Please help asap 25 pts

Mathematics

1 answer:

guajiro [1.7K]2 years ago

3 0

D because the y-intercept is at -5 like shown in the equation, and the slope equals to 1, and I do believe that the bold line means that it is less than or equal to, just like the equation says.

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Show how to solve the problem 378×6 using place value with regrouping. Explain how you knew when to regroup

nekit [7.7K]

1. 6 (378) = 2268 = (189 + 189)6

Properties are:
Addition, you can have 6 + 107 = 113 
Commutative Property by moving: 107 + 6 = 113 
Associative Property by grouping: (3 + 3) + (100 + 7 ) = 113 
Distributive Property by allotting: 2 (3) + 107 = 113 

Multiplication, you can have 6 x 107 = 642 
Commutative Property by moving: 107 x 6 = 642 
Associative Property by grouping: (3 + 3) x (100 + 7 ) = 642 
Distributive Property by allotting: 2(3) x 107 = 642

7 0

3 years ago

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 $s = \frac{\sigma}{\sqrt{n}}$ .