Find the functional values of r(0), r(3) and r(-3) for the rational function.

Answer:

217

Step-by-step explanation:

5425/25 = 217

Answer:

21/8x

Step-by-step explanation:

10x -20 = -6x+22

+6x-20 = 22

16x-20 = 22

16x +20= +20

16x/16x = 42/16x

x = 21/8x

Answer:

[tex]P(3) = ^9C_3 * 0.5^3 *0.5^6[/tex]

Step-by-step explanation:

Given

[tex]n = 9[/tex] --- number of flips

Required

[tex]P(x = 3)[/tex]

The probability of getting a head is:

[tex]p = \frac{1}{2}[/tex]

[tex]p = 0.5[/tex]

The distribution follows binomial probability, and it is calculated using:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]

So, we have:

[tex]P(3) = ^9C_3 * 0.5^3 * (1 - 0.5)^{9-3}[/tex]

[tex]P(3) = ^9C_3 * 0.5^3 *0.5^6[/tex]

Answer:

Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads?

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

> the equation given is x-y =0

> three points that will solve the equation could be

if x= -2 , y = -2 then x-y = 0 is -2 -(-2) =0 so it works point (-2,-2)

if x=1, y = 1 then x-y = 0 is 1-1 =0 is true so we have point (1, 1)

if x=2 ,y= 2 then x-y = 0 is 2-2 =0 is true so we have point (2, 2)

Answer:

[tex]x < 4368 \frac{8}{19} [/tex]

Step-by-step explanation:

[tex]28x < 83000 + 9x[/tex]

[tex]28x - 9x < 83000[/tex]

[tex]19x < 83000[/tex]

[tex]x < 4368 \frac{8}{19} [/tex]

Answer:

axis of symmetry=-2

y intercept=(0,-1)

Answer:

0.0783

Step-by-step explanation:

The probability of getting the first success on xtg trial ; this is a geometric distribution :

P(x) = p(1−p)^x−1

The probability of being a universal donor , p = 0.15

The probability of obtaining someone who is a universal donor on 5th trial will be :

P(5) = 0.15(1 - 0.15)^(5 - 1)

P(5) = 0.15(0.85)^4

P(5) = 0.15(0.52200625)

P(5) = 0.0783009375

P(5) = 0.0783

Answer:

412.5

Step-by-step explanation:

Answer:

[tex]412.5[/tex] miles

Step-by-step explanation:

Since 1 inch=75 miles you just multiply [tex]75*5.5[/tex] to get how many miles 5.5 inches is.

Answer:

The probability is 1/2500. (1/50)*(1/50)

Step-by-step explanation:

9514 1404 393

Answer:

  a. 1.48 seconds

Step-by-step explanation:

You want to find the larger value of t such that h(t) = 10.

  -16t^2 +25t +8 = 10

  16t^2 -25t +2 = 0 . . . . subtract the left side to get standard form

Using the quadratic formula, we find the values of t to be ...

  t = (-(-25) ± √((-25)^2 -4(16)(2)))/(2(16)) = (25±√497)/32

  t ≈ 0.08 or 1.48

The ball goes in the hoop about 1.48 seconds after it is thrown.

__

Additional comment

The quadratic formula tells us the solution to ...

  ax² +bx +c = 0

is given by ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here, we have a=16, b=-25, c=2. Of course, our variable is t, not x, but the relation is the same.

Answer:

0.0735 = 7.35% probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%.

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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A hotel manager calculates that 12% of the hotel rooms are booked.

This means that [tex]p = 0.12[/tex]

Sample of 556 rooms

This means that [tex]n = 556[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.12[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.12*0.88}{556}} = 0.0138[/tex]

What is the probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%?

This is the p-value of Z when X = 0.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.1 - 0.12}{0.0138}[/tex]

[tex]Z = -1.45[/tex]

[tex]Z = -1.45[/tex] has a p-value of 0.0735

0.0735 = 7.35% probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%.

Answer:

annual -  $9,231.74  

quarterly - $9,363.06  

monthly -  $9,394.09  

continuously -$9,409.87  

Step-by-step explanation:

Answer:

P=8(h)

Step-by-step explanation:

P is her total pay. You find that by multiplying what she makes an hour (8) by the total number of hours she has worked (h).

Answer:

p=8h

Step-by-step explanation:

Pay equals $8 per the number of hours

Answer:

(4%) ... $8200

Step-by-step explanation:

x + y = 15000

.04x + .032y = 545.60

y = 15000 - x

.04x + .032(15000 - x) = 545.60

.008x = 65.6

x=8200

The cost a company pays a lender for a loan is called interest.

The account received an initial investment of 8200 with 4% interest.

The cost of borrowing money is called interest, and it is typically expressed as a percentage, such as an annual percentage rate (APR). Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.

