PLEASE HELP. FINAL TEST QUESTION!!!!

Devon is having difficulty determining if the relation given in an input-output table is a function. Explain why he is correct or incorrect.

Answer:

a. 0.34885

b. 0.04651

c. 0.02404

d. 36

e. 14.7, say 15 trials

Step-by-step explanation:

Q17070205

Note:  

1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.

2. use R to find the probability values from the respective distributions.

a) the chance that the first 6 appears before the tenth roll

This means that a six appears exactly once between the first and the nineth roll.

Using binomial distribution, p=1/6, n=9, x=1

dbinom(1,9,1/6) = 0.34885

b) the chance that the third 6 appears on the tenth roll

This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.

Again, we have a binomial distribution of p=1/6, n=9, x=2

p1 = dbinom(2,9,1/6) = 0.27908

The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.

Thus the probability of both happening, by the multiplication rule, assuming independence  

P(third on the tenth roll) = p1*p2 = 0.04651

c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.

Again, using binomial distribution, probability of 3-6's in the first 10 rolls,

p1 = dbinom(3,10,1/6) = 0.15504

Probability of 3-6's in the NEXT 10 rolls

p1 = dbinom(3,10,1/6) = 0.15504

Probability of both happening  (multiplication rule, assuming both events are independent)

= p1 *  p1 = 0.02404

d) the expected number of rolls until six 6's appear

Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6

=  n(1-p)/p

Total number of rolls by adding n  

= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36

e) the expected number of rolls until all six faces appear

P1 = 6/6 because the firs trial (roll) can be any face with probability 1

P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials

P3 = 6/4 ...

P4 = 6/3

P5 = 6/2

P6 = 6/1

So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials

Answer:

see below

Step-by-step explanation:

Let x be the original price

x* discount rate = discount

x * 60% = 30

Change to decimal form

x * .60 = 30

Divide each side by .60

x = 30/.60

x =50

The original price was 50 dollars

Answer:

A-30     B-20    C-50

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Solution:-

The standard sinusoidal waveform defined over the domain [ 0 , 2π ] is given as:

                                   f ( x ) = sin ( w*x ± k ) ± b

Where,

                 w: The frequency of the cycle

                 k: The phase difference

                 b: The vertical shift of center line from origin

We are given that the function completes 2 cycles over the domain of [ 0 , 2π ]. The number of cycles of a sinusoidal wave is given by the frequency parameter ( w ).

We will plug in w = 2. No information is given regarding the phase difference ( k ) and the position of waveform from the origin. So we can set these parameters to zero. k = b = 0.

The resulting sinusoidal waveform can be expressed as:

                           f ( x ) = sin ( 2x )  ... Answer

Answer:

Option C

Step-by-step explanation:

The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.

It tests the claim that the row and column variables are independent of each other.

The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.

Answer:

2y (x^2+9) ( x-5)

Step-by-step explanation:

2x^3y + 18xy - 10x^2y - 90y

Factor out the common factor of 2y

2y(x^3+9x-5x^2-45)

Then factor by grouping

2y(x^3+9x     -5x^2-45)

Taking x from the first group and -5 from the second

2y( x (x^2+9)  -5(x^2+9))

Now factor out (x^2+9)

2y (x^2+9) ( x-5)

Answer:

0.007

Step-by-step explanation:

We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage

Step 1

We would have to find the sample standard deviation.

We use the formula = σ/√n

σ = 12.2 pounds

n = number of house holds = 51

= 12.2/√51

Sample Standard deviation = 1.7083417025.

Step 2

We find the z score for when the sample mean is more than 61

z-score formula is z = (x-μ)/σ

where:

x = raw score = 61 pounds

μ = the population mean = 56.8 pounds

σ = the sample standard deviation = 1.7083417025

z = (x-μ)/σ

z = (61 - 56.8)/ 1.7083417025

z = 2.45852

Finding the Probability using the z score table

P(z = 2.45852) = 0.99302

P(x>61) = 1 - P(z = 2.45852) = 0.0069755

≈ 0.007

Therefore,the probability that the sample mean will be more than 61 pounds is 0.007

Answer:

The depreciated value of the car after 1 yr is ​$16,353

The depreciated value of the car after 2 yr is ​$12,264.75

Step-by-step explanation:

Given

purchase amount P= $21,804

rate of depreciation R= 25%

applying the formula for the car deprecation we have

[tex]A= P*(1-\frac{R}{100} )^n[/tex]

Where,

A is the value of the car after n years,

P is the purchase amount,

R is the percentage rate of depreciation per annum,

n is the number of years after the purchase.

