a cube with a surface area of 6 square inches is removed from the corner of a cube with a surface area of of 96 square inches.
questions
a. what do you think removing the smaller cube from largers cubes has on its surface area? explain your answer
b. find the surface area of the new solid.

Does the relation represent a function: C. Yes, because for each input there is exactly one output.

In Mathematics and Geometry, a function can be defined as any mathematical equation which is typically used to define and represent a relationship that exists between two or more variables such as an ordered pair, points on a graph or table.

Based on the mapping diagram, we can reasonably infer and logically deduce that the relation represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the relation represent a function because for each input (independent value) there is exactly one output (dependent variable).

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The value of the expression 28 - {15 (3+2)} is -47.

To evaluate the expression 28 - {15 (3+2)}, we need to follow the order of operations (also known as PEMDAS/BODMAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break down the expression step by step:

First, we solve the expression inside the parentheses:

3 + 2 = 5

Now, we substitute the result back into the original expression:

28 - {15 * 5}

Next, we perform the multiplication:

15 * 5 = 75

Now, we substitute the result back into the expression:

28 - 75

Finally, we perform the subtraction:

28 - 75 = -47

Therefore, the value of the expression 28 - {15 (3+2)} is -47.

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The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

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The average value of f(x) over the interval [ - 16, 16] is found to be  0.

The average value of f(x) = 16x over the interval [ - 16, 16] is:

F_average  = (1/(b-a)) * ∫(a to b) f(x) dx,

where the value of

a = -16 and b = 16

F_average = (1/(16-(-16))) x ∫(-16 to 16) 16x dx

F_average = (1/32) x [8x²] from -16 to 16

F_average = (1/32) x [8(16² - (-16)²)]

F_average = (1/32) x [8(256 - 256)]

F_average = 0

In concluaion,  the average value of f(x) over the interval [ - 16, 16] is determined as 0.

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The missing number in the original division problem is 28.

The solution is 113 ÷ 4 = 28.

The given division problem is: 113 ÷ 4 = 2 18.

To find the missing number, we can perform the division calculation step by step.

First, we divide 4 into the first digit of 113, which is 1.

Since 4 cannot be divided evenly into 1, we bring down the next digit, which is 1.

Now we have 11.

Next, we divide 4 into 11.

We can divide 4 into 11 two times, which gives us 8.

We subtract 8 from 11, leaving us with a remainder of 3.

Now, we bring down the next digit, which is 3.

We have 33.

Finally, we divide 4 into 33. 4 can be divided into 33 eight times, which gives us 32.

We subtract 32 from 33, leaving us with a remainder of 1.

So, the complete division is 113 ÷ 4 = 28 remainder 1.

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Answer: (x+3)(x-4)

Step-by-step explanation:

Answer:

To find the slope of a line passing through four points, we can use the formula:

slope = (change in y) / (change in x)

We can use any two points to calculate the slope, but since we need to find the slope for the entire line passing through all four points, we need to make sure that the slope is the same for any two points that we choose.

Let's use the points (-6,7) and (-2,6) to calculate the slope:

slope = (6 - 7) / (-2 - (-6)) = -1/4

Now let's use the points (2,5) and (6,4) to calculate the slope:

slope = (4 - 5) / (6 - 2) = -1/4

Since the slope is the same for both pairs of points, we can conclude that the slope of the line passing through all four points is -1/4.

Step-by-step explanation:

The algebraic expression representing 6 added to x is given as follows:

x + 6.

The sentence in the context of this problem is given as follows:

"If x is a number, the number added do 6 is given by".

The number is given as follows:

x.

The addition by 6 means that the number 6 is added to the variable x, as follows:

x + 6.

Which is the algebraic expression.

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The value of ∠N is 54.38 degrees.

Given that in ΔNOP, n = 56 inches, p = 61 inches and ∠P=80°.

We need to find the value of ∠N,

According to the cosine rule, the following equation is true for every triangle with sides a, b, and c and the corresponding opposite angles A, B, and C:

c² = 2ab cos(C) - a² + b²

In this instance, we have:

A = P and B = P

C = ∠P

When we enter the values, we obtain:

n² = p² + p² - 2p² cos(∠P)

Substituting the known values:

56² = 61² + 61² - 2(61²) cos(80°)

Simplifying:

3136 = 3721 + 3721 - 2(3721) cos(80°)

3136 = 3721 + 3721 - 7442 cos(80°)

Now we can solve for cos(80°):

3136 = 7442 - 7442 cos(80°)

7442 cos(80°) = 7442 - 3136

cos(80°) = (7442 - 3136) / 7442

cos(80°) ≈ 0.5798

∠N = arccos(0.5798)

∠N = 54.38 degrees.

Hence the value of ∠N is 54.38 degrees.

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The apothem of the hexagon is 8√3 cm.

We are given that;

The area of a regular hexagon= 384√3Cm²

Now,

To find the side length, radius, and apothem of a regular hexagon given its area, we can use the following formulas:

Area = (3√3 s^2) / 2 Area = (1/2) a P Area = (3/2) r a

where s is the side length, a is the apothem, P is the perimeter, and r is the radius of the hexagon. We can solve for any of these variables by rearranging the formulas and plugging in the given area.

A. To find the side length, we can use the first formula and solve for s:

s^2 = (2 Area) / (3√3) s = sqrt((2 Area) / (3√3))

Plugging in Area = 384√3, we get:

s = sqrt((2 * 384√3) / (3√3)) s = sqrt(256) s = 16

Therefore, the side length of the hexagon is 16 cm.

B. To find the radius, we can use any of the formulas and solve for r. For example, using the third formula, we get:

r = (2 Area) / (3 a)

To find a, we can use the second formula and solve for a:

a = (2 Area) / P

To find P, we can use the fact that P = 6s and plug in s = 16:

P = 6 * 16 P = 96

Plugging in P and Area into the formula for a, we get:

a = (2 * 384√3) / 96 a = 8√3

Plugging in a and Area into the formula for r, we get:

r = (2 * 384√3) / (3 * 8√3) r = 32

Therefore, the radius of the hexagon is 32 cm.

C. To find the apothem, we can use any of the formulas and solve for a. For example, using the second formula, we get;

a = (2 Area) / P

Plugging in Area = 384√3 and P = 96, we get:

a = (2 * 384√3) / 96 a = 8√3

Therefore, by polygon the answer will be 8√3 cm.

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The relation C is the relation that does not represent a function.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

In the context of this problem, we look at option C, where there are two arrows departing from the input of 1, meaning that:

As the input of 1 is mapped to multiple outputs, the relation does not represent a function.

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Answer:

40

Step-by-step explanation:

For finding the surface area of this rectancular prism, or any, we find the area of each shape. Then, we add up all of the areas together to get the surface area. There are 2 squares with 2 as a side length for each side. To find the area of a square, we can multiply any 2 sides. That is because the sides of the square is equal to eachother, so 2•2=4. Being 2 squares, they are both have area of 4. Looking at the 4 rectangles, they have a length of 4 and a width of 2. We multiply the height and width of a rectangle to get the area. 4•2=8, the area of each rectangle is 8. Now, we add up all of our areas. Two squares, each are 4 for their area. Add them up, you get 8 for the 2 squares. Then, we have 4 rectangles each are 8 for their area. 4•8=32 since they all have the same area. 32+8=40! 40 is the surface area of this net. I hope this helps, and have good day

The solution has been explained below.

We will use the following equation, x² + y² = 81, where x and y are the pool's dimensions in feet, to determine the necessary estimations for the pool project.

1. Calculate the pool's diameter and radius:

We can infer that the radius of the pool is equal to the square root of 81 because the equation depicts a circle. As a result, r = 81 = 9 ft.

The pool's diameter is simply equal to twice its radius, or d = 2r = 18 feet.

2. Calculate the amount of water in the pool:

Since the pool is 4 feet high, we can determine its volume by multiplying the area of its circle-shaped base by the height.

The formula A = πr² can be used to calculate the area of the pool's base,

Therefore, V = Ah = πr²h = 1017.87 cubic feet represents the volume of water in the pool.

3. Determine the pool's total material cost:

There are 7.48 gallons in a cubic foot and a gallon of water costs $0.22.

As a result, Cw = V × 7.48 × 0.22 = 1017.87 × 7.48 × 0.22 = $1,619.72 is the entire cost of water for the pool.

