The least upper bound of the elements {8, 12} under the divisibility relation on the set {1, 2, 3, 6, 8, 12, 24, 36} is 24.
To find the least upper bound of a set of elements under a relation, we look for the smallest element in the set that is greater than or equal to all of the elements in the set.
Under the divisibility relation, an element a is said to be divisible by an element b (written as b divides a) if a is a multiple of b, that is, a = b * k for some integer k. For example, 8 divides 24 because 24 = 8 * 3.
We want to find the least upper bound of the elements {8, 12} under this relation on the set {1, 2, 3, 6, 8, 12, 24, 36}. That means we want to find the smallest element in the set that is a multiple of both 8 and 12.
We can list the multiples of 8 and 12 in the set as follows:
Multiples of 8: 8, 24
Multiples of 12: 12, 24, 36
We can see that the smallest element in the set that is a multiple of both 8 and 12 is 24.
Therefore, the least upper bound under the divisibility relation on the set {1, 2, 3, 6, 8, 12, 24, 36} is 24.
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match the quadratic equation with the easiest method that could be used to find the solutions.
The quadratic equation with the easiest method that could be used to find the solutions:
5x² + 24x + 21 = 0 :: Factoring
x² + 4x + 27 = 0 :: Completing the Square
x² + 8x + 15 = 0 :: Factoring
-3x² = -5x + 8 :: Dividing by x and simplifying gives Quadratic Formula
What is equation?An equation is a mathematical statement that uses an equal sign to show that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of an equation is to solve for the variable(s) that make the equation true.
Here,
The easiest method to find the solutions of a quadratic equation depends on the form of the equation and the tools available. Here are some common methods and when they are typically used:
Zero Product Property/Factoring: This method is used when the quadratic equation can be factored into two linear factors, each of which equals zero.
Square Root Property: This method is used when the quadratic equation is in the form of x² = a, where a is a positive number. For example, the equation x² = 9 can be solved using the Square Root Property: take the square root of both sides and remember to include both the positive and negative roots, giving x = ±3.
Completing the Square: This method is used when the quadratic equation is in the form of x² + bx + c = 0, where b and c are constants. Completing the square involves adding and subtracting a constant term to both sides of the equation to create a perfect square trinomial, which can then be factored and solved using the Square Root Property.
Quadratic Formula: This method is used when the quadratic equation is in the form of ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. The Quadratic Formula is x = (-b ± √(b² - 4ac)) / 2a.
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There are 20 students in a class. Everyone in the class scored 6 out of 10 in a test. What is the range of their scores?
The range of scores is 0 to 10. Since everyone in the class scored 6 out of 10, the lowest possible score is 0 and the highest possible score is 10.
The range is the difference between the highest and the lowest of the given scores. In this case, it's 4 (10-6).
Therefore, the range of scores is 0 to 10. It is important to note that the range is a measure of the spread of scores in a dataset, and in this case, the spread is from the lowest possible score of 0 to the highest possible score of 10.
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A rental car company charges $74. 90 per day to rent a car and $0. 13 for every mile driven. Tyee wants to rent a car, knowing that:
He plans to drive 175 miles. He has at most $210 to spend. Write and solve an inequality which can be used to determine
�
x, the number of days Tyee can afford to rent while staying within his budget
Tyee can afford to rent the car for at most 2 days while staying within his budget.
Let x be the number of days Tyee can rent the car within his budget.
The total cost of renting the car will be the sum of the daily rental fee and the cost of miles driven:
Total cost = rental fee + (cost per mile x miles driven)
Using the given information, we can write the inequality:
74.90x + 0.13(175)x ≤ 210
Simplifying the expression, we get:
74.90x + 22.75x ≤ 210
97.65x ≤ 210
x ≤ 2.15
Therefore, Tyee can afford to rent the car for at most 2 days while staying within his budget.
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luis wants to create a graph using powerpoint to show how much weight he lost after starting an exercise plan over six months. which type of graph should he use?
