which choice is equivalent to the fraction below?

Answer:

a) [tex]n=\frac{0.32(1-0.32)}{(\frac{0.03}{1.96})^2}=928.81[/tex]  

And rounded up we have that n=929

b) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Step-by-step explanation:

Part a

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

For a confidence of 95% we have that the significance is [tex]\alpha=0.05[/tex] and the critical value would be:

[tex] z = 1.96[/tex]

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.32(1-0.32)}{(\frac{0.03}{1.96})^2}=928.81[/tex]  

And rounded up we have that n=929

Part b

For this case since we don't have prior info we can use as estimator for the true proportion the value [tex]\hat p=0.5[/tex] and replacing we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Answer:

Equation- 7,250 divided by 500

Answer- 15

Step-by-step explanation:

thanks google for letting me look this up! ;)

Answer:

s = 7,250/500

Step-by-step explanation:

If you want a smoke detector every 500 feet you divide the total amount (7,250) into (s) many 500 foot spaces. This means that you could also divide 7,250 by 500 ft to get s or the number of smoke detectors needed.

Answer:

0.7969

Step-by-step explanation:

Given that: A sample of size n= 49 is obtained. The population mean  is m= 80 and the population standard deviation is s = 14.

The z score measures the number of standard deviation by which the raw sore is above or below the mean. It is given by the equation:

[tex]z=\frac{x-m}{\frac{s}{\sqrt{n} } }[/tex]

For x = 78.3, the z score is:

[tex]z=\frac{x-m}{\frac{s}{\sqrt{n} } }=\frac{78.3-80}{\frac{14}{\sqrt{49} } } =-0.85[/tex]

For x = 85.1, the z score is:

[tex]z=\frac{x-m}{\frac{s}{\sqrt{n} } }=\frac{85.1-80}{\frac{14}{\sqrt{49} } } =2.55[/tex]

P(78.3<x<85.1) = P(-0.85<z<2.55) = P(z<2.55) - P(z<-0.85) = 0.9946 - 0.1977 = 0.7969

Answer:

P(78.3 < x' < 85.1) = 0.7969

Step-by-step explanation:

Given:

Sample size, n = 49

mean, u = 80

Standard deviation [tex] \sigma [/tex] = 14

Sample mean, ux' = population mean = 80

Let's find the sample standard deviation using the formula:

[tex] \sigma \bar x = \frac{\sigma}{\sqrt{n}} [/tex]

[tex] = \frac{14}{\sqrt{49}} = \frac{14}{7} = 2 [/tex]

To find the probability that the sample has a sample average between 78.3 and 85.1, we have:

[tex] P(78.3 < \bar x < 85.1) = \frac{P[(78.3 -80)}{2} < \frac{(\bar x - u \bar x)}{\sigma \bar x} < \frac{(85.1 -80)}{2}] [/tex]

= P( -0.85 < Z < 2.55 )

= P(Z < 2.55) - P(Z <-0.85 )

Using the standard normal table, we have:

= 0.9946 - 0.1977 = 0.7969

Approximately 0.80

Therefore, the probability that the sample has a sample average between 78.3 and 85.1 is 0.7969

Answer:

121.1

Step-by-step explanation:

By law of sines, (sin <I)/i = (sin <J)/j. Plugging in the values we know, we get sin 72deg / 206 = sin 34deg / j. When we solve for k, we get that it is about 121.122. Rounded to the nearest tenth, we get that j is 121.1.

Answer:

Step-by-step explanation:

Confidence coefficient is also the confidence level. A confidence coefficient of 0.95 is the same as a confidence level of 95%.

Confidence level is used to express how confident we are that the population mean lies within the calculated confidence interval. It expresses the possibility of getting the same result if tests are repeated. Since the study reports that college students work, on average, between 4.63 and 12.63 hours a week, with confidence coefficient .95, then the true statement is

G. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week.

