The hypotenuse of a 45 -45 90 triangle measures 128 cm
What is the lenght of one leg of the triangle
Answers
As a result, one leg of the 45-45-90 triangle is 64 x sqrt(2) cm long.
How to calculate the length of the triangle ?The legs of a 45-45-90 triangle are congruent, and the length of each leg equals the square root of two times the length of the hypotenuse, or:
leg = hypotenuse / sqrt(2)
If we substitute the given value, we get:
leg = 128 / sqrt(2)
To simplify, multiply the numerator and denominator by sqrt(2), which is equivalent to multiplying by 1 because sqrt(2)/sqrt(2) = 1:
leg = (128 / sqrt(2)) x (sqrt(2) / sqrt(2))
leg = (128 x sqrt(2)) / 2
leg = 64 x sqrt(2)
As a result, one leg of the 45-45-90 triangle is 64 x sqrt(2) cm long.
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Related Questions
Correct answer please
Answers
Answer:
50.75
Step-by-step explanation:
We have:
\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)
\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)
Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?
Answers
1. A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
In this case, the spinner's outcome of landing on region three is independent of landing on region six. Each spin is unrelated to the previous spin, and the outcome of one region does not affect the outcome of the other region. Therefore, the events are independent. The probability of landing on both region three and region six is the product of their individual probabilities: 1/8 * 1/8 = 1/64.
2. A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?
In this scenario, the events are overlapping. A jersey can be both purple and have a number greater than 5 at the same time. Therefore, the probability of it being purple or having a number greater than 5 is the sum of their individual probabilities, minus the probability of the overlapping event (purple jerseys with a number greater than 5). There are 4 purple jerseys out of 10 total jerseys, and there is 1 jersey with a number greater than 5 out of 10. However, there is one jersey that satisfies both conditions (purple and number greater than 5), so we need to subtract it from the sum. So the probability is (4/10 + 1/10) - (1/10) = 4/10 = 2/5.
3. A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?
In this scenario, the events are mutually exclusive. A chocolate cannot be both a milk chocolate and have no peanuts inside at the same time. Therefore, the probability of it being a milk chocolate or having no peanuts inside is the sum of their individual probabilities. There are 6 milk chocolates out of 10 total chocolates, and there are 7 chocolates without peanuts out of 10. So the probability is 6/10 + 7/10 = 13/10, which is greater than 1. However, probabilities cannot exceed 1, so we need to take the maximum value of 1. Therefore, the probability is 1.
4. You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?
In this case, the events are independent. The outcome of the coin flip does not affect the outcome of the die roll. The probability of the coin landing heads up is 1/2, and the probability of the die showing an even number is 1/2. To find the probability of both events occurring, we multiply their individual probabilities: 1/2 * 1/2 = 1/4.
I hope this clarifies the nature of each event. Let me know if you have any further questions!
The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
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The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Which is always true about a trapezoid?
Answers
Answer: They always have one pair of parallel lines.
Step-by-step explanation:
I really don't get what the top box is asking me what to do
Answers
Answer:
See belowStep-by-step explanation:
The circle has a circumference:
C = 2πrThis the is arc of full length θ = 360°
Each degree of arc length is:
s = 2πr*θ / 360 = πrθ / 180We have:
r = 6 in and θ = 25°The arc length is:
s = π*6*25/180 = (5/6)π inches terms of πThe same arc is:
s = (5/6)*3.14 = 2.62 inches (rounded)7.
Write an equation for the translation of y = |x|.
5.5 units right
A. y = |x| + 5.5
B. y = |x – 5.5|
C. y = |x + 5.5|
D. y = |x| – 5.5
Answers
Answer:
D. y = |x| – 5.5
Step-by-step explanation:
Find the product: (8n - 3)(5n+7)
Answers
Answer:
\(40n^{2} +41n-21\)
Step-by-step explanation:
Remember to FOIL (first, outer, inner, last)
8n(5n)=\(40n^{2}\)
8n(7)=56n
-3(5n)=-15n
-3(7)=-21
Putting it all together, you get
\(40n^{2} +56n-15n-21\)
Collect like terms (the n's) and you get
\(40n^{2} +41n-21\)
Hope this helps!
