The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, we have:
V = 5 x 3 x 8
V = 120 cubic inches
The price of the popcorn is not given, so we cannot calculate the price per cubic inch.
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What number does the roman numeral LVII represent?
57
58
59
60
Option A. 57. Roman numerals use letters from the Latin alphabet to represent numbers. The Roman numeral LVII represents the number 57.
The basic symbols used in the Roman numeral system are I, V, X, L, C, D, and M, which represent the numbers 1, 5, 10, 50, 100, 500, and 1,000, respectively. By combining these symbols, larger numbers can be formed.
In the case of LVII, the symbol L represents 50, the symbol V represents 5, and the symbol II represents 2. To get the total value of the Roman numeral, we add up the values represented by each symbol. So:
LVII = L + V + II
= 50 + 5 + 2
= 57
Therefore, the Roman numeral LVII represents the number 57.
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What number does the roman numeral LVII represent?
A. 57
B. 58
C. 59
D. 60
14% out of 100% equals how many people out of 10?
Answer:
1.4 people out of 10
Step-by-step explanation:
Just divide it by 10
Answer:
only 4 people
One of the legs of a right triangle measures 8 cm and its hypotenuse measures 10 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
6
Step-by-step explanation:
delta math
The required measure of the other leg will be 6 cm in the given right triangle.
What is Pythagoras's theorem?Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
We have been given that one of the legs of a right triangle measures 8 cm and its hypotenuse measures 10 cm.
Let the measure of the other leg would be x cm.
According to Pythagoras's theorem,
⇒ c² = a² + b² ....(i)
As per the given question, we have
c = 10cm, a = 8 cm and b = x
Substitute the values in the above formula, and solve for x
⇒ 10² = 8² + x²
⇒ 100 = 64 + x²
⇒ x² = 100 - 64
⇒ x² = 36
⇒ x² = 6²
⇒ x = 6
Therefore, the required measure of the other leg will be 6 cm in the given right triangle.
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Please help 20 points question
Answer:
y>-2x-1 answer is b
-4x+y> 1 is c I believe
Step-by-step explanation:
A firm that manufactures grape juice has a machine that automatically fills bottles. The mean of the process is assumed to be the machine's setting. The process variation (standard deviation) is 1.2 oz. (Assume that the process has a normal distribution.) B1. Customers get unhappy if the actual level is less than 36 oz but do not mind if it is greater than 36 oz. If you set the machine at 37 oz. what % of the time would the bottle contain less than 36 oz.?
B2. The bottle will actually hold 40 oz. If you set the machine to 38, what percent of the time will the bottles overflow?
B3. If 10 bottles from this process (setting at 38) are filled, what is the probability that at least one will have overflowed? (Use basic probability concepts.)
B4. If 15 bottles from this process (setting at 38) are filled, what is the probability that exactly 3 will have overflowed? (binomial)
B5. With the machine set at 38 oz., how big would the bottle have to be not to overflow 99.8% of the time?
B1. the bottle would contain less than 36 oz approximately 20.33% of the time when the machine is set at 37 oz.
B2. The bottles will overflow approximately 4.75% of the time when the machine is set at 38 oz.
B3. The probability that at least one bottle will overflow out of 10 bottles filled when the machine is set at 38 oz is approximately 99.9%.
B4. The probability that exactly 3 bottles will overflow out of 15 bottles filled when the machine is set at 38 oz is approximately 25.0%.
B5. The bottle would need to be approximately 40.796 oz or larger to avoid overflowing 99.8% of the time when the machine is set at 38 oz.
B1. To find the percentage of time the bottle contains less than 36 oz when the machine is set at 37 oz, we need to calculate the probability that a random bottle will have a volume less than 36 oz.
Using the normal distribution, we can calculate the z-score (standardized score) for 36 oz using the formula:
z = (x - μ) / σ
where x is the desired value (36 oz), μ is the mean of the process (37 oz), and σ is the standard deviation (1.2 oz).
z = (36 - 37) / 1.2
z ≈ -0.833
Using a standard normal distribution table or a statistical calculator, we can find the cumulative probability associated with this z-score.
P(X < 36) = P(Z < -0.833) ≈ 0.2033
Therefore, the bottle would contain less than 36 oz approximately 20.33% of the time when the machine is set at 37 oz.
B2. To find the percentage of time the bottles will overflow when the machine is set at 38 oz, we need to calculate the probability that a random bottle will have a volume greater than 40 oz.
Using the normal distribution, we can calculate the z-score for 40 oz using the formula mentioned earlier:
z = (x - μ) / σ
z = (40 - 38) / 1.2
z ≈ 1.67
Using a standard normal distribution table or a statistical calculator, we can find the cumulative probability associated with this z-score.
P(X > 40) = P(Z > 1.67) ≈ 0.0475
Therefore, the bottles will overflow approximately 4.75% of the time when the machine is set at 38 oz.
B3. To find the probability that at least one bottle will overflow out of 10 bottles filled when the machine is set at 38 oz, we can use the complement rule and subtract the probability that none of the bottles overflow.
The probability of no overflow in a single bottle is given by:
P(X ≤ 38) = P(Z ≤ (38 - 38) / 1.2) = P(Z ≤ 0) ≈ 0.5
Therefore, the probability of no overflow in 10 bottles is:
P(no overflow in 10 bottles) = (0.5)¹⁰ ≈ 0.00098
The probability that at least one bottle will overflow is the complement of no overflow:
P(at least one overflow in 10 bottles) = 1 - P(no overflow in 10 bottles) ≈ 1 - 0.00098 ≈ 0.999
Therefore, the probability that at least one bottle will overflow out of 10 bottles filled when the machine is set at 38 oz is approximately 99.9%.
B4. To find the probability that exactly 3 bottles will overflow out of 15 bottles filled when the machine is set at 38 oz, we can use the binomial distribution formula:
P(X = k) = (nCk) * \(p^k * (1 - p)^{(n - k)\)
where n is the number of trials (15), k is the desired number of successes (3), p is the probability of success (probability of overflow), and (nCk) is the number of combinations.
Using the probability of overflow calculated in B2:
p = 0.0475
The number of combinations for selecting 3 out of 15 bottles is given by:
15C3 = 15! / (3! * (15 - 3)!) = 455
Plugging the values into the binomial distribution formula:
P(X = 3) = 455 * (0.0475)³ * (1 - 0.0475)¹² ≈ 0.250
Therefore, the probability that exactly 3 bottles will overflow out of 15 bottles filled when the machine is set at 38 oz is approximately 25.0%.
B5. To determine the required size of the bottle to avoid overflowing 99.8% of the time when the machine is set at 38 oz, we need to find the z-score corresponding to a cumulative probability of 0.998.
Using a standard normal distribution table or a statistical calculator, we find the z-score for a cumulative probability of 0.998 to be approximately 2.33.
Using the formula mentioned earlier:
z = (x - μ) / σ
Substituting the known values:
2.33 = (x - 38) / 1.2
Solving for x:
x - 38 = 2.33 * 1.2
x - 38 ≈ 2.796
x ≈ 40.796
Therefore, the bottle would need to be approximately 40.796 oz or larger to avoid overflowing 99.8% of the time when the machine is set at 38 oz.
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Please help me with this question it contains angles and measurements
Answer:
m∠ONP = 43*
m∠LNO = 137*
m∠MNP = 137*
Step-by-step explanation:
Each line segment is a straight line meaning they are each worth 180°, so if you take 43° from 180° you're eft with 137° which is what ∠LNO and ∠MNP are equal to. ∠ONP is 43° since it is a vertical angle to ∠MNL which is also 43°.
Consider an infinitely repeated game in which, in each period, two firms with zero costs choose quantities and prices are given by: Pi = 1 -q1-q2/2, P2 = 1 - q2-q 1/2. Firms have a common discount factor of d = 1/2. a) Explain what a trigger strategy is and determine whether the firms can attain the joint profit maximising outcome in a subgame perfect equilibrium using trigger strategies. b) Explain what a stick and carrot strategy is and discuss whether it is possible to attain the joint-profit maximising outcome in a subgame perfect equilibrium using stick and carrot strategies.
A trigger strategy is a strategy that specifies an action to take in response to certain observed actions by other players. In this context, a trigger strategy involves cooperating as long as the other player cooperates, but immediately defecting and pursuing a different strategy if the other player deviates from cooperation.
In the given game, the firms cannot attain the joint profit-maximizing outcome in a subgame perfect equilibrium using trigger strategies because there is no trigger that can effectively sustain cooperation in the repeated game. Both firms have an incentive to deviate and lower their price to increase their own profit.
A stick and carrot strategy combines punishment for deviating from cooperation (stick) and rewards for cooperating (carrot). In this case, a stick and carrot strategy could involve punishing the deviating firm by setting a low quantity or price in response to their deviation, while rewarding cooperation by maintaining high quantities and prices. However, it is unlikely to attain the joint-profit maximizing outcome in a subgame perfect equilibrium using stick and carrot strategies because the firms still have an incentive to deviate and lower their price to increase their own profit, even if they face punishments or rewards. Therefore, sustaining cooperation and achieving the joint-profit maximizing outcome is challenging in this repeated game.
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Solve the following equation by making 4x^((2)/(3))-27x^((1)/(3))-7=0
The solutions to the equation 4x^(2/3) - 27x^(1/3) - 7 = 0 are x = 343 and x = -1/64. To solve the equation 4x^(2/3) - 27x^(1/3) - 7 = 0, we can use a substitution to simplify the equation. Let's make a substitution: let y = x^(1/3).
By substituting y = x^(1/3), we can rewrite the equation in terms of y:
4(y^2) - 27y - 7 = 0.
Now, we have a quadratic equation in terms of y. To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, factoring might not be straightforward, so let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a).
Applying this formula to our equation, with a = 4, b = -27, and c = -7, we have:
y = [(-(-27)) ± sqrt((-27)^2 - 4(4)(-7))] / (2(4))
= (27 ± sqrt(729 + 112)) / 8
= (27 ± sqrt(841)) / 8
= (27 ± 29) / 8.
This gives us two possible values for y:
1. y = (27 + 29) / 8 = 56 / 8 = 7.
2. y = (27 - 29) / 8 = -2 / 8 = -1/4.
Now that we have the values of y, we can substitute them back into the equation y = x^(1/3) to find the corresponding values of x:
For y = 7:
7 = x^(1/3)
(7^3) = x
343 = x.
For y = -1/4:
-1/4 = x^(1/3)
(-1/4)^3 = x
-1/64 = x.
Therefore, the solutions to the equation 4x^(2/3) - 27x^(1/3) - 7 = 0 are x = 343 and x = -1/64.
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please help me i asked this question 3 times and no one helps me
please i need it for tomorrow
Answer:
wirking on it give me 10. minutes
Question 5(Multiple Choice Worth 1 points)
(05.06 LC)
Which of the following points lie in the solution set to the following system of inequalities?
ysx-5
ys-x-4
(1, 10)
(-1, 10)
(10, 1)
(1,-10)
Answer:
The point that lies in the solution set to the following system of inequalities is (1,10).
To check, substitute the values of x and y into each inequality:
ys > x-5
y < x+4
For the point (1,10):
10 > 1-5 is true (10 > -4)
10 < 1+4 is true (10 < 5)
Therefore, (1,10) satisfies both inequalities and lies in the solution set. The other three points do not satisfy at least one of the inequalities, and thus do not lie in the solution set.
Step-by-step explanation:
4. If you color the perfect squares on a multiplication table, you will be coloring a_______ line.
A. Diagonal
B. Vertical
C. Horizontal
D. Zig-zag
Please helpppp
Answer:
A. Diagonal line
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hmmmmmm i dont know
Step-by-step explanation:
Which of the following is equivalent to (2x^3)(7x^4)
Answer:
where are the answer choices
Step-by-step explanation:
Answer:
2x + 3 = 7x + 4
3 + 2x = 7x + 4
3 + 2x = 4 + 7x
3 + 2x = 4 + 7x
3 + 2x + -7x = 4 + 7x + -7x
2x + -7x = -5x
3 + -5x = 4 + 7x + -7x
7x + -7x = 0
3 + -5x = 4 + 0
3 + -5x = 4
3 + -3 + -5x = 4 + -3
3 + -3 = 0
0 + -5x = 4 + -3
-5x = 4 + -3
4 + -3 = 1
-5x = 1
x = -0.2
Can you please help me answer this thank you. A, B C or D
Since the Mean is of mean daily revenue of $5400
Also, the standard deviation is $54
For the sample mean
The mean and standard deviation will remain unchanged
Hence the answer is
Option A
Pls help asap!!! I need to solve for x for these three questions (39 , 41 and 43) PLS ASAP!!!
Answer: 39. x= 37, 41. x=7, 43. x = 29
Step-by-step explanation:
39. 2x + 4 + 2x - 9 + x = 180
5x - 5 = 180
5x=185
185/5
x=37
41. 90 + 8x - 1 + 4x+7 =180
8x-1+4x+7=90
12x+6=90
12x=84
84/12
x=7
36+x=2x+7
36=x+7
29=x
Hope this helps.
Answer:
Hope this helps
Can a relationship be proportional and linear at the same time?
Answer:
relationship between variable can be linear, non-linear, proportional or non-proportional.
A family went on a vacation. They drove 120 miles. Dad drove 80% of the distance How many miles did Dad drive?
Answer:96
Step-by-step explanation:
The perimeter of a fence must be no larger than 500 feet in length. The longer side of the fence must be 10 feet more than twice the length of the shorter side. Write and solve and inequality to determine the maximum length of the shorter side of the fence.
Answer:
The shortest side of the fence can have a maximum length of 80 feet
Step-by-step explanation:
Inequalities
To solve the problem, we use the following variables:
x=length of the longer side
y=length of the sorter side
The perimeter of a rectangle is calculated as:
P = 2x + 2y
The perimeter of the fence must be no larger than 500 feet. This condition can be written as:
\(2x + 2y \le 500\)
The second condition states the longer side of the fence must be 10 feet more than twice the length of the shorter side.
This can be expressed as:
x = 10 + 2y
Substituting into the inequality:
\(2(10 + 2y) + 2y \le 500\)
This is the inequality needed to determine the maximum length of the shorter side of the fence.
Operating:
\(20 + 4y + 2y \le 500\)
Simplifying:
\(20 + 6y \le 500\)
Subtracting 20:
\(6y \le 500 - 20\)
\(6y \le 480\)
Solving:
\(y \le 480 / 6\)
\(y \le 80\)
The shortest side of the fence can have a maximum length of 80 feet
Please help I will give you BRAINLIEST for the correct answer
Answer:
Im pretty sure it's the first one
Answer:
Third option is the correct answer
Step-by-step explanation:
14/18, 21/27, 28/36
Sandra scores 12 out of 30 in her maths test. Write this as a fraction in its simplest form.
Step-by-step explanation:
12/30
find highest common factor; 6
divide both sides by 6
(12/6) (30/6)
2/5
how can you get 6 with four 6s , the problem is
6 6 6 6 equals 6
Answer:
6666 divided by 1111 equals 6
Step-by-step explanation:
How can I find the sum please help!!
Answer:
Use mathpapa, it's a great calculator and it explains the steps
Can I have brainliest?
Step-by-step explanation:
The area of the unshaded region is 22.5cm. What is the area of the rectangle? A11.25cm . B22.5cm . C45cm . D90cm .
Answer:
45cm2
Step-by-step explanation:
because the shaded areas = to the non shaded one so just multiply it by 2 to get 45cm2
(Hope this helped you out)
jeff and chad decide to flip a coin 3 times to see who pays for lunch. chad picks heads and he must get heads at least twice out of 3 flips to win and have jeff pay for his lunch. what is the probability chad gets at least 2 heads on 3 flips?
The probability that chad gets at least 2 heads on 3 flips is 1/2 which was found using the sample space.
How does probability explain work?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.Given: To decide who will pay for lunch, Jeff and Chad decide to flip a coin three times. Chad chooses heads, and in order to win and have Jeff pay for his lunch, he must get heads at least twice out of three times.
Let,
H = Heads
T = Tails
Sample space = {HHH, HTH,THH,TTH, HHT, HTT,THT,TTT}
Total number of possible outcomes = 8
Probability that chad gets at least 2 heads is given as:
P(A)=P(getting two heads)+P(getting 3 heads)
= 3/8 + 1/8
= 4/8
= 1/2
Therefore, the probability chad gets at least 2 heads on 3 flips is 1/2 which was found using the sample space.
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what is 94 divided by 6? explain
Answer:
= 15 R 4
= 15 4/6
= 15 2/3
Step-by-step explanation:
1 5
6 9 4
− 6
3 4
− 3 0
4
94 divided by 6 is equal to 15, with a remainder of 4.
Here, we have,
To find 94 divided by 6, we perform the division operation.
94 ÷ 6
To do the division, we ask ourselves, "How many times does 6 fit into 94?"
Let's break it down step by step:
We start with the largest possible multiple of 6 that is less than or equal to 94.
The largest multiple of 6 that fits in 94 is 6 * 15 = 90.
Now, we have a remainder.
To find the remaining value, we subtract 90 from 94:
94 - 90 = 4
We still have 6 left to divide.
Since 4 is less than 6, we cannot form another complete group of 6.
So, the division is complete.
The result is:
94 ÷ 6 = 15 with a remainder of 4
So, 94 divided by 6 is equal to 15, with a remainder of 4.
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Lesson question: How does adding the two equations in a system allow you to solve it?
ANSWER FAST PLEASE
Answer:
Step-by-step explanation:
y-terms cancel out and are eliminated as a result of adding the two equations.
3. What percent of 150 is 15?
unknown:
Known:.
Answer:
Step-by-step explanation:
Simplify the expresson. Writevyour answer as a problem.
((-3)²)⁴
Answer:
9⁴
Step-by-step explanation:
\((( - 3 {)}^{2} {)}^{4} \\ ( {3}^{2} {)}^{4} = (3 \times 3 {)}^{4} \\ \)
\( = {9}^{4} \)
Answer:
6561
Step-by-step explanation:
(-3)² = 9
((-3)²)⁴ = (9)⁴ = 6561
How long did it take chi to complete the triathlon if she also got a flat tire that took 10 minutes to fix
it took her 10 minutes to fix
An aircraft flies due north from West to Z if y is equidistant from X and Z, find the bearing of X and Z
Amelie works on her homework for hour before her soccer practice and hour after her soccer practice.
How much time did Amelie spend on her homework altogether?
O hour
0 hour
O
hour
hour
4
Answer:
2 hours
Step-by-step explanation:
1 hour from before she does her soccer practice and another 1 hour after her soccer practice so it's going to be
1+1=2
Answer: she works on her homework in total for 2 hours.
Step-by-step explanation: 1+1=2, 60 minutes are in 1 hour, 60+60=120 minutes= 2 hours