Answer:

[tex]\frac{c^{2}-a^{2}-b^{2} }{-2ab}[/tex]=cos C

Step-by-step explanation:

Start with the parts that are more loosely attached to the cos C: the a² and the b², they are only attached with addition, which can be easily undone by subtracting from both sides. That gives you c²-a²-b²=-2abC

Next, since you want to isolate cosC, you will want to divide by everything attached to the cosC by multiplication: (c²-a²-b²)÷(-2ab)=cosC. Then you can neaten it up and put it in fraction form: [tex]\frac{c^{2}-a^{2}-b^{2} }{-2ab}[/tex]=cos C

Answer:

27.31

Step-by-step explanation:

Take the number of miles and multiply by the reimbursement rate

210.1 * .13

27.313

Round to the nearest cent

27.31

Answer:

5 CAUSE ITS PER PERSON

Answer:0.9306

Step-by-step explanation:

Given

Probability of winning [tex]p=0.632[/tex]

Probability of losing [tex]q=0.368[/tex]

Such that [tex]p+q=1[/tex]

Applying binomioal distribution for n=10 trials

Probability of winning no more than 8 time=P

[tex]P(r\leq 8)+P(r>8)=1[/tex]

[tex]P(r\leq 8)=1-P(r>8)[/tex]

[tex]P(r\leq 8)=1-^{10}C_9(p)^9(q)-^{10}C_{10}(p)^{10}(q)^0[/tex]

[tex]P(r\leq 8)=1-^{10}C_9(0.632)^9(0.368)-^{10}C_{10}(0.632)^{10}(0.368)^0[/tex]

[tex]P=P(r\leq 8)=0.9306[/tex]

Answer:

[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}[/tex]     to four decimal places.

[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}[/tex]  to four decimal places.

Step-by-step explanation:

a)

Assuming X to be the random variable which replace the amount of defectives and follows standard normal distribution whose mean  (μ) is 10 ounces and standard deviation (σ) is 0.15

The values of the random variable differ from mean  by ±  1 \such that the values are either greater than (10+ 0.15) or less than  (10-0.15)

= 10.15 or  9.85.

The  probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:

[tex]P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.15}< \dfrac{X-10}{0.15}< \dfrac{10.15-10}{0.15})[/tex]

[tex]P(X < 9.85 \ or \ X> 10.15) = 1- \phi (1) - \phi (-1)[/tex]

Using the Excel Formula ( = NORMDIST (1) ) to calculate for the value of z =1 and -1 ;we have: 0.841345 and 0.158655 respectively

[tex]P(X < 9.85 \ or \ X> 10.15) = 1- (0.841345-0.158655)[/tex]

[tex]P(X < 9.85 \ or \ X> 10.15) =0.31731[/tex]

[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) \approx 0.3171}[/tex]     to four decimal places.

b) Through process design improvements, the process standard deviation can be reduced to 0.05.

The  probability that the amount of defectives which are either greater than 10.15 or less than 9.85 can be calculated as follows:

[tex]P(X < 9.85 \ or \ X> 10.15) = 1-P ( \dfrac{9.85-10}{0.05}< \dfrac{X-10}{0.05}< \dfrac{10.15-10}{0.05})[/tex]

[tex]P(X < 9.85 \ or \ X> 10.15) = 1- \phi (3) - \phi (-3)[/tex]

Using the Excel Formula ( = NORMDIST (3) ) to calculate for the value of z =3 and -3 ;we have: 0.99865 and 0.00135 respectively

[tex]P(X < 9.85 \ or \ X> 10.15) = 1- (0.99865-0.00135)[/tex]

[tex]\mathbf{P(X < 9.85 \ or \ X> 10.15) =0.0027}[/tex]  to four decimal places.

(c)  What is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean?

The main advantage of reducing the process variation is that the chance of getting the defecting item will be reduced as we can see from the reduction which takes place from a to b from above.

Answer:

9 miles an hour

Step-by-step explanation:

9

Answer:

3.6666666.... and continuing

or 3.7 if you want to round

Step-by-step explanation:

To find the mean, I added all the numbers up:

4+3+1+ 6+ 1+7 = 22

Then I divided that by how many numbers there are total (6).

22/6= 3.66666.. or 3.6 with a bar symbol on top of the 6.

Thus, the answer is 3.666666...

