Find the volume of the figure. If necessary, round your answer to the nearest tenth.

Answer choices
A: 441.6 cm^3
B: 883.2 cm^3
C: 147.2 cm^3

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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Answer: a) 1/4; b) 96.

Step-by-step explanation:

a) what fraction of the houses have two bedroom?

\(1-\bigg (\dfrac{1}{3} +\dfrac{3}{8} +\dfrac{1}{24} \bigg)=\\\\=1-\bigg (\dfrac{8}{24} +\dfrac{9}{24} +\dfrac{1}{24} \bigg)\\\\=1-\dfrac{18}{24} \\\\=\dfrac{24}{24} -\dfrac{18}{24}= \dfrac{6}{24}=\dfrac{1}{4}\)

b) if 24 houses have two bedrooms, how many houses are on the development?

24 houses have two bedrooms - this is 1/4

\(24 : \dfrac{1}{4} =96\)

Thus, 96 houses are under development.

A) The fraction of houses with two bedrooms is 1/4.

B) If 24 houses have two bedrooms, there are a total of 96 houses on the development.

A) To find the fraction of houses with two bedrooms, we need to subtract the fractions of houses with other types of bedrooms from 1:

Fraction with two bedrooms = 1 - (1/3 + 3/8 + 1/24) = 1 - (8/24 + 9/24 + 1/24) = 1 - 18/24 = 6/24 = 1/4.

B) If 24 houses have two bedrooms and this represents 1/4 of the total number of houses, we can set up a proportion to find the total number of houses:

24 / (1/4) = Total number of houses

Total number of houses = 24 * 4 = 96 houses. Therefore, there are 96 houses on the development.

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Answer:

On my side I do not see an attached image.

To find the length of the curve defined by y = 4x^3 + 15x from the point (-3,-153) to the point (4,316), you'd have to compute the integral of √[1 + (f'(x))^2] dx, where f(x) = 4x^3 + 15x.

First, we need to find f'(x) by taking the derivative of f(x):
f'(x) = 12x^2 + 15

Next, we can plug f'(x) into the integral formula:
∫[-3,4] √[1 + (12x^2 + 15)^2] dx

This integral can be solved using trigonometric substitution. Let u = 12x^2 + 15, then du/dx = 24x and dx = du/24x. Substituting these values, we get:
∫[-3,4] √[1 + (12x^2 + 15)^2] dx
= ∫[177,693] √[1 + u^2]/24x du
= (1/72)∫[177,693] √[1 + u^2]/(u/2) du
= (1/72)∫[177/15,693/15] √[1 + (u/15)^2]/(u/30) du (substituting u/15 = tanθ)
= (1/36)∫[arctan(177/15),arctan(693/15)] secθ dθ
= (1/36)ln|sec(arctan(693/15)) + tan(arctan(693/15))| - (1/36)ln|sec(arctan(177/15)) + tan(arctan(177/15))|
≈ 18.24

Therefore, the length of the curve from (-3,-153) to (4,316) after integral is approximately 18.24 units.

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Answer:

The graph is shown below.

Step-by-step explanation:

Answer:

17.001>17.0001

Answer:

17.001>17.0001

Step-by-step explanation:

17.001 is greater than 17.0001

Answer:

yes

Step-by-step explanation:

65 divided by 6.25 =10.4

67 - 10.4 =56.6

brailiest please

Answer:

slope is -3/2

Step-by-step explanation:

Use the slope formula

y2-y1/x2-x1=m (rise over run)

(7,5) (5,8)

x1 y1 x2 y2

8-5/5-7=m

-(3/2)=m

Perimeter formula: p = 2(w + l)

The perimeter is 62.

p = 62

The width of a rectangle is 5 feet less than the length.

w = l - 5

Substitute and solve.

62 = 2[(l - 5) + l)]

62 = 2l + 2l - 10

62 = 4l - 10

72 = 4l

18 = l

Substitute and solve for the width

w = 18 - 5

w = 13

Therefore, the length is 18 and the width is 13.

Best of Luck!

Answer:

see below and attached.

Step-by-step explanation:

Perimeter (P) = 2 L (Length) + 2 W (Width)

where P = 62

          W = L - 5

P = 2L + 2W

62 = 2L + 2(L -5)

62 = 2L + 2L - 10

72 = 4L

L = 72/4

L = 18

W = L - 5

W = 18 - 5

W = 15

Variables :                           P, L, W

Model equation:                 P = 2L + 2W

Length of the rectangle:    18

Width of the rectangle:      13

The appropriate domain for the function would be:

{0, 1, 2, 3, 4, 5, ...}

The domain of a function represents the set of all possible values that the independent variable (in this case, the number of candles sold) can take.

In the context of the problem you described, the function's domain should be limited to the realistic range of possible values for the number of candles sold. For example, it wouldn't make sense for the domain to include negative values, since it's not possible to sell a negative number of candles.

Assuming there are no other constraints on the number of candles sold, a reasonable domain for the function could be any non-negative integer since it's unlikely that the seniors would sell a fractional number of candles.

Therefore, the appropriate domain for the function would be:

{0, 1, 2, 3, 4, 5, ...}

This set includes all non-negative integers, representing all the possible values for the number of candles sold.

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Answer: 5301.44 \(cm^{3}\), 5.301 litres, 1.4 gallons

Step-by-step explanation:

To find the volume of a sphere, use the equation V = \(\pi r^{2} h\) with r being the radius of the base of the cylinder and h being the height of the cylinder. Using the equation, we can find the volume which is

\(\pi (\frac{15}{2} )^{2} 30\) ≈ 5301.44 \(cm^{3}\)

We know that 1 \(cm^{3}\) is equal to 0.001 litres so

5301.44 \(cm^{3}\) = 5.301 litres

We know that 1 litre is equal to 0.264 gallons so

5.301 litres = 5.301 × 0.264 ≈ 1.4 gallons

Answer:

This is the first line.

point one (0,-2)

point two (5,-5)

This is the second line.

point one (0,6)

point two (1,7)

Answer:

Since you do not have any answer choices, I will step-by-step solve the equation for you. Typically what happens with problems like this is the answer choices will match the work when solving. So, pay attention to my scratch-work and if any answers match the answer choices, then that is most likely the correct answer. (Hint: the solution to the equation is most likely the correct answer)

Write the equation:

(2x^2 + 4x – 7)(x – 3)

Simplify and Distribute:

(2x^2 + 4x – 7)(x – 3)

2(x – 3)^2 + 4x(x – 3) – 7(x – 3)

2x^3 – 6x^2 + 4x

(x – 3) – 7(x – 3)

2x^3 – 6x^2 + 4

x^2 – 12x – 7(x – 3)

2x^3 – 6x^2 + 4

x^2 – 12x – 7x + 21

Combine Like Terms:

2x^3 – 2x^2 – 12x – 7x + 21

2x^3 – 2x^2 – 19x + 21

Solution:

2x^3 – 2x^2 – 19x + 21

Hope that helps! Have an amazing rest of your day! Please consider awarding me the Brainliest! :)

Answer:

A =7  B=14

Step-by-step explanation:

AREA OF RING

PERIMETER OF RING

Nina will take the shortest time finishing her book.

Division is the opposite of multiplication. If you divide 12 into three equally sized groups, you will get four in each group if the three groups of four sum up to 12, which they do when you multiply. The main goal of division is to count the total number of evenly distributed groups or the total number of people in each group following a fair distribution.

Let's calculate how many pages each person reads in one day:

Then we divide the number of pages of each book by reading speed of the respective person:

Thus Nina will take the shortest time finishing her book.

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Answer:

It is R, T.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I got it right

The evaluated lateral surface area is 261.8 square meters, under the condition that the base length is 20 m and height is 13 m.

The lateral surface area of a cylinder is given by the formula 2πrh
Here,
r = radius of the base
h = height of the cylinder.
For the given case, the base length is 20 m and height is 13 m. Then the base length is stated  instead of the radius, we have  to evaluate the radius first.
The radius of a cylinder can be found applying the formula r = l/2π
Here,
l = base length.
So, staging l = 20 m
, we get
r = 20/(2π)
≈ 3.18 m
Now that we have received the radius and height, we can evaluate the lateral surface area applying the formula mentioned above.
Staging
r = 3.18 m
h = 13 m,
we get:
Lateral surface area
= 2πrh
≈ 261.8 m²
Then, the lateral surface area of the given cylinder is approximately 261.8 square meters.
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The expression that represents h(x) is (f - g)(x).