If the radius of the pool is $185 per foot, then the cost of the materials is Cm = r × 185 = 9 × 185 = $1,665.

4. Calculate the pool's total labour hours:

A pool's construction is estimated to take 2.5 hours for every foot of its radius.

So, L = r × 2.5 = 9 × 2.5 = 22.5 hours of labour would be needed to complete this pool.

5. Calculate the total cost of labour for the project:

If you pay someone $19 per hour, Cl = L × 19 = 22.5 × 19 = $427.5.

6. Find the project's overall cost:

The project's overall cost is the product of its labour and material costs:

Cost as a whole equals Cm + Cw + Cl, which is 1,665 + 1,619.72 + 427.5, or $3,712.22.

In conclusion, the pool has an 18-foot diameter and a 9-foot radius according to the supplied equation. There are roughly 1017.87 cubic feet of water in the pool. Water and building supplies are included in the pool's projected material cost of $3,284.72. 22.5 hours of labour in total are needed, with a labour cost estimate of $427.5. Consequently, $3,712.22 is the expected final cost of the pool renovation.

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Answer:

Solution in attached photo.

Step-by-step explanation:

This question tests on the properties of angles, such as corresponding angles and sum of angles in a straight line.

If you get a perfect score of 100% on both assignments, your overall grade in the class would be 100%.

To calculate your grade, we need to consider the weight of each assignment.

Since each assignment is worth 5% of your grade, we can calculate the contribution of the assignments to your overall grade.

The total weight of the two assignments is 2×5% = 10%.

To find the impact of the assignments on your grade, we multiply your average score on the assignments (100%) by their weight (10%):

Contribution from the assignments = 100% * 10% = 10%

Since you currently have a grade of 79, the remaining 90% of your grade is based on other assessments, tests, or assignments.

To calculate your overall grade, we add the contribution from the assignments to the remaining 90%:

Overall grade = 90% + 10% = 100%

Therefore, if you get a perfect score of 100% on both assignments, your overall grade in the class would be 100%.

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Answer: B

Step-by-step explanation:

Amplitude will be half the distance from 28 to 50

one cycle is given to be 8 hrs, so thats all you need for the right answer choice.

The length of PN in the circle is 4√2 units.

The length of GN in the circle is 8 units and length of KP in the circle is 4.

Therefore, let's find the length PN in the circle as follows:

PM is perpendicular to the chord GH. Therefore, the length KH is equals to the length GK.

Hence,

GH = 8 units

GK = 4 units

KH = 4 units

Therefore,

MP is the radius of the circle just like PN.

PN = MP

Hence, using Pythagoras's theorem,

4² + 4² = PN²

PN = √16 + 16

PN = √32

PN = 4√2 units

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The option that represents shapes of the sampling distribution of p hat  is:

c. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.

Normal distribution is defined as the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

Because the requirement for normal is greater than 10, n×p is greater than 10 and nx(1-p) is also greater than 10.

This situation is abnormal because it is not valid. If p is close to 1 in a normal graph, then p is left skewed.

Thus, the option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution  is not approximate normal because p=0.87 is closer to 1 than zero. Sampling distribution  is skewed to the left.

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The length of the arcs are;

1. s = 6. 4π

2. s = 11. 0π

The formula for calculating the length of an arc is expressed as;

s = rθ

Such that;

From the information given, we have that;

s = 4.25 × 3π/2

Multiply the values, we get

s = 12.75π/2

Divide by the coefficient , we get;

s = 6. 4π

2. The length of the arc would be;

s = 6.62 × 5π/3

Multiply the values, we have;

s = 33. 1π/3

Divide by the value, we get;

s = 11. 0π

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The value of slope of line is,

⇒ m = - 1

We have to given that,

Two points on the line are (- 4, 5) and (- 7, 8).

Now, We know that,

Slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is,

m = (y₂ - y₁) / (x₂ - x₁)

Here, Two points on the line are (- 4, 5) and (- 7, 8).

Hence, Slope is,

m = (8 - 5) / (- 7 + 4)

m = 3 / - 3

m = - 1

Therefore, The value of slope of line is,

⇒ m = - 1

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For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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Answer:

If f(x) = +4, which of the following is the inverse of f(x)?