Answer:
\({40n^2 + 41n-21\)Step-by-step explanation:
Use the method FOIL
FOIL = First, outer, inner, last
Example: (a + b) (c + d) = ac + ad + bc + bd
(8n - 3)(5n + 7)
40n^2 + 56n - 15n - 21
40n^2 + 41n - 21
An instructor gives her class a set of 10 problems with the information that the final will consist of a random selection of 5 of them. If a student has figured ou how to do 7 (and only 7) of the questions, what is the probability that he or she will answer correctly:a) all 5 problemsb)at least 4 of the problems
Answers
a) The probability that the student will answer all 5 correctly is 1/252.
b) The probability that the student will answer at least 4 correctly is 1 - (1/252 + 1/126 + 1/84 + 1/63).
The probability of answering all 5 problems correctly on the final if the student has figured out how to do 7 of the questions is 1/252. This is because there are 10 questions in total and the student has figured out how to do 7 of them. That means there are 3 questions that the student does not know how to do, and therefore the probability of getting all 5 questions correct on the final is 1/252.The probability that the student will answer at least 4 of the problems is 1 - (1/252 + 1/126 + 1/84 + 1/63). This calculation takes into consideration the fact that there are 4 possible combinations of 5 questions that the student could get wrong out of the 10 questions. So, the probability of answering at least 4 questions correctly is 1 minus the probability of getting 4 or 5 questions wrong.
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Get the binary value of your first name initial. Show your solutions and checking.
First name: Nicy
First name initial: N
Convert:
Answers
Answer:
78778887
Step-by-step explanation:
Binary code of the letter N :
⇒ 01001110
Here the character 'N' has the decimal : 78
Change 0 into 7 and 1 into 8 :
⇒ 78778887
Solve for X
A.45
B.35
C.25
D.30
Answers
90+60=150
180-150=30
A national publication showed the following distribution of favorite class subjects for high school students.
Class Subject Math English Social Studies Physical Education Music Other
Percentage 5% 14% 28% 26% 20% 7%
Pasquale, a student from a high school of 1,200 students, wants to see whether the distribution at his school matches that of the publication. He stands at the school entrance in the morning and asks the first 40 students he sees what their favorite class is. Pasquale records the following table of observed values.
Class Subject Math English Social Studies Physical Education Music Other
Observed 7 8 7 6 6 6
He decides to conduct a chi-square goodness-of-fit test to see whether his high school's distribution differs significantly from that of the publication. Pasquale’s statistics teacher tells him that his information does not meet the conditions necessary for a goodness-of-fit test. Which condition has not been met?
Answers
Answer:
1 and 111 only
Step-by-step explanation:
The goodness of fit test is used to examine if there is significant evidence to say thatvthe observed and expected freqencies are from the desired distribution.
Condituis required for performing a goodness of fit test on a data include :
Randomness, sampled Data must have been chosen at random in other to be representative, here, randomness isn't exhibited as Pasquale used more of convenient sampling questioning the first 40 students.
Also, the expected value of the number of sample observation in each level of the variable should be atleast 5.
This is also violated, as the expected values for some of the levels are less than 5
Hence, conditions 1 and 111 are not met
A ball player is at bat 55 times as hits the ball 33 times. Want ratio of his times at bat does he not hit the ball?
Answers
Answer:55:33
Step-by-step explanation:
55:33
He hits it 33 times so his bat does not hit the ball 22 times. 55:22 > 5:2
Write an equation of the line passing through the points (3,9) and (-1,-15).
I
Answers
Answer:
y = 6x - 9
Step-by-step explanation:
equation of line y = mx + b
lets find the slope m = (y2-y1)/(x2-x1):
m = ((-15)-9)/((-1)-3)
m = 6
let's plug this into our equation:
y = 6x + b
now we can plug in a point, I choose (3,9)
9 = 6(3) + b
b = -9
lets plug everything into our equation
y = 6x - 9
Please help I am so so confused thank you all
Answers
y-(-9) = -6(x-(-4)), y = -6x-33
The manager of a local fast-food restaurant is interested in improving the service provided to customers who use the restaurant's drive-up window. As a first step in this process, the manager asks an assistant to record the time (in seconds) it takes to serve a large number of customers at the final window in the facility's drive-up system. The file P08 07 xlsx contains a random sample of 200 service times during the busiest hour of the day
a. Identify the relevant population.
b. Calculate and interpret a 95% confidence interval for the mean service time of all customers arriving during the busiest hour of the day at this fast-food operation.
c. If the manager wants to improve service, at least during the busiest time of day, does this contidence interval provide useful inlormation? What useful information does it not provide?
