Answer:1400
Step-by-step explanation:
Determine whether the following statements are True or False. Then, explain why.
(a) Throughout a hypothesis test, the alternative hypothesis is assumed to be true.
(b) No matter what the conclusion of a hypothesis test is, neither the null or alternative hypothesis has been proven to be true.
(c) When drawing a conclusion to a hypothesis test, compare the calculated p-value to the calculated test statistic.
(d) As a p-value approaches 0 it is more likely the hypothesis test conclusion will be "reject the null hypothesis."
Throughout a hypothesis test, the alternative hypothesis is assumed to be true.
Answer :-FALSE
What is hypothesis test ?
in hypothesis test we compare p-value with level of significance and conclude our null hypothesis is true or not true.
p-value decided null hypothesis is true or not true.
p-value <= level of significance then null hypothesis is true.
We do not say alternative hypothesis is assumed to be true.
Therefore Correct Options
FALASE
No matter what the conclusion of a hypothesis test is, neither the null or alternative hypothesis has been proven to be true.
Answer :- TRUE.
Because,
Yes, no matter what was the conclusion of hypothesis test.
We set always our claim in alternative hypothesis and conclude about the null hypothesis.
We check null hypothesis is true or do not true.
That's reason Correct Options TRUE.
When drawing a conclusion to a hypothesis test, compare the calculated p-value to the calculated test statistic.
Answer :- FALSE
Because,
We Calculate the test statistic.
Using this test Statistic we calculate p-value
We compare p-value with level of significance and conclude it.
That's reason statement is false. We do to compare p-value and test statistic.
As a p-value approaches 0 it is more likely the hypothesis test conclusion will be "reject the null hypothesis.".
Answer :- TRUE
Because,
p-value is the probability that test hypothesis is accepted or rejected.
We compare always p-value with level of significance.
p-value < 0.05
We reject the null hypothesis.
In given problem p-value = 0
That is we reject the null hypothesis.
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Determine the value of x, in dollars, that will make their weekly pay the same.
Guy and Jim work at a furniture store. Guy is paid $185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x)=185+.03x. Jim is paid $275 per week plus 2.5% of his total sales in dollars,x, which can be represented by f(x)=275+.025x.
The value of x, in dollars, so that they have equal weekly pay is $18,000.
Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h. The domain is defined as the set of all the values that the function can input while it can be defined. The range is all the values that come out as the output of the function involved. Co-domain is a set of values that have the potential of coming out as outputs of a function.
We are given that Guy and Jim earn the same weekly pay.
Then g(x) = f(x)
So, 185 + .03x = 275 + .025x
Rearranging terms so that the x's are together and the constants are together:
0.005x = 90
∴ x = 18,000
Thus, the value of x, in dollars, so that they have equal weekly pay is $18,000.
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Triangle ABC is transformed to triangle A′ B′ C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair 3, 0, B at ordered pair 4, negative 2, C at ordered pair 1, negative 3. A triangle A prime B prime C prime has A prime at ordered pair negative 3, 0, B prime at ordered pair negative 4, negative 2, C prime at ordered pair negative1, negative 3. Which equation shows the correct relationship between the measures of the angles of the two triangles?
The measure of angle BCA = The measure of angle C prime A prime B.
How to calculate the measure of each angle in triangle ?Given that
Triangle ABC is transformed to triangle A′B′C′, as shown below:
A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes.
A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0.
A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
According to the question
Triangle ABC is transformed to triangle A′B′C′, as shown below:
Here the triangle ABC is similar A'B'C' are similar triangles.
For similar triangles angles are congruent.
A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0.
A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
Therefore,
<BAC = <B'A'C'
<ABC = <A'B'C'
<ACB = <A'C'B'
Hence, The correct relationship between the measures of the angles of the two triangles is the measure of angle BCA = The measure of angle C prime A prime B.
The complete question is : Triangle ABC is transformed to triangle A′B′C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0. Which equation shows the correct relationship between the measures of the angles of the two triangles? The measure of angle CAB = The measure of angle C prime B prime A prime The measure of angle BCA = The measure of angle A prime B prime C The measure of angle CAB = The measure of angle C prime A prime B prime The measure of angle BCA = The measure of angle C prime A prime B prime
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A cylinder that has an ideal piston contains one mole of hydrogen gas and undergoes an isobaric expansion that doubles its initial volume.
