A batch of 484 containers for frozen orange juice contains 7 that are defective. Two are selected, at random, without replacement from the batch. a) What is the probability that the second one selected is defective given that the first one was defective? Round your answer to five decimal places (e.g. 98.76543).

Answer:

Total = N(1) +N(2)+N(3) = 10+14+200 = 224 sequences

224 sequences would NOT be permitted.

Step-by-step explanation:

1) all four digits identical

Number of possible PIN with all four digits identical N(1) = 1×1×1×10 = 10 possible PIN

2) sequence of consecutive ascending or descending digits N(2) = 14

Only Ascending starting with 0,1,2 = 3

only descending for 7,8,9 = 3

and both for 3,4,5,6 = (2×4)

Total = 3+3+(2×4) = 14

3) any sequence starting with 19 or 20 (birth years

N(3) = 2 × 1×1×10×10 = 2×100 = 200

N(3) = 200

(Note : 100 possible ways for each of 19 or 20s)

Total = N(1) +N(2)+N(3) = 10+14+200 = 224

224 sequences would NOT be permitted.

Answer: d, p = 0.4493

Step-by-step explanation: this question is solved using a possion probability distribution because the event is occurring at a fixed rate.

For this question of ours the fixed rate is the fact that 12 customers visiting the shop within 15 minutes.

For this question our fixed rate (u) = 12/15 = 0.8

The probability distribution for possion is given as

P(x=r) = (e^-u * u^r) / r!

At this point x = 0 ( no customers coming to the shop)

P(x=0) =( e^-0.8 * 0.8^0)/ 0!

P(x=0) = (e^-0.8 * 1)/1

P(x=0) = e^-0.8

P(x=0) = 0.4493

Final answer:

It took Mark 26 minutes to run from mile marker 1 to mile marker 4. His average speed was 0.5038 miles per minute for that segment. To complete the race in 110 minutes, Mark's average speed from mile marker 9 to the finish line must be 0.4415 miles per minute.

Explanation:

To find how long it took Mark to run from mile marker 1 to mile marker 4, we need to add the times it took him to run from mile marker 1 to mile marker 2 and from mile marker 2 to mile marker 4. Mark took 6 minutes to run from mile marker 1 to mile marker 2, and 20 minutes to run from mile marker 2 to mile marker 4. So the total time it took him to run from mile marker 1 to mile marker 4 is 6 minutes + 20 minutes = 26 minutes.

To find Mark's average speed as he ran from mile marker 1 to mile marker 4, we need to divide the total distance he ran by the total time it took him. The total distance from mile marker 1 to mile marker 4 is 13.1 miles. So the average speed is 13.1 miles / 26 minutes = 0.5038 miles per minute.

To complete the race in 110 minutes, Mark has 39 minutes left after passing mile marker 9. To find his average speed as he travels from mile marker 9 to the finish line, we need to divide the remaining distance by the remaining time. The remaining distance is 26.22 miles - 9 miles = 17.22 miles. So his average speed is 17.22 miles / 39 minutes = 0.4415 miles per minute.

Answer:

OPTION C: [tex]$ \textbf{37} \frac{\textbf{28}}{\textbf{8}} $[/tex] pounds.

Step-by-step explanation:

From the figure we can see that there are three dots against [tex]$ 3 \frac{7}{8} $[/tex].

That means it becomes [tex]$ 3 \times 3\frac{7}{8} $[/tex].

Note that if there is a mixed fraction of the form [tex]$ a \frac{b}{c} $[/tex]   =   [tex]$ a + \frac{b}{c} $[/tex].

Therefore, [tex]$ 3 \times 3\frac{7}{8} = 3 \times \bigg(3 + \frac{7}{8} \bigg ) $[/tex]                ... (1)

Similarly, against 4 there are 2 dots.

So, it should be [tex]$ 4 \times 2 $[/tex] pounds.                   ...(2)

3 dots against [tex]$ 4 \frac{1}{8} $[/tex].

So, it becomes [tex]$ 3 \times \bigg(4 + \frac{1}{8} \bigg) $[/tex]                       ...(3)

Similarly, 2 dots against [tex]$ 4 + \frac{2}{8} $[/tex].

