Select the correct answer.
The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30
pages, what can you conclude?

Answer: 9*x-5 = 6*x+7

Step-by-step explanation:

First we have to understand what it is saying.

9 times x (being a number) minus 5 equal to 6 times x plus 7

Now lets put it into an equation.

[tex]9*x-5 = 6*x+7[/tex]

Answer: [tex]16\pi \;cm^2[/tex]

Step-by-step explanation:

La longitud de una semicircunferencia es [tex]l=\pi r[/tex]

[tex]\pi r+2r=4(\pi+2)\\r(\pi+2)=4(\pi+2)\\r = 4\frac{\pi+2}{\pi+2} \\r=4[/tex]

[tex]A = \pi r^2 = \pi (4)^2=16\pi[/tex]

Answer:

a. Binomial random variable (n=4, p=0.25)

b. Attached.

c. X=1

Step-by-step explanation:

This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).

a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{4}{k} 0.25^{0}\cdot0.75^{4}[/tex]

The sample space for X is {0,1,2,3,4}

The associated probabilties are:

[tex]P(x=0) = \dbinom{4}{0} p^{0}(1-p)^{4}=1*1*0.3164=0.3164\\\\\\P(x=1) = \dbinom{4}{1} p^{1}(1-p)^{3}=4*0.25*0.4219=0.4219\\\\\\P(x=2) = \dbinom{4}{2} p^{2}(1-p)^{2}=6*0.0625*0.5625=0.2109\\\\\\P(x=3) = \dbinom{4}{3} p^{3}(1-p)^{1}=4*0.0156*0.75=0.0469\\\\\\P(x=4) = \dbinom{4}{4} p^{4}(1-p)^{0}=1*0.0039*1=0.0039\\\\\\[/tex]

b. The histogram is attached.

c. The most likely value for X is the expected value for X (E(X)).

Is calculated as:

[tex]E(X)=np=4\cdot0.25=1[/tex]

Answer:

  A  Only (2, 3)

Step-by-step explanation:

The given equation is in point-slope form:

  y -k = m(x -h) . . . . . a line with slope m through point (h, k)

The point in the given equation is ...

  (h, k) = (2, 3)

so you know the equation is satisfied at that point.

__

When you try the other point, you find ...

  For (x, y) = (3, 2), you have

  2 -3 = 5(3 -2)

  -1 = 5(1) . . . . FALSE

Point (3, 2) does not satisfy the equation.

  Only (2, 3) is a solution of the equation

_____

Of course, the equation of a line is satisfied by an infinite number of points. Of the two listed here, only (2, 3) is a solution.

Answer:

232 ÷ 5 = 46.4

you will need 47 cars.

Answer:

number 15 would be B sorry i dont understand number 14

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:

Probabilty of more than 3 =0.8474

Step-by-step explanation:

Probabilty of returned on time P= 0.39

Probabilty of not on time q=1-0.39= 0.61

Sample = 12 cars

Selected items = 3 cars

Probabilty of3 returned on time

= 12C3 * (0.39)^3 * (0.61)^9

= 220*(0.059319)*(0.011694146)

= 0.1526

Note**** C represents combination

So probability of more than 3 means greater than 3 = from 4 above

Probability of more than 3 = 1-probability of three

Probabilty of more than 3 = 1-0.1526

Probabilty of more than 3 =0.8474

Answer:

B 54in

Step-by-step explanation:

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:

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:

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: 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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Answer:

Yes

Step-by-step explanation:

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

Complete  Question

The function f determines the cost (in dollars) of a new Honda Accord in terms of the number of years t since 2000. That is, f ( t ) represents the cost (in dollars) of a new Honda Accord t years after 2000. Use function notation to represent each of the following. The cost (in dollars) of a new Accord in 2006?

A. How much more a new Accord costs in 2013 as compared to the cost of a new Accord in 2010?

B. A new Accord in 2013 is how many times as expensive as a new Accord in 2010?

C. In  2016 , some cars cost  $980 more than the cost of a new Accord.How much does the other cars cost (in dollars)in 2016?

