Consider this expression and the steps to evaluate it. 45(−2)9 48(−2)3 1. Apply the quotient of powers: (−2)a 4b 2. Evaluate powers: c d
Answers
Answer:
a = 6
b = 3
c = 64
d= 64
Step-by-step explanation:
1. Apply the quotient of powers:
\((-2)^a / 4^b\)
In the given expression:
\(4^5(-2)^9/4^8(-2)^3\)
base same then the powers are subtracting if the bases are in numerator and denominator
i.e \(a^m/a^n = a^{m-n}\)
Solving:
\(=(-2)^{9-3}/4^{-5+8}\\=(-2)^6/4^3\)
therefore, the values of a and b are: a = 6
b = 3
2. Evaluate Powers
c/d
We have
\((-2)^6/4^3\)
When power is even negative sign changes into plus sign
64/64
Therefore, we get the values of c and d
c = 64
d= 64
Answer:
a = 6
b = 3
c = 64
d= 64
Step-by-step explanation: i got it right
Related Questions
How can we find HCF of a number
Answers
Answer:
We can find the highest common factor of a number by listing down all the factors of that number. The greatest factor from that list is the highest common factor.
How to find HCF of two numbers
❒ Explanation -:We can find the HCF of any numbers using three methods -:
Common FactorPrime FactorisationDivision Method\( \small \underline {\underline{\bf Common \: Factor \: Method }}\)
\( \small \orange{\bf{ Step \: 1 :}}\)
Find all factors of the given number\( \small \blue{\bf{ Step \: 2 :}}\)
Find the common factor\( \small \purple{\bf{ Step \: 3 :}}\)
Find out the highest common factor from the common factor . The highest common factor is the HCF of the number.\( \small \underline{\underline{\bf{ Prime \: Factorisation }}}\)
\( \small \orange{\bf{ Step \: 1 :}}\)
Find the prime factor of the given number by division method.\( \small \blue{\bf{ Step \: 2 :}}\)
Find out the common prime factor.\( \small \purple{\bf{ Step \: 3 :}}\)
The product of the common prime factor gives the HCF of the number.\( \small \underline{ \underline{\bf{ Division \: Method}}}\)
\( \small \orange{\bf{ Step \: 1 :}}\)
Divide the greater number by the smaller number. By the remainder in step 1 divide the smaller number\( \small \blue{\bf{ Step \: 2 :}}\)
By the remainder in Step 2 divide the remainder obtained in Step 1.\( \small \purple{\bf{ Step \: 3 :}}\)
Complete in the same way till no remainder is left.\( \rule{91mm}{3pt}\)
how much natural gas can homeowners expect to use per month if they install 6 inches of insulation and the outdoor temperature is 47 degrees f? (round your answer to 2 decimal places.)
Answers
The amount of natural gas that homeowners can expect to use per month is influenced by various factors, including insulation levels and outdoor temperature.
However, without additional information or an established relationship between these factors, it is not possible to provide a precise estimate.
Insulation levels and outdoor temperature are just a few of the many factors that affect natural gas usage.
Other factors such as the size and efficiency of the heating system, the size and layout of the home, the insulation of walls and windows, and individual usage patterns can significantly impact gas consumption.
To obtain a more accurate estimate, it is recommended to consult energy professionals, utility companies, or use energy consumption calculators specifically designed for estimating natural gas usage based on multiple variables.
These tools take into account various factors to provide a more accurate estimation of monthly natural gas consumption.
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complete the square to solve
f(x)=x^2-6x+5
Answers
Explanation:
x^2 - 6x + 5 = 0
(x^2 - 6x + 9) + 5 - 9 = 0
(x - 3)(x - 3) - 4 = 0
(x - 3)^2 = 4
x - 3 = +-2 (sqrt both sides)
x - 3 = 2
x = 5
x - 3 = -2
x = 1
A scatter plot is shown on the coordinate plane. scatter plot with points at 1 comma 8, 2 comma 6, 4 comma 7, 5 comma 5, 7 comma 6, 8 comma 4, 10 comma 3, and 10 comma 5 Which of the following graphs shows a line on the scatter plot that fits the data? scatter plot with points at 1 comma 8, 2 comma 6, 4 comma 7, 5 comma 5, 7 comma 6, 8 comma 4, 10 comma 3, and 10 comma 5, with a line passing through the coordinates 7 comma 6 and 10 comma 5 scatter plot with points at 1 comma 8, 2 comma 6, 4 comma 7, 5 comma 5, 7 comma 6, 8 comma 4, 10 comma 3, and 10 comma 5, with a line passing through the coordinates 2 comma 6 and 5 comma 5 scatter plot with points at 1 comma 8, 2 comma 6, 4 comma 7, 5 comma 5, 7 comma 6, 8 comma 4, 10 comma 3, and 10 comma 5, with a line passing through the coordinates 2 comma 7 and 7 comma 5 scatter plot with points at 1 comma 8, 2 comma 6, 4 comma 7, 5 comma 5, 7 comma 6, 8 comma 4, 10 comma 3, and 10 comma 5, with a line passing through the coordinates 1 comma 8 and 10 comma 3
Answers
The line passing through the coordinates 7,6 and 10,5 seems to fit the data best, as it passes through several of the points and follows the general trend of the data. Therefore, the graph that shows a line passing through the coordinates 7,6 and 10,5 is the one that fits the data.
