5^-2 x ³√8

answer as a decimal

Answer:

a. 14:8

b. 6:14

Step-by-step explanation:

all books on the shelf = 6+8=14

a. 14:8

b. 6:14

The volume of the solid obtained by rotating the region over the function is given by the integral and V = 44.46 units³

Given data ,

The volume of the solid obtained by rotating the region underneath the graph of the function f(x)=√x² +9 over the interval [0,2] about the y-axis

The formula for Area under definite integral is

∫ₐᵇ f ( x ) = f ( b ) - f ( a )

Since we are rotating the region about the y-axis, the radius is simply the x-coordinate of each point on the curve, or r = x

The height h of each shell is equal to the difference between the y-coordinates of the curve at x and x + Δx, or h = f(x + Δx) - f(x)

Using these expressions for r and h, we can write the volume of each cylindrical shell as:

V(x) = 2πx[f(x + Δx) - f(x)]Δx

V = ∫₀² 2πx[f(x + Δx) - f(x)]dx

As Δx approaches zero, this integral becomes:

V = ∫₀² 2πx√(1 + (f'(x))²) dx

where f'(x) is the derivative of f(x), which is:

f'(x) = x/√(x² + 9)

Substituting this expression for f'(x) into the integral, we get:

V = ∫₀² 2πx√(1 + (x/√(x² + 9))²) dx

This integral can be evaluated using a substitution, u = x² + 9, du/dx = 2x, and dx = du/2x, to get:

V = ∫₉¹³ 2π(x² + 9)^(3/2)/2 dx

V = [4/5 π(x² + 9)^(5/2)]₉¹³

V = 44.46 units³

Hence , the volume of the solid is 44.46 units³

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There are 6435 ways to direct the inquiries to any two of the firm's real estate agents.

What is combinations?

Combinations are a mathematical concept used to count the number of ways that a certain number of items can be selected from a larger set of items without regard to the order in which they are selected.

We can use combinations to solve this problem. We need to choose 8 inquiries out of 16 for the first agent, and the remaining 8 inquiries will be handled by the second agent.

The number of ways to choose 8 inquiries out of 16 is:

C(16, 8) = 16! ÷ (8! * (16-8)!) = 12870

This is the number of ways the inquiries can be directed to one agent. Since there are two agents and each handles 8 inquiries, we need to divide this number by 2 to avoid counting each arrangement twice:

12870 ÷2 = 6435

Therefore, there are 6435 ways to direct the inquiries to any two of the firm's real estate agents.

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To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.

Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.

First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.

Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.

Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.

The equation of the line passing through the points (6, 5) and (8, -2) is[tex]y = -\frac{7}{2} x + 26[/tex].

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Determine the slope of the line.

Given the two points are (-7, -3) and (1, 2)

We can find the slope of the line by using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values:

m = (-2 - 5) / (8 - 6)

m = -7/2

Using the point-slope form, plug in one of the given points and slope m = -7/2 to find the equation of the line.

Let's use the point (6, 5):

y - y₁ = m(x - x₁)

[tex]y - 5 = -\frac{7}{2}( x - 6 )\\\\y - 5 = -\frac{7}{2} x + 21\\\\y = -\frac{7}{2} x + 21 + 5\\\\y = -\frac{7}{2} x + 26[/tex]

Therefore, the equarion of the line is [tex]y = -\frac{7}{2} x + 26[/tex].

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Answer:x=-8

Step-by-step explanation:

3.2+(−1/2)x−2=4.8x+2−5.2x

−0.1x=0.8

x=-8

Answer:

x=-8

Step-by-step explanation:

x=-8

The statement that is true on the linear relationship between the brochures and cost of printing is A. the printing fee is $ 2.50.

To find the printing fee, find the difference between the total cost of two different numbers of brochures printed.

The printing fee is:

= ( Total cost of 43 - total cost of 40 ) / ( Difference between 43 and 40 )

= ( 607.50 - 600 ) / ( 43 - 40 )

= 7. 50 / 3

= $ 2. 50

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Answer: (4x - √3)(4x + √3).

Step-by-step explanation: Use factoring. The equation (when factored out) is: ax^2 + bx + c. Hence, the equation you wrote rewritten is: 16x^2 + 0x - 3. (√3)(√3) = 3 and (4x)(4x) = 16x^2. It is divisible.

So, the quadratic function f(x) = 16x^2 - 3 can be expressed as a product of linear factors as (4x - √3)(4x + √3).

To find the multiplicative inverse of 2i, we need to find a complex number z such that:

(2i) * z = 1

Multiplying both sides by -i, we get:

z = -i/2

Therefore, the multiplicative inverse of 2i is -i/2.

To solve the equation -10(x-1.7)=-3 by expanding first, we need to apply the distributive property of multiplication.

Expanding -10(x-1.7), we get

-10x + 17 = -3

Now we can solve for x by isolating the variable on one side of the equation. To do this, we'll add 10x to both sides of the equation

-10x + 17 + 10x = -3 + 10x

Simplifying, we get

17 = 10x - 3

Next, we add 3 to both sides of the equation

17 + 3 = 10x - 3 + 3

Simplifying, we get

20 = 10x

Finally, we divide both sides of the equation by 10 to isolate x

20/10 = 10x/10

Simplifying, we get

2 = x

Therefore, the solution to the equation -10(x-1.7)=-3 by expanding first is x = 2.

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There were 56 students in Mr Tan's class.

To solve this problem, we can use the formula for average: average = (sum of all values) / (number of values). Let's assume that there were initially n students in Mr Tan's class, and the average amount collected was x. Then, we can write:

nx = sum of all amounts collected

Now, if three students each collected $32 less, the new sum of amounts collected would be:

(nx - 3*32) = (n-3)(x-32)

And the new average would be:

(n-3)(x-32) / n = 146

Similarly, if eight students each collected $18 more, the new sum of amounts collected would be:

(nx + 8*18) = (n+8)(x+18)

And the new average would be:

(n+8)(x+18) / n = 156

Now we have two equations with two unknowns (n and x). We can solve them using algebraic manipulation. After some simplification, we get:

n = 56 and x = 104

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Answer:

84

Step-by-step explanation:

Trust me

Answer:

84

Step-by-step explanation:

There are 9 pieces of luggage.

We can select the first piece 9 different ways, the second piece 8 different ways, since there are only 8 pieces left.  The third piece can be selected 7 different ways.

9*8*7

504

But order doesn't matter since we are taking 3 pieces.

Divide by (3*2*1)

504/6 = 84

There are 84 different combinations of luggage

a) The volume of the box can be expressed as V = x(20-2x)(6-2x) cm³.

b) The domain of V is [0, 3) in interval notation.

c) The dimensions of the box that maximize the volume are L = 40/3 cm, W = 2/3 cm, and H = 10/3 cm.

d) The maximum volume is 160/27 cm³.

(a) To form the box, squares of side x are cut out of each corner. So, the length of the box will be (20-2x) cm and the width of the box will be (6-2x) cm.

Since the height of the box is x cm, the volume of the box can be expressed as

V = x(20-2x)(6-2x) cm³.

(b) The domain of V is the set of all possible values of x for which the length, width, and height of the box are positive. This is equivalent to the condition that 0<x<3. So, the domain of V is [0, 3) in interval notation.

(c) To maximize the volume, we need to find the critical points of V. Differentiating V with respect to x, we get

dV/dx = 4x³ - 52x² + 120x.

Setting dV/dx = 0, we get

x = 0 or x = 3 or x = 10/3.

Since the domain of V is [0, 3), we need to check the values of V at x = 0 and x = 3.

We also need to check the value of V at the critical point x = 10/3. Evaluating V at these values, we get

V(0) = V(3) = 0

and

V(10/3) = 160/27.

(d) To find the dimensions of the box that maximize the volume, we substitute the value of x = 10/3 into the expressions for the length, width, and height of the box.

So, the length of the box is

20-2(10/3)

= 40/3 cm,

the width of the box is

6-2(10/3)

= 2/3 cm, and

the height of the box is 10/3 cm.

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Answer:

(x, -1/2x + 5/2) or infinitely many solutions

Step-by-step explanation:

We can solve the system of equations using substitution.  We can start by isolating x in the first equation.  Then, we can plug in the entire equation made from isolating for x in the second equation, which will allow us to find y:

Isolating:

x = -2y + 5

Plugging in and solving for y:

4(-2y + 5) + 8y = 20

-8y + 20 + 8y = 20

20 = 20

We see that we get a constant equal to another constant.  Whenever you get this as a solution to a system of equations, this means that there are infinitely many solutions. We can express the general rule for the solution in coordinate form by isolating y in at least one of the equations:

y = -1/2x + 5/2

Thus, the general rule for the solution to the system of equations is

(x, -1/2x + 5/2), so you can either put this general rule as the answer or write solution = infinitely many solutions

You can see that there are infinitely many solutions by plugging in any number for x into the two equations and see that you get 5 for the equation and 20 for the second equation.  Let's try 4 for x and 0 for x:

4 for x in first equation:

4 + 2(-1/2(4) + 5/2) = 5

4 + 2(0.5) = 5

4 + 1 = 5

5 = 5

4 for x in the second equation

4(4) + 8(-1/2(4) + 5/2) = 20

16 + 8(0.5) = 20

16 +4 = 20

20 = 20

0 for x in the first equation:

0 + 2(-1/2(0) + 5/2) = 5

0 + 2(2.5) = 5

5 = 5

0 for x in the second equation:

4(0) + 8(-1/2(0) + 5/2) = 20

0 + 8(2.5) = 20

20 = 20

The correct statements are,

B)It has two faces that are decagons.

C)It has 11 faces.

D)It has 20 edges.

What is decagonal pyramid?

A decagonal pyramid is a solid whose base is a decagon or a ten sided figure, regular or irregular. The surfaces are ten isosceles triangles, in case of a regular decagonal pyramid with all the ten vertices meeting at a point.

Here The decagonal prism is formed by two regular decagons as its bases and 10 squares as its other faces. the top of the decagonal prism is a regular decagon, so is the bottom face.

We know that decagonal pyramid has 11 faces and 20 edges and 11 vertices.

Hence the correct statements are,

B)It has two faces that are decagons.

C)It has 11 faces.

D)It has 20 edges.

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The expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.

The perimeter of a triangle is the sum of the lengths of its sides. Using the given expressions for the side lengths of the triangle, we can write the perimeter as:

(6.1w + 7.8) + (1.4w + 8.1) + (8.7x + 2.5)

Simplifying and combining like terms, we get:

7.5w + 11.2x + 18.4

Therefore, the expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.

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Answer:

Step-by-step explanation:

2

2-9=-7

In negative numbers, the greater number that is negative is less than the smaller negative number. For example, -9<-8. Even though 9 is a bigger number when positive, it's the opposite for negative numbers. While there can be many numbers for k like 0,1, or 2, 1 will probably be the best answer.

Answer:

Step-by-step explanation:

[tex]\mathrm{ k - 9 < - 6}[/tex]

Add both sides by 9 :-

Simplify :-

___________________

Hope this helps!

Answer:

Your answer is E) 1/2 , -6 , 5

Step-by-step explanation:

Find the slope between (-6,5) then simplify and you will get 1/2

Answer:

Step-by-step explanation:

well if you know the term than you know the pattern

Answer:

w≤9

Step-by-step explanation:

8w ≤ 72

Divide by 8 on both sides

w ≤ 9

For graph, draw a number line and label a point as 9. Draw a solid line facing to the left and having a closed point at 9. The line should not extend past 9.

There are 10,080 possible ways for the 15 people to stand if the people from each borough insist on standing together.

If there are 15 people from the Bronx, Brooklyn, Manhattan, Queens, and Staten Island, and each borough has 3 people, then there are 5 groups of 3 people. If the people from each borough insist on standing together, we can treat each group of 3 people as a single entity. So, we have 5 entities that need to be arranged.

The number of ways to arrange these 5 entities is 5!, which is equal to 120. However, within each group of 3 people, there are 3! ways to arrange the people. So, we need to multiply the number of ways to arrange the groups by the number of ways to arrange the people within each group. We will get the answer

5! × (3!)⁵ = 120 × 3⁵ = 10,080

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Answer:

False

Step-by-step explanation:

The reason for it being false is because 2X = 25 should be divided to by 2 to get to X, which should be half of 25.

therefore X should equal 12.5

VZ is 92.5. WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.

what is midsegment  ?

A midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle. It is also known as a midline. The midsegment of a triangle is parallel to the third side of the triangle, and its length is half the length of the third side.

In the given question,

Since WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.

