The solid's volume will be determined by rotating the area enclosed by the specified curve and the lines y = 2x, y = 2, and x = 0 around the x-axis.
V = 8π/3
Volume integration: What is it?
We refer to an integration as a volume integration when it is carried out in three dimensions using the three variables x, y, and z.
In order to establish my integration borders, I set y=2x y=2 to determine their intersection point.
Your aim is to locate the region so you can settle there. The region is going to be circular because we are rotating around the x-axis.
V = (r2)dr = A(x)dx
We subtract the two radiuses from one another since they are different.
∫(πr₂² - πr₁²)dr
∫(π(2)² - π(2x)²)dr
∫(4π - 4πx²)dr
4π∫(1 - x²)dr
Since our boundary is at 1, integrate between 0 and 1.
V = 4π∫(1 - x²)dr = 8π/3
Therefore, V = 8/3 will be the volume of the solid produced by rotating the area enclosed by the specified curve and lines y = 2x, y = 2, and x = 0 about the x-axis.
What Does a Solid's Volume Mean?
The amount of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid is used to calculate it.
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question 11 pts suppose is an -matrix such that has only the trivial solution. how many pivot columns does have?
A matrix A is said to have only the trivial solution if the only solution to the system of equations, A x = 0, is the zero vector, x = 0.
The number of pivot columns in a matrix is equal to the rank of the matrix. Therefore, if A has only the trivial solution, it has rank 0, and so it has 0 pivot columns. To calculate the rank of a matrix, we can use the following formula: rank(A) = min(m, n) - dim(null A), where m and n are the number of rows and columns of A, respectively, and dim(null A) is the dimension of the null space of A.
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complete question:
Given an m x n matrix A, what is the number of pivot columns for A if it has only the trivial solution?
if the average service rate is 6 customers per hour, and assuming the negative exponential distribution is used to describe the randomness of the service time distribution, what is the probability that the service time will be less than or equal to 6 minutes? a. 0.451 b. 0.549 c. 0.017 d. 0.632
If the average service rate is 6 customers per hour, and assuming the negative exponential distribution is used to describe the randomness of the service time distribution. The probability that the service time will be less than or equal to 6 minutes is 0.549 [B]
The average service rate of 6 customers per hour corresponds to a mean service time of 1/6 = 0.1 hour = 6 minutes. To find the probability that the service time will be less than or equal to 6 minutes, we need to find the cumulative distribution function (CDF) of the exponential distribution evaluated at 6 minutes. The CDF of the exponential distribution is given by:
F(x) = 1 - exp(-λx)
where,
λ = 1/mean = 1/0.1 = 10. Plugging in x = 6, we get:
F(6) = 1 - exp(-10 * 6) = 1 - exp(-60) ≈ 0.549
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based on the residual plot shown, is a linear model appropriate for comparing tree age to basal area? because the residuals are centered about zero, a linear model is appropriate. because the residual plot does not show a clear pattern, a linear model is appropriate. because the residual plot shows a random a scatter of points, a linear model is not appropriate. because the residual plot does not appear linear, it is likely that tree age and basal area do not have a linear relationship.
Answer:
Because the residual plot does not show a clear pattern, a linear model is appropriate.
Step-by-step explanation:
the college board reports that in the recent year, the mean mathematics sat score was 514 and standard deviation of 118. a sample of 50 scores is chosen. a) the probability that the sample mean score is less than 500 is [ select ] b) [ select ] c) the 80th percentile of the sample scores is [ select ]
The College Board reported that in a recent year, the mean mathematics SAT score was 514 and the standard deviation was 118. A sample of 65 scores was chosen.
a) The probability that the sample mean score is less than 500 can be found by using the mean and standard deviation of the SAT scores population. The formula to calculate this probability can be found in 3.
c) The 80th percentile of the sample scores is also not mentioned in the search results. To find the 80th percentile, a probability distribution of the sample mean scores must be created and then solved for the desired percentile.
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Distributive property 42÷3
Answer: 14
Step-by-step explanation: 42 divided by 3 is 14.
As a fraction: 42/3
Answer:
42÷3= 14?
Step-by-step explanation:
mr. Smith started 8 yards away from the motion detector, and two seconds later, he was 4 yards away from the detector. The graph below shows Mr. Smith’s motion. What is the difference between the rate of change of the intervals: 1,2 and 2,4?
