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viktelen [127]
3 years ago
12

PLEASE HELP ASAP 25 PTS + BRAINLIEST TO RIGHT/BEST ANSWER

Mathematics
2 answers:
LUCKY_DIMON [66]3 years ago
7 0

Answer:  d

Step-by-step explanation: when you bring 3 into the square root, it becomes isqrt(63). when you apply i, it makes the number sqrt(-63)

pretty sure I did it right this time

r-ruslan [8.4K]3 years ago
7 0

Answer:

d 3i sqrt(7)

Step-by-step explanation:

sqrt(-63)

±sqrt(-1) sqrt(63)

sqrt(-1) = i

±i sqrt(63)

±i sqrt(9)sqrt(7)

±i 3sqrt(7)

± 3i sqrt(7)

The principal square root is 3i sqrt(7)

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Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.8. (Round your ans
Alenkinab [10]

Answer:

a) 0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51

b) 0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51

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 = 50, \sigma = 1.8

(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 17 pins is at least 51?

Here n = 17, s = \frac{1.8}{\sqrt{17}} = 0.4366

This probability is 1 subtracted by the pvalue of Z when X = 51. So

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

By the Central Limit Theorem

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

Z = \frac{51 - 50}{0.4366}

Z = 2.29

Z = 2.29 has a pvalue of 0.9890

1 - 0.989 = 0.011

0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 45 pins is at least 51?

Here n = 17, s = \frac{1.8}{\sqrt{45}} = 0.2683

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

Z = \frac{51 - 50}{0.0.2683}

Z = 3.73

Z = 3.73 has a pvalue of 0.9999

1 - 0.9999 = 0.0001

0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51

8 0
3 years ago
ALLL MY POINTS PLSSS HELPPPPP
Rama09 [41]

Rewrite the given quadratic equation in standard form: Kx 2 + 2x - 1 = 0  

Discriminant = 4 - 4(K)(-1) = 4 + 4K  

For the equation to have two real solutions, the discriminant has to be positive. Hence we need to solve the inequality 4 + 4K > 0.  

The solution set to the above inequality is given by: K > -1 for which the given equation has two real solutions.

3 0
3 years ago
Read 2 more answers
Which graph correctly compares the volumes, V, of rectangular pyramids with different heights, h, when their bases all have the
VARVARA [1.3K]

Answer:the correct answer is D

Step-by-step explanation:

Hope this help but can you tell me what your answer?

8 0
3 years ago
Read 2 more answers
Can I get help please!
Naily [24]
55x5 - 40x5
The third one down
8 0
3 years ago
Right triangle ABC is shown. Triangle A B C is shown. Angle A C B is a right angle and angle C B A is 50 degrees. The length of
anzhelika [568]

Question:

Obtian the equation that can be used to solve for c

Answer:

Sin50 = 3/c

Step-by-step explanation:

A triangle showing the information given has been attached below for clarity :

Using trigonometry :

AC = 3 = opposite side of angle 50°

AB = c = hypotenus

Using the sine relation of a right angled triangle :

Sin θ = opposite / hypotenus

θ = 50°

Sin 50° = 3 / c

Sin50 = 3/c

6 0
3 years ago
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