Find the exact area of the surface obtained by rotating the given curve about the x-axis.
y = √x2 + 1, 0 ≤ x ≤ 2

The given measurement in scientific notation as \(6\times10^9\). Therefore, option D is the correct answer.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as \(1.56\times10^7\).

The given distance is 6,000,000,000 miles.

There are 9 zeros in the given number

So, scientific notation is \(6\times10^9\)

Therefore, the number in scientific notation is \(6\times10^9\).

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Answer:

It is 2 1/2

Step-by-step explanation:

Hope this helps :)

Answer:

the answer for this is B 9

Answer:

B

Step-by-step explanation:

Consecutive angles are supplementary, thus

30 + 5x + 15 + 10x = 180 , that is

15x + 45 = 180 ( subtract 45 from both sides )

15x = 135 ( divide both sides by 15 )

x = 9 → B

The solution which we get for the given question is , x = 5/2 and y = 5/4 answer.

Isolating x,

2x = 9x - 14y

2x-9x = 9x-9x -14y

-7x = -14y

-7x/-7 = -14y/-7

x = 2y

Therefore substituting value of x on equation 2,

9(2y) = 40 - 14y

18y = 40 - 14y

18y+14y = 40 -14y+14y

32y = 40

32y/32 = 40/32

y = 5/4

Therefore , x = 10/4 = 5/2

as because x =2y.

An equation is a mathematical statement which equated two value using the equal sign. Eg.) 2x = y

These expressions on either side of the equals sign are referred to as the equation's "left" and "right" sides. The right-hand side of an equation is usually assumed to be zero. The generality will still be there as  because we can balance it by subtracting the right-hand side expression from the expressions on both sides.

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We get that ∠5 can be written as ∠ HDC, ∠ 3 can be written as ∠ GDE and the vertex of ∠ 2 is D.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle. The word angle comes from a Latin word named 'angulus,' meaning “corner.”

We are given a diagram.

We need to name the angles.

∠5 can be written as ∠ HDC

∠ 3 can be written as ∠ GDE

Vertex of ∠ 2 is D

Therefore, we get that ∠5 can be written as ∠ HDC, ∠ 3 can be written as ∠ GDE and the vertex of ∠ 2 is D.

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Answer:

it's answer is SAS

hope it helps you

Answer:

SAS is the right answer

Step-by-step explanation:

.........

The incorrect rounding for 53.864 is 53.87

The decimal to be approximated is as follows;

53.864

The first option rounded the decimal to 2 significant figures or a whole number.

The second option is incorrect because they rounded it wrongly to 2 decimal places. The correct 2 decimal round is 53.86.

The third option is approximated rightly to one decimal place.

The last option is rounded to the closes tens term.

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a. The function that models the situation is  F(t) = 48(1.08)ˣ

b. The price of the stock 6 years from now is $76.17

c. Find the graph in the attachment

d. I receive a dividend of $0.026.

Since the stock price increases at a rate of 8% every year, and is initially $48, it follows exponential growth.

So, the current price \(F(t) = A(1 + r)^{t}\) where

So,  \(F(t) = A(1 + r)^{t}\)

\(F(t) = 48(1 + 0.08)^{t} \\= 48(1.08)^{t}\)

So, the function that models the situation is F(t) = 48(1.08)ˣ

The price of the stock 6 years from now is gotten when t = 6.

So,

\(F(t) = 48(1.08)^{t} \\= 48(1.08)^{6} \\= 48(1.5869)\\= 76.17\)

So, the price of the stock 6 years from now is $76.17

Find the graph in the attachment

Since every quarter, the company pays a dividend of 1.5 %, the rate per year would be r = 1.5 % ÷ 1/4 year = 1.5 % × 4 = 6 % per year.

Since they pay at a rate, r = 6 % = 0.06 of the stock price, F(t) as dividend.