Luis wants to create a graph using PowerPoint to show how much weight he lost after starting an exercise plan over six months. The type of graph that Luis should use is a line graph.
What is a line graph?A line graph is a method of displaying data or information on a two-dimensional Cartesian plane. It is mostly used to display changes over time or trends. It is ideal for data that has a lot of numeric data or that change frequently over time.The line graph is made up of two lines, one horizontal and the other vertical, which connect the data points in a sequential order. It is best used for visual representation of data, as it provides the viewer with a simple, visual representation of the data.
The x-axis and y-axis of a line graph represent the independent and dependent variables, respectively. The x-axis is often used to represent the time or the data being analyzed, while the y-axis represents the numerical values that are being analyzed.To create a line graph using PowerPoint, you can use the Insert Chart button to add your data, then choose Line Graph as the type of chart you want to create. You can then customize the chart as you like, including changing the colors, fonts, and background.
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A business owner applies for a credit card to cover $14,000 in emergency expenses. The credit card charges 16.99% annual interest compounded continuously. If no payments are made for 2 years, what will the balance on the card be, rounded to the nearest penny?
Credit card charges $19665.33 will the balance on the card be, rounded to the nearest penny.
What is interest in simple words?
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The interest rate for the loan is denoted by this proportion.
Interest is the cost of borrowing money and is typically stated as a percentage, such an annual percentage rate (APR). Lenders may charge interest to borrowers for the use of their funds, or borrowers may charge interest to lenders for the use of their funds.
amount applied for = $14,000
interest rate = 16.99%
the balance after 2 years
P₀ = $1400
r = 16.99% = 0.1699
t = 2
[tex]P_{0} = P_{0}e^{rt}[/tex]
[tex]P_{2} = 1400e^{0.1699 * 2}[/tex]
≈ $19665.33
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What is the value of angle X
Answer:
32
Step-by-step explanation:
PLEASE HELP NEED IT DONE RN !!
Answer: rectangleular pyramid
Step-by-step explanation:
SOMEONE, PLEASE HELP IM BEGGING
What are the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or leave in terms of π. SHOW YOUR WROK
Therefore , the solution of the given problem of angles comes out to be the arc length of the given arc 6.96 inches.
What does an angle mean?The curved lines which make up the ends of a skew are divided by its highest and bottom walls using Cartesian measurements. There is a possibility who two poles will collide at an intersection. Another result of two objects interacting is an angle. They most closely mimic dihedral shapes. Two line beams can be arranged in different ways between their extremities to form a two-dimensional curve.
Here,
The following is the algorithm for an arc's length:
=> (Central angle in degrees / 360°) x (2r) equals Arc Length
where r denotes the circle's radius.
The radius and central angle in this problem are both specified as 18 inches and 22 degrees. To determine the curve length, we can use the following formula:
=> Arc Length = 2 * 18 * (2 *360)
=> (0.0611) × (36) in, where:
=> 6.96 in
To the nearest hundredth or left in terms of, the arc length of the given arc is therefore roughly 6.96 inches.
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Which expression is not equal to 30? (2 x 60) x (24 + 2), (120 divided by 20) x (2 + 3), 2 + )30- 8 divided by 4), or (9 x 10) divided by (4 + 10) + 122
Option 3's expression, which is (2 x 60/30) x (24 + 2), is the only one that is not equal to 30.
We have to find the expression that is not equal to 30.
1) (120/20) x (2+3)
We'll start by using BODMAS to solve the brackets. The result is; = (120/20) 5
We therefore have:
= 6 x 5
= 30.
2) (9 x 10)/(4 + 1) + 12
Once more, answer the brackets first using BODMAS.
Hence, (90/5) + 12
Hence, (90/5) + 12
= 18 + 12
= 30.
3) (2 x 60/30) x (24 + 2)
Once more, answer the brackets first using BODMAS.
We'll utilize division instead of multiplication in the first bracket.
