What is the slope of the line through (-1,2) and (-3,-2)?

What is the volume of an icecream cone that has a radius of 4 and a height of 10?

Leni [432]

Answer:

167.55 units cubed

Step-by-step explanation:

Volume of a cone formula: πr^2(h/3)

r = 4, h = 10

Equation:

π(4^2)(10/3)

= π(16)(3.333333)

= 167.551608

4 0

3 years ago

Find the area and circumference of a circle which is 5cm

Nonamiya [84]

Answer: 31.416

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Fine the exact distance between the line 6x-y=-3 and the point (6,2). Show your work. Explain your answer.

AVprozaik [17]

Answer:

$\sqrt{37}$ units

Step-by-step explanation:

If we draw a perpendicular from point (6,2) on the line 6x - y = - 3, then we have to find the length of the perpendicular.

We know the formula of length of perpendicular from a point $(x_{1}, y_{1} )$ to the straight line ax + by + c = 0 is given by

$\frac{|ax_{1} + by_{1} +c |}{\sqrt{a^{2}+b^{2}}}$

Therefore, in our case the perpendicular distance is

$\frac{|6(6)-2+3|}{\sqrt{6^{2} +(-1)^{2} } } = \frac{37}{\sqrt{37} } = \sqrt{37}$ units. (Answer)

6 0

3 years ago

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

crimeas [40]

Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago

Jaime went to the mall with $42. If he bought a T-shirt and had $18 left, how much did the T-shirt cost Jaime in dollars?

nirvana33 [79]

Answer:

$24

Step-by-step explanation:

You simply do $42-$18

=24

4 0

3 years ago

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What is the slope of the line through (-1,2) and (-3,-2)?​

What is the slope of the line through (-1,2) and (-3,-2)?