Customers depart from a bookstore according to a Poisson process with rate A per hour Each customer buys a book with probability p, independent of everything else. Find the distribution of the time until the first sale of a book. Find the probability that no books are sold during a particular hour. Find the expected number of customers who buy a book during a particular hour.

Answer:

Mark's salary after 25 years is $52,499.39

Step-by-step explanation:

This situation can be modelled exponentially. We are given the starting amount, 32000, and the annual growth rate, 2%. This means that, for every year that passes, we'd have [tex][(32000)(1.02)][/tex] $ as the salary. As such, the model would be [tex]S(t) = 32000(1.02)^t[/tex]. We want to find Mark's salary 25 years from the starting point, t=25. Having developed a model for this situation, we can simply plug in 25 for t:

[tex]S(25) = 32000(1.02)^{(25)}[/tex]

[tex]S(25) = 52499.39[/tex]

The probability the card drawn is a face card is 3/13. The probability the card drawn is not a face card is 10/13. The odds in favor of drawing a face card is 3/10. The odds against drawing a face card are 10/3.

There are 52 cards in a standard deck, and 12 of them are face cards (jack, queen, and king). Therefore, the probability of drawing a face card is 12/52, or 3/13.

The probability of not drawing a face card is 1 minus the probability of drawing a face card. Since the probability of drawing a face card is 3/13, the probability of not drawing a face card is 1 - 3/13, which is 10/13.

The odds in favor of drawing a face card are 3:10, or 3/10. The odds against drawing a face card are 10:3, or 10/3.

In summary:

The probability the  card drawn is a face card: 3/13

The probability the card drawn is not a face card: 10/13

Odds in favor of drawing a face card: 3/10

Odds against drawing a face card: 10/3

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Answer:

Step-by-step explanation:

Analyzing the events a and b given in the question , the events are not mutually exclusive events, which are also called intersecting events in terms of venn diagram.

Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events. The probability of an occurrence if A and B are mutually exclusive is indicated by P(A Or B) or P. (A U B).

Mutually inclusive events permit the occurrence of both occurrences simultaneously or inside a single trial. It refers to events that are required to take place simultaneously by a rule or a natural law. When two occurrences are mutually inclusive, they cannot happen separately.

Here, the events a and b can occur simultaneously, since we can get a number greater than 3 and less than 5 at the same time while rolling a dice randomly.

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Answer: 50.24

Step-by-step explanation:

The formula to find the circumference of a circle is two pi r. So we just have substituted value into our formula. So we have To multiply by pi, so let's use 3.14 multiplied by our sequence to eight, so this is equal to 16, multiply by 3.14, which is equal to 50.24.

The probability of observing no positive reading if all suspects are telling the truth is d. 0.59. Probability theory is a branch of mathematics that is used to model and analyze random events.

Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

To solve this problem, we need to calculate the probability of observing no positive readings given that all suspects are telling the truth, which is equal to the probability that all 5 suspects receive a negative reading on the lie detector test. Since the lie detector will show a positive reading 10% of the time when a person is telling the truth, the probability that a suspect will receive a negative reading when telling the truth is 1 - 10% = 90%. Therefore, the probability that all 5 suspects will receive a negative reading when telling the truth is:

(90%)^5 = (0.9)^5 = 0.59049.

The correct answer is therefore (d) 0.59.

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Answer:

  -72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³

Step-by-step explanation:

You want to simplify (7x+5y)^3–(7x–5y)^3–30y(7x+5y)(7x–5y)^3.

We recognize that there are some repeated expressions here that may make it easier to simplify this without multiplying it all out.

Let a = 7x+5y, b = 7x -5y. Then the expression becomes ...

  a³ -b³ -30y·a·b³

  = (a³ -b³) -30yb²(ab)

  = (a -b)(a² +ab +b²) -30yb²·ab

Now ...

  a -b = (7x +5y) -(7x -5y) = 10y

  a² +b² +ab = (7x +5y)² +(7x -5y)² +(7x +5y)(7x -5y)

     = (7x)² +2(7x)(5y) +(5y)² +(7x)² -2(7x)(5y) +(5y)² +(7x)² -(5y)²

     = 3(7x)² +(5y)² = 147x² +25y²

So the first pair of terms expands to ...

  a³ -b³ = 10y(147x² +25y²) = 1470x²y +250y³

The last term becomes (with a positive sign) ...

