What is the greatest common factor of 250, 45, and 30?

1 + cot^2 x is equivalent to

zysi [14]

Answer:

csc^2x

Step-by-step explanation:

It's a trig identity where 1+cot^2x = csc^2x

6 0

2 years ago

Temperature transducers of a certain type are shipped in batches of 50. A sample of 58 batches was selected, and the number of t

andrew11 [14]

Answer:

a) X Freq. Rel Freq.

__________________________

0 7 (7/58) = 0.121

1 10 (10/58)=0.172

2 13 (13/58) =0.224

3 14 (14/58)=0.241

4 6 (6/58)=0.103

5 3 (3/58)=0.052

6 3 (3/58)=0.052

7 1 (1/58) =0.017

8 1 (1/58)=0.017

_________________________

Total 58 1.00

b) $\frac{7+10+13+14+6}{58}= \frac{50}{58}=0.862$

Step-by-step explanation:

Assuming this question: Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data:

2,1,2,4,0,1,3,2,0,5,3,3,1,3,2,4,7,0,2,3,

0,4,2,1,3,1,1,3,4,2,3,2,2,8,4,5,1,3,1,

5,0,2,3,2,1,0,6,4,2,1,6,0,3,3,3,6,2,3

(a) Determine frequencies and relative frequencies for the observed values of x = number of nonconforming transducers in a batch. (Round your relative frequencies to three decimal places.)

For this case first we order the dataset on increasing way and we got:

0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1

2 2 2 2 2 2 2 2 2 2 2 2 2

3 3 3 3 3 3 3 3 3 3 3 3 3 3

4 4 4 4 4 4

5 5 5

6 6 6

7

8

And we can construct the following table:

X Freq. Rel Freq.

__________________________

0 7 (7/58) = 0.121

1 10 (10/58)=0.172

2 13 (13/58) =0.224

3 14 (14/58)=0.241

4 6 (6/58)=0.103

5 3 (3/58)=0.052

6 3 (3/58)=0.052

7 1 (1/58) =0.017

8 1 (1/58)=0.017

_________________________

Total 58 1.00

(b) What proportion of batches in the sample have at most four nonconforming transducers? (Round your answer to three decimal places.)

For this case this proportion would be:

$\frac{7+10+13+14+6}{58}= \frac{50}{58}=0.862$

4 0

3 years ago

A survey found that women's heights are normally distributed with mean 63.3 in. and standard deviation 2.7 in. The survey also

mylen [45]

Answer:

A) There is a 100% chance of meeting the height requirement for women.

B) There is a 99.89% chance of meeting the height requirement for men.

C) New height requirements are:

71.9 inches for men and 58.9 inches minimum for women.

At least 58.9 inches and at most 71.9 inches.

Step-by-step explanation:

This question involves finding z values which tell us the percentage from 0 to x.

z = (x-μ)/σ

A) In this question, the minimum sample point is 4 ft 9 inches or converting to inches, we have;(4*12) + 9 =57 inches.

The maximum sample point is 6 ft 4 inches which in inches gives; (6*12) + 4 = 76 inches

For the minimum point;

z = (57 - 63.3)/2.7 = -2.33

From the z-distribution table, this equates to 0.0099.

The maximum;

z = (76 - 63.3)/2.7 = 4.70

From the z-table, it gives 0.999.. Basically 100%.

So there is a 100% chance of meeting the height requirement for women.

B) For men;

the minimum z = (57 - 67.3)/2.8 = -3.68 which gives 0.00012 from the z-distribution table.

The maximum;

z = (76 - 67.3)/2.8 = 3.07 which gives 0.9989 from the z-distribution table. Basically, 99.89%.

So there is a 99.89% chance of meeting the height requirement for men.

C) To exclude the tallest 5% of men, we need to find the z-value for 0.95 and then solve for x.

Thus from the z-table, z = 1.65. So;

1.645 = (x - 67.3)/2.8

4.606 = x - 67.3

x = 67.3 + 4.606

x ≈ 71.9 inches for men.

So, Current minimum is okay.

To exclude the shortest 5% of women, we need to find the z for 0.05.

From the z-distribution table, it has a value of -1.645. So;

-1.645 = (x - 63.3)/2.7

-4.4415 = x - 63.3

x = 63.3 - 4.4415

x ≈ 58.9 inches minimum.

So, Current maximum is okay.

5 0

3 years ago

Rank the following from most precise to least precise.1.4515100.0034

aalyn [17]

The level of precision is given by the number of decimal places.

1.45 has a precision of 2 ( two decimal digits)

.0034 has a precision of 4 ( 4 decimal digits)

Numbers that end in zeros have negative precision:

100: has a precision of -2 ( 2 zeros)

15 : Whole numbers has precision 0.

From most precise to least precise:

.0034 - 1.45- 15 - 100

8 0

1 year ago

5/7y=3-1/5 what is y?

denis23 [38]

You want y? One way to get y alone would be to mult. all 3 terms by (7/5):

(7/5)(5/7)y = (7/5)*3 - (7/5)(-1/5). This simplifies to:

y = 21/5 * 7/25, or y = 147 / 125.

You could check this using decimal fractions:

y = 4.20 * 0.28 = 1.176 = 147 / 125.

4 0

2 years ago