Volumes of the cylinder are given by:
(A) (1) Volume = 2486.88 cubic in.
(2) Volume = 108518.4 cubic ft.
(3) Volume = 47608.68 cubic yd.
(B) (4) Volume = 508.68 cubic ft.
(5) Volume = 8490.56 cubic yd.
(6) Volume = 43407.36 cubic in.
(7) Volume = 9420 cubic ft.
(8) Volume of cylindrical flower vase = 1105.28 cubic in.
Surface Area of the Cylinder are given by:
(1) Surface Area = 113.04 square in.
(2) Surface Area = 1444.4 square ft.
(3) Surface Area = 678.24 square yd.
(4) Surface Area = 1130.4 square yd.
(5) Surface Area = 602.88 square in.
(6) Surface Area = 1055.04 square ft.
(7) Surface Area = 1570 square ft.
(8) Surface Area = 791.28 square yd.
(9) Surface Area = 326.56 square in.
We know that the volume of a cylinder with radius 'r' and height 'h' is given by,
V = 2πr²h
(A) (1) From the figure, radius = 6 in and height = 11 in.
So the volume = 2π(6)²*11 = 2486.88 cubic in.
(2) Radius = 24 ft. and height = 30 ft.
Hence, the volume of cylinder = 2π(24)²*30 = 108518.4 cubic ft.
(3) Radius = 19 yd. and height = 21 yd.
Hence, the volume of cylinder = 2π(19)²*21 = 47608.68 cubic yd.
(B) (4) Radius = 3 ft. and height = 9 ft.
Hence, the volume of cylinder = 2π(3)²*9 = 508.68 cubic ft.
(5) Radius = 13 yd. and height = 8 yd.
Hence, the volume of cylinder = 2π(13)²*8 = 8490.56 cubic yd.
(6) Radius = 16 in. and height = 27 in.
Hence, the volume of cylinder = 2π(16)²*27 = 43407.36 cubic in.
(7) Radius = 10 ft. and height = 15 ft.
Hence, the volume of cylinder = 2π(10)²*15 = 9420 cubic ft.
(8) Cylindrical flower vase is 11 inch tall and radius of vase is 4 inches.
The volume of flower vase = 2π(4)²*11 = 1105.28 cubic in.
Now we know that the surface area of a Cylinder with radius 'r' and height 'h' is given by,
S = 2πrh + 2πr²
(1) Radius = 2 in. and Height = 7 in.
Hence the surface area = 2π*2*7 + 2π(2)² = 113.04 square in.
(2) Radius = 10 ft. and Height = 13 ft.
Hence the surface area = 2π*10*13 + 2π(10)² = 1444.4 square ft.
(3) Radius = 6 yd. and Height = 12 yd.
Hence the surface area = 2π*6*12 + 2π(6)² = 678.24 square yd.
(4) Radius = 9 yd. and Height = 11 yd.
Hence the surface area = 2π*9*11 + 2π*9² = 1130.4 square yd.
(5) Radius = 6 in. and Height = 10 in.
Hence the surface area = 2π*6*10 + 2π(6)² = 602.88 square in.
(6) Radius = 8 ft. and Height = 13 ft.
Hence the surface area = 2π*8*13 + 2π(8)² = 1055.04 square ft.
(7) Radius = 10 ft. and Height = 15 ft.
Hence the surface area = 2π*10*15 + 2π(10)² = 1570 square ft.
(8) Radius = 6 yd. and Height = 15 yd.
Hence the surface area = 2π*6*15 + 2π(6)² = 791.28 square yd.
(9) Radius = 4 in. and Height = 9 in.
Hence the surface area = 2π*4*9 + 2π(4)² = 326.56 square in.
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Convert 4/5 to a decimal and a percent.
Decimal (Edit the repeating and non-repeating part):
0.00
Percent (Edit the repeating and non-repeating part)
0.00%
The decimal form of 4/5 is 0.80, and it is equivalent to 80% as a percent.