So, the correct answer is: scatter plot with points at 1,8; 2,6; 4,7; 5,5; 7,6; 8,4; 10,3; and 10,5, with a line passing through the coordinates 7,6 and 10,5.
8. Aleks is writing a report about recycling in the local town. In 2021: There were 2341 people living in the town Each person in the town recycled an average of 264.6kg of waste. Aleks knows that 1tonne = 1000kg. How many tonnes of waste were recycled in town in total in 2022?
Answers
The tons of waste recycled in 2021 was 619.4286 tons.
According to the question,
We have the following information:
In 2021: There were 2341 people living in the town. Each person in the town recycled an average of 264.6kg of waste. Aleks knows that 1 ton = 1000kg.
Now, the total waste recycled in 2021 can be found using multiplication:
Number of people*waste recycled by each person
2341*264.6
619428.6 kg
Now, we will convert this from kilogram to tons.
1 ton = 1000 kg
1 kg = 1/1000 ton
So, we will divide the waste in kilogram by 1000:
Total waste recycled = 619428.6/1000
Total waste recycled = 619.4286 tons
Hence, the tons of waste recycled in 2021 was 619.4286 tons.
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4. Compare your two distributions of the proportions of heads observed in your simulations 5. What should have happened
Answers
Comparing distributions and understanding the expected outcomes of a simulation can help ensure accuracy and reliability in statistical analysis.
To compare two distributions of the proportions of heads observed in your simulations, you can create histograms and compare their shapes, centers, and spreads. Ideally, the histograms should be roughly symmetric, with similar centers and spreads. Additionally, you can calculate summary statistics such as mean and standard deviation to further compare the two distributions.
What should have happened is that the two distributions should have been similar, as each coin has an equal probability of landing heads or tails. If the distributions are very different, it may suggest that the simulation was not run properly or that the coins were biased in some way.
To ensure accuracy in the simulation, it is recommended to run multiple trials with a large sample size to account for any chance variation. This will help ensure that the results accurately reflect the true probabilities of the coins landing heads or tails. Additionally, it may be helpful to physically examine the coins to ensure that they are not biased in any way that could affect the results.
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the manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. what is the probability that three randomly monitored calls will each be completed in 5 minutes or more?
Answers
The probability for three randomly monitored calls will be 0.00001
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
Given in the question:
Call time, X ~ Normal (μ=8.21, σ=2.14)
For a single call,
P(X < 4) = P{(X - μ)/σ < (4 - 8.21)/2.14) = P{Z < -1.97} = F(-1.97) = 0.024 (lookup a standard normal distribution table)
For 3 independent calls, the probability that all the three are less than or equal to 4 min = \((0.024)^{3}\) = 0.00001
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C. Yesterday, on Kelly's class trip, 4 groups of 52 students visited the Sea Animal Park. The students attended a special dolphin show in which they were able to pet the dolphins. The students were placed in groups, with 7 students in each group.Kelly used division to find the total number of groups that were needed so that each student was able to pet the dolphins. She said that a total of 29 groups were needed.
Did Kelly correctly solve the division problem? Why or why not?
Answers
Answer:
the real answer is 29.714
Kelly's answer is almost correct.
What was the name of the physical barrier in ancient India?
Answers
Answer: Some natural barriers are the Himalayas isolating the Indian subcontinent from the rest of Asia, the Grand Canyon, the Dead sea, and the Mississippi river.
what appears to be ture about the three biesectors of any triangle
Answers
One thing that is true about the three bisectors of any triangle is that they are concurrent in a point equidistant from the sides of a triangle.