This will become [tex]$ 2 \times \bigg( 2 + \frac{2}{8} \bigg) $[/tex]                  ...(4)

Now, to calculate the total pound, we simply add (1), (2), (3) & (4).

⇒    [tex]$ 3 \times \bigg(3 + \frac{7}{8} \bigg ) $[/tex]     [tex]$ + $[/tex]      [tex]$ 4 \times 2 $[/tex]       +     [tex]$ 3 \times \bigg(4 + \frac{1}{8} \bigg) $[/tex]       [tex]$ + $[/tex]        [tex]$ 2 \times \bigg( 2 + \frac{2}{8} \bigg) $[/tex]

⇒    [tex]$ 9 + \frac{21}{8} + 8 + 12 + \frac{3}{8} + 8 + \frac{4}{8} $[/tex]

⇒    [tex]$ \bigg ( 9 + 8 + 12 + 8 \bigg) + \bigg( \frac{21 + 3 + 4}{8} \bigg ) $[/tex]

⇒ [tex]$ \textbf{37} \textbf {+} \frac{\textbf{28}}{\textbf{8}} $[/tex]  [tex]$ \textbf{=} \hspace{1mm} \textbf{37} \frac{\textbf{28}}{\textbf{8}} $[/tex] which is the required answer.

Answer:

Probability that the other side of this coin is a head = 0.5

Step-by-step explanation:

Given that there are two coins: a standard coin with head and tail and a 2 - headed coin.

When tossing a randomly chosen coin once the sample space obtained will be :

Now since we have to find the probability that the other side of this coin which is tossed is also a head which means probability of selecting a 2-headed coin.

From the above cases there are two outcomes which are in favour from total of four outcomes;

Hence, Probability that the other side of this coin is a head = [tex]\frac{1}{2}[/tex] = 0.5 .

Answer:

Step-by-step explanation:

Hypothesis testing invariably used to test a claim about a population parameter is widely used to check whether they hypothetical claim made is right.

For example, mean scores of a particular college is more than 75% is tested with hypothesis as setting null as equal to 75% and alternate >75%

Processes are done stepwise from the sample collected and conclusion made

Confidence interval on the other hand is the range of values within which the parameter is expected to lie at a certain confidence level

Estimated population parameter is provided for error known as margin of error depending upon the confidence level, and an interval is prepared which guarantees to the extent of confidence that parameters will fall within.

Hypothesis testing can be concluded with the use of confidence intervals also.

I think expanding means to remove the parentheses/brackets from a problem.

For example: Say we have the expression: 3 (4 + 5). I think expanding means to multiply 3, by every number in the parentheses. So that means:

(3 * 4) + (3 * 5) = 27.

Another way to think about it is to (if you're on paper) draw a line from 3, to all the numbers inside the parentheses. The line that connects from 3 to 4, is signaling for you to multiply 3 * 4 = 12. And the line from 3 to 5 = 3 * 5 = 15. And add them.

Final answer:

In mathematics, 'expand' refers to writing an expression in an extended form using distribution. This can result in a polynomial or an infinite series, as seen in binomial expansion or exponential arithmetic.

Explanation:

In mathematics, to expand means to increase the length of an expression by distributing multiplication over addition or subtraction. For example, expanding (a + b)(c + d) results in ac + ad + bc + bd. This does not change the value of the expression, but rather writes it in an alternative form that might be more useful for further operations, such as simplification or evaluation. Binomial expansion, specifically, refers to expressing a binomial raised to a power as a series of terms, using the binomial theorem, which can sometimes result in an infinite series or a polynomial of finite length. This expansion is applicable in situations like expanding (x + y)^n or when dealing with power series expansions of standard mathematical functions including exponential arithmetic where numbers are expressed as a product of a digit term and an exponential term such as in the notation 4.57 x 10^3.

Answer:

(A) The minimum sample size required achieve the margin of error of 0.04 is 601.

(B) The minimum sample size required achieve a margin of error of 0.02 is 2401.

Step-by-step explanation:

Let us assume that the percentage of support for the candidate, among voters in her district, is 50%.

(A)

The margin of error, MOE = 0.04.

