As per the volume, we need to to purchase 4 containers of punch.
To calculate the amount of punch required, we need to find the total volume of punch needed, which can be calculated as follows:
Total volume of punch = number of students * volume of punch per student
= 25 * 8 fluid ounces
= 200 fluid ounces
Now, we know that the punch is sold in half-gallon containers. One gallon is equal to 128 fluid ounces. Therefore, a half-gallon container is equal to 64 fluid ounces. We can use this information to find out how many containers of punch are needed:
Number of containers of punch = Total volume of punch / Volume of punch per container
= 200 / 64
= 3.125
Since we cannot purchase a fractional number of containers, we need to round up to the nearest whole number. Therefore, we need to purchase 4 containers of punch.
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PLEASE LOOK AT IMAGINE BELOW
Answer: D
Step-by-step explanation:
An 18- ounce jar of peanut butter retails for $1.30. What is the unit price in dollars? Round to the nearest cent
Answer:
7 cents
Step-by-step explanation:
0.072222 rounded to the nearest cent is 0.07
when taping a television commercial, the probability that a certain actor will get his lines straight on any one take is 0.40. what is the probability that this actor will get his lines straight for the first time on the fourth attempt? assume attempts are independent. round your answer to three decimal places.
The probability that the actor will get his lines straight for the first time on the fourth attempt is 0.0864, rounded to three decimal places.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
The probability that the actor will get his lines straight on any one take is 0.40. This means that the probability of him not getting his lines straight on any one take is 1 - 0.40 = 0.60.
P(getting lines straight on 4th attempt)
= P(not getting lines straight on 1st, 2nd, or 3rd attempt) x P(getting lines straight on 4th attempt)
P(not getting lines straight on any one attempt) = 0.60
P(not getting lines straight on 1st, 2nd, or 3rd attempt) = 0.60 x 0.60 x 0.60 = 0.216
P(getting lines straight on 4th attempt) = 0.40
P(getting lines straight for the first time on the fourth attempt) = P(not getting lines straight on 1st, 2nd, or 3rd attempt) x P(getting lines straight on 4th attempt)
= 0.216 x 0.40 = 0.0864
Therefore, the probability that the actor will get his lines straight for the first time on the fourth attempt is 0.0864, rounded to three decimal places.
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2 Gallons of Juice for $4.50. How much per Gallon?
Answer: 2.25 per gallon
Step-by-step explanation:
4.50 divided by 2 = 2.25
For the given matrix A find a 3x2 matrix B such that AB=I, where I is the 2x2 identity matrix. [Hint: If B1 and B2 are the columns of B, then ABj = Ij.]A =1 2 11 1 1
We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix
Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.
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Find the sum of each infinite geometric sequence
-50, -25, -12.5, ...
Sum of the given geometric sequence is -100.
What is geometric sequence?A geometric sequence is the special type of sequence in which the ratio of every two successive terms is constant.
Sum of each infinite geometric sequence
-50, -25, -12.5, ...
The infinite sum of geometric sequence is given by,
[tex]s_{\infty} =\frac{a}{1-r}[/tex]
Where a is the first term in the sequence and r is the common ratio.
[tex]s_{\infty} =\frac{-50}{1-(-0.5)}[/tex]
= -100.
Hence, sum of the given geometric sequence is -100.
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A system of linear equations is shown in the graph. How many solutions does the system have?br /> One solution at (0, 4) One solution at (−3, 0) Infinitely many solutions No solution
There are two solutions to the system of linear equations depicted in the graph: one at (0,4) and one at (-3,0). There is only one distinct solution to the system of equations where the two lines intersect at the points (-3,0) and (0,4).
How can the number of solutions to a system of linear equations be determined?If the slopes are the same but the y-intercepts vary, the system has no solution. If the slopes are different, the system only has one solution. The system has an endless number of solutions if the slopes and y-intercepts match.
How many possible solutions can there be for a system of two linear equations?There are therefore countless possible answers. A different kind of linear equation system is a system with two parallel lines represented by the equations is referred to be an inconsistent system. The lines have distinct y-intercepts but the same slope.
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What is the slope of the line that passes through the points (0, - 4) and (30, -9)?
Write your answer in simplest form.
The slope of the line that passes through the points (0, - 4) and (30, -9) is -1/6.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 30).Points on y-axis = (-4, -9).Substituting the given data points into the slope formula, we have the following;
Slope, m = (-9 + 4)/(30 - 0)
Slope, m = -5/30
Slope, m = -1/6.
