The volume of the solid of revolution is [tex]\frac{1674\pi}{5}[/tex] cubic units.
The volume of the solid of revolution can be determined by the following integral equation:
[tex]V = 2\pi\int\limits^a_b {|f(x)-g(x)|} \, dx[/tex] (1)
Where:
[tex]g(x)[/tex] - Lower bound function[tex]f(x)[/tex] - Upper bound function[tex]a[/tex] - Upper bound[tex]b[/tex] - Lower boundIf we know that [tex]b = 2[/tex], [tex]b = 1[/tex], [tex]g(x) = 0[/tex] and [tex]f(x) = 27\cdot x^{3}[/tex], then the volume of the solid of revolution is:
[tex]V = 2\pi\int\limits^2_1 {x\cdot |27\cdot x^{3}-0|} \, dx[/tex]
[tex]V = 54\pi \int\limits^2_1 {x^{4}} \, dx[/tex]
[tex]V = 54\pi \left(\frac{2^{5}}{5}-\frac{1^{5}}{5} \right)[/tex]
[tex]V = \frac{1674\pi}{5}[/tex]
The volume of the solid of revolution is [tex]\frac{1674\pi}{5}[/tex] cubic units.
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A shark can swim at an average speed of 25 miles per hour. At this rate, how far can a shark swim in 2.4 hours. Use r= d/t. (D over T)
Answer:
60 miles
Step-by-step explanation:
1 hour = 25 miles. To find how much the shark can swim during 2.4 hours, we just have to multiply 25 by 2.4, which is 60, and that's your answer.
Tell me if I'm wrong :)
There is a line that includes the point (-20, -7) and has a slope of 1. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=1x+13
Step-by-step explanation:
we can plug in the two points into the slope-intercept formula
-7=-20(1)+b
solve for the right side
-7=-20+b
add 20 to both sides
13=b
plug the y intercept into the equation
y=1x+13
what does the x length equal
Answer: 225
Step-by-step explanation:
in spring 2017, data was collected from a random selection of sta 2023 students. one of the question how many concerts they had attended in the past six months. for the 39 randomly selected upperclassmen, the sample mean was 2.31 and sample standard deviation was 2.32. for the 35 randomly selected underclassmen, the sample mean was 2.29 and the sample standard deviation was 2.64. what is the point estimate of the difference in the population mean difference in number of concerts attended between underclassmen and upperclassmen?
Answer:
Step-by-step explanation:
5
According to the point estimate, the population mean difference in the number of concerts attended by freshmen vs seniors is 0.02.
What is the difference in population mean's point estimate?The difference in sample means is a point estimate for the difference in population means.
What's the best way to respond to this query?Data were collected from a random sample of STA 2023 students in the spring of 2017 in order to answer the question. One of the questions they were asked was how many concerts they had gone to in the previous six months. The sample mean was 2.31, with a sample standard deviation of 2.32 for the 39 upperclassmen who were chosen at random. The sample mean was 2.29, and the sample standard deviation was 2.64 for the 35 randomly selected underclassmen.
The point estimate of the population mean difference in the number of concerts attended by underclassmen versus upperclassmen has been requested.
The difference between the sample means is a point estimate for the difference between the two population means, as we already know.
Upperclassmen sample mean - underclassmen sample mean = point estimate,
Alternatively, 2.31 - 2.29 = 0.02 is a point estimate.
The population mean difference in the number of concerts attended by underclassmen against upperclassmen is 0.02 according to the point estimate.
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Liam rented a surf boar which cost $12.50/hour plus a one-time service fee. He used the board or 5.5 hours and paid a total of $93.75.
Use this information to write an equation (in slope-intercept form) which represents how the rental cost is calculated.
Answer:
y = 12.5x + 25
Step-by-step explanation:
first, we need to find the cost of the one-time service.
12.50*5.5 = 68.75
93.75 - 68.75 = 25
therefore, the one-time service fee is $25.
liam had to pay $12.50 every hour and thats where we get 12.5x from.
he also had to pay $25 as the one-time service fee which gets us y = 12.5x + 25.
hope it helps :)
mark brainliest!!
Answer:
if y is the total cost of the rental, then y-93.75=12.5(x-5.5) models the cost of renting a surf board for x hours. Liam should rewrite the equation from the previous step so that y is isolated on one side. the constant on the other side is then the service fee.
