A bag contains 20 marbles. These marbles are identical, except they are labeled with the integers 1 through 20. Five marbles are drawn at random from the bag. There are a few ways to think about this.

a. Marbles are drawn one at a time without replacement. Once a marble is drawn, it is not replaced in the bag. We consider all the lists of marbles we might create. (In this case, picking marbles 1, 2, 3, 4, 5 in that order is different from picking marbles 5, 4, 3, 2, 1.)
b. Marbles are drawn all at once without replacement. Five marbles are snatched up at once. (In this case, picking marbles 1, 2, 3, 4, 5 and picking marbles 5, 4, 3, 2, 1 are considered the same outcome.)
c. Marbles are drawn one at a time with replacement. Once a marble is drawn, it is tossed back into the bag (where it is hopelessly mixed up with the marbles still in the bag). Then the next marble is drawn, tossed back in, and so on. (In this case, picking 1, 1, 2, 3, 5 and picking 1, 2, 1, 3, 5 are different outcomes.)

Required:
For each of these interpretations, describe the sample space that models these experiments.

Answer:

95% confidence interval for the population variance of the number of tissues per box is [5043.11 , 23401.31].

Step-by-step explanation:

We are given that a consumer magazine counts the number of tissues per box in a random sample of 15 boxes of No- Rasp facial tissues. The sample standard deviation of the number of tissues per box is 97.

Firstly, the pivotal quantity for 95% confidence interval for the population variance is given by;

                         P.Q. = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex]  ~ [tex]\chi^{2}__n_-_1[/tex]

where, [tex]s^{2}[/tex]  = sample variance = [tex]97^{2}[/tex] = 9409

              n = sample of boxes = 15

           [tex]\sigma^{2}[/tex]  = population variance

Here for constructing 95% confidence interval we have used chi-square test statistics.

So, 95% confidence interval for the population variance, [tex]\sigma^{2}[/tex] is ;

P(5.629 < [tex]\chi^{2}__1_4[/tex] < 26.12) = 0.95  {As the critical value of chi-square at 14

                                         degree of freedom are 5.629 & 26.12}  

P(5.629 < [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] < 26.12) = 0.95

P( [tex]\frac{5.629 }{(n-1)s^{2} }[/tex] < [tex]\frac{1}{\sigma^{2} }[/tex] < [tex]\frac{26.12 }{(n-1)s^{2} }[/tex] ) = 0.95

P( [tex]\frac{(n-1)s^{2} }{26.12 }[/tex] < [tex]\sigma^{2}[/tex] < [tex]\frac{(n-1)s^{2} }{5.629 }[/tex] ) = 0.95

95% confidence interval for [tex]\sigma^{2}[/tex] = [ [tex]\frac{(n-1)s^{2} }{26.12 }[/tex] , [tex]\frac{(n-1)s^{2} }{5.629 }[/tex] ]

                                                  = [ [tex]\frac{14 \times 9409 }{26.12 }[/tex] , [tex]\frac{14 \times 9409 }{5.629 }[/tex] ]

                                                  = [5043.11 , 23401.31]

Therefore, 95% confidence interval for the population variance of the number of tissues per box is [5043.11 , 23401.31].

Answer:

Step-by-step explanation:

The correct answer is (B).

Let X = the number of people that are displeased in a random sample of 25 people selected from a population of which 4.5% will be displeased regardless of the situation. Then X is a binomial random variable with n = 25 and p = 0.045.

P(X ≥ 2) = 1 – P(X ≤ 1) = 1 – binomcdf(n: 25, p: 0.045, x-value: 1) = 0.311.

P(X ≥ 2) = 1 – [P(X = 0) + P(X = 1)] = 1 – 0C25(0.045)0(1 – 0.045)25 – 25C1(0.045)1(1 – 0.045)24 = 0.311.

The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

This problem can be solved using the binomial distribution since we have a fixed number of trials (selecting 25 people) and each trial has two possible outcomes (displeased or not displeased).

Let p be the probability of an individual being displeased, which is given as 0.045 (or 4.5% as a decimal).

Then, the probability of an individual not being displeased is:

1 - p = 0.955.

Let X be the number of displeased people in a random sample of 25.

