Answer:
36.98 inches each
Step-by-step explanation:
He uses 857.77 inches of fabric on headbands for 29 players and 2 coaches
29 players + 2 couches = 31 people
Inches per person = 857.77 inches / 31 people
= 27.67 inches for headbands
He also uses 269.99 inches of fabric on wristbands for just the players.
Inches per person = 269.99 inches / 29 players
= 9.31 inches for wristband
How much fabric was used on a headband and wristband for each player = 27.67 inches for headbands + 9.31 inches for wristband
= 36.98 inches each
The amount of rainfall in January in a certain city is normally distributed with a mean of 3.3 inches and a standard deviation of 0.5 inches. Find the value of the 25th percentile, rounded to the nearest tenth.A. 0.8B. 3.0C. 3.6D. 3.1
Answer:
\(B\)Explanation:
Here, we want to find the value of the 25th percentile
Mathematically:
The 25th percentile represents a probability of p = 0.25
The z-score of this value is -0.68 (it is left of the mean)
To get z-score, we use the following formula:
\(\begin{gathered} z-\text{score = }\frac{x-\mu}{\sigma} \\ \mu\text{ = mean = 3.3} \\ \sigma=\text{ standard deviation = 0.5} \end{gathered}\)Substituting these values, we have it that:
\(\begin{gathered} -0.68\text{ = }\frac{x-3.3}{0.5} \\ 0.5(-0.68)\text{ = x-3.3} \\ -0.34\text{ = x-3.3} \\ x\text{ = 3.3-0.34} \\ x\text{ = 2.96} \\ x\text{ = 3.0 (to the nearest tenth)} \end{gathered}\)A painter is placing a ladder to reach the third story window, which is 22 feet above the ground and makes an angle with the ground of 80°.
How far out from the building does the base of the ladder need to be positioned? Round your answer to the nearest tenth.
The base of the ladder needs to be positioned
feet out from the building.
Step-by-step explanation:
okitnayohahahanagbobo kayo amin apay afda t oki u aya boto aso ah t adda kanya y
what is the sum?
\( \frac{2}{ {x}^{2} } + \frac{4}{ {x}^{2} } \)
Answer:
6/x^2
Step-by-step explanation:
Simplify the following:
2/x^2 + 4/x^2
2/x^2 + 4/x^2 = (2 + 4)/x^2:
(2 + 4)/x^2
2 + 4 = 6:
Answer: 6/x^2
Answer:
6/x²
Step-by-step explanation:
\(\frac{2}{x^{2} } + \frac{4}{x^{2} } \\\\\)
= (2+4) / x²
= 6/x²
11. Engineering The maximum load for a certain elevator is 2000 pounds. The total
weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs
243 pounds enters the elevator with a crate of weight w. Write, solve, and graph an
inequality to show the values of w that will not exceed the weight limit of the elevator.
The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.
What is inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.An inequality is a mathematical relationship between two expressions and is represented using one of the following -≤ : less than or equal to
≥ : greater than or equal to
< : less than
> : greater than
≠ : not equal to
Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].
We can write the inequality as follows -1400 + 243 + w ≤ 2000
w + 1643 ≤ 2000
Solving the inequality, we get -w + 1643 ≤ 2000
w ≤ 2000 - 1643
w ≤ 357
Refer to the graph attached.Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.
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how many 4-digit positive intergers have four different digits where the leading digit is not zero, the interger is amultiple of 5 and 5 is the largest digit
The 4-digit positive integers have four different digits where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit is 108.
\(5*4*3*1+4*4*3*1=60+28=108\)
Positive integers are the numbers we use to depend: 1,2, 3,4, 1 , 2, three, four, and so forth. Numbers with a fractional component not identical to zero and poor numbers are excluded from a fixed of high-quality integers. The operations of addition, subtraction, multiplication, and division can be finished with tremendous integers.