The formula for margin of error is:

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

The critical value of z for 95% confidence interval is: [tex]z_{\alpha/2}=1.96[/tex]

Compute the minimum sample size required as follows:

[tex]MOE=z_{\alpha /2}\sqrt{\frac{p(1-p)}{n}}\\0.04=1.96\times \sqrt{\frac{0.50(1-0.50)}{n}}\\(\frac{0.04}{1.96})^{2} =\frac{0.50(1-0.50)}{n}\\n=600.25\approx 601[/tex]

Thus, the minimum sample size required achieve the margin of error of 0.04 is 601.

(B)

The margin of error, MOE = 0.02.

The formula for margin of error is:

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

The critical value of z for 95% confidence interval is: [tex]z_{\alpha/2}=1.96[/tex]

Compute the minimum sample size required as follows:

[tex]MOE=z_{\alpha /2}\sqrt{\frac{p(1-p)}{n}}\\0.02=1.96\times \sqrt{\frac{0.50(1-0.50)}{n}}\\(\frac{0.02}{1.96})^{2} =\frac{0.50(1-0.50)}{n}\\n=2401.00\approx 2401[/tex]

Thus, the minimum sample size required achieve a margin of error of 0.02 is 2401.

Answer:

The value is 2401

Step-by-step explanation:

First we need to understand what's means 7 to the 4th power, or 7^4.

7 is the power base, the power base is the number that we are going to repeat the number of times the exponent says.

4 is the exponent, which will tell us how many times to multiply 7.

So , then we would have

1)                7 x 7 x 7 x 7

2)                  49 x 7 x 7

3)                     343 x 7

4)      finally       2401

Answer:

The correct option is D i.e. Quantitative because numerical values found by either measuring or counting are used to describe the data.

Step-by-step explanation:

As the number of respondents is a numerical value and is identified by counting thus it is a quantitative variable. Also all the other options are incorrect.

A is incorrect because the reason described is not the property of  quantitative data.

B is incorrect because the data is not described in descriptive terms.

C is incorrect because the reason described in not a property of qualitative data.

The Z-score for the 75th percentile is approximately 0.675. The mean insurance cost is $1,650, and the cut off for the 75th percentile is $1,800. The standard deviation of insurance premiums in LA is about $222.22.

(a) The Z-score corresponding to the 75th percentile of the standard normal distribution is approximately 0.675. This is determined referring to standard statistical tables or calculators.

(b) The mean insurance cost is given as $1,650.

The cut off for the 75th percentile is $1,800. This is based on the given information that 25% of California residents pay more than $1,800.

(c) To determine the standard deviation, we first subtract the mean from the 75th percentile value ($1,800 - $1,650 = $150), then divide by the Z-score (150 / 0.675 = approximately $222.22). So, the standard deviation for LA auto insurance premiums is about $222.22.

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The Z-score for the 75th percentile of the standard normal distribution is approximately 0.67. The mean insurance cost is $1,650, and the cutoff for the 75th percentile is $1,800. While we can't identify the standard deviation of insurance premiums in LA without additional data, it would be theoretically possible to find it using the Z-score formula.

In response to your question, let's take it step by step:

(a): The Z-score that corresponds with the 75th percentile of the standard normal distribution is approximately 0.67. You can find this value by utilizing a look-up table (table B.1).

(b): Given in the question, the mean insurance cost for California residents is $1,650.

The 75th percentile (or cutoff) is $1,800, signifying that 25% of residents pay more than this amount.

(c): Unfortunately, the information provided in the question doesn't offer enough data to figure out the standard deviation for insurance premiums in LA directly. However, based on the details given, you can conclude that for a Z-score of 0.67, the corresponding cost is $1,800. Using the Z-score formula, (X - μ) / σ, where X is the value from the dataset, μ is the mean, and σ is the standard deviation, you could theoretically solve for σ (standard deviation) if all other values are known.

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Answer:

Mean = 5; Standard Deviation: 1.5811

Step-by-step explanation:

Given Data:

number of times coin flipped = n = 10;

probability of each side of coin = p = 0.5;

Here mean is the product of number of times coin flipped and probability of each

m = n*p =10*0.5 = 5

Standard deviation is obtained by taking square root of product of n,p,q

St. Dev= [tex]\sqrt{npq}[/tex] = [tex]\sqrt{10*0.5*0.5}[/tex] = 1.5811

We have:

           Mean = 5         ;          Standard Deviation = 1.5811

Answer:

Step-by-step explanation:

Given that special deck of cards has 20 cards. Nine are green, seven are blue, and four are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin

A) Sample space will have Green, Head,  or Green, Tail .... Red, head, red, tail

No of elements in sample space = no of colours x no of outcomes in coin toss

= 4x2 = 8

B) A= getting (RT)

P(A) = Prob of getting red card and tail on coin

= P (R) *P(T)

=[tex]\frac{4}{20} *\frac{1}{2} \\=\frac{1}{10}[/tex]

C) B be the event that a green or blue is picked, followed by landing a tail on the coin toss

B = getting green card and tail

Getting green card tail is mutally exclusive with red card and tail as there is no common element between green and blue.

D) C= red or green card is picked followed by tail.

Here A and C have a common element as getting red and tail.  So not mutually exclusive

Final answer:

The sample space of the card and coin toss experiment consists of 40 elements. The probability of picking a red card followed by a tail coin toss is 0.1. Events A and B, as well as events A and C, are not mutually exclusive.

Explanation:

Probability in a Card and Coin Toss Experiment

When dealing with a special deck of cards and a subsequent coin toss, multiple steps are involved in determining outcomes and probabilities. As for the given student's question:

A). The sample space contains multiple elements based on the card colors and the side of the coin: each of the 20 cards can result in either heads or tails, creating a total of 40 possible outcomes.

B). For event A, where a red card is picked followed by a tails on the coin toss, the probability (P(A)) is calculated by dividing the number of successful outcomes by the number of total possibilities, resulting in P(A) = 4 (red cards) * 1 (tails outcome) / 40 (total outcomes) = 0.1.

C). Event A and event B are not mutually exclusive because event B involves picking either a green or blue card and also getting tails, which does not overlap with the specifics of event A.

D). Similarly, events A and C are not mutually exclusive. Although both involve picking a red card and landing a tail, event C also includes picking a green card, which does not interfere with the occurrence of event A.

Answer:

False

Step-by-step explanation:

The likelihood of an event happening added to its compliment's likelihood must equal 1. The compliment of rolling a number less than 3 on a normal six-sided die is rolling a 3 or more on a normal six-sided die. The probability of rolling 3 or more is 4/6 or 2/3. Adding 1/3 to 2/3 gives us 1 or 100%, thus those events complement each other.

Answer: $115.5

Step-by-step explanation:

The woman bought a coat for $99.95 and some gloves for $7.95. This means that the total amount of money that the woman would have paid for the coat without tax is

99. 95 + 7.95 = $107.9

If the sales tax was 7%, then the amount paid as sales tax would be

7/100 × 107.9 = 0.07 × 107.9 = $7.553

Therefore, the amount that she would pay to purchase the coat and the gloves is

107.9 + 7.553 = 115.453

= $115.5 rounded up to the nearest cent.

The woman spent

[tex]99.95+7.95=107.9[/tex]

dollars in total. Given the 7% sales tax, it means that she actually paid 107% of this amount. So, the final price was

[tex]107.9\cdot\dfrac{107}{100}=1.079\cdot 107=115.453\approx 115.45[/tex]

dollars.

Answer:

a)  P(2)=0.270

b) P(X>3)=0.605

c)  P=0.410

Step-by-step explanation:

We know that customers arrive at a grocery store at an average of 2.1 per minute. We use the  Poisson distribution:

[tex]\boxed{P(k)=\frac{\lambda^k \cdot e^{-\lambda}}{k!}}[/tex]

a)  In this case: [tex]\lambda=2.1[/tex]

[tex]P(2)=\frac{2.1^2 \cdot e^{-2.1}}{2}\\\\P(2)=0.270[/tex]

Therefore, the probability is P(2)=0.270.

b)  In this case: [tex]\lambda=2\cdot 2.1=4.2[/tex]

[tex]P(X>3)=1-P(X\leq 3)\\\\P(X>3)=1-\sum_{x=0}^3 \frac{4.2^x \cdot e^{-4.2}}{x!}\\\\P(X>3)=1-0.395\\\\P(X>3)=0.605[/tex]

Therefore, the probability is P(X>3)=0.605.

c)  We know that two customers came in in the first minute. That is why we calculate the probability of at least 5 customers entering the other 2 minutes.

