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ivanzaharov [21]
3 years ago
13

Simplify 4 + (30 + 2) Justify your steps​

Mathematics
1 answer:
Sveta_85 [38]3 years ago
6 0

Answer:

The answer is 36

Step-by-step explanation:

1) Add 30 + 2 and get 32

2) Then you just add 32+4 and get 36

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Select ONE of these problems to solve. STAR the problem and then write the expression first. After you write the expression, sol
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An expression that represents the total calories for ‘n’ Big Macs is:
550n
Use the expression to solve the total calories in 17 Big Macs:
550(17) = 9350

THEREFORE, there are 9350 calories in 17 Big Macs.
6 0
2 years ago
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Birds arrive at a birdfeeder according to a Poisson process at a rate of six per hour.
m_a_m_a [10]

Answer:

a) time=10 \frac{1}{6}=\frac{10}{6}=1.67 hours

b) P(T\geq 0.25h)=e^{-(6)0.25}=0.22313

c) P(T\leq 0.0833)=1-e^{-(6)0.0833}=0.39347

Step-by-step explanation:

Definitions and concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

P(X=x) =\lambda^x \frac{e^{-\lambda}}{x!}

And the parameter \lambda represent the average ocurrence rate per unit of time.

The exponential distribution is useful when we want to describ the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time btween two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:

P(T>t)= e^{-\lambda t}

a. What is the expected time you would have to wait to see ten birds arrive?

The original rate for the Poisson process is given by the problem "rate of six per hour" and on this case since we want the expected waiting time for 10 birds we have this:

time=10 \frac{1}{6}=\frac{10}{6}=1.67 hours

b. What is the probability that the elapsed time between the second and third birds exceeds fifteen minutes?

Assuming that the time between the arrival of two birds consecutive follows th exponential distribution and we need that this time exceeds fifteen minutes. If we convert the 15 minutes to hours we have 15(1/60)=0.25 hours. And we want to find this probability:

P(T\geq 0.25h)

And we can use the result obtained from the definitions and we have this:

P(T\geq 0.25h)=e^{-(6)0.25}=0.22313

c. If you have already waited five minutes for the first bird to arrive, what is the probability that the bird will arrive within the next five minutes?

First we need to convert the 5 minutes to hours and we got 5(1/60)=0.0833h. And on this case we want a conditional probability. And for this case is good to remember the "Markovian property of the Exponential distribution", given by :

P(T \leq a +t |T>t)=P(T\leq a)

Since we have a waiting time for the first bird of 5 min = 0.0833h and we want that the next bird will arrive within 5 minutes=0.0833h, we can express on this way the probability of interest:

P(T\leq 0.0833+0.0833| T>0.0833)

P(T\leq 0.1667| T>0.0833)

And using the Markovian property we have this:

P(T\leq 0.0833)=1-e^{-(6)0.0833}=0.39347

3 0
3 years ago
Factor 1 - 2.25x^8.
sleet_krkn [62]
<span>1 - 2.25x</span>⁸ =
1² - (1.5x⁴)² =
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5 0
3 years ago
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the sum of two numbers is 67 if three times the smaller number is subtracted by the larger the result is 7, find two numbers
just olya [345]
Um I think it's 3x7x4=81 or like this 40+20+7=67.
3 0
3 years ago
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Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame
lbvjy [14]

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{207.9 - 208}{0.1678}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

2*0.2743 = 0.5486

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

6 0
3 years ago
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