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STatiana [176]
3 years ago
10

MARK AS BRAINLIEST An artist has a block of clay in the shape of a cube. The edges of the cube measure 3 inches. The artist will

use the clay to make models of
pine trees. Each tree will be a solid cone with a base diameter of 1.5 inches and a height of 2 inches.
Part A
Determine the greatest number of clay pine trees that the artist can make. Show your work.
Mathematics
1 answer:
Xelga [282]3 years ago
7 0

Answer:

22

Step-by-step explanation:

The volume of a cube is given as:

Cube volume = length × length × length

Since the edges of the cube measure 3 inches, this means that the length of the cube is 3 inches, therefore:

Cube volume = 3 inches × 3 inches × 3 inches = 27 in³

The pine tree is the shape of a cone with diameter of 1.5 inches and a height (h) of 2 inches. The radius (r) = diameter / 2 = 1.5 inches / 2 = 0.75 inches.

The volume of the cone = πr²(h/3) = π × (0.75)² × (2/3) = 1.178 in³

The number of pine trees that can be made = Volume of cube / Volume of cone = 27 / 1.178 = 22.9

The number of pine trees = 22

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Step-by-step explanation:

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2 years ago
a motorcycle dealer paid a certain price for a motorcycle and marked it up by 1/5 of the price he paid. Later, he sold it for $1
katovenus [111]
Okay so $14,000 is the equivalent of 6/5ths
so divide $14,000 by 6= $2333.3r

you need 5/5
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5 0
3 years ago
A circle has a circumference of 266.9 inches. What is the Diameter of this circle? What is the Radius? Use 3.14 as the approxima
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Answer:

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Step-by-step explanation:

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4 0
3 years ago
Suppose x=c1e−t+c2e3tx=c1e−t+c2e3t. Verify that x=c1e−t+c2e3tx=c1e−t+c2e3t is a solution to x′′−2x′−3x=0x′′−2x′−3x=0 by substitu
Harrizon [31]

The correct question is:

Suppose x = c1e^(-t) + c2e^(3t) a solution to x''- 2x - 3x = 0 by substituting it into the differential equation. (Enter the terms in the order given. Enter c1 as c1 and c2 as c2.)

Answer:

x = c1e^(-t) + c2e^(3t)

is a solution to the differential equation

x''- 2x' - 3x = 0

Step-by-step explanation:

We need to verify that

x = c1e^(-t) + c2e^(3t)

is a solution to the differential equation

x''- 2x' - 3x = 0

We differentiate

x = c1e^(-t) + c2e^(3t)

twice in succession, and substitute the values of x, x', and x'' into the differential equation

x''- 2x' - 3x = 0

and see if it is satisfied.

Let us do that.

x = c1e^(-t) + c2e^(3t)

x' = -c1e^(-t) + 3c2e^(3t)

x'' = c1e^(-t) + 9c2e^(3t)

Now,

x''- 2x' - 3x = [c1e^(-t) + 9c2e^(3t)] - 2[-c1e^(-t) + 3c2e^(3t)] - 3[c1e^(-t) + c2e^(3t)]

= (1 + 2 - 3)c1e^(-t) + (9 - 6 - 3)c2e^(3t)

= 0

Therefore, the differential equation is satisfied, and hence, x is a solution.

4 0
3 years ago
The income distribution in a county is a normal distribution with a mean income of $10,000. The top 2.5% of the wage earners ear
earnstyle [38]

Answer:

<em>84%</em><em> of the wage earners earn less than $14,000 each. </em>

Step-by-step explanation:

The Empirical Rule (68-95-99.7%)-

According to this around 95% of the data will fall within two standard deviations of the mean.

As the bell curve is symmetrical, so the remaining 5% will be divided into 2 equal parts. So 2.5% will be above 2 standard deviation and 2.5% will be below 2 standard deviation.

As it is given that, the top 2.5% of the wage earners earn $18,000 or more, so 18,000 is 2 standard deviation away from the mean 10,000.

i.e 2\sigma=18000-10000=8000

\Rightarrow \sigma = 4000

We know that,

Z=\dfrac{X-\mu}{\sigma}

where,

X = raw score = 14,000

μ = 10,000

σ = 4,000

Putting the values,

Z=\dfrac{14000-10000}{4000}=\dfrac{4000}{4000}=1

Now, calculating the value from the z score table,

P(1)=0.8413=84.13\%

As the probability at z=1 is the area below that, so 84% of the wage earners earn less than $14,000 each.

6 0
4 years ago
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