:
B. the 1101 people interviewed.
Step-by-step explanation:
An opinion poll contacts 1101 adults and asks them, " Which political party do you think has better ideas for leading the country in the 21st century?"
The sample in this setting is the 1101 people interviewed.
Here sample space is 1101.
Answer:
B. the 1101 people interviewed.
Step-by-step explanation:
The sample is the subset of the population and it takes for making the experiment easy. Further, the sample is said to be best if it is the representation of the whole population.
Here, since opinion poll contacts all 1101 adults for knowing their opinion about political parties.
Hence the sample space is all 1101 people interviewed.
If 2^n + 1 is an odd prime for some integer n, prove that n is a power of 2. (H
Step-by-step explanation:
We will prove by contradiction. Assume that [tex]2^n + 1[/tex] is an odd prime but n is not a power of 2. Then, there exists an odd prime number p such that [tex]p\mid n[/tex]. Then, for some integer [tex]k\geq 1[/tex],
[tex]n=p\times k.[/tex]
Therefore
[tex]2^n + 1=2^{p\times k} + 1=(2^{k})^p + 1^p.[/tex]Here we will use the formula for the sum of odd powers, which states that, for [tex]a,b\in \mathbb{R}[/tex] and an odd positive number [tex]n[/tex],
[tex]a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b^2-...+b^{n-1})[/tex]
Applying this formula in 1) we obtain that
[tex]2^n + 1=2^{p\times k} + 1=(2^{k})^p + 1^p=(2^k+1)(2^{k(p-1)}-2^{k(p-2)}+...-2^{k}+1)[/tex].
Then, as [tex]2^k+1>1[/tex] we have that [tex]2^n+1[/tex] is not a prime number, which is a contradiction.
In conclusion, if [tex]2^n+1[/tex] is an odd prime, then n must be a power of 2.
Complete the following using compound future value. (Do not round intermediate calculations. Round your answers to the nearest cent.)
what is the amount
what is the interest
Time Principal Rate Compounded Amount Interest
4 years $16,900 8% Quarterly $ $
Answer:
The amount is $23200.08.
The interest is $6300.08.
Step-by-step explanation:
To find : Complete the following using compound future value ?
Solution :
The compound future value formula is given by,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where, A is the amount (future value)
P is the principal (present value) P=$16,900
r is the annual interest rate r=8%=0.08
n is the number of compounding periods per year n=4
t is the time in years t=4
Substitute the value in the formula,
[tex]A=16900(1+\frac{0.08}{4})^{4\times 4}[/tex]
[tex]A=16900(1+0.02)^{16}[/tex]
[tex]A=16900(1.02)^{16}[/tex]
[tex]A=16900\times 1.37278570509[/tex]
[tex]A=23200.078416[/tex]
Round to nearest cent 23200.078416=23200.08.
The amount is $23200.08.
The interest formula is
[tex]I=A-P[/tex]
Substitute the values,
[tex]I=23200.08-16900[/tex]
[tex]I=6300.08[/tex]
The interest is $6300.08.
To find the future value with compound interest for a principal of $16,900 at an 8% annual rate compounded quarterly over 4 years, use the compound interest formula. The future value minus the original principal gives the total compound interest, rounding the final values to the nearest cent.
Explanation:To calculate the future value with compound interest, use the formula:
Future Value = Principal × (1 + interest rate/n)n × t
Where:
Principal is the initial amount of money.n is the number of times the interest is compounded per year.t is the time the money is invested or borrowed for, in years.interest rate is the annual interest rate (decimal).For our scenario:
Principal = $16,900
Rate = 8% or 0.08 annually
Compounded Quarterly (4 times per year)
Time = 4 years
Future Value = $16,900 × (1 + 0.08/4)4 × 4
Calculate the amount within the parentheses and the exponent, and then compute the future value.
Once we have the future value, we can find the compound interest by subtracting the Principal from the Future Value:
Compound interest = Future Value - Principal
After doing the calculations, we can round the results to the nearest cent as requested for the answer.
