13. Imagine that you are taking a class and your chances of being asked a question in class are 1% during the first week of class and double each week thereafter (i.e., you would have a 2% chance in Week 2, a 4% chance in Week 3, an 8% chance in Week 4). What is the probability that you will be asked a question in class during Week 7?

Answer with explanation:

Let two uncountable sets A and B .

(a).Let A= [2,3]=uncountable

B= [3,4)=uncountable

[tex]A\cap B [/tex]={3}= finite

Hence, [tex] A\cap B [/tex] is finite set .

(b).Let A= Set of positive real  numbers=Uncountable

B= Set of   negative real numbers and positive integers= Uncountable

Now, [tex]A\cap B[/tex]=Set of positive integer numbers  =countably infinite set.

Hence, [tex]A\cap B[/tex]is countably infinite .

(c). Let A= Set of real numbers=Uncountable

B= Set of irrational numbers  =Uncountable

Then, [tex]A\cap B[/tex]= Set of irrational numbers= Uncountable.

Hence, [tex]A\cap B[/tex] is uncountable when A is set of real numbers and B is set of irrational numbers.

Real numbers A and B can be examples of the uncountable sets. By modifying these, their intersection could be finite, countably infinite, or uncountably infinite based on its definition. These sets and their intersections depict the distinct characteristics of uncountable sets.

In Mathematics, an uncountable set is a set that cannot be put into one-to-one correspondence with the set of natural numbers or integers. In other words, it has more elements than the set of natural numbers.

Since the intersection of two uncountable sets could be any size (from empty to uncountably infinite), we can creatively define the sets to meet the requirements. Consider the real numbers A = [0,1] and B = [1,2] as our uncountable sets.

For (a) finite, let's modify B and set B to only include the single element {1}, their intersection, which is finite.

For (b) countably infinite, instead B = {x in Q | 1 ≤ x ≤ 2}, where Q is the set of rational numbers. They intersect at countably infinite set of rational numbers between 1 and 2.

For (c) uncountably infinite. If both A and B are intervals on the real number line that have nonempty intersection, their intersection is uncountably infinite.

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Answer with explanation:

⇒689!=689×688×687×686×........×7×6×5×4×3×2×1

So, 689! is divisible by 7.

We have to find the remainder when,

 [tex]\frac{a}{m}=\frac{207^{321}+689!}{7}\\\\=\frac{207^{321}}{7}+\frac{689!}{7}\\\\=\frac{(210-3)^{321}}{7}+0\\\\=\frac{_{0}^{321}\textrm{C}\times (210)^{321}\times (3)^{0} -_{1}^{321}\textrm{C}\times (210)^{320}\times (3)^{1}+_{2}^{321}\textrm{C}\times (210)^{319}\times (3)^{2}-----(-1)\times _{321}^{321}\textrm{C}\times (321)^{0}\times (3)^{321}}{7}\\\\ \text{As ,210 is divisible by 7}\\\\=\frac{ (3)^{321}}{7}[/tex]

⇒[tex]3^7[/tex] ,when divided by 7, gives remainder 3.

[tex]\frac{ (3)^{321}}{7}=\frac{ (3)^{45\times 7+6}}{7}\\\\=3+\frac{3^6}{7}\\\\=3+1\\\\=4[/tex]

So,Remainder when

                    [tex]\frac{207^{321}+689!}{7}[/tex] is 4.

Answer:

[tex]2\sqrt{x}=\frac{5t^2}{2}+2[/tex]

Step-by-step explanation:

Given: [tex]\frac{\mathrm{d} x}{\mathrm{d} t}=5t\sqrt{x}\,,\, x(0)=1[/tex]

Solution:

A differential equation is said to be separable if it can be written separately as  functions of two variables.

Given equation is separable.