What is true of the three bisectors of any triangle?When the three bisectors of a triangle are drawn, what we notice is that they will be concurrent at a certain point known as the incenter.
The incenter is such that it is equally distant or equidistant from all the sides of that triangle in question.
In conclusion, the three bisectors of a triangle are concurrent in a point equidistant from the sides of a triangle.
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Kuta Software Infinite Algebra 2 Compound Inequalities Solve each compound inequality and graph 1) nis-3 or -4n 11 ntlezon ine-8 -3tis int3Ln-84-40 L+1-3 - na 8 -32 hotez - 4-86 -80-33!! and sa -8a31143 -80>14 17) 9m - 8 3) 2 < 2x < 6
Answers
That is absolute value.
\(|x|\text{ = +x or -x}\)\(\begin{gathered} |-8a\text{ - 3| > 11} \\ (-8a\text{ - 3) > 11 or -(-8a - 3) > 11} \\ (-8a\text{ - 3) > 11} \\ -8a\text{ > 11 + 3} \\ -8a\text{ > 14} \\ a\text{ < }\frac{-14}{8} \\ a\text{ < }\frac{-7}{2} \end{gathered}\)or
\(\begin{gathered} -(-8a\text{ - 3) > 11} \\ 8a\text{ + 3 > 11} \\ 8a\text{ > 11 - 3} \\ 8a\text{ > 8} \\ a\text{ > 8/8} \\ a\text{ > 1} \end{gathered}\)Therefore,
1 < a <-7/2
In which interval does a root exist for this equation? tan(x) = 3x^2
PLEASE HELP
Answers
To determine the interval for which a root exists, you can use the intermediate value theorem.
First, observe that the left-hand side of the equation, tan(x), is undefined for x = (n + 1/2) π, where n is an integer. Thus, we can restrict our attention to the interval (-π/2, π/2) where the tangent function is continuous and strictly increasing.
Next, note that tan(0) = 0 and tan(π/6) = 1/√3 < 3/36 = 1/12. Also, as x approaches π/2 from the left, tan(x) approaches infinity, while 3x^2 approaches infinity faster. Therefore, there exists at least one root of the equation in the interval (0, π/6).
Similarly, tan(-π/6) = -1/√3 > -1/12, and as x approaches -π/2 from the right, tan(x) approaches negative infinity, while 3x^2 approaches infinity faster. Therefore, there exists at least one root of the equation in the interval (-π/6, 0).
Therefore, the equation tan(x) = 3x^2 has at least one root in the interval (-π/6, π/6).
You roll a number cube. What is the probability you roll a multiple of 2 or a 5?
Answers
Answer:
d
Step-by-step explanation:
Trust
A motorboat travels 315 kilometers in 5 hours going upstream and 623 kilometers in 7 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? HELPP ASAP
Answers
When the boat is traveling upstream (against the current), its effective speed is slower, so we can use the formula:
distance = rate x time
to set up the equation:
315 = (b - c) x 5
Simplifying this equation:
b - c = 63
Similarly, when the boat is traveling downstream (with the current), its effective speed is faster, so we can use the same formula:
623 = (b + c) x 7
Simplifying this equation:
b + c = 89
Now we have two equations:
b - c = 63
b + c = 89
We can solve for "b" (the rate of the boat in still water) by adding these two equations:
2b = 152
b = 76
So the rate of the boat in still water is 76 km/h.
We can solve for "c" (the rate of the current) by substituting the value of "b" into one of the equations:
76 + c = 89
c = 13
So the rate of the current is 13 km/h.
Let's denote the rate of the boat in still water by "b" and the rate of the current by "c".
When the boat is traveling upstream (against the current), its effective speed is b - c. When it is traveling downstream (with the current), its effective speed is b + c.
We can use the following two equations based on the distance, speed and time relationship:
1. Distance = Speed x Time
2. Speed = Distance / Time
Using these equations, we can write two equations based on the given information:
1. (b - c) x 5 = 315 (Upstream journey)
2. (b + c) x 7 = 623 (Downstream journey)
Simplifying these equations, we get:
1. 5b - 5c = 315
2. 7b + 7c = 623
Dividing both sides of equation 1 by 5, we get:
b - c = 63
Adding equation 1 and equation 2, we get:
12b = 938
Dividing both sides by 12, we get:
b = 78.17 km/h
Substituting b = 78.17 in equation 1, we get:
78.17 - c = 63
Solving for c, we get:
c = 15.17 km/h
Therefore, the rate of the boat in still water is 78.17 km/h and the rate of the current is 15.17 km/h.
