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2 years ago

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What is the volume of a right circular cone that has a height of 11.7meters and a base with a circumference of 9 meters? Round t

he answer to the nearest tenth of a cubic meter

1 answer:

nekit [7.7K]2 years ago

7 0

Answer:

25.1 cubic meters

Step-by-step explanation:

The volume is given by ...

V = (1/3)Bh

where B is the area of the base.

B = πr² = π(C/(2π))² = C²/(4π)

Then the volume is ...

V = (1/3)(C²/(4π))h = C²h/(12π)

V = (9 m)²(11.7 m)/(12·3.14159) ≈ 25.1 m³

The volume of the cone is about 25.1 cubic meters.

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A football quarterback goes for a two-point conversion when the ball is within 10 yards of the end zone. During the game, he has

Crank

Answer:

$P=0.075$ , $P=7.5\%$

Step-by-step explanation:

We look for the probability that the player fails the first attempt and also fails the second attempt.

We know that the probability that the quarterback fails the first attempt is:

$P(1) = 0.5$

We know that the probability that the quarterback fails the second attempt after failing the first is:

$P(2|1) = 0.15$

Then the probability of failure of both attempts is:

$P(2|1)=\frac{P(1\ and\ 2)}{P(1)}$

$P(1\ and\ 2)=P(1)*P(2|1)$

$P(1\ and\ 2)=0.5*0.15$

$P(1\ and\ 2)=0.075$

6 0

2 years ago

In 2011, a train carried 8% more passengers than in 2010. In 2012 , it carried 8% more passengers than in 2011. Find the percent

konstantin123 [22]

Answer:

there was a 16% increase since 2010 to 2012

Step-by-step explanation:

lets say the train had 100 people on it in 2010 and in 2011 it had an 8% increase which then brings you to 8 plus 100 and you get 108.

Now in 2012 there was an increase 8%, so you will add 8 to your previous answer 108 and receive 116. So now there was 16 more passengers in 2012 than in 2010. Transfer the 16 passengers into 16% and you now have your answer.

5 0

2 years ago

A deli sells ham for $2.98 per half pound. Kyle incorrectly says that the unit rate is $1.49 per pound. Explain Kyle's mistake a

sveticcg [70]

The correct answer per pound is $1.49 per pound. Kyle is correct because dividing 2.98/2= 1.49 or multiplying Kyle's answer by 2 will give you the correct amount!

7 0

2 years ago

Read 2 more answers

Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute. The probability that

zloy xaker [14]

Answer:

0.0498 = 4.98%

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.

Each minute has 60 seconds.

So a rate of 1 inquire each 4 seconds.

The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately

Mean of 1 inquire each 4 seconds, so for 12 seconds $\mu = \frac{12}{4} = 3$

This probability is P(X = 0).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498$

5 0

2 years ago

In an orienteering class, you have the goal of moving as far (straight-line distance) from base camp as possible by making three

RUDIKE [14]

Answer:

The greatest distance we can be from the base camp at the end of the third displacement is 6.69 km

Step-by-step explanation:

We can think of each displacement as a vector, with a given magnitude and direction.

A vector can be written using its x and y coordinates like this

$\vec{t}=(x, y)$

So, for the displacements a and c their vector coordinates would be:

$\vec{a}=(2, 0)$

$\vec{c}=(-1, 0)$

As the b displacement has an angle of 30° toward the north from due east, we can find its x and y coordinates using the following formulas:

$x=(magnitude)*cos(angle)$

$y=(magnitude)*sin(angle)$

Note: the angle in the formula is the one formed with the east measured counterclockwise.

So, the x and y coordinates for the b displacement will be:

$\vec{b}=(2*cos(30), 2*sin(30))$

As the vector additon is commutative, the order won't affect the final position. Nevertheless, any change in the direction of any displacement will change the final position. So, in order to find the combination greatest distance we should calculate the following additions and find the one with the greatest magnitude:

$\vec{R_{1}} =\vec{a}+\vec{b}+\vec{c}$

$\vec{R_{2}} =\vec{a}-\vec{b}+\vec{c}$

$\vec{R_{3}} =\vec{a}+\vec{b}-\vec{c}$

$\vec{R_{4}} =\vec{a}-\vec{b}-\vec{c}$

Each resultant vector can be found adding each component. Afterwards, the magnitude can be found using the following formula:

$|\vec{R}|=\sqrt[ ]{(R_{x})^2 +{(R_{y})^2}}$

Now, let's calculate!

$\vec{R_{1}} =\vec{a}+\vec{b}+\vec{c}$

$R_{1_x}} =2+2*cos(30)-1=2.73$

$R_{1_y}} =0+2*sin(30)+0=1$

$\vec{R_{1}}=(2.73,1)$

$|\vec{R_{1}}|=\sqrt[ ]{(2.73)^2 +{(1)^2}}=3.86$

$\vec{R_{2}} =\vec{a}-\vec{b}+\vec{c}$

$R_{2_x}} =2-2*cos(30)-1=0.73$

$R_{2_y}} =0-2*sin(30)+0=-1$

$\vec{R_{2}}=(-0.73,-1)$ }

$|\vec{R_{2}}|=\sqrt[ ]{(-0.73)^2 +{(-1)^2}}=1.03$

$\vec{R_{3}} =\vec{a}+\vec{b}-\vec{c}$

$R_{3_x}} =2+2*cos(30)+1=4.73$

$R_{3_y}} =0+2*sin(30)-0=1$

$\vec{R_{3}}=(4.73,1)$

$|\vec{R_{3}}|=\sqrt[ ]{(4.73)^2 +{(1)^2}}=6.69$

$\vec{R_{4}} =\vec{a}-\vec{b}-\vec{c}$

$R_{4_x}} =2-2*cos(30)+1=1.26$

$R_{4_y}} =0-2*sin(30)-0=1$

$\vec{R_{4}}=(1.26,-1)$

$|\vec{R_{4}}|=\sqrt[ ]{(1.26)^2 +{(-1)^2}}=1.79$

So, after all the calculation, we can know for sure that the vector $\vec{R_{3}}$ has the biggest magnitude. Then, the greatest distance we can be from the base camp at the end of the third displacement is 6.69 km

7 0

2 years ago