We want to find the probability that at least two people are displeased, which can be expressed as:

P(X ≥ 2) = 1 - P(X < 2)

To calculate P(X < 2), we can use the binomial distribution formula:

[tex]P(X = k) = (^n C_k) \times p^k \times (1 - p)^{n-k}[/tex]

where n is the sample size (25), k is the number of displeased people, and (n choose k) is the binomial coefficient which represents the number of ways to choose k items from a set of n items.

For k = 0, we have:

[tex]P(X = 0) = (^{25}C_ 0) \times 0.045^0 \times 0.955^{25}[/tex]

≈ 0.378

For k = 1, we have:

[tex]P(X = 1) = (^{25}C_1) \times 0.045^1 \times 0.955^{24}[/tex]

≈ 0.42

Therefore,

P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.798.

Finally, we can calculate,

P(X ≥ 2) = 1 - P(X < 2)

= 1 - 0.798

= 0.202.

Thus,

The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.

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2/3 of 1 is simply 2/3 or 0.667

Answer:

The answer is C (3.5)(0.25)

Step-by-step explanation:

Because to find the area of a rectangle you multiply the base times the height . The formula looks like this.

A=bh

Answer:

Answer Is (3.5)(0.25)

Step-by-step explanation:

Because You'll Need To Multiply The Length,3.5,And The Width,0.25, To Find The Area Of This Rectangle.

Answer:

It will take 34.79 years before the solar panel is only able to produce 300 watts of power

Step-by-step explanation:

The equation for the amount of electricity that a solar panel is capable has the following format:

[tex]Q(t) = Q(0)e^{-kt}[/tex]

In which Q(t) is the amount after t years, Q(0) is the initial amount and k is the exponential decay constant.

After ten years, a solar panel produces 89% of the electricity that it was able to produce when it was brand new.

This means that [tex]Q(10) = 0.89Q(0)[/tex]. So

[tex]Q(t) = Q(0)e^{-kt}[/tex]

[tex]0.89Q(0) = Q(0)e^{-10k}[/tex]

[tex]e^{-10k} = 0.89[/tex]

[tex]\ln{e^{-10k}} = \ln{0.89}[/tex]

[tex]-10k = \ln{0.89}[/tex]

[tex]10k = -\ln{0.89}[/tex]

[tex]k = \frac{-\ln{0.89}}{10}[/tex]

[tex]k = 0.01165[/tex]

So

[tex]Q(t) = Q(0)e^{-0.01165t}[/tex]

Initially capable of producing 450 watts of power

This means that [tex]Q(0) = 450[/tex]

How long will it take before the solar panel is only able to produce 300 watts of power?

This is t for which Q(t) = 300. So

[tex]Q(t) = 450e^{-0.01165t}[/tex]

[tex]450 = 300e^{-0.01165t}[/tex]

[tex]e^{-0.01165t} = \frac{300}{450}[/tex]

[tex]\ln{e^{-0.01165t}} = \ln{\frac{300}{450}}[/tex]

[tex]-0.01165t = \ln{\frac{300}{450}}[/tex]

[tex]0.01165t = -\ln{\frac{300}{450}}[/tex]

[tex]t = -\frac{\ln{\frac{300}{450}}}{0.01165}[/tex]

[tex]t = 34.79[/tex]

It will take 34.79 years before the solar panel is only able to produce 300 watts of power

The decay constant 'k' for the solar panel's power production can be calculated using the formula for exponential decay, and turns out to be approximately -0.0116. Using this decay constant, it would take approximately 19.5 years for the solar panel to only produce 300 watts of power.

The subject of your question involves an understanding of exponential decay in the context of the power production of a solar panel. The decay is represented by the mathematical formula N=N0exp-kt, where N0 is the initial quantity of the substance, N is the quantity of the substance after time t, k is the decay constant, and e is Euler's number, a mathematical constant approximately equal to 2.71828.

In the scenario you've presented in your question, we know that the solar panel is producing 89% of its original power after 10 years. This can be expressed in our formula as: 0.89 = exp-10k. Solving this equation for k, we'll find that k is approximately equal to -0.0116.

