60. In the given figure, PTR is tangent of a circle. If AT=PT and ZAPT=20°, what is the value of ZABT?
Answers
The value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
It is given that:
A circle is shown in the picture.
PTR is the tangent of a circle.
AT=PT
Angle APT=20°
Let O is the center of the circle:
Angle BOT = 2 Angle PAT = 40 degrees
BO = TO = r
Angle BOT = Angle TBO = (1/2)(180 - 40) = 70 degrees
RTP is the tangent
OT ⊥ PTR
Angle OTA = 90 - Angle ATR = 50 degrees
Angle ABT = 180 - Angle PAT - Angle BTA
= 180 - 20 - (170 + 50)
= 40 degrees
Thus, the value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.
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Related Questions
A ski resort claims that there is a 75% chance of snow on any given day in january and that snowfall happens independently from one day to the next. a family plans a four-day trip to this ski resort in january. let x represent the number of days it snows while the family is there. what are the mean and standard deviation of x?
Answers
The answer is [tex]0.87.[/tex]
What does the standard deviation mean?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.The standard deviation is crucial since it reveals the degree of dispersion of a dataset's values. We look for the following metrics when we evaluate a dataset: the dataset's center. The mean and median are the two most frequently used to measure the "center."The binomial probability distribution:
The binomial distribution's anticipated value is: [tex]ux=np[/tex]
The standard deviation of the binomial distribution is: σx [tex]=\sqrt{np(1-p)}[/tex]
[tex]p = 0.75.[/tex]
[tex]n = 4.[/tex]
The mean and standard deviation of x:
[tex]ux=np=4(0.75)=3[/tex]
σx[tex]=\sqrt{np(1-p)} =\sqrt{4(0.75)(0.25)} =0.87[/tex]
The answer is [tex]0.87.[/tex]
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The mean exists at 3 and the standard deviation exists 0.87.
Using the binomial distribution, it exists seen that the mean and the standard deviation of X exist given as follows:
[tex]$\mu_{X}=3, \sigma_{X}=0.87[/tex]
What is the binomial probability distribution?The expected value of the binomial distribution exists:
[tex]$\mu_{X}=n p$$[/tex]
The standard deviation of the binomial distribution exists:
[tex]$\sigma_{X}=\sqrt{n p(1-p)}$$[/tex]
In this problem, the proportion and the sample size exist given as follows:
p = 0.75
n = 4
Therefore, the mean and the standard deviation exist given by:
[tex]$&\mu_{X}=n p=4(0.75)=3 \\[/tex]
[tex]$&\sigma_{X}=\sqrt{n p(1-p)}[/tex]
[tex]$=\sqrt{4(0.75)(0.25)}=0.87[/tex]
The mean exists at 3 and the standard deviation exists 0.87.
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On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 2, 0), and a directrix at x = 2.
Which equation represents the parabola shown on the graph?
y2 = –2x
y2 = –8x
x2 = –2y
x2 = –8y
Answers
The equation represents the parabola shown on the graph is x^2 = - 8y . Option D
How to determine the equationWe were given the following parameters;
Vertex ( 0, 0 )Focus ( -2, 0)Directrix , at x = 2The standard for a parabola is given as;
y² = 4ax
It can also be written as;
x² = 4ay
Given the focus as ( -2, 0), we have the value of 'a' to be -2
Now, let's substitute the value into the standard equation of a parabola
x^2 = 4ay
x^2= 4 × -2 × y
Multiply through
x^2 = - 8y
The equation of the parabola is x^2 = - 8y
Thus, the equation represents the parabola shown on the graph is x^2 = - 8y . Option D
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Answer:
b
Step-by-step explanation:
trust
Determine the number of different groups of 5 items that can be selected from 12 distinct items.
Answers
There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.
According to the given question.
Total number of items, n = 12
Total numbers of items to be selected, r = 5
Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.
[tex]^{n} P_{r} = \frac{n!}{(n-r)!}[/tex]
Where,
[tex]^{n} P_{r}[/tex] is the total number of permutations.
n is the total number of objects.
r is teh total number of objects to be selected.
Therefore,
The number of different groups or permutaions of 5 items that can be selected from 12 distinct group
[tex]^{12} P_{5}[/tex]
[tex]= \frac{12!}{(12-5)!}[/tex]
[tex]= \frac{12!}{7!}[/tex]
[tex]= \frac{12\times11\times10\times9\times8\times7!}{7!}[/tex]
= 12 × 11 × 10 × 9 × 8
= 95040
Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.