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Your Assignment
Is x = 6 a solution to the equation 5(x – 3) = x + 13?
Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
2. Simplify both sides. Show your work. (2 points)
3. Is x = 6 a solution to the equation? Why or why not? (3 points)
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
Your Assignment
Is x = 6 a solution to the equation 5(x – 3) = x + 13?
Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
2. Simplify both sides. Show your work. (2 points)
3. Is x = 6 a solution to the equation? Why or why not? (3 points)
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
Answer:
6 is not the solution. 7 is the solution.
Step-by-step explanation:
5(x -3) = x + 13 Substitute 6 for x
5(6 -3) = 6 + 13
5(3) = 19
15 ≠ 19
6 is not a solution because it results in a false statement. The two sides do not equal each other.
5(x - 3) = x + 13 Distribute the 5
5x -15 = x + 13 Subtract x from both sides
5x - x - 15 = x - x + 13
4x - 15 = 13 Add 15 to both sides
4x - 15 + 15 = 15 + 13
4x = 28 Divide both sides by 4
x = 7
7 is the solution to the equaion.
What is the area of this compound figure?
Answer:
98 km
Step-by-step explanation:
To find the area of the figure;
Total Area = Area A + Area B + Area C
Area A = 14 * 2 = 28 km2
Area B = 11 * 2 = 22 km2
Area C = 12 * 4 = 48 km2
Total Area = 98 km2
Make A the subject of the formula
r=√A/3
A cookie company made 40 batches of
cookies in 8.25 hours. Assuming a constant
rate of production, at what rate, in hour(s) per
batch, was the cookies made?
The hourly rate that the batches of cookies were made is given as follows:
4.85 batches per hour.
How to obtain the hourly rate?The hourly rate is obtained applying the proportions in the context of the problem.
A proportion is applied as the rate is obtained dividing the total production by the time in hours.
The parameters for this problem are given as follows:
Production of 40 batches.Time of 8.25 hours.Hence the rate is given as follows:
40/8.25 = 4.85 batches per hour.
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Ashton just launched a new business page on social media. After one month, she has
35 followers. She decides to take a course that promises to triple her number of
followers each month for 6 months. After 7 months, how many followers will Ashton
have if this is true?
3
Step-by-step explanation:
35 times 3.sub
Jamal mows lawns and wants to save money. Jamal currently
has $25 and plans to save an additional $25 per month. Which
graph represents the number of months it will take Jamal to
save at least $250?
Answer: eat grass whor
Step-by-step explanation:
k
m
(x-30)°
y
n
(x+50)
Find the values of x and y that make k || j and
m || n.
x=
y =
0
The value of variables x and y are,
⇒ x = 80°
⇒ y = 130°
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Since, A parallelogram is forming here,
Then, Opposite angels are going to be equal.
Thus, We get;
⇒ y = (x + 50)°
Now, As you know that sum of all angles of a quadrilateral equals 360°
Hence, We get;
2 {(x + 50) + (x - 30)} = 360°
(x + 50) + (x - 30) = 180°
2x + 20 = 180
2x = 160
x = 80°
So, We get;
⇒ y = (x+50)
= 80 +50
= 130°
And,
⇒ x = 80°
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I need explanations under similar shapes
The two major properties of similar shapes include the following:
They must have the same shape.They can have different sizes.What are the properties of similar geometric shapes?In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied because it would either enlarge (increase) or reduce (decrease) them.
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An online furniture store sells chairs for $100 each and tables for $450 each. Every
day, the store can ship at most 16 pieces of furniture and must sell at least $3000
worth of chairs and tables. If 9 chairs were sold, determine the minimum number of
tables that the store must sell in order to meet the requirements.
The minimum number of tables the store must sell is 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Using t and c as variables, we get
100c + 400t ≥ 3000
c+t≤16
The online furniture store must sell at least $3000 worth of chairs and tables each day, and can ship at most 16 pieces of furniture.
If the store sells 9 chairs for a total of $900, it needs to sell at least 5 tables to reach a total revenue of $3000.
Since the total number of pieces of furniture sold is 14 (9 chairs + 5 tables), which is less than the maximum of 16, the store meets the daily shipping requirement.
Therefore, the minimum number of tables the store must sell is 5.
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Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plan in still air.