To determine the duration before the solar panel's power production drops to 300 watts, we'll use the same formula, setting N0 at 450 watts and N at 300 watts. Therefore, the equation will be: 300 = 450 * exp-0.0116t. Solving this equation, you'll find that it will take approximately 19.5 years for the solar panel to only produce 300 watts of power.

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Answer:

  $500

Step-by-step explanation:

The amount of interest in one year is the product of the interest rate and the account balance:

  I = Prt = $10,000×0.05×1 = $500 . . . . . . interest earned in 1 year

Answer:

[tex]t=\frac{115.72-120}{\frac{57.49}{\sqrt{35}}}=-0.440[/tex]    

[tex]df=n-1=35-1=34[/tex]  

Since is a one side test the p value would be:  

[tex]p_v =P(t_{(34)}<-0.440)=0.3314[/tex]  

Step-by-step explanation:

Data given and notation  

[tex]\bar X=115.72[/tex] represent the sample mean

[tex]s=57.49[/tex] represent the sample standard deviation

[tex]n=35[/tex] sample size  

[tex]\mu_o =120[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is less than the historical value, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 120[/tex]  

Alternative hypothesis:[tex]\mu < 120[/tex]  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{115.72-120}{\frac{57.49}{\sqrt{35}}}=-0.440[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=35-1=34[/tex]  

Since is a one side test the p value would be:  

[tex]p_v =P(t_{(34)}<-0.440)=0.3314[/tex]  

Answer: -8 is greater than -10

Step-by-step explanation: When in the negatives, the smaller the number, the greater it is

Answer:

Average

6.8

Step-by-step explanation:

[tex]\frac{5+3+5+30+4+5+4+3+4+5}{10}=6.8[/tex]

Answer:

[tex]P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)[/tex]

And we can find this probability using the complement rule and the normal standard distribution and we got:

[tex]P(z>6.302)=1-P(z<6.302)=1-0.99999 \approx 0[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the number of attacks of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(510,14.28)[/tex]  

Where [tex]\mu=510[/tex] and [tex]\sigma=14.28[/tex]

We are interested on this probability

[tex]P(X>600)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)[/tex]

And we can find this probability using the complement rule and the normal standard distribution and we got:

[tex]P(z>6.302)=1-P(z<6.302)=1-0.99999 \approx 0[/tex]

Given the mean and standard deviation for the number of hacking attacks, the z-score for 600 attacks is about 6.30.

The question asks for the likelihood that the group will suffer an average of more than 600 hacking attacks per year over the next 10 years, given that over the past decade the mean number of hacking attacks experienced by members is 510 per year with a standard deviation of 14.28 attacks. Considering the normal distribution of these hacking attacks, we can calculate this probability by finding the z-score corresponding to 600 attacks and then using the standard normal distribution table to find the probability of exceeding this value.

To calculate the z-score for 600 attacks, we use the formula:

Z = (X - μ) / σ

Where X is the value in question (600 attacks), μ (mu) is the mean (510 attacks), and σ (sigma) is the standard deviation (14.28 attacks). Substituting the given values:

Z = (600 - 510) / 14.28 ≈ 6.30

Looking up a z-score of 6.30 in the standard normal distribution table, we find that the area to the left of this z-score is almost 1, meaning the probability of experiencing more than 600 attacks is extremely small, approaching 0. Thus, it is incredibly unlikely that this group will suffer an average of more than 600 attacks in the next 10 years if nothing changes in their environment.

Answer:

-7/2

Step-by-step explanation:

[tex]slope = \frac{ - 4 - 10}{7 - 3} \\ \hspace{24 pt} = \frac{ - 14}{4} \\ \hspace{24 pt}= - \frac{7}{2} \\ \huge{ \red{ \boxed{\therefore \: slope = - \frac{7}{2} }}}[/tex]

Answer:

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

[tex]\mu_{\bar X}= 112[/tex]

[tex]\sigma_{\bar X}=\frac{25}{\sqrt[300}}= 1.443[/tex]

And the best option for this case would be:

b. approximately Normal, mean 112, standard deviation 1.443.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the IQ of a population, and for this case we know the following info:

Where [tex]\mu=65.5[/tex] and [tex]\sigma=2.6[/tex]

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

[tex]\mu_{\bar X}= 112[/tex]

[tex]\sigma_{\bar X}=\frac{25}{\sqrt[300}}= 1.443[/tex]

And the best option for this case would be:

b. approximately Normal, mean 112, standard deviation 1.443.

