The required answer is P(at least 2) = P(at least 1) * (1/2) = (1 - e^(-λ * a)) * (1/2)
a. To find the long-term average number of people in line, we will use the following formula:
Average number of people in line = λ * a
Here, λ is the arrival rate of customers following a Poisson process, and a is the average time taken by the chef to process an order.
b. To find the long-term probability that there are at least two people in line, we first need to calculate the probability that there is at least one person in line. Then, we will subtract this probability from 1 to find the probability of having at least two people in line.
Probability of at least one person in line = 1 - Probability of no one in line
Since the arrival of customers follows a Poisson process, the probability of having no one in line is given by:
P(0) = e^(-λ * a)
Thus, the probability of at least one person in line is:
P(at least 1) = 1 - e^(-λ * a)
Now, we can calculate the probability of having at least two people in line by considering that the second person joins the line with probability 1/(1 + 1) = 1/2. So, the probability of at least two people in line is:
P(at least 2) = P(at least 1) * (1/2) = (1 - e^(-λ * a)) * (1/2)
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1. Given the function: f(x)=-2x+7 and g(x)=5x-16
Find the function for h(x)=f(x)+g(x)
The function h(x) can be represented by -3x-9 .
Linear Equation
An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+6. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=7 and b=6.
The question gives two linear equations that represent two functions: f(x)=-2x+7 and g(x)=5x-16.
For solving this you should sum both equations. See below
h(x)=f(x)+g(x)
h(x)=-2x+7 +5x-16
h(x)=-3x-9
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An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 75
Heads, Tails 40
Tails, Tails 35
Tails, Heads 50
What is the P(No Heads)?
85%
75%
37.5%
17.5%
The probability of no heads is given as follows:
P(No Heads) = 17.5%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of outcomes is given as follows:
200.
The desired outcomes, those without heads, are Tails, Tails, which happened 35 times, hence the probability is given as follows:
p = 35/200
p = 0.175
p = 17.5%.
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Find the distance between the two points in simplest radical form.
(
8
,
6
)
and
(
3
,
−
6
)
(8,6) and (3,−6)
The distance between the two points (8,6) and (3,-6) in simplest radical form is √169 units.
The complete question is :
Find the distance between the two points in simplest radical form.
(8,6) and (3,−6)
What is the distance between the two points?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given that. the two points are (8,6) and (3,-6).
Substituting the values into the formula, we get:
d = √((3 - 8)² + (-6 - 6)²)
Simplifying the expression inside the square root:
d = √((-5)² + (-12)²)
d = √(25 + 144)
d = √169
Therefore, the distance is √169 units.
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The cows on a farm were producing 12.8 liters of milk per cow each day. The farmer bought 60 new cows and began using a new feed for all the cows. Now each of his cows is producing 15 liters of milk each day. How many cows are on the farm now if the farmer gets 1340 more liters of milk per day than he did before any changes were made?
There are now 260 cows on the farm.
Let's start through calculating the amount of milk produced with the aid of the original cows before any modifications were made.
If every of the unique cows was producing 12.8 liters of milk in keeping with day, and there had been "x" cows, then the entire amount of milk produced by means of the original cows could be:
12.8x liters per day
After the adjustments, the farmer has 60 more cows and all cows produce 15 liters of milk per day. So, the full amount of milk produced with the aid of all cows after the modifications would be:
15(x + 60) liters per day
we're told that the new milk production is 1340 liters more according to day than before the changes. So, we can set up an linear equation:
15(x + 60) = 12.8x + 1340
Simplifying the equation, we get:
15x + 900 = 12.8x + 1340
2.2x = 440
x = 200
therefore, there were at first 200 cows on the farm. After the changes, the full number of cows would be:
x + 60 = 200 + 60 = 260 cows
So, there are now 260 cows on the farm.
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What does the mapping found in part b tell you about the relationship between the two circles? explain your reasoning.
The term "mapping" refers to the process of creating a mathematical correspondence between points or objects in two different sets. In this case, the mapping found in part b tells us that there exists a one-to-one correspondence between the points in Circle A and the points in Circle B.
