The Garcias have​ $12,000 in a saving account. The bank pays​ 3.5% interest on saving​ accounts, compounded monthly. Find the balance after 3​ years?

Answer:

Step-by-step explanation:

y=3.14x

Answer:

4mph

5mph

slower

Step-by-step explanation:

i did it

To calculate the average rate of change, divide the total change in distance by the total change in time. Without the specific distance covered in the given durations, it's impossible to provide absolute answers, but an example calculation has been given using an average speed of 9.5 mph.

In your question, the average rate of change refers to the change in distance with respect to time, also known as velocity or speed. Since there are no concrete values mentioned in your question for the distances covered by a runner between time 0.5 and 2 hours, and 1.5 to 2.5 hours, it would be impossible to provide an accurate answer without such data.

However, allow me to explain how you could calculate these values. If you assume that a runner has the marathon runner's average speed of 9.5 miles per hour, then the average rate of change, or average speed, over a certain time period is just the total change in distance divided by the total change in time. For instance, if the runner covered 9.5 miles between 0.5 and 2 hours, then the average rate of change would be 9.5 miles per 1.5 hours, or approximately 6.33 mph. This same method would apply to calculations between 1.5 and 2.5 hours.

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Final answer:

To evaluate the given integral, split the function at x = 3 and integrate separately. The integral evaluates to 18, which makes the correct answer 18.

Explanation:

The function we're integrating is 1, which makes this the same integral as the one in example 3 on p. 178. To evaluate this integral, we need to split it at x = 3 and integrate the corresponding functions separately.

For x ≤ 3, the function is f(x) = 3. So, the integral from 0 to 3 of 3 dx equals 9.

For x > 3, the function is f(x) = 6 - x. Integrate this from 3 to 6: ∫(6 - x) dx = 6x - 0.5x^2. Evaluating this from 3 to 6 gives 9.

Answer: C. The amount earned is a function of the number of hours worked.

Explanation:

Since, a function is always the type of y= f(x), where x is independent variable and y is dependent variable which is dependent on the value of x.

Here,  a graph of Olivia's earning per hour is given.

Since, it is the obvious thing that the earning will depend on hours she works.

Thus, we can say that earning is dependent variable while hours is independent variable.

Therefore, earning makes the y-axis and number of hours makes the x-axis.

So, option C is correct.

The sequence is given below:

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given:

The table showing the sequence of the first 15 terms is:

Sequence     Term                        Quotient

1                         2                                2

2                       1                               2 (2 / 1)

3                     3 (2 + 1)                  0.333 (1 / 3)

4                    4 (1 + 3)                  0.750 (3 / 4)

5                    7 (3 + 4)                  0.571 (4 / 7)

6                    11 (4 + 7)                0.633 (7 / 11)

7                    18 (7 + 11)               0.611 (11 / 18)

8                    29 (11 + 18)             0.621 (18 / 29)

9                    47 (18 + 29)             0.617 (29 / 47)

10                  76 (29 + 47)            0.618 (47 / 76)

11                  123 (47 + 76)            0.618 (76 / 123)

12                 199 (76 + 123)          0.618 (123 / 199)

13                 322 (123 + 199)         0.618 (199 / 322)

14                521 (199 + 322)         0.618 (322 / 521)

15                 843 (322 + 521)         0.618 (521 / 843)

The quotient converges around the value of 0.618, as shown in the above table.

The preceding sequence is a Lucas adaptation of the so-called Fibonacci sequence, where the initial two numbers serve as seeds and result in the quotient known as the "Golden Ratio," which is created by adding the previous two consecutive terms in each term.

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Answer:

2/5

Step-by-step explanation:

its asking in "simplest terms" so you would divide the number of marbles Kyle has by the 50 red marbles. 125 divide by 50 is 2.5 which equals to 2/5.

So 2/5 will be your answer. Hope this helps <3

9.3% of North Carolina is covered in water.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

To find the percent of North Carolina covered in water, we need to subtract the land area from the total area, and then express the result as a percentage.

The water area is:

53,800 - 48,800 = 5,000 square miles

To express this as a percentage, we need to divide the water area by the total area and then multiply by 100:

(5,000 / 53,800) x 100 = 9.3%

Therefore, 9.3% of North Carolina is covered in water.

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Answer:

Step-by-step explanation:

Given that the sophomore class sold a total of 700 adult and student tickets to the school play. adult tickets sold for $4.50 each, and student tickets cost $2.00 each.