Answers
Answer and explanation:
Find answer and explanation attached
The PTO is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $4. There is 1 winning ticket out of the 280 tickets sold. The winner gets a prize worth $62. Round your answers to the nearest cent.
What is the expected value (to you) of one raffle ticket? $
Calculate the expected value (to you) if you purchase 12 raffle tickets. $
What is the expected value (to the PTO) of one raffle ticket? $
If the PTO sells all 280 raffle tickets, how much money can they expect to raise for the classroom supplies? $
Answers
The expected values of the raffle ticket for you are given as follows:
One ticket: -$3.76.12 tickets: -$45.12.For the PTO, the expected values are given as follows:
One ticket: $3.76.12 tickets: $45.12.What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
For you, the distribution is given as follows:
P(X = 62) = 1/280.P(X = -4) = 279/280.Hence the expected value for one ticket is given as follows:
E(X) = 62/280 - 4 x 279/280
E(X) = -$3.76.
For twelve tickets, the expected value is given as follows:
12 x -3.76 = -$45.12.
For the PTO, we use the inverse signals, as the distribution is the inverse, that is:
P(X = -62) = 1/280.P(X = 4) = 279/280.More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
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Please help it’s due today!!!!
Answers
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
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find f(2) PLEASE HELP SOLVE!! MATH!!!
Answers
The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:
f(2) = 0.172.
How to obtain the numeric value of the function?The function for this problem is defined as follows:
f(x) = 14/[3 + ae^(kx)]
When x = 0, y = 2, hence we can obtain the coefficient a as follows:
2 = 14/(3 + a)
6 + a = 14
a = 8.
Hence:
f(x) = 14/[3 + 8e^(kx)]
When x = 1, y = 1/2, hence the coefficient k is given as follows:
0.5 = 14/(3 + 8e^k)
1.5 + 4e^k = 14
4e^k = 12.5
e^k = 12.5/4
k = ln(12.5/4)
k = 1.14.
Hence:
f(x) = 14/[3 + 8e^(1.14x)]
Then the numeric value of the function at x = 2 is given as follows:
f(2) = 14/[3 + 8e^(1.14(2))]
f(2) = 0.172.
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To the nearest tenth, what is the value of P(YB)?
0.2
0.3
0.4
0.5
Answers
Answer:
The 3rd one
Step-by-step explanation:
P(Y|B) = 0.4.
The probability is the ratio of the favorable event to the total number of events. Then the probability P(Y|B) will be 0.4, then the correct option is C.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.
The probability P(Y|B) will be given as
\(\rm P(Y|B) = \dfrac{34}{85}\\\\P(Y|B) = 0.4\)
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The point (2,6) lies on the graph of the equation y = kx^2 - 3x Find the value of K
Answers
Answer:
k = 3Step-by-step explanation:
y = kx² - 3x
Since the points lie on the graph we can substitute the values of x and y that's
( 2 ,6) into the equation to find k.
We have
6 = (2)²k - 3(2)
6 = 4k - 6
4k = 6 + 6
4k = 12
Divide both sides by k
That's
\( \frac{4k}{4} = \frac{12}{4} \)
We have the final answer as
k = 3Hope this helps you
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 9.
The range is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 9.
Answers
The range is the best measure of variability for this data, and its value is 4.
Which of the following is the best measure of variability for the data, and what is its value?The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).
The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:
Range = Maximum value - Minimum value = 4 - 0 = 4
Therefore, the range is the best measure of variability for this data, and its value is 4.
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Someone please help me with math. Thank You
Answers
Answer:
4) 64 cubic inches
Step-by-step explanation:
8x8 = 64
Rectangle JKLM is shown. To the nearest tenth of a centimeter, what is the distance from J to M?
Answers
Answer:
10.2
Step-by-step explanation:
Answer:10.2
Step-by-step explanation:
Your friend has a bag of yellow and purple candy. He wants to use them to play a game with you.
Purple is worth 2 points and yellow is worth three points. Pick 9 candies from the bag
Create a system of equations where the combination of the candies gives you a total of 22 points. Make sure you label and define your variables.
Answers
The system of equations where the combination of the candies gives you a total of 22 points are:
x + y = 9
2x + 3y = 22
How can we create system of equations?To create the equations, we shall first define the variables:
x = the number of purple candies
y = the number of yellow candies
Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.
Then, we would make sure that the total number of candies selected is 9.
