The probability that a randomly chosen citizen-entity of Cygnus is of pension age† is approximately 0.7. What is the probability that, in a randomly selected sample of four citizen-entities, all of them are of pension age?

Answer:

n = 601

Step-by-step explanation:

Since we know nothing about the percentage of computers with new operating system, we assume than 50% of the computers have new operating system.

So, p = 50% = 0.5

q = 1 - p = 1 - 0.5 = 0.5

Margin of error = E = 4 percentage points = 0.04

Confidence Level = 95%

z value associated with this confidence level = z = 1.96

We need to find the minimum sample size i.e. n

The formula for margin of error for the population proportion is:

[tex]E=z\sqrt{\frac{pq}{n}}[/tex]

Re-arranging the equation for n, and using the values we get:

[tex]n=(\frac{z}{E} )^{2} \times pq\\\\ n=(\frac{1.96}{0.04})^{2} \times 0.5 \times 0.5\\\\ n = 601[/tex]

Thus, the minimum number of computers that must be surveyed is 601

Answer: z= 1.51

Step-by-step explanation:

Test statistic for proportion is given by :-

[tex]z=\dfrac{p-P}{\sqrt{\dfrac{PQ}{n}}}[/tex]

Where n is sample size ,p is the sample proportion , P Is the population proportion and Q =1 - P.

Given : P=57% = 0.57

Q= 1- P = 1-0.57=0.43

n = 25

[tex]p=\dfrac{18}{25}=0.72[/tex]

Test statistic for proportion will be :-

[tex]z=\dfrac{0.72-0.57}{\sqrt{\dfrac{0.57\times0.43}{25}}}\approx1.51[/tex]

We should report the value of test statistic z= 1.51

Answer:

15%

Step-by-step explanation:

Answer:

Explanation:

The probability distribution of the standard normal variable, Z, is tabulated.

Z, the standard normal variable, is defined by:

You want to find the probablity that the systolic pressure of a woman between the ages of 18 and 24 is greater than 125, which means P (X > 125).

Then, to use a table of Z-score, you have to convert X > 125 into Z and find the corresponding probabiiity.

These are the calculations:

Now use a table for the normal standard probabiity. Most tables use two decimals for Z, so you can round to Z > 0.78, which will yield  P (Z > 0.78) = 0.2177.

Answer:

D.) Both (B) and (C)

Step-by-step explanation:

The slope upward depicts higher sales option (B) and (C) are causes for higher production

HOPE IT HELPS....

The supply curve slopes upward due to two primary reasons. Firstly, as a firm increases output, the cost of production typically increases, necessitating a higher price to cover the increasing costs. Also, at higher prices, it's more profitable for firms to supply more of a good. Both these factors cause an upward slope in the supply curve.

The supply curve in Economics slopes upward because it represents the relationship between the cost of production and the quantity supplied. The correct answer is option d. As a firm produces more goods (output), its cost of production often rises, typically due to diminishing returns in the short run. So, they require a higher price to cover their increasing costs, hence option (b). Further, when the price per unit of a good in a market is higher, it's more profitable for firms to supply more of that good, conforming with option (c). Both these factors together explain the upward slope of the supply curve.

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Answer:

19%

Step-by-step explanation:

First, let's notice that having 1 or more rotten oranges in the sample is the complement of having 0 rotten oranges in the sample. That means

proba (1 or more rotten oranges) + proba (0 rotten oranges) = 100%

We will focus in the case of 0 rotten oranges that's easier and then we go back to this last equation.

For 0 rotten oranges, we need that the customer picks 3 good oranges. As there are 4 rotten oranges in the crate of 60, we have [tex]60-4=56[/tex] good oranges.  

So, the customer has a 56/60 chance of getting a good orange. As he needs 3 good oranges at the same time, he has [tex]\frac{56}{60} *\frac{55}{59} *\frac{54}{60}= \frac{1386}{1711}[/tex] chance.