The speed of the plane is 135 km/h and wind speed is 23 km/h. The solution has been obtained by forming linear equations.
What is a linear equation?
This is the linear equation with the largest degree of one. This demonstrates that there are no variables in linear equations with exponents greater than 1. A straight line appears on the graph as a result of such an equation.
Let the plane speed be 'P' and the wind speed be 'W'.
We are given that while flying to Kampala with a tailwind a plane averaged 158 km/h.
So, we get an equation as
P + W = 158 ...(1)
Also, on the return trip plane only averaged 112 km/h while flying back into the same wind.
So, we get another equation as
P - W = 112 ...(2)
Now, on adding the equations we get,
⇒P + W + P - W = 158 + 112
⇒2P = 270
⇒P = 135
Now substituting the value into either equation, we get
⇒P + W = 158
⇒135 + W = 158
⇒W = 23
Hence, the speed of the plane is 135 km/h and wind speed is 23 km/h.
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ver the next 14 months you have to read at least 42 books. You have to read x books per month. The inequality 14x242 represents this situation. Solve the inequality to
nd the number of books you have to read per month.
ou have to read at leastbooks per month.
The number of books to read per month is 3 or more.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
14x ≥ 42
Solve for x.
14x ≥ 42
Divide both sides by 14.
x ≥ 42/14
x ≥ 3
This means,
The number of books to read per month is 3 or more.
Thus,
The number of books to read per month is 3 or more.
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State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Answer:
AAS
Step-by-step explanation:
[tex]\overline{PR} \cong \overline{PR}[/tex] by the reflexive property.
what is the size of the key space if all 8 characters are randomly chosen 8-bit ascii characters? how long does the average key search take with a single pc?
The size of the key space is 256^8, or 2^64. The average key search time would be 2^64/processing power of PC, which would be a very large number.
The question is asking about the size of the key space if 8 randomly chosen 8-bit ASCII characters are used, and how long it would take to find a key on a single PC.
The size of the key space if all 8 characters are randomly chosen 8-bit ASCII characters is 256^8 = 2^64 = 18,446,744,073,709,551,616.
The average key search time with a single PC would be 18,446,744,073,709,551,616 / 2,000,000,000,000 (2 trillion) operations per second = 9,223,372,036,854,775.8 seconds, which is approximately 292,030 years.
The size of the key space for an 8-bit ASCII character is 2^64 combinations. On average, it will take a single PC 2^64 / (processing speed of PC in Hz) seconds to search through the entire key space.
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Question 15 (5 points)
Anthony's teacher told him that he needed to read more than 20 minutes each day.
Which inequality represents the amount of time he needs to read daily if m
represents the number of minutes?
Om > 20
m < 20
Om > 20
Om ≤ 20
Answer:
m<20
Step-by-step explanation:
Let A={2,4,6} and B={135}
R={(2,2),(4,4),(6,6)} is a relation on A. Express the relation
The relation:
{x = y : x, y ε A}.
And this relation is a function.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
A={2,4,6} and B={135}
R={(2,2), (4,4), (6,6)} is a relation on A.
That means, each value of set A connects to the same point.
The relation:
{x = y : x, y ε A}
Hence, {x = y : x, y ε A}.
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Convert the Senary (base 6 number 54724 to decimal
Answer: To convert a Senary (base 6) number to decimal, we can use the following formula:
Decimal = (5 * 6^4) + (4 * 6^3) + (7 * 6^2) + (2 * 6^1) + (5 * 6^0)
= (5 * 1296) + (4 * 216) + (7 * 36) + (2 * 6) + (5 * 1)
= 6480 + 864 + 252 + 12 + 5
= 7603
So the Senary (base 6) number 54724 is equivalent to the decimal number 7603.
Step-by-step explanation:
In a class of 60 students, the number of students who passed Ga is 6 more than the number that passed fante. Every student passed at least one of the two subjects and 8 students passed both subjects. How many students passed only one subject?