  30yb²(ab) = 30y(7x -5y)²((7x)² -(5y)²)

     = 30y((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) . . . . see comment below

     = 30y((7x)⁴ -(5y)⁴ -70xy((7x)² -(5y)²))

     = 72030x⁴y -18750y⁵ -102900x³y² +52500xy⁴

Putting it all together gives ...

  = -72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³

__

Additional comment

The difference of squares form is used several times here:

  p² -q² = (p -q)(p +q)

The expression ((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) is decomposed to ...

  ((7x)² +(5y)²)·((7x)² -(5y)²) - 2(7x)(5y)((7x)² -(5y)²)

This lets us use the difference of squares form to simplify at least part of the expression. This whole thing gets multiplied by -30y.

Answer:

1. 600 yd^3

2. 103,680 in^3

Step-by-step explanation:

1. To find volume we do l*w*h

(15)(8)(5)

120(5)

600 yards^3

2. We also find the volume for this

(36)(60)(48)

2160(48)

103680 in^3

Hopes this helps

The critical values for a 99% confidence interval using the chi-square distribution with 10 degrees of freedom are 18.3278 and 28.3092.

The chi-square distribution is a continuous probability distribution that is used to determine the probability of a statistic being greater than or less than a certain value. The chi-square distribution with 10 degrees of freedom is used to calculate critical values for a 99% confidence interval.

To find the critical values, we need to use the chi-square distribution calculator. In the calculator, we should enter the degrees of freedom, which is 10 in this case, and the confidence level, which is 99% in this case. The calculator will then return the critical values for the 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

Step 1: Go to the chi-square distribution calculator.

Step 2: Enter the degrees of freedom, which is 10 in this case.

Step 3: Enter the confidence level, which is 99% in this case.

Step 4: Click the “Calculate” button.

Step 5: The calculator will return the critical values for a 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

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Answer:

Step-by-step explanation:

3250 : 156 = y : 40

y = 3250 × 40 : 156

y = 833.(3)                                    3 repeating

--------------------------

check

3250 : 156 = 833.(3) : 40

20,83333333333333 = 20,83333333333333

the answer is good

When the expected value and variance are 3.5 and 15.25, the statistic probability distribution will be 5/10, 3/10, and 2/10.

Given that,

A box contains ten sealed envelopes labelled 1, 2, 3, and 10. Six of them are empty, two have $5 apiece, and the remaining two each contain a $10 bill. You obtain the most money in any chosen envelope when replacement is used; a sample of size 3 is selected (forming a random sample). The statistic of interest is m if the quantities in the selected envelopes are represented by x1, x2, and x3.

We know that,

The probability distribution will be

P(X=0) = 5/10

P(X=5) = 3/10

P(X=10) = 2/10

In probability theory, the expected value is a development of the weighted average. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the expected value.

The expected value is

E =0(5/10)+5(3/10)+10(2/10) = 3.5

The variance is

V = 0² x (5/10) + 5² ( 3/10 ) + 10² x (2/10) - 3.5² = 15.25

Therefore, the statistic probability distribution will be 5/10, 3/10, and 2/10 when the expected value and variance are 3.5 and 15.25.

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There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.

Given that a recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent.

Let p1 be the proportion of local seniors and p2 national seniors.

H₀ : p₁ =  p₂

Hₐ : p₁ > p₂

(right tailed test at 5% significance level)

Group I II  

Success 69 60 129

Total 100 100 200

p 0.69 0.6 0.645

q 0.31 0.4 0.355

se 0.046249324 0.048989795 0.033836002

p diff 0.09  

Std error 0.03384  

Z 2.659574468 0  

p 0.00391  

we find that p value is 0.00391 < 0.05

Hence we reject null hypothesis. There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.

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Using the properties of confidence interval and probability we can conclude from the observations that the process is not a statistical control process.

(a) The process is not a statistical process .

b) The control & chart is not in control because there some false alarm at 8-15. There are some special causes in the clata (may be in manufacturing) exist.

(c) (i) Given that Target length = 37 USL + LSL = 37 USL+2SL= 74

and Tolerance = 0.01 USL LSL = 0.01

After Solving equation 1 & 2 we get VSL = 37.005, LSL = 36.995

cp =2 × 0.01 6/0.05 × 2.059 = 0.01 ×0.1457 = 0.0686

(ii) Cp = min (Cpu, CP).

