Answer:
P(C|Y) = 0.5.
Step-by-step explanation:
We are given the following table below;
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
Now, we have to find the probability of P(C/Y).
As we know that the conditional probability formula of P(A/B) is given by;
P(A/B) = [tex]\frac{P(A \bigcap B)}{P(B)}[/tex]
So, according to our question;
P(C/Y) = [tex]\frac{P(C \bigcap Y)}{P(Y)}[/tex]
Here, P(Y) = [tex]\frac{30}{146}[/tex] and P(C [tex]\bigcap[/tex] Y) = [tex]\frac{15}{146}[/tex] {by seeing third row and second column}
Hence, P(C/Y) = [tex]\frac{\frac{15}{146} }{\frac{30}{146} }[/tex]
= [tex]\frac{15}{30}[/tex] = 0.5.
Answer: 0.5
Step-by-step explanation:
edge
suppose a chemical engineer randomly selects 3 catalysts for testing from a group of 10 catalysts, 6 of which have low acidity & 4 have high acidity. What is the probability that exactly2 lower acidic catalysts are selected?
Step-by-step explanation:
Total catalysts = 10
Probability of 2 lower acidic catalysts = 2/10 = 1/5
Which option is correct and how would one solve for it?
Answer:
28
Step-by-step explanation:
We need to find the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex]
We know that,
[tex]\Sigma n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]
Here, n = 3
So,
[tex]\Sigma n^2=\dfrac{3(3+1)(2(3)+1)}{6}\\\\\Sigma n^2=14[/tex]
So,
[tex]\Sigma_{x=0}^3\ 2x^2=2\times 14\\\\=28[/tex]
So, the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex] is 28. Hence, the correct option is (d).
4(x/2-2) > 2y-11 which of the following inequalities is equivalent to the inequality above?
1) 4x+2y-3 > 0
2) 4x-2y+3 > 0
3) 2x+2y-3 > 0
4) 2x-26+3 > 0
4) 2x-2y+3 > 0
although it is spelt "26" on the choices
What is the area of polygon EFGH?
Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty.
Now, it look like there is some information missing in the answer. The whole problem should look like this:
Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?
Answer:
She sold 24 copies of the cd each day.
Step-by-step explanation:
In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:
x= Number of copies sold.
So we can start setting our equation up. So we take the first part of the problem:
"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."
This can be translated as:
40-x
where this expression represents the number of copies left on the shelf by the end of monday.
"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."
so we represent it like this:
(40-x)+(40-x)
"In other words, she doubled the number that was left in the display."
so the previous expression can be simplified like this:
2(40-x)
"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."
so the expression now turns to:
2(40-x)-x this is the number of copies left by the end of tuesday.
"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."
this translates to:
3[2(40-x)-x]
This is the number of copies on the shelf by the begining of Wednesday.
"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."
this piece of information lets us finish writting our equation:
3[2(40-x)-x] -x = 0
since there were no copies left on the shelf, then the equation is equal to zero.
So now we proceed and solve the equation for x:
3[2(40-x)-x] -x = 0
We simplify it from the inside to the outside.
3[80-2x-x]-x=0
3[80-3x]-x = 0
we now distribute the 3 so we get:
240-9x-x=0
we combine like terms so we get:
240-10x=0
we move the 240 to the other side of the equation so we get:
-10x=-240
and divide both sides into -10 so we get:
x=24
so she sold 24 copies each day.
Two balls are drawn in succession out of a box containing 5 red and 4 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw. (A) Find the probability that at least 1 ball was red, given that the first ball was replaced before the second draw. StartFraction 24 Over 49 EndFraction (Simplify your answer. Type an integer or a fraction.) (B) Find the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw.
Answer:
The answer is below
Step-by-step explanation:
The box contains 5 red and 4 white balls.
A) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was (Upper A )Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81
P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81
The probability that at least 1 ball was red = 25/81 + 20/81 + 20/81 = 65/81
B) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was not Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)
P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72
The probability that at least 1 ball was red = 20/72 + 20/72 + 20/72 = 60/72
A total of n bar magnets are placed end to end in a line with random independent orientations. Adjacent like poles repel while ends with opposite polarities join to form blocks. Let X be the number of blocks of joined magnets. Find E(X) and Var(X).
Answer:
E(x) [tex]= \frac{n+1}{2}[/tex]
Var(x) [tex]= \frac{1}{4} [ n - 1 ][/tex]
Step-by-step explanation:
Hint x = 1 + x1 + ......... Xn-1
[tex]X_{i} = \left \{ {{1} if the ith adjacent pair of magnets repel each other \atop {0} if ith adjacent pair of magnets join} \right.[/tex]
attached below is the detailed solutioN
usually like poles of magnets repel each other and unlike poles of magnets attract each other forming a block
f(x)=3x2+10x-25 g(x)=9x2-25 Find (f/g)(x).
Answer:
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Step-by-step explanation:
f(x) = 3x² + 10x - 25
g(x) = 9x² - 25
To find (f/g)(x) divide f(x) by g(x)
That's
[tex](f/g)(x) = \frac{3 {x}^{2} + 10x - 25 }{9 {x}^{2} - 25 } [/tex]
Factorize both the numerator and the denominator
For the numerator
3x² + 10x - 25
3x² + 15x - 5x - 25
3x ( x + 5) - 5( x + 5)
(3x - 5 ) ( x + 5)
For the denominator
9x² - 25
(3x)² - 5²
Using the formula
a² - b² = ( a + b)(a - b)
(3x)² - 5² = (3x + 5)(3x - 5)
So we have
[tex](f/g)(x) = \frac{(3x - 5)(x + 5)}{(3x + 5)(3x - 5)} [/tex]
Simplify
We have the final answer as
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Hope this helps you
someone please help me
Answer:
3 mL
Step-by-step explanation:
The fluid level is called the concave meniscus. The adhesive force causes it to crawl up on the sides, but you should ignore that while reading the level.
please answer this question please
Step-by-step explanation:
C = Amount (A) - Principal (P)
Where
C is the compound interest
To find the amount we use the formula
[tex]A = P ({1 + \frac{r}{100} })^{n} [/tex]
where
P is the principal
r is the rate
n is the period / time
From the question
P = Rs 12, 000
r = 5%
n = 3 years
Substitute the values into the above formula
That's
[tex]A = 12000 ({1 + \frac{5}{100} })^{3} \\ A = 12000(1 + 0.05)^{3} \\ A = 12000 ({1.05})^{3} [/tex]
We have the answer as
Amount = Rs 13891.50Compound interest = 13891.50 - 12000
Compound interest = Rs 1891.50Hope this helps you
Find two positive numbers satisfying the given requirements. The sum of the first and twice the second is 400 and the product is a maximum.
Answer:
100 and 200Step-by-step explanation:
Let the first number be 'a' and the second number be 'b'. If the sum of the first and twice the second is 400 then;
a+2b = 400 ....
From the equation above, a = 400 - 2b ... 2
If the product of the numbers is a maximum then;
ab = (400-2b)b
let f(b) be the product of the function.
f(b) = (400-2b)b
f(b) = 400b-2b²
For the product to be at the maximum then f'(b) must be equal to zero i.e f'(b) = 0
f'(b)= 400-4b = 0
400-4b = 0
400 = 4b
b = 400/4
b = 100
Substituting b= 100 into the equation a = 400 - 2b to get a;
a = 400 - 2(100)
a = 400 - 200
a = 200
The two positive integers are 100 and 200.
A United Nations report shows the mean family income for Mexican migrants to the United States is $26,500 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 24 Mexican family units reveals a mean to be $30,150 with a sample standard deviation of $10,560. State the null hypothesis and the alternate hypothesis.
