Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and t

Answer:

Let’s outline the sets:

Integers: The collection of all whole numbers.

Rational: Numbers that can be expressed as the ratio of two integers.

Natural: The collection of positive integers.

Whole numbers: All the values obtainable by repeatedly adding (or subtracting) 1 to a number.

Thus:

2 qualifies as a:

Whole number, because 1 + 1 = 2 (therefore, it’s also an integer).

We can express 2 as 4/2.

As 2 is the fraction of two integers, it is also considered rational.

Since 2 is positive and an integer, it falls into the category of natural numbers.

Therefore, the number 2 exemplifies all four sets.

If we include a negative example, we can consider -3.

-3 is classified as an integer, is not a whole number, and with 9/-3 = -3, thus it is also a rational number.

Now, addressing the questions:

a) Although a single example can be used across all four sets, I have chosen 2 in this instance.

b) Similarly, I demonstrated that 2, as a positive integer, belongs to all four sets, thus:

Positive integers belong to:

The set of integers.

The set of natural numbers.

The set of rational numbers.

The set of whole numbers.

Answer: C. Significant at 0.036

Step-by-step explanation:

Given:

Total samples selected Ns= 500

Airplanes that arrived on time Na = 482.

Airplanes that arrived late Nl = 500 - 482 = 18

Calculating the probability of an airplane arriving late:

P(L) = Nl/Ns

P(L) = 18/500

P(L) = 0.036

An event is deemed significant if its probability is equal to or less than 0.05.

As P(L) < 0.05

P(L) = Significant at 0.036

You have two kinds of data $ and %!
Align them properly and perform cross multiplication.

16% corresponds to $38 as
100% corresponds to $x

Following this, x = (38*100)/16 = $237.5, which is the original price before the discount.

Given data:
a₃ = 9/16
aₓ = -3/4 · aₓ₋₁
Here, x represents the number of terms ('x' can also be referred to as 'n')
To determine the 7th term (a₇):

We know that aₓ = -3/4 · aₓ₋₁
Thus,[ [TAG_10]]a₃ = -3/4 · a₃₋₁
a₃ = -3/4 · a₂
9/16 = -3/4 · a₂
a₂ = 9/16 × -4/3
a₂ = -36/48
a₂ = -3/4

Next,[ [TAG_20]]aₓ = -3/4 · aₓ₋₁
a₄ = -3/4 · a₄₋₁
a₄ = -3/4 · a₃
a₄ = -3/4 · 9/16
a₄ = -27/64
a₄ = -27/64

For a₅,[ [TAG_30]]aₓ = -3/4 · aₓ₋₁
a₅ = -3/4 · a₅₋₁
a₅ = -3/4 · a₄
a₅ = -3/4 × -27/64
a₅ = 81/256

For a₆,[ [TAG_39]]aₓ = -3/4 · aₓ₋₁
a₆ = -3/4 · a₆₋₁
a₆ = -3/4 · a₅
a₆ = -3/4 × 81/256
a₆ = -243/1024

Finally, for a₇,[ [TAG_48]]aₓ = -3/4 · aₓ₋₁
a₇ = -3/4 · a₇₋₁
a₇ = -3/4 · a₆
a₇ = -3/4 × -243/1024
a₇ = 729/4096

Answer:

The area calculates to 83.905 cm^3

Step-by-step explanation:

The overall ratio is 9 + 7 + 6 = 22

Thus, the side lengths are computed as follows;

9/22 * 44 = 18 cm

7/22 * 44 = 14 cm

6/22 * 44 = 12 cm

Heron’s formula allows us to determine the area of the triangle

First, we calculate s

s = (a + b + c)/2 = (18+14+12)/2 = 44/2 = 22

Heron’s formula can be expressed as;

A = √s(s-a)(s-b)(s-c)

where a, b, and c are 18, 14, and 12 respectively

Plugging in the values, we obtain;

A = √22(22-18)(22-14)(22-12)

A = √(22 * 4 * 8 * 10)

A = √(7,040)

A = 83.905 cm^3