The difference between the rate of change of the intervals: 1,2 and 2,4 is; 2
How to find the rate of change over an interval?The average rate of change over the intervals (x₁, y₁) and (x₂, y₂) is given by the formula;
Average rate of change = (y₂ - y₁)/(x₂ - x₁)
Thus, the average rate of change between the intervals (1, 2) and (2, 4) is;
Average rate of change = (4 - 2)/(2 - 1)
Average rate of change = 2/1
Average rate of change = 2
That is the difference between the rate of change over the two given intervals.
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Short answer need please.
The surface area of the right prism is equal 142 square inches.
How to calculate the surface area of a right prism
Surface area is the sum of the areas of all faces in a solid, herein we find the case of a right prism with six rectangular faces. The area formula for a rectangle is shown below:
A = w · l
Where:
A - Area, in square inches. w - Width, in inches.l - Length, in inches.Now we calculate the surface area of the rectangular prism:
A = 2 · (7 in) · (3 in) + 2 · (5 in) · (7 in) + 2 · (3 in) · (5 in)
A = 42 in² + 70 in² + 30 in²
A = 142 in²
The right prism has a surface area of 142 square inches.
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One more question before I leave my aunt house!
Grade 8th
Answer:
2. y = 3x + 6
3. y = 2x
4. y = 5x + 60
Step-by-step explanation:
Slope-intercept form: y = mx + b
2.
Pick 2 points (0,6) (1,9)
The y increase by 3, and the x increase by 1, so the slope is
m = 3
the y-intercept is located at (0,6)
Our equation is y = 3x + 6
3.
Pick 2 points (0,0) (1,2)
The y increase by 2, and the x increase by 1, so the slope is
m = 2
the y-intercept is located at (0,0)
Our equation is y = 2x
4.
Pick 2 points (0,60) (2,70)
The y increase by 10, and the x increase by 2, so the slope is
m = 10/2 = 5
the y-intercept is located at (0,60)
Our equation is y = 5x + 60
Question located in picture below:
Answer:
5a^2 + 1
Step-by-step explanation:
7a^2 - 4 - 2a^2 + 5
5a^2 + 1
Answer:
5a^2+1
Step-by-step explanation:
Combining like terms in polynomials can go based on the degree it has.
Since 7a^2 and -2a^2 have the same degree as one another, we can just add them, which gives us 5a^2
Now since -4 and 5 dont have any degree, they are liked terms.
Add: -4+5=1
Now when simplified, we get:
5a^2+1
Neil rents a canopy for $21.75 per
hour with a $25 delivery and
set-up fee. The rental costs a
total of $155.50. For how many
hours does Neil rent the canopy?
Create and solve the equation.
Answer:
21.75x + 25 = 155.50
-25 = -25
21.75x = 130.50
divide your slope from your variable
x = 6
50 apples cost $25. How much would 75 apples cost?
To find out how much 75 apples would cost, we need to find out the cost per apple and then multiply that amount by 75. If 50 apples cost $25, then the cost per apple is $25/50 = $0.50. So, 75 apples would cost $0.50 x 75 = $37.50.
Answer:
$37.50
Step-by-step explanation:
$25/50=$0.50 per apple
0.50 x 75 = $37.50
Suppose that the functions s and t are defined for all real numbers x as follows.
s(r) = 5,2
+(x) =3
write the expressions for (s + t) (x) and (s- t) (x) and evaluate (s-t) (-1).
When s and t are functions, the expression for (s + t) (x) is s(x) - t(x), and the result of (s-t)(-1) is -2.
What is function?A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this. If you enter anything for x, you will only get one output for y. Because x represents the input value, we may say that y is a function of x.
Here,
Given the functions s(x) = 5 and t(x) = 3, we can find the expressions for (s + t)(x) and (s - t)(x) as follows:
(s + t)(x) = s(x) + t(x) = 5 + 3 = 8
(s - t)(x) = s(x) - t(x) = 5 - 3 = 2
To evaluate (s - t)(-1), we simply plug in -1 for x in the expression for (s - t)(x):
(s - t)(-1) = 2
So, (s - t)(-1) = 2.