Therefore,  proba(0 rotten oranges) = [tex]\frac{1386}{1711}[/tex] = 81% (approximately)

Going back to the first paragraph, we have proba(1 or more rotten oranges) = 100% - proba(0 rotten oranges) = 100% - 81% = 19%

Answer:

The mean absolute deviation is $26.38

Step-by-step explanation:

$22+$16+$35+$19+$34+$20+$26= $211

$211 ÷ 8 (backpacks) = $26.375= $26.38

Answer:

2x

Step-by-step explanation:

Volume of a cylinder is:

V = πr²h

If V = 4πx³ and h = x, then:

4πx³ = πr²x

4x² = r²

r = 2x

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It's the radio

h: It's the height

We have as data that the volume of the cylinder is:

[tex]V = 4 \pi * x ^ 3[/tex]

They also tell us that the height is "x", then:

[tex]4 \pi * x ^ 3 = \pi * r ^ 2 * x[/tex]

We have similar terms on both sides of the equation:

[tex]4x ^ 2 = r ^ 2[/tex]

We apply root to both sides of the equation:

[tex]r = \pm \sqrt {4x ^ 2}\\r = \pm2x[/tex]

We choose the positive value. Now the radio is 2x

Answer:

[tex]2x[/tex]

Answer:

$15

Step-by-step explanation:

He had $20 and he spent [tex]\frac{3}{4}[/tex] of that in baseball cards, that is

[tex]20*\frac{3}{4}= \frac{20*3}{4} = \frac{60}{4} = 15.[/tex]

So, he spent $15 in baseball cards.

Answer with Step-by-step explanation:

We are given that tr(FG)=tr(GF) for any two matrix of order [tex]n\times n[/tex]

We have to show that if A and B are similar then

tr upper A=tr upper B

Trace of a square matrix A is the sum of diagonal entries in A and denoted by tr A

We are given that A and B are similar matrix  then there exist a inverse matrix P such that

Then [tex]B=P^{-1}AP[/tex]

Let [tex] G=P^{-1} [/tex] and F=AP

Then[tex] FG= APP^{-1}[/tex]=A

GF=[tex]P^{-1}AP=B[/tex]

We are given that tr(FG)=tr(GF)

Therefore, tr upper A=trB

Hence, proved

Answer:  The required number of ways is 46200.

Step-by-step explanation:  Given that a catering service offers 8 ​appetizers, 11 main​ courses, and 7 desserts.

A banquet committee is to select 7 ​appetizers, 8 main​ courses, and 4 desserts.

We are to find the number of ways in which this can be done.

We know that

From n different things, we can choose r things at a time in [tex]^nC_r[/tex] ways.

So,

the number of ways in which 7 appetizers can be chosen from 8 appetizers is

[tex]n_1=^8C_7=\dfrac{8!}{7!(8-7)!}=\dfrac{8\times7!}{7!\times1}=8,[/tex]

the number of ways in which 8 main courses can be chosen from 11 main courses is

[tex]n_2=^{11}C_8=\dfrac{11!}{8!(11-8)!}=\dfrac{11\times10\times9\times8!}{8!\times3\times2\times1}=165[/tex]

and the number of ways in which 4 desserts can be chosen from 7 desserts is

[tex]n_3=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.[/tex]

Therefore, the number of ways in which the banquet committee is to select 7 ​appetizers, 8 main​ courses, and 4 desserts is given by

[tex]n=n_1\times n_2\times n_3=8\times165\times35=46200.[/tex]

Thus, the required number of ways is 46200.

Answer:

[tex](a-2b)^{5}=-32b^{5}+80ab^{4}-80a^{2}b^{3}+40a^{3}b^{2}-10a^{4}b+a^{5}[/tex]

Step-by-step explanation:

The binomial expansion is given by:

[tex](x+y)^{n}=_{0}^{n}\textrm{C}x^{^{0}}y^{n}+_{1}^{n-1}\textrm{C}x^{1}y^{n-1}+...+_{n}^{n}\textrm{C}x^{n}y^{0}[/tex]

In our case we have

[tex]x=a\\y=-2b\\n=5[/tex]

Thus using the given terms in the binomial expansion we get

[tex](a-2b)^{5}=_{0}^{5}\textrm{C}a^{0}(-2b)^{5}+_{1}^{5}\textrm{C}a^{^{1}}(-2b)^{4}+{_{2}^{5}\textrm{C}}a^{2}(-2b)^{3}+_{3}^{5}\textrm{C}a^{3}(-2b)^{2}+_{4}^{5}\textrm{C}a^{4}(-2b)^{1}+_{5}^{5}\textrm{C}a^{5}(-2b)^{0}[/tex]