We can write this equation as follows:

[tex]\frac{dx}{\sqrt{x}}=5t\,dt[/tex]

On integrating both sides, we get

[tex]\int \frac{dx}{\sqrt{x}}=\int 5t\,dt[/tex]

Formulae Used:

[tex]\int \frac{1}{\sqrt{x}}=2\sqrt{x}\,\,,\,\,\int t\,dt=\frac{t^2}{2}[/tex]

So, we get solution as [tex]2\sqrt{x}=\frac{5t^2}{2}+C[/tex]

Applying condition: x(0) = 1, we get [tex]C=2[/tex]

Therefore, [tex]2\sqrt{x}=\frac{5t^2}{2}+2[/tex]

Answer:  After 3.75 seconds

Step-by-step explanation:

 For a Quadratic function in the form [tex]f(x)=ax^2+bx+c[/tex], if [tex]a<0[/tex] then the parabola opens downward.

Rewriting the given function as:

[tex]h(t) = - 16t^2+120t[/tex]

You can identify that [tex]a=-16[/tex]

Since [tex]a<0[/tex] the the parabola opens downward.

Therefore, we can conclude that the x-coordinate of the vertex is the time in seconds in which the ball will reach the maximum height. You can  find it with this formula:

[tex]t=\frac{-b}{2a}[/tex]

Substitute values, we get

[tex]t=\frac{-120}{2(-16)}=3.75\ seconds[/tex]

Final answer:

The time at which the ball reaches its maximum height is calculated using the vertex formula for a quadratic equation. In this case, the ball achieves maximum height after 3.75 seconds.

Explanation:

The function given is a quadratic equation in the form h(t) = 120t - 16t2, representing the height of a ball thrown vertically upward after t seconds. To find the time when the ball reaches its maximum height, we need to determine the vertex of the parabola represented by this equation.

The standard form of a quadratic equation is ax2 + bx + c. In this form, the time to reach the maximum height occurs at t = -b/(2a). Applying this to our equation, where a = -16 and b = 120, we calculate t = -120/(2*(-16)) = 120/32 = 3.75 seconds. Therefore, the ball reaches its maximum height after 3.75 seconds.

[tex]1\cdot2^4+1\cdot2^3+1\cdot 2^0=16+8+1=25[/tex]

[tex]11001_2=25_{10}[/tex]

Final answer:

To convert (11001)_2 to decimal, multiply each binary digit by the corresponding power of 2 based on its position, starting from the right. Add the products to get the decimal value, which in this case is 25.

Explanation:

To convert the binary number (11001)_2 to its decimal equivalent, you must understand that each digit represents a power of 2, starting from the rightmost digit which is the least significant bit (LSB). The leftmost digit is the most significant bit (MSB). Now, let's convert (11001)_2 to decimal:

The rightmost digit (1) is in the 20 place, so it is worth 1*20 = 1.

The next digit to the left (0) is in the 21 place, so it is worth 0*21 = 0.

Continuing to the left, the next digit (0) is in the 22 place, so it's worth 0*22 = 0.

The next digit (1) is in the 23 place, so it's worth 1*23 = 8.

Finally, the leftmost digit (1) is in the 24 place, so it's worth 1*24 = 16.

Add up all the values: 16+0+0+8+1 = 25. So, the decimal expansion of (11001)_2 is 25.

Answer:

20212

Step-by-step explanation:

Divide 185 by [tex]3^4[/tex] as [tex]3^4[/tex] is closest to 185

After dividing we get remainder 23 and quotient 2

Divide the remainder 23 by [tex]3^3[/tex] we get remainder 23 and quotient 0

Divide the remainder  23 by [tex]3^2[/tex] we get remainder 5 and quotient 2

Divide the remainder 5 by [tex]3^1[/tex] we get remainder 2 and quotient 1

Divide the remainder 2 by [tex]3^0[/tex] we get remainder 0 and quotient 2

Taking all the quotient values we get 20212

Hence, 185₁₀=20212₃

The chance you don't get an apple is:

                     [tex]\dfrac{38}{44}[/tex]

We know that the probability of an outcome is the chance of getting an outcome and it is calculated by:

Taking the  ratio of number of favorable outcomes to total number of outcomes.

A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangoes.

Total number of fruits in the refrigerator i.e. total number of outcomes are: 6+5+10+3+7+11+2

                                                                      = 44

Also the number of favorable outcomes i.e. number of fruits which are not apples in the refrigerator are: 44-6=38

This means that the probability of not getting an apple is:

[tex]\text{Probability(not\ getting\ an\ apple)}=\dfrac{38}{44}[/tex]

Final answer:

The chance you do not get an apple is38/44, or roughly86.36.

