Find the volume of the solid generated when R​ (shaded region) is revolved about the given line. x=6−3sec y​, x=6​, y= π 3​, and y=​0; about x= 6

Answer:

.18n+2400-.06n=6000

.12n=3600

n=3600/.12=$30000 at 18%, $10000 at 6%

Step-by-step explanation:

Answer:

[tex]y=5x-37[/tex]

Step-by-step explanation:

So we want to find the equation of a line with a slope of 5 and passes through (8,3).

To do so, we can use the point-slope form. This point-slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

Let's let (8,3) be x₁ and y₁ and let's let m equal 5. Therefore:

[tex]y-3=5(x-8)[/tex]

Distribute the right:

[tex]y-3=5x-40[/tex]

Add 3 to both sides:

[tex]y=5x-37[/tex]

That would be our equation in slope-intercept form.

And we're done!

=======================================================

Explanation:

If order mattered, then we'd have 17*16*15 = 4080 different permutations. Notice how I started with 17 and counted down 1 at a a time until I had 3 slots to fill. We count down by 1 because each time we pick someone, we can't pick them again.

So we have 4080 different ways to pick 3 people if order mattered. But again order doesn't matter. All that counts is the group itself rather than the individual or how they rank. There are 3*2*1 = 6 ways to order any group of three people, which means there are 4080/6 = 680 different combinations possible.

An alternative is to use the nCr formula with n = 17 and r = 3. That formula is

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

where the exclamation marks indicate factorials

The number of different ways that are there to select 3 players is 680.

Since there is A team of 17 softball players need to choose three players to refill the water cooler.

So here we can say there are [tex]17\times 16\times 15 = 4080[/tex]

And, since we have to select 3 people so the no of ways should be [tex]3\times 2\times 1 = 6\ ways[/tex]

So, here the number of different ways should be

[tex]= 4080\div 6[/tex]

= 680

Therefore, The number of different ways that are there to select 3 players is 680.

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Answer:

123.76

Step-by-step explanation:

a negative times a negative is a positive

22.1 times 5.6 is 123.76

Answer:

She has 28 pennies

Step-by-step explanation:

Janae has 280 dimes in her piggy bank she has 10 times as many pennies .

If she has 280 dimes in piggy bank

And has 10 times as many pennies

Let dimes= x

Let pennies= y

X= 10y

But x= 280

280= 10y

280/10 = y

28 = y

She has 28 pennies

Answer:

The answer for both apples and bananas is 21

The answer for only apples or only bananas is 45

Step-by-step explanation:

36 plus 30 minus 45

50-5 is 45

only apples or bananas is 15 + 9

Answer:

715,340 > 715,034

Step-by-step explanation:

Answer:

FG = 39

Step-by-step explanation:

From the question given:

FH = 9x + 15

GH = 5x + 4

FG = ?

From the question given above, we can say that G is the midpoint of FH. This implies that:

FH = FG + GH

With the above idea in mind, we can obtain FG as follow:

FH = 9x + 15

GH = 5x + 4

FG = ?

FH = FG + GH

9x + 15 = FG + 5x + 4

Rearrange

FG = 9x + 15 - 5x - 4

FG = 9x - 5x + 15 - 4

FG = 4x + 11

Next, we shall determine the value of x. This can be obtained as follow:

Since G is the midpoint of FH, it therefore means that FG and GH are equal i.e

FG = GH

With the above idea in mind, we can obtain the value of x as follow:

FG = 4x + 11

GH = 5x + 4

FG = GH

4x + 11 = 5x + 4

Collect like terms

11 - 4 = 5x - 4

7 = x

x = 7

Thus, we can obtain the value of FG as follow:

FG = 4x + 11

x = 7

FG = 4x + 11

FG = 4(7) + 11

FG = 28 + 11

FG = 39

***Check ***

FH = 9x + 15

x = 7

FH = 9(7) + 15 = 63 + 15 = 78

GH = 5x + 4

x = 7

GH = 5(7) + 4 = 35 + 4 = 39

FG = 4x + 11

x = 7

FG = 4(7) + 11 = 28 + 11 = 39

FH = FG + GH

FH = 78

FG = 39

GH = 39

FH = FG + GH

78 = 39 + 39

78 = 78

Answer:

as we know, the integral of [tex]x^{n}[/tex] is [tex]\frac{x^{n+1} }{n+1}[/tex]

so, the integral of x.[tex]2^{x}[/tex] will be found as follows:

here, we will use a trick called 'integration by parts'

let x = u and [tex]2^{x}[/tex] = v

∫uv dx = u∫v dx - ∫[(du/dx)* ∫v dx] dx

∫x.[tex]2^{x}[/tex] dx = x∫[tex]2^{x}[/tex] - ∫[(dx/dx) * ∫[tex]2^{x}[/tex] dx ] dx