Answer:
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
Step-by-step explanation:
The summary of the given statistics is:
Population Mean = 26,500
Sample Mean = 30,150
Standard deviation = 10560
sample size = 24
The objective is to state the null hypothesis and the alternate hypothesis.
An hypothesis is a claim with insufficient information which tends to be challenged into further testing and experimentation in order to determine if such claim is significant or not.
The null hypothesis is a default hypothesis where there is no statistical significance between the two variables in the hypothesis.
The alternative hypothesis is the research hypothesis that the researcher is trying to prove.
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
The test statistic can be computed as follows:
[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{30150 - 26500}{\dfrac{10560}{\sqrt{24}}}[/tex]
[tex]z = \dfrac{3650}{\dfrac{10560}{4.8989}}[/tex]
[tex]z = \dfrac{3650 \times 4.8989 }{{10560}}[/tex]
z = 1.6933
Please help me guys :)
Question:
In exercises 1 through 4, find the one-sided limits lim x->2(left) f(x) and limx-> 2(right) from the given graph of f and determine whether lim x->2 f(x) exists.
Step-by-step explanation:
For a left-hand limit, we start at the left side and move right, and see where the function goes as we get close to the x value.
For a right-hand limit, we start at the right side and move left, and see where the function goes as we get close to the x value.
If the two limits are equal, then the limit exists. Otherwise, it doesn't.
1. As we approach x = 2 from the left, f(x) approaches -2.
lim(x→2⁻) f(x) = -2
As we approach x = 2 from the right, f(x) approaches 1.
lim(x→2⁺) f(x) = 1
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
2. As we approach x = 2 from the left, f(x) approaches 4.
lim(x→2⁻) f(x) = 4
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
3. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are equal, so the limit exists.
lim(x→2) f(x) = 2
4. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches infinity.
lim(x→2⁺) f(x) = ∞
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
An economist is interested in studying the income of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval
Answer:
The width is [tex]w = 282.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The population standard deviation is [tex]\sigma = \$ 1000[/tex]
The sample size is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 90% then the level of significance can be mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{0.10 }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{0.10}{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{1000 }{\sqrt{50 }}[/tex]
=> [tex]E = 141.42[/tex]
The width of the 90% confidence level is mathematically represented as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 141.42[/tex]
[tex]w = 282.8[/tex]
Your job in a company is to fill quart-size bottles of oil from a full -gallon oil tank. Then you are to pack quarts of oil in a case to ship to a store. How many full cases of oil can you get from a full -gallon tank of oil?
Answer:
See below.
Step-by-step explanation:
1 gal = 4 qt
With a full gallon oil tank, you can fill 4 1-qt bottles.
The problem does not mention the number of quarts that go in a case, so there is not enough information to answer the question.
Also, is the full tank really only 1 gallon, or is there a number missing there too?
Change the polar coordinates (r, θ) to rectangular coordinates (x, y):(-2,sqrt2pi
Step-by-step explanation:
x=rcosθandy=rsinθ,. 7.7. r2=x2+y2andtanθ=yx. 7.8. These formulas can be used to convert from rectangular to polar or from polar to rectangular coordinates.
limit chapter~ anyone can help me with these questions?
please gimme clear explanation :)
Step-by-step explanation:
I(S) = aS / (S + c)
As S approaches infinity, S becomes much larger than c. So S + c is approximately equal to just S.
lim(S→∞) I(S)
= lim(S→∞) aS / (S + c)
= lim(S→∞) aS / S
= lim(S→∞) a
= a
As S approaches infinity, I(S) approaches a.
A librarian needs to package up all of the children's books and move them to a different location in the library. There are 625 books, and she can fit 25 books in one box. How many boxes does she need in order to move all of the books? 5 B. 25 C. 125 D. 600 E. 650
Answer: B. 25
Step-by-step explanation:
Given: Total books = 625
Number of books can fit in one box = 25
Now, the number of boxes she need to move all of the books = (Total books) ÷ (Number of books can fit in one box )
= 625÷25
= 25
hence, she requires 25 boxes in order to move all of the books.