The expressions for (s + t) (x) is s(x) - t(x) and value of (s-t)(-1) is -2 when s ad t are functions.
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What is 10x9+2
Anyways can someone help me with my other question on english.
Answer: 92
Step-by-step explanation: multiply first. 9x10=90. now add the two to the answer we just got. 90+2? 92.
i need help whatsb the answer
Answer:Simplify the expression.
Exact Form:
35
8
Decimal Form:
4.375
Mixed Number Form:
4 3/8
Step-by-step explanation:
defin the domen and range fanction
Answer:
The domain is the set of all the input values of a function and the range is the possible output given by the function.
assuming that this population successfully colonizes the island and persists until the present, add a histogram of the 21st century island population to your figure (make sure that they can be easily compared to each other). describe the population in terms of light, medium, and dark individuals. write a brief statement justifying your graph and answer.
a) A histogram representing coat color for the initial colony your graph is given below.
b) Due to the fact that beach mice, which often have light coast colors, outnumber Oldfield colonizers by a factor of several, making dark coat colors less prevalent as time passes.
a) It's critical to understand the geographic distribution of Oldfield mice prior to the histogram presentation. Santa Rosa Island is classified into two primary geographic locations: inland and coastal, although having various different geographical settings.
Oldfield mice come in a variety of colors; fawn-colored (medium or dark) individuals are typically found in inland regions, whilst lighter or white individuals are found in coastal regions. As a result, Santa Rosa Island should have more colored mice and the beach should have more light-hued mice.
b) Oldfield colonists have predominantly dark coat colors, according to the image. The second histogram shows the coast color of the population following 6000 years of Oldfield and beach mouse hybridization. This is due to the fact that beach mice, which often have light coast colors, outnumber Oldfield colonizers by a factor of several, making dark coat colors less prevalent as time passes.
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The complete question is:
Imagine you have a time machine and are able to go back in same so 6,000 years ago. You are standing on newly formed Santa Rosa Island, a barrier island off the coast of Florida that consists entirely of beach habitate. You see that a large and genetically diverse mainland population of oldfield mice have just colonized the island Using all of the information in this case study, answer the following questions and justify your answers with reasoning Questions ists on the island. Write a brief statement justifying.
1. Draw a histogram representing coat color for the initial colony your graph. Describe the population in terms of the proportion of light, medium, and dark individuals.
2. Assuming that this population successfully colonizes the island and persists until the present, add a histogram of the 21" century island population to your figure (make sure that they can be easily compared to each other) Describe the population in terms of light, medium, and dark individuals. Write a brief statement justifying your graph and answer
an orchard owner is investigating a new formula of fertilizer to determine if it produces more apples per tree compared to a current popular brand.part a: which of the following design is most appropriate: observational study, experiment, census, or sample survey? explain your reasoning. (3 points)part b: explain how you would implement the design you selected in part a. (4 points)part c: explain one benefit your design would provide. (3 points)
The most appropriate design would be experiment. Implementation of the design would be by selection of trees, then the application of fertilizer, followed by data collection and statistical analysis.
a) Most appropriate design: Experiment
The orchard owner wants to determine if a new formula of fertilizer produces more apples per tree compared to a current popular brand. To make a causal conclusion, an experiment would be the most appropriate design. In an experiment, the orchard owner would randomly assign the trees to receive either the new fertilizer formula or the current popular brand and then compare the number of apples produced. This allows the orchard owner to control for other variables and isolate the effect of the fertilizer on the number of apples produced.
b) Implementation:
Selection of trees: The orchard owner would randomly select a sample of trees from their orchard and divide them into two groups: the experimental group (receiving the new fertilizer formula) and the control group (receiving the current popular brand).
Application of fertilizer: Both the experimental and control groups would receive the same amount of fertilizer, but the experimental group would receive the new formula while the control group would receive the current popular brand.
Data collection: The orchard owner would measure the number of apples produced by each tree in both the experimental and control groups.
Statistical analysis: The orchard owner would use appropriate statistical tests to compare the number of apples produced by each group and determine if there is a significant difference between the two.
c) Benefit:
One benefit of this experimental design is that it allows the orchard owner to determine causality. By randomly assigning the trees to receive either the new fertilizer formula or the current popular brand, the orchard owner can be confident that any difference in the number of apples produced is due to the fertilizer and not other factors. This is important for making decisions about which fertilizer to use in the future.
