Keisha estimates 259+372 by rounding each number to the nearest 10. What is Keisha's estimate of the sum?

Answer:

The cabin is located 567 yards away.

Step-by-step solution:

The bearing angle of 21.2° corresponds to the interior angle near the cabin in the triangle.

Apply the tangent function:

Opposite side length: 220 yards

Adjacent side length: x (distance to cabin)

tan(21.2°) = opposite / adjacent

tan(21.2°) = 220 yards / x

Multiply both sides by x:

x × tan(21.2°) = 220 yards

Isolate x:

x = 220 yards / tan(21.2°)

x = 220 / 0.388

x = 567 yards

Hence, the cabin is 567 yards away.

Answer:

a) The first inequality is 100 + 55x > 150 + 51x;

b) The final inequality results in x > 12.5

c) Sal's mother will need to use the second phone for at least 13 months.

Step-by-step explanation:

a) Let x represent the number of months.

1. The first phone is priced at $100, with a monthly fee of $55 for unlimited use, leading to a total cost of $(100 + 55x) for x months.

2. The second phone costs $150 with a monthly fee of $51 for unlimited use, resulting in a total of $(150 + 51x) for x months.

3. For the second phone to be cheaper, we set up the inequality:

150 + 51x < 100 + 55x

which simplifies to

100 + 55x > 150 + 51x

b) Now solve this:

55x - 51x > 150 - 100

4x > 50

so x > 12.5

c) This means Sal's mother has to retain the second phone for at least 13 months (since x > 12.5).

Answer:

Possible values for X include;

15, 30, 45, 60, and so on

Step-by-step explanation:

The parameters provided are

Number of chocolates Tanmay possessed = X

Number of chocolates given to Akash = 1/3 × X

Number of chocolates given to Sharad = 1/5 × X

Consequently, since both 3 and 5 divide X,

3 × 5 = 15 is the smallest single factor of X.

Thus, the values of X based on this minimum factor are as follows;

15 × 1 = 15

15 × 2 = 30

15 × 3 = 45

15 × 4 = 60

Therefore, potential values for X form an arithmetic series: a + (n - 1) × d

Where:

a = 15

n = 1, 2, 3, 4,...

d = 15

This results in;

15, 30, 45, 60