How much heat is transferred to or from the gas?
a) heat flows into the gas by an amount greater than the mechanical work W
b) heat flows into the gas by an amount less than the mechanical work W
c) heat flows out of the gas by an amount greater than the mechanical work W
d) heat flows out of the gas by an amount less than the mechanical work W
The option A is correct
In other words, the amount of heat entering the system must be greater than the amount of mechanical effort leaving the system.
Recall the first law of thermodynamics' ideas in order to comprehend this.
dQ = dU + dW
Assuming perfect conditions. There is no heat loss outside. No matter how much heat we give the gas dQ , some of it will be utilised to boost the gas's internal energy while the rest will be used to produce work. This must be less than dQ in turn.
Because of this extremely fundamental characteristic of all engines, none of them can operate at 100% efficiency. Even the "Carnot engine," the most ideal engine, is not entirely efficient.
The option A is correct
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Find the additive inverse of −9x+3
let additive inverse of it is y
So, y + (-9x+3) = 0
y = 9x-3
the difference of -2 and a number is -14. find the number
Answer
I think the number is -16, hope this helps!
Answer: the number is -12
Step-by-step explanation:
x-2=-14
x=-12
Can you also mark the two points on the graph
A rectangular piece of paper is twice as long as a square piece and 3 inches wider. The area of the rectangular piece is 108 in^2. Find the dimensions of the square piece.
The dimension of the square piece of paper is 6 inches.
How to find the dimension of the square piece?A rectangular piece of paper is twice as long as a square piece and 3 inches wider.
The area of the rectangular piece is 108 in².
A square has all its side equal to each other and a rectangle has two opposite sides equal to each other.
Therefore,
let
x = length of the square
Therefore,
length of rectangular piece = 2x
width of the rectangular piece = 3 + x
Therefore,
area of the rectangular piece = lw
where
l = lengthw = widthTherefore,
area of the rectangular piece = 2x(3 + x)
area of the rectangular piece = 6x + 2x²
108 = 6x + 2x²
2x² + 6x - 108 = 0
divide through by 2
x² + 3x - 54 = 0
x² - 6x + 9x - 54 = 0
x(x - 6) + 9(x - 6) = 0
(x + 9)(x - 6)
Therefore, we can only use positive numbers.
Hence,
x = 6
Therefore,
dimension of the square piece is 6 inches.
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a number is between 58 and 60 it has prime factors between 2,3,and 5. what is the number?
Solution:
60
Step-by-step explanation:
60 is divisible by 2 -> 60 / 2 = 30
60 is divisible by 3 -> 60 / 3 = 20
60 is divisible by 5 -> 60 / 5 = 12
Hope that helped!Answer: 60
Step-by-step explanation:
60 has all prime factors of 2,3 and 5. :)
using division to find the ratios that are equivalent to 40:28 and please show the steps.
Answer:
10:7
Step-by-step explanation:
40:28 are both divisible by 4. 40/4 is 10. 28/4 is 7. So the ratio would be 10:7 since neither is divisible by both the same number, this is the final ratio.
What is
17/11 times 6/10
Answer:
0.92727272727
Please vote for Brainliest and I hope this helps!
Answer:
38/22
Step-by-step explanation:
you multiply the first numbers and the last numbers and combine it
A falcon is flying at a speed of 107,360 yards per
hour. How fast is the falcon flying in miles per
hour? (Hint: A mile is equal to 1760 yards.)
Help
NEED ASAP PLEASE
Determine the theoretical probability of rolling a two with one standard die. Write this probability in three equivalent forms: as a fraction, a decimal (rounded to three places), and a percentage (rounded to one decimal place).
Answer:
The theoretical probability of rolling a two with one standard die is 1/6. This can be written as a decimal by dividing 1 by 6, which is approximately 0.167. As a percentage, this is approximately 16.7%. Here are all three forms:As a fraction: 1/6As a decimal: 0.167As a percentage: 16.7%
Step-by-step explanation:
How much should you invest at 4.6% simple interest in order to earn $55 interest in 14 months?
The required money that should have been invested to earn $55 is $1024.84.
Given that,
How much should you invest at 4.6% simple interest in order to earn $55 interest in 14 months is to be determined.
When some apply for their money on something so that they can get higher value in returns of their money.
Here,
SI = [p × r ×t]/100
55 × 100 = p × 4.6 / 12 × 14
p = $1024.84
Thus, the required money that should have been invested to earn $55 is $1024.84.