There is a one-to-one correspondence between the points in Circle A and the points in Circle B, and that this correspondence preserves distance.
This means that for every point in Circle A, there is exactly one corresponding point in Circle B that is the same distance away from the center of the circle as the original point.
Since the correspondence is one-to-one, it follows that the two circles have the same number of points. That is, if Circle A has n points, then Circle B also has n points.
Therefore, we can conclude that the two circles have the same size.
Furthermore, because the correspondence preserves distance, any transformation that maps one circle onto the other must be a rigid motion, meaning it preserves angles and distances.
In particular, the transformation must be an isometry.
Therefore, we have shown that the two circles are congruent. That is, they have the same size and shape, and can be transformed onto one another by a combination of translations, rotations, and reflections.
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Write a number that is greater than 10,910,099,999 but less than 11,000,000,000
Answer: 10, 911,000,000
Step-by-step explanation:
10,911,000,000 < 11,000,000,000
10,911,000,000 > 10,910,099,999
Find and interpret the mean absolute deviation of the data. 46,54,43,57,50,62,78,42
In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units.
What is mean absolute deviation?Mean absolute deviation (MAD) is a statistical measure that represents the average distance between each data point and the mean of the data set. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences. MAD is a useful measure of the variability or spread of a data set, and is often used as an alternative to the more common measure of standard deviation. Like standard deviation, MAD gives an indication of how spread out the data is, but unlike standard deviation, MAD is less sensitive to extreme values or outliers.
Here,
To find the mean absolute deviation of the data, we first need to calculate the mean (average) of the data:
Mean = (46 + 54 + 43 + 57 + 50 + 62 + 78 + 42) / 8
Mean = 52
The mean of the data is 52.
Next, we need to calculate the absolute deviation of each data point from the mean. The absolute deviation is simply the absolute value of the difference between each data point and the mean:
|46 - 52| = 6
|54 - 52| = 2
|43 - 52| = 9
|57 - 52| = 5
|50 - 52| = 2
|62 - 52| = 10
|78 - 52| = 26
|42 - 52| = 10
Now, we can calculate the mean absolute deviation by taking the average of the absolute deviations:
Mean Absolute Deviation = (6 + 2 + 9 + 5 + 2 + 10 + 26 + 10) / 8
Mean Absolute Deviation = 8.5
The mean absolute deviation of the data is 8.5.
Interpretation: The mean absolute deviation represents the average distance between each data point and the mean of the data. In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units. This means that the data points are relatively spread out, with some points being much higher or lower than the mean.
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Please help... 100 points promised!
Answer:
Step-by-step explanation:
The probability of drawing 2 red cards from a standard 52-card deck can be calculated as follows:
There are 26 red cards in the deck, so the probability of drawing a red card on the first draw is 26/52.
After the first card is drawn, there are 25 red cards remaining in the deck out of 51 total cards, so the probability of drawing a red card on the second draw is 25/51.
To find the probability of both events happening together (drawing 2 red cards), we multiply the probabilities of each event:
(26/52) * (25/51) = 0.245 or approximately 24.5%
Therefore, the probability of drawing 2 red cards in a standard 52 card deck is approximately 24.5%.
In one month 382 adults and 65 children stayed in a hotel. How many people are there altogether?
In one month, a total of 447 people stayed at the hotel.
In one month, a hotel had 382 adults and 65 children staying as guests.
To find out the total number of people who stayed at the hotel, we simply need to add the number of adults and children together.
In one month, a total of 447 people (382 adults and 65 children) stayed at the hotel.
Overall, this problem is a simple example of addition in action. By adding the number of adults and children together, we can determine the total number of people who stayed in the hotel.
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The teacher could buy the shirt online 3.50 each she would also pay a fee of 9.50 for shipping the shirts.