The cost a company pays a lender (creditor) for a loan is called interest. Although many different arrangements are possible, interest payments are typically based on the remaining balance of a loan and paid on a monthly basis. At a predetermined interest rate, interest is typically calculated as a percentage of the loan balance.

From the given information, we get

x + y = 15000 ........(1)

0.04x + 0.032y = 545.60 ..........(2)

From (1),

y = 15000 - x

substitute the value of y in the above equation, we get

⇒ 0.04x + 0.032(15000 - x) = 545.60

simplifying the above equation, we get

⇒ 0.008x = 65.6

x = 8200

Therefore, 8200 was initially invested in the account with 4% interest.

To learn more about Interest refer to:

https://brainly.com/question/2294792

#SPJ2

9514 1404 393

Answer:

  -4, 0

Step-by-step explanation:

The denominator is x^2+4x. This is zero when ...

  x^2 +4x = 0

  x(x +4) = 0

The zero product rule tells you the product is zero when the factors are zero.

  x = 0

  x +4 = 0   ⇒   x = -4

The denominator is zero for x=0 and x=-4.

Answer:

Below.

Step-by-step explanation:

22-8 = 14x2 = 28.

Answer:

Step-by-step explanation:

they say by noon 4 inches of rain has fallen,    then the say that it's falling at  1/4 inch per hour

f(x) = 1/4x +4

where x is in hours, and  f(x)  represents the linear graph of the amount of rain that has fallen after noon   :)

so by 2:30   or  2.5 hours....  then

f(2.5) = 1/4x +4

y = 1/4 (2.5) +4  ( i moved to the y  b/c now there is an answer)

y =[tex]\frac{5}{8}[/tex] + 4

y =4[tex]\frac{5}{8}[/tex]   inches of rain

Answer:

a) y = 1/4x + 4

b) 4.625 inches

Step-by-step explanation:

a) y(0) = 4 inches

slope = 1/4 rate

y = 1/4x + 4

b) 12:00pm (noon) to 2:30pm = 2 hours 30 mins = 2.5 hours

y = 1/4x + 4

y = (1/4)(2.5) + 4

y = 0.625 + 4

y = 4.625 inches

Answer:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

Step-by-step explanation:

A

Let's start with the first function:

[tex]x^{3}cos(x^{2})=x^{3}-\frac{x^{7}}{2!}+\frac{x^{11}}{4!}-\frac{x^{15}}{6!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 3, 7, 11, 15...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 3. So the power is given by 4n+3.

so let's put the two things together:

[tex](-1)^{n}x^{4n+3}[/tex]

Finally the denominator, there is also a sequence there: 0!, 2!, 4!, 6!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2, so in this case the sequence can be written as: (2n)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

So now we can build the whole series:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

B

Now, let's continue with the next function:

[tex]x^{3}sin(x^{2})=x^{5}-\frac{x^{9}}{3!}+\frac{x^{13}}{5!}-\frac{x^{17}}{7!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 5, 9, 13, 17...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 5. So the power is given by 4n+5.

so let's put the two things together:

[tex](-1)^{n}x^{4n+5}[/tex]

Finally the denominator, there is also a sequence there: 1!, 3!, 5!, 7!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2 starting from a 1, so in this case the sequence can be written as: (2n+1)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

So now we can build the whole series:

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

Answer:

86°

Step-by-step explanation:

180° is the sum of all angles in a triangle

The two angles given are 68° and 26°

The equation is : 180° - 68° - 26° = x°

180° - 68° - 26° = 86°

x° = 86°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

16

Step-by-step explanation:

[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]

                   [tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]

The value of x^2-2xy+y^2

will be 16 .

Explanation is in the attachment .

hope it is helpful to you ☺️

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that [tex]\mu = 273, \sigma = 100[/tex]

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that [tex]n = 30, s = \frac{100}{\sqrt{30}}[/tex]

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}[/tex]

[tex]Z = 0.88[/tex]

[tex]Z = 0.88[/tex] has a p-value of 0.8106

X = 257

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}[/tex]

[tex]Z = -0.88[/tex]

[tex]Z = -0.88[/tex] has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that [tex]n = 50, s = \frac{100}{\sqrt{50}}[/tex]

X = 289

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}[/tex]

[tex]Z = 1.13[/tex]

[tex]Z = 1.13[/tex] has a p-value of 0.8708

X = 257

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}[/tex]

[tex]Z = -1.13[/tex]

[tex]Z = -1.13[/tex] has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that [tex]n = 100, s = \frac{100}{\sqrt{100}}[/tex]

X = 289

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a p-value of 0.9452

X = 257

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}[/tex]

[tex]Z = -1.6[/tex]

[tex]Z = -1.6[/tex] has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

C is actually 0.8904

for anybody else stuck on this wondering why cengage is telling you c is wrong

Answer:

The expected value of the proposition is of -0.29.

