If you save two pennies on January 1, four pennies on January 2, six pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars, at the end of that one year? Express your answer as a decimal without commas.

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⇒Polar Coordinate of point (x,y)=(r,Ф)

The Point (x,y) lies in First Quadrant.

r=Distance from Origin to point (x,y)

[tex]r=\sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{y}{x}\\\\ \theta=A[/tex]

⇒The Point (-x,y) lies in Second Quadrant.

[tex]r=\sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{y}{-x}\\\\ \theta=\pi-A[/tex]

Polar Coordinate of point (-x,y)=(r,π-Ф)

⇒The Point (-2x,-2y) lies in Third Quadrant.

[tex]r=\sqrt{(-2x)^2+(-2y)^2}\\\\r=\sqrt{4x^2+4y^2}\\\\r=2\times \sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{-2y}{-2x}\\\\=\tan^{-1}\frac{y}{x}\\\\ \theta=\pi+A[/tex]

Polar Coordinate of point (-2x,-2y)=(2r,π+Ф)

⇒The Point (3x,-3y) lies in Fourth Quadrant.

[tex]r=\sqrt{(3x)^2+(-3y)^2}\\\\r=\sqrt{9x^2+9y^2}\\\\r=3\times \sqrt{x^2+y^2}\\\\ \theta=\tan^{-1}\frac{-3y}{3x}\\\\=\tan^{-1}\frac{-y}{x}\\\\ \theta=-A[/tex]

Polar Coordinate of point (3x,-3y)=(3r,-Ф)

The total return you want is 0.09 * 1600 = $144

Let a be the amount invested at 12% and b be the amount invested at 6% 

0.12a + 0.06b = 144 - 44

12a + 6b = 10000

a + b = 1200

Put those 2 equations together and solve for a and b: 

12a + 6b = 10000 

a + b = 1200

Using elimination, a = $466.67 and b = $733.33

So, out of an additional $1200, invest $466.67 at a rate of 12% and $733.33 at a rate of 6%

To determine how much to invest at 12% and 6% to achieve a total return of 9% on $1,600, set up and solve the equation based on the given information.

To calculate how much of the additional $1,200 should be invested at 12% and how much at 6%:

4x-y=19 is the correct answer for this problem

Answer:

A. 216

Step-by-step explanation:

This is because the volume of a cube is worked out by doing .  being the edge. Therefore, you just have to do  (6 × 6 × 6), which is 216.

Answer: The answer is (c) - 5, (e) 0 and (f) - 200.

Step-by-step explanation:  We are to select the correct numbers from the given options that cannot represent the area of a polygon.

We know that the area of any figure cannot be a negative number or zero.

So, the numbers which cannot represent the area of a polygon are - 5, 0 and - 200.

Thus, (c), (e) and (f) are the correct options.

The projection of the space curve C, resulting from the intersection of the two given paraboloids, onto the xy-plane is the line y=0.

The surfaces provided are of the paraboloids x^2 + y^2 + z = 4 and x^2 + 3y^2 = z. We can find the space curve, which is the curve of intersection of these two surfaces, by setting the two equations equal to each other. We would get x^2 + y^2 + z = x^2 + 3y^2 which simplifies to 2y^2 - z = 0. The projection of this space curve C onto the xy-plane would just be the shadow this curve casts on the xy-plane. Thus, we eliminate the z variable and the result would be 2y^2 = 0 -> y = 0 , so, the projection of the curve on the xy-plane is y=0.

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The graph is attached and 68 sunflowers will be taller than 71 inches in the field.

Given that:

- Mean (average height) = 64 inches

- Standard deviation = 3.5 inches

Standardizing the height 71 inches using the z-score formula, we have

[tex]\[ z = \frac{{x - \mu}}{{\sigma}} \][/tex]

Substitute the known values into the equation

[tex]\[ z = \frac{{71 - 64}}{{3.5}} \][/tex]

[tex]\[ z = \frac{{7}}{{3.5}} \][/tex]

[tex]\[ z = 2 \][/tex]

Using the standard distribution table, we have

P(z > 2) = 0.02275

To find the number of sunflowers taller than 71 inches:

[tex]\[ 3000 \times 0.02275[/tex]

Evaluate

68

Hence, 68 sunflowers will be taller than 71 inches in the field.

To multiply the complex numbers (2 - 7i) and (9 + 5i), we use the distributive property to get the result of 53 - 53i.