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6(2x-3)-2(2x+1) please help me :)
8x-20
Step-by-step explanation:
12x-18-4x-2
8x-20
A right rectangular prism has the dimensions 4 by 6 by 3 feet. Enter the volume, in cubic feet, of the rectangular prism.
At December 31, the records of Nortech Corporation provided the following selected and incomplete data:
Common stock (par $1; no changes during the current year).
Shares authorized, 500,000.
Shares issued, 2; issue price $12 per share.
Common Stock account, $100,000.
Shares held as treasury stock, 2,000 shares, cost $10 per share.
Net income for the current year, $24,500.
Dividends declared and paid during the current year, $14,700.
Retained Earnings balance, beginning of the year, $145,000.
Required:
Complete the following: TIP: To determine the number of shares issued, divide the balance in the Common Stock account by the par
value per share. (Round "per share" answers to 2 decimal places.)
1-a. Shares authorized
1-b. Shares issued
1-c. Shares outstanding
2. The balance in Additional Paid-in Capital would be
3. Earnings per share is
4. Dividends paid per share of common stock is
5. Treasury stock should be reported in the stockholders' equity section of the balance
sheet in the amount of
6. Assume that the board of directors approved a 2-for-1 stock split. After the stock split,
the par value per share will be
500,000
290,000
A company's balance sheet is its financial statement at a given point in time and lists its assets, liabilities, equity capital, total debt, and other items.
What is meant by balance sheet?A balance sheet is a list of all your capital, obligations, and assets. The assets and liabilities of a firm are described in detail on a balance sheet, which is a financial statement.
The Equity Section of the Nortech Corporation's Balance Sheet exists as follows:
Common Stock:
500,000 shares, Authorized at $1 par value
200,000 Issued Shares at $1 = $200,000
Additional Paid-in Capital 4,143,000
3,000 shares, Treasury stock (3,000)
Retained Earnings 253,500
Total Equity $4,593,500
1c. Shares Outstanding = 197,000 (200,000 - 3,000)
2. Balance in Additional Paid-in Capital = $4,143,000
3. Earnings per share = $0.75 ($147,750/197,000)
4. Dividend per share = $0.25 ($49,250/197,000)
5. The Treasury stock is reported as $3,000 on the balance sheet.
6. With a 2-for-1 stock split, the par value becomes $0.50 ($1/2)
Data and Calculations:
Par value of Common Stock = $1
Authorized Shares = 500,000 shares
Issue price per share = $22
Common Stock Account = $200,000
Issued Shares = 200,000 shares ($200,000/$1)
Treasury Stock = $3,000 (3,000 x $1)
Additional Paid-in Capital = $4,200,000 (200,000 x $21)
Additional Paid-in Capital (Treasury Stock) = $57,000 ($19 x 3,000)
Balance of Additional Paid-in Capital = $4,143,000 ($4,200,000 - $57,000)
Retained earnings for the year:
Beginning Balance $155,000
Net income 147,750
Dividends paid (49,250)
Ending Balance $253,500
The complete question is:
At December 31, the records of Nortech Corporation provided the following selected and incomplete data: Common stock (par $1; no changes during the current year).Shares authorized, 500,000.Shares issued, ?; issue price $22 per share. Common Stock account, $200,000.Shares held as treasury stock, 3,000 shares, cost $20 per share. Net income for the current year, $147,750.Dividends declared and paid during the current year, $49,250.Retained Earnings balance, beginning of the year, $155,000.Required: Complete the following: TIP: To determine the number of shares issued, divide the balance in the Common Stock account by the par value per share. (Round "per share" answers to 2 decimal places.)
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Assume that x and y are both differentiable functions of t and are related by the equation y=cos(5x). Find [tex]\frac{dy}{dt}[/tex] when x= [tex]\frac{\pi }{10}[/tex], given
[tex]\frac{dx}{dt}[/tex] = -4 when x= [tex]\frac{\pi }{10}[/tex]
Enter an exact answer.
[tex]\frac{dy}{dt}[/tex]=______
Assume that x and y are both differentiable functions of t and are related by the equation y=cos(5x). The value of dy/dx is 25.
What is differentiable functions?
Differentiable simply means that the derivative exists at each location within its domain. As a result, the function must also exist (i.e., be continuous) on its domain in order for the derivative to exist. Because of this, a differentiable function can also be continuous.
