(50 POINTS) Express each sum using summation notation.
14. 3 + 3^2/2 + 3^3/3 ... + 3^n/n
15. 1 + 3 + 5 + 7 +... [2(12) - 1]

Answer:

A. 7✓6 - 6x✓6

Explanation:

7✓6 - 5x✓6 - x✓6

= 7✓6 - (5x + x)✓6

= 7✓6 - 6x✓6

Answer:

[tex] {x}^{3} {y}^{3} [/tex]

Step-by-step explanation:

Given,

Width of the rectangular prism

= x

Length of the rectangular prism

[tex] = {x}^{2} y[/tex]

Height of the rectangular prism

[tex] = {y}^{2} [/tex]

Therefore,

Volume of the rectangular prism

= Width × Length × Height

[tex] = x \times {x}^{2} y \times {y}^{2} [/tex]

[tex] = {x}^{3} {y}^{3} [/tex]

Hence,

The required volume of the rectangular prism is

Option J:

[tex] {x}^{3} {y}^{3} [/tex]

Answer:

b

Step-by-step explanation:

took the test good luck

Answer:

Explained below

Step-by-step explanation:

I shall explain this

Add all the numbers together and divide by the number of numbers

[tex]78 + 81 + 89 + 75 + 76 + 91 + 10963 + 80 + 87 + 91 + 95 = answer \div 11 [/tex]

Answer:

I don't understand the language

Step-by-step explanation:

am not form Paris

Answer:

140÷440(you can write it as a fraction)

=0.318181882

=0.32

Answer:

1.96428571429

Step-by-step explanation:

Answer:

55/28

Step-by-step explanation:

5×2+7/14+3/4

17/14+3/4

68+42/56

110/56

55/28

Answer:

is there an equation to find y? Because all you gave was x=-1

Answer:

" Pythagoras established the first Pythagorean community in Crotone, Italy. Early Pythagorean communities spread throughout Magna Graecia. "

"was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism . " <---------- Credits to: Yahoo

He was born in about 570 BC on the Greek island of Samos

He died in 495 BC

The statement "Some unsound arguments are valid" is false.

The statement "Some unsound arguments are valid" is false.

A valid argument is a statement that follows the rules of logic.

An argument is known to be sound when it is valid and has true premises. When the premises of an argument are correct, the argument is considered sound. When an argument is valid, it follows logically from its premises, which are the statements that provide evidence or support for the argument's conclusion.

The unsound argument is the one that contains at least one false premise.

The sound argument is the one that contains only true premises and is valid (that is, follows logically from the premises).

If an argument is unsound, it can never be valid because it contains at least one false premise.

Therefore, the statement "Some unsound arguments are valid" is false.

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Answer:

I wanna say 16 but im not sure

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation:

Answer:

the answer is I think 2/3

Fraction of boys brought lunch today is 16/25.

Here,

Given that:

The ratio of boys at certain school = 8/9

And 2/5 of boys brought lunch today

We have to find fraction of boys brought lunch today.

What is fraction?

Fractions denote the parts of a whole or collection of objects.

Now,

The ratio of boys at certain school = 8/9

And 2/5 of boys brought lunch today

Since, the ratio of boys 8/9 denotes 8 boys out of 9 students

Therefore, number of boys = 8

Thus, Fraction of boys brought lunch today = 8 x 2/5

                              = 16/25

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To solve the initial value problems using the Laplace transform, we can apply the Laplace transform to the given differential equations and initial conditions.

For the first problem, the Laplace transform of the differential equation is s^2Y(s) + 5sY(s) + 2Y(s) = 0. Solving for Y(s), we find Y(s) = -3/(s+1).

Taking the inverse Laplace transform, we obtain the solution y(t) = -3e^(-t). For the second problem, the Laplace transform of the differential equation is sY(s) + 4Y(s) + 3/(s+1) = -2. Solving for Y(s), we find Y(s) = (-2s - 1)/(s^2 + 4s + 3). Taking the inverse Laplace transform, we obtain the solution y(t) = (-2t - 1)e^(-t).

a) The Laplace transform of the given differential equation is:

s^2Y(s) + 5sY(s) + 2Y(s) = 0

Using the initial condition Y(0) = -1 and Y'(0) = 3, we can apply the initial value theorem to obtain:

Y(s) = -1/s + 3

Taking the inverse Laplace transform of Y(s), we find:

y(t) = -3e^(-t)

b) The Laplace transform of the given differential equation is:

sY(s) + 4Y(s) + 3/(s+1) = -2

Using the initial condition Y(0) = -1, we can apply the initial value theorem to obtain:

Y(s) = (-2s - 1)/(s^2 + 4s + 3)

Taking the inverse Laplace transform of Y(s), we find:

y(t) = (-2t - 1)e^(-t)

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Answer:

3

Step-by-step explanation:

The closest angle to F in the triangle is 52 degrees.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that Right triangle EFG it is known that the side opposite of acute angle F has a length of 18 inches and the leg adjacent to F has a length of 14 inches.

We can use the tangent function to find the measure of angle F:

tan(F) = opposite/adjacent = 18/14

we can find the inverse tangent of this value:

F = tan⁻¹(18/14)

= tan⁻¹(1.28)

F= 52.15°

Hence, the closest angle to F in the triangle is 52 degrees.

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The radian measure of angle A is (16/9)π.