So, correct option is B. 25.
What is the median of these figure skating ratings?
6.0 6.0 7.0 7.0 7.0 8.0 9.0
Answer:
The median would be 7.0.
Step-by-step explanation:
The median of a set of numbers means it is the middle number. since this set has 7 numbers you would need to find the number that is in the middle of the set. This would be the 4th number since it is in the middle. 7.0 is your answer.
perform the following division (-2/3) ÷ (4/7)
Answer:
-7/6
Step-by-step explanation:
-2/3 x 7/4 = -14/12 = -7/6
Answer: -7/6
Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).
Remember that dividing by a fraction is the same thing
as multiplying by the reciprocal of the fraction.
Before multiplying however, notice that we
can cross-cancel the 2 and 4 to 1 and 2.
So multiplying across the numerators and denominator and
remembering our negative in the first fraction, we have -7/6.
PLEASE HELP- MATH
simplify the fraction
5bc/10b^2
[tex]\dfrac{5bc}{10b^2}=\dfrac{\not 5\cdot \not b\cdot c}{2\cdot \not 5\cdot \not b\cdot b}=\dfrac{c}{2b}[/tex]
Answer:
c / ( 2b)
Step-by-step explanation:
5bc/10b^2
Lets look at the numbers first
5/10 = 1/2
Then the variable b
b / b^2 = 1/b
Then the variable c
c/1 = c
Putting them back together
1/2 * 1/b * c/1
c/ 2b
Given a sample of 35, what is the sample standard deviation of a pair of jeans if the 90% confidence interval is [37.14, 42.86]
Answer:
10.295Step-by-step explanation:
Using the value for calculating the confidence interval as given;
CI = xbar + Z*σ/√n
xbar is the mean = 37.14+42.86/2
xbar= 80/2
xbar = 40
Z is the z-score at the 90% confidence = 1.645
σ is the standard deviation
n is the sample size = 35
Given the confidence interval CI as [37.14, 42.86]
Using the maximum value of the confidence interval to get the value of the standard deviation, we will have;
42.86 = xbar + Z*σ/√n
42.86 = 40 + 1.645* σ/√35
42.86-40 = 1.645*σ/√35
2.86 = 1.645*σ/√35
2.86/1.645 = σ/√35
1.739 = σ/√35
1.739 = σ/5.92
σ= 1.739*5.92
σ = 10.295
Hence, the sample standard deviation of a pair of jeans is 10.295
Find the sum to infinity of the series 2+5/4+11/16+23/64+..........up to the infinity.
infinity
We have
[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]
(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)
Recall for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
So we have
[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]
A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200.
Explain in context the conclusion of the test if H0 is rejected.
Answer:
For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value
Step-by-step explanation:
Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.
Mathematically, the null hypothesis is as expressed as below;
H0: μ = 1,200
The alternative hypothesis H1 would be;
H1: μ > 1,200
Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics
For us to reject the null hypothesis, one of two things, or two things must have occurred.
The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.
If this happens, then we can make a rejection of the null hypothesis
A group of pirates captures Kevin, Lisa, Matt and Neal, and forces them to play a game. They each roll a fair 6-sided-die once. If the product of their roll is a multiple of 3, they all have to walk the plank, but otherwise they are safe. What is the probability that they survive? A)2/3 B)16/81 C)145/1296 D)65/81 E)625/1296 PLZ answer been waiting. I'll give 30 points
Answer: Option B, 16/81
Step-by-step explanation:
So we have 4 prisoners, they will roll a fair six side die and the product of the four rolls must NOT be a multiple of 3.
We know that every integer number can be "decomposed" into a product of prime numbers.
Then a number N, that is divisible by 3, can be written as:
N = 3*k
Where k is another integer.
Here we will have a product of 4 numbers, each of them are in between 1 and 6.