Given that x, y are both differentiable function of t. and
[tex]y=\cos (5 x)[/tex]
Find [tex]\frac{d y}{d t}=$.[/tex] when [tex]$x=\frac{\pi}{10}$[/tex] given that [tex]$\frac{d x}{d t}=-5$[/tex], when [tex]$x=\frac{\pi}{10}$[/tex]
Given function is
[tex]$ y=\cos 5 x $[/tex]
[tex]$\frac{d y}{d t}=-\sin (5 x) \cdot \frac{d}{d t}(5 x) \text { (By chain } $[/tex]
[tex]$ =-\sin 5 x \cdot 5 \frac{d x}{d t} $[/tex]
[tex]$ \text { at } x=\frac{\pi}{10}$[/tex]
[tex]$ \frac{d y}{d t}=-\sin \left(8 \times \frac{\pi}{10}\right) \times 5 \times-5$[/tex]
[tex]$-\frac{d x}{d t}=-5 $[/tex]
[tex]$2^{20} $[/tex]
[tex]$\text { at } x=\frac{\pi}{10}$[/tex]
[tex]$ =25 \sin \frac{\pi}{2} $[/tex]
[tex]$=25 \times 1 $[/tex]
[tex]$ \frac{d y}{d t}=25 $[/tex]
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A new gaming chair costs $309.99. You have already saved $144.99 and earn PLEASE HURRY $27.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
27.5w − 144.99 = 309.99; w = 17
27.5 + 144.99w = 309.99; w = 6
27.5w − 309.99 = 144.99; w = 17
27.5w + 144.99 = 309.99; w = 6
Answer:
Step-by-step explanation:35.5 136.45w = ...
Missing: $309.99. $144.99 PLEASE HURRY $27.50
Find the monthly payment on a VCR with an installment price of $994.01, 12 monthly payments, and a down payment of $200.
Answer:
62.16
Step-by-step explanation:
994.01 - 200.00 / 12
the layers, in deep learning, represent the data processing that occurs in order to achieve the correct output. select one:
The layers, in deep learning, represent the data processing that occurs in order to achieve the correct output is true.
Deep learning is part of machine learning methods and is based on artificial neural networks with representation learning. It is a machine learning technique that teaches computers to carry out operations that comes naturally to humans: learn by example. Deep learning is a key technology behind driverless cars, enabling them to recognize a stop sign, or to distinguish a pedestrian from a lamppost. Deep learning networks learn by identifying intricate data structures in the data they experience. By developing computational models that are composed of multiple processing layers, the networks can create multiple levels of abstraction to represent the data. A layer is the highest-level building block in deep learning. A layer is a container that usually receives weighted input, transforms it with a set of functions through data processing and passes these values as output to the next layer.
Note: The question is incomplete. The complete question probably is: The layers, in deep learning, represent the data processing that occurs in order to achieve the correct output. select one: true false.
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The following cards are dealt to three people at random, so that everyone gets the same number of cards. What is the probability that everyone gets a red card?
[There are three red cards and three blue cards]
The probability that everyone gets a red card will be 0.125.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The accompanying cards are managed by three individuals indiscriminately, so everybody gets a similar number of cards. There are three red cards and three blue cards.
Then the probability that everyone gets a red card is given as,
P = (3/6) × (3/6) × (3/6)
P = (1/2) × (1/2) × (1/2)
P = 1/8
P = 0.125
The probability that everyone gets a red card will be 0.125.
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5. Write both an inequality and a negated inequality that describe this graph.
The inequality of the graph is x > -3, and Negated inequality of the graph is x ≤ -3
How to solve inequality?
The inequality is represented as negative one-fifth is greater than or equal to the product of negative two-thirds and a number.
We have,
Given the graph line,
Write both an inequality and a negated inequality that describe this graph:
Let
The inequality of the graph is x > -3
Negated inequality of the graph is x ≤ -3
Hence, the inequality of the graph is x > -3, and Negated inequality of the graph is x ≤ -3
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Mohammad says that there is 5/8 of a ham sandwich left that he bought in LULU Supermarket and 1/2 of a turkey sandwich left. What is NOT a pair of equivalent fractions for 5/8 and ½.
The option that is not a pair of equivalent fractions for 5/8 and ½ is C. 3/8.
How to illustrate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
From the information, Mohammad says that there is 5/8 of a ham sandwich left that he bought in LULU Supermarket and 1/2 of a turkey sandwich left.
It should be noted that 3/8 is not an equivalent fraction. Therefore, the correct option is C.