To convert the fraction 4/5 into a decimal and a percent, we start by dividing the numerator (4) by the denominator (5). The result is 0.80 as a decimal.
In decimal form, 4/5 is written as 0.80. The "0" before the decimal point represents whole units, and the "80" after the decimal point represents hundredths.
To express this decimal as a percent, we multiply it by 100, as a percent is a representation of parts per hundred. So, 0.80 multiplied by 100 equals 80. Therefore, 4/5 is equivalent to 80% when expressed as a percentage.
In summary, 4/5 as a decimal is 0.80, which means it represents 80 hundredths, and as a percent, it is 80%, which signifies 80 parts per hundred. This conversion is particularly useful in various mathematical and real-world applications, such as calculating discounts, grades, proportions, and percentages in everyday life and business contexts.
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You are setting the combination on a three-digit lock. You want to use the numbers 123 but you don't care what order they are in.
6 different permutations using the number 1 , 2 , 3 can be masde for the lock .
Given,
1 , 2 , 3 numbers to be used for a three digit lock .
There are 3 options for the first digit, 2 options for the second digit, and 1 option for the third digit.
To find the total number of permutations, we can use the formula for permutations:
Permutations of n items taken r at a time, which is n!/(n-r)!.
Here,
In this case,
n is 3
r is 3,
So the total number of permutations is 3!/(3-3)! = 3! = 3 x 2 x 1 = 6.
Hence,
So, you can make 6 different permutations using the numbers 1, 2 and 3 in any order.
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The diagram represents a model of a ramp the skateboard club wants to create at the neighborhood skate park. If one pint of paint covers 200 square inches, how many pints of paint will the club need to purchase? Paint is only sold in whole pints.
The number of pints of paint that the club will need is given as follows:
2 pints of paint.
How to obtain the amount of paint?Before obtaining the amount of paint, we must obtain the surface area of the figure.
The figure in this problem is composed as follows:
One rectangle of dimensions 19 in and 8 in.One rectangle of dimensions 6 in and 19 in.Two right triangles of sides 6 in and 8 in.Hence the surface area is given as follows:
S = 19 x 8 + 19 x 6 + 2 x 0.5 x 6 x 8
S = 314 in².
If one pint of paint covers 200 square inches, hence the number of pints is given as follows:
314/200 = 2 -> rounded up, as there is not a decimal amount of pints, and one pint is not enough.
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can someone help me?
Answer:12
Step-by-step explanation:
Distribution that results in all the data intervals that have the same frequency is
called __________.
A) uniform distribution
B) bell-shaped distribution
C) skewed distribution
D)frequency distribution
Distribution that results in all the data intervals that have the same frequency is called D)frequency distribution
A frequency distribution is a way of summarizing and displaying a dataset by showing the number of times each value or range of values appears in the data.
When all the intervals in a frequency distribution have the same frequency, it means that the data is evenly distributed across those intervals. This type of distribution is useful when analyzing data that falls into discrete categories or groups, such as survey responses or test scores.
By organizing the data into intervals with equal or same frequencies, patterns in the data can become more apparent and it can be easier to draw conclusions or make predictions.
Overall, a frequency distribution is a helpful tool for understanding the distribution of data and can provide valuable insights into the characteristics of a dataset.