Answer:

1/9

Step-by-step explanation:

(243/32)^-2/5*2^ -2 = (3/2)^(5*-2/5) * 1/4 = (3/2)^-2 * 1/4 = 4/9 * 1/4 = 1/9

Answer:0.04

Step-by-step explanation:numbers from 0-4 are rounded off while numbers from 5-9 are rounded up by adding 1 to the number before. Significant number are numbers from 1above

Therefore 0.043118 to 1 significant number is 0.04

The number 0.043118 rounded to 1 significant figure is given by the equation A = 0.04

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Non-zero digits are always significant

Zeros between non-zero digits are always significant

Leading zeros are never significant

Trailing zeros are only significant if the number contains a decimal point

Given data ,

Let the number be represented as n

The value of n = 0.043118

Let the rounded number be represented as A

So , when rounding the number to one significant number , the leading zeros are never significant and non-zero digits are always significant

Substituting the values in the equation , we get

A = 0.04

Hence , the rounded number is 0.04

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Answer:

cos0 = 4/3

Step-by-step explanation:

If sin0 = 5/3 then cos0 = 4/3

Sin is opposite/hypotenuse or 5/3.

Cos is adjacent/hypotenuse or 4/3

I found 4 because of Pythagorean Theorem on the triangle, which is known as a 345 triangle.

Answer:

a) probability that the sample will have between 50% and 60% of the identification correct = 0.498

b) The probability is 90% that the sample percentage  is contained 45.5% and 54.5% of the population percentage

c) Probability that the sample percentage of correct identifications is greater than 65% = 0.01

Step-by-step explanation:

Sample size, n = 200

Since the brands are equally likely, p = 0.5, q = 0.5

The Standard deviation, [tex]\sigma_p = \sqrt{\frac{pq}{n} }[/tex]

[tex]\sigma_p = \sqrt{\frac{0.5 * 0.5}{200} } \\\sigma_p = 0.0353[/tex]

a) probability that the sample will have between 50% and 60% of the identification correct.

[tex]P(0.5 < X < 0.6) = P(\frac{0.5 - 0.5}{0.0353} < Z < \frac{0.6 - 0.5}{0.0353} )\\P(0.5 < X < 0.6) = P( 0 < Z < 2.832)\\P(0.5 < X < 0.6) = P(Z < 2.832) - P(Z < 0)\\P(0.5 < X < 0.6) = 0.998 - 0.5\\P(0.5 < X < 0.6) = 0.498[/tex]

Probability that the sample will have between 50% and 60% of the identification correct is 0.498

b) p = 90% = 0.9

Getting the z value using excel:

z = (=NORMSINV(0.9) )

z = 1.281552 = 1.28 ( 2 dp)

Then we can calculate the symmetric limits of the population percentage as follows:

[tex]z = \frac{X - \mu}{\sigma_p}[/tex]

[tex]-1.28 = \frac{X_1 - 0.5}{0.0353} \\-1.28 * 0.0353 = X_1 - 0.5\\-0.045+ 0.5 = X_1\\X_1 = 0.455[/tex]

[tex]1.28 = \frac{X_2 - 0.5}{0.0353} \\1.28 * 0.0353 = X_2 - 0.5\\0.045+ 0.5 = X_2\\X_2 = 0.545[/tex]

The probability is 90% that the sample percentage  is contained 45.5% and 54.5% of the population percentage

c) Probability that the sample percentage of correct identifications is greater than 65%

P(X>0.65) = 1 - P(X<0.65)

[tex]P(X<0.65) = P(Z< \frac{X - \mu}{\sigma} )\\P(X<0.65) = P(Z< \frac{0.65 - 0.5}{0.0353} )\\P(X<0.65) = P(Z < 4.2372) = 0.99\\P(X>0.65) = 1 - P(X<0.65)\\P(X>0.65) = 1 - 0.99\\P(X>0.65) = 0.01[/tex]

Answer:

72

Step-by-step explanation:

9 * (19 - 11)

= 9 * 8 = 72

Answer:

the answer is D.

Step-by-step explanation:

Triangle (3 sides) 5 9 6

Rectangle (4 sides) 6 12 8

Pentagon (5 sides) 7 15 10

Hexagon (6 sides) 8 18 12

b) 300 edges and 200 vertices

(a) The complete table describes a number of faces, edges, and vertices shown below.

(b) There are 300 edges and 200 vertices in a prism with a 100-sided end face

In the given figure one is a triangular prism and the lower one is a pentagonal prism. With the help of the figure, we have to calculate the complete table and the number of edges and vertices a prism with a 100-sided end face has.