Upon solving we get

[tex](a-2b)^{5}=-32b^{5}+5\times a\times16b^{4}+10\times a^{2} \times (-8b^{3})+10\times a^{3}\times 4b^{2}+5\times a^{4}\times (-2b)+a^{5}\\\\(a-2b)^{5}=-32b^{5}+80ab^{4}-80a^{2}b^{3}+40a^{3}b^{2}-10a^{4}b+a^{5}[/tex]

Answer:78

Step-by-step explanation:

For N=13 candidates

For pairwise comparison to determine the winner in an election we need to use combination

a pair of distinct candidates can be chosen in [tex]^NC_{2}=\frac{N\left ( N-1 \right )}{2}[/tex]

Therefore no of comparison to be made =[tex]^{13}C_{2}=frac{13\left ( 13-1 \right )}{2}=78[/tex]

Thus a total of 78 comparison is needed

To determine the number of comparisons needed using the pairwise comparison method when there are 13 candidates, we can use the formula (n-1) + (n-2) + ... + 1, where n represents the number of candidates. By substituting n = 13 into the formula, we find that a total of 78 comparisons must be made.

To determine the number of comparisons needed using the pairwise comparison method, we can use the formula:

(n-1) + (n-2) + ... + 1

where n represents the number of candidates. Substituting n = 13, we get:

(13-1) + (13-2) + ... + 1

Simplifying the equation, we find:

12 + 11 + ... + 1 = 78

Therefore, a total of 78 comparisons must be made when there are 13 candidates.

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Step-by-step explanation:

Consider the provided set {2,3,4,6,8,9,10,12}

Let the set is A.

[tex]A={(2 \prec 4), (2 \prec 6), (2 \prec 8), (2 \prec 10), (2 \prec 12), (3 \prec 6), (3 \prec 9), (4 \prec 8), (4 \prec 12), (6 \prec 12)}[/tex]

Hence the required Hasse diagram is shown in figure 1:

In the Hasse diagram 2 and 3 are on the same level as they are not related.

The next numbers are 4, 6, 9, and 10. 4, 6 and 10 are divisible by both 2. 6 and 9 are divisible by 3. Then 8 and 12 are divisible by 4 also 12 is divisible by 6.

Hence, the required diagram of the partial order of the set {2,3,4,6,8,9,10,12} is shown in figure 1.

Answer: 0.1061

Step-by-step explanation:

Given : An insurance company found that 9% of drivers were involved in a car accident last year.

Thus, the probability of drivers involved in car accident last year = 0.09

The formula of binomial distribution :-

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

If seven (n=7) drivers are randomly selected then , the probability that exactly two (x=2) of them were involved in a car accident last year is given by :-

[tex]P(X=2)=^7C_2(0.09)^2(1-0.09)^{7-2}\\\\=\dfrac{7!}{2!5!}(0.09)^2(0.91)^{5}=0.106147867882\approx0.1061[/tex]

Hence, the required probability :-0.1061

Final answer:

The null hypothesis (H₀) for the test is μₖ = 0, meaning on average there is no age difference between Best Actresses and Best Actors, while the alternative hypothesis (Hᴏ) is μₖ < 0, suggesting that Best Actresses are, on average, younger than Best Actors.

Explanation:

To test the claim that the population of ages of Best Actresses is generally younger than Best Actors, we can set up the following null and alternative hypotheses:

To conduct this hypothesis test at a 0.05 significance level, we calculate the differences (actress's age - actor's age) for each paired set of data and examine whether the mean difference is significantly less than 0 using the appropriate statistical methods (such as a t-test, if assumptions are met).

Final answer:

The null hypothesis (H0) is that there is no difference in mean age (mu Subscript d) between Best Actresses and Best Actors, represented as H0: mu Subscript d = 0. The alternative hypothesis (Ha) claims that actresses are younger on average, represented as Ha: mu Subscript d < 0. A t-test at the 0.05 significance level is used to test these hypotheses.

Explanation:

To test the claim that the population of ages of Best Actresses and Best Actors have a mean difference of ages less than 0, we need to set up null and alternative hypotheses for a hypothesis test. The null hypothesis (H0) will claim that there is no difference in the mean age (mu Subscript d) between actresses and actors, which is mathematically represented as H0: mu Subscript d = 0. The alternative hypothesis (Ha) claims that the mean age of actresses is less than that of actors, which is represented as Ha: mu Subscript d < 0.