The function that represents the total cost (y) of buying x shirt online of $3.50 each and shipping charges of $9.50 is 3.50x + 9.50 = y
Cost of each shirt = $3.50
The fee for shipping the shirts is = $9.50
Total number of shirts bought by shirt online = x
The total cost of buying x shirts is represented by y
The total cost will be the sum of each cost of the shirt and shipping charges
y = 3.50x + 9.50
Hence, the function that represents the total cost y of buying x shirt online of $3.50 each and shipping charges of $9.50 is 3.50x + 9.50 = y
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The question is incomplete complete question is :
The teacher could buy the shirt online at 3.50 each she would also pay a fee of 9.50 for shipping the shirts. Write a function that can be used to find y the total cost in dollars of buying x shirts online.
find the first derivative x cos(14x + 13y) = y sin x
To find the first derivative of the equation x cos(14x + 13y) = y sin x, we will need to use the chain rule and product rule.
First, we will differentiate each term separately:
d/dx(x) = 1
d/dx(cos(14x + 13y)) = -sin(14x + 13y) * d/dx(14x + 13y)
= -sin(14x + 13y) * 14
d/dx(y) = 0 (since y is a constant)
d/dx(sin(x)) = cos(x)
Next, we will apply the product rule to differentiate the left-hand side of the equation:
d/dx(x cos(14x + 13y)) = cos(14x + 13y) + x * (-sin(14x + 13y) * 14)
Now, we can set this expression equal to the derivative of the right-hand side of the equation and solve for the first derivative:
cos(14x + 13y) - 14x sin(14x + 13y) = y cos(x)
Our final answer for the first derivative is:
cos(14x + 13y) - 14x sin(14x + 13y) = y cos(x)
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Pls help me with this! Will give points!
Answer:
Subtract 1 from both sides.
Answer:
subtract 1 from both sides. because taking out the 1 from 1 and 1 from 17 will equal 16. which leaves t/4=16
Procter & Gamble reported that an American family of four washes an average of 1
ton (2000 pounds) of clothes each year. If the standard deviation of the distribution
is 187. 5 pounds, find the probability that the mean of a randomly selected sample of
50 families of four will be between 1980 and 1990 lbs.
The required probability is approximately 0.1253 or 12.53%.
We can use the central limit theorem to approximate the sampling distribution of the mean of the weights of clothes washed by 50 families of four. According to the central limit theorem, the sampling distribution of the mean will be approximately normal if the sample size is large enough (n > 30), regardless of the shape of the population distribution.
The mean of the sampling distribution of the mean will be equal to the population mean, which is 2000 lbs
[tex]SEM=\frac{\sigma}{\sqrt{n} }[/tex]
σ = population standard deviation
n = sample size.
[tex]SEM=\frac{187.5}{\sqrt{50} }[/tex]
= 26.5
Now we need to find the z-scores corresponding to the two values of the mean.
[tex]z_1=\frac{1980-2000}{26.5}[/tex]
= -0.75
[tex]z_2=\frac{1990-2000}{26.5}[/tex]
= -0.38
Using a standard normal table, we can find the probability that a z-score is between -0.75 and -0.38.
P(-0.75 < Z < -0.38) = 0.1253
Therefore, the required probability is approximately 0.1253 or 12.53%.
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Kevin has three classes in a row. Eight classes two hours long. Kevin’s first class is at seven. When will Karen’s last class and?
Karen's last class will end at three in the afternoon.
At what time will Karen’s final class conclude?Given that Kevin has three classes in a row, each lasting two hours, we can calculate the total duration of his classes. Three classes, each two hours long, amount to a total of 6 hours.
Since Kevin's first class starts at seven in the morning, we add 6 hours to that time, resulting in the conclusion of Karen's last class at three in the afternoon.
Understanding schedules and timetables is essential for effective time management. In academic settings, students often have multiple classes with varying durations throughout the day.
Calculating the end time of a class or event based on its start time and duration helps individuals plan their activities and allocate their time efficiently.
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How long does it take time a car to move 150 centimeters? we all have a good idea that if it takes a smaller period of time to move 50 centimeters? the car must be moving faster. But how do we measure the space of a toy car in your own car, its is easy because engineers have designed a speedometer that automatically tells you how fast your car is moving.
If you record the time it takes for the car to move 50 centimeters and then record the time it takes to move 150 centimeter, will there be a difference in the speed of the car between the tow runs? Explain your prediction
There may be a difference on speed based on various factors
How to determine speedThough it would be reasonable to conclude that if it takes less time for a car to move 50 centimeters than 150 centimeters, they must be traveling faster; we do not know exactly when they did this and whether their speed changed accordingly.
Furthermore, it could have taken the same time covering both distances; thus leaving unanswered questions regarding their relative speeds.
Due to variables affecting car speed such as changes in terrain or obstacles in its path, we cannot accurately predict its speed without more information regarding these two runs.
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The sum of twice a nuber,n, and 14 is 30.
2x+14=30
2x =30-14
2x=16
x =8
Answer:
8
Step-by-step explanation:
Twice means 2 so twice a number,n, means 2 times n thus 2n
sum means add so, 2n + 14
"is" means equal so 2n + 14 = 30
Solve for n:
2n=16
N=8
Find the critical points of f(x) = x - 18x² + 96x and use the Second Derivative Test (if possible) to determine whether each corresponds to a local minimum or maximum. (Use symbolic notation and fractions when needed)
To find the critical points of f(x) = x - 18x² + 96x, we need to find the values of x where f'(x) = 0.
f'(x) = 1 - 36x + 96
Setting f'(x) = 0, we get:
-36x + 97 = 0
x = 97/36
So the critical point is (97/36, f(97/36)).
To use the Second Derivative Test, we need to find f''(x):
f''(x) = -36
At the critical point x = 97/36, f''(97/36) = -36 < 0.
Since f''(97/36) is negative, the Second Derivative Test tells us that the critical point corresponds to a local maximum.
Therefore, the critical point (97/36, f(97/36)) is a local maximum.
To find the critical points of the function f(x) = x - 18x² + 96x, we first need to find its first derivative, f'(x), and then set it to zero to find the critical points.
1. Find the first derivative, f'(x):
f'(x) = d/dx (x - 18x² + 96x) = 1 - 36x + 96
2. Set f'(x) to zero and solve for x:
0 = 1 - 36x + 96
36x = 95
x = 95/36
Now, let's use the Second Derivative Test to determine if this critical point corresponds to a local minimum or maximum.
3. Find the second derivative, f''(x):
f''(x) = d/dx (1 - 36x + 96) = -36
4. Evaluate f''(x) at the critical point x = 95/36:
f''(95/36) = -36
Since f''(95/36) is negative, the Second Derivative Test tells us that the critical point x = 95/36 corresponds to a local maximum.
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What is the given function below in vertex form
if Ashely sold 98 cups for $1 each, how much profit did she make
Answer:
After selling 98 cups, she made $98
Step-by-step explanation:
If she sold 98 cups, and each one went for $1, then you can set up an equation:
98(1)=98
Answer:
Ashley made $98.
Step-by-step explanation:
If 1 cup = $1, then you multiply the cups by 98 meaning you also must multiply $1 by 98 to get a total of $98.
A student takes a measured volume of 3. 00 m hcl to prepare a 50. 0 ml sample of 1. 80 m hcl. What volume of 3. 00 m hcl did the student use to make the sample?.
The student used 30.0 mL of 3.00 M HCl to make the 50.0 mL sample of 1.80 M HCl.
To find the volume of 3.00 M HCl needed to make a 50.0 mL sample of 1.80 M HCl, we can use the equation:
M₁V₁ = M₂V₂
Where M₁ is the initial concentration, V₁ is the initial volume, M₂ is the final concentration, and V₂ is the final volume.
We are given M₁ = 3.00 M, M₂ = 1.80 M, and V₂ = 50.0 mL. We can rearrange the equation to solve for V₁:
V₁ = (M₂V₂) / M₁
V₁ = (1.80 M * 50.0 mL) / 3.00 M
V₁ = 30.0 mL
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Factor 21r–56. Write your answer as a product with a whole number greater than 1.
