What is 2 to the power of 3?

Answer:

\( \frac{3( {5}^{8} - 1) }{5 - 1} = 292968\)

The table can be summarized as follows:

|          | Has a dog | Does not have a dog |

|----------|-----------|---------------------|

| Has a cat     | 2         | 3                   |

| Does not have a cat | 12        | 10                  |

To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.

The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.

The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.

So, the probability that a student chosen randomly from the class has a cat is 5/27.

Answer:

(5,0)

Step-by-step explanation:

The # 5 is on the x axis and there is no value for the y since it is 0. This means that this ordered pair will be located on the x-axis.

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

Answer:

4x^2 - 12x + 9

Explanation:

(2x - 3)^2

(2x - 3)(2x - 3)

2x(2x - 3) -3 (2x - 3)

4x^2 - 6x - 3 (2x - 3)

4x^2 - 6x - 6x + 9

4x^2 - 12x + 9

Answer:

The probability that a  randomly selected point within the  circle falls in the red shaded area is p=0.75.

Step-by-step explanation:

We have to calculate the probability that a randomly selected point within the circle falls in the red shaded area.

This probability can be calculated as the quotient between the red shaded area, that is a regular pentagon inscribed in the circle, and the area of the circle.

We start by calculating the area of the circle:

\(A_c=\pi r^2\approx 3.14(4)^2=3.14\cdot 16=50.24\)

Then, we can calculate the area of the pentagon as:

\(A_p=\dfrac{1}{2}\cdot (5a)\cdot S=\dfrac{1}{2}\cdot (5\cdot3.2)\cdot 4.7=37.6\)

Then, we can calculate the probability p as the quotient between the areas:

\(p=\dfrac{A_p}{A_c}=\dfrac{37.6}{50.24}\approx 0.75\)

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

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The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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Answer: 24

Step-by-step explanation:

To find the area of the composite figure, we need to find the area of the sector and the area of the triangle and then add them together.

Area of sector = (θ/360) * π * r^2, where θ is the angle of the sector in degrees, r is the radius of the circle.

The angle of the sector can be found by subtracting the angle of the triangle from 360 degrees. The radius of the circle can be found by dividing the length of the arc by the angle of the sector.

Length of the arc = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 4 = 4.19

Radius of the circle = 4.19/60 = 0.07

Angle of sector = 360 - 60 = 300 degrees

Area of sector = (300/360) * 3.14 * 0.07^2 = 0.0041

The area of the triangle can be found using the formula:

Area of triangle = (1/2) * base * height = (1/2) * 8 * 6 = 24

Therefore, the total area of the composite figure is:

0.0041 + 24 = 24.0041

Rounding to the nearest hundredth, the area of the composite figure is approximately 24.00.

The ratio of diameter to height that minimizes the surface area of a cylindrical can while holding a specific volume is: diameter/height = 2r/h

= 2(√(V/2π))/(2√(V/2π)) = 1

What is area ?

Area is a measure of the size of a two-dimensional surface or shape. It is the amount of space inside a closed boundary, such as a square, rectangle, circle, or any other shape.

A = 2πrh + 2πr²

where r is the radius of the can, h is the height of the can, and π is a constant (approximately equal to 3.14).

The volume of the can is given by:

V = πr²h

We want to find the ratio of diameter to height that minimizes the surface area of the can while holding a specific volume. We can use the volume formula to solve for one variable in terms of the other:

h = V/πr²

Substituting this expression for h into the surface area formula, we get:

A = 2πr(V/πr²) + 2πr²

Simplifying, we get:

A = 2V/r + 2πr²

To minimize the surface area, we need to find the value of r that makes the derivative of A with respect to r equal to zero:

dA/dr = -2V/r² + 4πr

Setting this equal to zero, we get:

-2V/r² + 4πr = 0

Solving for r, we get:

r = √(V/2π)

Substituting this value of r back into the expression for h, we get:

h = 2√(V/2π)

Therefore, the ratio of diameter to height that minimizes the surface area of a cylindrical can while holding a specific volume is: diameter/height = 2r/h = 2(√(V/2π))/(2√(V/2π)) = 1

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d) n + (n +1) = 67

1) Let's call the first number as n, and its consecutive as n +1

Then we can write:

n + (n +1) = 67

n +n +1 = 67

2n +1 = 67

2n = 66

n= 33

and n+1 = 34

2) Hence, the answer is n + (n +1) = 67

Answer:

4 batches

Step-by-step explanation:

one batch calls for:

3/4 PB

1 1/2 cup SG

1 EGG

3/.75(3/4)= 4

9/1.5(1 1/2)=6

5/1= 5

The maximum number of batches she can make before running out of ingredients is 4

The equation of the line is y = 3x + 8

The equation is given as:

y = 3x - 5

A linear equation is represented as:

y = mx + b

Where m represents slope;

This means that:

m = 3

Let the slope of the required line be n.

Since the lines are parallel, then

n = m = 3

The linear equation is then calculated as:

y = n(x - x1) + y1

Where:

(x1,y1) = (-2,2)

This gives

y = 3(x +2) + 2

Expand

y = 3x + 8

Hence, the equation of the line is y = 3x + 8

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Answer:

I think there's 502

Step-by-step explanation:

if this is a olunomical question that should be it I believe, because you have to write in standered form then when it equals zero, then factor it

Answer:

\(\displaystyle S = \frac{N + F}{P - V}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

\(\displaystyle N = S(P - V) - F\)

Step 2: Solve for S

Rearrange.

Answer:

r = 3.5 acre/hour

Step-by-step explanation:

Rate of Change

Farmer Fran had harvested 2 acres of pomegranates at 10:00 A.M. At noon (12:00 P.M.) she had harvested 9 acres.

From both times, 2 hours had passed. During that time, she harvested 9-2=7 acres.

The rate of harvesting is:

\(r=\frac{7}{2}\ acre/hour\)

Or, expressed in decimal:

r = 3.5 acre/hour

Answer:

with one pound of pizza dough you can make one large pizza or two 10-inch pizzas.

so 15 Large pizzas or 30 10 in pizzas

Step-by-step explanation:

Answer: 1.9 inches

Step-by-step explanation:

- the equation to find the volume of a cylinder is V = π r^2 h

- so we can just change this equation around to H = V / π r^2

- so H = 384/ π 8^2 = 1.91 or 1.9

hope this helps :)

Answer:

$63

Step-by-step explanation:

Find out the total amount of units that Jack and Molly have.

5 + 6 = 11

11 units = $77

Find out 1 unit to be able to find out how much Evan receives.

1 unit = $77 ÷ 11 = 7

Evan has 9 units, so find out how much money is 9 units.

9 units = 7 x 9 = $63

A and B measure the same because they are Exterior opposite angles.

Then,

5x = 4x + 12

5x - 4x = 12

x = 12

Check

5x = 5(12) = 60

4(12) + 12 = 48 + 12 = 60

Then, x = 12

Ok, so

Here we have a rectangular prism with the following measures:

-Length = 4ft

-Height = 3ft

-Width = 3ft.

Remember that the surface area of a rectangular prism can be found using:

Where "l" is the length, "w" is the width, and "h" is the height.

If we replace our values in the equation given, we got that:

Therefore, the surface area of the prism is 66 ft2.

9514 1404 393

Answer:

  $0 -- y-intercept

  $10 per hour -- slope

Step-by-step explanation:

We would need to see grid lines on the graph, or the point in the upper right corner to be sure. It appears as though the slope is about $40 / 4 h, or $10 per hour.

The y-intercept is the point at lower left, (0, 0).

Answer:

Step-by-step explanation:

Surface area is:

Substitute x:

Answer: 64 boots in total

Step-by-step explanation:

Since a pair is 2, and there are 32 students that need a pair each, 32 x 2 = 64.

Answer:

263.76in^2

Step-by-step explanation:

210/360*3.14*12*12

7*3.14*12

263.76

Answer:

A is the correct answer.

Step-by-step explanation:

good luck with college.

The answer to the given problem can be stated as, "The quadrilateral is most specifically a square because all of its sides are equal and angles are right angle."

A square is type of rectangle of which all sides are equal.

The diagonals of a square are perpendicular bisector of each other.

The given diagram of the quadrilateral clearly shows the following information,

All the angles of the quadrilateral are equal to right angle,

And, all of its sides are equal.

The given information matches with the property of a square which implies that the given quadrilateral is a square.

Hence, the given quadrilateral is a square.

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Answer:

Step-by-step explanation:

We need to identify the quadrilaterals given in the question.

For first image , we can see that;

These are the properties of rhombus in which all sides and opposite angles are equal.

Hence in the first image quadrilateral is a " Rhombus" .

\(\rule{200}2\)

In the second image , the most appropriate option is all sides are equal , as in rhombus all sides are congruent.

Answer:

Area : (25*7)/2=87,5m²

Step-by-step explanation: