Find the volumes of the solid generated by revolving the regions bounded by the graphs of the graphs of the equations about the given lines:
y=5x2y=0x=3
a) on the y-axis.
b) on the x-axis.
c) on the line y = 45.
d) on the line x = 3.

Answer:Value of x are 16 and -2

Step-by-step explanation:

Solve for x in the equation:

Subtract 63 from both sides we have;

To factor this equation as:

⇒

Take (x-16) common we have;

⇒

By zero product property we have;

x-16 = 0 or x+2 = 0

⇒x = 16 or x = -2

Therefore, the value of x are: 16 and -2

The value of x in the equation are x = -2 or x = 16.

Quadratic equations are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Given is a quadratic equation,

x² - 14x + 31 = 63

We have to find the value of x.

x² - 14x + 31 - 63 = 0

x² - 14x - 32 = 0

Using the quadratic formula,

x = [14 ± [tex]\sqrt{(-14)^2-(4*1*-32)}[/tex]] / 2

  = (14 ± √324) / 2

  = (14 ± 18) / 2

x = 14 + 18 / 2 or x = 14 - 18 / 2

x = 16 or x = -2

Hence the value of x are x = 16 or x = -2.

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Answer:

AB - [tex]\frac{2}{1}[/tex]

BC - [tex]\frac{4}{2}[/tex]

AC - [tex]\frac{6}{3}[/tex]

Slope = 2

Step-by-step explanation:

For AB the rise (counting upwards) is 2 and the run (counting to the right) is 1. If you simplify it, it would be 2. The reason why it's not a negative is that the slope is going upwards not downwards.

Answer:

54.33

Step-by-step explanation:

Answer:

54.33

Step-by-step explanation:

Addition or a calculwtor can be used

Answer: 113% = 9153

100% = ?

100/113 X 9153 = 915300/113 = Rs 8100 = sale price

90 % = 8100

100% = ?

100/90 X 8100 = Rs 9000 = marked price

108% = 8100

100% = ?

100/108 X 8100 = Rs7500 = cost

Difference = 9000 -7500 = Rs 1500

1500/7500 X 100 = 20%

ANSWER Marked price is 20% above cost price

Step-by-step explanation:

Answer:

  B.  216 in²

Step-by-step explanation:

You want to know the area of a triangle with a base of 36 inches and a height of 12 inches.

The area of a triangle is given by ...

  A = 1/2bh

where b is the base of the triangle (one side), and h is the height to the opposite vertex, measured perpendicular to the base.

The figure shows a base of 36 inches and a height of 12 inches. Using these values in the formula, we have ...

  A = 1/2(36 in)(12 in) = 216 in²

The area of the triangle is 216 in².

Answer: 216

Step-by-step explanation: I got it right sorry for the late comment

Yes, the deviation is greater than it was in tossing them 40 times.

A standard deviation (or σ) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.

Given:

n= 400 trials

Tossing 2 coins 400 times gives 800 trials

so, [tex]\sigma_1[/tex]² = np(1- p)

        = 800 x 1/2 x 1/2

      [tex]\sigma_1[/tex]  = √200

      [tex]\sigma_1[/tex] = 10√2

Now, n=40

and,  [tex]\sigma_2[/tex]² = np(1- p)

        = 80 x 1/2 x 1/2

      [tex]\sigma_2[/tex]  = √20

      [tex]\sigma_2[/tex] = 2√5

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{5x + 2(x - 1) = 6(x + 1) +x}------------------------No solution

{5x + 2(x - 1) = 6(x - 1) - x}------------------------- x = -2

{5x + 2(x - 3) = 6(x - 1) - x}-------------------------x = 0

{5x + 2(x - 3) = 6(x - 1) + x}-------------------------All real numbers

What is linear equation?

A linear equation is an algebraic equation of the shape y= mx + b. regarding simplest a consistent and a first-order (linear) term, wherein m is the slope and b is the y-intercept.