Given:

Given that the pie chart shows the relative frequency distribution resulting from a survey of 6000 US rural households with internet connections in a certain year.

We need to determine the total number of households with each type of internet in the survey.

Cable modem:

Since, the relative frequency distribution for cable modem is 0.142

The total number of households that use cable modem is given by

[tex]0.142 \times 6000=852[/tex]

Thus, 852 households use cable modem.

DSL:

Since, the relative frequency distribution for DSL is 0.092

The total number of households that use DSL is given by

[tex]0.092 \times 6000=552[/tex]

Thus, 552 households use DSL.

Dialup:

Since, the relative frequency distribution for dialup is 0.747

The total number of households that use dialup is given by

[tex]0.747 \times 6000=4482[/tex]

Thus, 4482 households use dialup.

Others:

Since, the relative frequency distribution for others is 0.019

The total number of households that use others is given by

[tex]0.019 \times 6000=114[/tex]

Thus, 114 households use others.

Answer:

[tex]2\sqrt[3]{x^{2}y^{2} }[/tex]

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

AAS triangle congruence theorem. These triangle have the same side, angle and other angle

The theorem that would determine if two right triangles are congruent or not are AAS Triangle Congruence Theorem.

If two right triangles have similar sizes and shapes, they are considered to be congruent triangles. In other terms, two right triangles are described to be congruent if the lengths of their respective sides and angles are the same.

The angle-angle-side (AAS) theorem posits that when two angles and any side of a triangle are equivalent to two angles and any side of some other triangle, then the triangles are considered to be congruent triangles.

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Answer:

[tex]z=\frac{0.55 -0.6}{\sqrt{\frac{0.6(1-0.6)}{80}}}=-0.913[/tex]  

[tex]p_v =P(z<-0.913)=0.181[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduate students show that only 44 students have ever done so is not significantly lower than 0.6

Step-by-step explanation:

Data given and notation

n=80 represent the random sample taken

X=44 represent the students that have bought merchandise on-line at their site

[tex]\hat p=\frac{44}{80}=0.55[/tex] estimated proportion of graduate students show that only 44 students have ever done so

[tex]p_o=0.6[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion of interest is lower than 0.6 or 60%, so then the system of hypothesis are.:  

Null hypothesis:[tex]p \geq 0.6[/tex]  

Alternative hypothesis:[tex]p < 0.6[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.55 -0.6}{\sqrt{\frac{0.6(1-0.6)}{80}}}=-0.913[/tex]  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed for this case is [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

[tex]p_v =P(z<-0.913)=0.181[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of graduate students show that only 44 students have ever done so is not significantly lower than 0.6

Answer:

15.525 feet

Step-by-step explanation:

GIVEN: A watermelon is thrown down from the [tex]7th[/tex] floor of Urey Hall at UCSD. If the initial height of the watermelon is [tex]21.0\text{ meters}[/tex], and it is thrown straight downward with an initial downward velocity of [tex]3.00\text{ m/s}[/tex].

TO FIND: How far will the watermelon have fallen from its starting height after [tex]1.5[/tex] seconds.

SOLUTION:

initial height of watermelon [tex]=21\text{ meter}[/tex]

initial velocity of watermelon[tex]=3\text{ m/s}[/tex]

acceleration due to gravity [tex]=9.8\text{m/s}^2[/tex]

According to newton's law of motion

[tex]S=ut+\frac{1}{2}at^2[/tex]

when [tex]t=1.5[/tex] seconds

[tex]S=3\times1.5+\frac{1}{2}\times9.8\times1.5^2[/tex]

[tex]S=4.5+11.025[/tex]

[tex]S=15.525\text{ feet}[/tex]

Hence watermelon will have fallen 15.525 feet from its starting height after 1.5 seconds

Answer: C. 8.1

I just got that one wrong, but there is the right answer

The diameter of the circle is C. 8.125 inches.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Given is a circle.