To conduct the hypothesis test, we compare the actual mean differences we calculate from the sample with the null hypothesis using a t-test at a 0.05 significance level. If our test statistic falls within the critical region, we will reject the null hypothesis in favor of the alternative hypothesis, suggesting that actresses, on average, are younger than actors when they win the awards.

The three vectors [tex]\langle0,0,1\rangle[/tex], [tex]\langle1,0,8\rangle[/tex], and [tex]\langle0,1,9\rangle[/tex] each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,

[tex]\langle1,0,8\rangle-\langle0,0,1\rangle=\langle1,0,7\rangle[/tex]

[tex]\langle0,1,9\rangle-\langle0,0,1\rangle=\langle0,1,8\rangle[/tex]

Then the cross product of these two results is normal to the plane:

[tex]\langle1,0,7\rangle\times\langle0,1,8\rangle=\langle-7,-8,1\rangle[/tex]

Let [tex](x,y,z)[/tex] be a point on the plane. Then the vector connecting [tex](x,y,z)[/tex] to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that

[tex]\langle-7,-8,1\rangle\cdot(\langle x,y,z\rangle-\langle0,0,1\rangle)=0[/tex]

which reduces to the equation of the plane,

[tex]-7x-8y+z-1=0\implies z=7x+8y+1[/tex]

Let [tex]z=f(x,y)[/tex]. Then the volume of the region above [tex]R[/tex] and below the plane is

[tex]\displaystyle\int_0^1\int_0^1(7x+8y+1)\,\mathrm dx\,\mathrm dy=\boxed{\frac{17}2}[/tex]

The problem involves finding the volume of a region under a plane defined by three points in a 3-dimensional space. Calculus and analytical geometry can be used to find the answer. Solution can only be provided if the equation of the plane is provided.

The question involves finding the volume of a specific region defined within spatial coordinates in a three-dimensional Cartesian space. The three points provided (0,0,1), (1,0,8) and (0,1,9) define a plane. Unfortunately, the problem does not provide enough details to solve the problem. Having said this, the volume of a region R under a plane can usually be found by integrating over the area of R. This essentially involves setting up a double integral over the area R with the integrand being the height of the plane above each point in R. The solution, however, requires the equation of the plane, which can be found using the three points mentioned. This method relies on the understanding of the fundamentals of calculus and analytic geometry

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Answer:

  C.  (-4,10,7)

Step-by-step explanation:

Use the first equation to substitute for y in the last equation:

  x = (x +2z) -14

  14 = 2z . . . . . . add 14-x

  7 = z . . . . . . . . divide by 2

Now, find x:

  7 = -1 -2x . . . . substitute for z in the second equation

  8/-2 = x = -4 . . . . . add 1, divide by -2

Finally, find y:

  y = -4 +2(7) = 10 . . . . . substitute for x and z in the first equation

The solution is (x, y, z) = (-4, 10, 7).

Answer:

C

Step-by-step explanation:

EDGE

Answer:

  x = {kπ, arccos(1/5) +2kπ, 2kπ -arccos(1/5)}

Step-by-step explanation:

The double-angle trig identity for sine is useful:

  5(2sin(θ)cos(θ)) -2sin(θ) = 0

  2sin(θ)(5cos(θ) -1) = 0

This has solutions that make the factors zero:

  θ = arcsin(0) = kπ

and ...

  cos(θ) = 1/5

  θ = arccos(1/5) +2kπ . . . . or . . . . 2kπ -arccos(1/5)

_____

Some numerical values are shown on the graph attached. values for multiples of pi are ...

  {..., -12.566, -9.425, -6.283, -3.142, 0, 3.142, 6.283, 9.425, 12.566, ...}

Answer:

68600 will there be at​ midnight ( approx )

Step-by-step explanation:

Let P shows the population of the bacteria,

Since, the number of bacteria in a culture grew at a rate proportional to its size,

[tex]\implies \frac{dP}{dt}\propto P[/tex]

[tex]\frac{dP}{dt}=kP[/tex]

Where, k is the constant of proportionality,

[tex]\frac{dP}{P}=kdt[/tex]

[tex]\int \frac{dP}{P}=\int kdt[/tex]

[tex]ln P=kt + C_1[/tex]

[tex]P=e^{kt+C_1}[/tex]

[tex]P=e^{kt}.e^{C_1}=C e^{kt}[/tex]

Now, let the population of bacteria is estimated from 10:00 AM,

So, at t = 0, P = 4,000 ( given )

