I have 1 hundreds, 4 ones, 2 tens, and 1 tenths. What number am I?

If the sphere shown has a radius of 9 units, what is the volume of the sphere?

kirill [66]

V = 4/3 * 3.14 * 9^3 = 3052.08

Answer is B

6 0

3 years ago

Matti built a greenhouse in his backyard as shown below

Vanyuwa [196]

well, Matti's house is a triangular prism, and to get the volume of it, we simply get the area of the triangle upfront and multiply by its length of 15.

$\bf \stackrel{\stackrel{\textit{area of }}{\textit{triangular front}}}{\cfrac{1}{2}(7)(7)}\times \stackrel{\textit{length}}{15}\implies \cfrac{49}{2}\cdot 15\implies 367.5~ft^3$

4 0

3 years ago

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Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose

Furkat [3]

Answer:

a) 0.164 = 16.4% probability that a disk has exactly one missing pulse

b) 0.017 = 1.7% probability that a disk has at least two missing pulses

c) 0.671 = 67.1% probability that neither contains a missing pulse

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the binomial distribution(for item c).

Poisson distribution:

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 interval.

Binomial distribution:

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

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

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

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

And p is the probability of X happening.

Poisson mean:

$\mu = 0.2$

a. What is the probability that a disk has exactly one missing pulse?

One disk, so Poisson.

This is P(X = 1).

$P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164
$

0.164 = 16.4% probability that a disk has exactly one missing pulse

b. What is the probability that a disk has at least two missing pulses?

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

In which

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

$P(X = 0) = \frac{e^{-0.2}*0.2^{0}}{(0)!} = 0.819$

$P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164
$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.819 + 0.164 = 0.983$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.983 = 0.017$

0.017 = 1.7% probability that a disk has at least two missing pulses

c. If two disks are independently selected, what is the probability that neither contains a missing pulse?

Two disks, so binomial with n = 2.

A disk has a 0.819 probability of containing no missing pulse, and a 1 - 0.819 = 0.181 probability of containing a missing pulse, so $p = 0.181$

We want to find P(X = 0).

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

$P(X = 0) = C_{2,0}.(0.181)^{0}.(0.819)^{2} = 0.671$

0.671 = 67.1% probability that neither contains a missing pulse

8 0

3 years ago

A student expanded an expression, as shown. Is the student's work correct? Explain why or why not.

alex41 [277]

The work is incorrect.

(-6) multiplies both terms inside parentheses. For some reason, the student changed the sign of that multiplier for the second term. The second term of the result should have a positive sign, the result of multiplying (-6)(-2/13) = +12/13.

4 0

3 years ago

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Solve this quadratic equation by completing the square x^2+8x=10

AURORKA [14]

Answer:

1.1 ,-9.1

Step-by-step explanation:

6 0

3 years ago