Positive integers are definitely your counting numbers. wonderful integers are in reality a part of a larger institution of numbers referred to as integers. Integers are all of the whole numbers, each advantageous and poor. by complete numbers, we imply numbers without fractions or decimals.
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We make four cases based on where the multiple of the 5 digits (0 or5) is. The number has to end with either 5 or 0 since it's a multiple of5. In all but the last case, 5 and 0 are used at the end and in another spot that separates the cases.
Case 1: The first digit can't be 0 so it must be 5. There are 4.3 to choose the middle two digits. After that, the last digit has to be 0, so there are a total of 1.4.3.1=12 numbers.
Case 2: The second digit can be 5, leaving 2 choices. The first and third numbers can be chosen in 4.3 ways, like last time. The last digit has to be 0 or 5, but not the one we already used. There are a total of 4.2.3.1=24 numbers.
Case 3: There are the same choices, but the digits 0 and 5 are at the last and second-to-last spots. So there are 4.2.3.1 =24 numbers again.
Case 4: There are 4.3.2 ways to choose the first three numbers. There has to be a 5 in the number because the largest digit is 5. Coincidentally, there are 4.2.3.1 numbers again.
There are a total of 12 + 24.3= (D)84 numbers.
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A machine depreciates by 1/4 of its value each year. If it cost $50,000 new,
what is its value after 8 years?
Step-by-step explanation:
The price of machine=$50000
depreciates rate (R )=1/4×100%
=25%
Use the transitive property of equality to finish the equation.
10x8y + 3 = 2x and 9y = 2x
So: 9y =
Answer:
Step-by-step explanation:
The transitive property of equality says--in very informal terms--if thing 1 = thing 2 and thing 2 = thing 3, then thing 1 = thing 3. See how thing 2 appears twice? That's a "spoiler alert" for this question.
So, what are thing 1, thing 2, and thing 3?
Take a look at how the answer space begins: 9y. That must be thing 1 because the conclusion of the transitive property is thing 1 = ...
Now, what is mentioned twice? 2x. That must be thing 2.
The remaining expression is thing 3: 10x - 8y + 3.
So it goes like this:
9y = 2x
2x = 10x - 8y + 3
Therefore, 9y = 10x - 8y + 3
HELP WILL MARK BRAINLIEST
Answer:
3*3*3-1*1
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
3x3=9
1x2=2
so 9-2=7
ind the limit of the following sequence or determine that the sequence diverges. {In (n° +8) - In (6n° +17n) Select the correct choice below and fill in any answer boxes to complete the choice. O A. The limit of the sequence is O B. The sequence diverges. (Type an exact answer.)
The limit of the sequence exists, and it's equal to ln(1/23). Therefore, the sequence converges.
The sequence given is {ln(n + 8) - ln(6n + 17n)}, analyse the given sequence and determine if it converges or diverges.
To find the limit of this sequence, we can first simplify it by using the properties of logarithms.
Specifically, we'll use the property ln(a) - ln(b) = ln(a/b). Applying this property, the sequence becomes:
{ln[(n + 8)/(6n + 17n)]}.
Now we can further simplify the sequence as:
{ln[(n + 8)/(23n)]}.
To determine if the sequence converges or diverges, we'll find the limit as n approaches infinity:
lim (n→∞) ln[(n + 8)/(23n)].
To find this limit, we can analyze the argument inside the logarithm:
lim (n→∞) (n + 8)/(23n).
To find this limit, we can divide both the numerator and denominator by n:
lim (n→∞) [(n/n) + (8/n)] / [(23n/n)] = lim (n→∞) [1 + (8/n)] / [23].
As n approaches infinity, the term (8/n) approaches 0:
lim (n→∞) [1 + 0] / [23] = 1/23.
Now, we can rewrite the original limit:
lim (n→∞) ln[(n + 8)/(23n)] = ln(1/23).
The limit exists, and it's equal to ln(1/23). Therefore, the sequence converges, and the limit of the sequence is ln(1/23).
