A school newpaper reporter decides to randomly survey 19 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, he knows that 22% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. X~ B 22 .19 9 For the following questions, round to the 4th decimal place, if need be. Find the probability that exactly 9 of the students surveyed attend Tet festivities. Find the probability that no more than 7 of the students surveyed attend Tet festivities. Find the mean of the distribution. Find the standard deviation of the distribution. According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select peanut M&M's from an extra-large bag looking for a yellow candy. Round all probabilities below to four decimal places. Compute the probability that the first yellow candy is the seventh M&M selected. .0566 Compute the probability that the first yellow candy is the seventh or eighth M&M selected. .1047 Compute the probability that the first yellow candy is among the first seven M&M's selected. .6794 If every student in a large Statistics class selects peanut M&M's at random until they get a yellow candy, on average how many M&M's will the students need to select? (Round your answer to two decimal places.) yellow M&M's
Answers
6.67 is the average that the students need to select of M&M to get a yellow candy.
Given that, X ~ B(22, 0.19), where B stands for the binomial distribution, n = 19, p = 0.22, and we are interested in the number of students who will attend the festivities.
a) The probability that exactly 9 of the students surveyed attend Tet festivities is:
P(X = 9) = (19C9)(0.22)⁹(0.78)¹⁰ = 0.2255 (rounded to four decimal places)
Therefore, the probability that exactly 9 of the students surveyed attend Tet festivities is 0.2255.
b) The probability that no more than 7 of the students surveyed attend Tet festivities is:
P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) ≈ 0.2909
Therefore, the probability that no more than 7 of the students surveyed attend Tet festivities is 0.2909.
c) The mean of the distribution is:
µ = np = 19 × 0.22 = 4.18 (rounded to two decimal places)
Therefore, the mean of the distribution is 4.18.
d) The standard deviation of the distribution is:
σ = √(np(1 - p)) = √(19 × 0.22 × 0.78) ≈ 1.7159 (rounded to four decimal places)
Therefore, the standard deviation of the distribution is 1.7159.
According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange, and 15% are green. You randomly select peanut M&M's from an extra-large bag looking for a yellow candy. Round all probabilities below to four decimal places.
Compute the probability that the first yellow candy is the seventh M&M selected:
Using the geometric distribution formula, P(X = k) = (1 - p)^(k-1)p, where X is the number of trials until the first success occurs, p is the probability of success, and k is the number of trials until the first success occurs. Here, p = 0.15, and k = 7.
P(X = 7) = (1 - p)^(k-1)p = (1 - 0.15)^(7-1)(0.15) ≈ 0.0566
Therefore, the probability that the first yellow candy is the seventh M&M selected is 0.0566.
Compute the probability that the first yellow candy is the seventh or eighth M&M selected:
The probability that the first yellow candy is the seventh or eighth M&M selected is:
P(X = 7 or X = 8) = P(X = 7) + P(X = 8) ≈ 0.1047
Therefore, the probability that the first yellow candy is the seventh or eighth M&M selected is 0.1047.
Compute the probability that the first yellow candy is among the first seven M&M's selected:
Using the geometric distribution formula, P(X ≤ k) = 1 - (1 - p)^k, where X is the number of trials until the first success occurs, p is the probability of success, and k is the maximum number of trials. Here, p = 0.15, and k = 7.
P(X ≤ 7) = 1 - (1 - p)^k = 1 - (1 - 0.15)^7 ≈ 0.6794
Therefore, the probability that the first yellow candy is among the first seven M&M's selected is 0.6794.
Using the geometric distribution formula, E(X) = 1/p, where X is the number of trials until the first success occurs, and p is the probability of success. Here, p = 0.15.
E(X) = 1/p = 1/0.15 ≈ 6.67 (rounded to two decimal places)
Therefore, on average the students need to select about 6.67 M&M's to get a yellow candy.
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Related Questions
when assigning subjective probabilities, use experience, intuition, and any available data.
Answers
The statement is a suggestion or guideline for how to assign subjective probabilities.
Subjective probabilities are probabilities that are based on personal beliefs or judgments rather than on empirical evidence. Experience and intuition can be used to make informed guesses about the likelihood of an event occurring.
Available data can also be used to inform subjective probabilities, such as historical data or expert opinions. However, subjective probabilities may not always be reliable as they can be influenced by personal biases or limited information.
Therefore, it is important to use critical thinking and consider multiple sources of information when assigning subjective probabilities.
Additionally, subjective probabilities may be useful in situations where empirical data is not available or difficult to obtain, but they should be used with caution and always be subject to reassessment as new information becomes available.