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select all expressions equivalent to (3^3*3^-4)^-3
The expressions that are equivalent to (3^3*3^-4)^-3 are (3^-1)^-3, 3^3 and 27
Selecting all expressions that are equivalent to (3^3*3^-4)^-3From the question, we have the following parameters that can be used in our computation:
(3^3*3^-4)^-3
Evaluating the expression in the brackets using the law of indices, we have
(3^3*3^-4)^-3 = (3^-1)^-3
Next, we open the brackets
This gives
(3^3*3^-4)^-3 = 3^(-1 *-3)
When evaluated, we have
(3^3*3^-4)^-3 = 3^3
Evaluate the exponents
This gives
(3^3*3^-4)^-3 = 27
Hence, the expressions that are equivalent to (3^3*3^-4)^-3 are (3^-1)^-3, 3^3 and 27
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The height of the roof is 30ft and the radius of the base is 15tf. what is the area of the roof? what is the lateral surface area of the roof
The lateral surface area of the roof can be found by subtracting the area of the base from the total surface area:1581.84 sq ft
Assuming the roof is a cone:
The slant height of the cone can be found using the Pythagorean theorem:
l = √(r^2 + h^2) = √(15^2 + 30^2) = 33.541 ft
The area of the roof can be found using the formula for the surface area of a cone:
A = πr^2 + πrl = π(15)^2 + π(15)(33.541) ≈ 1800.66 sq ft
The lateral surface area of the roof can be found by subtracting the area of the base from the total surface area:
L = πrl = π(15)(33.541) ≈ 1581.84 sq ft
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The radius of a circle is 8 centimeters. What is the area of a sector bounded by a 180° arc? Give the exact answer in simplest form.
Will mark brainliest!
The area of a sector bounded by a 180° arc with a radius of 8 centimeters is 32π square centimeters in simplest form.
To find the area of a sector bounded by a 180° arc with a radius of 8 centimeters, you can follow these steps:
Step 1: Recall the formula for the area of a circle: A = πr², where A is the area and r is the radius.
Step 2: Calculate the area of the entire circle with a radius of 8 centimeters: A = π(8)² = 64π square centimeters.
Step 3: Determine the fraction of the circle represented by the 180° arc. Since a full circle is 360°, the fraction is 180°/360°, which simplifies to 1/2.
Step 4: Multiply the area of the entire circle by the fraction to find the area of the sector: (1/2) * (64π) = 32π square centimeters.
So, the area of a sector bounded by a 180° arc with a radius of 8 centimeters is 32π square centimeters in simplest form.
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How do I find the value of X
Answer:
x = 30
Step-by-step explanation:
you can find it by vertical opposite angle which is their non adjecent angle are equal.
2x- 30 = 30
2x = 30 + 30 ..... take 30 to the left it change sighn
2x /2 = 60 / 2 ..... divided both side by 3
x = 30 ..... so the unknown no. is 30
Sneha’s mother is 12 years more than twice Sneha’s age. After 8 years, she will be 20 years
less than three times Sneha’s age. Find Sneha’s age and Sneha’s mother’s age.
Sneha's current age is 16 years old. Sneha's mother is 44 years old.
Let's assume Sneha's current age is x.
Sneha's mother's current age = 2x + 12
After 8 years, Sneha's age = x + 8
After 8 years, Sneha's mother's age = 2x + 12 + 8 = 2x + 20
After 8 years, Sneha's mother's age will be 20 less than three times Sneha's age: 2x + 20 = 3(x + 8) - 20
Now we can solve for x:
2x + 20 = 3(x + 8) - 20
2x + 20 = 3x + 24 - 20
2x + 20 = 3x + 4
x = 16
Therefore, Sneha's current age is 16 years old.
Sneha's mother's current age = 2x + 12
= 2(16) + 12 = 44
So, Sneha's mother is 44 years old.
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Help please! This is for a grade... (35 points)
Drag each set of dots to the correct location on the dot plot. Each set of dots can be used more than once. Not all sets of dots will be used Tricia recorded the number of pets owned by each of her classmates. These data points represent the results of her survey 032. 41. 2. 1. 2. 1. 1. 3,4,2,0,0. 1. 1. 1. 0. 3 Create a dot plot that represents the data 1 Number of Students 2 Numbers of Pets
To create a dot plot that represents the given data, we need to place each data point on a number line and then represent it with a dot above its corresponding value. The number line should range from 0 to the maximum number of pets owned by any student, which in this case is 4.