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Line GH contains points G(-2, 6) and H(5, -3). What is the slope of CH?
1:-7/3
2:-9/7
3:-7/9
4:-3/7
The slope of line GH that contains points G(-2, 6) and H(5, -3) is equal to: 2. -9/7.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (-2, 5).Points on y-axis = (6, -3).Substituting the given data points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-3 - 6)/(5 - (-2))
Slope (m) = -9/7
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a number n is rounded to 2 decimal place
the result is 3.87
using inequalities write down the error interval for n
Answer:
3.90
hope its help
Step-by-step explanation:
y=3.87
n=d/3.90
Excute. by down interval 34.0
if you are tossing a six-sided die, what is the probability of getting either a 1 or a 2 on your first toss and your second toss?
It is based on the likelihood of something occurring. The reasoning behind probability is the foundation of theoretical probability. The probability of getting one or two in first and second toss is [tex]\frac{1}{9}[/tex].
Probability is a number that represents the likelihood or chance that an event will occur. Probabilities can be expressed as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
The probability of getting one or two in first toss will be:-
[tex]\frac{1}{6} + \frac{1}{6} = \frac{1+1}{6} = \frac{2}{6} = \frac{1}{3}[/tex] ( as the probability of getting one in first toss is [tex]\frac{1}{6}[/tex] and getting two is also [tex]\frac{1}{6}[/tex]).
Similarly the probability of getting one or two in second toss will be:-
[tex]\frac{1}{6} +\frac{1}{6} = \frac{1+1}{6} = \frac{2}{6} = \frac{1}{3}[/tex]
The total probability of getting one or two in first and second toss will be:-
[tex]\frac{1}{3} *\frac{1}{3} = \frac{1}{9}[/tex]
Hence, Henceprobability is [tex]\frac{1}{9}[/tex].
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question 8 Mathmatics
The appropriate sales price for a home in 2020 would be = 480 thousands. That is option A.
How to calculate tye appropriate sales price?The price of home in year 1990 = 149 thousand
The price of home in the year 1995 = 158 thousand
The difference in years = 2000-1995 = 5 years
The difference in the average sales price for the both years = 158-149 = 49 thousand.
The years difference between 2000 and 2020 = 20 years
If 5 years = 49 thousand
20 years = X
Make X the subject of formula;
X = 20×49/5
X = 980/5
X = 196 thousand
Therefore, the sales price for a home in 2020 would be = 207+196 = 403 thousands. The appropriate sales price would be = 480 in 2020.
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The price of an item has been reduced by 80%. The original price was $95. What is the price of the item now?
Answer: $19
Step-by-step explanation:
100% - 80% = 20%
20% ÷100 = 0.2
$95 x0.2 = $19
0r
10% of $95 = $9.50
9.50 x 2 = 19
what are the z scores for the middle 68%? (see example in canvas right above this assignment.) b) what are the z scores for the middle 95%? c) what are the z scores for the middle 99.7%?
The z-scores for the middle 68% of the normal distribution are -1.0 and +1.0, for the middle 95% are -2.0 and +2.0, and for the middle 99.7% are -3.0 and +3.0.
a) The z-scores for the middle 68% of the normal distribution are -1.0 and +1.0. This means that 68% of the data falls between the mean and 1 standard deviation above and below the mean. The formula for calculating z-scores is z-score = (x - μ) / σ, where x is the data point, μ is the mean and σ is the standard deviation.
b) The z-scores for the middle 95% of the normal distribution are -2.0 and +2.0. This means that 95% of the data falls between the mean and 2 above and below the mean. The formula for calculating z-scores is z-score = (x - μ) / σ, where x is the data point, μ is the mean and σ is the standard deviation.
c) The z-scores for the middle 99.7% of the normal distribution are -3.0 and +3.0. This means that 99.7% of the data falls between the mean and 3 standard deviations above and below the mean. The formula for calculating z-scores is z-score = (x - μ)/ σ, where x is the data point, μ is the mean and σ is the standard deviation.
The z-scores for the middle 68% of the normal distribution are -1.0 and +1.0, for the middle 95% are -2.0 and +2.0, and for the middle 99.7% are -3.0 and +3.0.
