(3)
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 8x^3, y = 0, x = 1; about x = 2
Answer is 24pi/5
I just don't know how to get it.

The probability that they are both left-handed is 0.01

Probability is the number of ways of achieving success.

the total number of possible outcomes.

Probability takes values between 0 (no chance) and 1 (certain) inclusive.

Complement Rule (probability that an event doesn't occur): P(A') = 1 - P(A) .

Addition rule: P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .

Multiplication rule: P(A ∩ B) = P(A) × P(B) for independent events. P(A ∩ B)

For both, the persons selected at random are left-handed

10 % out of 100 % are left-handed.

Hence the probability that the person is left-handed

P(L) = 10 /100 = 1 / 10 = 0.1

where P(L) is the probability that the person is left-handed.

Therefore both the persons selected are left-handed

= 0.1 * 0.1

= (0.1)^2

= 0.01

Hence the probability that they are both left-handed is 0.01.

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JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Answer:

\(\huge\boxed{-1}\)

Step-by-step explanation:

\(\frac{-5^2}{(-5)^2}\)

=> \(\frac{-25}{25}\)

=> -1

Answer:

-1

Step-by-step explanation:

-5^2 is -25 because you have to do exponents first, so 5^2 is 25. Add a negative symbol there, it becomes -25.

For the denominator, we do the exact same process, except a little different. Since there are parentheses around the negative five, we have to apply the negative symbol on the 5 before we do the exponents. After, we do -5^2 which is 25 because when you are multiplying negative, you always get a positive.

When we are all done with that, we put the numerator over the denominator to get -25/25, which is equivalent to -1.

Answer:

Required probability:

Required probability:

At least 2 students pass:

Number of x's:

Answer:

x ≈ 44.4°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = \(\frac{opposite}{hypotenuse}\) = \(\frac{7}{10}\) , then

x = \(sin^{-1}\) (\(\frac{7}{10}\) ) ≈ 44.4° ( to the nearest tenth )

Answer:

D

Step-by-step explanation:

used guess-and-check and (1,5) is the only ordered pair that made each inequality true

Answer:

y= -3/5x-4

Step-by-step explanation:

Answer:

Answer is the 2nd one

Hope it was helpful

\(\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log(49)=y\implies \log_{10}(49)=y\implies 1.690196\approx y \\\\\\ \log_{10}(49)\approx 1.690196\implies \stackrel{\textit{then we can say}}{10^{1.690196}\approx 49}\)

Answer:

1 in=4 ft

5 in=20 ft

5 x 4=20 ft

1in =4 ft

8 in=32 ft

8 x 4=32 ft

A=L*W

A=32*20

A=640 SQUARE FEET

Step-by-step explanation:

GOOD LUCK

Answer:

10 liters

Step-by-step explanation:

x=12% solution, y=16% solution

x+y=40

0.12x+0.16y=6 .   (12x+16x=600)

-12x-12y=-480

      12x+16x=600

+     -12x-12y=-480

-------------------------------

             4x=120

x=30

12% solution= 30 liters

16% solution= 10 liters

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

10L of the 12% of solutions and 30L of the 16% of solutions were used to produce 40L of the 15% of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Let 12% brine solution be x.

Let 16% brine solutions be y.

12% brine solution was mixed with a 16% brine solution to produce 40L of the 15% solution.

This can be written as,

x + y = 40 ______(1)

0.12x + 0.16y = 0.15 x 40

0.12x + 0.16y = 6 _______(2)

We will solve for x and y.

From (1) we get,

x + y = 40

x = 40 - y _____(3)

Putting ( 3) in (2)

0.12 (40 - y) + 0.16y = 6

4.8 - 0.12y + 0.16y = 6

4.8 + 0.04y = 6

0.04y = 6 - 4.8

0.04y = 1.2

y = 1.2/0.04

y = 30

Putting in (3) we get,

x = 40 - 30 = 10

Thus,

10L of the 12% of solutions and 30L of the 16% of solutions were used to produce 40L of the 15% of solutions.

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Answer:

2 < h <= 3

Step-by-step explanation:

4 + h <= 7

h <= 3          (subtract 4 on both side)

h + 1 > 3

h > 2           (subtract 1 on both side)

So, 2 < h <= 3

Answer:

1.8%

Step-by-step explanation:

2.85-2.80=$0.05

$0.05 x 100 = 5

5/2.80=1.78

1.8

Answer:

k=-1

Step-by-step explanation:

- 8 = -7+k

+7     +7

k=-1

The amount of blue paint required = 3/2 cups

Ratio:

Comparing two or more quantities that have units is known as the Ratio. It shows the numerical relation between two quantities like how small or big a quantity is when compared to each other.