First, we place a dot above the value 0, which occurs twice in the data set. Then, we place three dots above the value 1, which occurs five times in the data set. Next, we place two dots above the value 2, which occurs twice in the data set. Finally, we place one dot above the value 3 and one dot above the value 4.
In summary, the dot plot will have one dot above 3 and one dot above 4 for the number of pets axis, and for the number of students axis, we will have two dots above 0, five dots above 1, two dots above 2, and no dots above 3 or 4. This represents the distribution of the data in a visual way.
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Describe at least two advantages to using stem plots rather than frequency distributions
Stem plots (also known as stem-and-leaf plots) have several advantages over frequency distributions, including:
1. Stem plots show individual data points: Unlike frequency distributions, which group data into intervals, stem plots show each individual data point. This makes it easier to see the distribution of the data, including the shape, the range, and any outliers or gaps. Stem plots can also reveal patterns and trends in the data that may not be apparent from a frequency distribution.
2. Stem plots are easy to construct: Constructing a stem plot requires minimal computation and is relatively simple to create by hand. It involves only sorting the data and then splitting each data point into a stem (the leading digits) and a leaf (the trailing digit). This makes stem plots a convenient tool for quick exploratory data analysis, especially when dealing with small to moderate-sized datasets. In contrast, constructing a frequency distribution can be more time-consuming, as it requires choosing appropriate intervals and counting the number of data points in each interval.
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Customer: "I prepaid 70% of the total cost of $127. 50 last week. "
Employee: "Okay. The total you still owe is
The total amount the customer still owe is $38.25. Customer: "I prepaid 70% of the total cost of $127.50 last week."
Employee: "Okay. The total you still owe is $38.25."
Here the customer prepaid 70% of total cost of $127.50 last week and the employee need to replay how much amount the customer still owe is. To find out the total amount the customer still owes after prepaying 70% of the total cost of $127.50,
Calculate the prepaid amount: 70% of $127.50 = 0.7 * 127.50 = $89.25Subtract the prepaid amount from the total cost: $127.50 - $89.25 = $38.25So the total amount the customer still owe is $38.25.
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Tell whether finding the answer requires finding a greatest common factor or a least common multiple. You do not need solve the problem. A string of holiday lights at a store have three colors that flash at different times. Red lights flash every fifth second. Blue lights flash every third seconds. Green light flashes every four seconds. The store owner turns on the lights. After how many seconds will all three lights flash at the same time for the first time?
A. ) Greatest Common Factor
B. ) Lest Common Multiple
Finding the answer requires finding the least common multiple (LCM) of 5, 3, and 4, making the correct answer B. ) Least Common Multiple.
To determine whether finding the answer requires finding a greatest common factor (GCF) or a least common multiple (LCM), we need to analyze the given information.
In this scenario, the red lights flash every fifth second, the blue lights flash every third second, and the green lights flash every fourth second. We want to find the first time when all three lights flash simultaneously.
To find this time, we need to find the smallest number that is divisible by all three given numbers (5, 3, and 4). This means we are looking for the least common multiple (LCM) of these numbers.
To calculate the LCM, we can use the formula:
LCM(a, b) = (a * b) / GCF(a, b),
where GCF(a, b) represents the greatest common factor of numbers a and b.
Therefore, in this case, finding the answer requires finding the least common multiple (LCM) of 5, 3, and 4, making the correct answer:
B. ) Least Common Multiple.
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a chain letter starts when a person sends it to 7 others. these people either ignore it or send it to 7 more. if 211 are involved in this chain letter (including the sender), (1) how many sent the letter? (2) how many did not continue the chain?
There are 22 people who sent the chain letter, and 189 people did not continue the chain.
We know that the chain started with one person who sent it to 7 others, so that makes a total of 8 people in the first round. In the second round, each of those 7 people could either send it to 7 more people or ignore it, so there are two possibilities for each of those 7 people: they either continue the chain or they don't.
Therefore, there are 2⁷ = 128 possible outcomes for the second round.