Cpu = 37.005-37 0.073 = 0.06849

CPL = 0.06859

Срк = 2 × 0.06849 = 0.024

The application of statistical methods to monitor and regulate the quality of a manufacturing process is known as SPC (statistical process control) or SQC (statistical quality control).

This increases the efficiency of the process, resulting in more specification-conforming goods with less waste (rework or scrap). SPC can be used to any process that can measure the output of a "compliant product" (a product that fulfils standards).

The primary tools of SPC are run charts, control charts, a focus on continuous improvement, and experiment design. Manufacturing lines are one example of a process that employs SPC.

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We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.

What is Normally distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

results obtained are 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15

            [tex]\overline {X} = \frac{0.06 + 0.11 + 0.16 + 0.15 + 0.14 + 0.08 + 0.15}{7}\\\\ \overline {X} = 0.1214\\[/tex]

            [tex]S=\sqrt[2]{\frac{0.0091}{n-1} } \\\\S= \sqrt[2]{\frac{0.0091}{7-1} }\\\\S=0.039\\\\n-1 = 6\\\\E= 3.143 * \frac{0.039}{\sqrt[2]{7} } \\\\E= 0.0462\\\\[/tex]

The confidence interval ⇾ 0.0752 < µ < 0.1676

We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.

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The derivative of given function is D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814  

We have to find the directional derivative of the given function  

f(x,y,z) = yz+e^x at (x0,y0,z0)=(1,1,1) in the direction of the vector

d⃗ =(3,−5,5)  

Find the gradient of the function and evaluate it at the given point:  

To find the gradient of a function (which is a vector), differentiate the function with respect to each variable.  

∇f= (∂f/∂x,∂f/∂y,∂f/∂z)  

∂f/∂x = ∂( yz+e^x )/∂x  

The derivative of a sum/difference is the sum/difference of derivatives:  

∂f/∂x = ∂( yz)/∂x +∂(e^x )/∂x since the derivative of y and z with respect of x is zero.  

∂f/∂x = e^x The derivative of exponential is d(e^x)/dx=e^x.  

Similarly  

d(yz+e^x)/dy = z and d(yz+e^x)/dz = y  

∇(yz+e^x)(x0,y0,z0)=(e^x,z,y)  

Finally plug in the point we get the result  

∇(yz+e^x)|(x0,y0,z0)=(1,1,1)=(e,1,1)  

∇(yz+ex)|(x0,y0,z0)=(1,1,1)=(e,1,1)  

Now we Find the length of the vector: |d⃗ |=((3)^2+(−5)^2+(5)^2)^1/2 =(59)^1/2  

To normalize the vector, divide each component by length:  

d = ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)  

Finally, the directional derivative is the dot product of the gradient and the normalized vector:  

D(yz+e^x)d(1,1,1) = (e,1,1). ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)  

D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814  

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well, he has left only 6 oz.

now, if we take the 16(origin amount) to be the 100%, what is 6 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 16 & 100\\ 6& x \end{array} \implies \cfrac{16}{6}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 8 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 8x=300\implies x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]

Answer:

The correct answer is 15 potatoes.

Step-by-step explanation:

To solve this problem, we can determine the unit rate and use proportions. We know that Sarai needs 6 potatoes for 16 latkes. We want to know how many potatoes she will need to make 40 latkes. Let's call this unknown value x. We can set up the following equation:

6 potatoes/16 latkes = x potatoes/40 latkes

To solve this equation, we can first simplify the left side to find the unit rate.

3 potatoes/8 latkes = x potatoes/40 latkes

To solve, we can recognize that 40 latkes is 5 times the amount shown in the unit rate (8 latkes), which means that we need 5 times the amount of potatoes.

3 potatoes * 5 = 15 potatoes

Therefore, the correct answer is 15 potatoes. Note that you could have also just solved the equation for x to find your answer as well.

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Answer:

1095

Step-by-step explanation:

The polynomial that is the product of (4x−3)(x²+2x−6) is 4x³ + 5x² - 30x + 18

A polynomial simply refers to the expression that is composed of constant, variables, and exponents that are combined by mathematical operations.

The product of the polynomial will be:

= (4x −3)(x² + 2x − 6)

= 4x³ + 8x² - 24x - 3x² - 6x + 18

= 4x³ + 5x² - 30x + 18

The product is 4x³ + 5x² - 30x + 18.