Solution:

Simplifying First equation,

5x + 2x - 2 = 6x + 6 + x

⇒7x - 2 = 7x + 6

⇒ -2 = 6, which is not possible

Similarly second equation,

5x + 2x - 2 = 6x - 6 -x

⇒ 7x - 2 = 5x - 6

⇒ 2x = -4

⇒ x = -2

Similarly third equation,

5x + 2x - 6 = 6x - 6 - x

⇒7x - 6 = 5x -6

⇒ 2x = 0

⇒ x = 0

Similarly fourth equation,

5x + 2x - 6 = 6x - 6 + x

⇒ 7x - 6 = 7x - 6

⇒ 0 = 0

It means all real numbers are the solutions.

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The volume of a sphere is 33409.6 cm³ and the volume of a cube is 8000 cm³. Therefore, the volume of water 8000 cm³ can fit in the sphere.

Given that, a cube with an edge of 20 cm is filled with water.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

We know that, the volume of cube =a³, where a=edge

Here, volume of cube =20³

= 8000 cm³

Radius of sphere is 20 cm

As we know, the volume of sphere = 4/3πr³

= 4/3 ×3.14×20³

= 1.33×3.14×8000

= 33409.6 cm³

The volume of a sphere is 33409.6 cm³ and the volume of a cube is 8000 cm³. Therefore, the volume of water 8000 cm³ can fit in the sphere.

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Answer:

1.135,

3.718,

and 8.389

Step-by-step explanation:

Answer:

[tex]x=-2,\;y\approx\boxed{1.135}[/tex]

[tex]x=1,\;y\approx\boxed{3.178}[/tex]

[tex]x=2,\;y\approx\boxed{8.389}[/tex]

Step-by-step explanation:

Euler's number, denoted as the letter "e", is a mathematical constant approximately equal to 2.7182818 ( 7 d.p.).

To evaluate [tex]y=e^x+1[/tex] for the given values of x, substitute the value of x into the equation and evaluate using a calculator, rounding the final answer to 3 decimal places (nearest thousandth).

[tex]\begin{aligned}x = -2\implies y&=e^{-2}+1\\y&=0.135335...+1\\y&=1.135335...\\y&=1.135\end{aligned}[/tex]

[tex]\begin{aligned}x =1\implies y&=e^1+1\\y&=2.7182818...+1\\y&=3.7182818...\\y&=3.718\end{aligned}[/tex]

[tex]\begin{aligned}x = 2\implies y&=e^{2}+1\\y&=7.389056...+1\\y&=8.389056...\\y&=8.389\end{aligned}[/tex]

The horizontal force that the student exert on the boat is 120 N toward the front of the boat.

What is third law of Newton ?

As per the third law of Newton, the force exerted by the boat over the student is equal in magnitude to the force that the student exerted on the boat.

So, calculate the force on the student using the second law of Newton, Force = mass * acceleration.

Force on the student = 60 kg * 2.0 m/s^2 = 120 N.

=> horizontal force exerted by the student on the boat = 120 N

Answer: option d. 120 N. toward the back of the boat.

Of course it is toward the back because that is where the student jumped from..

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Answer:

The answer is $14.224.

Step-by-step explanation:

The volume, in milliliters, of hbrhbr solution required to neutralize 28.0 mlml of a 0.210 mm liohlioh solution is 1.176 ml.

Volume is a degree of the quantity of area that be counted occupies. Matter is described as a bodily substance that occupies area and has a mass. In bodily sciences like chemistry, the usual unit of extent is cubic metres (m3). From this, different gadgets are derived inclusive of litre (L) and millilitre (mL).

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The fraction in the question is 9 / 14

Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

To solve this problem, we have to write an algebraic equation and solve for the unknown.

Assuming x represents the unknown value

Original fraction = x - 5 / x

When 1 is added to both numerator and denominator;

x - 5 + 1 / x + 1 = 2/3

x - 4 / x + 1 = 2/3

Cross multiplying both sides

2(x + 1) = 3(x - 4)

2x + 2 = 3x - 12

Collect like terms and solve for x

2 + 12 = 3x - 2x

x = 14

The fraction is 14 - 5 / 14 = 9 /14

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Answer:

here,

simple interest (S)=12.50$

Principal(p)=30.00$

time(t)=0.5 year

Now,

S=PTR/100

or,12.50=30×0.5×R/100

or,1250=15R

or,1250/15=R

:.R=83.33% per annum

Answer:

RS, SQ, QR

Step-by-step explanation:

The three angles in a triangle add up to 180° Two angles are given, so we can find the third angle.