(2 x 60/30) x (26)
= 2 x 2 x 26
= 104
4) 2 + (30 - 8/4)
Once more, answer the brackets first using BODMAS.
Division comes first in the second bracket. So,
2 + (30 - 8/4)
= 2 + (30 - 2)
= 2 + 28 = 30
Hence, option 3's expression, which is (2 x 60/30) x (24 + 2), is the only one that does not equal 30.
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On the first day of school, the principal said Chase had the chance to
-2√8 as a mixed number please
Answer:
-√8
Step-by-step explanation:
Which expression can be used to model the phrase "the sum of three and a number"?
O 3+x
O x-3
O 3-х
O x•3
Answer: "3 + x".
Step-by-step explanation:
What is the answer to
(P-q) (3)
Answer: 3P-3q
Step-by-step explanation:
1. Rearrange the terms so that the constants are on the left
(P-q) x 3 ( Is times 3)
3(P-q)
2. distribute
3(P-q)
3P-3q
3.Solution
3P-3q
I NEED HELP PLEASE ANSWER ASAP
The value οf x = 4√2 in the given right angle triangle.
What is triangle?A clοsed triangle has three vertices, three sides, and three angles.
The symbοl fοr a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signbοards in the shape οf triangles are the mοst prevalent triangle-shaped οbjects.
A triangle is made up οf several cοmpοnents. It has 3 sides, 3 vertices, and 3 angles.
Three vertices, three internal angles, and three sides make up a triangle.
Accοrding tο the triangle's "angle sum prοperty," a triangle's three inner angles can never add up tο mοre than 180 degrees.
Using the Pythagοras theοrem
x² = 4² + 4² (both sides are equal as opposite angles are equal)
x² = 16 + 16
x² = 32
x = √32
x = [tex]\sqrt{16 \times 2}[/tex]
x = 4√2
Thus, the value of x = 4√2 in the given right angle triangle.
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paint is sold in one-gallon cans. one gallon of paint is needed to cover 350 ft2. if calvin wants to paint a wall that has an area of 2,000 ft2, how many cans of paint will calvin need to purchase to completely cover the wall with paint?
Paint is sold in one-gallon cans. one gallon of paint is needed to cover 350 [tex]ft^2[/tex]. If calvin wants to paint a wall that has an area of 2,000 [tex]ft^2[/tex]. There Calvin needs 6 cans of paint to completely cover the wall with paint.
As per given information,
Paint is sold in one-gallon cans.
One gallon of paint is needed to cover 350 [tex]ft^2[/tex].
If Calvin wants to paint a wall that has an area of 2,000 [tex]ft^2[/tex],
how many cans of paint will Calvin need to purchase to completely cover the wall with paint?
Calvin needs 5.71 cans of paint to completely cover the wall with paint.
Conversion formula for a gallon to feet:
1 gallon of paint = 350 [tex]ft^2[/tex]
To determine the number of gallons required to cover a wall that has an area of 2,000 [tex]ft^2[/tex], the number of gallons is calculated as follows:
Gallons = (Area / 350)
= (2,000 / 350)
= 5.71 cans (approx) ≅ 6 cans
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A scientist measures the amount of water collected in a tub at different times during the day. The table shows the time the water had been running and the amount of water in the tub.
Based on the information in the table, write an equation that can be used to find t, the number of minutes it took to collect w liters of water in the tub.
As a result, the following equation can be used to determine t, or how many minutes it took to fill the tub with w liters of water: t = (w - 0.2) / 0.4
what is slope ?Slope is a unit used to describe how steep or slope a line is. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on the line is what is referred to as the slope. In other words, the slope of the line going through the two points (x1, y1) and (x2, y2), which are on a line, is given by: Slope is equal to y2 - y1 / x2 - x1. Positive, negative, zero, or undefinable slopes are all possible.
given
With the slope and y-intercept in hand, we can now write the line's equation:
y = 0.4x + 0.2
Given a value for y, we wish to find a solution to this equation for x. In this instance, we're looking for t, or how many minutes it took to fill the tub with w liters of water. We can solve for x by substituting w for y:
w = 0.4t + 0.2
0.4t = w - 0.2
t = (w - 0.2) / 0.4
As a result, the following equation can be used to determine t, or how many minutes it took to fill the tub with w liters of water: t = (w - 0.2) / 0.4.