To multiply the complex numbers (2 - 7i) and (9 + 5i), we use the distributive property, also known as the FOIL method in this context (First, Outer, Inner, Last). Applying this method, we get:

First: 2 × 9 = 18

Outer: 2 × 5i = 10i

Inner: (-7i) × 9 = -63i

Last: (-7i) ×5i = -35i²

Recall that i² = -1, so -35i² = -35(-1) = 35. Combine like terms (the real numbers with real numbers, and the imaginary numbers with imaginary numbers):

18 + 35 (real parts) + 10i - 63i (imaginary parts) equals to 53 - 53i.

Thus, the product of (2 - 7i) and (9 + 5i) is 53 - 53i.

The answer is B.) $210

To round 15.8% to the nearest whole percent, we round up due to the digit after the decimal point is 8, resulting in 16%.

To round off 15.8% to the nearest whole percent, we look at the first digit after the decimal point, which is 8. Since this digit is 5 or greater, we round up. Therefore, 15.8% rounded to the nearest whole percent is 16%. This rounding method ensures accuracy in representing percentages, particularly in contexts like statistical analysis, grading, and financial reporting. By rounding to the nearest whole percent, the value becomes more concise and easier to interpret, aiding in clear communication and decision-making processes where precise percentage values are essential for understanding and comparison.

[tex]\( C' \cap A' \)[/tex] contains only the element [tex]\( r \).[/tex]

To find [tex]\( C' \cap A' \)[/tex], we first need to determine the complement of sets ( A ) and ( C ) with respect to the universal set ( U ).

The complement of set ( A ), denoted as ( A' ), consists of all elements in ( U ) that are not in (A). So, [tex]\( A' = \{r, t, v, x, z\} \).[/tex]

Similarly, the complement of set [tex]\( C \),[/tex] denoted as [tex]\( C' \)[/tex], contains all elements in (U) that are not in (C). Hence, [tex]\( C' = \{q, r, s, t, u\} \).[/tex]

Now, to find the intersection of [tex]\( C' \) and \( A' \)[/tex], we list the elements that are common to both sets:

[tex]\[ C' \cap A' = \{r\} \][/tex]

Therefore,[tex]\( C' \cap A' \)[/tex] contains only the element [tex]\( r \).[/tex]

To solve the system of equations, rewrite them in standard form, eliminate x, solve for y, and substitute the value of y into the equations to solve for x. The solution to the system of equations is x = 4 and y = 2.

To solve the system of equations:

The solution to the system of equations is x = 4 and y = 2.

To solve the provided system of linear equations, the elimination method can be used. The solution to the equations 3x - 2y = 14 and 5x + 6y = 42 is x = 6 and y = 2.

The student has provided two linear equations which form a system of equations:

To solve this system, we can use either the substitution method, the elimination method, or graphical method. In this case, the elimination method may be more straightforward. Here's a step-by-step explanation:

Therefore, the solution to the system of equations is x = 6, y = 2.

To calculate the proceeds from discounting a note, subtract the bank discount from the face value.

To calculate the proceeds from discounting a note, we need to use the formula:

Proceeds = Face Value - Bank Discount

First, let's calculate the bank discount using the formula:

Bank Discount = Face Value * Discount Rate * Time

For the given note:

Face Value = $15,000

Discount Rate = 9%

Time = 120 days / 365 days/year (assuming a 365-day year)

Plugging in the values, we get:

Bank Discount = $15,000 * 0.09 * (120/365)

Next, we can calculate the proceeds by subtracting the bank discount from the face value:

Proceeds = $15,000 - Bank Discount

Step-by-step explanation:

Arrangement according to her priorities are as follow:

1) Finish homework which is due the next day (Tuesday).

2) Prepare for a French test that is due on Thursday.

3) Prepare  a science project that is due on the following Monday.

4) Prepare for the algebra test that is on the next friday.

5) Complete her essay that is due in two weeks.

6) Plan a surprise party for her best friend's birthday that is on weekend after next.

Answer:

D on edge 2020 :)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

he answer is D.)y = 400(1/2)X-1

Step-by-step explanation:

Option D is correct, y=400(1/2)ˣ⁻¹ is the equation  that models the sequence 400, 200, 100, 50, ..

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

The sequence 400, 200, 100, 50, ... is a geometric sequence with a common ratio of 1/2, since each term is half the previous term.

To write an equation that models this sequence, we can use the general formula for a geometric sequence:

aₙ = a.rⁿ⁻¹

where aₙ is the nth term of the sequence, a is the first term of the sequence, r is the common ratio of the sequence and n is the number of the term we want to find

Since the first term is 400 and the common ratio is 1/2, we have:

a= 400

r = 1/2

aₙ=400(1/2)ˣ⁻¹

y=400(1/2)ˣ⁻¹

Hence, option D is correct, y=400(1/2)ˣ⁻¹ is the equation  that models the sequence 400, 200, 100, 50, ..

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