11 + 40 + S = 180

51 + S = 180

subtract 51

S = 129°

S is the biggest angle, so the biggest side will be opposite from S. QR is the biggest side.

AngleQ is 11°, the smallest angle. The smallest side will be opposite from the smallest angle. The smallest side is RS.

The 40° angle, AngleR is in the middle. The medium length side is opposite from the medium size angle. SQ is the medium length side.

From small to big:

RS, SQ, QR

Answer:

The 4th answer down

RS, SQ, RQ

Step-by-step explanation:

There is a relationship between the angle measurement and the length of the side opposite of the angle.  The side opposite of the largest angle measurement has the longest side opposite to that angle, the same is true for the middle angle and the smallest angle.

Geometric mean will be a line segment with length x such that x² = a × c.

Geometric mean of two line segments p and q is a line x such that it satisfies the formula x² = a × b or x/a = b/x.

To construct geometric mean, first simply draw a line segment and mark a point P anywhere on this line.

Mark the length of the line segment 'a' from the point P and mark the endpoint of 'a' as A. Now, in the same line, from the point P, mark the length of the given line 'c' and mark its endpoint as C.

Now, draw a perpendicular bisector of the resulting line PC. Then we get the midpoint of PC. Let this point be O.

Draw a semicircle with center O and the endpoints P and C.

Now draw a vertical perpendicular line from the point A until it cuts the semicircle. Let N be the point where this line touches the semicircle.

Now join P with N.

The line PN will be the geometric mean x such that a × c = x².

Hence the line segment PN is the geometric mean with length x.

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The correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams

A confidence interval, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.

Since the 95% confidence interval for the mean weight of apples in an orchard at a specific given time is between 147 grams to 151 grams.

This follows that from our definition of confidence interval and 95 % confidence interval, that there is a 95 % confidence that the mean weight of the apples in the orchard lies between 147 grams to 151 grams.

So, the correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams

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Given average speed=340 miles per hour

                         speed= distance/time (formula)

                         speed= 340/60

                         speed=5.6 miles/min

now,we have to calculate time,

                             time=distance/speed

                             time=1190/5.6

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The first possible date on which she will complete 25 hours of exercise for the year is on March 1.

In general, dates can refer to a specific day on the calendar, such as January 1 or December 31. Dates can also refer to a specific point in time, such as a specific hour, minute, or second. In some cases, dates can also refer to a specific period of time, such as a year, month, or week.

Since Nora plans to do a 45-minute workout four times a week,

she will exercise for a total of 4 * 45 minutes = 180 minutes per week.

This means that each week, she will exercise for a total of 180 / 60 = 3 hours.

To complete 25 hours of exercise for the year,

Nora will need to exercise for a total of 25 / 3 = 8.3 weeks.

The first possible date on which she will complete 25 hours of exercise is therefore 8.3 weeks after Jan 1,

Which is approximately 8.3 * 7 = 58 days after Jan 1.

Therefore, the first possible date on which Nora will complete 25 hours of exercise is 58 days after Jan 1, which is on March 1.

Overall, if Nora sticks to her New Year's resolution to exercise four times a week, the first possible date on which she will complete 25 hours of exercise for the year is on March 1.

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Answer:  The following that could represent the side lengths of a triangle are A, C, D.

Step-by-step explanation:

The sum of the first two numbers of the triangle must be greater than the third.

A. 6+10= 16>14             -----------a triangle

B. 12+15= 27<29           -----------not a triangle

C. 8+8= 16>11                -----------a triangle

D. 19+24= 43>40          ------------a triangle

E. 9+17= 26=26            -------------not a triangle

The system of equation to describe Tammy and Luke's outcome is as follows:

5x + y = 23

8x + 5y = 30

Tammy and Luke take part in a game in which they earn the same number of points for each catch and lose the same number of points for each miss.

let

x =  number of points for a catch

y = the number of points for a miss.

Tammy makes 5 catches and misses 1, ending the game with 23 points.

Therefore,

5x + y = 23

Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points. Therefore,

8x + 5y = 30

Hence, the combine equation to describe the outcome is as follows:

5x + y = 23

8x + 5y = 30

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The mean and standard deviation of X are 0.9 and 1.68 points.