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(1) if the number of bacteria in a culture is 5 million at the end of 6 hours and 8 million at the end of 9 hours, how many were present initially?
There were initially 4 million bacteria in the culture.
To determine the initial number of bacteria in the culture, we can follow these steps:
Step 1: Identify the given data.
At the end of 6 hours, there are 5 million bacteria.
At the end of 9 hours, there are 8 million bacteria.
Step 2: Find the rate of bacterial growth.
Since the number of bacteria increased by 3 million (8 million - 5 million) over 3 hours (9 hours - 6 hours), the rate of bacterial growth is 1 million per hour (3 million ÷ 3 hours).
Step 3: Calculate the initial number of bacteria.
The number of bacteria increased by 5 million over the 6 hours. Therefore, if we divide this number by the rate of growth, we can determine the initial number of bacteria. Divide 5 million by 1 million per hour, which results in 5 hours.
Step 4: Subtract the time from the initial time.
Since we know that the culture was growing for 5 hours before reaching 5 million, we can subtract 5 hours from 6 hours, which equals 1 hour.
Step 5: Calculate the initial number of bacteria at 1 hour.
Since the bacteria grow at a rate of 1 million per hour, at the end of the 1st hour, there would be 1 million bacteria. Subtracting this number from the 5 million at the end of 6 hours will give us the initial number of bacteria: 5 million - 1 million = 4 million bacteria.
So, there were initially 4 million bacteria in the culture.
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(1 point) in a baseball league of 10 teams, how many games are needed to complete the schedule if each team plays 9 games with each other?
Answer:
90
Step-by-step explanation:
In a baseball league of 10 teams, 405 games are needed to complete the schedule if each team plays 9 games with each other.
Each team must play 9 games against each other, and there are 10 teams in the baseball league. We'll need to figure out how many games that means each team will play.Each team will play 9 games against every other team, for a total of 9 x 9 = 81 games played by each team (including games they play against themselves).Since there are 10 teams in the league, the total number of games played will be:
81 x 10 = 810.
However, each game is played between two teams, so we must divide by 2 to get the total number of games:
810 / 2 = 405.So, there will be 405 games played in the league.
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-1/x-1+2/x+5=1 State any restrictions on the variable if they exist
The solution to the equation is x = -2 if x ≠ 0.
The equation -1/x-1+2/x+5=1 can be rearranged to 2/x+1/x+5 = 0. To solve this equation, we must find the values of x for which the equation is true.
Since the equation involves dividing by x, we need to ensure that x is not equal to 0. Therefore, the restriction on the variable is x ≠ 0.
To solve the equation, we can first add -1/x to both sides to get 2/x + 5 = 1. Then, we can subtract 5 from both sides to get 2/x = -4. Finally, we can divide both sides by 2 to get x = -2.
Therefore, the solution to the equation is x = -2 if x ≠ 0.
To solve the given equation, we need to first find a common denominator. Here, the common denominator is (x - 1)(x + 5).-1(x + 5) + 2(x - 1) = (x - 1)(x + 5)Multiplying both sides by (x - 1)(x + 5), we get:-1(x + 5)(x - 1) + 2(x - 1)(x + 5) = (x - 1)(x + 5)(1)Expanding, we have:-x² - 4x + 5 + 2x² + 8x - 10 = x² + 4x - 5Simplifying,-x² + 2x² + x² - 4x + 8x + 4x + 5 + 10 - 5 = 0- x² + 8x + 10 = 0Rearranging, we have:x² - 8x - 10 = 0To solve the quadratic equation x² - 8x - 10 = 0, we use the quadratic formula. The formula is given byx = [-b ± sqrt(b² - 4ac)] / 2a Where a = 1, b = -8, and c = -10.Substituting these values, we get:[tex]x = [8 ± sqrt((-8)² - 4(1)(-10))] / 2(1)[/tex]
Simplifying = [8 ± sqrt(64 + 40)] / 2x = [8 ± sqrt(104)] / 2x = 4 ± sqrt(26)Therefore, the restrictions on the variable Are's ≠ 1 and x ≠ -5.
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a daily mail is delivered to your house between 1:00 p.m. and 6:00 p.m. assume delivery times follow the continuous uniform distribution. determine the percentage of mail deliveries that are made after 5:00 p.m.
The percentage of mail deliveries that are made after 5:00 p.m is 33.3%.
The continuous uniform distribution is a probability distribution that is used when all outcomes are equally likely, and they are spread out over a given interval.
In this case, the interval is from 1:00 p.m. to 6:00 p.m.
To determine the percentage of mail deliveries that occur after 5:00 p.m., we need to calculate the probability that the delivery time falls after 5:00 p.m.
The probability of a delivery time falling after 5:00 p.m. can be found by subtracting the probability of it falling before 5:00 p.m. from 1.
The probability of a delivery time falling before 5:00 p.m. is found by calculating the area under the probability density curve between 1:00 p.m. and 5:00 p.m.
This can be found using the following formula:
P(x ≤ 5:00 p.m.) = (5:00 p.m. – 1:00 p.m.) / (6:00 p.m. – 1:00 p.m.)
This gives us a probability of 0.667.
Therefore, the probability of a delivery time falling after 5:00 p.m. is 1 – 0.667 = 0.333, or 33.3%.
This means that 33.3% of the daily mail deliveries are made after 5:00 p.m.
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you randomly choose one of the chips. without replacing the first chip, you choose a second chip. find the probability of choosing a green chip, then a black chip.
The probability of randomly choosing a green chip, then a black chip without replacing the first chip is 1/6.
To explain, we need to consider the probability of choosing a green chip first, then a black chip. The probability of selecting a green chip is 1/3, since there are 3 green chips out of 9 chips in total. After selecting the green chip, there are still 8 chips left in the bag. Since there are 2 black chips, the probability of selecting the black chip is 2/8.
Therefore, the probability of randomly selecting a green chip, then a black chip without replacing the first chip is 1/3 * 2/8 = 1/6.
In conclusion, the probability of randomly choosing a green chip, then a black chip without replacing the first chip is 1/6.
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on a business retreat, your company of 32 businessmen and businesswomen go golfing. you need to divide up into foursomes (groups of 4 people): a first foursome, a second foursome, and so on. how many ways can you do this?
There are 4,845 ways to divide a group of 20 people into foursomes, and there are 1,800 ways to form foursomes with at least one Board member in each.
(a) The number of ways to divide a group of 20 people into foursomes can be calculated using the combination formula:
C(20,4) * C(16,4) * C(12,4) * C(8,4) * C(4,4)
where C(n,r) represents the number of ways to choose r items from a set of n items.
Plugging in the values, we get:
[C(20,4)] [C(16,4)] [C(12,4)] [C(8,4)] [C(4,4)] = 4,845,120
Therefore, there are 4,845,120 ways to divide the 20 people into foursomes.
(b) If we want to include one of the five Board members in each foursome, we can first choose the Board member for the first foursome (5 ways to do this), then choose the Board member for the second foursome (4 ways to do this), and so on. After choosing the Board members, we can then assign the remaining people to the foursomes in the same way as in part (a).
Therefore, the total number of ways to form the foursomes with one Board member in each foursome is:
5 [C(16,3)] [C(12,3)] [C(8,3)] [C(4,3)] = 1,254,720
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Complete question:
On a business retreat, your company of 20 businessmen and businesswomen go golfing.
(a) You need to divide up into foursomes (groups of 4 people): a first foursome, a second foursome, and so on. How many ways can you do this?
(b) After all your hard work, you realize that in fact, you want each foursome to include one of the five Board members. How many ways can you do this?
how many different arrangements are there of eight peo- ple seated at a round table, where two arrangements are considered the same if one can be obtained from the other by a rotation?
The number of different arrangements of eight people seated at a round table, where two arrangements are considered the same if one can be obtained from the other by a rotation, is (8-1)!/2 = 7!/2 = 2,520.
To solve this problem, we use the formula for arranging objects in a circle, which is (n-1)!, where n is the number of objects. In this case, there are 8 people, so the formula gives us (8-1)! = 7! arrangements if we do not consider rotations.
However, we need to eliminate the arrangements that are the same due to rotations. Since there are 8 people, we can rotate the table 8 times and still get the same arrangement. Thus, we divide 7! by 8 to eliminate these duplicate arrangements, which gives us (7!)/8.
But we are not done yet, because there is an additional duplicate arrangement that is not eliminated by the division. Specifically, we can flip the table over and get another arrangement that is the same as the original. Since we do not want to count this duplicate, we divide (7!)/8 by 2, giving us the final answer of 2,520.
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1. a certain tennis racquet at bob’s tennis racquet emporium costs $180.00 with a sales tax of 7%. what is the total cost of the racquet?2. tennis pro, a store across the street, offers a before-tax price of 10% less than bob’s store for a similar racquet. what will the price tag be on the similar racquet at tennis pro?
Total cost of racquet at Bob's Tennis Racquet Emporium is $192.60 with a 7% sales tax on the original price of $180.00. The price tag on a similar racquet at Tennis Pro, which offers a 10% discount, is $162.00 before tax.
To calculate the total cost of the tennis racquet at Bob's Tennis Racquet Emporium, we need to add the sales tax to the original price.
Sales tax = 7% of $180.00 = 0.07 x $180.00 = $12.60
Total cost = $180.00 + $12.60 = $192.60
Therefore, the total cost of the tennis racquet at Bob's Tennis Racquet Emporium is $192.60.
If Tennis Pro offers a before-tax price that is 10% less than Bob's store for a similar racquet, we can calculate the price tag as follows:
Price at Bob's store = $180.00
Discounted price at Tennis Pro = 10% less than $180.00 = 0.10 x $180.00 = $18.00 discount
Price at Tennis Pro = $180.00 - $18.00 = $162.00
Therefore, the price tag on the similar racquet at Tennis Pro is $162.00 before tax. The sales tax amount will depend on the applicable tax rate in the area where the store is located.
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PLEASE HELP ASAP!! NEED THIS RIGHT NOW
A crafts worker is knitting a circular rug that has a diameter of 80 inches. He would like to put trim around the outer edge of the rug. If 1 inch = 2.54 centimeters, how many centimeters of trim would
he need? Use π = 3.14 and round to the nearest centimeter.
O 638 centimeters
O 254 centimeters
O213 centimeters
O 33 centimeters
Answer:254
Step-by-step explanation:
I just did it
Answer: 254
Step-by-step explanation: i did a test and it was right
when using the empirical rule and you have a mean of 10 and a standard deviation of 1, approximately what percentage of values falls between 9 and 11?
When using the empirical rule and you have a mean of 10 and a standard deviation of 1, approximately 68% of values fall between 9 and 11.
The empirical rule is also known as the three-sigma rule, which states that the values under a normal distribution curve are given by:
Approximately 68% of values fall within one standard deviation from the mean
Approximately 95% of values fall within two standard deviations from the mean
Approximately 99.7% of values fall within three standard deviations from the mean
To solve the problem, we have to calculate how many standard deviations the given values are from the mean:
Lower value = 9Mean = 10
Upper value = 11
Standard deviation = 1
Now, calculate the z-scores:
Lower z-score = (9 - 10) / 1 = -1
Upper z-score = (11 - 10) / 1 = 1
The values between 9 and 11 are within one standard deviation from the mean, so we use the first part of the empirical rule:
Approximately 68% of values fall within one standard deviation from the mean
Therefore, approximately 68% of the values fall between 9 and 11.