1. The depreciated value of the car after 1 yr is ​

n=1

[tex]A= 21,804*(1-\frac{25}{100} )^1\\\\A= 21,804*(1-0.25 )^1\\\\A= 21,804*0.75\\\\A= 16353[/tex]

The depreciated value of the car after 1 yr is ​$16,353

2. The depreciated value of the car after 2 yr is ​

n=2

[tex]A= 21,804*(1-\frac{25}{100} )^2\\\\A= 21,804*(1-0.25 )^2\\\\A= 21,804*0.75^2\\\\A= 21,804*0.5625\\\\A= 12264.75[/tex]

The depreciated value of the car after 2 yr is ​$12,264.75

Answer:

0.07

Step-by-step explanation:

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

[tex]\large \boxed{0.07}[/tex]

Step-by-step explanation:

The usual question is, "What is the probability of A, given B?"

They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"

We must first complete your frequency table by calculating the totals for each row and column.

The table shows that there are 30 students, two of whom drive to school.

[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]

median=order them and find the middle=6

mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4

range= the difference between the smallest and largest number=9-3=6

mode= the one that appears the most= 7

The median, mean, range and mode will be 6, 5.4, 9 and 7.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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Answer:

C and D

Step-by-step explanation:

khan acedemy

An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the given equation v²=25/81 can be found as shown below.

v²=25/81

Taking the square root of both sides of the equation,

√(v²) = √(25/81)

v = √(25/81)

v = √(5² / 9²)

v = ± 5/9

Hence, the solutions of the given equation are A, B, and C.

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Answer:

x < 11.5

Step-by-step explanation:

2x + 9 < 32

(2x + 9) - 9  < 32 - 9

2x < 23

2x/2 < 23/2

x < 11.5

Answer:

x < 11 1/2

Step-by-step explanation:

2x+9<32

Subtract 9 from each side

2x+9-9 < 32-9

2x<23

Divide by 2

2x/2 <23/2

x < 11 1/2

X is any number less than 11 1/2

Answer:

100%

Step-by-step explanation:

Start with x.

x = x/1

Increase the numerator by 60% to 1.6x.

Decrease the numerator by 20% to 0.8.

The new fraction is

1.6x/0.8

Do the division.

1.6x/0.8 = 2x

The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.

The increase is 100%.

Answer:

33%

Step-by-step explanation:

let fraction be x/y

numerator increased by 60%

=x+60%ofx

=8x

denominator increased by 20%

=y+20%of y

so the increased fraction is 4x/3y

let the fraction is increased by a%

then

x/y +a%of (x/y)=4x/3y

or, a%of(x/y)=x/3y

[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]

therefore a=33

anda%=33%

The area bounded by region between the curve [tex]y = x^2- 24[/tex]  and [tex]y = 1[/tex] is

[tex]0[/tex] square units.

To find the Area,

Integrate the difference between the two curves over the interval of intersection.

Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .

The point of Intersection is the common point between the two curve.

Value of [tex]x[/tex] and [tex]y[/tex] coordinate  will be equal for both curve at point of intersection

In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].

[tex]1 = x^2-24[/tex]

Rearrange, like and unlike terms:

[tex]25 = x^2[/tex]

[tex]x =[/tex]  ±5

The point of intersection for two curves are:

[tex]x = +5[/tex]  and  [tex]x = -5[/tex]

Integrate the difference between the two curve over the interval [-5,5] to calculate the area.

Area =   [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]

Simplify,

[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]

Integrate,

[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]

Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.

[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]

= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]

[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]

[tex]= 0[/tex]

The Area between the two curves is [tex]0[/tex] square  units.