Explanation:

The chance you do not get an apple is38/44.

To calculate this, add up the total number of fruits in the refrigerator banning apples, which is 5 oranges 10 bananas 3 pears 7 peaches 11 catches 2 mangos = 38 fruits. The total number of fruits in the refrigerator is 6 apples 5 oranges 10 bananas 3 pears 7 peaches 11 catches 2 mangos = 44 fruits.

simplifies to19/22 or roughly0.8636, so the chance you do not get an apple is0.8636 or86.36.

Answer:

520 girls attended the picnic

Step-by-step explanation:

Hello

step 1

Let

Homewood middle school total students=1200

A=unknown=total of girls

(2/3)A=total girls attended the picnic

B=unknown= total of boys

(1/2)B=total boys attended the picnic

step2

replace

[tex]A+B=1200\ equation (1) \\\frac{2A}{3}+\frac{B}{2}=730\ equation(2)\\[/tex]

Step 3

find A and B

from equation (1)

[tex]A=1200-B\ equation\ (3)\\\\[/tex]

from equation (2)

[tex]\frac{2A}{3}+\frac{B}{2}=730\\\frac{2A}{3}=730-\frac{B}{2}\\A=(730-\frac{B}{2})*\frac{3}{2} \\1200-B=1095-\frac{3B}{4}\\A=A\\-B+\frac{3B}{4}=1095-1200\\-\frac{B}{4}=-105\\ B=420\\\\hence\\\\A=1200-B\\A=1200-420\\A=780[/tex]

total girls attended  the picnic=(2/3)A=(2/3)780=520

520 girls attended the picnic

Answer:

520

Step-by-step explanation:

i also got the problem and got it wrong - i found the answer is 520

Answer: (0.066,0.116)

Step-by-step explanation:

The confidence interval for proportion is given by :-

[tex]p_1-p_2\pm z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}[/tex]

Given : The proportion of men have red/green color blindness = [tex]p_1=\dfrac{89}{950}\approx0.094[/tex]

The proportion of women have red/green color blindness = [tex]p_2=\dfrac{6}{2050}\approx0.003[/tex]

Significance level : [tex]\alpha=1-0.99=0.01[/tex]

Critical value : [tex]z_{\alpha/2}=z_{0.005}=\pm2.576[/tex]

Now, the 99% confidence interval for the difference between the color blindness rates of men and women will be:-

[tex](0.094-0.003)\pm (2.576)\sqrt{\dfrac{0.094(1-0.094)}{950}+\dfrac{0.003(1-0.003)}{2050}}\approx0.091\pm 0.025\\\\=(0.09-0.025,0.09+0.025)=(0.066,\ 0.116)[/tex]

Hence, the 99% confidence interval for the difference between the color blindness rates of men and women= (0.066,0.116)

Answer:

probability  is 0.778

Step-by-step explanation:

Given data in question

success of probability (p) = 41% = 0.41

no of sample (n)  = 400

individual = 150

to find out

probability that the sample proportion will be at least 135/400

solution

first we calculate the mean i.e

mean = p × n

mean = 400 × 0.41

mean = 164

now we calculate standard deviation = [tex]\sqrt{400(0.41) 0.59}[/tex]

standard deviation =  9.83666

we know P(X ≥ 135) = P(Z ≥ (150 - 164)/9.83666)

P(X ≥ 135) = P(Z ≥ (-1.42324)

from table 1 find corresponding probability

P(X ≥ 135) = 1 - P(Z ≥ (-1.42324)

= 1 - 0.9222 = 0.778

probability  is 0.778

Final answer:

Using the least squares line equation given, by substituting 844 for the number of reported dead birds, we calculate an expected number of approximately 31 human cases of West Nile virus.

Explanation:

To estimate the number of human cases of West Nile virus based on the number of reported dead birds using the least squares line equation ŷ = −10.2638 + 0.0491x, we need to substitute x with the number of reported dead birds. In this case, x = 844.