Now, if only one of the prisoners rolls a 3, then the product of the rolls will always be a multiple of 3. And if one of the rolls is 6 the same will happen, because 6 = 3.2
Then the probability of surviving is when in none of the four rolls we have a 3 or a 6.
Then we must have a 1, 2, 4 or 5.
The probability of 4 outcomes out of 6, is:
P = 4/6.
But we have 4 rolls, so we have that probability four times, and the joint probability will be equal to the product of the probabiliities for each roll, then the probability of surviving is:
P = (4/6)^4 = (2/3)^4 = 16/81
Answer:
16
Step-by-step explanation:
a family spent $93 at a carnival.
*they spent $18 on tickets and $30 on food. they spent the rest of the money on games.
which equation can be used to to find "g", the amount of money used on games.
Answer: 93-(18+30)=g
93-48=g
45=g
Step-by-step explanation: yup
The answer is 93-18-30-g=0 or 18+30+g=93
What is 45x62 Please help.
Answer:
45
62x
______
90
2700+
_________
2790
Step-by-step explanation:
Evaluate the double integral ∬Ry2x2+y2dA, where R is the region that lies between the circles x2+y2=16 and x2+y2=121, by changing to polar coordinates.
Answer:
See answer and graph below
Step-by-step explanation:
∬Ry2x2+y2dA
=∫Ry.2x.2+y.2dA
=A(2y+4Ryx)+c
=∫Ry.2x.2+y.2dA
Integral of a constant ∫pdx=px
=(2x+2.2Ryx)A
=A(2y+4Ryx)
=A(2y+4Ryx)+c
The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2
The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]
The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between
the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].
Let consider x = rcosθ and y = rsinθ because x² + y² = r²;
Now, the double integral can be written in polar coordinates as:
[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]
[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]
[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]
Thus, the integral becomes:
[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]
since 2sin² = 1 - cos2θ∴
[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]
[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]
Learn more about double integral here:
https://brainly.com/question/19756166
in the factory 25 men working 26 hour can produce 1300 radios . how manny hours must the same group of men work to produce 450 radios
Answer:
9 hours
Step-by-step explanation:
Since the group of men remains the same, number of hours is proportional to number of radios.
1300/26 = 450/h
h = 26 * 450 / 1300 = 9 hours
Calcule o valor de x nas equações literais: a) 5x – a = x+ 5a b) 4x + 3a = 3x+ 5 c) 2 ( 3x -a ) – 4 ( x- a ) = 3 ( x + a ) d) 2x/5 - (x-2a)/3 = a/2 Resolva as equações fracionárias: a) 3/x + 5/(x+2) = 0 , U = R - {0,-2} b) 7/(x-2) = 5/x , U = R - {0,2} c) 2/(x-3) - 4x/(x²-9) = 7/(x+3) , U = R - {-3,3}
Answer:
1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]
Step-by-step explanation:
1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]
[tex]5\cdot x - x = 5\cdot a + a[/tex]
[tex]4\cdot x = 6\cdot a[/tex]
[tex]x = \frac{3}{2}\cdot a[/tex]
b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]
[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]
[tex]x = 5-3\cdot a[/tex]
c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]
[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]
[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]
[tex]-x = a[/tex]
[tex]x = -a[/tex]
d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]
[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]
[tex]2\cdot x = 5\cdot a[/tex]
[tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]
[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]
[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]
[tex]3\cdot x +6 +5\cdot x = 0[/tex]
[tex]8\cdot x = - 6[/tex]
[tex]x = -\frac{3}{4}[/tex]
b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]
[tex]7\cdot x = 5\cdot (x-2)[/tex]
[tex]7\cdot x = 5\cdot x -10[/tex]
[tex]2\cdot x = -10[/tex]
[tex]x = -5[/tex]
c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]
[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]
[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]
[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]
[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]
[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]
[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]
[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]
[tex]-9\cdot x = -27[/tex]
[tex]x = 3[/tex]