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Answer:

k = -6

Step-by-step explanation:

hello

saying that (x-2) is a factor of [tex]x^2+x+k[/tex]

means that 2 is a zero of

[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]

and we can verify as

[tex](x^2+x-6)=(x-2)(x+3)[/tex]

so it is all good

hope this helps

Answer:

Step-by-step explanation:

Since there are  2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.

Probability that at least 1 ball was​ red, given that the first ball was replaced before the second can be calculated as shown;

Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.

Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49

Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49

The probability that at least 1 ball was​ red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49

If the balls were not replaced before the second draw

Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21

Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21

The probability that at least 1 ball was​ red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

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Answer:

3, 12

Step-by-step explanation:

Et x and y be the required integers.

Case 1: x = 5y - 3...(1)

Case 2: xy = 36

Hence, (5y - 3)*y = 36

[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]

Hence, the required integers are 3 and 12.

let

x  = one integer

y = another integer

x = 5y - 3

If the product of the two integers is 36, then find the integers.

x * y = 36

(5y - 3) * y = 36

5y² - 3y = 36

5y² - 3y - 36 = 0

Solve the quadratic equation using factorization method

That is, find two numbers whose product will give -180 and sum will give -3

Note: coefficient of y² multiplied by -36 = -180

5y² - 3y - 36 = 0

The numbers are -15 and +12

5y² - 15y + 12y - 36 = 0

5y(y - 3) + 12 (y - 3) = 0

(5y + 12) (y - 3) = 0

5y + 12 = 0      y - 3 = 0

5y = - 12           y = 3

y = -12/5

The value of y can not be negative

Therefore,

y = 3

Substitute y = 3 into x = 5y - 3

x = 5y - 3

x = 5(3) - 3

= 15 - 3

= 12

x = 12

Therefore,

(x, y) = (12, 3)

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Answer:

  11/10

Step-by-step explanation:

The area ratio is the square of the radius ratio (k):

  (121/100) = k²

  k = √(121/100) = 11/10

The ratio of radii is 11/10.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Answer:

a. Cumulative Probability Distribution

Grade             P(X ≤ x)

F                      0.145

D                     0.310

C                     0.670

B                     0.910

A                         1

b. P(at least B) = 0.330

c. P(pass) = 0.855

Step-by-step explanation:

Professor Sanchez has been teaching Principles of Economics for over 25 years.

He uses the following scale for grading.

Grade     Numerical Score      Probability

A                       4                            0.090

B                       3                            0.240

C                       2                            0.360

D                       1                            0.165

F                       0                            0.145

a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

The cumulative probability distribution is given by

Grade = F

P(X ≤ x) = 0.145

Grade = D

P(X ≤ x) = 0.145 + 0.165 = 0.310

Grade = C

P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670

Grade = B

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910

Grade = A

P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1

Cumulative Probability Distribution

Grade             P(X ≤ x)

F                      0.145

D                     0.310

C                     0.670

B                     0.910

A                         1

b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

At least B means equal to B or greater than B grade.

P(at least B) = P(B) + P(A)

P(at least B) = 0.240 + 0.090

P(at least B) = 0.330

c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Passing the course means getting a grade of A, B, C or D

P(pass) = P(A) + P(B) + P(C) + P(D)

P(pass) = 0.090 + 0.240 + 0.360 + 0.165

P(pass) = 0.855

Alternatively,

P(pass) = 1 - P(F)

P(pass) = 1 - 0.145

P(pass) = 0.855

Answer:

21=2w+2w+3    18=4w     w=4.5

Answer:  width = 300

Step-by-step explanation:

Area (A) = Length (L) x width (w)

Given: A = 268,500

           L = 3w - 5

           w = w

268,500 = (3w - 5) x (w)

268,500 = 3w² - 5w

            0 = 3w² - 5w - 268,500

            0 = (3w + 895) (w - 300)

   0 = 3w + 895        0 = w - 300

  -985/3 = w             300 = w

Since width cannot be negative, disregard w = -985/3

So the only valid answer is: w = 300

Answer:

Step-by-step explanation:

Length of an arc is expressed as [tex]L = \frac{\theta}{2\pi } * 2\pi r\\[/tex]. Given;

[tex]\theta = \frac{5\pi }{6} rad\\ radius = 24in\\[/tex]

The length of the minor arc SV is expressed as:

[tex]L = \frac{\frac{5\pi }{6} }{2\pi } * 2\pi (24)\\L = \frac{5\pi }{12\pi } * 48\pi \\L = \frac{5}{12} * 48\pi \\L = \frac{240\pi }{12} \\L = 20\pi \ in[/tex]

Hence, The length  of the arc SV is 20π in

Answer:

20 pi

Step-by-step explanation:

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Step-by-step explanation:

Critical points:

The critical points of a function f(x) are the values of x for which:

[tex]f'(x) = 0[/tex]

For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.

The critical points help us find these intervals.

In this question:

[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]

So

[tex]P'(x) = -0.008x + 6[/tex]

Critical point:

[tex]P'(x) = 0[/tex]

[tex]-0.008x + 6 = 0[/tex]

[tex]0.008x = 6[/tex]

[tex]x = \frac{6}{0.008}[/tex]

[tex]x = 750[/tex]

We have two intervals:

(0, 750) and [tex](750, \infty)[/tex]

(0, 750)

Will find P'(x) when x = 1

[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]

Positive, so increasing.

Interval [tex](750, \infty)[/tex]

Will find P'(x) when x = 800

[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]

Negative, then decreasing.

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)  

Answer:

it we'll be 0.3

Step-by-step explanation:

trust me man I like to explain but it's long

Answer:

0.3 meter or 3/10 meter

Step-by-step explanation:

As there are 100cm in 1 meter and you want to find 30cm in terms of meters.

It will be as

100cm = 1 meter     (rule/lax)

100/100 cm = 1/100  meter   (divide both sides of equation with 100)

1 cm = 1/100 meter

1 *30 cm = (1/100)*30  meter    (multiply both sides with 30)

30 cm = 30/100 meter

30/100 more shortly can be written as  3/10 meter or in decimals 0.3 meter.

Answer:

85.932 cm³

Step-by-step explanation:

The volume of rectangular prism is obtained as the product of its length (l) by its width (w) and by its height (h):

[tex]V=l*w*h[/tex]

The volume of a prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm is:

[tex]V=4.4*3.1*6.3\\V=85.932\ cm^3[/tex]

The volume of this prism is 85.932 cm³.

Answer:

Step-by-step explanation:

Least common denominator = a²b²

[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

Answer:

Dy/Dx=1/√ (2x+3)

Yeah it's correct

Step-by-step explanation:

Applying differential by chain differentiation method.

The differential of y = √(2x+3) with respect to x

y = √(2x+3)

Let y = √u

Y = u^½

U = 2x +3

The formula for chain differentiation is

Dy/Dx = Dy/Du *Du/Dx

So

Dy/Dx = Dy/Du *Du/Dx

Dy/Du= 1/2u^-½

Du/Dx = 2

Dy/Dx =( 1/2u^-½)2

Dy/Dx= u^-½

Dy/Dx=1/√ u

But u = 2x+3

Dy/Dx=1/√ (2x+3)

we just have to use the Pythagoras theorem and then calculate the value of x and y.

Answer:

-10, 40, -240, 1,920 and -19, 200

Step-by-step explanation:

Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.

when n= 1;

aₙ₊₁ = -2naₙ

a₁₊₁ = -2(1)a₁

a₂ = -2(1)(5)

a₂ = -10

when n = 2;

a₂₊₁ = -2(2)a₂

a₃ = -2(2)(-10)

a₃ = 40

when n = 3;

a₃₊₁ = -2(3)a₃

a₄ = -2(3)(40)

a₄ = -240

when n= 4;

a₄₊₁ = -2(4)a₄

a₅ = -2(4)(-240)

a₅ = 1,920

when n = 5;

a₅₊₁ = -2(5)a₅

a₆ = -2(5)(1920)

a₆ = -19,200

Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200