(a)

The complete table is given as:

Triangle (3 sides)     5           9          6

Rectangle (4 sides)  6          12          8

Pentagon (5 sides)   7          15         10

Hexagon (6 sides)   8           18         12

(b)
The number of vertices in a prism is determined by the number of vertices on its base polygon. Therefore, there are 300 edges and 200 vertices in a prism with a 100-sided end face.

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Answer:

Yes

Step-by-step explanation:

10,20,30,40,50 are all divisible by 5.

Answer:

Step-by-step explanation:

The amplitude is the difference between the peak value (3.8) and the midline (-3.8). You find it by subtracting the midline from the peak:

  amplitude = 3.8 -(-3.8)

  amplitude = 7.6

Answer:

True

Step-by-step explanation:

Isosceles triangles are a subset of equilateral triangles

Equilateral have all three sides the same while isosceles have at least 2 sides the same

Equilateral have all three angles equal while isosceles have at least 2 angles equal

Answer:

Yes

Step-by-step explanation:

An equilateral triangle is one where all three sides are of equal length.  (3)

An isosceles triangle has at least two sides of equal length. (2)

But, if it's the other way around than no

Answer:

2

Step-by-step explanation:

50 and 60

Answer: 35 whole numbers.

Step-by-step explanation:

You could just find the difference between the numbers or list the numbers.

75-40=35

Or, 41,42,43,44,45,46,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74.

All these numbers are whole numbers between 40 and 75 and they all count up to 35.

Answer:

  13√7

Step-by-step explanation:

  [tex]5\sqrt{28} +\sqrt{63} =5\sqrt{2^2\cdot 7}+\sqrt{3^2\cdot 7}\\\\=5\cdot 2\sqrt{7}+3\sqrt{7}=(10+3)\sqrt{7}\\\\=\boxed{13\sqrt{7}}[/tex]

Answer:

Step-by-step explanation:

71 grams would definitely be an outlier on the high side, whereas "most" species would weigh much less.  Thus, the graph of this distribution of weights would be skewed towards the lower side, that is, to the left.

The skewness of a dataset is a measure of deviation of a random  variable from the normal distribution.

The shape of the distribution is skewed to the right

From the question, we understand that:

71 is a very large dataset, compared to the other weight of the species.

This means that

When there are much data at the left of a distribution, then the distribution is positively skewed.

Hence, the shape of the is skewed to the right

See attachment for illustration of skewness of a distribution.

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Answer:

The exact values of the tangent, secant and cosine of angle theta are, respectively:

[tex]\cos \theta = -\frac{11}{61}[/tex]

[tex]\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}[/tex]

[tex]\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}[/tex]

Step-by-step explanation:

The components of the unit vector are [tex]x = -\frac{11}{61}[/tex] and [tex]y = -\frac{60}{61}[/tex]. Since [tex]r = 1[/tex], then [tex]x = \cos \theta[/tex] and [tex]y = \sin \theta[/tex]. By Trigonometry, tangent and secant can be calculated by the following expressions:

[tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}[/tex]

[tex]\sec \theta = \frac{1}{\cos \theta} = \frac{1}{x}[/tex]

Now, the exact values of the tangent, secant and cosine of angle theta are, respectively:

[tex]\cos \theta = -\frac{11}{61}[/tex]

[tex]\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}[/tex]

[tex]\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}[/tex]

Answer: 4.98

Step-by-step explanation:fractions are dividing so if j=25 and k=5 the division problem would be 25 divided by 5 then u would subtract 0.02 to get 4.98

Answer: The correct answer is

Step-by-step explanation:

The probability of P(odd number) for  odd numbers is 8/15

Probability is a branch of mathematics that deals with the occurrence of a random event. For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.

According to question

A spinner that has 15 equal-sized sections numbered 1 to 15.

Total number of selection = 15

therefore odd no's are = 1,3,5,7,9,11,13,15 in total 8

And even no's are = 2,4,6,8,10,12,14 in total 7

Now  probability of: P(odd number) = [tex]\frac{Total odd no's }{Total number of selection}[/tex]

= 8/15

Hence, the probability of odd number is 8/15

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