What’s the scale factor
Answer:
Step-by-step explanation:
The scale is depending on the size of each cat. Lets say the larger cat is A and the smaller one is B. The scale factor from B to A is 1.75 (or 3.5/2)
when solving for scale factor you divide the original drawing and scale drawing. Original is denominator, Scale is Numerator.
y=1/2x-4 in Standard Form
[tex]y =\dfrac 12 \cdot x -4\\\\\implies y = \dfrac{x-8}2\\\\\implies 2y = x-8\\\\\implies x -2y=8[/tex]
list three rational number between -3 and -2
correct answer needed full explanation
Answer:
-3×4= -12
-2×4= -8
three rational number between them are -11 , -10 , -9
Step-by-step explanation:
hope that it will help you
The rational numbers between -3 and -2 are;
-5/2, -9/4 and -11/4
Rational NumbersRational numbers are numbers that can be represented as the quotient of two integers but not equal to zero.
Now, to find the rational number between -3 and -2, we will use the formula;
x = ½(a + c)
x = ½(-3 + (-2))
x = -5/2
Another rational number is;
x = ½(-(5/2) + (-2))
x = ½(-9/2)
x = -9/4
Using the same pattern, we can still get another one as -11/4
In conclusion, the three rational numbers will be -5/2, -9/4 and -11/4
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Ella buys a computer for $785 her local tax rate is 7% how much does Ella pay for the computer
Answer:
$839.95
Step-by-step explanation:
There are 2 ways to go about this. First, the logical method is to calculate the tax and then add it to the price:
7%=7/100=0.07
7% “of” the amount says to multiply. The word “of” in maths means multiply:
0.07×$785=$54.95. The tax is $54.95
The computer costs $785. Plus the tax $54.95: $785+$54.95=$839.95
She pays $839.95 for the computer, including tax.
You can do this calculation in 1 step. If you are like me, I like to do my math as quickly and as efficiently as possible. What we did above is this:
100% of the computer price plus 7% of the computer price to get the total cost taxes in.
100% + 7% = 107%. And 107% = 1.07
So we have the following:
$785×1.07=$839.95
Hope this helps :)
Answer:
$839.95
Step-by-step explanation:
From the question, we are informed that Ella buys a computer for $785 and that her local tax rate is 7%. The amount that Ella pay for the computer, including tax will be:
= $785 + (7% × $785)
= $785 + (0.07 × $785)
= $785 + $54.95
= $839.95
help help help pls I have to do it
I am struggling with my math. help me please
HELP ME!!!!
Answer: 234
Step-by-step explanation:
If one angle of a triangle is 30° more than twice another angle, and the third angle is equal to the sum of the first two angles, find the measure of each angle.
Answer:
Answer:first angle = 25 degrees
Second angle = 35 degrees
Third side = 120/degrees
Step-by-step explanation:
What is the product in simplest form −6/11⋅3/4
Hey can someone please help me in this question?
Answer:
£48
Step-by-step explanation:
Area of walls = area of four rectangular walls + area of two triangular shape at front and back
Area of a rectangular wall = l *w = 8 * 4 = 32 m²
Area of 4 rectangular walls = 4 *32 = 128 m²
Triangle:
Base = 6m
height = h = 7 - 4 = 3 m
Area of triangle = (1/2)*b*h
[tex]= \dfrac{1}{2}*6*3 = 3*3 = 9 \ m^{2}[/tex]
Area of 2 triangles = 2*9 = 18 m²
Area of four walls = 128 + 18 = 146 m²
Number of paint tins required = 146 ÷ 25 = 5.84 = 6
6 tins are required.
Cost of 6 tins = 8 * 6 = £48
Decrease £5480 by 10%
Step-by-step explanation:
the currency does not matter (only if we get into any fractions of the main unit and have to name the fractions properly). % is usually about the number itself.
so,
5480 = 100%
1% = 100%/100 = 5480/100 = 54.8
10% = 1% × 10 = 54.8×10 = 548
and so,
£5480 - 10% = 5480 - 548 = £4932
if course, because of the special number 10% we could have gotten the answer faster, but I wanted to show you the full line of thinking when dealing with %. and needed when the number is not so nice.
What is the the cube root of 310 to the nearest integer
Answer:
6.7679
Please mark this brainiest?
Step-by-step explanation:
Cube root of 310 can be represented as 3√310. The value of cube root of one is 310.The nearest previous perfect cube is 216 and the nearest next perfect cube is 343 .
