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Answer:

It is necessary to invest $5,000 in the 8% option

And, $15,000 in the 12% option

Step-by-step explanation:

Let’s begin by calculating the total expected return.

With an anticipated total return of 11%, the expected amount back is;

11/100 * 20,000 = $2,200

Let x represent the amount put into the 8% investment, and y represent the investment in the 12% option

From this, we have the equation;

x + y = 20,000 ••••••(i)

Now considering the interest portion;

The interest for the 8% portion is 8/100 * x

For the 12% part, it’s 12/100 * y

Thus, we express that as;

(8/100 * x) + (12/100 * y) = 2,200

Consolidating, we have;

8x/100 + 12y/100 = 2,200

Multiplying throughout by 100 gives us

8x + 12y = 220,000 ••••••(ii)

Next, we can solve this system of equations;

x + y = 20,000

8x + 12y = 220,000

Using i, we find x = 20,000 - y

Substituting into ii yields;

8(20,000-y) + 12y = 220,000

160,000-8y + 12y = 220,000

Combining yields 4y = 220,000 - 160,000

Thus, 4y = 60,000

So, y = 60,000/4

y = $15,000

From this, x can be calculated as follows:

x = 20,000 - y

x = 20,000 - 15,000

x = $5,000

The maximum number of identical dental care bags the dentist can create with the smallest leftover is 1.

The counts of bags are 2, 4, and 3, respectively.

Clarification:

Total tubes of toothpaste = 56

Total packets of floss = 112

Total toothbrushes = 85

Therefore, the greatest number of identical dental care bags the dentist can assemble with minimal leftover for toothbrushes is found by calculating the H.C.F of 56, 112, 85 = 1 ( ∵ as they are coprime to each other )

Given that there is no common factor among 56, 112, and 85, except for the commonality between 56 and 112, which is 56, the remainder of toothbrushes will be 85-56=29.

Thus considering 28,[TAG_24]]

The numbers can be expressed as follows: 56 = 28×2, 112 = 28×4, and 84 = 28×3

Consequently, the dentist can create 28 bags containing all three supplies, with no leftover from toothpaste and floss, but with leftover from toothbrushes as we substitute 84 for 85 to maintain divisibility by 28 for common factor demonstration.

This results in 2 bags for toothpaste, 4 bags for floss, and 3 bags for toothbrushes.

There are a total of 20,000 available numbers. To ascertain how many phone numbers are available, the number of digits in each number must be known. Here, I will assume each number has 7 digits. This leads to the format starting with either 373XXXX or 377XXXX, where each X can be any digit from 0 to 9. This results in 10 options for each X. Therefore, there are 10×10×10×10 = 10,000 distinct phone numbers starting with 373 and another 10,000 with 377, totaling 20,000 numbers.

Answer:

The area of the new pumpkin patch can be represented as    =  15 x² + 380 x + 2400

Step-by-step explanation:

Given as:

The length of the original patch is L = 40 meters

The width of the original patch is W = 60 meters

Thus, the area of the rectangular patch is calculated as Length × Width

Or, =  L × W

So,    =  40 meters × 60 meters

Or,   =  2400 meters²

Moreover, the width of the new patch becomes (40 + 3 x) meters

And the length of the new patch becomes (60 + 5 x) meters

Or,  =  L × W

Thus,  =  (40 + 3 x) meters × (60 + 5 x) meters

Or,    = 2400 + 200 x + 180 x + 15 x²

Or,    =  15 x² + 380 x + 2400

Therefore, the area of the new pumpkin patch is given by    =  15 x² + 380 x + 2400  Answer

x = 3

-2 | 2.2(3) - 3.3 | = -6.6

-2 | 6.6 - 3.3 | = -6.6

-2 | 3.3 | = -6.6

-2 * 3.3 = -6.6

-6.6 = -6.6