Grace is comparing cell phone plans. A prepaid phone plan costs $0.20 per minute and has no monthly fee. A contracted phone plan

Answer:

13%

Detailed breakdown:

Information provided:

• MP = 2080
• Discount = d%
• VAT = (d-2)%
• Cost = 1997.84

Applying the discount:

• 2080 - d% = 2080*(1 - 0.01d)

Including VAT:

• 2080*(1 - 0.01d) + (d - 2)%
• 2080*(1 - 0.01d) * (1 + (d -2)/100)
• 2080*(1 - 0.01d) * (0.98 + 0.01d) = 1997.84
• (1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080
• 0.98 + 0.01d - 0.0098d - 0.0001d² = 0.9605
• - 0.0001d² + 0.0002d + 0.98- 0.9605 = 0
• 0.0001d²- 0.0002d - 0.0195 = 0
• d² - 2d + 195 = 0

Solving this quadratic equation yields:

• d = 15

Therefore

• VAT rate = 15 - 2 = 13%

Answer:

The fat percentage in the blend amounts to 8%.

Step-by-step explanation:

Let

x -----> represent the fat percentage in the mix.

We understand that

The total of milk's volume times its fat percentage, added to cream's volume times its fat ratio, must match the overall mixture's volume times its fat percentage.

Keep in mind that

15% = 15/100 = 0.15

3% = 3/100 = 0.03

therefore

Now, solve for x

Convert that into a percentage

In this scenario, we'll define the following variables:

x: total volume of potting soil in liters.

y: quantity of potting soil allocated to each pot in liters.

To determine the number of pots, we can use the expression:

Substituting in the respective values yields:

Reformatting gives us:

When rounding down to the nearest whole number, we find:

The conclusion is:

Yao Xin is capable of filling 18 pots.

Step

Calculate the volume of a cylinder

We understand that

the volume of a cylinder can be expressed as

In this scenario

Insert the values

Step

Calculate the volume of a cone

We are aware that

the volume of a cone equals

In this example

Use the Pythagorean Theorem to determine the height h

Step

Calculate the empty volume inside the cylinder

Thus

the final result is

the empty volume inside the cylinder is

The diagrams for parts A and C are included here. For part B, we have circle O. We begin by drawing two radii OA and OC, connecting points A and C to create chord AC. The radius intersects chord AC at point B, bisecting AC into equal segments AB and BC. This gives us two triangles, ΔOBA and ΔOBC, where OA equals OC (since they're radii), OB equals OB (by the reflexive property), and AB is equal to BC (as stated in the question). By applying the SSS triangle congruence criterion, we conclude that ΔOBA is congruent to ΔOBC, allowing us to deduce that ∡OBA equals ∡OBC, both measuring 90°. Thus, OB is perpendicular to AC. Moving on to part D, we again work with circle O and draw the two radii OA and OC, joining points A and C to create chord AC. The radius intersects AC at point B, where AB is perpendicular to AC, meaning ∡B equals 90°. We then consider the right triangles ΔOBA and ΔOBC, and given OA equals OC (the radii), and OB equals OB (reflexive property), we conclude through the HL triangle congruence that ΔOBA is congruent to ΔOBC. Consequently, we find BA equal to BC, thus OB bisects AC.