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either the player will make it, or he will miss it. The probability of a player making a free throw is independent of any other free throw, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Suppose a basketball player has made 231 out of 361 free throws.

This means that [tex]p = \frac{231}{361} = 0.6399[/tex]

Probability of the player making the next 2 free throws:

This is P(X = 2) when n = 2. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,2}.(0.6399)^{2}.(0.3601)^{0} = 0.4095[/tex]

Find the expected value of the proposition:

0.4095 probability of you paying $31(losing $31), which is when the player makes the next 2 free throws.

1 - 0.4059 = 0.5905 probability of you being paid $21(earning $21), which is when the player does not make the next 2 free throws. So

[tex]E = -31*0.4095 + 21*0.5905 = -0.29[/tex]

The expected value of the proposition is of -0.29.

Answer:

4 times  longer

Step-by-step explanation:

1/2 of a hour is 30 minutes

2 hours is 120 minutes

120 ÷ 30  = 4

4 times longer

Answer:

The answer is 4 hours.

Step-by-step explanation:

Think of it like this:

1/2 = 0.5 in decimal form.

2 ÷ 0.5 = 4

I hope this helps. Have a GREAT day!

Answer:

Attached images

It was just easier for me this way.

Let me know in comments if you have questions.

Step-by-step explanation:

Answer:

14=-2x-4

18=-2x

x=-9

Hope This Helps!!!

Answer:

The answer is [tex]b=3, a=-2[/tex], and [tex]c=3[/tex].

Step-by-step explanation:

To solve this system of equations, start by solving for (a) in the third equation.

To solve for (a) in the third equation, add [tex]3b[/tex] to both sides of the equation, which will look like [tex]2a=-13+3b\\-a+b-c=2\\2a+3b-4c=-7[/tex]. Next, divide each term in [tex]2a=-13+3b[/tex] by 2 and simplify, which will look like [tex]\frac{2a}{2}=\frac{-13}{2} +\frac{3b}{2} \\-a+b-c=2\\2a+3b-4c=-7[/tex]   =  [tex]a=\frac{-13}{2} +\frac{3b}{2} \\-a+b-c=2\\2a+3b-4c=-7[/tex].

Then, replace all variables of (a) with [tex]-\frac{13}{2} +\frac{3b}{2}[/tex] in each equation and simplify, which will look like [tex]-13+6b-4c=-7\\-\frac{2c-13+b}{2}=2\\a=-\frac{13}{2}+\frac{3b}{2}[/tex].

The next step is to reorder [tex]-\frac{13}{2}[/tex] and [tex]\frac{3b}{2}[/tex], which will look like [tex]\frac{3b}{2}-\frac{13}{2}\\-13+6b-4c=-7\\-\frac{2c-13+b}{2} =2[/tex].

Then, solve for (b) in the second equation. To solve for (b) in the second equation start by moving all terms not containing (b) to the right side of the equation, which will look like [tex]6b=6+4c\\a=\frac{3b}{2}-\frac{13}{2} \\-\frac{2c-13+b}{2} =2[/tex]. Next, divide each term in                ([tex]6b=6+4c[/tex]) and simplify, which will look like [tex]b=1+\frac{2c}{3} \\a=\frac{3b}{2} -\frac{13}{2\\}\\-\frac{2c-13+b}{2} =2[/tex].

Then, replace all variables of (b) with [tex]1+\frac{2c}{3}[/tex] in each equation and simplify, which will look like [tex]-\frac{2(2c-9)}{3}=2\\a=c-5\\b=1+\frac{2c}{3}[/tex].

The next step is to solve for (c) in the first equation. To solve for (c) in the first equation start by multiplying both sides of the equation by [tex]-\frac{3}{2}[/tex] and simplify, which will look like [tex]2c-9=-3\\a=c-5\\b=1+\frac{2c}{3}[/tex]. Then, move all terms not containing (c) to the right side of the equation, which will look like [tex]2c=6\\a=c-5\\b=1+\frac{2c}{3}[/tex]. Next, divide each term in [tex]2c=6[/tex] by 2 and simplify, which will look like [tex]c=3\\a=c-5\\b=1+\frac{2c}{3}[/tex].

Then, replace all variables of (c) with 3 in each equation and simplify, which will look like [tex]b=3\\a=-2\\c=3[/tex]. Finally, the list of all the solutions are [tex]b=3,a=-2[/tex], and [tex]c=3[/tex].

Answer:

0.5 liters of milk are available per child.

Step-by-step explanation:

Amount of milk available per children:

The amount of milk, in liters, available for x children is given by:

[tex]m(x) = \frac{25}{x}[/tex]

50 children are present on a day

This means that [tex]x = 50[/tex]

How much milk is available per child?

This is m(50). So

[tex]m(50) = \frac{25}{50} = 0.5[/tex]

0.5 liters of milk are available per child.