After n years, the dividend is D = (r)ⁿF(t)

= (0.06)ⁿF(t)

So, \(D = (0.06)^{t}F(t) \\= (0.06)^{t}[4.8(1.08)^{t}]\)

So, after 3 years when t = 3,

\(D = (0.06)^{t}[4.8(1.08)^{t}]\\D = (0.06)^{3}[4.8(1.08)^{3}]\\D = 0.000216 \times 48 \times 1.2597\\D = 0.013\)

Since there are 3 shares, the total dividend would be D' = 3D

= 3 × 0.013

= 0.026

So, i receive a dividend of $0.026

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Step-by-step explanation:

Elijah runs at constant speed

2.4 hours -----------> 13.8 miles

1 hour ---------------> 13.8/2.4

1 hour ---------------> 5.75 miles

Elijah run 5.75 miles in each hour at constant speed

To find the volume of an oblique hexagonal prism, you need to multiply the base area by the height.

Given that the base area is 136 square centimeters and the height is 15 centimeters, we can use the formula: Volume = Base Area x Height.


The volume of the oblique hexagonal prism is calculated by multiplying the base area by the height. Therefore, the volume is equal to 136 square centimeters multiplied by 15 centimeters.


To find the volume of an oblique hexagonal prism, we first need to know the base area and the height of the prism. In this case, the base area is given as 136 square centimeters and the height is 15 centimeters. The formula for the volume of a prism is Volume = Base Area x Height.

By substituting the given values into the formula, we can calculate the volume. Thus, the volume of the oblique hexagonal prism is equal to 136 square centimeters multiplied by 15 centimeters, which gives us the final answer.


The volume of the oblique hexagonal prism with a height of 15 centimeters and a base area of 136 square centimeters is equal to the product of the base area and the height, which is 2040 cubic centimeters.

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Using it's concept, the experimental probability of getting an odd number and a number greater than 6 is given by:

1/5.

A probability is given by the number of desired outcomes divided by the number of total outcomes. An experimental probability is calculated considering the results of previous trials.

In this problem, there are 10 trials, and of those, 2 of them, trial 8 and trial 10, resulted in an odd number and a number greater than 6, hence the probability is:

p = 2/10 = 1/5.

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Answer: D

Step-by-step explanation: It is the only answer showing the x^2 + 3, x > 1 for the top graph, and the x > 1 refers to the function having an open circle going to the right. Therefore it is D

(edited because I mixed up y-intercepts (sorry ) )

Answer:

300 inches cubed

Step-by-step explanation:

12 x 10 x 2.5 = 12 x 25
                    = (3 x 4) x 25
                    = 3 x (4 x 25)
                    = 3 x 100
                    = 300

Answer:

The answer is 56 yards

Step-by-step explanation:

Im sorry I'm not smart enough to answer I just look around for it but I'm sorry I can't explain.

Answer:

-36/35  or -1 1/35

Step-by-step explanation:

-8/5 + 4/7

Get a common denominator of 35

-8/5 * 7/7   + 4/7 *5/5

-56/35  + 20/35

-36/35

-35/35 - 1/35

-1  1/35

Answer:

-36/35

Step-by-step explanation:

First, we need to find the LCM of 5 and 7 (the denominators) which is 35.

-8*7/35 + 4*5/35 = -56/35 + 20/35 =  -36/35

Your answer is -36/35, or if it asks for a mixed number it's -1 1/35.

Hope this helps

Answer:

18

Step-by-step explanation:

3/6 =1/2

1/2 of 36 is 18

Answer:

81 cm

Step-by-step explanation:

Answer:

Length of side = 14.7 cm

Perimeter = 58.7 cm

Step-by-step explanation:

Find the root of 215 to find the side length.

It is about 14.7 cm.

Then, multiply the length of the side by 4 to find the perimeter.

Answer:

n\(\geq\)8

Step-by-step explanation:

You add 4 to both sides to make n the only thing on one side. Then to make the answer look better you move n to the left side and flip the symbol because n changed sides.

\(4\leq n-4\\ 4+4\leq n-4+4\\ 8\leq n\\ n\geq 8\)

The subspace U = span{g(x)}, the set {g(x)} is a basis of U.