Total = 1200

x, the number of student tickets sold, and y, the number of adult tickets sold

Then we have

[tex]x+y =700\\4.5x+2y = 1200[/tex]

These are the system to solve for x

see the attached figure to better understand the problem

we know that

the area of the figure is the area of the square minus the areas marked with x

area of the square is equal to

[tex]A1=8*8=64\ ft^{2}[/tex]

the areas marked with x is equal to

[tex]A2=15\ ft^{2}[/tex]

so

the area of the figure is

[tex]A=A1-A2 \\ A=64-15=49\ ft^{2}[/tex]

therefore

the answer is

[tex]50\ ft^{2}[/tex]

Answer: here is the k12 test answer

Step-by-step explanation:

Answer:

10 meters per second

Step-by-step explanation:

Great question, it is always good to ask away and get rid of any doubts that you may be having.

The best representation would be 10 meters per second. Usain Bolt, The fastest person person alive runs at approximately 12.5 meters per second.

10 miles per minute would be insanely fast. That is equivalent to 600 miles per hour, no human can run at that speed. Cars do not even reach that speed. Same goes for 10 kilometers per second.

10 centimeters per hour is incredibly slow. Although 470 times faster than a snail it is incredibly slow for a human.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Given: the triangle is a right triangle, find a. 

(The side opposite angle A.)

Answer:

a = 8.8104 ≈ 8.8

Step-by-step explanation:

∠A = ?, ∠B = 51°, ∠C = 90°

∠A = 180° - ( ∠B + ∠C )

∠A = 180° - ( 51° + 90° ) = 180° - 39°

∠A = 39°

[tex]\frac{a}{sin A}=\frac{b}{sin B} =\frac{c}{sin C}\\\\\frac{a}{sin39degrees}=\frac{14}{sin90degrees}\\\\\frac{14}{sin90degrees}*sin39degrees\\\\= 14 * 0.629\\= 8.8104[/tex]

So side a or BC = 8.8

We can actually solve this problem using the cosine law. We know that Gustavo ran 23° above the horizontal, while Aiden ran 33° below, hence the total angle between them is 56°. Therefore the distance between them is:

c^2 = a^2 + b^2 – 2 a b cos θ

c^2 = (300)^2 + (250)^2 – 2 (300) (250) cos 56

c^2 = 68,621.06

c = 262 m

They are 262 meters apart.

Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal. So, they are 262 meters apart.

Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.

Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal.

The total angle between them = 23 + 33 = 56°.

Let the distance between them be c. by using cosine law we have,

c² = a² + b² – 2ab cos θ

Where a and b are distances traveled by Gustavo and Aiden. θ is the angle between them.

Therefore,

[tex]c^2 = a^2 + b^2 - 2 a b cos \theta[/tex]

[tex]c^2 = (300)^2 + (250)^2 -2 (300) (250) cos 56[/tex]

[tex]c^2 = 68,621.06[/tex]

c = 262 m

Thus, the distance between them is 262 meters.

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Answer:

[tex]10^5 * 10^6 = 10^{5+6} = 10^{11}[/tex]

Step-by-step explanation:

find the product of 100,000 and 1,000,000 using scientific notation

All whole numbers have a decimal point at the end

convert each number into scientific notation. To get scientific notation move the decimal point after 1

100000.  -----> 1.00000 ----> 1* 10^5 ----> 10^5

1000000.  -----> 1.000000 ----> 1* 10^6 ----> 10^6

a^m * a^n = a^m+n

[tex]10^5 * 10^6 = 10^{5+6} = 10^{11}[/tex]

The step that would not be necessary in solving 5x + 15 + 2x = 24 + 4x is D. Use the distributive property.

An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.

To solve the equation 5x + 15 + 2x = 24 + 4x, we need to simplify and manipulate the equation to isolate the variable on one side.

First, we can combine like terms:

5x + 2x - 4x = 24 - 15

3x = 9

Then, we can isolate x by dividing both sides by 3:

x = 3

Therefore, the correct steps to solve this equation are:

B. Collect variable terms on one side.

C. Collect like terms.

A. Isolate the variable.

We do not need to use the distributive property in this problem.

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The dimensions of the swimming pool are 51 feet (length) and 12 feet (width), determined by setting up equations based on the given information (perimeter and difference between the sides) and solving these equations using substitution.

The problem at hand is a classic algebraic word problem. It involves determining the length (x) and width (y) of a swimming pool given the perimeter and the difference between the length and width. The formulas we'll use are for the perimeter of a rectangle (2x + 2y = perimeter) and a given equation based on the description (x - y = difference).

So the dimensions of the swimming pool are 51 feet (length) and 12 feet (width).

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