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Nimfa-mama [501]
3 years ago
14

The base of a rectangular prism is a square. The height of the prism is half the length of one edge of the base. The volume of t

he rectangular prism is 13.5 cubic units. What are the dimensions of the prism?
Mathematics
1 answer:
ki77a [65]3 years ago
4 0

Answer:

The prism is 3 by 3 by 1.5.

Step-by-step explanation:

The prism has a length x and a width x. Since it is a square at the base both length and width are the same amount x. The height is "half the length of one edge of the base". Since the base is x, this makes it 1/2x.

The volume's prism is found using V = l*w*h. Substitute and simplify.

13.5 = x*x*1/2x

13.5 = 1/2 x^3

27 = x^3

3 = x

The prism is 3 by 3 by 1.5.

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KatRina [158]

Answer:

Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

||Vel_jet_r|| =  465.993 mph

Step-by-step explanation:

We need to decompose the velocity of the wind into a component that can be added  (or subtracted from the velocity of the jet)

The velocity of the jet

500 mph North

Velocity of the wind

50 mph SouthEast = 50 cos(45) East + 50 sin (45) South

South = - North

Vel_ wind = 50 cos(45) mph  East  -  50 sin (45) mph North

Vel _wind =  35.35 mph  East  -  35.35 mph North

This means that the resulting  velocity of the jet is equal to

Vel_jet_r =  (500 mph - 35.35 mph) North + 35.35 mph East

Vel_jet_r =  (464.645 mph)  North + (35.35 mph) East

An the jet has a magnitude velocity of

||Vel_jet_r|| =  sqrt ((464.645 mph)^2 + (35.35 mph)^2)

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7 0
3 years ago
21 is 35% of what number ​
spin [16.1K]

Answer:

21 is 35% of 60

Step-by-step explanation:

35% can be written as 0.35

0.35x = 21   ----- 0.35 times a number is 21

divide both sides by 0.35:

x = 60

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Step-by-step explanation:

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3 years ago
12ft 6ft 6ft 6ft what is the area of this face
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Answer:

2,592ft

Step-by-step explanation:

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3 years ago
The chances of a tax return being audited are about 21 in 1 comma 000 if an income is less than​ $100,000 and 29 in 1 comma 000
vladimir2022 [97]

Answer:

a) p=0.021

b) p=0.029

c) Exactly one audit: P=0.0965

More than one audit: P=0.0042

Step-by-step explanation:

a) If the income is less than $100,000, there is a probability of 21 in 1,000 of being audited. This is:

p_1=\dfrac{21}{1,000}=0.021

If the income is equal or more than $100,000, there is a probability of 29 in 1,000 of being audited. This is:

p_2=\dfrac{29}{1,000}=0.029

b) If we have 5 taxpayers with incomes under $100,000, and we want to know the probability that exactly one will be audited, we can model this a binomial randome variable, with p=0.021 and n=5:

P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\

There is a probability of 0.0965 that exactly one out of a sample of five taxpayers with incomes under $100,000 will be audited.

To calculate the probability that more than one will be audited, we use the same distribution:

P(x>1)=1-[P(x=0)+P(x=1)]\\\\\\P(x=0) = \dbinom{5}{0} p^{0}q^{5}=1*1*0.8993=0.8993\\\\\\P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\\\P(x>1)=1-[P(x=0)+P(x=1)]\\\\P(x>1)=1-(0.8993+0.0965)\\\\P(x>1)=1-0.9958\\\\P(x>1)=0.0042

There is a probability of 0.0042 that more than one out of a sample of five taxpayers with incomes under $100,000 will be audited.

8 0
2 years ago
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