The calculation would be:
ŷ = −10.2638 + (0.0491 × 844)

This simplifies to:
ŷ = −10.2638 + 41.4474

Which further simplifies to:
ŷ = 31.1836

After rounding the result to the nearest whole number, we get that approximately 31 human cases of West Nile virus can be expected.

The expected number of human cases of West Nile virus when 844 dead birds are reported is approximately 31, calculated using the given least squares line equation.

To predict the number of human West Nile virus cases when 844 dead birds are reported, we use the least squares line equation:

Here, x represents the number of dead birds, which is 844.

Y = -10.2638 + 0.0491 * 844

0.0491 * 844 = 41.4404

Y = -10.2638 + 41.4404

Y = 31.1766

Rounding to the nearest whole number, the expected number of human cases of West Nile virus is 31.

Answer:

0.75

Step-by-step explanation:

We have been given that 400  people were asked whether gun laws should be more stringent. 300 hundred said "yes," and 100 said "no".

To find the point estimate of the proportion in the population who will respond "yes", we need to divide number of people who said yes by total number of people that is 300 by 400.

[tex]\text{People who will respond yes}=\frac{300}{400}[/tex]

[tex]\text{People who will respond yes}=\frac{3}{4}[/tex]

[tex]\text{People who will respond yes}=0.75[/tex]

Therefore, the  point estimate of the proportion in the population who will respond "yes" is 0.75.

Answer:

(-2,2)

Step-by-step explanation:

Let's find the answer.

Because a tangent line for a parabola function is equal to 0 only at its vertex then:

[tex]f(x)=(x+2)^{2}+2[/tex]

[tex]f'(x)=2*(x+2)[/tex]

[tex]f'(x)=2x+4[/tex] so then:

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

[tex]0=2x+4[/tex]

[tex]-2=x[/tex]

For x=-2 f(x) is:

[tex]f(x)=(x+2)^{2}+2[/tex]

[tex]f(1)=(-2+2)^{2}+2[/tex]

[tex]f(x)=2[/tex]

In conclusion, the vertex of the given parabola is (-2,2), so the answer is C. Although in your answer is reported as (-2.2) but I think was a typing mistake.

The confidence interval is [tex]\fbox{(5.8, 8.1)}[/tex] and [tex]\fbox{\text{Option A}}[/tex] is correct.

Further Explanation:

Given:

The least value is [tex]1[/tex] that is the least attractive.

The highest value is [tex]10[/tex] that is the most attractive.

The observations are,

7, 7, 3, 8, 5, 6, 6, 9, 9, 8, 6, 9.

Calculation:

The sum of all observations is [tex]83[/tex].

The population mean is [tex]\mu[/tex].

The standard deviation [tex]s[/tex] is [tex]1.832[/tex].

The sample mean [tex]\bar^{X}[/tex] is [tex]6.92[/tex].

Level of significance [tex]\alpha[/tex] =  [tex]5\%[/tex].

Formula for confidence interval = [tex]\left( \bar{X} \pm t_{n-1, \frac{\alpha}{2}\%} \frac{s}{\sqrt{n}} \right)[/tex]

Confidence interval =[tex]\left( 6.92 \pm t_{12-1, \frac{5}{2}\%} \frac{1.832}{\sqrt{12}} \right)[/tex]

The value of [tex]t_{11, \frac{5}{2}\%[/tex]=[tex]2.201[/tex]

Confidence interval = [tex]( 6.92 \pm 2.201}\times \frac{1.832}{\sqrt{12}}) \right)[/tex]

Confidence interval = [tex]( 6.92 - 2.201}\times 0.5288 ,6.92 + 2.201}\times \0.5288) \right)[/tex]

Confidence interval = [tex](6.92-1.1639,6.92+1.1639)[/tex]

Confidence interval = [tex]\fbox{(5.8, 8.1)}[/tex]

The [tex]95\%[/tex] confidence interval gives us an idea that [tex]95\%[/tex] chances of the true mean or population mean lies in the interval.

A. We are [tex]95\%[/tex] confident that the interval from [tex]5.8[/tex] to [tex]8.1[/tex] actually contains the true mean of attractiveness rating of all adult females.