To convert degrees to radians, we use the conversion factor:

[tex]1\ degree = \pi /180\ radians[/tex]

Given that angle A is 320 degrees, we can calculate its radian measure as follows:

Angle A in radians = (320 degrees) * (π/180 radians/degree)

                    = (320π)/180 radians

                    = (16/9)π radians

Therefore, the radian measure of angle A is (16/9)π.

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Answer:

if 4 is 120° then 2 is also 180° since they are opposite angles.

Answer:

pt B: (-1, -8)

Step-by-step explanation:

(x - 7)/2 = -4

x - 7 = -8

x = -1

(y-6)/2 = -7

y - 6 = -14

y = -8

Answer:

1196 cm3

Step-by-step explanation:

Answer:

1196

Step-by-step explanation:

Answer:

124

Step-by-step explanation:

the top square is 16 by 6 which will give you an area of 124 the bottom square has dimensions of 2 by 14 which is 28 add those numbers together to get your answer.

To build a binary search tree using alphabetical order for the given words, we start with an empty tree and insert each word in the appropriate position based on its alphabetical order.

Here's the step-by-step process:

Start with an empty tree.

Insert the first word, "banana," as the root of the tree.

Insert the second word, "peach," comparing it to the root. Since it comes after "banana," it becomes the right child of the root.

Insert the third word, "apple." Comparing it to the root, it comes before "banana," so we traverse to the left child of the root. Since the left child is empty, "apple" becomes the left child of "banana."

Insert the fourth word, "pear." Comparing it to the root, it comes after "banana," so we traverse to the right child. Comparing it to "peach," it comes before "peach," so we traverse to the left child of "peach." Since the left child is empty, "pear" becomes the left child of "peach."

Insert the fifth word, "coconut." Comparing it to the root, it comes before "banana," so we traverse to the left child. Comparing it to "apple," it comes after "apple," so we traverse to the right child. Comparing it to "pear," it comes before "pear," so we traverse to the left child of "pear." Since the left child is empty, "coconut" becomes the left child of "pear."

Insert the sixth word, "mango." Comparing it to the root, it comes after "banana," so we traverse to the right child. Comparing it to "peach," it comes before "peach," so we traverse to the left child. Comparing it to "pear," it comes after "pear," so we traverse to the right child. Comparing it to "coconut," it comes after "coconut," so we traverse to the right child. Since the right child is empty, "mango" becomes the right child of "coconut."

Insert the seventh word, "papaya." Comparing it to the root, it comes after "banana," so we traverse to the right child. Comparing it to "peach," it comes after "peach," so we traverse to the right child. Comparing it to "pear," it comes after "pear," so we traverse to the right child. Comparing it to "coconut," it comes after "coconut," so we traverse to the right child. Comparing it to "mango," it comes after "mango," so we traverse to the right child. Since the right child is empty, "papaya" becomes the right child of "mango."

The resulting binary search tree will look like this:

        banana

       /      \

   apple    peach

       \        \

      pear  papaya

      /

 coconut

      \

      mango

Note: The tree might have different structures depending on the order of insertion, as long as it maintains the binary search tree property.

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Answer:

Infinitely many solutions

Step-by-step explanation:

7x - 11 = 5(x - 2) + 2x - 1

7x - 11 = 10x - 10 + 2x - 1

7x - 11 = 7x - 11

No matter what number you plugin, it will always be equal.

1) 7x-11 = 5(x-2)+2x-1

2) 7x-11=5x-10+2x-1

3)7x-11=7x-11

4)0=0

5)Would cancel each other out.

6) So I guess no solutions?

Answer:

The speed is: 0.0142MHz

Step-by-step explanation:

Given

[tex]C(s) = 1234s^2 - 35s + 1900[/tex]

Required

The processor speed when the cost is at minimum

First, differentiate C(s) with respect to s

[tex]C(s) = 1234s^2 - 35s + 1900[/tex]

[tex]C'(s) = 2468s - 35[/tex]

The cost is at minimum when [tex]C'(s) = 0[/tex]

So, we have:

[tex]C' = 2468s - 35 = 0[/tex]

[tex]2468s - 35 = 0[/tex]

Solve for s

[tex]2468s = 35[/tex]

[tex]s=\frac{35}{2468}[/tex]

[tex]s\approx0.0142[/tex]

Answer:

11 meters square.

Step-by-step explanation:

if the painted area is the gray it would be 10m

if its the white area its 9m

Answer:

Step-by-step explanation:

If Bryan receives a 15% tip, then he will receive an amount of approximately $16.55 as a tip.

In order to calculate the tip-amount, we need to multiply the total-bill by the tip percentage. In this case, the "bill-amount" is $110.31, and the tip percentage is 15%.

To find the tip amount, we can use the formula:

Tip amount = (Total bill) × (Tip percentage),

Simplifying further,

We get,

Tip amount = $110.31 × 0.15,

= $16.5465 (rounded to the nearest cent)

Therefore, Bryan will receive approximately $16.55 as a tip.

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Answer:

Choice D

Step-by-step explanation:

Choice D, 3072ft^2 is the correct answer.

Here's how! The length AND width are both 24, so we know that 24 * 24 is our start. Then the height of the pyramid is 16, which now makes our equation 24 * 24 * 16. When finding the volume of a pyramid, you must divide by 3, so now the answer is (24 * 24 * 16) / 3. Making the answer 3072ft^2.

Hope this helped!

Answer:

3072

Step-by-step explanation:

volume =(1/3) hight ×width×length

v=(1/3) × 16 × 24 × 24

v=3072

Answer:

45 meters

Step-by-step explanation:

I hope this helps.