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3 years ago

Help please with # 24, 25, 26, 27

Mathematics

1 answer:

Elis [28]3 years ago

6 0

24. C

25. B

26. A

27. C

I hope this helped!

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A worker at a cabinet shop is cutting out pieces of wood for a dresser. He needs pieces that are 4 1/4inches long. Each saw cut

ella [17]

Answer: he will be able to make 19 full pieces

Step-by-step explanation:

1. Start off by making 7 feet into 84 inches so the measurements can match.

2. Add 4/14 inches and the 1/8 a inch together so you know how much is being taken off 84 inches. The amount will be 35/8 inches.

3. Divide 84 inches by 35/8 inches = 19 1/5

4. The whole number of the answer will be how many boards you can make from the board.

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3 years ago

Given that 3^x = 4^y = 12^z, show that z = (xy)/(x+y).

irinina [24]

$3^{x} = 4^{y} = 12^{z}$
$3^{x} = 4^{y} = (4 \cdot 3)^{z}$
$3^{x} = 4^{y} = 4^{z} \cdot 3^{z}$

$\text{Let a } = 3^{x} = 4^{y} = 4^{z} \cdot 3^{z}$
$log_3a = x$
$log_4a = y$
$log_{(4 \cdot 3)}a = z$

Using change of base:
$x = \frac{lna}{ln3}$
$y = \frac{lna}{ln4}$
$z = \frac{lna}{ln(4 \cdot 3)}$

$ln3 = \frac{lna}{x}$
$ln4 = \frac{lna}{y}$
$ln(4 \cdot 3) = \frac{lna}{z}$

Now, ln(4 · 3) = ln(4) + ln(3)

$\frac{lna}{z} = \frac{lna}{x} + \frac{lna}{y}$
$\frac{1}{z} = \frac{1}{x} + \frac{1}{y}$
$\frac{1}{z} = \frac{x + y}{xy}$

$\therefore z = \frac{xy}{x + y}$

8 0

4 years ago

A thermos in the shape of a cylinder is filled with coffee. The height of the cylinder is 12 inches and its radius is 2 inches.

serg [7]

Answer:

The volume of coffee in the thermos is 150.72 inches³ .

Step-by-step explanation:

Formula

$Volume\ of\ a\ cylinder = \pi r^{2}\ h$

Where r is the radius and h is the height .

As given

A thermos in the shape of a cylinder is filled with coffee.

The height of the cylinder is 12 inches and its radius is 2 inches.

$\pi = 3.14$

Put all the value in the formula

$Volume\ of\ a\ cylinder = 3.14\times 2\times 2\times 12$

= 150 .72 inches ³

Therefore the volume of coffee in the thermos is 150 .72 inches ³ .

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3 years ago

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