B. The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of the population of all adult females.

C. We are confident that [tex]95\%[/tex] of all adult females have attractiveness ratings between [tex]5.8[/tex] and [tex]8.1[/tex].

[tex]\fbox{\text{Option A}}[/tex] is Correct as we are [tex]95\%[/tex] confident that the interval from [tex]5.8[/tex] to [tex]8.1[/tex] actually contains the true mean of attractiveness rating of all adult females.

Option B is not correct as the confidence interval tells us about the population mean.

Option C is not correct as the individual rating can be more than [tex]5.8[/tex] or less than the [tex]8.1[/tex].

Learn More:

1. Learn more about collinear https://brainly.com/question/5795008

2. Learn more about binomial term https://brainly.com/question/1394854

Answer Details:

Grade: College Statistics

Subject: Mathematics

Chapter: Confidence Interval

Keywords:

Probability, Statistics, Speed dating, Females rating, Confidence interval, t-test, Level of significance , Normal distribution, Central Limit Theorem, t-table, Population mean, Sample mean, Standard deviation, Symmetric, Variance.

The confidence interval for the population mean attractiveness rating of all adult females is 5.8 to 8.1, and we are 95% confident that this interval contains the true mean attractiveness rating.

In this study of speed dating, male subjects were asked to rate the attractiveness of their female dates on a scale from 1 (not attractive) to 10 (extremely attractive). A sample of attractiveness ratings was provided: 7, 7, 3, 8, 5, 6, 6, 9, 9, 8, 6, 9. The objective is to construct a confidence interval with a 95% confidence level to estimate the true mean attractiveness rating of all adult females.

The calculated confidence interval is 5.8 to 8.1. This means that we are 95% confident that the interval from 5.8 to 8.1 contains the true mean attractiveness rating of all adult females. The margin of error, represented by the range of the interval, provides a level of precision in our estimation.

The confidence interval suggests that the true mean attractiveness rating for all adult females falls within the specified range. It does not provide an exact value for the mean, but it indicates a plausible interval within which the true mean is likely to be found. Additionally, the confidence interval does not imply a causal relationship, but rather a statistical estimate based on the observed sample.

Answer:

The company needs to sell 9000 units in order to turn a profit of $40,000

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

From the question we can get some important hints before creating our formula. First the Selling Price will be profit so it will be a positive number, but both unit cost and fixed costs are losses so they will be negative values in our formula. Also our formula will depend on the amount sold which we can represent as the variable x. With these hints we can create our formula as the following

[tex](60x-20x)-400,000 = y[/tex]

Where:

Now that we have our formula the question asks how many units need to be sold in order to earn a profit of $40,000. We can calculate this by replacing the $40,000 with y and solving for x like so,

[tex](60x-20x)-400,000 = 40,000[/tex] .... add 400,000 on both sides

[tex]40x= 360,000[/tex] ... divide both sides by 40

[tex]x= 9000[/tex]

The company needs to sell 9000 units in order to turn a profit of $40,000

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Answer:

D. x=7√3 , y=4√2

Step-by-step explanation:

Step 1: Lets assume an imaginary line from A to B to make the triangle ABC( (refer to the attached image).

AB = 4

BD = 3

Step 2: Find the value of y by the sin formula.

opposite = 4

adjacent = BC

hypotenuse = AC

sin (angle) = opposite/hypotenuse

sin (45) = 4/AC

√2/2 = 4/AC

AC = y = 4√2

Step 3: Find the value of x

Tan (45) = opposite/adjacent

1 = 4/CB

CB = 4

x = CB + BD

x = 4 + 3

x = 7

Therefore, the answer is D where x = 7 and y = 4√2

!!

Answer:

The correct option is A.

Step-by-step explanation:

It is given that the probability of exactly 44 green marbles.

We need to use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability.

A continuity correction is an adjustment that is made when a discrete distribution is approximated by a continuous distribution.

For example: In discrete x=7, then in continuous 6.5<x<7.5. It means we need to subtract 0.5 in the number to find the lower limit and we need to add 0.5 in the given number to find the upper limit.