[tex]4000 = Ce^{0}[/tex]

[tex]\implies C=4000[/tex]

Now, at noon there are 4,600 bacterias,

That is, at t = 2, P = 4600

[tex]4600=Ce^{2k}[/tex]

[tex]4600 = 4000 e^{2k}[/tex]

[tex]\implies e^{2k}=\frac{4600}{4000}=1.15[/tex]

[tex]2k=ln(1.5)\implies k=\frac{ln(1.5)}{2}=0.202732554054\approx 0.203[/tex]

Hence, the equation that represents the population of bacteria after t hours,

[tex]P=4000 e^{0.203t} [/tex]

Therefore, the population of the bacteria at midnight ( after 14 hours ),

[tex]P=4000 e^{0.203\times 14}=4000 e^{2.842}= 68600.1252903\approx 68600[/tex]

Answer:

  49 m/s

Step-by-step explanation:

We don't know what your model is, so we'll solve this based on the balance of forces. Air resistance exerts an upward force of ...

  (4 N/(m/s))v

Gravity exerts a downward force of ...

  (20 kg)(9.8 m/s²) = 196 N

These are balanced (no net acceleration) when ...

  (4 N/(m/s))v = 196 N

  v = (196 N)/(4 N/(m/s)) = 49 m/s

The terminal velocity is expected to be 49 m/s.

Answer:

dy/dt = 7y / (t − 1000)

Step-by-step explanation:

Change in mass of salt = mass of salt going in − mass of salt going out

dy/dt = 0 − (C kg/L × 7 L/min)

where C is the concentration of salt in the tank.

The concentration is mass divided by volume:

C = y / V

The volume in the tank as a function of time is:

V = 1000 + 6t − 7t

V = 1000 − t

Therefore:

C = y / (1000 − t)

Substituting:

dy/dt = -7y / (1000 − t)

dy/dt = 7y / (t − 1000)

If we wanted, we could separate the variables and integrate.  But the problem only asks that we find the differential equation, so here's the answer.

The differential equation for the change in the mass of salt over time in the tank is expressed as dy/dt = -(y/(1000-1*t))*7. This is based on the concentration of salt in the water and the rates at which water enters and leaves the tank.

To set up the differential equation for the student's question, we must take into account the rate at which the water (and hence the salt solution) is entering and leaving the tank. Let's denote the amount of salt in the tank after t minutes as y (kg). The rate of water entering the tank is 6 L/min of pure water, so no additional salt is added. The water leaving the tank, which has a concentration of salt, is 7 L/min.

The concentration of the salt at any time t is given by the mass of the salt y divided by the volume of the solution in the tank. Since the solution is leaving the tank at 7 L/min, the rate at which salt leaves the tank is the concentration times the outflow rate, which is (y/(1000-1×t))×7 kg/min. The negative sign represents the loss of salt from the tank.

The differential equation accounting for this change in mass of salt over time would be: dy/dt = -(y/(1000-1×t))×7. Note that this equation is valid until the tank is empty, at which point a different model would be needed as there would be no more solution left to leave the tank.

Answer:

D. None of the Above

Step-by-step explanation:

Answer:

120 minutes

Step-by-step explanation:

Total plants are 16 and only 5 can be placed in one go. so total number of rounds for the plants will be: 16/5 = 3.2 rounds ≅ 4 rounds

As there are four rounds to go in 8 hours, so the time for 1 round will be: 8/4 = 2 hours.

Therefore, 2 hours or 120 minutes of sunlight are possible for one plant ..

Answer:

The answer is actually 150 minutes.

Step-by-step explanation:

Answer:

Option C (f(x) = [tex]-x^2 + 2x + 4[/tex])

Step-by-step explanation:

In this question, the first step is to write the general form of the quadratic equation, which is f(x) = [tex]ax^2 + bx + c[/tex], where a, b, and c are the arbitrary constants. There are certain characteristics of the values of a, b, and c which determine the nature of the function. If a is a positive coefficient (i.e. if a>0), then the quadratic function is a minimizing function. On the other hand, a is negative (i.e. if a<0), then the quadratic function is a maximizing function. Since the latter condition is required, therefore, the first option (f(x) = [tex]4x^2 + 6x - 1[/tex]) and the last option (f(x) = [tex]x^2 + 4x - 4 [/tex]) are incorrect. The features of the values of b are irrelevant in this question, so that will not be discussed here. The value of c is actually the y-intercept of the quadratic equation. Since the y-intercept is 4, the correct choice for this question will be Option C (f(x) = [tex]-x^2 + 2x + 4[/tex]). In short, Option C fulfills both the criteria of the function which has a maximum and a y-intercept of 4!!!

Answer:

it is c: f(x) = –x2 + 2x + 4

Answer:

The equation to find the number of fish after t years where y is the number of fish is:

y(t) = 160×3^(t) ( t <= 2.93 assuming that the maximum number of fish is 4000 )

Therefore when y(t) = 2000 2000 = 160×3^(t)

3^(t) = 25/2 log 3 (3^(t)) = log 3 (25/2) t = 2.29 years.

Using the logistic equation, we have that:

a)

The equation is:

[tex]P(t) = \frac{4000}{1 + 24e^{-1.1856t}}[/tex]

b)

It will take 2.68 years for the population to increase to 2000.

The logistic equation is:

[tex]P(t) = \frac{K}{1 + Ae^{-kt}}[/tex]

With:

[tex]A = \frac{K - P(0)}{P(0)}[/tex]

The parameters are:

In this problem:

Then:

[tex]A = \frac{4000 - 160}{160} = 24[/tex]

Thus:

[tex]P(t) = \frac{4000}{1 + 24e^{-kt}}[/tex]

Item a:

Tripled during the first year, thus [tex]P(1) = 3P(0) = 3(160) = 480[/tex].

This is used to find k.

[tex]480 = \frac{4000}{1 + 24e^{-k}}[/tex]

[tex]480 + 11520e^{-k} = 4000[/tex]

[tex]e^{-k} = \frac{3520}{11520}[/tex]

[tex]\ln{e^{-k}} = \ln{\frac{3520}{11520}}[/tex]

[tex]k = -\ln{\frac{3520}{11520}}[/tex]

[tex]k = 1.1856[/tex]

Thus, the equation is:

[tex]P(t) = \frac{4000}{1 + 24e^{-1.1856t}}[/tex]

Item b:

This is t for which P(t) = 2000, thus:

[tex]P(t) = \frac{4000}{1 + 24e^{-1.1856t}}[/tex]

[tex]2000 = \frac{4000}{1 + 24e^{-1.1856t}}[/tex]

[tex]\frac{1}{1 + 24e^{-1.1856t}} = 0.5[/tex]

[tex]0.5 + 12e^{-1.1856t} = 1[/tex]

[tex]e^{-1.1856t} = \frac{1}{24}[/tex]

[tex]\ln{e^{-1.1856t}} = \ln{\frac{1}{24}}[/tex]

[tex]t = -\frac{\ln{\frac{1}{24}}}{1.1856t}[/tex]

[tex]t = 2.68[/tex]

It will take 2.68 years for the population to increase to 2000.

A similar problem is given at https://brainly.com/question/24215157

The number of  Degrees of Freedom is the answer.

The term 'degrees of freedom' refers to the number of sample values that can vary after specific restrictions have been placed on all data values. It is a critical concept in statistics, playing a role in areas such as hypothesis testing and confidence intervals.

The blank should be filled with 'degrees of freedom'. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.

For instance, in a set of sample data with a fixed mean, if you know the values of all but one data point, you can calculate the value of the remaining one due to the restriction of the fixed mean. Therefore, in this case, the degrees of freedom would be n-1 (with 'n' representing the total number of sample data points).

The concept of degrees of freedom is an important aspect in various areas of statistics, including hypothesis testing and estimating confidence intervals.

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Answer:

actual rate of interest is 2.08 %

Step-by-step explanation:

Given data

borrowed = $2100

time = 15 months

rate = 2.6%

to find out

interest and receive from the bank and actual rate of interest

solution

we know bank discounted the loan at 2.6%

so interest will be 2.6% of $2100

that is  = 2.6/100 × 2100

interest = $54.60

so receive from the bank  is  borrowed money - interest

receive = 2100 - 54.60

receive from the bank is $2045.40

and we can say that interest is directly proportional to time

so interest of 12 months / interest of 15 month = 12 month time/ 15 month time

here  interest of 12 months = 12/15 ×  interest of 15 month

interest of 12 months = 12/15 × 54.60

interest of 12 months is $43.68 (annually)

now we can calculate actual rate of interest

that is = interest / borrowed money × 100

actual rate of interest = 43.68/2100 × 100

actual rate of interest is 2.08 %

Final answer:

Dylan borrowed $2100 which was discounted at a 2.6% rate by the bank over 15 months, incurring $68.25 in interest, leaving him to receive $2031.75. The actual annual rate of interest calculated is approximately 2.667%.