In this case: [tex]\lambda=2\cdot 2.1=4.2[/tex]

[tex]P(X\geq 5)=1-P(X<5)\\\\P(X\geq 5)=1-P(X\leq 4)\\\\P(X\geq 5)=1-\sum_{x=0}^4 \frac{4.2^x\cdot e^{-4.2}}{x!}\\\\P(X\geq 5)=1-0.590\\\\P(X\geq 5)=0.410[/tex]

Therefore, the probability is P=0.410.

Suppose X indicates the number of customers that enter a grocery store within one minute.

[tex]\to X \sim \text{Poisson}(2.1)[/tex]

X's probability mass function:

[tex]\to P(X=x)=\frac{e^{-2.1} \times 2.1^{x}}{x!} ,x =0,1,2,..[/tex]

For question 1:

The likelihood of exactly two consumers arriving in a minute:

[tex]P(X=2)=\frac{e^{-2.1} \times 2.1^{2}}{2!}= 0.270016 \approx 0.270[/tex]

For question 2:

Suppose Y represents the average group of consumers who enter a grocery shop in a two-minute period.

[tex]Y \sim \text{Poisson}(2.1\times 2) \ or\ Y \sim \text{Poisson}(4.2)[/tex]

Y's probability mass function:

[tex]P(Y = y) = \frac{e^{-4.2} \times 4.2^{y}}{y!}, y =0,1,2..[/tex]

This is possible that more than three clients will arrive within a two-minute timeframe.

[tex]= P(Y > 3) \\\\= 1 - P(Y \leq 3)\\\\=1- \Sigma^{3}_{y=0} \frac{e^{-4.2} \times 4.2^y}{y!}\\\\=1-0.395403\\\\= 0.604597\approx \ 0.605[/tex]

For question 3:

Given that exactly two customers arrive in the first minute, the likelihood of at least seven clients arriving in three minutes is  

[tex]= \text{P( at least 5 customers arrive in two minutes)} \\\\= P(Y \geq 5)\\\\= 1 - P(Y<5)\\\\=1-P(Y \leq 4)\\\\= 1 - 0.589827\\\\= 0.410173 \approx \ 0.410[/tex]

Learn more:

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Answer:

For this case is wrong use the multiplication for P(X=2):

0.42*0.42*0.58*0.58*0.58 = 0.0344

Because we don't take in count the possible nCx ways in order to have the two consumers comfortable, and we are assuming that the first two people are comfortable and the rest is not, and that's not the only possibility. The correct probability for X=2 people comfortable is given by:

[tex]P(X=2)=(5C2)(0.42)^2 (1-0.42)^{5-2}=0.344[/tex]

And as we can see the real answer is 10 times the assumed answer, for this reason is wrong the claim.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=5, p=0.42)[/tex]

The probability mass function for the Binomial distribution is given as:

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

Where (nCx) means combinatory and it's given by this formula:

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

For this case is wrong use the multiplication for P(X=2):

0.42*0.42*0.58*0.58*0.58 = 0.0344

Because we don't take in count the possible nCx ways in order to have the two consumers comfortable, and we are assuming that the first two people are comfortable and the rest is not, and that's not the only possibility. The correct probability for X=2 people comfortable is given by:

[tex]P(X=2)=(5C2)(0.42)^2 (1-0.42)^{5-2}=0.344[/tex]

And as we can see the real answer is 10 times the assumed answer, for this reason is wrong the claim.

Answer:

147000 J

Step-by-step explanation:

We are given that

Length of chain=L=50 m

Density of chain=[tex]\rho=10kg/m^3[/tex]

We have to find the work done required to wind the chain into the cylinder if a 50 kg block is attached to the end of the chain.