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Give an example of either Inductive or Deductive reasoning. Try to use a "real world" example of something you might have encountered or found on the internet. Your example could involve numbers, or some other kind of scientific information. If you have trouble coming up with an example, just use "Google" for some ideas.
Answer:
See answer below
Step-by-step explanation:
In inductive reasoning we arrive to a general conclusion based on particular observations.
For example:
"My friends Peter and Mary study at XYZ University. Peter and Mary are brilliant.
Yesterday I met Joe in a party. Joe also studies at XYZ University and he happens to be brilliant, too.
I conclude that all the students of XYZ University are brilliant"
Notice that this kind of reasoning might lead to a false conclusion.
In deductive reasoning, we arrive to a particular conclusion based on general observations. So, deductive reasoning is the opposite of inductive reasoning.
An example of deductive reasoning could be the following:
"To be accepted in the XYZ University you must pass a test with a score greater than 70%.
My friend Peter studies at XYZ University, so he passed the test with a score greater than 70%"
In deductive reasoning you may arrive to a false conclusion if your general assumption is false.
Answer:
but did now am the am
Step-by-step explanation:
the scale of a map is 1 cm : 72km. What is the actual distance between two towns that are 4 cm apart on the map
What is the negation of the following: "If n is divisible by 6 then n is divisible by both 2 and 3."
A. n is divisible by 6 or n is divisible by both 2 and 3.
B. If n is divisible by both 2 and 3 then n is divisible by 6.
C. If n is divisible by 6 then n is divisible by both 2 and 3.
D. n is divisible by 6 and n is not divisible by both 2 and 3.
E. If n is not divisible by 6 then n is not divisible by both 2 and 3.
F. n is not divisible by 6 or n is divisible by both 2 and 3.
G. n is divisible by 6 and n is divisible by both 2 and 3.
H. n is not divisible by 6 and n is divisible by both 2 and 3.
I. If n is not divisible by 6 then n is divisible by both 2 and 3.
J. If n is not divisible by both 2 and 3 then n is not divisible by 6.
K. n is divisible by 6 or n is not divisible by both 2 and 3.
Answer:
D. n is divisible by 6 and n is NOT divisible by both 2 and 3.
Step-by-step explanation:
The statement we want to negate is:
"IF n is divisible by 6 THEN n is divisible by both 2 and 3"
you should think of it as having one single antecedent (the sentence that follows after the IF) and one single consequent (the sentence that follows after THEN), as:
"IF ( n is divisible by 6 )THEN ( n is divisible by both 2 and 3 )"
This kind of statements are negated by saying that the antecedent is true, but the consequent isn't true (which is kind of saying that the antecedent being true doesn't necessarily make the consequent also true).
So the negation of the original statement is just:
"(n is divisible by 6) and NOT (n is divisible by both 2 and 3)"
which in common english is just
"n is divisible by 6 and n is NOT divisible by both 2 and 3."
Answer:
hippioo
Step-by-step explanation:
hippi hipppokmkmkouse
Jemer lost his ball and decided to buy a new one. the new ball cost $300. which is three times the price of his old ball. how much did he pay for the old ball.
Answer:
The cost of the old ball was $100.
Step-by-step explanation:
The cost of the new ball = $300
The new ball has three times the price of his old ball.
So, let the price of the old ball be = x
As per situation, we get the equation:
[tex]3x=300[/tex]
Dividing both sides by 3:
[tex]\frac{3x}{3}= \frac{300}{3}[/tex]
=> x = 100
Hence, the cost of the old ball was $100.
Use the "at least once" rule to find the probabilities of the following events. Getting at least one tail when tossing nine fair coins The probability is (Type an integer or a simplified fraction.)