If we assume that everyone who received the letter in the second round sent it to 7 more people, then there would be 7 x 128 = 896 people in the third round.
Continuing this pattern, we can see that the number of people in each round is given by the formula of combination 8 x 7ⁿ⁻¹, where n is the round number (starting with n = 1 for the first round).
We want to find the round number such that the total number of people in the chain is 211. Setting the formula above equal to 211 and solving for n gives
8 x 7ⁿ⁻¹ = 211
7ⁿ⁻¹ = 26.375
n - 1 = log_7(26.375)
n = 2.78 (rounded to two decimal places)
Since we can't have a fractional round number, we can assume that the chain ended after the second round (since the third round would have too many people). Therefore, the total number of people who sent the letter is
8 + 7(2) = 22
To find the number of people who did not continue the chain, we can subtract the number of people who sent the letter from the total number of people in the chain
211 - 22 = 189
Therefore, 189 people did not continue the chain.
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If f(x) = x - 7, then what is ƒ (8)?
Step-by-step explanation:
we use a function as a kind of recipe or template for an actual calculation (or actual "ingredients").
as long as we don't handle the actual food items or actual numbers, it all stays theoretical. variables have no actual value and represent every possible case with every possible value.
but as soon as we get an actual unit value (like 8 in our case), we can put it in place of the variables (that are really nothing else but placeholders for actual values) and simply caucuses the result.
so,
when the question asks what is f(8), it really means what is the result when x = 8.
therefore,
f(8) = 8 - 7 = 1
that's it. that is the whole thing. no mystery, magic or genius strikes necessary.
Answer:
[tex] \sf \: f(8) = 1[/tex]
Step-by-step explanation:
Given function,
→ f(x) = x - 7
Now we have to,
→ Find the required value of f(8).
We have to use,
→ x = 8
Then the value of f(8) will be,
→ f(x) = x - 7
→ f(8) = 8 - 7
→ [ f(8) = 1 ]
Hence, the value of f(8) is 1.
a qualitative researcher studied womens decisions to delay birth until their late 30s. initial participants referred other women who had made similar decisions. what type of sampling approach i sbeing used with such referrals
The sample is being used with such referrals of a qualitative researcher studied women's decision to delay childbearing until their late 30s is Snowball, option C.
A non-probability sampling technique called snowball sampling entails the recruitment of new units by existing units to make up the sample. Research regarding people with certain characteristics who would be hard to find otherwise can benefit from snowball sampling (e.g., people with a rare disease).
Snowball sampling, sometimes referred to as chain sampling or network sampling, starts with one or more research participants. Following then, it proceeds based on recommendations from those individuals. This procedure is repeated until the required sample is obtained or a saturation point is reached.
The selection is based on a variety of factors, including:
A minimum of five years must have passed from the beginning of the relationship.Now the pair must cohabitate.The pair must reside in a specific region.The pair must be able to provide examples of changes or difficulties they have faced together (e.g., long-distance, illness or loss of a loved one).Learn more about Snowball sample:
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Complete question;
A qualitative researcher studied women's decision to delay
childbearing until their late 30s. Initial study participants
referred friends who had made similar decisions. What type
of sample is being used with such referrals?
A.Convenience
B.Volunteer
C.Snowball
D. Purposive
What is the midpoint of the line segment that joins points (4,-2) and (-2,5)
Answer:
(1, 1.5).
Step-by-step explanation:
Midpoint of (x1, y1) and (x2, y2)
(x1 + x2)/2 , (y1 + y2)/2
=(4+-2)/2, (-2+5)/2
= (1, 1.5).
You buy a movie ticket for $5.25
and popcorn for $2.98
.
You pay with a $10
bill.
The side lengths of the base of a triangular prism are 5 meters, 8 meters, and 10 meters. the height of the prism is 16.5 meters. what is the lateral surface area of the prism in square meters? (please show work i beg you)
a)356.1 m²
b)388.9 m²
c)363.2 m²
d)379.5 m²
The lateral surface area of the triangular prism with side lengths of the base of a triangular prism are 5 meters, 8 meters, and 10 meters the height of the prism is 16.5 meters is 379.5 m²
Lateral surface area of prism = (a + b + c )h
a = base side = 5m
b = base side = 8m
c = base side = 10m
h = height = 16.5 m
Lateral surface area of prism = (5 + 8 + 10)16.5
The lateral surface area of the prism = 379.5m²
The lateral surface area of the triangular prism is 379.5 m²
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Nadia bought five tickets to attend a spaghetti supper fund raiser at her school. The equation 5x = 32. 50 can be used to find X, the cost of each ticket in dollars. Which equation represents the cost of each ticket. A. X=32. 50/5
B. X=32. 50(5)
C. X= 32. 50-5
D. X= 32. 50+5
Nadia brought five tickets to attend a spaghetti supper fund rasier at her school. The equation 5x = 32.50 can be used to find x, the cost of each ticket in dollars. The equation x = 32.50/5 will represent the cost of each ticket.
This is because the equation 5x = 32.50 is asking us to find the cost of each ticket (represented by x) when there are five tickets in total and the total cost is $32.50.
To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 5, which gives us:
X=32.50/5.
So, each ticket costs $6.50.
Therfore, the correct equation that represents the cost of each ticket is X=32.50/5, option A.
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Ofra tried to solve an equation.
3x = 4.5
3x 4.5
3
3
=
Setting up
x = 1.5 Calculating
Where did Ofra make her first mistake?
Choose 1 answer:
Setting up
B Calculating
Ofra correctly solved the equation.
If Ofra tried to solve an equation 3x = 4.5, The statement "Ofra correctly solved the equation" is correct. So, correct option is C.
We can see this by substituting x = 1.5 into the original equation 3x = 4.5:
3(1.5) = 4.5
Simplifying the left-hand side, we get:
4.5 = 4.5
This is a true statement, which means that x = 1.5 is a valid solution to the equation 3x = 4.5.
Therefore, Ofra did not make any mistakes in solving the equation. She correctly set up the equation 3x = 4.5 by multiplying both sides by 3 to isolate x, and then calculated the value of x to be 1.5, which is the correct solution.
Option (c) is the correct answer.
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Complete question is:
Ofra tried to solve an equation.
3x = 4.5, Setting up x = 1.5 Calculating
Where did Ofra make her first mistake?
Choose 1 answer:
a) Setting up
b) Calculating
c) Ofra correctly solved the equation.
Pls Help fast! Find the diameter of the circle
11 Points and brainliest!
Answer: 16
Step-by-step explanation: to find diameter its radius x 2, so 2 x 8 is 16
ANALYZE In Europe, fuel economy is measured in liters per 100 kilometers. On a 2500 km road trip a car used 150 liters of fuel. The car used an average of how many liters per 100 km?
To find out the car's average fuel consumption in liters per 100 kilometers, we need to use the following formula:
Fuel consumption (liters per 100 km) = (Total fuel used / Total distance traveled) x 100
Using the information given, we know that the car traveled 2500 km and used 150 liters of fuel. Plugging these values into the formula, we get:
Fuel consumption (liters per 100 km) = (150 / 2500) x 100 = 6
Therefore, the car used an average of 6 liters of fuel per 100 kilometers on its 2500 km road trip.
It is important to note that fuel economy is an important factor in Europe, where fuel prices are generally higher than in other parts of the world.
By measuring fuel consumption in liters per 100 kilometers, European consumers can easily compare the fuel efficiency of different vehicles and make more informed purchasing decisions.
Additionally, analyzing fuel consumption data can help drivers identify ways to improve their fuel efficiency, such as reducing their speed, maintaining proper tire pressure, and avoiding excessive idling.
This not only saves money on fuel costs, but also reduces carbon emissions and contributes to a more sustainable transportation system.