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Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 44 and 54 minutes is 0.8150= 81.5%.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean  and standard deviation  is given by:

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

The relative frequency of classical CDs with playing time X between 44 and 54 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 44, hence:

X = 54:

Z = 3

Z = 3 has a p-value of 0.9987.

X = 54:

Z = -1

Z = -1 has a p-value of 0.1584.

0.9987 - 0.1584 = 0.8150

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Answer:

There are 5 possible outcomes when the first spinner is spun, and 2 possible outcomes when the second spinner is spun. Therefore, the sample space of possible outcomes when both spinners are spun is 5 x 2 = <<5*2=10>>10.

The possible outcomes are:

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

Of these, 3A, 2A, 1A, and 4B have a number less than 3 or an A. Therefore, there are 4 possible outcomes that have a number less than 3 or an A.

Step-by-step explanation:

Answer:

C {(7, 2), (7, 0), (3,-2), (1,4)}

Step-by-step explanation:
In a function, x = 7 can't be at both 2 and 0 because it would not pass the vertical line test.

Answer: 19/7

Step-by-step explanation:

Your goal is to isolate x or get x by itself.

Move all other variables to the opposite side.

70x+10-10=200-10

70x=190

Divide both sides by 70

x= 19/7

Answer:

[tex]x= \frac{19}{7}[/tex]   OR   [tex]2 \frac{5}{7}[/tex]

Step-by-step explanation:

To do this you need to:

  1. Subtract 10 from both sides {As shown below}

[tex]70x+10-10=200-10[/tex]

  2. Simplify {As shown below}

[tex]70x=190[/tex]

   3. Divide both sides by the same factor {As shown below}

[tex]\frac{70x}{70} = \frac{190}{70}[/tex]

    4. Simplify {As shown below}

        {a. Cancel terms that are in both the numerator and the denominator}

        {b. Divide the numbers}

[tex]x= \frac{19}{7}[/tex] OR [tex]2 \frac{5}{7}[/tex]

{Please give Brainliest}

In the given circle with center O, DF is congruent to BC.

What is congruent?

When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.

Consider the given circle with center O.

We have to find DF is congruent to which line.

Let point E and A are the midpoints of chord DF and BC.

There is angle 90 degrees on both the points.

The chords DF and chord BC are on the same distance from the center of the circle which is 3.09.

So, the chords DF and BC are of same measure.

Therefore, the chord BC is congruent to DF.

Hence, in the given circle with center O, DF is congruent to BC.

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Answer:

2n + 5 ≤ 7  The first choice

Step-by-step explanation:

2n + 5 ≤ 7  Subtract 5 from both sides.

2n + 5 - 5 ≤ 7 - 5

2n ≤ 2  Divide both sides by 2

[tex]\frac{2n}{2}[/tex] ≤ [tex]\frac{2}{2}[/tex]

n [tex]\leq[/tex] 1

Answer:

2x +5 ≤ 7

I hope my answer helps you.

Answer:$85.5

Step-by-step explanation:

So divide 66.50 by 7 and that will get you 9.5 then multiply that by 9 which is then 85.5

The solution for the given equation is am = -15.

The given equation is -2(am + 4) = 22

On simplifying the given equation for its solution, we get

-2(am + 4) = 22

⇒ -2am - 8 = 22

⇒ -2am = 22 + 8

⇒ -2am = 30

∴ am = -30/2 = -15

So, the solution for the given equation is -15.

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The resulting conditional mean squared error of the LMS estimator, given N=3 is 0.0383746

In general, the conditional distribution of X given Y does not equal the conditional distribution of Y given X, i.e., pX|Y(x|y)≠pY|X(y|x). If X and Y are independent, discrete random variables, then the following are true: pX|Y(x|y)=pX(x)pY|X(y|x)=pY(y)

The full conditional for a given node (parameter) is simply the product of the probability model (likelihood or prior) for that node and its parent node (at least up to a constant of proportionality).

1) fY|N(y∣N=3)=84 y^6 (1-y)^3

2)0.0636363

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Answer: x=3

Step-by-step explanation:

6*6=36

36*6=216

6*6*6=216

6*6*6=[tex]6^{2}[/tex]

[tex]6^{x} =6^{3}[/tex]

x=3

Answer:

Step-by-step explanation:

we need to find a base for 216 that is equal to 6.

216 / 6  = 36

36 / 6 = 6,

So 6 * 6 = 36 and 36 * 6 = 216.

From this we know that 216 = 6^3

6^x = 6^3

x=3