Answer:
the cube too of 310 is 7
Step-by-step explanation:
as cube root of 310 is 6.76
Tell whether the rates are equivalent.
0.8 kilometer for every 2 minutes
0.2 kilometer for every 0.5 minute
Answer:
Yes.
Step-by-step explanation:
0.5 minutes is 1/4 of 2 minutes.
0.2 is also 1/4 of 0.8
you get what I'm sayin?
Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
Answer:
Read image
Step-by-step explanation:
Desmos
a line has a slope of m=-2 and the point (3, -1) lies on the line.what is the represent the equation of the line in point slope form
Answer:
Step-by-step explanation:
To find out if a point (x, y) is on the graph of a line, we plug in the values and see if we get a true statement, such as 10 = 10.
A math student made the following conjecture:
When you add a multiple of 5 and a multiple of 8, the answer is a multiple of 5.
Which of the following numbers can be used as a counterexample to the conjecture?
A. 80 + 8 = 88
B. 16 + 16= 32
C. 10 + 5 = 15
D. 10 + 40 = 50
Answer:
D is the answer
Step-by-step explanation:
10 is multiple of 5 and 40 is the multiple of 8
50 is the multiple of 5
Please mark as brainliest answer
Carley beat the school record for the 400 meter run by 1.3 seconds. If she ran in 55.7 seconds, what was the record?
Answer:
57 seconds
Step-by-step explanation:
55.7 + 1.3 = 57
Hope this helps!
Answer:
57 seconds
Step-by-step explanation:
Since she beat the record by 1.3 seconds, it means the previous record was 55.7 + 1.3. Therefore, the record was 57 seconds.
Helpppp what is Log70
Answer:
Log 70
What is Log 70? - The value of Log 70 is 1.84509804001. The log base 10 of 70 is the base 10 logarithm of 70 which can be written as log10(70) or lg(70).
What is log10(70) - The logarithm base 10 of a number is its logarithm to the base of 10 where lg(70) = 1.84509804001.
Step-by-step explanation:
log10 70
Result 1.84509804001425
check the attached file pls it might be needed for you !!
Mark brilliant
Work out the percentage change when a price of £40 is decreased to £18
The segments shown below could form a triangle.
A
с
B
4
9
B
15
A
A. True
B. False
Answer: True.
Step-by-step explanation:
do the math and u will see
No, The segments shown below could not form a triangle.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Three line segment with measure 9 , 4 and 15 are shown.
We know that;
The sum of two sides of a triangle are always greater than the third side,
Here, 9 + 4 = 13 < 15
Hence, The segments shown below could not form a triangle.
Thus, The segments shown below could not form a triangle.
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Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was three years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5 years. Conduct a hypothesis test at a 5% significance level to determine if the mean length of jail time has increased. Assume the distribution of the jail times is approximately normal.
Using the z-distribution, it is found that since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.
At the null hypothesis, it is tested if the mean length of jail time is still of 2.5 years, that is:
[tex]H_0: \mu = 2.5[/tex]
At the alternative hypothesis, it is tested if it has increased, that is:
[tex]H_1: \mu > 2.5[/tex]
We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 3, \mu = 2.5, \sigma = 1.5, n = 26[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3 - 2.5}{\frac{1.5}{\sqrt{26}}}[/tex]
[tex]z = 1.7[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05, is of [tex]z^{\ast} = 1.645[/tex]
Since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.
A similar problem is given at https://brainly.com/question/24166849
solve 3(2x - 3) + 4x = -59
Answer:-5
Step-by-step explanation:
please help solve 11x+10>=150
Answer:
12.7272
Step-by-step explanation:
subtract 10 on both sides
divide by 11 on both sides 11/11>140/11
Answer:
x=130
Step-by-step explanation:
11x+10>=150
11x>= 150-10
11x>=140
x>=140-11
x>=129
so, because "x" is bigger than 129,
so, x=130
i am stuck on this zearn lesson someone pls help
Answer:
2 or 2/1
Step-by-step explanation:
For every cup of water there is 1 cup of water. As seen in the ration 6:12 (reduced to 1:2) and 1/2:1 (increased to the whole number of 1:2)
Factor the trinomial
10x^2+11X-6
Answer:
Not factorable with rationable numbers
Step-by-step explanation:
You cannot factor this expression with rationable numbers.
if mai runs 21 labs at the same rate ( 4 minutes ), how long does it take her ?