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EleoNora [17]
3 years ago
13

Find the gcf. 12 and 45 a. 180 b. 3 c. 45 d. 12

Mathematics
1 answer:
densk [106]3 years ago
7 0
The greatest common factor of 12 and 45 is 3. So its B. 12.
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Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to
polet [3.4K]

Answer:

(a) The probability that X is at most 30 is 0.9726.

(b) The probability that X is less than 30 is 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.

Step-by-step explanation:

We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.

Let X = <u><em>the number among these that are nonconforming and can be reworked</em></u>

The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).

Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, \mu = n \times p = 200 \times 0.11 = 22

and the new standard deviation of X, \sigma = \sqrt{n \times p \times (1-p)}

                                                                  = \sqrt{200 \times 0.11 \times (1-0.11)}

                                                                  = 4.42

So, X ~ Normal(\mu =22, \sigma^{2} = 4.42^{2})

(a) The probability that X is at most 30 is given by = P(X < 30.5)  {using continuity correction}

        P(X < 30.5) = P( \frac{X-\mu}{\sigma} < \frac{30.5-22}{4.42} ) = P(Z < 1.92) = <u>0.9726</u>

The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.

(b) The probability that X is less than 30 is given by = P(X \leq 29.5)    {using continuity correction}

        P(X \leq 29.5) = P( \frac{X-\mu}{\sigma} \leq \frac{29.5-22}{4.42} ) = P(Z \leq 1.70) = <u>0.9554</u>

The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 \leq X \leq 25) = P(X < 25.5) - P(X \leq 14.5)   {using continuity correction}

       P(X < 25.5) = P( \frac{X-\mu}{\sigma} < \frac{25.5-22}{4.42} ) = P(Z < 0.79) = 0.7852

       P(X \leq 14.5) = P( \frac{X-\mu}{\sigma} \leq \frac{14.5-22}{4.42} ) = P(Z \leq -1.70) = 1 - P(Z < 1.70)

                                                          = 1 - 0.9554 = 0.0446

The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.

Therefore, P(15 \leq X \leq 25) = 0.7852 - 0.0446 = 0.7406.

5 0
3 years ago
You plan on purchasing a blouse for $32.98, a pair of jeans for $45.99,
Alik [6]

Answer:

$166.66

Step-by-step explanation:

45.99 + 32.98 + 74.99 =153.96

153.96(1.0825)= 166.66

8 0
3 years ago
Wx+yz=bc , solve for z .
Aleksandr-060686 [28]
Wx+yz=bc
minus wx on both sides
yz=bc-wx
dividing 'y' on both sides
Hence,
z=(bc-wx)/y
Here is what you need.
Hope it helped
8 0
3 years ago
Read 2 more answers
If a parallelogram has diagonals that are perpendicular bisectors of each other, what is the most descriptive name for it?
Feliz [49]
Both a rhombus and a rectangle have diagonals that are perpendicular bisectors, but the ones formed in a square are all congruent, so that is probably the most descriptive one.
6 0
3 years ago
I need help solving 11 3/4 minus 8 2/10
melomori [17]

Answer:

The answer is 3 11/20

Step-by-step explanation:

Subtract whole numbers, 11 - 8 = 3

Then combine fractions 3/4 - 2/10= 11/20

hope this helps! :D


4 0
3 years ago
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