Since Nikola gets 3 points for each ringer which he scores, then total points he gets from ringers could be determined by multiplying the number of ringers by 3.

So, X = R * 3 = 3R

Where:

R = numbers of ringers

X = total points Nikola gets from ringers

Given:

Mean : μR = 0.3

Standard deviation : σR = 0.56

Thus, multiplying by 3 will effects the mean as follows:

μX = 3 (μR)

= 3 (0.3)

= 0.9

And, multiplying by 3 also will effects the standard deviation as follows:

σX = 3 (σR)

≈ 3 (0.56)

≈ 1.68

Hence, the mean of X is 0.9 and and the standard deviation of X is 1.68.

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Answer:

-4

Step-by-step explanation:

[tex]-3*2 + 2=-4[/tex]

The number of goals scored in a hockey game is a discrete random variable.

A discrete random variable has a countable number of different possible values, such as 0,1,2,3,4, etc. Usually, but not always, discrete random variables are counted. If a random variable has a limited range of possible values, it is discrete.

The number of children in a household, the Friday night movie attendance, the number of patients at a doctor's office, and the number of faulty light bulbs in a box of ten are a few examples of discrete random variables. A discrete random variable's probability distribution is a table of the probabilities connected to each of its potential values.

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Answer:

11/20

Step-by-step explanation:

4/5 - 1/4

find greatets common denominator aka 20 cuz 5 and 4 can go into 20

multiply that many tiems it goes into 20 for the numerator

you now have 16/20 - 5/20
the answer is 11/20

Answer:

25%

Step-by-step explanation:

we know that you have to do amount of error/ correct amount

so the amount of error is 10 and the correct amount is 40, so its 10/40.

10 divided by 40 is 0.25.  They want the answer as a percent, so in order to turn 0.25 to a percent, you have to move the decimal 2 times over. It then turns into 25%

The ways to assign for different people is 126 ways

From the question, we have

Total number of questions, n = 9

Numbers to people, r = 4

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 9 and r = 4

Substitute the known values in the above equation

Total = 9C4

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 9!/5!4!

Evaluate

Total = 126

Hence, the number of ways is 126

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Answer:

Step-by-step explanation:

You want the solutions to the following inequalities by any convenient method:

We choose to rewrite these inequalities to be comparisons to zero. This is because our graphing calculator easily identifies the x-intercepts of a graph. We can look a the graph to tell where the function is above or below the x-axis.

The attached graph shows the solutions to be ...

The values obtained for the first equation will be  x ≤ 3/5 and x ≤ -5/2 and the values obtained for the second equation will be x < 1/2 and x < -3/4.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given inequalities in the question,

1.

x(10x + 19) ≤ 15

Firstly, simplify it to the simpler form,

10x² + 19x - 15 ≤ 0

Solve the quadratic equation,

D = b² - 4ac

= 19² - 4(10)(-15).

D = 961

Now, use the formula,

(-b±√D)/2a

√D = √961 = 31

(-19 ± 31)/2(10)

So, the roots are:

1.

(-19 + 31)/20 = 12/20 = 3/5

Or, x ≤ 3/5

2.

(-19 - 31)/20 = -50/20 = -5/2

Or, x ≤ -5/2

2.

(x + 2)² > (3x + 1)²

Simplify the equation first.

x² + 4x + 4 > 9x² + 6x + 1

x² - 9x² + 4x - 6x + 4 - 1 > 0

-8x² - 2x + 3 >

8x² + 2x - 3 < 0

Now, find the roots for the equation,

D = b² - 4ac

D = 4 + 96

D = 100

Now, use the formula,

(-b ± √D)/2a

(-2 ± 10)/16

So, the roots are:

1. (-2 + 10)/16 = 1/2

Or, x < 1/2

2. (-2 - 10)/16 = -12/16 = -3/4

Or, x < -3/4

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Answer:

b

Step-by-step explanation:

when the object is on the ground then h = 0 , then

- 16t² + 140 = 0 ( subtract 140 from both sides )

- 16t² = - 140 ( divide both sides by - 16 )

t² = [tex]\frac{-140}{-16}[/tex] = 8.75 ( take square root of both sides )

t = [tex]\sqrt{8.75}[/tex] ≈ 2.96 seconds ( to the nearest tenth )