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Mr. Forest drew a diagram of his office on a coordinate grid. He placed his chair at (4, 3), his podium at (4, -4), and his desk at (-6, -4). The length of each square on the grid represented one yard. What was the distance between the podium and the desk?
Answers
The distance between the podium and the desk is given as follows:
10 yards.
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates given by \((x_1,y_1)\) and \((x_2,y_2)\).
The distance between them is given by the equation presented below as follows, derived from the Pythagorean Theorem:
\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
The coordinates for this problem are given as follows:
Podium: (4, -4).Desk: (-6, -4).Hence the distance is obtained as follows:
\(D = \sqrt{(4 - (-6))^2 + (-4 - (-4))^2}\)
D = 10 yards. (as each unit is 10 yards).
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The ages of people in a movie theater are normally distributed with a mean of 32 years and a standard deviation of 6.2 years. What is the age of a movie attendee with a z-score of -1.2?
enter the answer, rounded to the nearest tenth.
Answers
The age of a movie attendee with a z-score of -1.2 is approximately 24.2 years old (rounded to the nearest tenth).
We can use the standard normal distribution to find the age of a movie attendee with a z-score of -1.2:
z = (x - mu) / sigma
where z is the z-score, x is the age we want to find, mu is the mean age, and sigma is the standard deviation.
Rearranging this formula, we get:
x = mu + z * sigma
Substituting the given values, we get:
x = 32 + (-1.2) * 6.2
x = 24.16
Therefore, the age of a movie attendee with a z-score of -1.2 is approximately 24.2 years old (rounded to the nearest tenth).
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help...…. this math question hurts my head a lot
Answers
Answer:
Both are NO
Step-by-step explanation:
18+ 23=41. The other side of ΔUWV equals 41. Therefore, ΔUWV is not equal to ΔUCB
consider the following repeating decimal. 0.8 (a) write the repeating decimal as a geometric series.
Answers
The repeating decimal 0.8 as a geometric series 0.8 = 8/10 + (8/10)^2 + (8/10)^3 + ...
To express the repeating decimal 0.8 as a geometric series, we can start by observing the repeating pattern. In this case, the digit 8 repeats indefinitely. We can write 0.8 as follows:
0.8 = 0.8888...
To convert this into a geometric series, we need to identify a common ratio that will generate each subsequent term. In this case, the common ratio can be obtained by dividing the repeating digit by 10, which represents the shifting of the decimal point to the right. Thus, the common ratio is 8/10, which simplifies to 4/5.
Now we can express the repeating decimal 0.8 as a geometric series using the formula for an infinite geometric series:
0.8 = 8/10 + (8/10)^2 + (8/10)^3 + ...
In general, the nth term of the series is given by (8/10)^n. Since the repeating decimal has an infinite number of terms, we have successfully represented 0.8 as a geometric series.
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Please help! Write an equation, then solve for x!
Answers
What is 2x2x4 I’m asking from my big brothers account
Answers
Step-by-step explanation:
2×2×4=16
Hope it helps uß
a 127 foot tower is located on a hill a guy-wire is to be attached to the top of the tower and anchored at a point 64 feet downhill from the base of the tower the guy-wire is 175 feet long find the angle the tower makes with the hill
Answers
The angle the tower makes with the hill is approximately 44.77 degrees.
To find the angle the tower makes with the hill, we can use trigonometry. Let's denote the angle the tower makes with the hill as θ.
Using the given information, we can form a right triangle with the tower, the guy-wire, and the horizontal distance between the anchor point and the base of the tower.
The vertical leg of the triangle represents the height of the tower, which is 127 feet.
The hypotenuse of the triangle represents the length of the guy-wire, which is 175 feet.
The horizontal leg of the triangle represents the distance from the anchor point to the base of the tower, which is 64 feet.
We can use the sine function to find the angle θ:
sin(θ) = opposite/hypotenuse
sin(θ) = 127/175
To find θ, we can take the inverse sine (sin^(-1)) of both sides:
\(θ = sin^(-1)(127/175)\)
Using a calculator, we find that θ is approximately 44.77 degrees
Therefore, the angle the tower makes with the hill is approximately 44.77 degrees.
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The equation y = 5x represents a proportional relationship. what is the constant of proportionality
A. 1/5
B. x
C. 0
D. 5
Answers
Answer:
the constant of proportionality is 5-D
the ratio of dividends to the average number of common shares outstanding is:
Answers
The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.
To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.
For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.
In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.
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how much do i need to make to afford a $425,000 house
Answers
The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.
To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.
These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.
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A store charges a restocking fee for any returned item based upon the item price. An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9. What percentage of the item price is the restocking fee?
Answers
Answer:
6%
Step-by-step explanation:
for this is divided the fee by the price of the item.
Which radical expression is equivalent to k^2/9. Please give me a step-by-step explanation.
Answers
Answer:
Apply the rule x^m/n = n√ x^m to rewrite the exponentiation as a radical.
9√k^2
Let's simplify
\(\\ \rm\Rrightarrow \dfrac{k^2}{9}\)
\(\\ \rm\Rrightarrow \dfrac{k^2}{3^2}\)
\(\\ \rm\Rrightarrow (\dfrac{k}{3})^2\)
HELP RIGHT NOW AND ILL GIVE BRAINLY IF CORRECT
Answers
Answer:
-9
Step-by-step explanation:
\(3^{-36}\)= \(27^{-12}\)
What is the factored form of 2x2 + 20x + 50? (1 point) 2(x + 5)(x-4) 2(x - 5)(x + 4) 2(x + 5)2 2(x + 5)(x - 5)
Answers
Answer:
Hope it can help you.....Mark me as a brainlist...
What is 5g+7g and g(5+7)?
Answers
24 grams
Answer:
12g and 12g
Step-by-step explanation:
5g + 7g = 12g
g(5+7) = g(12) = 12g
Julio can sprint at a speed of up to 14. 6 miles per hour over short distances. At this rate, about how many seconds would it take him to run from first base to second base, which are 75 ft apart? Round your answer to the nearest tenth of a second
Answers
Step-by-step explanation:
Find what 14.6 mi/hr is in f/s
14.6 mi / hr * 1 hr / 3600 s * 5280 ft / mi = 21.413 f/s
Then distance / rate = time :
75 f / 21.413 f/s = 3.5 sec
It would take Julio approximately 3.5 seconds to run from first base to second base at his top speed. Rounded to the nearest tenth of a second, it is approximately 3.5 seconds.
To calculate the time it takes for Julio to run from first base to second base, we first need to convert the distance between the bases from feet to miles.
1 mile = 5280 feet
So, 75 feet is equal to:
75 feet / 5280 feet per mile = 0.0142 miles (approximately, rounded to four decimal places)
Now, we'll use the formula for time:
Time = Distance / Speed
Time = 0.0142 miles / 14.6 miles per hour
Time ≈ 0.00097222222 hours
Now, we need to convert the time from hours to seconds:
1 hour = 3600 seconds
Time = 0.00097222222 hours * 3600 seconds per hour ≈ 3.5 seconds
So, it would take Julio approximately 3.5 seconds to run from first base to second base at his top speed. Rounded to the nearest tenth of a second, it is approximately 3.5 seconds.
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A right angled triangle has base ( x + 3) cm and height (x + 8) cm.
Given that its area is 42 cm , calculate the length of the base and height of the triangle.
height should be 15
Answers
The length of the base and height of the triangle are 7 cm and 12 cm, respectively.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The area of a right angled triangle is given by the formula:
Area = (1/2) × base × height
Area of the triangle is 42 cm and the base is (x + 3) cm and the height is (x + 8) cm.
42 = (1/2) (x + 3) (x + 8)
Multiplying both sides by 2 to eliminate the fraction, we get:
84 = (x + 3)(x + 8)
84 = x² + 11x + 24
x² + 11x - 60 = 0
We can now factorize the quadratic equation:
(x + 15) (x - 4) = 0
Solving for x, we get:
x = -15 or x = 4
Therefore, x = 4, which means the base of the triangle is (x + 3) = 7 cm and the height is (x + 8) = 12 cm.
Hence, the length of the base and height of the triangle are 7 cm and 12 cm, respectively.
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can someone tell me what’s the answer please ?!
Answers
Answer:
no se
Step-by-step explanation:
Explanation: The Y-intercept goes through 1 not -1 so you know the last part will be +1. That limits it to A and B. Secondly, It goes rise/run. So look at how the line goes through points. For example From the intercept to the next line. It goes up 2 over one. So 2/1 which is 2. This way it is Y=2x+1! Hope this helps!
Bob has a coin cup with four $1 tokens and two $5 tokens in it. He also has two $10 tokens and one $25 token in his pocket. He
randomly draws a token from the cup, and then randomly draws a token from his pocket. What is the probability that he will draw
$30 in tokens?
