RR = 12. What is the length of RZ? 3 6 12 18

the lawn on the lawn order lawn mower Factory can produce 12 lawn mowers in 8 hours how many hours will it take the factory to p

Elena L [17]

It will take the factory 45 hours to make 30 lawnmowers.

3 0

2 years ago

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The half-life of cesium-137 is 30 years. Suppose we have a 170 mg sample.(a) Find the mass that remains after t years.(b) How mu

saul85 [17]

Answer:

212.9 years

Step-by-step explanation:

Given that the half-life of cesium-137 is 30 years. Suppose we have a 170 mg sample

P0 = 175

P(30) = 87.5

So we can write equation as

$P(t) = 170(\frac{1}{2} )^{\frac{t}{30} }$

b) After 60 years t = 30

In 30 years it becomes half and hence in 60 years it would become 1/4

i.e. $P(60) = 137(1/2^4) = 34.25$ mg

c) If P(t) =1, let us find t

$137(1/2)^{\frac{t}{30} } =1\\\\n = 7.098 years\\n = 7.1*30 = 212.9 years$

212.9

5 0

2 years ago

Suppose the average price for new cars in 2012 has a mean of $30,100 and a standard deviation of $5,600. Based on this informati

KatRina [158]

Answer:

($13,300,$46,900)

Step-by-step explanation:

We are given the following in he question:

Mean, μ = $30,100

Standard Deviation, σ = $5,600

Chebyshev's Theorem:

According to theorem atleast $1 - \dfrac{1}{k^2}$ percent of data lies within 2 standard deviations of mean.
For k = 3,

$1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%$

Thus, 89% of data lies within three standard deviation of mean.

$\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900$

Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)

3 0

2 years ago

MO, MN, and ON are the midsegments of △JKL. What is the perimeter of △JKL? 6 9.5 11.5 19

ipn [44]

Answer is 19 just got it right

6 0

2 years ago

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A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square pr

guajiro [1.7K]

Step 1

Find the Volume of the two balls

we know that

the Volume of a sphere is equal to

$V=\frac{4}{3} \pi r^{3}$

In this problem we have

$r=1.5\ in$

Substitute

$V=\frac{4}{3} \pi 1.5^{3}=4.5\pi\ in^{3}$

so

the volume of the two balls is equal

$V=2*4.5\pi=9 \pi\ in^{3}$

Step 2

Find the volume of a cylinder

we know that

The Volume of a cylinder is equal to

$V=\pi r^{2}h$

In this problem we have

$r=1.5\ in$

$h=4*r=4*1.5=6\ in$

Substitute

$V=\pi (1.5^{2})(6)=13.5 \pi\ in^{3}$

Step 3

Find the amount of wasted space in the cylinder

Subtract the volume of the two balls from the volume of the cylinder

$13.5\pi\ in^{3}-9\pi\ in^{3}=4.5\pi\ in^{3}=14.14\ in^{3}$

Step 4

Find the volume of the square prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

$B=(2*1.5)^{2}=9\ in^{2}$ -----> the base is equal to the diameter

$h=4*r=4*1.5=6\ in$

Substitute

$V=9*6=54\ in^{3}$

Step 5

Find the amount of wasted space in the prism

Subtract the volume of the two balls from the volume of the prism

$54\ in^{3}-9\pi\ in^{3}=25.73\ in^{3}$

Step 6

Compare the amount of wasted space

the amount of wasted space in the cylinder is $14.14\ in^{3}$

the amount of wasted space in the prism is $25.73\ in^{3}$

Find the difference

$25.73\ in^{3}-14.14\ in^{3}=11.59\ in^{3}=11.6\ in^{3}$

The package that has the least amount of wasted space is the cylinder

therefore

the answer is the option

the cylinder because it has approximately 11.6 in.3 less wasted space than the prism

5 0

2 years ago

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