Given, chord FE is a perpendicular bisector of chord BC.

Here FE is the diameter of the circle.

We have a chord theorem which states that products of the lengths of the segments of line formed by two intersecting chords on each chord are equal.

Let X be the intersecting point of the chords.

Here, using the theorem,

BX . CX = FX . EX

3.5 × 3.5 = 2 × EX

EX = 6.125

Diameter = FE = FX + EX = 2 + 6.125 = 8.125

Hence the diameter is 8.125 inches.

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The complete question is given below.

Answer:

[tex]5\sqrt{3} - 4[/tex]

Step-by-step explanation:

[tex]\sqrt{(4-5\sqrt{3} )^{2} }[/tex]

[tex]5\sqrt{3} - 4[/tex]

Answer:

$102.96

Step-by-step explanation:

Lets take this one part at a time.

the dealership pays 12000 for the car, so they start at -12000 for how much money they have.

The dealership wants to make a 32% profit.  This means they want to make back the 12000 plus 32% of that.  what is 32% of 12000?  just multiply 12000 bty .32  In the end it works out that the price they sell it for is 15840

I do want to mention that there is a chance the 32% might also be accounting the bonus.  So in other words the dealership spent 12000 for the car then however much in paying the bonus, and they want to make a 32% profit on both of these combined.  I do not think that is what it is asking for, but I wanted to mention it.

Anyway, with a sales price of $15,840 it says the bonus is 6.5% of that.  to find that just do the multiplication .065 * 15840 = 1029.60.  So this is the bonus normally.

Now the question says the salesperson offers a 10 percent discount.  This changes the sales price (by 10%) and the bonus they earn.  let's calculate both.

First 10% discount of the sales price is .9*15840 = 14,256

Then 6.5% of that is .065*14256 = 926.64 So this is the new bonus.

The question wants the difference of the two bonuses, and difference is subtraction.  so 1029.60 - 926.64 = 102.96 So if the salesperson offers a 10% discount they lose $102.96

Answer:

x1= 2/3, x2 = -4

Step-by-step explanation:

3x² + 10x + c = 0

Formula for the roots of the quadratic equation is

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

Where  a = 3, b=10, c=c  for our equation 3x² + 10x + c = 0.

[tex]x=\frac{-10+/-\sqrt{10^{2}-4*3c} }{2*3} \\\\x=\frac{-10+/-\sqrt{100-12c} }{6} \\\\x_{1} =\frac{-10+\sqrt{100-12c} }{6} \\\\x_{2} =\frac{-10-\sqrt{100-12c} }{6} \\\\x_{1}-x{_2}=\frac{-10+\sqrt{100-12c} }{6} -(\frac{-10-\sqrt{100-12c} }{6} )\\\\x_{1}-x{_2}= \frac{2\sqrt{100-12c} }{6} =\frac{\sqrt{100-12c} }{3} \\\\x_{1}-x{_2}=\frac{\sqrt{100-12c} }{3} = 4\frac{2}{3} =\frac{14}{3} \\\\\sqrt{100-12c} =14\\(\sqrt{100-12c} )^{2}=14^{2}100-12c = 196\\12c=100-196\\c=-8[/tex]

[tex]x=\frac{-10+/-\sqrt{100-12(-8)} }{6} = \frac{-10+/-\sqrt{196} }{6} =\frac{-10+/-14}{6} \\\\x_{1} =\frac{4}{6} =\frac{2}{3} \\x_{2} =\frac{-24}{6} =-4[/tex]

Decimal:0.273 or 0.273273273

Fraction:273/999=91/333

Answer:

0.273 as a fraction is 273/1000

0.273273273... as a repeating decimal, (273/999) as repeating decimal fraction.

Answer:

Step-by-step explanation:

0.4

Answer: 0.4

P (Manny wins) + P (Rachelle wins) + P (Peg wins) = 1

0.35 + P (Rachelle wins) + 0.25 = 1

P (Rachelle wins) = 1 - 0.35 - 0.35

P (Rachelle wins) = 0.4

The probability that Rachelle will win any given race is 0.4.

Answer:

The answer is $5.