Work done=[tex]\int_{a}^{b}F(y)dy[/tex]

We have F(y)=[tex]\rho g(50-y)dy[/tex]

a=0 and  b=50

[tex]g=9.8m/s^2[/tex]

Using the formula

Work done=[tex]w_1=10\times 9.8\int_{0}^{50}(50-y)dy[/tex]

Where Length of chain is (50-y) has to be lifted.

Work done=[tex]w_1=10\times 9.8[50y-\frac{y^2}{2}]^{50}_{0}[/tex]

By using the formula [tex]\int x^ndx=\frac{x^{n+1}}{n+1}+C[/tex]

Work done=[tex]w_1=10\times 9.8\times (50(50)-\frac{(50)^2}{2})=98\times (2500-1250)=122500 J[/tex]

When the chain is weightless then the work done required to lift the block attached to the 50 m long chain

Again using the formula

Where f(y)=mg

[tex]w_2=\int_{0}^{50}mgdy[/tex]

We have m=50 kg

[tex]w_2=\int_{0}^{50}50\times 9.8 dy=490[y]^{50}_{0}=490\times 50=24500 J[/tex]

The work done required  to wind the chain into the cylinder if a 50 kg block is attached to the end of the chain=[tex]w_1+w_2=122500+24500=147000 J[/tex]

answer :- y = 9/2

and x = 1/2

Answer:

Step-by-step explanation:

The given system of equations is expressed as

4x + 2y = 16 - - - - - - - - - - - - -1

3x + 3y =15- - - - - - - - - - - - - -2

We would eliminate x by multiplying equation 1 by 3 and equation 2 by 4. It becomes

12x + 6y = 48 - - - - - - - - - - - -3

12x + 12y = 60 - - - - - - - - - - - -4

Subtracting equation 4 from equation 3, it becomes

- 6y = - 12

Dividing the left hand side and the right hand side of the equation by - 6, it becomes

- 6y/-6 = - 12/ - 6

y = 2

Substituting y = 2 into equation 1, it becomes

4x + 2 × 2 = 16

4x + 4 = 16

Subtracting 4 from the left hand side and the right hand side of the equation, it becomes

4x + 4 - 4 = 16 - 4

4x = 12

Dividing the left hand side and the right hand side of the equation by 4, it becomes

4x/4 = 12/4

x = 3

Answer:

$9,979,032,100 or $9.979 billion

Step-by-step explanation:

The approximate weight of a $100 bill is 1 gram.

All of the calculations bellow assume that the volume of the bills would not be an issue and only concerns weight.

1 pound is equivalent to approximately 453.59237 grams.

The weight in grams that the Big Falcon Rocket can carry is:

[tex]W= 220,000*453.59237=99,790,321.4\ g[/tex]

Since each bill weighs 1 gram, the number of bills it could carry, rounded to nearest whole bill is 99,790,321. The total amount it could carry is:

[tex]A=99,790,321*\$100=\$9,979,032,100[/tex]

Answer:

Step-by-step explanation:

The problem relates to filling 8 vacant positions by either 0 or 1

each position can be filled by 2 ways so no of permutation

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 256

b )

Probability of opening of lock in first arbitrary attempt

= 1 / 256

c ) If first fails , there are remaining 255 permutations , so

probability of opening the lock in second arbitrary attempt

= 1 / 255 .

Answer:

option 4

The value is not unusual.

Step-by-step explanation:

If the probability of revenue between $747.89 and $818.68 million is low i.e. less than 5% then we can say that it would be unusual for a randomly selected company to have a revenue between $747.89 and 818.68 million.

We are given that revenue found to follow a bell curve. Also, we are given that mean=815.425 and standard deviation=22.148.

P(747.89<x<818.68)=?

P((747.89-815.425)/22.148<z<(818.68-815.425)/22.148)=P(-3.05<z<0.15)

P(747.89<x<818.68)=0.4989+.0596=0.5585

Thus, the probability for a randomly selected company to have a revenue between $747.89 and 818.68 million is not low and so the value is not unusual.