Given set, U = {p ∈ P2(R) : p(x) is divisible by (x - 3)}.

Part (a) - We have to find the basis of the given subspace, U.

Let's consider a polynomial

g(x) = x - 3 ∈ P1(R).

Then the set, {g(x)} is linearly independent.

Since U = span{g(x)}, the set {g(x)} is a basis of U. (Note that {g(x)} is linearly independent and U = span{g(x)})

We have to find another subspace, W of P2(R) such that P2(R) = U ⊕ W. The sum is direct and the sum is equal to P2(R).

Let's consider W = {p ∈ P2(R) : p(3) = 0}.

Let's assume a polynomial f(x) ∈ P2(R) is of the form f(x) = ax^2 + bx + c.

To show that the sum is direct, we will have to show that the only polynomial in U ∩ W is the zero polynomial.  

That is, we have to show that f(x) ∈ U ∩ W implies f(x) = 0.

To prove the above statement, we have to consider f(x) ∈ U ∩ W.

This means that f(x) is a polynomial which is divisible by x - 3 and f(3) = 0.  

Since the degree of the polynomial (f(x)) is 2, the only possible factorization of f(x) as x - 3 and ax + b.

Let's substitute x = 3 in f(x) = (x - 3)(ax + b) to get f(3) = 0.

Hence, we have b = 0.

Therefore, f(x) = (x - 3)ax = 0 implies a = 0.

Hence, the only polynomial in U ∩ W is the zero polynomial.

This shows that the sum is direct.

Now we have to show that the sum is equal to P2(R).

Let's consider any polynomial f(x) ∈ P2(R).

We can write it in the form f(x) = (x - 3)g(x) + f(3).

This shows that f(x) ∈ U + W. Since U ∩ W = {0}, we have P2(R) = U ⊕ W.

Therefore, we have,Basis of U = {x - 3}

Another subspace, W of P2(R) such that P2(R) = U ⊕ W is {p ∈ P2(R) : p(3) = 0}. The sum is direct and the sum is equal to P2(R).

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occurringGiven a total of 52 playing cards, comprising of Club, Spade, Heart, and Spade.

Probability of an event is given as

Probability of choosing a club is evaluated as

Probability of choosing a spade, without replacement

Thus, the probability of both events occuring (choosing a club, and then without replacement a spade) is given as

Hence, the probability of choosing a club, and then without replacement a spade is

The expectation, E(X²) of the random variable X is 2/3

Here we are given that the pdf or the probability density function of X is given by

4x³, where 0 < x < 1

clearly this is a continuous distribution. Hence we know that the formula for expectation for random variable X with probability density function f(x) is

∫x.f(x)

and, the formula for expectation

E(X²) = ∫x².f(x)

Hence here we will get

\(\int\limits^1_0 {x^2 . 4x^3} \, dx\)

here we will get the limits as 0 and 1 as we have been given that x lies between 0 and 1

simplifying the equation gives us

\(4\int\limits^1_0 {x^5} \, dx\)

we know that ∫xⁿ = x⁽ⁿ⁺¹⁾ / (n + 1)

hence we get

\(4[\frac{x^6}{6} ]_0^1\)

now substituting the limits will give us

\(4[\frac{1^6 - 0^6}{6} ]\)

= 4/6

= 2/3

The expectation, E(X²) of the random variable X is 2/3

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Answer:

The system of equations:

Solve by elimination.

Triple the first equation, double the second one, subtract the second from the first and solve for y:

Find x:

The solution is:

Simplifying in steps:

the point on the plane 7x - y + 7z = 70 nearest to the origin is (x, y, z) = (490/99, -70/99, 490/99).

What is Origin?

Origin is the beginning, middle, or beginning of something, or where one comes from. An example of origin is when an idea comes to you while you are sleeping. An example of an origin is the soil where oil comes from. An example of ancestry is your ethnicity.

To find the point on the plane 7x - y + 7z = 70 nearest to the origin, we can use the concept of perpendicular distance. The point on the plane closest to the origin will lie along the line perpendicular to the plane that passes through the origin.

The equation of the plane is 7x - y + 7z = 70. We can rewrite it in the form Ax + By + Cz + D = 0, where A, B, C are the coefficients of x, y, z respectively, and D is a constant.

In this case, A = 7, B = -1, C = 7, and D = -70.

The direction ratios of the line perpendicular to the plane are equal to the coefficients of x, y, z in the plane equation. Therefore, the direction ratios are (7, -1, 7).

Let's assume the coordinates of the point closest to the origin on the plane are (x, y, z).

The line passing through the origin and perpendicular to the plane can be parametrically represented as:

x = 7t

y = -t

z = 7t

Substituting these values into the equation of the plane, we get:

7(7t) - (-t) + 7(7t) = 70

49t + t + 49t = 70

99t = 70

t = 70/99

Substituting the value of t back into the parametric equations, we get:

x = 7(70/99) = 490/99

y = -(70/99) = -70/99

z = 7(70/99) = 490/99

Therefore, the point on the plane 7x - y + 7z = 70 nearest to the origin is (x, y, z) = (490/99, -70/99, 490/99).

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The area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ) is 294π square units.

To find the area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ), we need to evaluate the integral for half of the area and then double the result.

The curve of the limacon has a loop when 0 ≤ θ ≤ π, so we integrate from 0 to π. The area can be calculated as follows:

A = 2 ∫₀^π 1/2 r² dθ

Using the equation for r given, we can substitute and simplify:

A = 2 ∫₀^π 1/2 (7 - 14sin(θ))² dθ

A = 2 ∫₀^π 1/2 (49 - 196sin(θ) + 196sin²(θ)) dθ

A = ∫₀^π (98 - 392sin(θ) + 392sin²(θ)) dθ

Using the trigonometric identity 1 - cos(2θ) = 2sin²(θ), we can simplify further:

A = ∫₀^π (98 - 392sin(θ) + 196 - 196cos(2θ)) dθ

A = ∫₀^π (294 - 392sin(θ) - 196cos(2θ)) dθ

Integrating with respect to θ:

A = [294θ + 392cos(θ)sin(θ) + 98sin(θ)]₀^π

Evaluating at the limits of integration, we get:

A = [294π + 0 + 0] - [0 + 392cos(0)sin(0) + 98sin(0)]

A = 294π - 0 - 0 = 294π

Therefore, the area inside the loop of the limacon r = 7 - 14sin(θ) is 294π square units.

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The correct graph is A,

All the mentioned points are labelled into the graph.

The given equation is,

y = x² - 2x  - 3

Since we can see that it has degree 2

Therefore,

This is a quadratic equation.

Now after graphing this equation we get a parabolic curve,

A parabolic curve is a group of points that form a curve with each point on the curve being equidistant from the focus and the directrix.

Then,

The curve attached below.

Now in the graph,

when we reach at x = 2.5

We get value of y - 1.75

And when we go across y = 1 in the graph we get,

x = 0.75

These points are labelled on the graph below.

Brad needs to score between 26 and 78 on the fourth test to achieve a C for the semester.

To achieve a C for the semester, Brad's average score on the four tests needs to fall within the range of 70 to 79. Given that Brad has already completed three tests with scores of 83, 95, and 76, we can calculate the score he needs on the fourth test to maintain a C average.

Let's assume Brad's score on the fourth test is x. Since all four tests are equally weighted, the average score will be the sum of all four scores divided by four. Thus, we can write the equation:

(83 + 95 + 76 + x) / 4 = C

To find the range of scores that will give Brad a C (between 70 and 79), we can substitute the values for C:

70 ≤ (83 + 95 + 76 + x) / 4 ≤ 79

Now, we can solve this inequality to determine the range of scores for the fourth test:

280 ≤ 254 + x ≤ 316

Subtracting 254 from all sides:

26 ≤ x ≤ 78

Therefore, Brad needs to score between 26 and 78 on the fourth test to achieve a C for the semester.

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The formula for the total number of factors for a given number is given by; Total Number of Factors for N = (a+1) (b+1) (c+1)