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Mohammad says that there is 5/8 of a ham sandwich left that he bought in LULU Supermarket and 1/2 of a turkey sandwich left. What is NOT a pair of equivalent fractions for 5/8 and ½.
10/16
3/6
3/8
5/10
help meeeeeeeeeee pleaseee
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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Immediate assistance needed, please
The jumper is in free fall for 7.07 s if the parachute is opens at 1000 ft
The jumper is in free fall for 7.29 s if the parachute is opens at 950 ft
The reasonable domain for the function h is
0 ≤ t ≤ 10
The reasonable range for the function h is
0 ≤ h ≤ 1800
How to find the time of free fallThe duration of free fall is calculated using the given function
h = -16t² + 1800
the parachute is opens at 1000 ft
h = -16t² + 1800
1000 = -16t² + 1800
16t² = 1800 - 1000
16t² = 800
t² = 800 / 16
t² = 50
t = √50
t = 7.07 s
the time at this situation is 7.07s
the parachute is opens at 950 ft
h = -16t² + 1800
950 = -16t² + 1800
16t² = 1800 - 950
16t² = 850
t² = 850 / 16
t² = 53.125
t = √53.125
t = 7.2887 s
the time at this situation is 7.29s
reasonable domain
minimum t = 0
for maximum t, h = -16t² + 1800 = 0
16t² = 1800
t = 10.61
0 ≤ t ≤ 10
the reasonable domain is 0 ≤ t ≤ 10
reasonable range
h = -16t² + 1800
at t = 0, h = 1800
at t = 10.606, h = 0
0 ≤ h ≤ 1800
the reasonable range is 0 ≤ h ≤ 1800
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Find the interest rate for the given deposit and compound amount. $4200 accumulating to $5994.74, compounded monthly for 7 years. The interest rate is ___%. (Do not round until the final answer. Then round to the nearest hundredth as needed.)
The rate of interest monthly is 0.55%.
What is rate of interest?
An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the total loan amount.
Given that,
The deposit amount is $4,200.
The future value is $5,994.74
The number of months = 7(12) = 84.
The payment i.e. PMT = $0
Based on the above information, the calculation is as follows:
The formula is
= RATE(NPER,PMT,-PV,FV,TYPE)
After applying the above formula, the rate of interest monthly is 0.55%.
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Use cylindrical shells to find the volume of the solid generated when the region enclosed by the curves y=x3, x=1, and y=0 is revolved about the y-axis.
To calculate the total volume of the solid we will divide it into n shell cyline thickness of [tex]$\Delta y$.[/tex]
The internal shell cylinder circumference C shall be[tex]$2 \pi r_i$[/tex]
where r is the in The shell cylinder internal area A shall be C.
where h is the height
The volume of the shell cylinder[tex]$\Delta v$[/tex] shall be[tex]$A \cdot \Delta y$.[/tex]
Then we will have:
[tex]\Delta v=A \cdot \Delta y=C \cdot h \cdot \Delta y=2 \pi r_i h \cdot \Delta y \Rightarrow d v=2 \pi r_i h \cdot d y$$[/tex]
The total volume of the solid shall be the summation of all n shell cylinders
[tex]\int d v=\int 2 \pi r_i h d y \Rightarrow V=\int_a^b 2 \pi r_i h d y \Rightarrow V=2 \pi \int_a^b r_i h d y$$[/tex]
[tex]\int d v=\int 2 \pi r_i h d y \Rightarrow V=\int_a^b 2 \pi r_i h d y \Rightarrow V=2 \pi \int_a^b r_i h d y[/tex]
[tex]The value $a$ is the value of $y$ at the point where $x=0$ then:For $x=0 \Rightarrow y=0^3 \Rightarrow y=0$ then $a=0$.The value $b$ is the value of $y$ at the point where $x=1$ then:[/tex]