∫x.[tex]2^{x}[/tex] dx = x*[tex]\frac{2^{x+ 1}}{x+ 1}[/tex] - 1 * [tex]\frac{2^{x + 1} }{x + 1}[/tex]

= [tex]\frac{2^{x} }{x + 1}[/tex]( x - 1 )

Answer:

rational numbers

Step-by-step explanation:

Answer:

53.5 DEGREES

Step-by-step explanation:

90 + 36.5 = 125.6

180 - 126.5 = 53.5 degrees

The measure of the other small angle will be 53.5 degree.

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;

In a right triangle, One angle measures 36.5 degrees.

Now,

Since, The triangle is a right triangle.

So, One of the angle = 90 degree

And, One angle measures 36.5 degrees.

Let the measure of the other small angle = x degree

Since, The sum of all the interior angles in a triangle = 180 degree

So, We can formulate;

⇒ x + 90 + 36.5 = 180

⇒ x + 126.5 = 180

⇒ x = 180 - 126.5

⇒ x = 53.5 degree.

Thus, The measure of the other small angle will be 53.5 degree.

Learn more about the triangle visit:

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#SPJ6

Answer: 32/3

Step-by-step explanation:

To find the area of the region between the curves, you first want to find the interval of both curves. You can do that by setting both curves equal to each other.

[tex]-\frac{1}{2}x^2+2=\frac{1}{2} x^2-2[/tex]                   [subtract both sides by 2]

[tex]-\frac{1}{2}x^2= \frac{1}{2} x^2-4[/tex]                         [subtract both sides by [tex]\frac{1}{2} x^2[/tex]]

[tex]-x^2=-4\\x=2,-2[/tex]        

Now that we know the interval, we set this into an integral and subtract the top curve by the bottom curve. *Note: I can't type in -2 into the interval, therefore only a "-" will be displayed.

[tex]\int\limits^2_- {|-\frac{1}{2}x^2+2-(\frac{1}{2}x^2-2) | } \, dx[/tex]                     [distribute -1]

[tex]\int\limits^2_-{|-\frac{1}{2}x^2+2-\frac{1}{2}x^2+2 |} \, dx[/tex]                       [combine like terms]

[tex]\int\limits^2_- {|-x^2+4|} \, dx[/tex]                                          [solve integral]

[tex]\frac{32}{3}[/tex]

The area between the curves is 32/3. This was also the reason why we had the absolute values because area can never be negative.

Answer:

By contradiction it can be proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

Step-by-step explanation:

Method of contradiction means we assume opposite to the facts to be proved and then we contradict our assumption.

As a result, we prove the fact.

Here, let the four number be:

[tex]p, q, r, s[/tex]

The average will be Sum of all numbers divided by count of numbers.

[tex]\dfrac{p+ q+ r+ s}4[/tex]

Now, let us assume the opposite that the average is less than all the numbers.

i.e.

[tex]\dfrac{p+ q+ r+ s}4 <p[/tex]

[tex]\dfrac{p+ q+ r+ s}4 <q\\\dfrac{p+ q+ r+ s}4 <r\\\dfrac{p+ q+ r+ s}4 <s[/tex]

Now, let us add all of them:

[tex]\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 < p+q+r+s\\\Rightarrow \dfrac{4(p+q+r+s)}4<p+q+r+s\\\Rightarrow p+q+r+s<p+q+r+s[/tex]

Which can never be possible hence, our assumption is contradicted.

our assumption is wrong.

Therefore, by contradiction it is proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

An average of four real numbers will be greater than or equal to at least one of the four real numbers.

What is average?

An average is simply defined as the mean of the given set of numbers. The mean is said to be an arithmetic mean. It is the ratio of the sum of the observation to the total number of observations.

Prove the following using proof by contradiction.