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How can you use rational expressions and equations to describe relationship and solve problems?
Rational expressions and equations can be used to describe relationships and solve problems that involve proportions or rates of change.
They involve expressions that are fractions of polynomials, where the numerator and denominator can be thought of as values that change according to some variable.
For example, rational expressions can be used to represent rates of change in physics or finance, such as the speed of an object or the interest rate on a loan. By setting up equations with rational expressions, we can solve for unknown values or relationships between variables.
Rational equations can also be used to describe relationships between quantities that are proportional, such as the volume of a container and the amount of liquid it can hold. By solving for an unknown variable in a rational equation, we can determine the relationship between the two quantities and use it to make predictions or solve practical problems.
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what are the first three terms of the sequence 40-2n
Answer:
1 term-38. ,2nd term-36. ,3rd tern is34
Suppose the height of a cylinder is cut in half and the radius is doubled. how will this affect the volume of the cylinder ?????
Cutting the height of a cylinder in half would divide its volume by 2, while doubling the radius would multiply its volume by 4. Therefore, the overall effect on the volume of the cylinder is to multiply it by 2. So, if the original volume of the cylinder was V, after cutting the height in half and doubling the radius, the new volume would be 2V.
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Suppose that the weekly profit, in dollars, of producing and selling x cars is P(x) = -0.005x*-0.2x2 + 1000x - 1300. and currently 80 cars are produced and sold weekly. Use P(80) and the marginal profit when x-SAP(80)) to estimate the weekly profit of producing and selling 81 cars. Round to the nearest dollar.
• $75,731 • $75,732 • $75,645 • $77,032
To estimate the weekly profit of producing and selling 81 cars, we first need to find the current weekly profit for producing and selling 80 cars using P(80):
P(80) = -0.005(80)^(2) - 0.2(80) + 1000(80) - 1300
P(80) = $75,800
Now we need to find the marginal profit at x = 80, which is the derivative of the profit function P(x):
P'(x) = -0.01x - 0.4x + 1000
P'(80) = -0.01(80) - 0.4(80) + 1000
P'(80) = $920
The marginal profit at x = 80 is $920. This means that for each additional car produced and sold beyond 80, the profit will increase by $920.
To estimate the weekly profit of producing and selling 81 cars, we can use the approximation formula:
ΔP ≈ P'(80)Δx
where ΔP is the change in profit, Δx is the change in the number of cars produced and sold, and P'(80) is the marginal profit at x = 80.
We want to find the change in profit when the number of cars produced and sold increases from 80 to 81, so Δx = 1. Plugging in the values we have:
ΔP ≈ $920(1)
ΔP ≈ $920
This means that the estimated weekly profit for producing and selling 81 cars is:
P(81) ≈ P(80) + ΔP
P(81) ≈ $75,800 + $920
P(81) ≈ $75,720
Rounding to the nearest dollar, the answer is $75,720. So the correct option is: $75,720.
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Question 4 < > Find the volume of the solid obtained by rotating the region bounded by y 4x2, 1 = 1, and y = 0, about the x-axis. V Submit Question
The volume of the solid obtained by rotating the region bounded about the x-axis is 3π/4 cubic units.
How to find the volume of a solid by rotating a region?To find the volume of the solid obtained by rotating the region bounded by y = 4x^2, y = 1, and y = 0 about the x-axis, we can use the method of cylindrical shells.
First, we need to find the limits of integration. The region is bounded by y = 4x^2 and y = 1, so we can set up the integral as follows:
V = ∫[0,1] 2πx(1-4x^2)dx
Next, we can simplify the integrand:
V = ∫[0,1] 2πx dx - ∫[0,1] 8πx^3 dx
V = π - 2π/4
V = 3π/4
Therefore, the volume of the solid obtained by rotating the region bounded by y = 4x^2, y = 1, and y = 0 about the x-axis is 3π/4 cubic units.
Learn more about the volume of a solid.
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