[tex]For $x=1 \Rightarrow y=1^3 \Rightarrow y=1$ then $b=1$.Since the integration will be with variable $y$ we have to express the function $y=x^3$ in terms of $y$ :$$[/tex]
y=x^3 \[tex]Rightarrow x=\sqrt[3]{y}[/tex]
Substituting in V, we will have:
[tex]V= & 2 \pi \int_a^b r_i h d y=2 \pi \int_0^1(1-y)(1-\sqrt[3]{y}) d y=2 \pi[/tex]\[tex]int_0^1(1-y)\left(1-y^{\frac{1}{3}}\right) d y \\[/tex]
&[tex]1-y \\& \frac{1-y^{\frac{1}{3}}}{1-y} \\& \frac{-y^{\frac{1}{3}}+y^{\frac{1}{3}} \cdot y^{\frac{1}{1}}}{} \\[/tex]
[tex]& 1-y-y^{\frac{1}{3}}+y^{\frac{1}{3}+\frac{1}{1}}= \\& =1-y-y^{\frac{1}{3}}+y^{\frac{1+3}{3}}= \\[/tex]
[tex]& =1-y-y^{\frac{1}{3}}+y^{\frac{4}{3}}= \\& =y^{\frac{4}{3}}-y^{\frac{1}{3}}-y+1[/tex]
Substituting in V:
[tex]V=2 \pi \int_0^1\left(y^{\frac{4}{3}}-y^{\frac{1}{3}}-y+1\right) d y=2[/tex][tex]{1}{3}+1}}{\frac{1}{3}+1}-\frac{y^{1+1}}[/tex]{[tex]1+1}+y\right]_0^1=2[/tex] [tex]\pi\left[\frac{y^{\frac{4+3}{3}}}{\frac{4+3}{3}}[/tex]-[tex]\frac{y^{\frac{1+3}{3}}}{\frac{1+3}{3}}-\frac{y^2}{2}+y\right]_0^1$$[/tex]
Calculating the definite integral:
By definition[tex], $\int_a^b f(x) d x=\left.F(x)\right|_a ^b=F(b)-F(a)$[/tex] then:
[tex]& V=\frac{\pi}{14}\left[\left(12 \cdot 1^{\frac{7}{3}}-21 \cdot 1^{\frac{4}{3}}-14[/tex][tex]\cdot 1^2+28 \cdot 1\right)-\left(12 \cdot 0^{\frac{7}{3}}-21 \cdot[/tex] [tex]0^{\frac{4}{3}}-14 \cdot 0^2+28 \cdot 0\right)\right] \\[/tex]
& V=[tex]\frac{\pi}{14}[(12 \cdot 1-21 \cdot 1-14 \cdot 1+28 \cdot 1)-\underbrace{(12 \cdot 0-21 \cdot 0-14 \cdot 0+28 \cdot 0)}_0][/tex]
[tex]& V=\frac{\pi}{14}(12-21-14+28)=\frac{\pi}{14}(12+28-21-14)=\frac{\pi}{14}(40-35)=\frac{5 \pi}{14} \approx \frac{5 \cdot 3,1416}{14} \approx \frac{15,708}{14} \\& V \approx 1,122[/tex]
Answer:[tex]$V \approx 1,122 u . v$. (units of volume)[/tex]
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8. 1/2.6+1/4.8+1/6.10+,..+1l20.24
The answer is 0.1657
Solution:
Given: [tex]\frac{1}{2*6}[/tex]+[tex]\frac{1}{4*8}[/tex]+ .. . . . . . . . +[tex]\frac{1}{20*24}[/tex]
∴ [tex]\frac{1}{12}[/tex] + [tex]\frac{1}{32}[/tex] + [tex]\frac{1}{60}[/tex] + [tex]\frac{1}{96}[/tex] + . . . . . . + [tex]\frac{1}{480}[/tex]
∴ [tex]\frac{40}{480}[/tex] + [tex]\frac{15}{480}[/tex] + [tex]\frac{8}{480}[/tex] + . . . . . . +[tex]\frac{1}{480}[/tex] --------- (multiplying the numerator with quotient of 480/denominators)
∴[tex]\frac{79.54}{480}[/tex]
= 0.1657
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After carefully calculating the sequence we have come to find that The answer of the given equation is 0.1657
What is a sequence?
A sequence is an ordered collection of enumerated objects in mathematics where repetitions are permitted. It has members, just like a set (also called elements, or terms). The length of the sequence refers to the total (possibly infinite) number of elements.
Contrary to a set, the same elements may appear more than once at various points in a sequence, and in contrast to a set, the order is important. The formal definition of a sequence is a function from natural numbers (the positions of the sequence's elements) to the elements at each position. A function from any index set is what is meant by an indexed family, which is a generalisation of the idea of a sequence.
[tex]\frac{1}{2\times6} + \frac{1}{4\times8} + \frac{1}{6\times10}.....\frac{1}{20\times24}[/tex] --------- (multiplying the numerator with quotient of 480/denominators)= 0.1657
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What is positive [15]+ negative [-1]=