Similarly,

In discrete x=44, then in continuous

44-0.5<x<44+0.5

43.5<x<44.5

The area between 43.5 and 44.5. Therefore the correct option is A.

Answer: 0.375

Step-by-step explanation:

The given interval : (0,6)  [in minutes]

Let X represents the waiting time of a passenger.

We know that the cumulative uniform distribution function for interval (a,b) is given by :_

[tex]F(x)=\begin{cases}0,&\text{ for } x<a\\\frac{x-a}{b-a},& \text{for } a\leq x\leq 1\\1,& \text{for }x>b\end{cases}[/tex]

Then , the  probability that a randomly selected passenger has a waiting time greater than 2.25 minutes. is given by :_

[tex]P(2.25<x)=\dfrac{2.25-0}{6-0}=0.375[/tex]

Hence, the required probability : 0.375

Answer:

Step-by-step explanation:

the answer is 0.625 reason is the probability is 62.5% and when you take

(6-2.25)/(6-0)

= (3.75)/(6)

=0.625

Answer:

postpositivist

Step-by-step explanation:

Of the all four options "post positivist" philosophical assumption are reflected in quantitative research designs

"post positivist" believes that, theory, hypothesis, background knowledge,believes and values of researchers can alter the actual observations. Post positivist consider both quantitative and qualitative methods to be a valid form of approaches unlike "positivist" which emphasize only on quantitative methods.

The philosophical assumption reflected in quantitative research designs is postpositivist. Postpositivism believes in the existence of an objective reality that can be studied through empirical observation and measurement.

The philosophical assumption reflected in quantitative research designs is postpositivist. Postpositivism is a philosophical stance that believes in the existence of an objective reality that can be studied through empirical observation and measurement. Quantitative research designs aim to gather numerical data that can be analyzed statistically to uncover patterns and relationships in the data. A postpositivist approach to research values objectivity, generalizability, and the use of rigorous methodologies.

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Answer:

p(A and B) =0.1316

Step-by-step explanation:

We know that [tex]p(B|A)=\frac{p(A\cap B)}{p(A)}\\\\p(B\cap A )=p(B|A)\times p(A)[/tex]

Applying values we get

[tex]p(A and B)=0.47\times 0.28\\\\p(AandB)=0.1316[/tex]

Answer with explanation:

The Fibonacci series is as follows:and it's first ten entries are

0,1,1,2,3,5,8,13,21,34,.....

You can see that after first two terms, each term that is from third term,sum of previous two consecutive terms.

1→1

2→0

3→1=1+0

4→2=1+1

5→3=2+1

6→5=3+2

7→8=5+3

8→13=5+8

9→21=13+8

10→34=21+13

[tex]\rightarrow f_{11}=f_{10}+f_{9}\\\\=34+21\\\\f_{11}=55\\\\\rightarrow f_{12}=f_{11}+f_{10}\\\\=55+34\\\\f_{12}=89\\\\\rightarrow f_{13}=f_{12}+f_{11}\\\\=89+55\\\\f_{13}=144\\\\\rightarrow f_{ia}=f_{i(a-1)}+f_{i(a-2)}[/tex]

Answer: Population mean = [tex]\mu=5.5[/tex]

Sample mean = [tex]\overline{x}=6.25[/tex]

Step-by-step explanation:

We know that the population mean [tex]\mu[/tex] is the average of the entire population.

The sample mean [tex]\overline{x}[/tex] is the mean of the sample which is derived from the whole population randomly.

Given : A recent article in a college newspaper stated that college students get an average of 5.5 hrs of sleep each night.

Thus , the population mean = 5.5 hrs

Also, On average, the sampled students slept 6.25 hours per night.

It implies , the sample mean =  6.25 hours

Final answer:

The sample mean is 6.25 hours of sleep per night from the student's survey of 25 students, while the claimed population mean is 5.5 hours as stated in the college newspaper article.

Explanation:

In this scenario, the sample mean is the average amount of sleep that the 25 randomly sampled students reported, which is 6.25 hours per night.