The average of four real numbers is greater than or equal to at least one of the numbers.

Method of a contradiction means we assume opposite to the fact to be proved and then we contradict our assumption.

Let the four numbers be a, b, c, and d.

The average will be

[tex]\rm \dfrac{a+b+c+d}{4}[/tex]

Now let us assume the opposite that the average is less than all the numbers.

[tex]\rm \dfrac{a+b+c+d}{4} < a\\\\\rm \dfrac{a+b+c+d}{4} < b\\\\\rm \dfrac{a+b+c+d}{4} < c\\\\\rm \dfrac{a+b+c+d}{4} < d[/tex]

Let us add all of them.

[tex]\rm \rightarrow \dfrac{a+b+c+d}{4} +\dfrac{a+b+c+d}{4} +\dfrac{a+b+c+d}{4}+\dfrac{a+b+c+d}{4} < a+b+c+d\\\\\rightarrow \dfrac{4(a+b+c+d)}{4} < a+b+c+d\\\\\rightarrow a+b+c+d < a+b+c+d[/tex]

That can never be possible hence, our assumption is contradicted.

Our assumption is wrong.

Therefore, by contradiction, it is proved that;

An average of four real numbers will be greater than or equal to at least one of the four real numbers.

More about the average link is given below.

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Answer:

The answer is below

Step-by-step explanation:

a)Given that the length of fencing available is 400 yards. This means that the perimeter of the rectangle is 400 yards.

the perimeter of a rectangle is given as:

Perimeter = 2(length + width) = 2(l + w)

Hence;

400 = 2(l + w)

200 = l + w

l = 200 - w

The area of a rectangle is given as:

Area = length × width

Area = (200 - w) × w

Area = 200w - w²

b) For a quadratic equation y = ax² + bx + c. it has a maximum at x = -b/2a

Hence, for the area = 200w - w² a=-1, b = 200, the maximum width is at:

w = -b/2a = -200/2(-1) = -200/-2 = 100

A width of 100 yard has the largest area

c) l = 200 - w = 200 - 100 = 100 yards

Area = l × w = 100 × 100 = 10000 yd²

The maximum area is 10000 yd²

Step-by-step explanation:

Part 1

To find out the amount of water ten big water bottles can hold, we have to find out how much water is in each water bottle. To do this, we divide the amount we are looking for by the number of items.

8 ÷ 4 = 2

Part 1 answer: Each water bottle can hold 2 gallons of water.

Part 2

Now that we know the amount of water in each water bottle, we can find out how much water 10 water bottles can hold. To do so, we multiply our previous answer, 2, by the number of items (10).

2 • 10 = 20

Part 2 answer: 10 water bottles can hold 20 gallons of water.

Our final answer: 20 gallons

I hope this helps you!

Complete question is;

Multiple-choice questions each have 5 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions.

Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, find P(WWWWC), where C denotes a correct answer and W denotes a wrong answer.

P(WWWWC) =

Answer:

P(WWWWC) = 0.0819

Step-by-step explanation:

We are told that each question has 5 possible answers and only 1 is correct. Thus, the probability of getting the right answer in any question is =

(number of correct choices)/(total number of choices) = 1/5

Meanwhile,since only 1 of the possible answers is correct, then there will be 4 incorrect answers. Thus, the probability of choosing the wrong answer would be;

(number of incorrect choices)/(total number of choices) = 4/5

Now, we want to find the probability of getting the 1st 4 guesses wrong and the 5th one correct. To do this we will simply multiply the probabilities of each individual event by each other.

Thus;

P(WWWWC) = (4/5) × (4/5) × (4/5) × (4/5) × (1/5) = 256/3125 ≈ 0.0819

P(WWWWC) = 0.0819

Answer:

(a)   x follows a poisson distribution with parameter λ = 8 / hour

(b)   P( X = 5 ) = 0.09160

      P( X ≥ 5 ) = 0.9004

(c)   the expected value  of the number of nonconforming parts produced during a 120-min period = 16 nonconforming parts per 120 minutes

The standard deviation = 4

(d)   P(X ≥ 20) = 0.5297

      P( X ≤  10) = 0.0108

Step-by-step explanation:

Suppose nonconforming parts are produced with a rate = 8 / hour (i.e. on average, 8 nonconforming parts will be made during a production period of one hour).