The first equation represents the total number of candies selected:
x + y = 9
The second equation represents the total number of points obtained:
2x + 3y = 22
Therefore, the system of equations is:
x + y = 9
2x + 3y = 22
This is a system of linear equations.
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the sum of two number is twenty-six using x to represent the smaller of the two numbers, translate "the difference between five more then the larger number and twice the smaller number' into a variable expression. then simplify
Answers
"the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, the sum of two numbers is twenty-six the difference between five is more than the larger number and twice the smaller number' into a variable expression.
Since x represents the smaller of the two numbers,
Thus the larger number will be 26 - x
The expression asked above will be:
=> 5 + larger number - 2 * smaller number
=> 5 + 26 - x - 2 * x
=> 31 -3x
therefore, "the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.
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the question is in the photo
Answers
is it me or is the photo not showing?
Answer:
no photo lol
Step-by-step explanation:
Select the correct answer. Which equation represents the vertical line passing through (14,-16)? A. X = -16 B.y=-16 C.x=-16 D.y= 14
Answers
Answer:
c.x=-16
Step-by-step explanation:
i think so...........ggggfewaaaaaa
Answer: x = 14
Step-by-step explanation:
Can someone help me it’s due today
Answers
Answer:
1 quart must be added
Step-by-step explanation:
To do this, set up an equation.
Let x be the number of quarts of antifreeze to be added. Then, you know that the new solution will have a total of 4 quarts with 2/5 of it being antifreeze, so \(\frac{2}{5} (x+3)\) would be the amount of antifreeze. Another way to represent the amount of antifreeze is \(x + \frac{3}{5}\) because the original mixture has 3/5 of quart of antifreeze, while the added stuff is fully antifreeze.
Now, you just solve the equation:
\(\frac{2}{5} (x + 3) = x + \frac{3}{5}\)
multiply both sides by 5
\(2(x + 3) = 5x + 3\)
Use the distributive property on the left
\(2x + 6 = 5x + 3\)
subtract 2x from both sides
\(6 = 3x + 3\)
subtract 3 from both sides
\(3 = 3x\)
divide both sides by 3
\(1 = x \\x = 1\)
Therefore the answer is 1 quart
The perimeter of a rectangular room is 80 feet. Let x be the width of the room (in feet) and let y be the length of the room (in feet). Write the equation that could model this situation.
Answers
Answer:
2x+2y=80
Step-by-step explanation:
a rectangles perimeter has the formula of width+width+length+length
we can combine like terms so we get 2x+2y and according to the problem this rectangle has the perimeter of 80
You roll a 6-sided die.
What is P(not divisor of 6)?
Write your answer as a fraction or whole number.
Answers
1/3
Step-by-step explanation:The notation P(x) is used to describe the probability of event x occurring.
Divisors
Before we can do the probability question, we need to find the divisors of 6. Divisors are numbers that can evenly divide another number. The factors and divisors of a number are the same. So, 6 has 4 divisors:
1, 2, 3, and 6All of these values are on a 6-sided dice. So, in this probability question, there are 4 unsuccessful outcomes.
Probability
The probability of a simple event is the number of successful outcomes divided by the number of possible outcomes. In this situation, there are 6 possible outcomes, each side of the dice. Four of these outcomes do not satisfy the given condition (not a divisor of 6). Thus, there are 2 successful outcomes.
\(\frac{2}{6} =\frac{1}{3}\)The probability of rolling a number that is not a divisor of 6 is 1/3.
15 points! The data set shows the weights of pumpkins, in pounds, that are chosen for a photograph in a farming magazine. The rest of the question is on the screenshot. Please help!
Answers
Answer:
Step-by-step explanation:
a). Mean of the given data set = \(\frac{32+28+18+40+22}{5}\)
= 28
b). x \(x-\overline{x}\) \((x-\overline{x})^2\)
32 32-28 = 4 16
28 28 - 28 = 0 0
18 18 - 28 = -10 100
40 40 - 28 = 12 144
22 22 - 28 = -6 36
\(\sum({x-\overline x})^2\) = 296
c). Standard deviation = \(\sqrt{\frac{\sum (x-\overline{x})^2}{n}}\)
= \(\sqrt{\frac{296}{5} }\)
= 7.69
d). Mean of the new set of weights = \(\frac{32+33+34+35+36}{5}\)
= 34
Since mean of the data set is more close to each data, standard deviation will be less than the deviation given in part (c).