True or false The coefficient of (x^(k)) (y^(n-k)) in the expansion of (x+y)^n equals (n choose k)

Final answer:

The amount in the savings account increased by 3%. This was calculated by determining the amount of the increase ($9), dividing by the original amount ($300), and then multiplying by 100 to get the percent increase.

Explanation:

The question is asking to calculate the percent of increase in the amount of money in a savings account that went from $300 to $309. To determine the percent increase, you subtract the original amount ($300) from the new amount ($309) to find the amount of the increase, which is $9. Then, you divide the increase ($9) by the original amount ($300) and multiply by 100 to get the percentage:

Percent Increase = (Increase ÷ Original Amount) × 100%

Percentage Increase = ($9 ÷ $300) × 100% = 0.03 × 100% = 3%

Therefore, the percent of increase is 3%.

Answer:

the quotient of this problem is 3x^3+6x^+8x+24+47/x-2

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

Speed of Milla = 5 km per hour

Speed of Luka = 4 km per hour

Distance between Milla and Luka = 3 km

Let the time be 't'.

As we know that

[tex]Distance=Speed\times time[/tex]

So, it becomes,

Distance covered by Milla + Distance covered by Luka = Total distance

[tex]5t+4t=3[/tex]

Hence, Second option is correct.

sqrt(1234) = 35.1283

 you don't say how it should be rounded, so round off as needed

30 x 20 x 24 = 14400 cubic cm

30 x 20 x 15 = 9000 cubic cm

14400-9000 = 5400 cubic cm left

 1 cubic cm = 0.001 liters

5400x 0.001 = 5.4 liters

6.5-5.4 = 1.1 liters overflow

1.1 L

Given:

A rectangular container that has:

It is filled with water to a depth of 15 cm.

When an additional 6.5 L of water are poured into the container, some water overflows.

Question:

How many liters of water overflow the container?

The Process:

Step-1: calculate the volume of rectangular container

[tex]\boxed{ \ V = length \times width \times depth \ }[/tex]

[tex]\boxed{ \ V = 30 \times 20 \times 24 \ }[/tex]

[tex]\boxed{ \ V = 14,400 \ cm^3 \ }[/tex]

The volume of rectangular container is 14,400 cm³, then converted to 14,4 L.

Step-2: calculate the volume of water filled in the container to a depth of 15 cm

[tex]\boxed{ \ V = length \times width \times depth \ }[/tex]

[tex]\boxed{ \ V = 30 \times 20 \times 15 \ }[/tex]

[tex]\boxed{ \ V = 9,000 \ cm^3 \ }[/tex]

The volume of water filled is 9,000³ cm, then converted to 9 L.

Step-3: calculate the volume of water overflow when an additional 6.5 L of water is poured into a container.

The volume of water overflow equals the initial water volume is added to the additional water volume then subtracted by the container volume.

The volume of water overflow = [tex]\boxed{ \ 9 \ L + 6.5 \ L - 14.4 L \ }[/tex]

Thus, the volume of water overflow of the container is 1.1 L.

Notes:

[tex]\boxed{ \ 1 \ cm^3 = 1 \ mL \ }[/tex]

[tex]\boxed{ \ 1,000 \ cm^3 = 1 \ L \ }[/tex]

[tex]\boxed{ \ 1 \ dm^3 = 1 \ L \ }[/tex]

Keywords: a rectangular container, has a length of 30 cm, a width of 20 cm, height of 24 cm, is filled with water, to a depth of 15 cm, an additional 6.5 L of water, are poured into the container, some water overflows, the formula, volume

8 7/16 - (-2 4/9) =

8 7/16 + 2 4/9 =

8 7/16 = 135/16 = 1215/144

2 4/9 = 22/9 = 352/144

1215/144 + 352/144 = 1567/144 =10 127/144

First option is correct i.e. [tex]v = \frac{D}{2z}[/tex] .

Variable is a symbol( usually a letter) standing in for an unknown numerical value in an equation.

To solve or isolate a variable means to get the variable on one side of the equation by itself.

According to the given question

we have an equation

D = 2zv and to solve for variable v

For solving the above equation for the variable v, make the variable v on one side of the equation by itself.

⇒ [tex]\frac{D}{2z} = \frac{2zv}{2z}[/tex]    ( dividing both the sides by 2z)

⇒ [tex]v = \frac{D}{2z}[/tex]

Hence, option first is correct.

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Final answer:

To find the two numbers, we created a system of equations with the sum being 70 and the larger number as five less than twice the smaller number. Solving the equations, we found that the smaller number is 25 and the larger number is 45.