Answer:

Work done will be equal to 5.2059 lb-ft

Step-by-step explanation:

We have given force F = 10 lb

Spring is stretched to 2 in

So x = 2 in

As 1 inch = 0.0833 feet

So 2 inch = 2×0.0833 = 0.1666 feet

From hook's law we know that F = Kx , here K is spring constant and x is spring elongation

So [tex]10=K\times 0.1666[/tex]

K = 60.024 lb/feet

Now new elongation x = 5 in

So 5 in = 5×0.0833 = 0.4165 feet

Work done is given by [tex]W=\frac{1}{2}Kx^2[/tex]

So [tex]W=\frac{1}{2}\times 60.02\times 0.4165^2=5.205lb-ft[/tex]

So work done will be equal to 5.2059 lb-ft

Answer:

Taylor = 50%

Moore = 25%

Jenkins = 25%

Step-by-step explanation:

Assuming there are no other candidates and that someone has to win the election, the probabilities of Taylor, Moore, and Jenkins winning the election must add up to 1 or 100%.

[tex]T+M+J = 1\\[/tex]

Since Moore and Jenkins have about the same probability of winning, and Taylor is believed to be twice as likely to win as either of the others:

[tex]M=J\\T=2J\\J+J+2J=1\\J=0.25\\M=J=0.25\\T=2*0.25=0.5[/tex]

Taylor has a probability of 50% of winning the election.

Moore has a probability of 25% of winning the election.

Jenkins has a probability of 25% of winning the election.

Answer:

[tex] \bar X = \frac{\sum_{i=1}^n X_i f_i}{n}= \frac{1394}{88}=15.8[/tex]

[tex] s^2 = \frac{88(32372) -(1394)^2}{88(88-1}=118.3[/tex]

[tex]Sd(X) = \sqrt{118.273}=10.9[/tex]

Step-by-step explanation:

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.  

Solution to the problem

For this case we can calculate the properties required with the following table:

Interval     Mid point (x)     f           x*f         x^2 *f

_________________________________________

1-10               5.5               40        220         1210

11-20             15.5              15        232.5       3603.75

21-30            25.5             23       586.5       14955.75

>31                35.5             10        355          12602.5

________________________________________

Total                                 88        1394         32372

We assume that the mid point for the class >31 is 35.5 using the problem information.

For this case the expected value would be given by:

[tex] \bar X = \frac{\sum_{i=1}^n X_i f_i}{n}= \frac{1394}{88}=15.8[/tex]

The variance owuld be given by this formula"

[tex] s^2 = \frac{n(\sum x^2 f) -(\sum xf)^2}{n(n-1}[/tex]

And if we replace we got:

[tex] s^2 = \frac{88(32372) -(1394)^2}{88(88-1}=118.3[/tex]

The standard deviation would be just the square root of the variance:

[tex]Sd(X) = \sqrt{118.273}=10.9[/tex]

To compute mean age, sample variance, and standard deviation, establish class midpoints, then follow steps of calculating mean, variance, and standard deviation methodologies. Utilize relevant class midpoints, frequencies and population size.

Given the prehistoric Native American family group of 88 members, we can compute the mean age, sample variance, and sample standard deviation using the group's age ranges and sizes.

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Final answer:

The correct answer is c. The three groups do not add up to 100%. A pie chart is used to display the parts of a whole, where each category represents a proportion of the total. In this case, the categories of cigarette use, smokeless tobacco use, illicit drug use, and pain reliever/sedative use do not add up to 100% when combined. As a result, a pie chart would not accurately represent the data.

Explanation:

The correct answer is c. The three groups do not add up to 100%.

A pie chart is used to display the parts of a whole, where each category represents a proportion of the total. In this case, the categories of cigarette use, smokeless tobacco use, illicit drug use, and pain reliever/sedative use do not add up to 100% when combined. As a result, a pie chart would not accurately represent the data.

Answer:

[tex]16c+15[/tex]

Step-by-step explanation:

we have the expression

[tex]10c+6c+15[/tex]

step 1

We can simplify the expression by combining like terms. That is, the terms with the same variable

[tex](10c+6c)+15[/tex]

[tex]16c+15[/tex]

Answer: 16c+15

Step-by-step explanation:

Step 1

Write down the given expression (10c+6c)+15

Step 2

10+6 = 16c

So, 16c+15

Hope this helps! (✿◡‿◡)

Answer:

a) 4.076

b) 3.9

c) variance for executives=1.128

variance for middle mangers=0.73

d)standard deviation for executives=1.062

standard deviation for middle mangers=0.854

e) Overall job satisfaction for senior executives is higher than middle manager.

Step-by-step explanation:

IS senior executives

Job Satisfaction       1    2          3       4     5

Probability          0.05 0.093 0.03 0.425 0.41

IS middle manager

Job Satisfaction  1       2    3        4    5

Probability         0.01 0.1 0.12 0.46 0.28

Let X denotes IS senior executive and Y denotes IS middle manager.

a)

E(X)=∑x*p(x)=1*0.05+2*0.093+3*0.03+4*0.425+5*0.41

E(X)=0.05+0.186+0.09+1.7+2.05

E(X)=4.076

b)

E(Y)=∑y*p(y)=1*0.1+2*0.1+3*0.12+4*0.46+5*0.28

E(Y)=0.1+0.2+0.36+1.84+1.4

E(Y)=3.9

c)

V(x)=∑x²*p(x)-(∑x*p(x))²

∑x²*p(x)=1*0.05+4*0.093+9*0.03+16*0.425+25*0.41

∑x²*p(x)=0.05+0.372+0.27+6.8+10.25

∑x²*p(x)=17.742

V(x)=17.742-(4.076)²

V(x)=1.128

V(y)=∑y²*p(y)-(∑y*p(y))²

∑y²*p(y)=1*0.1+4*0.1+9*0.12+16*0.46+25*0.28

∑y²*p(y)=0.1+0.4+1.08+7.36+7

∑y²*p(y)=15.94

V(y)=15.94-(3.9)²

V(y)=0.73

d)

S.D(x)=√V(x)

S.D(x)=√1.128

S.D(x)=1.062

S.D(y)=√V(y)

S.D(y)=0.854

e)

Overall job satisfaction for senior executives is more than middle manager as expected value of senior executives is greater than expected value of middle manger with relatively higher variability than middle manager.

[tex]\boxed{t=11.3h}[/tex]

In this problem we have the following data:

[tex]r:speed \\ \\ d:distance \\ \\ t:time \\ \\ \\ r=33.2m/h \\ \\ d=375.16m \\ \\ \\ So \ our \ goal \ is \ to \ find \ t[/tex]

Speed, time and distance are related with the following formula:

[tex]r=\frac{d}{t} \\ \\ \\ Solving \ for \ t: \\ \\ t=\frac{d}{r} \\ \\ t=\frac{375.16}{33.2} \\ \\ \boxed{t=11.3h}[/tex]

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The entries that will be interpreted as numbers are a) 1.56e-9, b) -4.99, d) 1.9435, and g) 3.25E4. Entries c), e), f), h), and i) violate the restrictions mentioned.

The entries that will be interpreted as numbers are:

Entries a), b), d), and g) are written in proper scientific notation and do not violate any of the restrictions mentioned. Entry c) violates the rule of substituting the letter O for zero or the letter l for 1. Entry e) has a space between the number and the exponent, violating the rule of not having a space in a number. Entry f) includes a dollar sign in the number, which is not allowed. Entry h) has a comma, violating the rule of not having commas in numbers. Entry i) includes the units 'inches', which is not allowed.

Final answer:

Entries 1.56[tex]e^{-9[/tex], -4.99, and 1.9435 are valid numbers that would be interpreted by WebAssign, while 3.25E4 is also correct as it is proper scientific notation. (Option a, b,d,g)

Explanation:

When entering numbers in WebAssign, it is important to use the correct format to ensure that the numbers are interpreted accurately. Here are which of the entries will be interpreted as numbers:

a) 1.56[tex]e^{-9[/tex]: This is a correct representation of a number in scientific notation.

b) -4.99: This is a valid negative number.

c) 40O0: This contains a letter and would not be interpreted as a number.

d) 1.9435: This is a simple decimal number.

e) 1.56 [tex]e^{-9[/tex]: This is not correctly formatted for scientific notation due to the space.

f) $2.59: This includes a dollar sign, which is not valid for a number entry.

g) 3.25E4: This is correctly written in scientific notation.

h) 5,000: Commas are not allowed in number entries.

i) 1.23 inches: This includes units, which should not be included in a number entry.