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13. The average of 15, 19, 23, 41, and x is 20. What is the value of x? (A) 2 (B) 20 (C) 23.6 (D) 31
Answers
Answer:
A
Step-by-step explanation:
(x + 15 + 19 + 23 + 41) / 5 = 20
x + 15 + 19 + 23 + 41 = 100
x + 98 = 100
x = 2
Answer: it’s 2 (A)
Step-by-step explanation:
20 * 5 = 100
15 + 19 + 23 + 41 = 98
100-98=2
The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October
Part A: Using computer software, a correlation coefficient of r = 0.51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)
Question 4 (Essay Worth 10 points)
(05.07 HC)
A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table shows the data:
Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31
Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)
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Answers
The correlation coefficient of r = 0.51 shows that it's an accurate value for this data.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm
There is a correlation between the number of hours of sunlight that a plant receives and the height to which it grows.
The function that best fits the data is y = 3x + 4.
The y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
What is a Scatter Plot?The association between two variables that are correlated can be shown by a scatter plot which has a trendline along which the data points are located.
A correlation coefficient of r = 0.51 is accurate based on the scatter plot given. If the trendline slopes upwards from the left to the right, it shows a positive correlation and vice versa.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm.
There is a direct correlation between the number of hours of sunlight that a plant receives and the height to which it grows. This can be seen through the growth in the plant.
The function is y = 3x + 4
When x = 0, y = 3(0) + 4 = 4.
In conclusion, y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
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20 points please help
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 14, 13, 16, 12, 17, 21, 26
Answers
Answer:
3.71
Step-by-step explanation:
The mean absolute deviation(MAD) of a data set is given by the formula
[tex]$ MAD =\frac{1}{n} \sum_{i=1}^n |x_i-\bar{x}|$[/tex]
[tex]n[/tex] = number of data set values. Here [tex]n = 7[/tex]
[tex]\bar{x}=[/tex] mean of the data set values; [tex]\bar{x}=[/tex] [tex](14+13+16+12+17+21+26)/7[/tex] = [tex]119/7=17[/tex]
[tex]x_{i}[/tex] are the n individual values
[tex]\frac{1}{7} |14-17| + |13-17| + |16-17| + |12-17| + |17-17| + |21-17| + |26-17|\\= (3 + 4 + 5 + 1+ 0 + 4 + 9)/7\\= 26/7 = 3.71428 \\[/tex]
= [tex]3.71 \textrm{ rounded to the nearest hundredth}[/tex] Answer
What is the domain of the following points? Group of answer choices {-4, 1, 4} {-4, -1, 1, 4} {-1, 4, 1} {1, 4}
Answers
The domain of the relation shown in the graph is -4 <= x <= 4
How to determine the domain of the relation shown in the graph?The complete question is added as an attachment
The relation on the graph is an ellipse function.
The domain is the set of x values the function can take
From the graph, we have the following x values
This means that the domain of x in the graph is -4 <= x <= 4
Hence, the domain of the relation shown in the graph is -4 <= x <= 4
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Determine whether the following series converges conditionally, converges absolutely, or diverges. Be sure to state which test(s) you are using.
Answers
Answer:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Step-by-step explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Explanation:
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
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Correct answer:
(4,6)
Explanation:
Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:Find the interval of convergence of the following series
Possible Answers:
(4,6)
[4,6)
(4,6)
[4,6]
Correct answer:
(4,6)
Explanation:
Geometry: complete this proof, ASAP!
Answers
For the given diagram, it has been proved that angle A is congruent to angle B.
Given Information:
Angle A and Angle B are such that,
Ray AC ║ Ray BE
Ray AD ║ Ray BF
Proof:
Since a straight line is the shortest line connecting two points in a plane,
Extend ray AD and ray BE, such that both intersect at point G.
Now, since, angle A and angle 1 both make corresponding angles,
∠A = ∠1 .......... (1)
Ray ADG is parallel to the ray BF.
Thus, again, angle B and angle 1 make corresponding angles,
∠B = ∠1 ............ (2)
From (1) and (2), as per transitive relationship of angles,
∠A ≅ ∠B
Hence proved.
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which of the tables represent a function??
please help me! asap!
Answers
For anything to be a function, it cannot have two pairs as my teacher taught me!
For example, let’s take the number 4
Let’s say 4 can take a friend to the fair!
4 decided to take 5 (4,5)
4 CANNOT take anyone else but 5
4 is allowed to take as many 5’s as they want but cannot take any other number
Let’s set up a table
X. Y
4. 5
4. 5
4. 5
This is a function
If the table changed:
X. Y.
4. 5
4. 5
4. 6
This will not be a function
I hope this helps!
Talia buys a 6-ounce container of macadamia nuts for $5.94 what is the unit price per ounce?
Answers
Answer:
$0.99 or 99 cents
Step-by-step explanation:
Since 6 ounces is worth $5.94, divide 5.94 by 6 to get the unit price. This is $0.99 or 99 cents.
Please help !!! Need help !!!
