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2 years ago

Zoe buys a new car that is valued at $24,000. The car will depreciate at

Mathematics

1 answer:

Yakvenalex [24]2 years ago

8 0

Answer:

120

Step-by-step explanation:

Principal = 24,000

Rate = 1%

Time = 6 months = 0.5

Simple Interest = 24000×1×0.5 ÷ 100

= 120

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Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

2.21 and 2.23 are proved by contrapositive
2.22 is proved by induction

2.21: If $n^3$ is even, then n is even (By contrapositive)

The contrapositive of the above statement is that:

If n is odd, then $n^3$ is odd

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

i.e. If n is odd, then $n^3$ is odd

2.22 $3n + 4$ is even, if and only if n is even

We have: $3n + 4$

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

Hence, $3n + 4$ is even, if and only if n is even

2.22: $s \ne -1$ and $t \ne -1$ , then $s + t + st \ne -1$

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

Read more about proofs at:

brainly.com/question/19643658

7 0

2 years ago

What is the value of x a. 25 b. 12 c. 7 d. 5

tia_tia [17]

The answer is 5 because a^2 + b^2 = c^2

8 0

2 years ago

Read 2 more answers

HURRY GIVING BRAINLIEST !!

sashaice [31]

Answer:
15ft
Step-by-step explanation:
If you redraw it and use a ruler it will be 15 feet.

5 0

1 year ago

Identify the coefficient(s), constants, and number of terms for the following expression:

shusha [124]

The given expression is: $4 x^{2} -5$

So, there are two terms in the expression
1) $4 x^{2}$
2) -5

The constant term is -5.
The co-efficient of $4 x^{2}$ is 4.

7 0

2 years ago

I need to show my work, could anyone help? (need by tonight 3/10/20

marishachu [46]

Answer:

14 gallons....$42

Step-by-step explanation:

The car requires one gallon every 32 miles...

The car requires c gallons for 448 miles

c = 448 × 1 / 32

= 14 gallons..

One gallon = $3

Fourteen gallons = ??

14 × 3 / 1 = $42

3 0

2 years ago