A. 1/3
B. 1/9
C. 2/9
D. 4/9
Answers
Answer:
;-;
There is no 30$ tokens
Step-by-step explanation:
i guess its A or b
like the heck
Answer:
n[$1]=4
n[$5]=2
n[$10]=2
n[$15]=1
n[total]=9
getting 10=2/9
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Answers
Answer:
ok i guess...
Step-by-step explanation:
Answer:
Thank you so much!
Step-by-step explanation:
Rewrite into standard form A. 4.23 x 10^-8
B. 1.89 x 10^12
C. 6.2 x 10^-1
Pls help
Answers
4n-6 (n - 2) = -24 + 7n
O No Solutions
O All Real Numbers
O n = 4
O n = 2.9
Answers
4n-6 (n-2) = -24 + 7n
You first multiply the six with the equation in the parentheses making it:
4n-6n + 12= -24 + 7n
You then subtract 4n from -6n changing it to:
-2n + 12 = -24 + 7n after that you switch the 12 and 7n so that the equation can be
-2n -7n = -24 - 12
After that combine the numbers together:
-9n = -36
Then divide both sides by -9 making
n= 4
need help asap please
Answers
Your answer is C.
I hope this helps! :)
In the diagram of triangle ADC below, EB || DC, AE = 9, ED = 5, and AB = 9.2. What is the length of AC, to the nearest tenth?
Answers
Answer:
14.3
Step-by-step explanation:
9/5= 9.2/x (cross multiply)
5 x 9.2= 46
46 ÷ 9 = 5.1
9.2 + 5.1 = 14.3
The length of AC is 14.3 cm.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that In the diagram of triangle ADC, EB || DC.
AE = 9, ED = 5, and AB = 9.2.
We need to find the length of AC.
To find the length of AC firstly we need to find BC.
This can be find by using proportionality.
AE/ED=AB/BC
9/5=9.2/x
Apply cross multiplication.
9x=9.2×5
9x=46
Divide both sides by 9
x=5.11
where x is BC which is 5.11
Now add AB+BC=AC
9.2+5.1=14.3
Hence, the length of AC is 14.3 cm.
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For an increase of 6% what is the multiplier
Answers
For an increase of 6% the multiplier is 1.06
How to find the correspondent multiplier?If we have a value A, and we want to increase it by a percentage X, the formula that we need to use to find the new value is:
new value = A*(1 + X/100%)
Where the multiplier is (1 + X/100%).
Here the percentage is 6%, then the multiplier for this case will be:
(1 + 6%/100%) = (1 + 0.06) = 1.06
The new value would be:
new value = A*1.06
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Shelly and Terrence completed a different number of tasks in a game. Shelly earned 90 points on each task. Terrence's total points were 20 less than Shelly's total. The expression below shows Terrence's total points in the game:
90x − 20
What does the factor x of the first term of the expression represent? (2 points)
Group of answer choices
The total number of tasks Terrence completed
The total number of tasks Shelly completed
The sum of Shelly's and Terrence's total points
The difference between Shelly's and Terrence's total points
Answers
The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed
The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.
To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.
On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.
So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.
Therefore, the correct answer is: The total number of tasks Terrence completed.
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help
Three concrete models are shown. Each model represents an algebraic expression. In each of the given algebraic expressions, n represents the figure number. Match each model with the algebraic expression it best represents.
Answers
Answer:
this algrebraic expression
Answer:
ur welcome :D :D :D :D : D :D
The temperature fell 16 degrees between noon and 3 pm. at 3 pm the temperature was -3 degrees. write and solve an equation to determine the temperature at noon.
Answers
Answer:
13 degrees or, x-16=-3
Step-by-step explanation:
(x is a variable that is unknown)
x-16=-3
x=13 degrees
How many 5/6 are in 2/3
Answers
Answer:
The amount is 4/5 of 5/6 is in 2/3.
Step-by-step explanation:
There 4/5 is 5/6 in the fraction 2/3 which is determined by the division operation.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
For example 4/2 = 2
We have to determine how many 5/6 are in the fraction 2/3.
The numbers are given in the question below
2/3 and 5/6
According to the given question, the required solution would be as:
⇒ 2/3 ÷ 5/6
⇒ (2/3) / (5/6)
Reciprocal the terms of the numerator in the above expression
⇒ (2/3) × (6/5)
Apply the multiplication operation,
⇒ 12 / 15
Reduce the fraction in the simplest form,
⇒ 4/5
Therefore, there 4/5 is 5/6 in the fraction 2/3.
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