The general form of a ratio is a: b

Here we have,

2/3 cups of white paint and 2 and 2/3 cups of blue paint

Then ratio of white to blue paint = 2/3 : 2 (2/3)

= 1:2   [ divided by 2/3 ]

In the second condition, we have 3/4 cups of white paint, here we want to give the same shade then the ratio of paint must be the same as above

Let x be the amount of blue paint that we need  

Then the ratio of white paint to blue = 3/4: x

From the given condition,

=>  3/4 : x  = 1 : 2

=> 3/4 / x = 1/2

=> 3/4x = 1/2  

=> 3(2) = 4x(1)

=> x = 6/4 =

=> 3/2

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Answer:

\(A=157.07\ cm^2\)

Step-by-step explanation:

Given that,

The radius of a cylinder, r = 5 cm

Height of the cylinder, h = 5 cm

We need to find the lateral surface area of the  cylinder. The formula for the lateral surface area of the cylinder is given by :

\(A=2\pi r h\)

Put all the values,

\(A=2\pi\times 5\times 5\\\\=157.07\ cm^2\)

So, the lateral surface area of the cylinder is \(157.07\ cm^2\).

Step-by-step explanation:

If 5 is substracted from a number it becomes -5.

solution,

Let the number be x, then

x-5=-5

Step-by-step explanation:

Equation. x+5=0

× = 0-5

Answer ×= -5

Answer:

hope this helps.

Step-by-step explanation:

Answer:

Available Digits = 4 (1, 2, 3 , 4)

Step-by-step explanation:

Now, if the digits can be used only once, it is a case of permuting 4 things out of 4 things i.e. 4P4=24ways

Alternatively, the units place can be filled in 4 ways, tens place can be filled in 3 ways, hundreds place can be filled in 2 ways and thousands place in 1 way.

So, TOTAL=4×3×2×1=24

HOPE IT HELPS

Answer:

10(6)

Step-by-step explanation:

Hope it's right.....

Answer:

b

Step-by-step explanation:

cosecx is the reciprocal of sinx so if cosec(x) = 10 then sin (x) = 1/10

1/10 = 0.1

Answer:$6.87

Step-by-step explanation:

if you add them up you end up wit $6.87

The rate of change of the area of a square with respect to the length z, the diagonal of the square is  dA/dz = 2z; rate = 6. The correct answer is C.

We know that the area A of a square is given by A = s², where s is the length of the sides of the square. Also, we know that the diagonal of the square (z) is related to the sides by the Pythagorean theorem: s² + s² = z² or 2s² = z² or s² = z²/2.

Taking the derivative of both sides of the equation s² = z²/2 with respect to z, we get:

2s ds/dz = 2z/2

s ds/dz = z

Now, since the area A is given by A = s², we can take the derivative of both sides of this equation with respect to z:

dA/dz = d/dz (s²) = 2s ds/dz

Substituting the value of s ds/dz obtained earlier, we get:

dA/dz = 2s (z/s) = 2z

Therefore, the correct option is (c) dA/dz = 2z, and the rate of change of the area of the square with respect to the length z is 2z. When z = 3, the rate of change is 2(3) = 6. So, the answer is (c) dA/dz = 2z; rate = 6.

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Answer:

He purchased 15 tickets.

Step-by-step explanation:

First you gather your important information/ numbers

-7

-8

- how many tickets did he purchase?(+)

Then you create your equation and solve

7+8=15

Answer:

1.7 hours

Step-by-step explanation:

6.25/1.25= 5

8.5/5= 1.7

It would take Fred 1.7 hours to run 8.5 miles.

The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

∴ l₁ = h₁/(sin(x°))

Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

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Answer: 6750.50

Step-by-step explanation: 6750.50 because I did the math and got it correct on FLVS

Use the PeRT equation and just solve it algebraically to find P the principal investment

Answer:

-1

Step-by-step explanation:

i = \(\sqrt{-1}\)

so square that

i^2 = \((\sqrt{-1} )^2\)

you get rid of square root sign, just becomes -1

Answer:

see explanation

Step-by-step explanation:

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

NQ is an angle bisector then ∠ MNQ = ∠ PNQ

∠ M = ∠ N , so the triangle is isosceles with 2 equal legs, then

MN = PN

----------------------------------------------

∠ MNQ = ∠ PNQ

MN = PN ( included sides between the 2 angles )

∠ M = ∠ N

Δ MNQ ≅ Δ PNQ by the ASA postulate

Answer:

Step-by-step explanation:

In Δ MNP,

∠NMQ ≅ ∠NPQ

⇒ NM = NP - ------> (I)     {Sides opposite to equal angles are equal}

In ΔMNQ & ΔPNQ,

∠MNQ  ≅ ∠PNQ             {NQ is angle bisector}

NM  = NP                     {from (I)}

∠NMQ ≅ ∠NPQ           {Given}

ΔMNQ ≅ ΔPNQ          -  Angle Side Angle  {ASA congruent}