Use what you know about transformations to describe the
relationship between figure PQRS and figure P'Q'R'S'.
Use at least three math or academic vocabulary terms from
this unit in your answer. Underline each term you use.
Answers
Figure PQRS may be mapped onto image P'Q'R'S using only one transformation, which is a reflection.
Describe transformation.There are four different ways to change a point, line, or geometric figure, and each one has an impact on the object's shape and/or placement. Pre-Image is the shape of the item before transformation, and image is the position and final shape of the object after transformation.
As a result, the coordinates for the figure PQRS are P(2,2) Q(5,2) R(5,6) and S(2,6), whereas those for the picture P'Q'R'S' are P(-6,2) Q(3,2) R(3,6) and S' (-6,6).
Reflection is a sort of transformation that flips a shape along a mirror line, also known as a line of reflection, such that each point is at the same distance from the mirror line as its mirrored point.
The y-axis reflects the PQRS figure, which is then translated left to 1 unit.
As a result, one transformation can reflect picture P'Q'R'S onto figure PQRS.
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In chole’s closet there are 10 shirts and 15 shirts
A. What is the simplest ratio of shirts to shorts
B. What is the simplest ratio of shirts to total items
C. What percent of the item in the closet are shirts
D. Chris has 4 shirts and 5 shorts in his closet is the ratio of shirts to shorts in Chris closet the same as the ratio of Chloe’s closet explain
Answers
Ratio:-
10:15=2:3#2
Total items=10+15=25Ratio:-
10:25=2:5#3
Ratio of Chris=4:5
If we take decimals
2/3=0.64/5=0.8Approximately they are equal
#A
Ratio:-
10:15=2:3#B
Shirts=10Total=10+15=25Ratio:-
10/25=2/5=2:5#C
Percentage:-
\(\\ \rm\rightarrowtail \dfrac{2}{5}(100)=2(20)=40\%\)
#D
Ratio for Chris=4:5
No it's not sameA vehicle was valued at $36,000 in the year 2011. The value depreciated to $12,000 by the year 2015. Assume that the car continues to drop at a constant rate. How long will it take for the car to be valued at $800?
Answers
The car will cost $ 800 after a depreciation time of approximately 6 years.
In what year does a car cost $ 800 due to depreciation?
Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:
c(t) = c' + m · t
Where:
c' - Initial cost of the car, in monetary unit.m - Depreciation rate, in monetary unit per year.t - Time, in years.If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:
m = (12,000 - 36,000) / (4 - 0)
m = - 24,000 / 4
m = - 6,000
800 = 36,000 - 6,000 · t
6,000 · t = 35,200
t = 35,200 / 6,000
t = 5.867
The expected depreciation time is approximately 6 years.
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Which function is most likely graphed on the coordinate plane below? f(x) = 3x – 11 f(x) = –4x + 12 f(x) = 4x + 13 f(x) = –5x – 19
Answers
Answer:
D
Step-by-step explanation:
It's D on Enginuity
The graph of the function in the coordinate plane is f(x) = –5x – 19.
What is a Graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
As per the given diagram:
The x intercept of the line = -ve
The y intercept of the line = -ve
For f(x) = 3x - 11
x intercept = +ve
y intercept = -ve
Hence, not possible
For f(x) = -4x + 12
x intercept = +ve
y intercept = +ve
Hence, not possible
For f(x) = 4x + 13
x intercept = -ve
y intercept = +ve
Hence, not possible
For f(x) = -5x - 19
x intercept = -ve
y intercept = -ve
Hence, possible
The function plotted on the coordinate plane is f(x) = –5x – 19.
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Suppose you want to throw a party. you have $214 to spend. so far you have purchased 5 decorations that each cost d dollars. which expression represents the amount of money that you have left to spend?
Answer: 214 - 5d
Which of the following real-world scenarios could be represented by the algebraic expression 7.65 - 2p? Select all that apply.
Answers:
1) You buy 2 equally priced party favors, spending from your $7.65 gift card.
4) you give Tim twice the amount of face paint he had from your supply of 7.65 ounces.
You decide to order pizzas for your party. A large pizza is cut into 12 slices. If each pizza is shared evenly among G guests, which expression represents the number of slices that each guest will eat?