Explanation:

The question asks us to find two numbers where the sum is 70, and the larger number is five less than twice the smaller number. To solve this, we'll set up a system of equations with two variables, which we'll call x and y. The first equation would be x + y = 70, since their sum is 70. The second equation is derived from the statement that the larger number is five less than twice the smaller number, which can be expressed as y = 2x - 5. Now we substitute the second equation into the first to solve for x. We get x + (2x - 5) = 70. Simplifying, we have 3x - 5 = 70, thus 3x = 75, and therefore x = 25. With the smaller number found, we can determine the larger number using the second equation y = 2(25) - 5, resulting in y = 45. Hence, the two numbers are 25 and 45.

Final answer:

The probability that a bridge hand chosen at random contains at least 3 kings is 0.0000244.

Explanation:

To find the probability that a bridge hand chosen at random contains at least 3 kings, we need to first determine the total number of possible bridge hands and then calculate the number of favorable outcomes.

The total number of bridge hands is calculated using the combination formula: C(52, 13) = 52! / (13! * (52-13)!) = 635,013,559,600.

To calculate the number of favorable outcomes, we count the number of ways we can select 3 kings and then fill the remaining 10 positions with the remaining 39 cards. The number of ways to select 3 kings is C(4, 3) = 4 and the number of ways to fill the remaining 10 positions is C(48, 10) = 17,259,390.

Therefore, the probability is given by: P(At least 3 kings) = favorable outcomes / total outcomes = (4 * 17,259,390) / 635,013,559,600 = 0.0000244.

The product of height and square of the radius of the open-top right circular cylindrical should be equal or more than 550 cm³ in order to hold a volume of 1728 cm³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

The volume of the cylinder is = πr²h
In order to hold the volume of 1728 cm³,
πr²h ≥ 1728
r²h ≥ 550

Thus, the product of height and square of the radius of the open-top right circular cylindrical should be equal to or more than 550 cm³ in order to hold a volume of 1728 cm³.

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Answer:

Step-by-step explanation:

Let the American Population = x

1/10 x = 32,000,000  Multiply by sides by 10

x = 320,000,000 Thirty two followed by 7 zeros is the population of America.

T=I÷pr

T=60÷(500×0.02)

T=6 years  <-- Answer

Final answer:

The equation of a circle with a center at (-7, -7) and a radius of 7 is  [tex](x + 7)^2 + (y + 7)^2 = 49.[/tex]

Explanation:

The equation of a circle is typically expressed in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. For a circle with a center at (–7, –7) and a radius of 7, the equation would be (x + 7)² + (y + 7)² = 7². Here, we squared the radius to get 49, which gives us the final equation (x + 7)² + (y + 7)² = 49.

Answer:

Option C is the correct answer.

Step-by-step explanation:

Volume of box = Length x width x height.

Volume of box = 36 cubic centimetres.

Option A:

Length = 12 cm

Width = 12 cm

Height = 12 cm

Volume = 12 x 12 x 12 = 1728 cubic centimetres.

Option A is wrong.

Option B:

Length = 4 cm

Width = 4 cm

Height = 2 cm

Volume = 4 x 4 x 2 = 32 cubic centimetres.

Option B is wrong.

Option C:

Length = 3 cm

Width = 4 cm

Height = 3 cm

Volume = 3 x 4 x 3 = 36 cubic centimetres.

Option C is correct.

Option C is the correct answer.

The summation of 4.392 g + 102.40 g + 2.51 g with three decimal places is 109.302 g.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, thousand, or a million.

Given the expression for sum,

4.392 g + 102.40 g + 2.51 g

⇒ (4.392 + 102.40 + 2.51)g

⇒ 109.302 g

Hence "The summation of 4.392 g + 102.40 g + 2.51 g with three decimal places is 109.302 g".

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The sum of the masses 4.392 g, 102.40 g, and 2.51 g is 109.30 g.

A summation, which can sometimes be shortened to "sum," is the result of multiplying two or more quantities by one another. A summation always has an integer number of terms. One hundred, thousand, or a million phrases could exist, but there could only be two.

The sum of the masses 4.392 g, 102.40 g, and 2.51 g is 109.302 g.

To ensure the correct number of decimal places, we need to consider the measurement with the least number of decimal places, which is 2.51 g.

Since 2.51 g has two decimal places, we round the sum to two decimal places as well.

Therefore, the answer is 109.30 g.

11)

 x*y = -5*2 = -10, absolute value is 10

y*z = 2 * -2 = -4, absolute value is 4

10+4 = 14