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3 years ago

What is the value of the fourth term in a geometric sequence for which a1= 30 and are= 1/2?

Mathematics

1 answer:

serious [3.7K]3 years ago

3 0

Answer:

15/4.

Step-by-step explanation:

4th term = a1 r^3

= 30(1/2)^3

= 30/8

= 15/4.

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a garage floor measures 150 feet by 120 feet. a scale drawing of the floor on grid paper uses a scale of one unit : 15 feet. wha

Nadya [2.5K]

1 unit = 15 feet

150 feet / 1 unit = 150 / 15 = 10 units

120 feet / 1 unit = 120 / 15 = 8 units

The dimensions of the drawing equates :

10 units by 8 units .

hope this helps!

4 0

3 years ago

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

3 years ago

Ms Melissa and Ms ryanne went for a walk and they got back at 8:02am their walk was actually 45 minutes what time did they leave

dimaraw [331]

Answer: 7: 17

Step-by-step explanation:

This doesn't really make sense but it's how I do it

8:02 = 7:62

7:62

- 45

7: 17

6 0

3 years ago

6. In both Mr. Jacquez's Math 2 classes, Period 2 and Period 3 were given the same test. The table below shows the results from

umka2103 [35]

Answer: pass 12 fail 12 passes 15 fail1 3

Step-by-step explanation:

pass 12 fail 12

pass 15 fail 13

3 0

2 years ago

-3(4x-8.2)< -11.98x + 14 3 /4

Leona [35]

The answer would be C

6 0

3 years ago