The claimed population mean is the value mentioned in the college newspaper article, stating that college students get an average of 5.5 hours of sleep each night.

The sample mean represents the average found from the sample taken by the student, while the claimed population mean represents the average that is supposedly true for the entire population of college students.

Answer:

  no

Step-by-step explanation:

The total number of coins in all sets is 21, an odd number. In order for there to be equal numbers in all sets, the total number of coins must be even. Each step adds an even number of coins, so there is no number of steps that will add an odd number of coins to make the total be even.

Answer:

first trip 20 mph, trip back 35 mph, distance = 70 miles.

Step-by-step explanation:

A round trip takes 3.5 hours going one way and 2 hour to return.

Let the speed of first trip = v mph

Given that the trip back is at a speed 15 mph faster than the speed of first trip.

Therefore, the speed of trip back  =  ( v+15 ) mph

Let the Distance between places = d miles

Now we use the formula

[tex]Time=\frac{Distance}{Velocity}[/tex]

[tex]\frac{Distance}{Velocity}[/tex] = 3.5

and [tex]\frac{D}{V+15}[/tex] = 2

dividing these two

[tex]\frac{v+15}{v}[/tex] = [tex]\frac{3.5}{2}[/tex]

2v + 30 = 3.5v

v = 20 mph

d = 3.5 × 20 = 70 miles

The speed of the first trip is 20 mph and the speed of trip back (20+15) 35 mph. and the distance is 70 miles.

The probability that the time between two unplanned shutdowns of a power plant is between 18 and 24 days, following an exponential distribution with a mean of 30 days, is approximately 0.0033.

For an exponential distribution, the probability density function (PDF) is given by:

[tex]\[ f(x) = \lambda e^{-\lambda x} \][/tex]

where [tex]\( \lambda \)[/tex] is the rate parameter, and for an exponential distribution, [tex]\( \lambda = \frac{1}{\text{mean}} \)[/tex].

Given a mean of 30 days, [tex]\( \lambda = \frac{1}{30} \)[/tex].

Now, to find the probability that the time between two unplanned shutdowns is between 18 and 24 days, integrate the PDF over this interval:

[tex]\[ P(18 < X < 24) = \int_{18}^{24} \lambda e^{-\lambda x} \, dx \]\[ P(18 < X < 24) = \int_{18}^{24} \frac{1}{30} e^{-\frac{x}{30}} \, dx \][/tex]

Let's complete the calculations step by step.

[tex]\[ P(18 < X < 24) = \int_{18}^{24} \frac{1}{30} e^{-\frac{x}{30}} \, dx \]\[ P(18 < X < 24) = -\frac{1}{30}e^{-\frac{x}{30}} \Big|_{18}^{24} \][/tex]

Now, evaluate the integral at the upper and lower limits:

[tex]\[ P(18 < X < 24) = -\frac{1}{30} \left(e^{-\frac{24}{30}} - e^{-\frac{18}{30}}\right) \]\[ P(18 < X < 24) = -\frac{1}{30} \left(e^{-0.8} - e^{-0.6}\right) \][/tex]

Using a calculator:

[tex]\[ P(18 < X < 24) \approx -\frac{1}{30} \left(0.44933 - 0.54881\right) \]\[ P(18 < X < 24) \approx -\frac{1}{30} \times (-0.09948) \]\[ P(18 < X < 24) \approx 0.003316 \][/tex]

Therefore, the probability that the time between two unplanned shutdowns is between 18 and 24 days is approximately 0.0033 (rounded to four decimal places).

Answer:

The correct option is 2.

Step-by-step explanation:

According to the the center-of-gravity technique, the coordinates of the center-of-gravity location are

[tex](\frac{\sum x_iL_i}{\sum L_i},\frac{\sum y_iL_i}{\sum L_i})[/tex]

Where ([tex](x_i,y_i)[/tex] represent the coordinates and [tex]L_i[/tex] is demand.

We have to find the Y-coordinate of the center-of-gravity location.