Step-by-step explanation:

$10 divided by 2 packs = $5

OR

$10 divided by 4 to get the per pack price which is $2.50 each

Then multiply $2.50 times 2 packs = $5

Hope this helps!!

Answer:

b = 28

Step-by-step explanation:

8*21 then 168/6 = 28

Answer:

b = 28

Step-by-step explanation:

[tex] \frac{6}{8} = \frac{21}{b} \\ \\ b = \frac{21 \times 8}{6} \\ \\ b = \frac{7\times 8}{2} \\ \\ b = 7 \times 4 \\ \\ \huge \red{ \boxed{ b = 28}}[/tex]

Answer:

Step-by-step explanation:

X = cost of PB  

Y = cost of J

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Dividing everything in the first equation by 2:

3X + 2Y =  966 <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Elimination method... let's multiply the first equation by 3 and the second equation by -2.

   9X +   6Y =   2898

-10X + -6Y  = -3134

-X = -236

X =  236 --> so the price of the PB is 236 pennies or $2.36

Plugging into the second equation as the numbers are a bit smaller,

5X + 3Y = 1567

5(236) + 3Y = 1567

1180 + 3Y = 1567

3Y = 387

Y = 129. So the price of the jelly is 129 pennies or $1.29.

Now we check:  4 x $1.29 + 6*2.36 = $19.32

                       3 x $1.29 + 5 x 2.36 = $15.37

The answers are verified and highlighted in bold.

6X + 4Y = 1932  <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

By setting up a system of equations to represent the cost of the items bought by Erin and Adam, you can solve to find the cost of the 'j' (jelly) and 'p' (peanut butter). It's similar to solving a problem to find the cost of different fruits in a fruit basket.

We can solve this problem using algebra, particularly the system of linear equations. Let's denote 'j' as the cost of a jar of jelly and 'p' as the cost of a jar of peanut butter. We will use the information given in the question to set up two equations:

For Erin's purchases, it is 4j + 6p = $19.32. For Adam's purchases, it is 3j + 5p = $15.67.

Now, you can solve this system of equations using the substitution or elimination method, and find the cost of the jar of peanut butter and jelly.

Notice that this example is similar to finding the cost of fruit when we know the total price and the number bought, like in the fruit basket example provided earlier. This is an example of solving for unknowns using algebraic equations.

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Answer:

The distance across the lake from A to B = 690.7 ft

Step-by-step explanation:

Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that

∠CAB=46.5∘. He also measures CA as 312 ft and CB as 527 ft. Find the distance between A and B.

Given

A = 46.5°

a = 527 ft

b = 312 ft

To find; c = ?

Using the sine rule

[a/sin A] = [b/sin B] = [c/sin C]

We first obtain angle B, that is, ∠ABC

[a/sin A] = [b/sin B]

[527/sin 46.5°] = [312/sin B]

sin B = 0.4294

B = 25.43°

Note that: The sum of angles in a triangle = 180°

A + B + C = 180°

46.5° + 25.43° + C = 108.07°

C = 108.07°

We then solve for c now,

[b/sin B] = [c/sin C]

[312/sin 25.43°] = [c/sin 108.07°]

c = 690.745 ft

Hope this Helps!!!

To find the distance across the lake from A to B, use trigonometry and the length of side AC and angle CAB to find the length of side AB.

To find the distance across the lake from point A to point B, we can use trigonometry.

Given that ∠CAB = 46.5°, we can find the distance across the lake by finding the length of side AB in triangle CAB.

Since we know the length of side AC (53 m) and the angle CAB (46.5°), we can use the sine function to find side AB:

AB = AC * sin(CAB) = 53 m * sin(46.5°) = 39.6 m

Therefore, the distance across the lake from point A to point B is approximately 39.6 meters.

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Answer:

Step-by-step explanation:

You need to subtract the prices of the medium and large from the total

Small = 46.24 - medium -  large

17.50 + 15.75 = 33.75

S = 46.24 - 33.75

S = 12.99

Answer:

47

Step-by-step explanation:

x is games won

y is hats sold

[tex]y=3.75x+13.75\\y=3.75(9) + 13.75\\y=47.5[/tex]

Since you can't sell .5 of a hat- you need to round this answer.

Answer:

48

Step-by-step explanation: