A cook is adding soup to a 10-liter
capacity pot. The equation
y = 1.5x + 2.5 relates the liters
of soup y added to the pot in
x minutes.
Part A
How much soup was in the pot to
start with?
____liters
Part B
At what rate does the cook fill
the pot?
_______liters per minute
Answers
The required answers are 2.5 liters and 1.5 liters per minute.
How to deal with the equation of variable at different value?Part A:
If we know that the pot has a capacity of 10 liters, we can use the equation y = 1.5x + 2.5 to determine how much soup was in the pot to start with, since at x = 0 minutes, no soup has been added yet.
Substituting x = 0 in the equation, we get:
y = 1.5(0) + 2.5
y = 2.5
Therefore, the pot had 2.5 liters of soup to start with.
Part B:
The equation y = 1.5x + 2.5 tells us how much soup is added to the pot in x minutes, so the rate at which the cook fills the pot can be found by taking the derivative of y with respect to x:
dy/dx = 1.5
Therefore, the rate at which the cook fills the pot is 1.5 liters per minute.
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Related Questions
The green parallelogram is a dilation of the black parallelogram. What is the scale factor of the dilation?
A) 1/3
B) 1/2
C) 2
Answers
Your answer will depend on the measurements you obtain from the parallelograms.
To determine the scale factor of the dilation between the green parallelogram and the black parallelogram, follow these steps:
1. Choose corresponding sides of both parallelograms (e.g., the base or the height).
2. Measure the length of the chosen side in the green parallelogram and the same side in the black parallelogram.
3. Divide the length of the side in the green parallelogram by the length of the corresponding side in the black parallelogram.
The result will be the scale factor of the dilation. Compare the result with the given options:
A) 1/3
B) 1/2
C) 2
Your answer will depend on the measurements you obtain from the parallelograms.
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he circumference of an inflated basketball is 29.516 inches. What is the volume of the basketball? Use 3.14 for π. Round final answer to the nearest whole number.
Use 3.14 for π. PLSSSS HELPPP
Answers
the volume of the basketball is approximately 490 cubic inches. we can get this answer by using volume formula of volume
what is approximately ?
"Approximately" means almost, but not exactly. It is used to indicate that a value or quantity is very close to the true or exact value, but there may be a small difference or error. In mathematical terms, an approximate value is an estimate or a rounded value that is used
In the given question,
To find the volume of the basketball, we first need to find its radius.
Circumference of a sphere = 2πr
29.516 = 2 * 3.14 * r
r = 29.516 / (2 * 3.14) ≈ 4.7 inches (rounded to one decimal place)
Now, we can use the formula for the volume of a sphere:
Volume of sphere = (4/3) * π * r^3
Volume of basketball = (4/3) * 3.14 * (4.7)^3
Volume of basketball ≈ 490 cubic inches (rounded to the nearest whole number)
Therefore, the volume of the basketball is approximately 490 cubic inches..
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Which table shows a proportional relationship between x and y?
Answers
Shari bought 3 breath mints and received $2. 76 change. Jamal bought 5 breath mints
and received $1. 20 change. If Shari and Jamal had the same amount of money, how
much does one breath mint cost?
A. Each breath mint costs $0. 28.
B. Each breath mint costs $0. 49.
c. Each breath mint costs $0. 78.
D. Each breath mint costs $1. 98.
Answers
Each breath mint costs $0.78. The correct answer is C.
To solve this problem, we can use the concept of a system of linear equations. Let x be the cost of one breath mint and y be the total amount of money Shari and Jamal had.
We know that Shari bought 3 breath mints and received $2.76 change, so her equation will be:
3x + 2.76 = y
Jamal bought 5 breath mints and received $1.20 change, so his equation will be:
5x + 1.20 = y
Now we have a system of two equations with two variables:
3x + 2.76 = y
5x + 1.20 = y
We can solve for x by setting the two equations equal to each other:
3x + 2.76 = 5x + 1.20
Now, solve for x:
2x = 1.56
x = 0.78
So, each breath mint costs $0.78. The correct answer is C.
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The area of a rectangle is 72x^13y^9z^16 square yards. The length of the rectangle is 3x9y4z^5 yards. Find the simplified expression of the width of the rectangle in yards.
Answers
The expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.
Given that the area of a rectangle is 72x¹³y⁹z¹⁶ sq. yds and the length of the rectangle is 3x9y4z⁵, we need to find the width,
Using these expressions, we have,
Area = length × width
72x¹³y⁹z¹⁶ / 3x9y4z⁵ = width
Width = 72x¹³/3x × y⁹/9y × z¹⁶/4z⁵
Width = 24x¹²y⁸z¹¹/36 = 2x¹²y⁸z¹¹/3
Hence the expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.
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Mr.Franklin drives 37 miles each day to and from work. How many miles does he drive in 20 work days
Answers
Answer:
740
Step-by-step explanation:
37 times 20
Answer:
740 miles
Step-by-step explanation:
37 miles in 1 day
So we need to multiply 37*20 to find the number of miles for 20 days
So, he travels 740 miles
Every day, Carmen walks to the bus stop and the amount of time she will have to wait for the bus is between 0 and 12 minutes, with all times being equally likely (i. E. , a uniform distribution). This means that the mean wait time is 6 minutes, with a variance of 12 minutes. What is the probability that her total wait time over the course of 60 days is less than 5. 5 hours
Answers
The probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.
The total wait time over 60 days will have a mean of 360 minutes (6 minutes per day x 60 days) and a variance of 720 minutes (12 minutes per day x 60 days). Since the wait times are uniformly distributed, the total wait time over 60 days will follow a normal distribution.
To find the probability that the total wait time over 60 days is less than 5.5 hours, we need to standardize the value using the z-score formula:
z = (x - μ) / σ
where x is the total wait time in minutes, μ is the mean total wait time in minutes, and σ is the standard deviation of the total wait time in minutes.
Substituting the values, we get:
z = (330 - 360) / sqrt(720) = -1.4434
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.4434 is 0.0746.
Therefore, the probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.
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You are going to calculate what speed the kayaker 's are paddling, if they stay at a constant rate the entire trip, while kayaking in Humboldt bay.
key information:
River current: 3 miles per hour
Trip distance: 2 miles (1 mile up, 1 mile back)
Total time of the trip: 3 hours 20 minutes
1) Label variables and create a table
2) Write an quadratic equation to model the problem
3) Solve the equation. Provide supporting work and detail
4) Explain the results
Answers
Let's label the speed of the kayaker as "k" and the speed of the current as "c". We can use the following table to organize the information:
| Distance | Rate | Time |
|------------|--------|--------|
| 1 mile | k - c | t1 |
| 1 mile | k + c | t2 |
| 2 miles | | 3h20m |
Note that we use "t1" and "t2" to represent the time it takes to travel one mile in each direction, since the kayaker is traveling at a different rate relative to the current in each direction.
2) Quadratic Equation:
To solve for "k", we can use the formula:
distance = rate x time
For the first leg of the trip, we have:
1 = (k - c) x t1
Solving for t1, we get:
t1 = 1 / (k - c)
For the second leg of the trip, we have:
1 = (k + c) x t2
Solving for t2, we get:
t2 = 1 / (k + c)
Since the total time of the trip is 3 hours 20 minutes, or 3.33 hours, we can write:
t1 + t2 = 3.33
Substituting the expressions for t1 and t2, we get:
1/(k-c) + 1/(k+c) = 3.33
Multiplying both sides by (k-c)(k+c), we get:
(k+c) + (k-c) = 3.33(k-c)(k+c)
Simplifying, we get:
2k = 3.33(k^2 - c^2)
Multiplying out the right side, we get:
2k = 3.33k^2 - 3.33c^2
Rearranging and setting the equation equal to zero, we get:
3.33k^2 - 2k - 3.33c^2 = 0
This is a quadratic equation in "k".
3) Solving the Equation:
We can solve this quadratic equation using the quadratic formula:
k = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3.33, b = -2, and c = -3.33c^2. Substituting these values, we get:
k = (-(-2) ± sqrt((-2)^2 - 4(3.33)(-3.33c^2))) / 2(3.33)
Simplifying, we get:
k = (2 ± sqrt(4 + 44.286c^2)) / 6.66
4) Explanation of Results:
The quadratic equation has two solutions for "k", but one of them is negative and therefore not physically meaningful. The other solution gives the speed of the kayaker relative to the water:
k = (2 + sqrt(4 + 44.286c^2)) / 6.66
This equation shows that the speed of the kayaker depends on the speed of the river current. As the current gets stronger (i.e., as "c" increases), the kayaker needs to paddle faster to maintain a constant speed relative to the water. Conversely, if the current is weaker, the kayaker can paddle more slowly and still maintain the same speed.
Dolly went to the Walmart and he buy 14 teddy bears and 3 dolls for 158 $ and her sister went to the Gwinnett place mall and she buy 8 teddy bears and 12 dolls for 296 $. If they both buy same brand bears and dolls, then what is price of one teddy bear and one doll? (use matrices multiplication to solve system of equations. ) (Show work)
Answers
The price of one teddy bear is $7 and the price of one doll is $14.
Let's use matrices to solve this system of equations:
First, we need to define the variables:
x = price of one teddy bear
y = price of one doll
Then we can write the system of equations:
14x + 3y = 158
8x + 12y = 296
system of matix:
| 14 3 | | x | | 158 |
| 8 12 | * | y | = | 296 |
To solve for x and y, we can use matrix multiplication and inversion:
| x | | 12 -3 | | 158 | | 99 |
| y | = | -8 14 | * | 296 | = | -14 |
So, x = $7 and y = $14. Therefore, the price of one teddy bear is $7 and the price of one doll is $14.
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 Solve for the value of p
Answers
Answer:
p = 38
Step-by-step explanation:
We Know
The 104° angle + (2p) angle must be equal to 180°.
Solve for the value of p.
Let's solve
104° + 2p = 180°
2p = 76°
p = 38
If x-2 and x+2 are the factors of the polynomial p(x) = x³− 4mx²− 2nx + 1 = 0, then find the values of m and n.
Answers
If x-2 and x+2 are the factors of the polynomial p(x) = x³− 4mx²− 2nx + 1 = 0, then the values of m and n are 5/4 and 1/2, respectively.
Given that the factors of the polynomial p(x) = x³ - 4mx² - 2nx + 1 are x - 2 and x + 2, we can write:
p(x) = (x-2)(x+2)(x-a)
where a is the remaining root of p(x).
Expanding this equation, we get:
p(x) = (x²-4)(x-a) = x³ - (4+a)x² + 4ax - 4a
Comparing the coefficients of this expression with the coefficients of the original polynomial, we get the following system of equations:
4+a = 4m
4a = -2n
-4a = 1
Solving these equations, we get:
a = -1/4, m = 5/4, n = -2a = 1/2
Therefore, the values of m and n are 5/4 and 1/2, respectively.
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Write the product using exponents.
4⋅4⋅4⋅4⋅4
Answers
What connection does the author draw between the workers’ rights and their quality of life? in the st. Petersburg workmen's petition to the tsar
Answers
The "St. Petersburg Workmen's Petition to the Tsar" was a document written in 1870 by a group of Russian workers, which expressed their grievances and called for greater rights and protections in the workplace.
While the text of the petition is too long to summarize in its entirety, the following points illustrate some of the connections that the authors draw between workers' rights and their quality of life:
- The petitioners argue that workers have the right to a fair wage that allows them to support themselves and their families, and that without this right, workers are forced to live in poverty and squalor.
- They also argue that workers have the right to safe and healthy working conditions, and that without this right, workers are subjected to disease and injury that can shorten their lives and reduce their quality of life.
- The petitioners further argue that workers have the right to organize and advocate for their own interests, that without this right, workers are powerless to negotiate with their employers and to protect themselves against exploitation.
- They also argue that workers have the right to education and self-improvement, and that without this right, workers are trapped in a cycle of ignorance and subservience that limits their potential and reduces their quality of life.
- Overall, the authors of the petition argue that workers' rights and their quality of life are inextricably linked, and that without the former, the latter is impossible to achieve.
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Joey is 20 years younger than becky in two years becky will be twice as old as joey what are their present ages
Answers
Becky is currently 38 years old and Joey is currently 18 years old.
Let's start by assigning variables to their ages. Let Joey's age be "J" and Becky's age be "B".
From the first piece of information, we know that Joey is 20 years younger than Becky. This can be expressed as:
J = B - 20
Now, let's use the second piece of information. In two years, Becky will be twice as old as Joey. So, we can set up an equation:
B + 2 = 2(J + 2)
We add 2 to Becky's age because in two years she will be that much older. On the right side, we add 2 to Joey's age because he will also be two years older. Then we multiply Joey's age by 2 because Becky will be twice his age.