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A rectangular prism has a volume of 840 cubic inches. The height of the prism is 6 inches and the width
iS 10 inches. Find the length of the prism and explain how you found it.?
Answer:50400cm2
Step-by-step explanation:lxWxH
Answer:
The length of the prism can be found by using the formula for volume of a rectangular prism, which is: V = lwh. Rearranging the formula to solve for l, the length, we get l = V / (wh). In this case, V is 840, w is 10, and h is 6. Plugging these values into the equation, we get l = 840 / (10 * 6) = 14 inches. Therefore, the length of the rectangular prism is 14 inches.
Step-by-step explanation:
The length of the prism can be found by using the formula for volume of a rectangular prism, which is: V = lwh. Rearranging the formula to solve for l, the length, we get l = V / (wh). In this case, V is 840, w is 10, and h is 6. Plugging these values into the equation, we get l = 840 / (10 * 6) = 14 inches. Therefore, the length of the rectangular prism is 14 inches.
the variables y and x have a proportional relatinship and y=9 when x=2 what is the value of y when x=30
The value of y for proportional relationship when x = 30 is y = 135.
What is proportional relationship?Relationships among two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relation, one variable is consistently equal to the other's constant value.
A "constant of proportionality" is the name of this constant.
the importance of proportional relationship are-
Students' grasp of numerous areas in science and maths depends on their ability to use ratios and proportions. They play a crucial role in the development of slopes, uniform rate of change and other concepts and abilities that are essential to understanding and mastering algebra.Calculation the for the value of y.
According to the question,
The variables y and x have a proportional relationship.
Where, y=9 when x=2
Thus,
y/x = 9/2
Cross multiplying the above result;
2y = 9x
The value of y when x = 30.
2y = 9×30
2y = 270
y = 135
Therefore, the value of y when x=30 is 135.
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The probability that you will win a prize in a carnival game is about 1/7. During the last nine attempts, you have failed to win. you decide to give it one last shot. Assuming the outcomes are independent from game to game, the probability is what?
The probability of winning on the last attempt is approximately 0.3762 or 37.62%.
The probability of winning a prize in a carnival game is provided as 1/7. This means that in any single attempt, the probability of winning is 1/7 and the probability of losing is 6/7.
Since the outcomes of the carnival games are assumed to be independent from game to game, the probability of losing in each attempt remains the same.
If you have failed to win in the last nine attempts, the probability of losing in each of those attempts is (6/7) multiplied by itself nine times:
Probability of losing in 9 attempts = (6/7)^9
To find the probability of winning on the tenth attempt, we subtract the probability of losing in nine attempts from 1:
Probability of winning on the tenth attempt = 1 - (6/7)^9
Calculating this value, we find:
Probability of winning on the tenth attempt = 1 - (6/7)^9 ≈ 0.3762
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Consider a biased coin for which a head is twice as likely to occur as a tail. Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin. Find the probability mass function of W.
The probability mass function of W is P(W=-3) = 1/27, P(W=-1) = 6/27, P(W=1) = 12/27, and P(W=3) = 8/27.
Let us consider the possible outcomes of three tosses of the biased coin. There are a total of 8 possible outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT.
Since a head is twice as likely to occur as a tail, the probability of getting a head is 2/3 and the probability of getting a tail is 1/3.
Let W be a random variable giving the number of heads minus the number of tails in three tosses of the coin. Then, W can take on any value between -3 and 3.