52 students passed only one subject
How to find the number of students who passed each subject
Let's use the following variables to represent the number of students who passed each subject:
P(Ga): the number of students who passed Ga
P(Fante): the number of students who passed Fante
From the problem statement, we know that:
P(Ga) = P(Fante) + 6, since the number of students who passed Ga is 6 more than the number who passed Fante
P(Ga ∩ Fante) = 8, since 8 students passed both subjects
P(Ga ∪ Fante) = 60, since every student passed at least one subject
We want to find the number of students who passed only one subject, which is equal to the total number of students who passed Ga minus the number of students who passed both subjects, plus the number of students who passed Fante but not Ga. In symbols:
P(Ga) - P(Ga ∩ Fante) + (P(Fante) - P(Ga ∩ Fante))
Substituting the values we know:
(P(Fante) + 6) - 8 + (P(Fante) - 8)
Simplifying:
2P(Fante) - 10
We also know that P(Ga) + P(Fante) - P(Ga ∩ Fante) = P(Ga ∪ Fante) = 60.
Substituting the values we know:
P(Ga) + P(Fante) - 8 = 60
P(Ga) + P(Fante) = 68
Substituting P(Ga) = P(Fante) + 6:
2P(Fante) + 6 = 68
2P(Fante) = 62
P(Fante) = 31
Therefore, the number of students who passed only one subject is:
2P(Fante) - 10 = 2(31) - 10 = 52
Therefore, 52 students passed only one subject.
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A bag contains only red and blue marbles. There are a total of 36 marbles in the bag. There are 5 red marbles for every 4 blue marbles in the bag.
Part A) How many of each color marble are in the bag?
Part B) A student removes 1 blue marble from the bag. The student reasons that the ratio of red to blue marbles is now 5:3 since 4 - 1 = 3.
Explain the error in the student's reasoning.
Compute the correct ratio of red to blue marbles after 1 blue marble is removed.
Answer:
The ratio computed shows that the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.
How to illustrate the ratio?
From the information given, there are 36 marbles in the bag. The number of red marbles will be:
= 5/9 × 36
= 20 marbles
The number of blue marbles will be:
= 4/9 × 36
= 16 marbles
When a student removes 1 blue marble from the bag, the number of blue marbles will be:
= 16 - 1
= 15 marbles.
Therefore, the ratio of red to blue marbles will be:
= 20:15 = 4:3
Therefore, the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.
10+3s≥19 Need help pls
Answer: s≥3
Step-by-step explanation: fist you need to get the variable by itself on one side. So subtract the 10 from each side and you have 3s≥9. Then you divide each side ny 3 to get s by itself, divide 9 by 3. Then your answer is s≥3
2. Suppose the New York Yankees play a double-header (two games). Using W for a win and L
for a loss, list all the possible outcomes for the double-header. If we are only interested in the
total number of games the Yankees win, what are the possible events for the two games?
If we are only interested in the total number of games the Yankees win, the possible events for the two games are: 0 wins: LL , 1 win: LW, WL and 2 wins: WW
What is event in probability ?
In probability, an event is a subset of the sample space of a random experiment. In other words, an event is a collection of possible outcomes of the experiment.
For example, consider flipping a fair coin. The sample space of this experiment is {heads, tails}. An event could be defined as "getting heads", which is a subset of the sample space that includes only one outcome.
There are four possible outcomes for the double-header, which can be represented using W for a win and L for a loss:
WW (Yankees win both games)
WL (Yankees win the first game, but lose the second game)
LW (Yankees lose the first game, but win the second game)
LL (Yankees lose both games)
Therefore , If we are only interested in the total number of games the Yankees win, the possible events for the two games are: 0 wins: LL , 1 win: LW, WL and 2 wins: WW
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Jude types 1,274 characters in 7 minutes. What is her typing rate in characters per minute?
A.
187 characters per minute
B.
184 characters per minute
C.
182 characters per minute
D.
179 characters per minute
Using arithmetic operation Jude's typing rate is 182 characters per minute, which is option C.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
To find the typing rate in characters per minute, we need use arithmetic operation of division.
Divide the number of characters by the number of minutes -
Typing rate = Number of characters / Number of minutes
In this case, Jude types 1,274 characters in 7 minutes, so her typing rate is -
Typing rate = 1274 / 7 = 182
Therefore, the typing rate is 182 characters/minute.
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By what percent will a fraction decrease if its numerator is decreased of 85% and the denominator is decreased by 25%. BRAINLEST FOR FIRST CORRECT ANSWER
The percent will the fraction decrease should be 80%.
Important information:
In the case when its numerator is decreased by 85% and its denominator is decreased by 25%
Calculation of percentage:
= (100-85) ÷ (100 - 25)
= 15%÷ 75%
= 20%
Now the decrease in percentage should be
= 100% - 20%
= 80%
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The correct answer is 80%