The sum of product of demand and corresponding y coordinates is

[tex]\sum y_iL_i=65\times 2200+55\times 900+95\times 1300+200\times 1750+175\times 3100=1208500[/tex]

The sum of demanded units is

[tex]\sum L_i=2200+900+1300+1750+3100=9250[/tex]

The Y-coordinate of the center-of-gravity location is

[tex]y_0=\frac{\sum y_iL_i}{\sum L_i}[/tex]

[tex]y_0=\frac{1208500}{9250}[/tex]

[tex]y_0=130.6486[/tex]

[tex]y_0\approx 131[/tex]

The Y-coordinate of the center-of-gravity location is 131. Therefore the correct option is 2.

The center-of-gravity Y-coordinate is calculated by summing the product of the Y-coordinates and their respective demands, then dividing by the sum of all demands. The Y-coordinate of the center-of-gravity location is approximately 131 miles.

The center-of-gravity location is calculated by using a specific formula: (Sum of (Demand * Y-coordinate) /Sum of Demand). Let's use the Y-coordinates given and their corresponding demands.

It would look like this:
((2200*65) + (900*55) + (1300*95) + (1750*200) + (3100*175)) / (2200+900+1300+1750+3100)

Do the math to find out the Y-coordinate:
143,000 + 49,500 + 123,500 + 350,000 + 542,500 = 1,208,500
2200+900+1300+1750+3100 = 9250
1,208,500/9250 = 130.59
So the Y-coordinate of the center-of-gravity location is approximately 131 miles.

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The 99% confidence interval for the proportion of returned surveys is between 35.378% and 40.4213%, based on 931 responses from 2455 surveyed subjects.

To construct a 99% confidence interval for the proportion of returned surveys, we will use the formula for a proportion confidence interval which includes the sample proportion (π), the z-value that corresponds to the desired level of confidence, and the standard error of the proportion.

The sample proportion (π) can be calculated as the number of returned surveys divided by the total number of surveys sent:

π = 931 / 2455 = 0.379

The z-value for a 99% confidence interval is approximately 2.576. The standard error (SE) of π is calculated using the formula:

SE = √(π(1 - π) / n)

SE = √(0.379(1-0.379)/2455)

SE = √(0.379 * 0.621 / 2455)

SE = √(0.2353 / 2455)

SE = √(0.0000958)

SE = 0.009788

Now, we can calculate the margin of error (ME):

ME = z * SE

ME = 2.576 * 0.009788

ME = 0.025213

Finally, the 99% confidence interval (CI) is calculated as:

CI = π ± ME

CI = 0.379 ± 0.025213

CI = [0.353787, 0.404213]

We can be 99% confident that the true proportion of returned surveys falls between 35.378% and 40.4213%.

Answer and Step-by-step explanation:

Since we have given that

AB = 0

where A and B are n  x n matrices.

Consider determinant on both sides,

[tex]\mid AB\mid=\mid 0\mid\\\\\mid A\mid \mid B\mid =0\\\\either\ \mid A\mid =0\ or\ \mid B\mid =0[/tex]

since A is invertible, then |A| ≠ 0

so, it means |B| = 0.

Hence, B is not invertible.

Hence proved.

Answer:

  C.  Hyperbola opening up and down

Step-by-step explanation:

A graph tells the tale.

___

The term with the positive coefficient identifies the axis along which the hyperbola opens. Here, that is the y-axis, so the figure opens up and down.

The minus sign between the squared terms indicates it is a hyperbola, rather than a closed curve (ellipse or circle). The fact that both terms are squared indicates it is not a parabola.

Answer: The probability that the racket is wood or defective is 0.6.

Step-by-step explanation:

Since we have given that

Number of wood tennis rackets = 100

Number of graphite tennis rackets = 100

Total number of rackets = 200

Number of wood are defective = 12

Number of graphite are defective = 20

Total number of defectives = 32

We need to find the probability that the racket is wood or defective.

Let A be the event of wood tennis rackets.

Let B be the event of defective.

So, it becomes,

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\P(A\cup B)=\dfrac{100}{200}+\dfrac{32}{200}-\dfrac{12}{200}\\\\P(A\cup B)=\dfrac{100+32-12}{200}=\dfrac{120}{200}=0.6[/tex]

Hence, the probability that the racket is wood or defective is 0.6.