To find the probability mass function (PMF) of W, we need to calculate the probability of each possible outcome. When all three coins come up heads (HHH), W = 3 - 0 = 3. The probability of this outcome is:
P(HHH) = (2/3)^3 = 8/27
When two coins come up heads and one comes up tails (HHT, HTH, THH), W = 2 - 1 = 1. The probability of each of these outcomes is:
P(HHT) = (2/3)^2 × (1/3) = 4/27
P(HTH) = (2/3)^2 × (1/3) = 4/27
P(THH) = (2/3)^2 × (1/3) = 4/27
So, P(W=1) = P(HHT) + P(HTH) + P(THH) = 12/27
When one coin comes up heads and two come up tails (HTT, THT, TTH), W = 1 - 2 = -1. The probability of each of these outcomes is:
P(HTT) = (2/3) × (1/3)^2 = 2/27
P(THT) = (2/3) × (1/3)^2 = 2/27
P(TTH) = (2/3) × (1/3)^2 = 2/27
So, P(W=-1) = P(HTT) + P(THT) + P(TTH) = 6/27
When all three coins come up tails (TTT), W = 0 - 3 = -3. The probability of this outcome is:
P(TTT) = (1/3)^3 = 1/27
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is -0.625 less than -2/3
Answer:
No, its more
Step-by-step explanation:
-2/3 is -0.6666667
-0.625 is greater than -0.666667
write a for loop that prints the integers 0 through 39, each value on a separate line.
In programming, a loop is a control structure that allows us to execute a block of code repeatedly. A for loop is a type of loop that is commonly used when we need to repeat a set of instructions for a specific number of times.
In this case, we want to print the integers 0 through 39, each value on a separate line.
Here's an example of a for loop in Python that accomplishes this:
for i in range(40):
print(i)
In this loop, the variable `i` takes on the values 0 through 39, one at a time, on each iteration of the loop. The range(40) function generates a sequence of integers from 0 to 39, which is used to control the loop.
The print() function outputs the value of `i` to the console on each iteration, followed by a newline character which creates a new line for each value.
To break this down further, the 'for' keyword initiates the loop and the `in` keyword specifies the range of values for the loop. The `range()` function generates a sequence of integers starting at 0 and ending at 39.
The `print()` function outputs each value to the console followed by a newline character which creates a new line for each value. This loop will execute a total of 40 times, printing each value on a separate line.
In summary, the for loop is a powerful and flexible tool in programming that allows us to automate repetitive tasks. In this example, we used a for loop to print the integers 0 through 39, each on a separate line, in a concise and efficient manner.
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Nicky is making cookies. She needs to add 1 1/2 teaspoons of baking soda, but she can only fined 1/4 teaspoons measuring spoon. How many 1/4 teaspoons measures should she use.
Answer:
6
Step-by-step explanation:
1 and 1/2 is equal to 1 and 2/4, or 6/4. This means that it would take 6 teaspoons to add 1 1/2 teaspoons of baking soda. hope this helps!
Based on the 99% confidence interval, (â€"0.43, â€"0.02), is there convincing evidence of a difference in the proportions of sales that are SUVs for the two stores?
a. There is convincing evidence because the entire interval is below 0.
b. There is convincing evidence because the two sample proportions are different.
c. There is not convincing evidence because another confidence interval that uses a higher level of confidence might contain 0.
d. There is not convincing evidence because two different sample sizes were used. In order to determine a difference, the same number of sale records should be selected from each population.
The correct choice is c. There is not convincing evidence because another confidence interval that uses a higher level of confidence might contain 0.
In hypothesis testing, when the confidence interval includes the value of interest (in this case, 0), it suggests that there may not be a significant difference between the proportions being compared. The confidence interval (-0.43, -0.02) contains the value 0, indicating that the difference in proportions may not be statistically significant.
Choosing a higher level of confidence would result in a wider confidence interval, making it more likely to include the value 0. Therefore, the evidence is not convincing enough to conclude a significant difference in the proportions of sales that are SUVs for the two stores.
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assume the average speed on the 405 freeway is 42 mph and is normally distributed with a standard deviation of 15 mph. what is the probability that someone is driving slower than 20 mph?
The probability that someone is driving slower than 20 mph on the 405 freeway is approximately 7.08%.