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What is the vertex, opening, width, and axis of symmetry for f(x)=1/9(x-9)^2+3?
The vertex is (9, 3), the width of the parabola is 2/3 units, the axis of symmetry is the vertical line passing through x = 9.
What is quadratic function?f(x) = ax2 bx c, where x is the variable and a, b, and c are constants, is the formula for a quadratic function. It falls under the category of a degree two polynomial function.
In the given equation of a quadratic function:
f(x) = (1/9)(x - 9)² + 3
The vertex is (h, k), where h and k are the x-coordinate and y-coordinate of the vertex, respectively.
Here, the equation is in vertex form:
f(x) = a(x - h)² + k
Comparing this to the given equation, we can see that h = 9 and k = 3. Therefore, the vertex is (9, 3).
The opening of the parabola is upward because the coefficient "a" of the quadratic term (x - h)² is positive (1/9 in this case).
The width of the parabola can be determined using the formula:
w = 2√(a/k)
where a is the coefficient of the quadratic term and k is the y-coordinate of the vertex.
Plugging in the values, we get:
w = 2√[(1/9)/3] = 2/3
Therefore, the width of the parabola is 2/3 units.
The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two equal halves.The axis of symmetry's equation is as follows:.
x = h
Substituting h = 9, we get:
x = 9
Therefore, the axis of symmetry is the vertical line passing through x = 9.
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Becky made 10 cups of chocolate mousse for dessert. If she plans to serve each person 1/3 of a cup of chocolate mousse, how many people can she serve? 1/30 people 10 people 3 1/3 people 30 people
The answer is 30 people. Becky can serve 30 people. (Option 4).
To find the number of people Becky can serve, we need to divide the total amount of chocolate mousse she has by the amount each person will be served.
Since Becky has 10 cups of chocolate mousse, we can convert that into the number of 1/3 cup servings by multiplying by 3, which gives us 30 servings.
10 cups ÷ (1/3) cup/serving = 30 servingsTherefore, Becky can serve 30 people with the 10 cups of chocolate mousse she made.
It's important to note that an answer is a whole number, so the options of 1/30 people and 3 1/3 people are not reasonable answers. The correct answer is 30 people.
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Complete Question:
Becky made 10 cups of chocolate mousse for dessert. If she plans to serve each person 1/3 of a cup of chocolate mousse, how many people can she serve?
1/30 people 10 people 3 1/3 people 30 people3. Reasoning In Example 2, what happens to the
value of the dependent variable, a, the amount
still owed, when the value of the independent
variable, w, the number of weeks Ethan pays $5,
is increased by 1?
Answer:
In Example 2, the relationship between the dependent variable a, the amount still owed, and the independent variable w, the number of weeks Ethan pays $5, is given by the equation:
a = 100 - 5w
If we increase the value of w by 1, then the new value of w becomes w + 1. To find out what happens to the value of the dependent variable a, we substitute w + 1 for w in the equation:
a = 100 - 5(w + 1)
a = 100 - 5w - 5
Simplifying this expression, we get:
a = 95 - 5w
Comparing this expression to the original equation, we see that the value of the dependent variable a decreases by 5 when the value of the independent variable w is increased by 1. Therefore, if Ethan pays $5 for one more week, the amount still owed will decrease by $5.
650 of those surveyed said their favorite color was blue. if 65% of the students surveyed said their favorite color was blue, how many students were surveyed in total?
Answer:
let X be the value of the total students
[tex] \frac{65}{100} \times x = 650 \\ \\ \frac{65x}{100 } = 650 \\ if \: w \:e \: crossmultipl \\ 65x = 65000 \\ x = 65000 \div 65 \\ x = 1000[/tex]