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2 years ago

How many different pairs of parallel edges are there on a rectangular solid?

Mathematics

1 answer:

Monica [59]2 years ago

4 0

Answer:

Step-by-step explanation:

A rectangular prism has four parallel edges along its length, four parallel edges along its width, and four parallel edges along its height.

We want to know how many different pairs of parallel edges there are. Starting with the length, the number of unique pairs is:

₄C₂ = 6

The same is true for the width and height. So the total number of different pairs of parallel edges is:

3 × 6 = 18

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Samantha had 11/12 of a cup of sugar. She used 5/12 of a cup of sugar to bake muffins. How much sugar, in cups, does Samantha ha

baherus [9]

Answer:

1/2 cup

Step-by-step explanation:

11/12-5/12=6/12=1/2

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3 years ago

The expression 475 * 1.076 ^ t the average annual per capita health care costs, in dollars, in the US as a function of the numbe

Alik [6]

Answer:

$Y(t)= 475 (1.076)^t$

Where Y(t) represent the average annual per capita health care costs

475 represent the initial amount for the average annual per capita health care costs

t represent the number of years since 1970

And 1.076 represent the growth factor given by:

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And solving for r we got:

$r = 1.076-1 =0.076$

So for this case we can say that the value 1.076 represent the growth factor.

Step-by-step explanation:

For this case we have the following model given:

$Y(t)= 475 (1.076)^t$

Where Y(t) represent the average annual per capita health care costs

475 represent the initial amount for the average annual per capita health care costs

t represent the number of years since 1970

And 1.076 represent the growth factor given by:

$1+r = 1.076$

And solving for r we got:

$r = 1.076-1 =0.076$

So for this case we can say that the value 1.076 represent the growth factor.

7 0

3 years ago

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Line z has a slope of 2.5 and goes through point (4, 13). Which equation best represents line z?

AnnyKZ [126]

Answer:

y - 13 = (5/2)(x - 4)

Step-by-step explanation:

Here we know the slope and one point on the line. Use the point-slope formula:

y - k = m(x - h).

Substituting 13 for k, 4 for x and 2.5 for m, we get:

y - 13 = (5/2)(x - 4)

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3 years ago

10 The collection of distinct vowel letters from the words PNEUMONOULTRAMICROSCOPICSILICOVOLCANOCONIOSIS

irina1246 [14]

The collection of distinct vowel letters from the words PNEUMONOULTRAMICROSCOPICSILICOVOLCANOCONIOSIS

The words' vowel letters are [A,,E,I,O,U].

A, E, I, O, U, Y, and, as we'll see, W are vowels, but let's go more precise now. They are symbols (letters) that represent a certain kind of spoken sound called a vowel. According to phoneticians, a vowel is a spoken sound that is made without severely limiting the airflow from the lungs.

The alphabet consists of 26 letters, five of which are vowels (a, e, I, o, and u). The other letters are consonants. A vowel is a sound made by opening the mouth and allowing air to escape without closing it or clearing the throat.

Learn more about Vowels brainly.com/question/11388415

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1 year ago

The graph shows the feasible region for the system with constraints:

Dimas [21]

Answer:

The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

The minimum value of the objective function C is 125

Step-by-step explanation:

* Lets look to the graph to answer the question

- There are 3 inequalities

# y ≤ 15 represented by horizontal line (purple line) and cut the

y-axis at point (0 , 15)

# x + y ≤ 25 represented by a line (green line) and intersected the

x-axis at point (25 , 0) and the y- axis at point (0 , 25)

# x + 2y ≥ 30 represented by a line (blue line) and intersected the

x-axis at point (30 , 0) and the y-axis at point (0 , 15)

- The three lines intersect each other in three points

# The blue and purple lines intersected in point (0 , 15)

# The green and the purple lines intersected in point (10 , 15)

# The green and the blue lines intersected in point (20 , 5)

- The three lines bounded the feasible region

∴ The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

- To find the minimum value of the objective function C = 4x + 9y,

substitute the three vertices of the feasible region in C and chose

the least answer

∵ C = 4x + 9y

- Use point (0 , 15)

∴ C = 4(0) + 9(15) = 0 + 135 = 135

- Use point (10 , 15)

∴ C = 4(10) + 9(15) = 40 + 135 = 175

- Use point (20 , 5)

∴ C = 4(40) + 9(5) = 80 + 45 = 125

- From all answers the least value is 125

∴ The minimum value of the objective function C is 125

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3 years ago

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