We are given that the average speed on the 405 freeway is 42 mph and is normally distributed with a standard deviation of 15 mph.
To solve this problem, we need to use the standard normal distribution since we are given the mean and standard deviation of the speed on the 405 freeway.
We know that
\(Z=\frac{X-\mu}{\sigma}\)
Here, X = 20
\(\mu=42\)
\(\sigma=15\)
Z=(20-42)/15
Z=-22/15
Z=-1.47
Using a standard normal distribution table
P(Z<-1.47)=0.0708
or 7.08%
Therefore, the probability that someone is driving slower than 20 mph on the 405 freeway is approximately 0.0708 or 7.08%.
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On the SAT exam, a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the time allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes. What are the appropriate hypotheses?
H0: μ = 23.5 versus Ha: μ < 23.5, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam
H0: μ = 23.5 versus Ha: μ > 23.5, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam
H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam
H0: μ = 25 versus Ha: μ > 25, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam
Answer:
H0: μ = 23.5 versus Ha: μ < 23.5, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam
The hypothesis is H0: μ = 25 versus Ha: μ < 25, So option (C) is the correct answer.
What is mean and standard deviation?Mean is the ratio of the sum of all the observations and the total number of observations in a data set. The standard deviation is a statistic that measures the dispersion of a data set relative to its mean and is calculated as the square root of the variance.
For the above suituation,
There are 20 math questions to be answered in 25 minutes.
After investigation with 35 students, the meantime needed for them is 23.5 and the standard deviation is 4.8.
From the above information, we can say that the hypothesis, H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed for students of this school to complete this portion of the exam.
Hence we can conclude that the hypothesis (C) is the correct answer.
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Of the flags in Albert's Flag Shop, 1/10 are pink and another 1/2 are orange. What fraction of the flags are either pink or orange?
Answer: 6/10
Step-by-step explanation: The answer is 6/10 because: first you convert the 1/2 to tenths which would be 5/10. Then, you add 1/10 and 5/10 and you get 6/10 of the flags were either pink or orange.
Which kinds of decoration did artists use on Tutankhamen’s throne? Choose all answers that are correct. A.unadorned columns B.uraeus on headdress and top of throne C.sun disk with rays ending with hands D.hieroglyphics and cartouches helppppppppppppppppppppppppppppppppppppp asappppppppppppppppppp
Answer:
answer is 3 because the decoration is so nice
In class we derived the equilibrium equation for displacements in the x-direction as. (λ+μ) ∂x
∂
div u
+μ∇ 2
u x
+p x
=0. Following this process, derive its companion equation in y-direction, (λ+μ) ∂y
∂
div u
+μ∇ 2
u y
+p y
=0
The companion equation for displacements in the y-direction can be derived by following a similar process to the equilibrium equation in the x-direction. It can be expressed as (λ+μ) ∂y∂div u+μ∇ 2u y+p y=0.
To derive the companion equation for displacements in the y-direction, we start by considering the equilibrium equation in the x-direction as (λ+μ) ∂x∂div u+μ∇ 2u x+p x=0. Here, λ and μ are the Lamé parameters, ∂x∂ represents the partial derivative with respect to x, div u represents the divergence of the displacement vector u, ∇ 2u x represents the Laplacian of the x-component of the displacement vector u, and p x represents the body force per unit volume in the x-direction.
To obtain the companion equation in the y-direction, we replace the x-subscripts with y-subscripts. Thus, the equation becomes (λ+μ) ∂y∂div u+μ∇ 2u y+p y=0. Here, ∂y∂ represents the partial derivative with respect to y, div u represents the divergence of the displacement vector u, ∇ 2u y represents the Laplacian of the y-component of the displacement vector u, and p y represents the body force per unit volume in the y-direction.
The derivation process involves applying principles of continuum mechanics and elasticity theory. By following this process, we obtain the companion equation for displacements in the y-direction as (λ+μ) ∂y∂div u+μ∇ 2u y+p y=0. This equation allows us to analyze the behavior and equilibrium of deformable solids in the y-direction, considering factors such as elastic properties, forces, and displacements.