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elzny I NEED HELP PLS
Answer:
105
vsvsbbshshsbxhxhxhggxxggxgx
At the nut farm, the cost price of a bag of almonds is R290. It is sold with a profit of 45%. What is the selling price?
The selling price of the bags of almonds that yields a profit of 45% is $420.5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The formula for profit is given by:
Profit = [(selling price - cost price) / cost price] * 100%
At the nut farm, the cost price of a bag of almonds is R290. It is sold with a profit of 45%. Hence, substituting:
45% = [(selling price - 290)/290] * 100%
0.45 = (selling price - 290)/290
selling price - 290 = 130.5
selling price = 420.5
The selling price is $420.5
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How do you solve
-6y+2=4x
y-2=x
In elimination for linear equations
The solution to the given system of linear equations is (x, y) = (-1, 1).
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The system of equations is given in the question, as follows:
-6y + 2 = 4x
y - 2 = x
Here's how to solve this system of equations using the elimination method:
Multiply the first equation by 2:
-12y + 4 = 8x
Add the two equations:
-12y + 4 + y - 2 = 8x + x
-11y + 2 = 9x
Solve for x:
x = (2 - 11y)/9
Substitute the value of x back into one of the original equations to find y:
-6y + 2 = 4x
-6y + 2 = 4((2 - 11y)/9)
-6y + 2 = (8 - 44y)/9
-54y + 18 = 8 - 44y
26y = 26
y = 1
Use the value of y to find x:
x = (2 - 11y)/9
x = (2 - 11 * 1)/9
x = (2 - 11)/9
x = -9/9
x = -1
Thus, the solution is (x, y) = (-1, 1).
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what is the arithmetic mean of $\frac{2}{5}$ and $\frac{4}{7}$ ? express your answer as a common fraction.
The arithmetic mean of the two fractions is 68/35.
The arithmetic mean can be calculated using the mentioned formula -
Arithmetic mean = sum of the numbers / frequency of numbers.
Sum of the fractions = 2/5 + 4/7
Performing division of the two numbers
Sum of the fractions = (14 + 20)/35
Sum of the fractions = 34/35
Arithmetic mean = (34/35)/2
Rewriting the average
Arithmetic mean = (34 × 2)/35
Performing multiplication on Right Hand Side of the equation
Arithmetic mean = 68/35
Hence, the Arithmetic mean is 68/35.
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What is the image point (70,0) after a rotation of 270° counterclockwise about the origin?
Answer: ( 0, -70)
Step-by-step explanation: make a sketch on the x-y plane to see why
an experiment consists of observing the gender of a baby when it is born. a. list the outcomes in the sample space. b. list all possible events. c. if the baby is a girl, which event(s) in (b) has (have) occurred?
The concept is an experiment conducted on Probability. Probability tells us how frequently some event will be after numerous repeated trials.
Probability is a branch of mathematics that deals with numerical descriptions of the probability that an event will occur or the probability that a statement is true. The probability of an event is a number between 0 and 1,
The sample space refers to the list of all possible issues of a trial. Each possible outgrowth is represented by a single point in the sample space, irrespective of the number of ways that outgrowth can do.
Given:
A) In an experiment, the gender of a child is observed at birth.
A child can be of two sexes: male and female.
Let (M) be male and (F) be female and denote (S) the pattern space.
Then: S = {M,F}
B) The list of all possible outcomes is called the pattern space. If we name two children in the order of their birth, there are 4 possible outcomes. Using M for men and F for women can shorten the results. The list of all possible outcomes:
S={M, F} ,{M,M}, {F,F}
c) If the child were a girl, then from the previous scenario S= {F, F} would result.
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Identify the initial amount a and the rate of decay r (as a percent) of the exponential function f(t)=475(0.5)t. Evaluate the function when t=3. Round your answer to the nearest tenth.
The function when t=3 to the nearest tenth is 59.4.
How did we get the value?The initial amount is a = 475, and the rate of decay r is 50%.
To evaluate the function when t=3, we plug in t=3:
f(3) = 475(0.5)^3 = 475 * (0.125) = 59.375
Rounding to the nearest tenth, f(3) = 59.4.
Therefore, the correct answer is as given above. It could be concluded that the rounded answer to the nearest tenth is 59.4
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