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3 years ago

12

A stack of boards is 21 inches high. Each board is 1 and 3/4 inches thick. How many boards are there?

1 answer:

hichkok12 [17]3 years ago

6 0

12 boards
divide 21 by 1 3/4

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Match each series with the equivalent series written in sigma notation

PIT_PIT [208]

Answer:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

$3 + 12 + 48 + 192 + 768$

The expression can be written as:

$3 \to 3*4^{0$ --- 0

$12 \to 3 * 4^{1$ ---- 1

$48 \to 3 * 4^{2$ --- 2

$192 \to 3 * 4^{3$ ---- 3

$768 \to 3 * 4^{4$ ---- 4

For the nth term, the expression is:

$Term = 3 * 4^{n$ ---- n

So, the summation is:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

Solving (b):

$4 + 32 + 256 + 2048 + 16384$

The expression can be written as:

$4 \to 4 * 8^0$ --- 0

$32 \to 4 * 8^1$ ---- 1

$256 \to 4 * 8^2$ --- 2

$2048 \to 4 * 8^3$ ---- 3

$16384 \to 4 * 8^4$ ---- 4

For the nth term, the expression is:

$Term \to 4 * 8^n$ ---- n

So, the summation is:

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

Solving (c):

$2 + 6 + 18 + 54 + 162$

The expression can be written as:

$2 \to 2 * 3^0$ --- 0

$6 \to 2 * 3^1$ ---- 1

$18 \to 2 * 3^2$ --- 2

$54 \to 2 * 3^3$ ---- 3

$162 \to 2 * 3^4$ ---- 4

For the nth term, the expression is:

$Term \to 2 * 3^n$ ---- n

So, the summation is:

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

Solving (d):

$3 + 15 + 75 + 375 + 1875$

The expression can be written as:

$3 \to 3 * 5^0$ --- 0

$15 \to 3 * 5^1$ ---- 1

$75 \to 3 * 5^2$ --- 2

$375 \to 3 * 5^3$ ---- 3

$1875 \to 3 * 5^4$ ---- 4

For the nth term, the expression is:

$Term \to 3 * 5^n$ ---- n

So, the summation is:

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

5 0

2 years ago

The variables x and y vary inversely. When y is 725, x is 20. What is x when y is 50?

Ipatiy [6.2K]

I think it is 2.5 but not sure correct me if i am wrong

6 0

3 years ago

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One meter is approximately equal to 39.39 inches.About how many inches are in 3 meters? A 40 B 90 C 120 D 150

WITCHER [35]

There are 118.11 inches in 3 meters. So rounding up the answer would be C

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3 years ago

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Four farmers are picking apples in an orchard. Farmer A picks 38 of the apples, Farmer B picks 22% of the apples, Farmer C picks

AfilCa [17]

The amount of apples picked by the farmers is:
Farmer A=38%=0.38
Farmer B=22%=0.22
Farmer C=0.29
Farmer D=0.2
Thus the order from the least to greatest by th number of apples they pick will be:
D,B,C,A
that is:
Farmer D, Farmer B, Farmer C, Farmer A

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3 years ago

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Maths giving 10 point asap 1 question only

erik [133]

Answer:

Price of shirt=RM9.8

Step-by-step explanation:

Shirt=x Trouser=y

x+y=RM20

5x+y=RM59.20

y=20-x

5x+20-x=59.20

4x=39.20

x=9.8

y=20-9.8

y=10.2

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2 years ago