(a)  If x denotes the number of nonconforming parts made during one hour, then : x follows a poisson distribution with parameter λ = 8 / hour

(b)

What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?

the probability that exactly 5 nonconforming parts are produced during a 1-hour period can  be computed as:

P( X = 5 ) = [tex]e^{- \lambda } \lambda^x /x![/tex]

P( X = 5 ) = [tex]e^{- 8 }(8)^5 /5![/tex]

P( X = 5 ) = 0.09160

the probability that at least 5 nonconforming parts are produced during a 1-hour period

P( X ≥ 5 ) = 1 -  P( X ≤ 4)

[tex]P( X \geq 5 ) = 1 - \sum \limits ^4_{x=0} e^{-\lambda} \lambda ^x/x![/tex]

[tex]P( X \geq 5 ) = 1 - (e^{-8} 8 ^4/4! + e^{-8} 8 ^3/3! + e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]

[tex]P( X \geq 5 ) = 1 - 0.0996[/tex]

P( X ≥ 5 ) = 0.9004

c)  What are the expected value and standard deviation of the number of nonconforming parts produced during a 120-min period?

the expected value  of the number of nonconforming parts produced during a 120-min period [tex]\lambda = 8 \times \dfrac {120}{60}[/tex]

= 16 nonconforming parts per 120 minutes

The standard deviation = [tex]\lambda^{1/2}[/tex]

The standard deviation = [tex](16)^{1/2}[/tex]

The standard deviation = 4

(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?

During a 2.5 - hour period , the expected value = 8 × 2.5 = 20

As such, the probability  that at least 20  nonconforming parts produced during a 2.5-hour period is:

P(X ≥ 20) = 1 - P(X ≤ 19)

[tex]P( X \geq 20 ) = 1 - \sum \limits ^{19}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]

[tex]P( X \geq 20 ) = 1 - (e^{-8} 8 ^{19}/19! + e^{-8} 8 ^{18}/{18}! + e^{-8} 8 ^{17}/17!+...+e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]

P(X ≥ 20) = 1 -  0.4703

P(X ≥ 20) = 0.5297

Probability that at most  10 nonconforming parts produced during this period is:

P( X ≤  10) = [tex]\sum \limits ^{10}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]

[tex]P( X \leq 10) = e^{8} 8 ^{10}/{10}! + e^{8} 8 ^{9}/{9}! + e^{8} 8 ^{8}/{8}! + ...+ e^{8} 8 ^{2}/{2}!+ e^{8} 8 ^{1}/{1}! + e^{8} 8 ^{0}/{0}![/tex]

P( X ≤  10) = 0.0108

Following are the calculation to the given points:

For point a)

With parameter, x follows the poisson distribution is [tex]\lambda=\frac{8}{hour}[/tex]

For point b)

The probability that exactly 5 nonconforming parts are generated in a one-hour period.

[tex]\to P(X=5)=e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0916[/tex]

There is a good chance that at least 5 nonconforming parts exist.

[tex]\to P(X\geq 5) =1-P(X\leq 4)[/tex]

                 [tex]=1 -\sum_{x=0}^{4} \ e^{-\lambda } \frac{\lambda ^{x}}{x!} \\\\=1-0.0996\\\\=0.9004[/tex]

For point c)

Expected value for 120-minute period [tex]\lambda=8\times \frac{120}{60} =16[/tex] 120 minutes of nonconforming sections

[tex]\to \sigma ==(\lambda)^{\frac{1}{2} =(16)^{\frac{1}{2}} =4[/tex]

For point d)

Expected value for 2.5 hours

[tex]\to \lambda =8\times 2.5=20[/tex]

As a result, there is a good chance that at least 20 nonconforming items were manufactured.

[tex]\to P(X\geq 20)=1-P(X\leq 19)[/tex]

                   [tex]=1-\sum_{x=0}^{19}\ e^{-\lambda }\frac{\lambda^{x}}{x!}\\\\=1-0.4703\\\\=0.5297[/tex]

There is a chance that no more than 10 nonconforming parts were created.

[tex]\to P(X\leq 10)=\sum_{x=0}^{10}e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0108[/tex]

Learn more:

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Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf k = - 13}}}}[/tex]

Step-by-step explanation:

[tex] \sf{k + ( - \frac{5}{3} ) = - \frac{44}{3} }[/tex]

When there is a ( + ) in front of an expression in Parentheses, there is no need to change the sign.

That means the expression remains the same.

⇒[tex] \sf{k - \frac{5}{3} = - \frac{44}{3} }[/tex]

Move 5/3 to right hand side and change it's sign

⇒[tex] \sf{k = - \frac{44}{3} + \frac{5}{3} }[/tex]

While performing the addition or subtraction of like fractions , you just have to add or subtract the numerator respectively in which the denominator is retained same.

⇒[tex] \sf{k = \frac{ - 44 + 5}{3} }[/tex]

Calculate

⇒[tex] \sf{k = \frac{ - 39}{3} }[/tex]

Divide -39 by 3

⇒[tex] \sf{k = - 13}[/tex]

Hope I helped!

Best regards!!

Answer:

67

Step-by-step explanation:

Answer:

3rd Option: -1

5th Option: 2

7th Option: i√6

8th Option: -i√6

Step-by-step explanation:

Graph the function first to find our real root factors.

When you find your real root factors, factor the equation down with x + 1 and x - 2 and then use Quadratic Formula to find complex roots.

Answer:

-2, 1. i[tex]\sqrt{6}[/tex], and -i[tex]\sqrt{6}[/tex]

Step-by-step explanation:

just took the test

Answer:

[tex]\Huge \boxed{-2.3, \ \frac{-1}{3} , \ \sqrt{3} , \ \sqrt{7} , \ 5.1}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

We will convert the values into decimals for simplicity.

[tex]\sqrt{7} = 2.64575131106...[/tex]

[tex]-2.3=-2.3[/tex]

[tex]\sqrt{3} = 1.73205080757...[/tex]

[tex]5.1=5.1[/tex]

[tex]\displaystyle \frac{-1}{3} =-0.333333333...[/tex]

Arranging from least to greatest:

[tex]\displaystyle -2.3, \ \frac{-1}{3} , \ \sqrt{3} , \ \sqrt{7} , \ 5.1[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

  all real numbers except x=2

Step-by-step explanation:

We assume you intend c(x) = 5/(x-2), rather than c(x) = (5/x) -2 as written.

__

The domain of c(x) is real numbers, excluding 2. Multiplying c(x) by d(x) doesn't change that.

The domain of (cd)(x) = c(x)×d(x) = 5(x+3)/(x-2) is "all real numbers except 2".

__

2 is excluded because c(x) is undefined for that value.

Answer:

-12

Step-by-step explanation:

Answer: x=4

Step-by-step explanation:

8x-13=19

first, add 13 to both sides.

8x= 32

then, divide both sides by 8 to isolate x.

x= 32/8

x=4

Answer:

Step-by-step explanation:

Least to greatest:

2/5, 4/7,  5/8, 2/3, 3/4

$915 I’m pretty sure

Answer:

5

can be done by multiplication multiplicative property

Step-by-step explanation:

2/3 * (3/2 * 5)

1st = 2/3 * 3/2 * 5

2nd = 2 * 3 * 5

             3 * 2

3rd = 3 * 5

            3

therefore

the answer = 5

Answer:

[tex]\Large \boxed{\mathrm{associative \ property \ of \ multiplication}}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

The associative property of multiplication can be use to make the problem easier to solve.

In associative property of multiplication, when we multiply a bunch of numbers, we can group the numbers in any combination.

[tex]a \times (b \times c) = (a \times b) \times c[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

- 1/2

Step-by-step explanation:

(-4/5) × (- 5/8)

- 4/5 × - 5/8

First we mulitply across

The top and the bottom.

- 20 / 40

because -4 × -5 = +20

and -5 × -8 = +40

Now we simplify the fraction

- 20 / 40

= - 2 /4

= - 1/2

Because we have to simplify it and so I divided it by 10 first.

-20 ÷ 10 = -2 and -40 ÷ 10 = -4

Then I simplified it again by dividing it by 2.

-2 ÷ 2 = -1 and -4 ÷ 2 = -2

So finally we have:

-1/2

And we cannot simplify that anymore so that is the answer.

Hope that helped!

Answer:

1/2

Step-by-step explanation:

since negative * negative= positive we multiply the top and bottom to get. 20/40 which simplifies