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slava [35]
2 years ago
6

1. Sally said that when you add or subtract positive or negative decimals, you can change the order of the decimals and still ge

t the same answer.
Use these decimals to answer the questions:
–6.2, 5.71, –3.96, 2.84

(a) Is Sally’s statement always true, sometimes true, or always false? Write two pairs of equations using addition and two pairs of equations using subtraction to support your answer.
(b) Write a rule about changing the order of the numbers in adding and in subtracting positive and negative decimals.
Mathematics
1 answer:
siniylev [52]2 years ago
3 0
Always true because addition and subtraction is commutative
-6.2-(-3.96) = -2.24
-3.96-(-6.2)= -2.24
5.71+2.84=8.55
2.84+5.71=8.55  
Hope this helped :)
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Step-by-step explanation:

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The automatic opening device of a military cargo parachute has been designed to open when the parachute is 185 m above the groun
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Answer:

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Step-by-step explanation:

For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.

To find the probability of damage on a parachute, the normal distribution is used.

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}.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.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Probability of a parachute having damage.

The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that \mu = 185, \sigma = 32

Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of  Z when X = 100. So

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

Z = \frac{100 - 185}{32}

Z = -2.66

Z = -2.66 has a p-value of 0.0039.

What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

0.0039 probability of a parachute having damage, which means that p = 0.0039

5 parachutes, which means that n = 5

This probability is:

P(X \geq 1) = 1 - P(X = 0)

In which

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

P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807

Then

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

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The orange arrow is adding up to 0.90 and the blue arrow is subtracting 1.30 so the answer is (-0.40)
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