Estimate the following product using a power of ten

Answer:

3/36 or 1/12

Step-by-step explanation:

there are a possible 36 outcomes

probability of rolling a ten has 3 chances of happening:

5, 5

4, 6

6, 4

Answer:

the domain of f/g consists of numbers x for which g(x) IS NOT EQUAL 0 that are in the domain of both f(x) and g(x)

Step-by-step explanation:

The denominator of a rational function can't be zero (see the first row in the attached table)

The required fill in the blanks is ≠ , f(x) and g(x).

It is required to fill in the blanks.

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The domain of f/g consists of numbers x for which g(x) IS NOT EQUAL 0 that are in the domain of both f(x) and g(x).

The domain of (f/g) (x) consists of all x-values that are in the domain of both f and g, where g(x) ≠ 0. Both f and g have domain all real numbers.

Therefore, the required fill in the blanks is ≠ , f(x) and g(x).

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A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces connecting them. It is a polyhedron with six faces, nine edges, and six vertices.

The two triangular bases of a triangular prism are congruent and parallel to each other. The rectangular faces are perpendicular to the triangular bases, and their lateral edges connect the corresponding vertices of the triangular bases.

The triangular bases are identical and parallel to each other. Each base has three vertices, three edges, and one face.There are three rectangular lateral faces connecting the corresponding vertices of the triangular bases. Each lateral face has two edges and one face.

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The perimeter of Max's sandbox is 21 feet.

The sum of each length of external sides or boundary of a given figure is called its perimeter. To determine the perimeter of an object, add up the length of its boundaries.

Given the dimension of the Ohio park, then we have to determine the representative fraction of Max's sandbox.

Representative fraction = 10/ 25

                                       = 2/ 5

So that;

x = 15 * 2/5

  = 6 ft

y = 12.5 *2/5

  = 5 ft

The perimeter of Max's sandbox = 10 + y + x

                                                      = 10 + 5 + 6

                                                      = 21 ft

The perimeter of Max's sandbox is 21 feet.

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The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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Answer:

249798.8

Hope this helps! <3

The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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Answer:

3

Step-by-step explanation:

Answer:

please mark brainliest!

Step-by-step explanation:

15 centavos

The reflection of F(x) = x⁴, across the line y = x, results in the function \(y = F(x) = \pm \sqrt[4]x\), making option A the right choice.

For any function f(x), the reflection across the line y = x, gives the inverse of the function f(x).

In the question, we are asked for the equation, representing the reflection of f(x) = x⁴, across the line y = x.

The function can be shown as:

y = f(x) = x⁴,

or, x⁴ = y,

or, \(x = \pm\sqrt[4]{y}\)

Changing the variables to general form, that is, y as the dependent variable and x as the independent variable, we get the inverse function as, \(y = F(x) = \pm \sqrt[4]x\).

Thus, the reflection of F(x) = x⁴, across the line y = x, results in the function \(y = F(x) = \pm \sqrt[4]x\), making option A the right choice.

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The complete question is:

"Which of the following equations represents F(x) = x⁴ reflected across the line y = x?

A. \(F(x)= \pm\sqrt[4]{x}\)

B. \(F(x)= \sqrt[4]{x}\)

C. \(F(x)= \pm x^4\)

D. \(F(x)=- \sqrt[4]{x}\) "

Answer:

Step-by-step explanation:

8 in × (1 ft)/(12 in) = ⅔ ft

36 ft × 58 ft × ⅔ ft = 1392 ft³

1392 ft³ × (1 yd³)/(27 ft³) ≅ 52 yd³

52 yd³ × $123/yd³ = $6396

The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

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The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

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Answer:

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time =

Time =

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

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Step-by-step explanation:

The value of the double integration is 7776 after solving and integration. the answer is 7776.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

It is given that:

Double integration (x + y) dA

y = x²

y² = 216x

y = √216 √x

∫∫(√216 √x +  x²)

After solving:

\(\rm \int _0^{36}\int _0^6\:\left(\sqrt{216}\:\sqrt{x}\:+\:\:x²\right)dxdy\)

=7776

Thus, the value of the double integration is 7776 after solving and integration. the answer is 7776.

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Answer:

Use the drop-down menus to complete the statements.

What is 4 ÷  

1

3

?

This problem asks how many groups of  

1/3

are in  

4

.

The quotient of 4 ÷  

1

3

 is  

12

.

Step-by-step explanation:

The completed statements with respect to the parts on the number line are;

What is 4 ÷ 1/3; 12

This problem asks how many groups of 1/3 are in 4

The quotient of 4 ÷ (1/3) is; 12

A number line is a visual representation of the set of real numbers. A number line is a straight line on which each point corresponds to a number. The points on the line are evenly spaced, with the distance between two points representing the difference between the numbers.

The question asks how many groups of 1/3 are in 4, which is equivalent to dividing 4 by 1/3, which can be expressed as 4 ÷ 1/3

To divide a number by a fraction, we can multiply the number by the reciprocal of the fraction.

The reciprocal of a fraction is obtained by flipping the numerator and denominator. The reciprocal of 1/3 is 3/1 which is 3. The expression can therefore, be expressed as follows;

4 ÷ (1/3) = 4 × 3 = 12

The quotient of 4 ÷ (1/3) is 12, which indicates that the number of groups of 1/3 in 4 are 12

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The central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

Given that, a survey was conducted in which 2400 people were asked to name their favorite sport to watch and the table below shows their answers: Sport percentage of people are:

Football 29%

Soccer 9%

Baseball 14%

Basketball 8%

Hockey 8%

Other 32%

We need to find the central angle measure, x, for the Baseball slice in the circle graph.

For this, we need to use the formula that gives the central angle measure in degrees for a sector of a circle:

Central angle measure = (Percentage/100) × 360°

Now, using the above formula, we can calculate the central angle measure for each sport as shown below:

Football: (29/100) × 360° = 104.4°

Soccer: (9/100) × 360° = 32.4°

Baseball: (14/100) × 360° = 50.4°

Basketball: (8/100) × 360° = 28.8°

Hockey: (8/100) × 360° = 28.8°

Other: (32/100) × 360° = 115.2°

The sum of all central angle measures should be 360°, which is the measure of a full circle.

So we can check if the calculations are correct: 104.4° + 32.4° + 50.4° + 28.8° + 28.8° + 115.2° = 360°

We see that the sum is indeed 360°, so the calculations are correct. The central angle measure for the Baseball slice is 50.4°.

Therefore, the central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

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Answer:

180

Step-by-step explanation:

From the table :

Slope :

m = (y2 - y1) / (x2 - x1)

m = (100 - 80) / (5 - 4)

m = 20 / 1

m = 20

y = 20x

Hence, when, x = 12

y = 20 * 12

y = 240

From the graph:

Slope :

m = (y2 - y1) / (x2 - x1)

m = (280 - 70) / (8 - 2)

m = 210 / 6

m = 35

y = 35x

When x = 12

Graph :

y = 35 * 12

y = 420

Difference :

420 - 240

= 180

The simplified expression is 1,675,616. the value of the expression is 1,675,616.

To find the simplified expression and the value of 6 raised to a power, follow the steps given below:

Step 1: Simplify the expression Firstly, the simplified expression is obtained by using the rule of exponents, which states that if a number raised to a power is multiplied by the same number raised to another power, then the resulting power is the sum of the two powers.

6 raised to the power of 2 is 6 × 6 = 36.6 raised to the power of 3 is 6 × 6 × 6 = 216.6 raised to the power of 4 is 6 × 6 × 6 × 6 = 1296.6 raised to the power of 5 is 6 × 6 × 6 × 6 × 6 = 7776.

Step 2: Find the value of the expression

From these results, it can be seen that when 6 is raised to an even power, the resulting number is even, and when 6 is raised to an odd power, the resulting number is odd. This is because 6 is an even number.

In general, if a number is even, then the result obtained when it is raised to an even power is even, and the result obtained when it is raised to an odd power is odd.

If a number is odd, then the result obtained when it is raised to any power is odd. 6 raised to the power of 8 can be written as 6 raised to the power of 4 raised to the power of 2, as shown below 6 raised to the power of 8 = (6 raised to the power of 4) raised to the power of 2= 1296 raised to the power of 2= 1,675,616

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Answer: You are correct, the answer if F. If I got it correct, can you please tell me?

Answer:

60

Step-by-step explanation:

TOTAL SURFACE AREA = AREA OF SQUARE+2×(AREA OF TRIANGLE)

=(6×6)+2×(1/2×6×4)

=36+24=60 square inches

I hope it helped you

Answer:

The area of the full figure is 60 square inches.

Step-by-step explanation:

There are 4 triangles and one square in this figure. We can start by figuring out the area of the middle square, which would be \(6*6=36\) because we know the sides are all 6 inches.