Let's call the length of AX as L. Then, we have:

WY = 11t = 1/2 L

Multiplying both sides by 2, we get:

22t = L

Now, we can use this information to find VZ. Since WY is also parallel to VZ, we have:

WV = VZ

Substituting WV = L/2 and VZ = 5t + 51, we get:

L/2 = 5t + 51

Substituting L = 22t, we get:

22t/2 = 5t + 51

11t = 5t + 51

6t = 51

t = 8.5

Substituting t = 8.5 in the equation for VZ, we get:

VZ = 5t + 51 = 5(8.5) + 51 = 92.5

Therefore, VZ is 92.5.

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The simplified form of given expression a³/a⁶b⁻¹ is b/a³.

Hence, the correct option is C.

Exponents are a shorthand notation used in mathematics to represent repeated multiplication of a number by itself. The exponent is a small number written to the right and above a base number, and indicates how many times the base should be multiplied by itself.

In the given expression, a³/a⁶b⁻¹

We can apply the rules of exponents, and we get

= a³⁻⁶/b⁻¹

= a⁻³/b⁻¹

= b/a³

Hence, the correct option is C.

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The total area of the front of the figure is 21 [tex]feet^{2}[/tex].

What is the area?

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.

To find the total area we need to add the area of the refrigerator and the area of the freezer.

The top part i.e refrigerator has a height of 5 feet and 3 feet width

Area of the refrigerator section = height * width

                                                       = 5 * 3

                                                       = 15 [tex]feet^{2}[/tex]

The bottom part i.e freezer has a height of 2 feet and 3 feet width

Area of the refrigerator section = height * width

                                                       = 2 * 3

                                                       = 6 [tex]feet^{2}[/tex]

The total area of the front of the figure is = Area of the refrigerator section + Area of the freezer section

                                                                   = 15 + 6 = 21[tex]feet^{2}[/tex]

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The equation of the ellipse  derived as is

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1.

The equation of foci is

F₁ = (h - √(a^2 - b^2), k) , F₂ = (h + √(a^2 - b^2), k)

An ellipse is  described as a set of points in a plane such that the sum of the distances from each point to two fixed points, called foci, is constant.

We can write the equation of an ellipse as:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

where (h, k) = the center of the ellipse,

a = the semi-major axis,

and b = the semi-minor axis.

The foci of the ellipse are located along the major axis and are equidistant from the center, with a distance of : √(a^2 - b^2).

we know also the formula to find the foci of an ellipse is:

F₁ = (h - √(a^2 - b^2), k)

F₂ = (h + √(a^2 - b^2), k)

The sum of the distances from each point on the ellipse to the foci is constant. The equation can then be written as:

2a = √((x - h + √(a^2 - b^2))^2 + (y - k)^2) + √((x - h - √(a^2 - b^2))^2 + (y - k)^2)

Simplifying, we then can write  the equation of the ellipse as:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

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The weight of the empty tank is given as follows:

4 pounds.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The weight of the empty tank is the intercept of the function, which is of b = 4, hence:

4 pounds.

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An ordered pair that describes a point that should be removed from the graph so that the graph represents a function include the following: A. (1, 1).

In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the graph shown below, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);

3  → 1

1 → 1

In this context, we can reasonably infer and logically deduce that either (3, 1) or (1, 1) must be removed from the graph in order to represent a function.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

-13n + 5

Step-by-step explanation:

Give:

– 7n + –3 – 6n + 3 + 5

To Find:

simplify

Explanation:

– 7n + –3 – 6n + 3 + 5

= (-7n - 6n) + (-3 + 3 + 5)

=  - 13n + 0 + 5

= -13n + 5

Final Answer:

-13n + 5

Answer:

Step-by-step explanation:

There are 6 possible outcomes when rolling a single cube (1, 2, 3, 4, 5, or 6). When rolling two cubes, the possible sums range from 2 (1+1) to 12 (6+6). Using the chart provided, we can see that the sum of two cubes being equal to 5 only occurs once in the 36 possible combinations: when one cube shows a 1 and the other cube shows a 4.

To find the expected number of times this sum will occur if Tamara rolls the cubes 180 times, we need to multiply the probability of this event occurring on any given roll by the number of rolls. The probability of rolling a sum of 5 is 1/36, since there is only one way to get a sum of 5 out of the 36 possible combinations. Therefore, the expected number of times this sum will occur in 180 rolls is:

(1/36) x 180 = 5

So Tamara should expect to roll a sum of 5 about 5 times in 180 rolls of two cubes.