O A. ƒ˜¹(x) = 2(2+4)

B. ƒ˜¹(x) = 7(2-4)

C. ƒ˜¹(x) = 7(2+4)

D. f¯¹(x) = ²(2-4)

Step-by-step explanation:

Nina's average cost per day for these four services is $5.

Since, Nina's monthly cost for the cable TV services is $99, and her monthly cost for cell phone calls and text messages is $59.70.

So her total monthly cost is:

$99 + $59.70 = $158.70

Now we need to find the number of days in a month.

Since, There are different ways to do this, but if we assume a month has 30 days,

= $158.70 / 30

= $5.29 (rounded to the nearest cent)

Therefore, Nina's average cost per day for these four services is $5.29. Rounded to the nearest dollar, her average cost per day is $5.

So, Nina's average cost per day for these four services is $5.

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Answer:

sec B = [tex]\frac{15}{8}[/tex]

Step-by-step explanation:

using the identity

sec B = [tex]\frac{1}{cosB}[/tex]

cos B = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{CD}[/tex] = [tex]\frac{8}{15}[/tex]

then

sec B = [tex]\frac{1}{\frac{8}{15} }[/tex] = [tex]\frac{15}{8}[/tex]

The length f the diagonal of the square is

The marked points represents the diagonal hence we find the distance between the points

The distance between them is calculated using the following formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using the points (3, 5) and (12, 14), we can substitute the values into the formula and calculate the length of the line segment:

d = √((12 - 3)² + (14 - 5)²)

= √(9² + 9²)

= √(81 + 81)

= √162

≈ 12.73

Therefore, the length of the line segment between (3, 5) and (12, 14) is approximately 12.73 units.

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As per the given data, Focus: (0, 16.44), Directrix: y = -16.44, Focal Diameter: 32.88, Vertex: (0, 0), and Axis of Symmetry: x = 0 (y-axis).

To determine the focus, directrix, focal diameter, vertex, and axis of symmetry for the given parabola equation, we can rewrite it in standard form, which is of the form [tex](x - h)^2[/tex] = 4p(y - k), where (h, k) represents the vertex.

16.44y = x²

Divide both sides of the equation by 16.44 to isolate y:

y = (1/16.44)x²

Comparing this equation to the standard form, we can see that h = 0 and k = 0.

Therefore, the vertex is (h, k) = (0, 0).

The general equation for a parabola in standard form is given by (x - h)^2 = 4p(y - k), where p is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p can be found using the coefficient of y in the equation (1/4p = 1/16.44).

Thus, p = 16.44.

The focus is located at a distance of p units above the vertex, so the focus is (0, p) = (0, 16.44).

The directrix is located at a distance of p units below the vertex, so the directrix is the horizontal line y = -p, which gives us y = -16.44.

The focal diameter is twice the value of p, so the focal diameter is 2p = 2 * 16.44 = 32.88.

Therefore:

- The focus is (0, 16.44).

- The directrix is y = -16.44.

- The focal diameter is 32.88.

- The vertex is (0, 0).

- The axis of symmetry is the vertical line passing through the vertex, which is the y-axis (x = 0).

Thus, Focus: (0, 16.44), Directrix: y = -16.44, Focal Diameter: 32.88, Vertex: (0, 0), and Axis of Symmetry: x = 0 (y-axis).

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Answer: 10

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]1c-0.25c=0.75c[/tex]

Answer:

$148

Step-by-step explanation:

Expected winnings = ($0.00 x 0.83) + ($100.00 x 0.08) + ($500.00 x 0.08) + ($10,000.00 x 0.01)

Expected winnings = $0.00 + $8.00 + $40.00 + $100.00

Expected winnings = $148.00

The answer to the equation 9s + 13 = 10s + 12

We must place the variable s on one side of the equation in order to solve the equation 9s + 13 = 10s + 12. Here's how to accomplish it:

9s + 13 = 10s + 12

First, by taking 9s away from both sides of the equation, let's move all the terms containing s to one side:

9s - 9s + 13 = 10s - 9s + 12

That amounts to:

13 = s + 12

Next, take 12 off of both sides to isolate the variable s:

13 - 12 = s + 12 - 12

1 = s

As a result, s = 1 is the answer to the equation 9s + 13 = 10s + 12

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