In the given options, we need to determine the expression that represents h(x). The expression (f - g)(x) represents the subtraction of g(x) from f(x). By subtracting the value of g(x) from f(x) at a given x, we obtain the value of h(x). This expression captures the concept of finding the difference between the two functions at a specific input value.

To understand the concept further, let's break down the expression (f - g)(x) into its components. The subtraction operation (f - g) indicates that we are subtracting the values of g(x) from f(x). This means that for each value of x, we evaluate f(x) and g(x), and then subtract the latter from the former. By doing so, we obtain the value of h(x), which represents the difference between the two functions.

The expression (f - g)(x) is a concise and clear way to denote the function h(x). It helps us understand the relationship between f(x) and g(x) by focusing on the difference between their values at each x. By utilizing this expression, we can analyze the behavior and properties of h(x) in various mathematical contexts.

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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He makes $8/49 for every 7 cups of juice, so his overall profits will be some multiple of $8/49.

Finding the worth of one unit of a quantity, then using this value to determine the value of a specified number of units of the quantity, is known as the unitary technique. When solving issues involving rates, ratios, and proportions, this approach is helpful. The fundamental tenet of the unitary technique is that we can use the value of one unit of a quantity to determine the value of any number of additional units of the same quantity.

given

Let's symbolise the cost of a cup of apple juice by the variable x.

So, a cup of lemon juice is sold for 3/2 times x, or (3/2)x.

Mr. Tan offers 5 cups of apple juice for every 2 cups of lemon juice. This indicates that there are 2.5 sales of lemon juice for every 1 sales of apple juice.

Assume Mr. Tan sells 5y cups of apple juice and 2y cups of lemon juice.

Based on the information provided, we can conclude that apple juice generates $12 more revenue than lemon juice.

in order to create an equation:

5yx = 2(3/2)x + 12

Simplifying:

5yx = 3x + 12

adding two to both sides:

10yx = 6x + 24

x(10y - 3) = 12

x = 12 / (10y - 3) (10y - 3)

We can now re-use this number of x to represent the revenue from apple juice in the equation:

5yx = 3x + 12

5y(12 / (10y - 3)) = 3(12 / (10y - 3)) + 12

Therefore, Mr. Tan charges $1/7 for each cup of apple juice and (3/2)($1/7) Equals $3/14 for each cup of lemon juice.

He charges (5/7)($1/7) = $5/49 for 5y = 5(1/7) = 5/7 glasses of apple juice.

For a sum of (2/7)($3/14) = $3/49, he sells 2y = 2(1/7) = 2/7 cups of lemon juice.

For each 7 cups of juice sold, Mr. Tan makes a sum of $5/49 + $3/49 = $8/49.

Consider that he offers 2n cups of lemon juice and 5n glasses of apple juice. (2n)($3/14) + (5n)($1/7) = $6n/49 + $5n/49 = $11n/49

He makes $8/49 for every 7 cups of juice sold, so his overall profits will be some multiple of $8/49.

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Answer:

2 + x > 8

Step-by-step explanation:

Answer:

98%

Step-by-step explanation:

The correct equation is,

⇒ (5 - 6i) (2 + 4i)

Let us assume that;

⇒ (a + bi) (c + di)

⇒ ac + adi + bci + bdi²

⇒ (ac − bd) + (ad + bc)i

Matching coefficients:

30 < ac − bd < 80

ad + bc = 0

Hence, We need to pick four integers between -9 and 9 such that these two equations are satisfied.  One possible combination is:

a = 8, b = -4, c = 6, d = 3

The number would be:

ac − bd = (8)(6) − (-4)(3) = 60

Puzzle 2

Using the result from Puzzle 1:

ac − bd = 34

ad + bc = 8

Like before, it makes sense to assume b is negative.  With some trial and error, one possible answer is:

a = 5, b = -6, c = 2, d = 4

Thus, The correct equation is,

⇒ (5 - 6i) (2 + 4i)

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Answer:

4x+2(2x−5)−(3−5x) = 8x-10-3+5x

Step-by-step explanation:

We need to find the equivalent expression to 4x+2(2x−5)−(3−5x).

Using distributive property as follows :

a(b+c) = ab+ac

4x+2(2x−5)−(3−5x) = 4x+4x-10-3+5x

= 8x-10-3+5x

Option (e)

Hence, the correct option is (e) "8x-10-3+5x"

The height of the rectangular prism is 1.148 centimeters.

Let the height of the rectangular prism be y centimeters. The surface area of the composite figure is the sum of the surface areas of the rectangular prism and the rectangular pyramid.

Surface area of rectangular prism = 2lw + 2lh + 2wh

= 2(18)(10) + 2(18)(y) + 2(10)(y)

= 360 + 36y + 20y

= 360 + 56y

Surface area of rectangular pyramid = lw + (l/2)\(\sqrt{w/2^{2} +h^{2} }\)+ (w/2)\(\sqrt{l/2^{2} +h^{2} }\) + l*\(\sqrt{w/2^{2} +l/2^{2} +h^{2} }\)

= (1810)/2 + (18/2)*\(\sqrt{5^{2} +12^{2} }\)+ (10/2)\(\sqrt{9^{2} +12^{2} }\) + 18\(\sqrt{5^{2} +9^{2} +12^{2} }\)

= 90 +( 54 + 45 + 324)\(\sqrt{29}\)

= 414\(\sqrt{29}\) + 90

Therefore, the surface area of the composite figure = Surface area of the rectangular prism + Surface area of the rectangular pyramid

844 = 360 + 56y + 414\(\sqrt{29}\) + 90

Subtracting 450 from both sides and then dividing by 56, we get:

y + 15\(\sqrt{\frac{29}{2} }\) = 7

y = 1.148

Therefore, the height of the rectangular prism is approximately 1.148 centimeters when rounded to three decimal places.

Hence, the height of the rectangular prism is 1.148 centimeters.

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Answer:

Step-by-step explanation:

The height of the rectangular prism is 1.148 centimeters.

Let the height of the rectangular prism be y centimeters. The surface area of the composite figure is the sum of the surface areas of the rectangular prism and the rectangular pyramid.

Surface area of rectangular prism = 2lw + 2lh + 2wh

= 2(18)(10) + 2(18)(y) + 2(10)(y)

= 360 + 36y + 20y

= 360 + 56y

Surface area of rectangular pyramid = lw + (l/2)+ (w/2) + l*

= (1810)/2 + (18/2)*+ (10/2) + 18

= 90 +( 54 + 45 + 324)

= 414 + 90

Therefore, the surface area of the composite figure = Surface area of the rectangular prism + Surface area of the rectangular pyramid

844 = 360 + 56y + 414 + 90

Subtracting 450 from both sides and then dividing by 56, we get:

y + 15 = 7

y = 1.148

Therefore, the height of the rectangular prism is approximately 1.148 centimeters when rounded to three decimal places.

Hence, the height of the rectangular prism is 1.148 centimeters.

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Answer:

The height of the garden will be 3 ft.

Step-by-step explanation:

Given;

area of trapezoid, A = 1/2(B+b)h

Where;

A is the area

h is the height

B is the big base

b is the small base

If; A = 27 ft²

B = 10 ft

b = 8 ft

h = ?

\(A= \frac{1}{2} (B+b)h\\\\27= \frac{1}{2} (10+8)h\\\\27*2 = 18h\\\\54 = 18h\\\\h = \frac{54}{18}\\\\ h = 3 \ ft\)

Therefore, the height of the garden will be 3 ft.

The image of (-8,6) after a reflection over the line y = -x is (-6, 8).

Given:

The image of (-8,6) after a reflection over the line y = -x.

The x-coordinate and y-coordinate of a point change positions and are negated when it is reflected across the line y = -x.

So, the reflection of the point (-8, 6) across the line y = -x is (-6, 8).

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