Answer: 12/g
(these are the rest of the answers for the rest of the 7 slides of "Writing expression" assignment on e2020
4th: $25 dollars is the constant team so the cost for h hours is 15h and the correct expression is 15h+25 and 15(h+25) would be interpreted as adding 25 hours to the number of hours rented, and then multiplying by 15.
5th: m + 2m - s
6th: No it's not true. Each table began with x/8 balloons. If two pop then you will not be able to distribute it equally among 8 tables. There are x/8 - 2 balloons left. Not all tables will be equal.
7th: n - (1/4)n - 15
8th: 12n/r
9th: (x+3)/5
10th: (3r)/2 is what the second DJ had. 3 times as many songs as 3r and half as many is translated as division to 2 so half as many is translated as multiplication by 1/2. So therefore, the second DJ had (3r)/2 songs.
Answers
Answer: 214 - 5d
Which of the following real-world scenarios could be represented by the algebraic expression 7.65 - 2p? Select all that apply.
Answers:
1) You buy 2 equally priced party favors, spending from your $7.65 gift card.
4) you give Tim twice the amount of face paint he had from your supply of 7.65 ounces.
You decide to order pizzas for your party. A large pizza is cut into 12 slices. If each pizza is shared evenly among G guests, which expression represents the number of slices that each guest will eat?
Answer: 12/g
(these are the rest of the answers for the rest of the 7 slides of "Writing expression" assignment on e2020
4th: $25 dollars is the constant team so the cost for h hours is 15h and the correct expression is 15h+25 and 15(h+25) would be interpreted as adding 25 hours to the number of hours rented, and then multiplying by 15.
5th: m + 2m - s
6th: No it's not true. Each table began with x/8 balloons. If two pop then you will not be able to distribute it equally among 8 tables. There are x/8 - 2 balloons left. Not all tables will be equal.
7th: n - (1/4)n - 15
8th: 12n/r
9th: (x+3)/5
10th: (3r)/2 is what the second DJ had. 3 times as many songs as 3r and half as many is translated as division to 2 so half as many is translated as multiplication by 1/2. So therefore, the second DJ had (3r)/2 songs.
Step-by-step explanation:
Answer:
214-5d
Step-by-step explanation:
The terminal side of angle λ intersects the unit circle at point (-0.358, 0.934). Based on these coordinates, what is the approximate decimal value of cot(λ)
Answers
Answer: -0.383
Step-by-step explanation:
Since this is on the unit circle, the cosine is equal to the x coordinate and the sine is equal to the y coordinate.
Since cot = 1/tan = cos/sin, the approximate value is (-0.358)/(0.934), which is about -0.383.
Solve the system.
4x+2y+3z=12
2x−3y+5z=−7
6x−y+4z=−3
Answers
Adriel buys 20 bottles of grapefruit juice at the corner store for a total cost of $7.80.
If each bottle costs the same amount, how much is 6 bottles of juice?
Answers
The cost of 6 bottles of juice is $2.34 if the each bottle costs the same.
According to the question,
We have the following information:
Adriel buys 20 bottles of grapefruit juice at the corner store for a total cost of $7.80.
Cost of 20 bottles of juice = $7.80
Now, from here we can find the cost of 1 bottle of juice by dividing the total cost by the number of bottles purchased.
Cost of 1 bottle of juice = $(7.80/20)
Cost of 1 bottle of juice = $0.39
Now, we can easily find the cost of 6 bottles of juice by multiplying the cost of 1 bottle of juice by 6.
Cost of 6 bottles of juice = $(0.39*6)
Cost of 6 bottles of juice = $2.24
Hence, the cost of 6 bottles of juice is $2.24.
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9 = ? − 30..................................................................................................
Answers
Answer: 39
Step-by-step explanation: 9 = ? - 30, add 30 on both sides you get 39=?
Janelle is considering two options for saving money. One option earns simple interest while the other option earns interest compounded monthly. If there are no additional deposits or withdraws, how much more will Janelle earn with the compound interest option? Assume Janelle deposits $3,000 at 3% interest for 7 years for both options
Answers
Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.
The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:
\(A = P(1 + r/n)^{(nt)}\)
Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.
For the simple interest option, the interest is calculated using the formula:
I = P * r * t
Where:
I is the total interest earned
Using the given values, we can calculate the interest earned with simple interest:
I = 3000 * 0.03 * 7
I = 630
Now, let's calculate the total amount earned with the compound interest option.
Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:
r = 0.03/12
t = 7 * 12
Using these values, we can calculate the total amount with compound interest:
\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)
A ≈ 3,729.19
To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:
Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19
Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.