The factored form of 21r-56 is: 21r-56 = 7r(-5) or 7r*(-5)
What is factoring?Factoring is the process of finding the factors (or divisors) of a given mathematical expression or number. In algebra, factoring involves breaking down an expression into simpler parts (called factors) that can be multiplied together to obtain the original expression. The goal of factoring is to simplify the expression or solve an equation by expressing it in terms of its factors.
In the given question,
To factor 21r-56, we first need to find the greatest common factor (GCF) of the two terms. The GCF of 21 and 56 is 7. We can also factor out r since it is a common factor of both terms. Therefore, we can write:
21r-56 = 7r(3-8)
Simplifying the expression inside the parentheses, we get:
21r-56 = 7r(-5)
Therefore, the factored form of 21r-56 is:
21r-56 = 7r(-5) or 7r*(-5).
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The angle of depression from the top of a 150m high cliff to a boat at sea is 7°. How much closer to the cliff must the boat move for the angle of depression to become 19°?
The boat must move 785.82 m closer to the cliff for the angle of depression to become 19°.
We need to find how much closer to the cliff the boat must move for the angle of depression to change from 7° to 19°.
Calculate the distance from the boat to the base of the cliff at 7° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(7°) = 150m/distance
distance = 150m/tan(7°)
distance=1221.49
Calculate the distance from the boat to the base of the cliff at 19° angle of depression.
Using the tangent function, we have:
tan(angle) = height/distance
tan(19°) = 150m/distance
distance = 150m/tan(19°)
distance=435.6665
Calculate the difference between the two distances to find out how much closer the boat must move.
difference = distance at 7° angle of depression - distance at 19° angle of depression
Plugging in the values from Steps 1 and 2, we get:
difference = (150m/tan(7°)) - (150m/tan(19°))
difference=1221.49-435.6665
difference=785.8235
After calculating, we find that the boat must move approximately 785.82 meters closer to the cliff for the angle of depression to change from 7° to 19°.
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M&m are produced so that 20% are yellow, 20% are red, orange, blue and green are all 10 % each. The rest are brown. If an m&m is picked at random, what is the probability that it’s brown
The probability that an M&M picked at random is brown is 30% if m&m picked brown at random. Probability refers to the measure of the likelihood of an event occurring.
To find the probability that an M&M picked at random is brown, we need to consider the given percentages of the other colors. Given that 20% are yellow, 20% are red, 10% are orange, 10% are blue, and 10% are green. First, let's add these percentages together:
20% + 20% + 10% + 10% + 10% = 70%
Since the total percentage should add up to 100%, we can find the percentage of brown M&Ms by subtracting the sum of the other colors' percentages from 100%:
100% - 70% = 30%
So, the probability that an M&M picked at random is brown is 30%.
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Given m||n, find the value of x
Answer:
x=32°
Step-by-step explanation:
3x-2=2x+30
x-2=30
x=32°
Federico enjoys catching pokemons in university campus. One day, while trying to catch charmander, he found the best spot next to a
perfectly circular pond. He was 43 feet from the bank and 75 feet from the point of tangency. Determine the radius of the pond using the
given information. Round to the nearest integer,
The radius of the pond is 32 feet, under the condition that 43 feet from the bank and 75 feet from the point of tangency.
Let us consider that the center of the circle O, the point of tangency T, and Federico's position P.
We can utilize these two points to form a line. The point of tangency is the place where Federico is closest to the pond. The radius of the pond is considered perpendicular to this line and passes through the point of tangency.
Firstly, we have to the distance between Federico's position P and covers passes through points T and B (the bank). This distance is equivalent to the given radius of the circle. We have to apply the formula for the distance between a point and a line to find this distance.
Let us assume this distance as d.
d = (|BT x BP|) / |BT|
Here
|BT| = line segment length of BT,
|BP| = line segment length of BP,
BT x BP = vectors cross product of BT and BP.
Here we evaluate |BT| applying the Pythagorean theorem
|BT|² = 75²+ r²
Here,
r = radius concerning the circle.
Then,
|BP|² = 43² + r²
Staging these values into our formula for d:
d = (|BT x BP|) / |BT|
= (|BT| × |BP|) / |BT|
= |BP|
= √(43² + r²)
We want to solve for r, so we can square both sides:
d² = 43² + r²
r² = d² - 43²
r = √(d² - 43²)
Placing in d = 75,
r = √(75² - 43²)
≈ 32 feet
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Find the derivative of y with respect to x if y= e⁻¹⁷ˣ.
dy/dx = ...
The derivative of y with respect to x when y = e⁻¹⁷ˣ is dy/dx = -17eˣ
Find the derivative?
To find the derivative of y with respect to x when y = e⁻¹⁷ˣ, we'll use these terms: "derivative", "respect", and "with".
Identify the function. In this case, y = e⁻¹⁷ˣ
Find the derivative (dy/dx) of the function with respect to x. To do this, we'll apply the chain rule, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
The outer function is e^(u) (where u is the inner function), and its derivative with respect to u is e^(u). The inner function is -17x, and its derivative with respect to x is -17.
Apply the chain rule. The derivative of y with respect to x (dy/dx) is the product of the derivative of the outer function and the derivative of the inner function: (e^(u)) * (-17).
Substitute u with the inner function (-17x). So, dy/dx = (e⁻¹⁷ˣ * (-17).
The derivative of y with respect to x when y = e⁻¹⁷ˣ is dy/dx = -17eˣ
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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
To determine the scale factor of the dilation between the green parallelogram and the black parallelogram, you would need to compare the corresponding side lengths of the two parallelograms. For example, if the green parallelogram has a side length that is half of the black parallelogram's side length, the scale factor would be 1/2 (Option B).
If the green parallelogram's side length is twice the black parallelogram's side length, the scale factor would be 2 (Option C). And if the green parallelogram's side length is one-third of the black parallelogram's side length, the scale factor would be 1/3 (Option A). Without specific measurements or a visual representation, it is not possible to accurately identify the scale factor between the two parallelograms. Please provide the side lengths or a diagram to help determine the correct scale factor.
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Find the volume of a cylinder with a diameter of 28 meters and a height of 6 and one half meters. Approximate using pi equals 22 over 7.
28,028 cubic meters
4,004 cubic meters
1,274 cubic meters
572 cubic meters
The volume of the cylinder is 4004 cubic metres.
How to find the volume of a cylinder?The diameter of the cylinder is 28 metres and the height of the cylinder is 6.5 metres.
Therefore, the volume of the cylinder can be found as follows:
Hence,
volume of a cylinder = πr²h
where
r = radiush = heightTherefore,
volume of the cylinder = 22 / 7 × 14² × 6.5
volume of the cylinder = 22 / 7 × 196 × 6.5
volume of the cylinder = 28028 / 7
volume of the cylinder = 4004 cubic metres
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Please help me! It's due today!
Answer:
i think it would be...5^-5, 5^0, 5^4
Step-by-step explanation:
pls mark brainliest
Match the formulas for volume and calculate the volumes of the sphere, cylinder, and cone shown below. Each shape has a radius of 2.5 and the cylinder and cone have a height of 4.
options for each drop down box [choose]:
Sphere - volume measure
Sphere - volume formula
Cone - volume formula
Cone - volume measure
Cylinder - volume measure
Cylinder - volume formula
None of these options
Answer:
The formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the cone.The volume of any sphere is 2/3rd of the volume of any cylinder with equivalent radius and height equal to the diameter.The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h
Step-by-step explanation:
The formula for volume is: Volume = length x width x height
Answer:
Step-by-step explanation:
Volume of a sphere: 4/3 π r³
4/3 (3.14) (2.5)³ =
4/3 (3.14) (15.625) = 65.42 units³
Volume of a cylinder = π r² h
(3.14) (2.5)² (4)
(3.14) (6.25)(4) = 78.5 units²
Volume of a Cone = 1/3 π r² h
(1/3)(3.14)(2.5)²(4) =
(1/3)(3.14)(6.25)(4) = 26.17 units²