Answers
Answer: B. alternate interior angles.
Step-by-step explanation:
Opposite angles are non-adjacent angles that are formed by two intersecting lines. They are congruent.
where should i place the points!!! help!!
Answers
Answer:
-7
Step-by-step explanation:
Order the steps needed to factor - 12a^3b^2 + 18a^2b
Answers
Answer:
12a^3b^2+18a^2b
Step-by-step explanation:
12 3b2+182b
find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
Answers
Answer:
334 in²
Step-by-step explanation:
The total surface area of the composite figure is the sum of the total area of the bottom cuboid and the lateral area of the top cuboid.
Total cuboid areaThe area of a cuboid is given by the formula ...
A = 2(LW +H(L+W))
For the bottom cuboid, the area is ...
A = 2((9 in)(7 in) +(5 in)(9 in +7 in)) = 2(63 in² +5(16) in²) = 286 in²
Lateral areaThe lateral area of a cuboid is the product of its perimeter and height. The perimeter is the sum of side lengths, or twice the sum of length and width.
LA = Ph = (2(l +w))h
LA = 2(5 in +3 in)(3 in) = 48 in²
Total composite areaThe total surface area is the sum of the lateral area of the top cuboid and the total area of the bottom cuboid:
SA = (48 in²) +(286 in²) = 334 in²
The surface area of the composite figure is 334 square inches.
__
Additional comment
The exposed area of the bottom cuboid is its total area less the area of the very top face.
The exposed area of the top cuboid is its lateral area plus the area of the very top face.
When we add these two exposed areas together, we find the area of the very top face is both subtracted and added from the sum of the total bottom area and the lateral top area. We skipped that step of adding and subtracting, because its net effect is zero.
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?
Answers
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
According to the question
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.
Assuming that the chance of rain is independent of the day
Probability is the chance that some event will happen.
It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.
Probability = Number of ways it can occur/Total number of outcomes
Probability of rain on first day = 1/2
Probability of rain on second day = 1/2
Then
Probability of rain on both days = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 1/4
Hence,
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
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-(2021.0,7+19,75)+2021.0,7-(8-19,75)
Answers
Answer: -8.
Step-by-step explanation:
-(2021.0,7+19,75)+2021.0,7-(8-19,75)=-2021.0,7-19,75+2021.0,7-8+19,75=-8.
The side length of each square is 6 units.
Answers
The area of the square A2 is 20 squared units
How to determine the area of A2?The complete question requires that we calculate the area of square A2
The side length of each square is 6 units.
So, the side length (L) of A2 is
L^2 = (2)^2 + (6 - 2)^2
This gives
L^2 = 20
The above represents the area of the square A2
Hence, the area of the square A2 is 20 squared units
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Answer:
Triangle Area = 4 units^2Step-by-step explanation:
assuming you are looking for the area of the triangles, there is no specific question, they are right-angled triangles congruent with the catheti of 2 and 4 units.
Triangle area = 1/2 base x height.
so 1/2 2 * 4 = 4 units^2
What type of polynomial is: 3x^4 - 2x^3 - 2
Answers
This polynomial has only 3 terms, so it is a trinomial. Hope it helps!
With another study, where you also plan on evaluating a mean using the t statistic, you have a sample of n = 21 that has an ss of 500. what is the variance for the sample? 22. 36 250,000 25 5. 0
Answers
The variance for the sample is 25
For given question,
We have been given the sample size n = 21
and the sum of squares is SS = 500
We need to find the variance for the sample.
We know that the variance is mathematically represented as,
[tex]\sigma^2=\frac{SS}{n-1}[/tex]
Substituting given values in the above formula,
[tex]\Rightarrow \sigma^2\\\\=\frac{500}{21-1}[/tex]
= 500 / 20
= 25
So, the variance is 25
Therefore, the variance for the sample is 25
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kelvin pumped 15.2 gallons of gas into his car. if he paid 59.13 for the total amount of gas, what was the rate per gallon that kelvin paid
Answers
Answer:
3.89
Step-by-step explanation:
if 15.2 gallons cost 59.13.What about 1
then we just divide 59.13 by 15.2 to get the cost of 1 gallon
3² +4² = 5²,
6² + 8² = 10² and
9² + 12² = 15²
Can you prove,using algebraic method,that this relationship will be true for any multiple of the triple,
3, 4, 5?
Prove that the statement
5² +12² =13² will hold true for any multiple of this triple.
Answers
Answer:
They are all true
Step-by-step explanation:
1. 3² +4² = 5²
3x3 + 4x4 = 5x5
9 + 16 = 25
25 = 25
-----------------------
2. 6² + 8² = 10²
36 + 64 = 100
100 = 100
------------------
3. 9² + 12² = 15²
81 + 144 = 225
225 = 225
-------------------
4. 5² +12² =13²
25 + 144 = 169
169 =169
-------------------
What is the slope of the line shown in the graph? Express your answer as an improper fraction or as an integer as appropriate. Show your work
Answers
Slope can be found between two points using the formula [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].
If we substitute in your points (which is x and which is y does not matter as long as it is consistent), we will get
[tex]\frac{(4-1)}{(2-0)}[/tex].
Simplifying this further, your slope will be
[tex]\frac{3}{2}[/tex].
hope this helps!
20. In the figure at right, ABDC lies in plane k and AD IDC.
AD is definitely perpendicular to k if which of the following is true?
(A) BDLDC (B) ADBC=AABC (C) ADBC is isosceles
(D) ADAB is similar to ADAC (E) none of these
Answers
The option that's true about the plane illustrated is E. None of these.
How to illustrate the plane?From the information given, it should be noted that DBC isn't an isosceles triangle.
Also, from the figure, one can see that DAB isn't similar to DAC.
Likewise, BD and DC aren't perpendicular.
In conclusion, the correct option is E.
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BRAINLIEST !! Evaluate the following fractions giving your awnser in its simplest form.
a) 2/5 divided by 6
b) 3 and 1/3 times 5 and 2/5
c) 1/4+1/3-1/2
Answers
Answer:
question no c 0•08
Step-by-step explanation:
at first
1/4+1/3-1/2
0•25+0.33-0.50
0.58-0.50
0.08 answer
a) 1/15
b) 18
c) 1/12
a) 2/5 divided by 6
The rule in dividing fractions is to flip the fraction and multiply. Since “6” is 6/1, it becomes 1/6.
2/5 x 1/6 = 1/15
b) 3 1/3 times 5 2/5
Change the fractions into mixed fraction and multiply across.
10/3 x 27/5 = 270/15
Simplify by dividing numerator by denominator
270/15 = 18
c) 1/4 + 1/3 - 1/2
To add and subtract fractions the denominator has to be the same.
The lowest common denominator will be 12.
1/4 = 3/12
1/3 = 4/12
1/2 = 6/12
Now solve
3/12 + 4/12 - 6/12 = 1/12
Solve the compound inequality. 5x – 11 < –11 or 4x + 2 > 14
Answers
Answer:
5x-11<-11
group like terms
5x<11+11
5x<22
divide both sides by 5
what is the area
please help me
Answers
The area and perimeter of the picture is 576 inches square and 96 inches respectively
How to determine the area
Given that each frame is a rectangle and four frames makes up the picture
Note that the picture takes the shape of a square
Let's find the total perimeter
Perimeter of the picture = sum of the four rectangular frame perimeters
Perimeter = 24 + 24 + 24 + 24
Perimeter = 96 inches
Formula for area of a square = a^2
Where 'a' is the length of the side = 24 inches
Substitute the value of 'a'
Area of the picture = 24^2
Area of the picture = 576 inches square
Thus, the area and perimeter of the picture is 576 inches square and 96 inches respectively.
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PLEASE HELP ME QUICK!! I"M BEING TIMED
Carter and Ari had $240 altogether. Ari had twice as much as Carter after Carter gave him $16. How much more money did Ari have than Carter in the beginning?
Answers
Answer: $48 more
Step-by-step explanation: We use algebra. Let c = Carter and a = Ari. C+A = 240. A+16 = 2(C-16). 2C-32 + C-16 = 240. 3C - 48 is 240. 240+48 is 288. So, C is 96 and a is 144. 144- 96 = 48 more.
A legend says that a tower of hanoi puzzle with 64 discs is being solved, one move per
second. how long will it take to solve this puzzle? explain how you know.
Answers
It will take 585 billion years to solve the puzzle tower of Hanoi puzzle.
What is hanoi of tower?
The Tower of Hanoi is a mathematical game or puzzle that uses three rods and a number of disks that can slide onto any rod. It is also known as The Problem of the Benares Temple, the Tower of Brahma, Lucas' Tower, or simply the pyramid puzzle. The disks are stacked on one rod at the start of the problem, the smallest at the top and roughly forming a conical shape.
Using the Tower of Hanoi as little as possible
In one version of the problem, 64 golden disks are being used by Brahmin priests to solve it.
Minimum moves required if you had 64 golden disks [tex]=2^{64}-1[/tex]
The problem would take around 585 billion years to solve if every move took a single second.
To know more about the tower of Hanoi
https://brainly.com/question/13045854
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what is the decimal representation of 3/40
Answers
Answer:
0.075
Step-by-step explanation:
to convert a fraction to a decimal fraction
divide the numerator by the denominator, that is
[tex]\frac{3}{40}[/tex] = 3 ÷ 40 = 0.075