Answer: [tex]\dfrac{511}{512}[/tex]
Step-by-step explanation:
We know that the total number of faces on a coin [Tail, Heads] =2
The probability of getting a tail = [tex]\dfrac{1}{2}=\dfrac{1}{2}[/tex]
The probability of getting no tail = [tex]1-\dfrac{1}{2}=\dfrac{1}{2}[/tex]
The "at least once" rule says that the when a coin is tossed n times , then the probability of getting at least one tail is given by :-
[tex]\text{P(Atleast one tail)}=1-(\text{P(No tail)})^n[/tex]
Since , n=9
Then, the probability of getting at least one tail is given by :-
[tex]\text{P(Atleast one tail)}=1-(\text{P(No tail)})^9\\\\=1-(\dfrac{1}{2})^9\\\\=1-\dfrac{1}{512}\\\\=\dfrac{511}{512}[/tex]
The probability is [tex]\dfrac{511}{512}[/tex]
The probability of getting at least one tail when tossing nine fair coins is 511/512. This is computed by finding the complement of getting no tails (only heads) when flipping the coins.
Explanation:In this problem, we are looking for the probability of getting at least once a tail when tossing nine fair coins. To solve it, we use the rule of complementary probability. Rather than finding the probability for one or more tails, it's easier to find the probability of the complement, which is getting no tails (only heads). With a fair coin, the probability of getting a head on one toss is 1/2, so for nine tosses, it's (1/2)^9 = 1/512. However, this is the probability of getting no tails at all. We want the exact opposite; at least one tail. So, we subtract this probability from 1: P(at least one tail) = 1 - P(no tails) = 1 - 1/512 = 511/512.
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Customers arrive at a bank drive-up window every 6 minutes based on a Poisson distribution. Once they arrive at the teller, service time is exponentially distributed based on a rate of 5 minutes per transaction,a.What is the probability that 3 or fewer customers will arrive in one hour?b.How many customers are most likely in line (waiting) at any one point in time?c.What will be the average time waiting in the system?d.What will be the average time in the system?
Answer:
(a) 0.01029 (b) 4.167 customers (c) 0.4167 hours or 25 minutes (d) 0.5 hours or 30 minutes
Step-by-step explanation:
With an arrival time of 6 minutes, λ=10 clients/hour.
With a service time of 5 minutes per transaction, μ=12 transactions/hour.
(a) The probability of 3 or fewer customers arriving in one hour is
P(C<=3)=P(1)+P(2)+P(3)
[tex]P(X)=\lambda^{X}*e^{-\lambda} /X![/tex]
[tex]P(1)=10^{1}*e^{-10} /1!=0.00045\\P(3)=10^{3}*e^{-10} /3!=0,00227\\P(2)=10^{2}*e^{-10} /2!=0,00757\\P(x\leq3)=0.00045+0.00227+0.00757 = 0.01029[/tex]
(b) The average number of customers waiting at any point in time (Lq) can be calculated as
[tex]L_{q}=p*L=\frac{\lambda}{\mu}*\frac{\lambda}{\mu-\lambda}\\L_{q}=\frac{10}{12}*\frac{10}{12-10}\\\\L_{q}=100/24=4.167[/tex]
(c) The average time waiting in the system (Wq) can be calculated as
[tex]W_{q}=p*W=\frac{\lambda}{\mu}*\frac{1}{\mu-\lambda}\\W_{q}=(10/12)*(1/(12-10))\\W_{q}=(10/24)=0.4167[/tex]
(d) The average time in the system (W), waiting and service, can be calculated as
[tex]W=\frac{1}{\mu-\lambda}\\W=\frac{1}{12-10}=0.5[/tex]
Trig: A sector of a circle has area 25 cm2 and centralangle
0.5 radians. Find its radius and arc length.
Answer: Radius = 10 cm and Arc length = 5 cm
Step-by-step explanation:
The area of a sector with radius r and central angle [tex]\theta[/tex] (In radian) is given by :-
[tex]A=\dfrac{1}{2}r^2\theta[/tex]
Given : A sector of a circle has area [tex]25 cm^2[/tex] and central angle 0.5 radians.
Let r be the radius , then we have
[tex]25=\dfrac{1}{2}r^2(0.5)\\\\\Rightarrow\ r^2=\dfrac{2\times25}{0.5}\\\\\Rightarrow\ r^2=\dfrac{50}{0.5}=100\\\\\Rightarrow\ r=\sqrt{100}=10\ cm[/tex]
Thus, radius = 10 cm
The length of arc is given by :-
[tex]l=r\theta=10\times0.5=5\ cm[/tex]
Hence, the length of the arc = 5 cm
Final answer:
To find the radius and arc length of a sector of a circle, we use formulas related to the circumference and central angle of a circle. The radius of the sector is 10 cm and the arc length is 5 cm.