Answer:

a

     The cost of  a new Accord in 2013 compared to 2010 is  z  =  f(13) -  f(10)

b

   The magnitude at which the cost of   a new Accord in 2013 is greater          than the cost in 2010 is  

          [tex]x = \frac{f(13)}{f(10)}[/tex]

c

    The cost of the other cars is 2016 is   r  =  980 + f(16)

Step-by-step explanation:

From the question we are told that

     The cost (in dollars) of a new Honda Accord is  f(t)

       Where t is  number of years after 2000

The cost of the  Honda Accord at 2013 is  

        f(2013 - 2000) =  f(13)

The cost of the  Honda Accord at 2010 is  

        f(2010 - 2000) =  f(10)

So the cost difference between 2013 and 2010 is mathematically evaluated as

         z  =  f(13) -  f(10)

Let constant at which the cost of Honda Accord in 2013 is greater than its cost at 2010 be  x

So

      f(13) =  x f(10)

=>      [tex]x = \frac{f(13)}{f(10)}[/tex]

  The cost of the Honda Accord in 2016 is mathematically evaluated as

          f(2016 - 2000) =   f(16)    

Now the cost of these other cars is  mathematically evaluated as  

         r  =  980 + f(16)

The difference between the cost of Accord in 2013 and 2010 is [z = f(13) - f(10)] and this can be determined by using the given data.

Given :

f(t) represents the cost (in dollars) of a new Honda Accord t years after 2000.

A). The cost of Accord in 2013 is given by:

[tex]f(2013-2000) = f(13)[/tex]

The cost of Accord in 2010 is given by:

[tex]f(2010-2000) = f(10)[/tex]

So, the difference between the cost of Accord in 2013 and 2010 is:

z = f(13) - f(10)

B). Let the constant be 'a' then the value of 'a' is:

[tex]a = \dfrac{f(13)}{f(10)}[/tex]

So, the new Accord in 2013 'a' times as expensive as a new Accord in 2010.

C). Cost of the Honda Accord in 2016 is:

[tex]f(2016-2000) = f(16)[/tex]

The cost of the other cars is:

r = 980 + f(16)

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Answer:

Step-by-step explanation:

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The inverse of the function G(X)=-2(x-4) is G'(x) = -(1/2)x +4

A function is a law that relates a dependent and an independent variable.

The function is g(x) = -2(x-4)

The inverse of a function is found by interchanging the position of the x an d y variable and then solving for y in terms of x.

g(x) = -2 (x-4)

y = -2(x-4)

Interchanging y to x

x = -2( y-4)

x = -2y +8

(x - 8)/ -2 = y

y = 4 - (1/2)x

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Answer:

The test statistic for this test is 3.82.

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 8500[/tex]

The alternate hypotesis is:

[tex]H_{1} > 8500[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

[tex]X = 8745, \mu = 8500, \sigma = 1200, n = 350[/tex]

So

[tex]t = \frac{8745 - 8500}{\frac{1200}{\sqrt{350}}} = 3.82[/tex]

The test statistic for this test is 3.82.

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:

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:

A.

Step-by-step explanation:

JLK = 360-154 (Circle is 360°)

So

JLK = 206

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:

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:

144

Step-by-step explanation:

4 triangles = 1/2 x 6 x 9 x 4 = 108

1 sq base = 6 x 6 = 36

total surface area = 36 + 108 = 144

if 3 triangles the base wouldn't be a square thus not possible to solve

Answer:

144

Step-by-step explanation:

SA = Area of base + 4 area of triangles

6² + 4(9 × 6 × 1/2)

36 + 4(27)

= 144

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: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:

[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:

One million, thirty four thousand, four hundred and seventy three dollars and forty five cents.

Answer:

-1.6

Step-by-step explanation:

4x +8y=0

y=0.8 ⇒