Now, we can substitute the first equation into the second equation:
B + 2 = 2((B - 20) + 2)
Simplifying the right side:
B + 2 = 2B - 36
Add 36 to both sides:
B + 38 = 2B
Subtract B from both sides:
38 = B
So, Becky is currently 38 years old. Using the first equation, we can find Joey's age:
J = B - 20
J = 38 - 20
J = 18
So, Joey is currently 18 years old.
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Tony is playing a games there is 1/8 chance the spinner will land on red and 3/8 chance that the spinner will land on yellow what is the probabilty chance the the spinner will not land on red then land on red
Answers
The probability of the spinner not landing on red and then landing on red is 7/64.
What is the probability that none is red?
The probability chance that the spinner will not land on red then land on red is calculated as follows;
The probability of the spinner not landing on red is 1 - 1/8 = 7/8.
To find the probability that the spinner will not land on red and then land on red, we multiply the probabilities:
(7/8) x (1/8) = 7/64
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After pouring 4.8 liters of water into a bucket, the bucket contains 14.3 liters. Write an equation to represent the situation.
Answers
Answer: x + 4.8 = 14.3
Step-by-step explanation:
Let x be the initial amount of water that was already in the bucket before the additional 4.8 liters of water was poured in.
Then the total amount of water in the bucket after pouring in the 4.8 liters is the sum of the initial amount x and the amount of water poured in, which is 4.8 liters. This can be represented by the equation:
x + 4.8 = 14.3
We can simplify this equation by solving for x:
x = 14.3 - 4.8
x = 9.5
Therefore, the initial amount of water in the bucket was 9.5 liters, and after pouring in 4.8 liters, the bucket contained a total of 14.3 liters.
suppose discrete random variables x and y have a joint distribution: a. what is the expectation of x y? that is, what is e(x y)?
Answers
The expectation of the product of two discrete random variables x and y is given by E(xy) = ∑(x∑(yP(x,y))) where P(x,y) is the joint probability distribution of x and y.
To find the expectation of the product of two random variables, we need to use the formula:
E(XY) = ΣΣ(xy)p(x,y)
where p(x,y) is the joint probability mass function of X and Y.
So, for the given joint distribution of X and Y, we have:
E(XY) = ΣΣ(xy)p(x,y)
We need to sum this over all possible values of X and Y. If the joint distribution is given in a table or a function form, we can simply plug in the values of X and Y and calculate the sum.
However, without any specific information about the joint distribution of X and Y, it is impossible to calculate the expectation of X times Y. We would need to know either the joint probability mass function or the joint probability density function of X and Y.
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What is the probability that the drug will wear off between 200 and 220 minutes?
P(200
Answers
The probability that the drug will wear off between 200 and 220 minutes is 0.4.
To calculate the probability that the drug will wear off between 200 and 220 minutes, we need to know the cumulative distribution function (CDF) of the drug's effect duration. Let's say the CDF is denoted by F(t), where t is the time in minutes.
Then, the probability that the drug will wear off between 200 and 220 minutes is given by:
P(200 < T < 220) = F(220) - F(200)
This is because the probability of the drug wearing off between two specific times is equal to the difference between the CDF values at those times.
For example, if F(200) = 0.2 and F(220) = 0.6, then:
P(200 < T < 220) = 0.6 - 0.2 = 0.4
Therefore, the probability that the drug will wear off between 200 and 220 minutes is 0.4.
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A sample of an element with a half-life of 8 years has a mass of 10 grams after 100 years. What was the mass of the original sample?
Answers
The mass of the original sample was approximately 1592.5 grams.
A sample of an element with a half-life of 8 years has a mass of 10 grams after 100 years. What was the mass of the original sample?The half-life of an element is the time it takes for half of a given sample of that element to decay.
Let's assume that the original mass of the sample was x grams.
After the first half-life of 8 years, the mass of the sample would be x/2 grams.
After the second half-life (16 years total), the mass would be x/4 grams.
After the third half-life (24 years total), the mass would be x/8 grams.
We can continue this pattern until we get to 100 years (which is 12.5 half-lives):
Mass after 100 years = x/2^12.5
We also know from the problem that the mass after 100 years is 10 grams:
x/2^12.5 = 10
Solving for x:
x = 10 x 2^12.5
x ≈ 1592.5 grams
Therefore, the mass of the original sample was approximately 1592.5 grams.
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Find the absolute (i.e., global) maximum and absolute minimum values of the function f(x) = 8x/6х + 4 on the interval (1,5) Absolute maximum = Absolute minimum =
Answers
The absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.
To find the absolute maximum and minimum values of the function f(x) = 8x/(6x + 4) on the interval (1, 5), we need to find the critical points of the function within the interval and evaluate the function at those points, as well as at the endpoints of the interval.
First, let's find the derivative of the function:
f(x) = 8x/(6x + 4)
f'(x) = [8(6x + 4) - 8x(6)] / (6x + 4)^2
f'(x) = [8(2)] / (6x + 4)^2
f'(x) = 16 / (6x + 4)^2
The critical points occur when f'(x) = 0 or is undefined. However, since f'(x) is always positive on the interval (1, 5), there are no critical points within the interval.
Next, let's evaluate the function at the endpoints of the interval:
f(1) = 8(1)/(6(1) + 4) = 8/10 = 4/5
f(5) = 8(5)/(6(5) + 4) = 40/34 = 20/17
Finally, we need to determine which of these values is the absolute maximum and which is the absolute minimum.
Since f(x) is always positive on the interval (1, 5), the function can never be less than 0. Therefore, the absolute minimum value is the smallest value of f(x) on the interval, which occurs at x = 5, where f(5) = 20/17.
To find the absolute maximum value, we compare the values of f(1), f(5), and the maximum value of f(x) as x approaches the endpoints of the interval. We can use the fact that the function is continuous on the closed interval [1, 5] to find the maximum value.
As x approaches 1, we have:
f(x) = 8x/(6x + 4) → 8/10 = 4/5
As x approaches 5, we have:
f(x) = 8x/(6x + 4) → 40/34 = 20/17
Therefore, the absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.
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In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less
find the sample size needed to estimate that percentage. use a 0.01 margin of error and use a confidence level of 95%. assume that nothing is known about the percentage to be estimated
Answers
A sample size of 9604 is needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, with a 95% confidence level and a margin of error of 0.01.
To find the sample size needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, we can use the following formula:
n = [Z^2 * p * (1 - p)] / E^2
where:
Z is the z-score associated with the desired confidence level (95%), which is 1.96
p is the estimated proportion of students who earn a bachelor's degree in four years or less (since we don't have any prior knowledge, we can use 0.5 as a conservative estimate)
E is the margin of error, which is 0.01
Plugging in the values, we get:
n = [(1.96)^2 * 0.5 * (1 - 0.5)] / (0.01)^2
n = 9604
Therefore, a sample size of 9604 is needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, with a 95% confidence level and a margin of error of 0.01.
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Laura is driving to Los Angeles. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.85. See the figure below. Laura has 52 miles remaining after 41 minutes of driving. How many miles were remaining after 33 minutes of driving?
Answers
The remaining distance after 33 minutes of driving = 58.8 miles.
Here, the slope of a linear function the remaining distance to drive (in miles) is -0.85
For this situation, we can write a linear equation as,
remaining distance = (slope)(drive time) + (intercept)
remaining distance = -0.85(drive time) + (intercept)
y = -0.85x + c ..........(1)
where y represents the remaining distance
x is the drive time
and c is the y-intercept
Here, Laura has 52 miles remaining after 41 minutes of driving.
i.e., x = 41 and y = 52
Substitute these values in equation (1)
52 = -0.85(41) + c
c = 52 + 34.85
c = 86.85
So, equation (1) becomes,
y = -0.85x + 86.85
Now, we need to find the remaining distance after 33 minutes of driving.
i.e., the value of y for x = 33
y = -0.85(33) + 86.85
y = -28.05 + 86.85
y = 58.8
This is the remaining distance 58.8 miles.
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(1 point) Evaluate the line integral Sc 2y dx + 2x dy where is the straight line path from (4,3) to (9,6). Jc 2g dc + 2z du =
Answers
the value of the line integral ∫_C 2y dx + 2x dy along the straight line path from (4,3) to (9,6) is 84.
To evaluate the line integral ∫_C 2y dx + 2x dy along the straight line path from (4,3) to (9,6), follow these steps:
Step:1. Parametrize the straight line path: Define a vector-valued function r(t) = (1-t)(4,3) + t(9,6) = (4+5t, 3+3t), where 0 ≤ t ≤ 1. Step:2. Calculate the derivatives: dr/dt = (5,3). Step:3. Substitute the parametric equations into the line integral: 2(3+3t)(5) + 2(4+5t)(3). Step:4. Calculate the line integral: ∫(30+30t + 24+30t) dt, where the integration is from 0 to 1. Step:5. Combine the terms and integrate: ∫(54+60t) dt from 0 to 1 = [54t + 30t^2] from 0 to 1.
Step:6. Evaluate the integral at the limits: (54(1) + 30(1)^2) - (54(0) + 30(0)^2) = 54 + 30 = 84.
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An electronics company has two contract manufacturers in Asia. Foxconn assembles its tablets and smart phones while Flextronics assembles its laptops. Monthly demand for tablets and smartphones is 10,000 units while that for laptops is 4,000. Tablets cost the company $100 while laptops cost $400 and the company has a holding cost of 25 percent. Currently the company has to place separate orders with Foxconn and Flextronics and receives separate shipments. The fixed cost of each shipment is $10,000
Answers
To optimize the company's inventory costs, we need to determine the optimal order quantities for both tablets and laptops.
Let's start by finding the optimal order quantity for tablets:
Total cost (TC) = ordering cost + holding cost
Ordering cost = (demand rate/order quantity) x ordering cost per shipment
Holding cost = (order quantity/2) x unit cost x holding cost rate
We can set these two costs equal to each other and solve for the optimal order quantity (Q):
(demand rate/Q) x ordering cost per shipment = (Q/2) x unit cost x holding cost rate
Solving for Q, we get:
Q = sqrt((2 x demand rate x ordering cost per shipment)/(unit cost x holding cost rate))
Plugging in the values given in the problem, we get:
Q = sqrt((2 x 10000 x 10000)/(100 x 0.25)) = 2000
Therefore, the optimal order quantity for tablets is 2000 units per shipment.
Next, let's find the optimal order quantity for laptops:
Following the same procedure as for tablets, we get:
Q = sqrt((2 x 4000 x 10000)/(400 x 0.25)) = 2000
Therefore, the optimal order quantity for laptops is also 2000 units per shipment.
In summary, the company should place orders of 2000 units each for both tablets and laptops to minimize its inventory costs.
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FRACTIONS It is John's birthday and his mother decided to give him a birthday party. She bought him three cakes for his party; cake one was sliced into 8 pieces, cake two was sliced into 10 pieces, and cake three was sliced into 12 pieces. If the guests at the party ate 4 slices of cake one, 7 slices of cake two and 5 slices of cake three; calculate the amount of cake that was eaten in total.
Answers
There are 30 slices in total, so our denominator would be 30.
Now we simply have to add 4, 7 and 5. The answer to this would be 16.
So the amount of cake eaten in total is 16/30.
If your assignment is for improper fractions, I'm guessing the answer would be 16/3 instead.
Answer:
1 37/60 cakes
Step-by-step explanation:
You want the total cake eaten if 4 of 8 slices, 7 of 10 slices, and 5 of 12 slices were eaten.
SumThe sum of the three fractions is ...
4/8 +7/10 +5/12
= 5/10 +7/10 +5/12 . . . . . . . 4/8 = 1/2 = 5/10
= 12/10 +5/12
= 6/5 +5/12
= (6·12 +5·5)/(5·12) = 97/60 = 1 37/60
The total amount of cake that was eaten was equivalent to 1 37/60 cakes.
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Additional comment
Your calculator can relieve the tedium of this calculation.
Mr. Lance designed a class banner shaped like a polygon shown what is the name of the polygon
Answers
Step 1: Answer
The point (2, 8) is the point (x1, y1) identified from the equation y - 8 = 3(x - 2).
Step 2: Explanation
The equation y - 8 = 3(x - 2) is in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope of the line. In this case, the slope of the line is 3, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.
Comparing the given equation with the point-slope form, we can see that x1 = 2 and y1 = 8. Therefore, the point (2, 8) is the point identified from the equation.
Evaluate the integral ∫√5+x/5-x dx
Answers
To evaluate the integral ∫√5+x/5-x dx, we first need to simplify the integrand. We can do this by multiplying the numerator and denominator of the fraction by the conjugate of the denominator, which is 5+x. This gives us:
∫√(5+x)(5+x)/(5-x)(5+x) dx
Simplifying further, we get:
∫(5+x)/(√(5-x)(5+x)) dx
We can now make a substitution by letting u = 5-x. This gives us du = -dx, and we can substitute these values into the integral to get:
-∫(4-u)/(√u(9-u)) du
To simplify this expression, we can use partial fraction decomposition to break it up into simpler integrals. We can write:
(4-u)/(√u(9-u)) = A/√u + B/√(9-u)
Multiplying both sides by √u(9-u), we get:
4-u = A√(9-u) + B√u
Squaring both sides and simplifying, we get:
16 - 8u + u^2 = 9A^2 - 18AB + 9B^2
From this equation, we can solve for A and B to get:
A = -B/3
B = 2√2/3
Substituting these values back into the partial fraction decomposition, we get:
(4-u)/(√u(9-u)) = -√(9-u)/3√u + 2√2/3√(9-u)
We can now substitute this expression back into the integral to get:
-∫(-√(9-x)/3√x + 2√2/3√(9-x)) dx
This integral can be evaluated using standard integral formulas, and we get:
(2/3)√(5+x)(9-x) - (2/9)√(5+x)^3 + C
where C is the constant of integration.
In summary, to evaluate the integral ∫√5+x/5-x dx, we simplified the integrand by multiplying the numerator and denominator by the conjugate of the denominator, made a substitution to simplify the expression further, used partial fraction decomposition to break it up into simpler integrals, and evaluated the integral using standard integral formulas. The final answer is (2/3)√(5+x)(9-x) - (2/9)√(5+x)^3 + C.
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Your supervisor asks you to separate 4,780 castings into 25 piles. When you complete the job, how many castings will you have left over
Answers
Answer:5
Step-by-step explanation:
4780/25=191.2
You don't want an odd amount of castings in different piles.
191*25=4755
4780-4755=5
I think i read the question wrong. Sorry if i did
When separating 4,780 castings into 25 piles, there will be 5 castings left over.
Explanation:A fraction is a numerical expression representing a part of a whole. It consists of a numerator (the top number) that indicates how many parts are considered, and a denominator (the bottom number) that shows the total number of equal parts in the whole. Fractions are typically expressed as a/b, where "a" is the numerator and "b" is the denominator. They are used in various mathematical operations, including addition, subtraction, multiplication, and division, and in real-life scenarios involving proportions and portions.
In order to determine the number of castings left over when separating 4,780 castings into 25 piles, we can use division. Divide 4,780 by 25 to find the number of castings in each pile.
The quotient is 191.2. Since we can't have a fraction of a casting, we round down to 191.
To find the number of castings left over, subtract the total number of castings in the piles from the original total. 4,780 - (191 x 25)
= 4,780 - 4,775
= 5
Therefore, when you complete the job, you will have 5 castings left over.
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Pls help it’s due tonight and I don’t understand it xx
Answers
Answer:
n = 10
Step-by-step explanation:
36 can be written as 6^2 because 6*6 = 36.
Since exponents multiply, 36^5 = (6^2)^5 = 6^(2*5) = 6^10 = 6^n.
n = 10.
Alternatively, 36^5 = 36 * 36 * 36 * 36 * 36.
If you replace each 36 with 6*6, the new equation is (6*6) * (6*6) * (6*6) * (6*6) * (6*6).
n = the number of 6's = 10.
Explain the relationship between -41/2 and its opposite postiton in relation to yhe postitoon of zero on a number line
Answers
Answer:
Step-by-step explanation:
To understand the relationship between -41/2 and its opposite position in relation to zero on a number line, let's first plot them on the number line.
We start by marking the position of zero at the center of the number line, and then we can represent -41/2 and its opposite position by moving to the left and right of zero respectively.
When we move 41/2 units to the left of zero on the number line, we reach the point -41/2. This means that -41/2 is located to the left of zero on the number line.
On the other hand, the opposite position of -41/2 is obtained by moving the same distance (41/2 units) to the right of zero. This position is represented by the point 41/2 on the number line.
Therefore, we can see that -41/2 and its opposite position (41/2) are equidistant from zero on the number line, with zero located exactly halfway between them. In other words, -41/2 and 41/2 are located at equal distances from zero but in opposite directions. This relationship is often referred to as the symmetry property of the number line.