Explanation:
To find the radius and arc length of a sector of a circle, we need to use the formulas related to the circumference and central angle of a circle. The formula for the area of a sector is given by:
Area = (θ/2) * r^2
where θ is the central angle and r is the radius of the circle. We are given that the area of the sector is 25 cm^2 and the central angle is 0.5 radians. Setting up this equation, we get:
25 = (0.5/2) * r^2
Simplifying, we find:
r^2 = 100
Taking the square root of both sides, we find:
r = 10 cm
To find the arc length, we use the formula:
Arc Length = θ * r
Substituting the values, we find:
Arc Length = 0.5 * 10 = 5 cm
Begin by clearly stating the problem; you can copy this from the problem set file. Show how you solved the problem step by step, including any formulas or equations that you used. Finally, state your final answer in a complete sentence, and make sure that you include the correct units with you answer.
1.)Albert borrowed $19,100 for 4 years. The simple interest is $9932.00. Find the rate.
Answer: 13%
Step-by-step explanation:
We know that the formula to find the simple interest :
[tex]I=Prt[/tex], where P is the principal amount , r is rate (in decimal )and t is the time period (in years).
Given : Albert borrowed $19,100 for 4 years. The simple interest is $9932.00. Find the rate.
i.e. P = $19,100 and t= 4 years and I = $9932.00
Now, Substitute all the values in the formula , we get
[tex]9932=(19100)r(4)\\\\\Rightarrow\ r=\dfrac{9932}{19100\times4}\\\\\Rightarrow\ r=0.13\ \ \ \text{[On simplifying]}[/tex]
In percent, [tex]r=0.13\times100\%=13\%[/tex]
Hence, the rate of interest = 13%
If f(x)=8x then what is the area enclosed by the graph of the function, the horizontal axis, and vertical lines at x=2 and x=6
Answer:
[tex]A=128[/tex]
Step-by-step explanation:
First of all we need to graph f(x)=8x, (First picture)
Now we have to calculate the area enclosed by the graph of the function, the horizontal axis, and vertical lines at [tex]x_{1}=2[/tex] and [tex]x_{2}=6[/tex] ,
The area that we have to calculate is in pink (second picture).
The function is positive and the domain is [tex][2,6][/tex] then we can calculate the area with this formula:
[tex]A=\int\limits^b_a {f(x)} \, dx[/tex],
In this case [tex]b=x_{2} , a=x_{1}[/tex]
[tex]A=\int\limits^6_2 {8x} \, dx = 8\int\limits^6_2 {x} \, dx[/tex]
The result of the integral is,
[tex]A=8\frac{x^{2}}{2}[/tex], but the integral is defined in [2,6] so we have to apply Barrow's rule,
Barrow's rule:
If f is continuous in [a,b] and F is a primitive of f in [a,b], then:
[tex]\int\limits^b_a {f(x)} \, dx =F(b)-F(a)[/tex]
Applying Barrow's rule the result is:
[tex]A=8.\frac{6^{2} }{2}-8.\frac{2^{2} }{2}[/tex]
[tex]A=8.\frac{36}{2} -8.\frac{4}{2}[/tex]
[tex]A=144-16[/tex]
[tex]A=128[/tex]
if one pie is shared equally by 6 people, then each person will get
what fraction of the pie?
Answer: Each person will take [tex]\dfrac{1}{6}[/tex] of the pie.
Step-by-step explanation:
Given : One pie is shared equally by 6 people.
The total number of persons = 6
Now, the fraction of the whole pie each person will take :-
[tex]\dfrac{\text{Number of pie}}{\text{total persons}}\\\\=\dfrac{1}{6}[/tex]
Therefore, the fraction of the whole pie each person will take= [tex]\dfrac{1}{6}[/tex]