Explanation:

The calculation of the interest on a discounted loan involves understanding the interest rate and the method by which the interest is calculated. In Dylan's case, the bank used a discount rate of 2.6% on a loan of $2100 over a period of 15 months.

To calculate discounted interest, you need to multiply the principal amount by the discount rate and then adjust for the loan term. In this case, the formula for interest (I) looks like this: I = Principal (P) × Discount Rate (r) × Time (t), where 't' is in years. Since the loan term is 15 months, we convert it to years by dividing by 12, resulting in 1.25 years.

So, the interest can be calculated as follows:
I = $2100 × 0.026 × (15/12) = $2100 × 0.026 × 1.25 = $68.25. Therefore, the interest on the loan is $68.25, rounded to the nearest penny.

The actual amount Dylan received from the bank can be found by subtracting the interest from the principal: $2100 - $68.25 = $2031.75.

To calculate the actual interest rate, we compare the amount of interest paid over the loan term to the amount received. The actual interest for 15 months is the interest Dylan would be paying, divided by the amount he received, all divided by the time in years: Actual Rate (R) = ($68.25 / $2031.75) / 1.25. After solving for R, we get an actual rate of approximately 2.667%, rounded to the nearest hundredth.

Answer:

hence proceeds is $2513.05 and discount is $443.47

Step-by-step explanation:

Lauren pays = $3,400

interest = 15%

time = 1 yr

[tex]P(1+\dfrac{r}{100} )^n = 3400\\P(1+\dfrac{15}{100} )^1 = 3400\\P=2956.52[/tex]

the amount to be discounted is

[tex]\dfrac{15}{100} \times 2956.52 = 443.47[/tex]

discount = $443.47

proceeds = $2956.52 -$443.47

proceeds = $2513.05

hence proceeds is $2513.05 and discount is $443.47

The discount on the loan is $510, calculated as 15% of $3,400. Lauren receives proceeds of $2,890 after the discount is subtracted from the principal amount.

To calculate the discount and proceeds given to Lauren by the bank, we use the interest rate and the principal amount. Since the bank subtracts the interest upfront (known as discounting), we need to find 15% of $3,400.

First, find the discount:
Discount = Principal x Interest Rate
Discount = $3,400 x 0.15 = $510

Next, to calculate the proceeds, subtract the discount calculated above from the principal:
Proceeds = Principal - Discount
Proceeds = $3,400 - $510 = $2,890

Therefore, the bank subtracts the discount of $510 from the original $3,400 and gives Lauren the remaining proceeds of $2,890.

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The five-number summary for the given data set of strontium-90 levels in baby teeth is 124 (minimum), 131.5 (Q1), 139 (median), 149.5 (Q3), and 160 (maximum).

The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Here's the calculation using the given data, already sorted in ascending order:

Determine the minimum and maximum values.

- The minimum value is the first element of the sorted data set: 124.

- The maximum value is the last element of the sorted data set: 160.

Calculate the median (Q2).

- Since there are 20 numbers, the median is the average of the two middle values (10th and 11th):

[tex]\[ \frac{138 + 140}{2} = 139. \][/tex]

Calculate the first quartile (Q1).  

- The first quartile is the median of the lower half of the data (the first 10 numbers):

[tex]\[ \frac{131 + 132}{2} = 131.5. \][/tex]

Calculate the third quartile (Q3).

- The third quartile is the median of the upper half of the data (the last 10 numbers):

[tex]\[ \frac{149 + 150}{2} = 149.5. \][/tex]

Thus, the five-number summary for this data set is 124, 131.5, 139, 149.5, 160.

The complete question is : Listed below are amounts of strontium-90 (in millibecquerels, or mBq) in a simple random sample of baby teeth obtained from residents in a region born after 1979. Use the given data to construct a boxplot and identify the 5-number summary.

124 125 128 131 132 134 134 135 137 138

140 140 142 144 146 149 150 150 154 160

The 5 – number summary is _, _,_,_ and _ all in mBq. (use ascending order. Type integers or decimals do not round