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tia_tia [17]
3 years ago
9

Susan has a 12-inch board for constructing a wooden chair.The directions say to use a board that is 29 centimeters long.Id her b

oard kind enough to cut?
Mathematics
1 answer:
Advocard [28]3 years ago
6 0

We have been given that Susan has a 12-inch board for constructing a wooden chair.The directions say to use a board that is 29 centimeters long. We are asked to determine if Susan's board is long enough to cut or not.

We know that 1 inch is equal to 2.54 cm.

Let us convert 12 inches into cm by multiplying 12 by 2.54.

12\text{ inches}=12\times 2.54\text{ cm}

12\text{ inches}=30.48\text{ cm}

Since 12 inches is equal to 30.48 centimeters and 30.48 is greater than 29, therefore, Susan's board in long enough to cut.

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The third and the sixth term of a geometric progression are 24 and 64/9 respectively. Find
Ratling [72]

Answer:

Ai. Common ratio = 2/3

Aii. First term = 54

B. Sum of the first five terms = 422/3

Step-by-step explanation:

From the question given above, the following data were obtained:

3rd term (T3) = 24

6Th term (T6) = 64/9

First term (a) =?

Common ratio (r) =?

Sum of the first five terms​ (S5) =?

Ai. Determination of the common ratio (r).

T3 = ar²

T3 = 24

24 = ar²....... (1)

T6 = ar⁵

T6 = 64/9

64/9 = ar⁵......... (2)

The equation are:

24 = ar²....... (1)

64/9 = ar⁵......... (2)

Divide equation 2 by equation 1.

64/9 ÷ 24 = ar⁵ / ar²

64/9 × 1/24 = r³

8/27 = r³

Take the cube root of both side

r = 3√(8/27)

r = 2/3

Thus, the common ratio is 2/3

Aii. Determination of the first term (a).

T3 = ar²

3rd term (T3) = 24

Common ratio (r) = 2/3

First term (a) =?

24 = a(2/3)²

24 = 4a/9

Cross multiply

24 × 9 = 4a

216 = 4a

Divide both side by 4

a = 216/4

a = 54

Thus, the first term (a) is 54

B. Determination of the sum of the first five terms.

Common ratio (r) = 2/3

First term (a) = 54

Number of term (n) = 5

Sum of first five terms (S5) =?

Sn = a[1 –rⁿ] / 1 – r

S5 = 54[1 – (⅔)⁵] / 1 – ⅔

S5 = 54 [1 – 32/243] / ⅓

S5 = 54 (211/243) × 3

S5 = 54 × 211/81

S5 = 6 × 211/9

S5 = 2 × 211/3

S5 = 422/3

Thus, the sum of the first five terms is 422/3

8 0
3 years ago
Jack's family spent $16,848 for one years home rental. What is the average amount that Jack's family spent per month?
lyudmila [28]

A year is divided into <u>12 months.</u>

Jack' family spent <u> $16,848</u> for one years's home rental.

16 848 ÷ 12 = 1404 ≈ 1400 → so the correct answer is<u> A. </u>

:)

5 0
3 years ago
PLEASE HELP HOMEWORK DUE IN 5 MINUTES
VARVARA [1.3K]

Answer:

????

Step-by-step explanation:

what is the question

4 0
4 years ago
Read 2 more answers
If the discriminant of a quadratic equation is 6, how many solutions does the equations have?
rjkz [21]
If d=6, there are two real solutions.

Rule if d=discriminant:

d>0, two real solutions

d=0, one real solution

d<0, no real solutions  (but there are two imaginary solutions)
6 0
3 years ago
You buy a notebook for $6.25 and there is 7.5% sales tax. You pay with a $20 bill. How much change should you expect?
a_sh-v [17]

Answer:

Step-by-step explanation:

1. •6.25 × 7.5 = "the answer"

2. •20 - "the answer"

5 0
4 years ago
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