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first answer = brainliest
Answers
Answer:
A=28.26 in²
Step-by-step explanation:
We are given the formula for the area of a circle which is:
\(A=\pi r^2\)
Which means:
Area = π*radius of circle²
The radius of a circle is the length from the center of the circle to the edge of the circle.
The image tells us the radius of the circle is 3 in and the questions asks us to use 3.14 for π, therefore...
A=3.14*3²
A=3.14*9
A=28.26 in²
Answer:
28.26 in²Step-by-step explanation:
We know that:
Area of circle = πr²Radius = 3 in.π = 3.14Solution:
πr² = Area of circle=> 3.14 x 3² = Area of circle=> 3.14 x 9 = Area of circle=> 28.26 in² = Area of circleHence, the area of the circle is 28.26 in².
the radius of a sphere is incerasing at a rate of 2 ft/min. how fast is the volume changing when the radius is 3 feet
Answers
V=4/3• π•(2x)^3, where x=elapsed time and r=2ft./min multiplied by time (x).
We are given tho find volume when the radius is 3ft.
So, we need to find the volume when r=2 and r=3 to compare the volume and find the increase:
When r=2:
V=4/3•π•(2)^3
Simplify:
V=4/3•π•8
V=4(π•8)/3
V=33.51ft.^3
When r=3:
V=4/3•π•(3)^3
Simplify:
V=4/3•π•9
V=4(π•9)/3
V=113.1ft.^3
So, let’s find the increase in volume by taking the difference of the two volumes calculated above:
when r=3 - when r=2:
113.1 - 33.51 = 79.59
So, the volume increased 79.59ft^3.
Now, we must find the time interval to produce the rate of increase based on time:
Recall that when r=2x, x=minutes elapsed.
So, let’s set 2x=3 to find x (time in minutes)
Solve for x:
x=3/2
x=1.5
So, 1.5 minutes have elapsed when for the radius to equal 3.
This means we can create a rate of increase with the volume and time:
79.59/1.5
This ratio means that the volume is increasing at 79.59in^3 per every 1.5 minutes. We can simplify and find the unit rate by dividing the numerator by the denominator:
53.06in^3/min
So, the volume is increasing at 53.06in^3 per minute.
what is the difference between relative frequency and cumlative relative frequency
Answers
The difference between relative frequency and cumulative relative frequency is that relative frequency is the ratio of the frequency of a particular value in a dataset to the total number of values, expressed as a percentage. Cumulative relative frequency is the sum of all relative frequencies up to a certain point in the data set.
For example, if a data set has 8 values and 4 are the same, the relative frequency would be 50%. Cumulative relative frequency would be 50% at this point since it is the sum of all relative frequencies up to this point in the data set. If there were another 4 of the same values after this point, the relative frequency would remain at 50%, but the cumulative relative frequency would increase to 100% since it includes all previous relative frequencies.
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Write 5.24 as a mixed number in simplest form.
5.24 =
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Step-by-step explanation:
5 +0.24 = 5 + 24 = 12 = 6
100 50 25
= 5 6
25
If each triangle is the right Triangle yes or no?
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Answer:
This is not a right triangle
Step-by-step explanation:
right triangle has a 90° angle and this triangle does not have a 90° angle
find all abelian groups (up to isomorphism) of order 360
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The abelian groups (up to isomorphism) of order 360 are:
1. C360: The cyclic group of order 360.2. C2 x C2 x C3 x C3 x C5: The direct product of cyclic groups of orders 2, 2, 3, 3, and 5.
How can we determine the abelian groups of order 360?To find all abelian groups of order 360, we need to consider the prime factorization of 360, which is 2^3 × 3^2 × 5. The abelian groups will be direct products of cyclic groups whose orders divide 360.
First, we consider the cyclic groups. Since the order of an element in a cyclic group divides the order of the group, we can have cyclic subgroups of orders 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
Now, we can combine these cyclic subgroups to form the abelian groups. We can take direct products of the cyclic groups to obtain different possibilities. The order of the resulting group will be the product of the orders of the cyclic subgroups.
In this case, we can form the following abelian groups of order 360:
C360: This is the cyclic group of order 360 itself.
C2 x C2 x C3 x C3 x C5: This is the direct product of cyclic groups of orders 2, 2, 3, 3, and 5.
These are the two abelian groups (up to isomorphism) that can be formed using the prime factorization of 360.
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