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y-5=6(x-2)
Solve for y using inverse operations
Please help!!!! I’m unsure of the answers
Answer:
table:
.1, .25, .35, .2, .1
p(x=4) = .1
p(x<2) = .35
p(3≤x≤4)= .55
1.95, 1.12
Step-by-step explanation:
this is kind of hard to read, but i think i've got it
mean:
0*.1+1*.25+2*.35+3*.2+4*.1= 1.95
The second moment:
0²*.1+1²*.25+2²*.35+3²*.2+4²*.1= 5.05
the variance is the second moment minus the first moment squared (first moment is the mean) and then the standard deviation is the square root of the mean
5.05-1.95²= 1.2475 √1.2475= 1.1169 or 1.12
The sum of the first and second terms of an AP is 4 the tenth term is 19 find the sum of the fifth and sixth terms
Answer:
20
Step-by-step explanation:
first term + second term = 4
tenth term = 19
fifth term + sixth term = ?
Since this is an arithmetic sequence:
first term = a
second term = a+d
tenth term = a+9d
Then we have
\(2a+d=4 \\ a+9d=19\)
Upon solving the system of equation we have:
\(a=1 \\ d=2\)
Since:
fifth term = a+4d
sixth term = a+5d
The final answer is:
fifth term + sixth term = \(2a+9d=2+18=20\)
HELPP i need explanation for number 12
Answer:
\frac{\left(x+5\right);p}{\left(x+5\right);}=\frac{2x^2}{\left(x+5\right);}-\frac{6x}{\left(x+5\right);}-\frac{1}{\left(x+5\right);};\quad \:x\ne \:-5p=\frac{2x^2-6x-1}{;\left(5+x\right)};\quad \:x\ne \:-5
Step-by-step explanation:
HELP!!!! Due in 1 hour.
Answer
these nut in you'er mouth
Step-by-step explanation:
Look at the picture pleaseee
Chase and Simon (1973) studied the memory of chess novices and experts for positions of chess pieces on a chessboard. Although experts generally have a far better memory for chess positions than do novices, they found that the novices performed as well or better than the experts when asked to recall random arrangements of chess pieces on the chessboard. The random arrangements included arrangements that could not possibly occur in a real game of chess. Why did novices do as well as experts when the pieces were arranged at random
Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.
One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.
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Probability will be the basis of all future topics, and you will find that the resulting interpretation of a probability and the conclusion that you can make from a probability is more important than that calculation itself. Consider the following probabilities found for the given situations, then answer the questions that follow: Situation 1: If randomly guessing, the probability that a person can correctly guess your birthday (month and day) on the first try is 1365=0.00271365=0.0027. The probability that a person can correctly guess the birthday of two people in a row is (1365)2=0.0000075(1365)2=0.0000075. You and a friend are out one night and you meet a magician who bets that she can randomly guess both of your birthdays on the first try. QUESTION: If the magician does guess both of your birthdays, would you believe it was by pure chance, or would you believe that the magician knew your birthdays by some other means (whether that be magic, being a creepy stalker, etc.)? Explain.
If the magician correctly guesses both of your birthdays on the first try, it would be very unlikely to have occurred by pure chance. The probability of correctly guessing the birthday of one person on the first try is already very low at 0.0027. The probability of correctly guessing the birthday of two people in a row is even lower at 0.0000075.
Therefore, it is more likely that the magician had some other means of knowing your birthdays, rather than simply guessing them by chance. This could be through previous knowledge or research, such as being a stalker, or it could be through some sort of trick or illusion, such as using a hidden device or subtle cues to deduce the birthdays. In any case, it is highly unlikely that the magician would have been able to correctly guess both of your birthdays on the first try purely by chance.
Learn more about probability here:
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