Next, we can look at the triangles and see that their hypotenuses (the longest sides) are all the same length, that being 5 inches. This means that we only need to find the length of the third side and then multiply the area of one triangle by 4 to get the area of all the triangles.

The pythagorean theorem states that in any right triangle, \(a^2 +b^2=c^2\), with \(c^2\) being the length of the hypotenuse. Since we know the length of the hypotenuse is 5 and one of the legs of the triangle is 4, we can insert this into the equation: \(a^2+4^2=5^2\), which when simplified all the way gives us that \(a=3\).

Since a right triangle is half of a rectangle, the easiest way to find the area of the triangle is to multiply the measures of the two legs together and then divide by two: \((3*4)/2=6\). Therefore, we know that each triangle in the picture has an area of 6.

Finally, you need to add all of the areas together to find the area of the full figure: \(36+6+6+6+6=60 in^2\)

The area of the full figure is 60 square inches.

Hope this helps! :)

Answer:

6x+6x2+3

Step-by-step explanation:

6x2+5x+1+x+2

Combine 5x and x to get 6x.

6x2+6x+1+2

Add 1 and 2 to get 3.

6x2+6x+3

The volume of the solid is 250r³ when  the base of s is a circular disk with radius 5r.

Given that,

We have to discover the described solid's volume, v. The parallel cross-sections perpendicular to the base of s are squares, and the base of s is a circular disk with radius 5r.

We know that,

A cylinder is a solid with square cross sections parallel to the bases and circular bases. Its height is equal to the base circle's diameter.

The radius = 5r,

So the height = diameter = 10r

Volume of the cone is base × height= πr²×h

=π(5r)²×(10r)

=250πr³

Therefore, The volume of the solid is 250r³ when  the base of s is a circular disk with radius 5r.

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Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

\(\begin{array}{|c|ll}\cline{1-1}\textit{a\% of b}\\\cline{1-1}\\\left( \cfrac{a}{100} \right)\cdot b\\\\\cline{1-1}\end{array}~\hspace{5em}\implies \stackrel{\textit{6.25\% of 859.99}}{\cfrac{6.25}{100}\cdot 859.99} ~~\approx ~~53.75\\\\\\~\hfill \stackrel{\textit{total cost for the bike}}{859.99+53.75 ~~\approx~~ 913.74}~\hfill\)

The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.

As per the given data, the given formula is:

\($T=2 \pi \sqrt{\left(\frac{L}{32}\right)}\) gives the time it takes in seconds.

Where,

T is the time it takes for a pendulum to make one full swing back and forth (in seconds).

L is the length of the pendulum, in feet.

Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.

Substitute the given parameters into the formula will give;

\($1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}\)

Now divide both sides by 2π.

\($ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\\)

\($ 0.3024=\sqrt{\left(\frac{L}{32}\right)}\)

Then taking square on both sides.

\($ (0.3024)^2=\frac{L}{32} \\\)

0.09144576 = \($\frac{L}{32}\)

Later multiply both sides by 32.

2.9262 = L

The approximate value of the length of a pendulum:

L ≈ 3

Therefore, the length of a pendulum is about 3 feet.

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Answer:

y=2.9

Step-by-step explanation:

The constant proportion of y = 2.9x is 2.9.

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

Example:

2x + 3 = 9 is an equation.

We have,

y = 2.9x

This can be written as,

y ∝ x

y = kx

Where k is the constant of proportionality.

Now,

Comparing y = kx and y = 2.9x

k = 2.9

Thus,

The constant proportion is 2.9.

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Answer:

70cm

Step-by-step explanation:

Given height of the lamp;

    Height of lamp = 28inches

 Unknown:

The height in cm;

Solution:

       1 inch = 2.5cm

So;

          28 inches will be 28  x 2.5  = 70cm

Answer:

The surface area is \(379.94in^2\)

Step-by-step explanation:

Given

Shape: Sphere

\(D= 11\ in\) - -- Diameter

Required

Determine the surface area (A)

This is calculated using:

\(A = 4\pi r^2\)

Where

\(r = \frac{1}{2}D\)

\(r = \frac{1}{2}*11\)

\(r = 5.5\)

So, we have:

\(A = 4 * 3.14 * 5.5^2\)

\(A = 4 * 3.14 * 30.25\)

\(A = 379.94\)

Hence, the surface area is \(379.94in^2\)

Answer:

379.94

Step-by-step explanation: