How much work is required to lift a 1400-kg satellite to an altitude of 2⋅106 m above the surface of the Earth? The gravitational force is F=GMm/r2, where M is the mass of the Earth, m is the mass of the satellite, and r is the distance between the satellite and the Earth's center. The radius of the Earth is 6.4⋅106 m, its mass is 6⋅1024 kg, and in these units the gravitational constant, G, is 6.67⋅10−11.

Answer:

The answer to your question is below

Step-by-step explanation:

Inequality 1

                        7(x + 2) - 8 ≥ 13

                        7x + 14 - 8 ≥ 13

                        7x + 6 ≥ 13

                         7x ≥ 13 - 6

                         7x ≥ 7

                           x ≥ 7/7

                           x ≥ 1

Inequality 2

                       8x - 3 < 4x - 3

                        8x - 4x < - 3 + 3

                               4x < 0

                                 x < 0 / 4

                                 x < 0

Interval notation   (-∞ , 0) U [1, ∞)

See the graph below

Answer:

a) 4.5

b) x = 11.2, s = 4.65

c) 93.33%                                                

Step-by-step explanation:

We are given he following data in the question:

8, 12, 11, 15, 14, 10, 8, 3, 8, 7, 21, 12, 9, 19, 11

a) Estimation of standard deviation using range

Sorted data: 3, 7, 8, 8, 8, 9, 10, 11, 11, 12, 12, 14, 15, 19, 21

Range = Maximum - Minimum = 21 - 3 = 18

Range rule thumb:

[tex]s = \dfrac{\text{Range}}{4} = \dfrac{18}{4} = 4.5[/tex]

b) Mean and standard deviation

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{168}{15} = 11.2[/tex]

Sum of squares of differences = 302.4

[tex]S.D = \sqrt{\dfrac{302.4}{14}} = 4.65[/tex]

c)  fraction of the scores actually lie in the interval x ± 2s

[tex]x \pm 2s = 11.2 \pm 2(4.65) = (1.9,20.5)[/tex]

Since 14 out of 15 entries lie in this range, we can calculate the percentage as,

[tex]\dfrac{14}{15}\times 100\% = 93.33\%[/tex]

Answer:

  37.35 in

Step-by-step explanation:

The volume of a cone is given by the formula ...

  V = (π/3)r²h

where r is the radius of the base and h is the height. We want to find the diameter of the base, so we can rewrite this in terms of diameter and solve for d. Please note that the height is given in millimeters, not inches, so a conversion is necessary.

  V = (π/3)(d/2)²h

  12V/(πh) = d²

  d = 2√(3V/(πh)) = 2√(3(2.2×10^4 in^3)/(π·1530 mm/(25.4 mm/in))

  = 2√(1.6764×10^6/(π·1.53×10^3) in^2)

  d ≈ 37.35 in

The base diameter of the cone is about 37.35 inches.

The diameter of the base of the cone is found to be approximately 18.28802 inches after substituting the given values into the volume formula for a cone and solving for radius, and then doubling to get diameter.

The volume V of a right circular cone is given by the formula V = 1/3πr²h, where r represents the radius of the cone's base and h is the cone's height. The diameter of the base of a cone is double the radius, so we will be solving for diameter instead of radius.

We were given V = 2.2 x 104 in³ and h = 1530 mm. Firstly it is important to note that 1 mm is equal to approximately 0.0393701 in, so h becomes approximately 60.2362205 in. Now we substitute these values into the equation and solve for r as follows: 2.2 x 104 = 1/3πr²*60.2362205. Solving for r we get r = approximately 9.14401 in.

We obtain the diameter by doubling the radius, so the diameter d = 2r = 18.28802 in.

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Answer:

the probability that Ron will get hit by a pitch exactly once is 36.71%

Step-by-step explanation:

The random variable X= number of times Ron is hits by pitches in 23 plate appearances  follows ,a binomial distribution. Where

P(X=x) = n!/(x!*(n-x)!)*p^x*(1-p)^x

where

n= plate appearances =23

p= probability of being hit by pitches = 21/602

x= number of successes=1

then replacing values

P(X=1) = 0.3671 (36.71%)

The probability that Ron will get hit by a pitch exactly once in his 23 playoff plate appearances, given his regular season hit rate, is approximately 0.37 or 37%.

The subject of this problem is probability; it's asking us to calculate the chances of a specific event happening. It is given that during the regular season, Ron was hit by pitches 21 times out of 602 plate appearances. Thus, the probability of him getting hit by a pitch is 21/602, or approximately 0.035.

In the playoffs, he has 23 plate appearances. We want to find the probability that he gets hit exactly once. This is a binomial probability problem, using the formula:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

Where n is the number of trials (plate appearances), k is the number of successes we want (getting hit by the pitch), p is the success probability, and C(n, k) is the combination operator. Substituting the given values:

P(X=1) = C(23, 1) * (0.035^1) * ((1-0.035)^(23-1))

Performing this calculation gives a pitch hitting probability of about 0.37 or 37%, which means Ron is likely to be hit by one pitch during the 23 plate appearances in the playoffs.

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Answer:

S ={(1+1=2), (1+2=3), (1+3=4), (1+4=5), (1+5=6), (1+6=7),

     (2+1=3), (2+2=4),(2+3=5),(2+4=6),(2+5=7),(2+6=8),

     (3+1=4), (3+2=5),(3+3=6),(3+4=7),(3+5=8),(3+6=9),

     (4+1=5), (4+2=6),(4+3=7),(4+4=8),(4+5=9),(4+6=10),

     (5+1=6), (5+2=7),(5+3=8),(5+4=9),(5+5=10),(5+6=11),

     (6+1=7), (6+2=8),(6+3=9),(6+4=10),(6+5=11),(6+6=12)}

Step-by-step explanation:

By definition the sample space of an experiment "is the set of all possible outcomes or results of that experiment".

For the case described here: "Toss a six-sided die twice and record the sum of the results".

Assuming that we have a six sided die with possible values {1,2,3,4,5,6}

The sampling space denoted by S and is given by:

S ={(1+1=2), (1+2=3), (1+3=4), (1+4=5), (1+5=6), (1+6=7),

     (2+1=3), (2+2=4),(2+3=5),(2+4=6),(2+5=7),(2+6=8),

     (3+1=4), (3+2=5),(3+3=6),(3+4=7),(3+5=8),(3+6=9),

     (4+1=5), (4+2=6),(4+3=7),(4+4=8),(4+5=9),(4+6=10),

     (5+1=6), (5+2=7),(5+3=8),(5+4=9),(5+5=10),(5+6=11),

     (6+1=7), (6+2=8),(6+3=9),(6+4=10),(6+5=11),(6+6=12)}

The possible values for the sum are 2,3,4,5,6,7,8,9,10,11,12

Answer:

a) There are 10 different samples of size 2.

b) See the explanation section

c) See the explanation section

Step-by-step explanation:

a) We need to select a sample of size 2 from the given population of size 5. We use combination to get the number of difference sample.

[tex]\{ {{5} \atop {2}} \} = \frac{5!}{2!(5-2)!} \\= \frac{5!}{2!3!} \\= \frac{120}{2*6} \\= \frac{120}{12} \\=10[/tex]

b) Possible sample of size 2:

Peter Hankish 8 Connie Stallter 6 Juan Lopez 4 Ted Barnes 10 Peggy Chu 6

c) The mean of the population is:

[tex]mean = \frac{(8+6+4+10+6)}{5} \\= \frac{34}{5} \\= 6.8[/tex]

Comparing the mean of the population and the sample; we can say that most of the 2-size sample have their mean higher than that of the population sample. And the variation with the mean is not much. Some sample have their mean greater than population mean, while some sample have their mean greater than the population mean.

This question is based on the statistics. Therefore, the answers of all the  questions are explained below.

Given:

There are five sales associates at Mid-Motors Ford. Sales Associate Cars Sold Peter Hankish 8 Connie Stallter 6 Juan Lopez 4 Ted Barnes 10 Peggy Chu 6.

(a) We have to find different samples of size 2 are possible.

Thus, we have to select sample of size 2 from given population of size 5.

So, by using combination,

[tex]5_{c_2} = \dfrac{5!}{2! (5-2)!} =\dfrac{120}{12} = 10[/tex]

Thus, 10  different samples of size 2 are possible.

(b) We have to find list all possible samples of size 2, and compute the mean of each sample.

Peter Hankish 8 ,Connie Stallter 6, Juan Lopez 4, Ted Barnes 10, Peggy Chu 6.

(c) The mean of the population is:

[tex]Mean = \dfrac{8+6+4+10+6}{5}\\\\Mean = \dfrac{34}{5}\\\\Mean = 6.8[/tex]

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Answer:

b. 0.6592 and 0.7044

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence interval [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

A survey of an urban university showed that 750 of 1,100 students sampled attended a home football game during the season. This means that [tex]n = 1100, p = \frac{750}{1100} = 0.6818[/tex]

90% confidence interval

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6818 - 1.645\sqrt{\frac{0.6818*0.3182}{1100}} = 0.6592[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6818 + 1.645\sqrt{\frac{0.6818*0.3182}{1100}} = 0.7044[/tex]

So the correct answer is:

b. 0.6592 and 0.7044

Answer:

a. $1773.82

b. $1592.1

Step-by-step explanation:

1. If he pays k dollar in the first year, then the amount that he owned without interest is

7277 - k

The amount that he owned including interest of 11% in the 2nd year is

(7277 - k)*1.11 or 7277*1.11 - 1.11k

After 2nd year and paying k then the amount he owned (without interest is)

(7277 - k)*1.11 - k

With interest

[(7277 - k)*1.11 - k]1.11 or [tex]7277*1.11^2 - 1.11^2k - 1.11k[/tex]

So after 5 years

[tex]7277*1.11^5 - (1.11^5 + 1.11^4 + 1.11^3 + 1.11^2 +1.11)k[/tex]

[tex]12262.17 - 6.91 k[/tex]

Since he's dept-free after 5 year then

[tex]12262.17 - 6.91 k = 0[/tex]

[tex]k = 12262.17 / 6.91 = 1773.82[/tex] dollar

2. The total amount he would have to pay over 5 years is 5k = 5*1773.82 = 8869.1

So the interest we has to pay over 5 years is the total subtracted by the principal, which is 8869.1 - 7277 = 1592.1 dollar

Answer:

P(O|R)

Step-by-step explanation:

The conditional probability notation of two events A and B can be written as either P(A|B) or P(B|A).

The '|' sign is read as 'given'. So, P(A|B) is read as the probability of event A given event B which implies that it is the probability that event A will occur given that event B has already occurred.

In the question,

Event R = Person lives in the city of Raleigh

Event O = Person is over 50 years old

The statement says, 'given that the person lives in Raleigh' which means that event R has already occurred and we need to find the probability of event O (the randomly chosen person is over 50 years old).

Hence, this statement can be given in conditional probability notation as

P(O|R)

The question pertains to conditional probability (P(O|R)) and requires specific data to calculate the probability that a randomly chosen person is over 50 years old given they live in Raleigh.

The student is asking about the concept of conditional probability, which in this case refers to the probability of a randomly chosen person being over 50 years old, given that they live in Raleigh. To express this mathematically, we say P(O|R), which means the probability of event O occurring given that event R has occurred.

To find this probability, one would typically use information from a study or a survey giving population counts or percentages of those over 50 within the city of Raleigh population. Without specific data, one cannot provide a precise probability value.

However, the concept is important in probability theory and widely applied across different domains.

Answer:

d = 7.51 cm

θ = 60°

Step-by-step explanation:

The baffle used in the notch of a whistle is a triangular baffle (Isosceles triangle OAB).

For the isosceles triangle, the sides with equal dimension are OA and OB which is represented with d

d = the vertical component of the side of a triangle

It is given by

6.5cm = d sin60

d = 6.5/sin60

d = 7.505553499465134

d = 7.51 cm -------- Approximated

To calculate angle θ

Angle on a straight line is = 180

So, 60 + 60 + θ = 180

θ= 180 - 120

θ = 60°

(See attachments below)

Answer:

There is a 50% probability that its total life will exceed 20,000 miles.

Step-by-step explanation:

To solve this question, we use the following formula:

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]

In which P(A|B) is the probability of A happening, given that B has happened, [tex]P(A \cap B)[/tex] is the probability of A and B happening, and P(B) is the probability of B happening.

In this problem, we want:

The probability of the total life of the car battery exceeding 20,000 miles, given that it exceeded 10,000 miles.

[tex]P(A \cap B)[/tex] is the probability of exceeding 20,000 and 10,000 miles. It is the same as the probability of exceeding 20,000 miles(If it exceeded 20,000 miles, necessarily it will have exceeded 10,000 miles). So [tex]P(A \cap B) = 0.4[/tex]

P(B) is the probability of exceeding 10,000 miles. So [tex]P(B) = 0.8)[/tex]

So

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.4}{0.8} = 0.5[/tex]

There is a 50% probability that its total life will exceed 20,000 miles.

Final answer:

If a new car battery is still working after 10,000 miles, the probability that its total life will exceed 20,000 miles is 0.5 or 50%.

Explanation:

The question pertains to conditional probability, which is the probability of an event occurring given that another event has already occurred. Here, we are asked to find the probability that a new car battery will exceed 20,000 miles given that it has already functioned for more than 10,000 miles. This question essentially requires us to calculate conditional probability.

Given:

To find the conditional probability that its total life will exceed 20,000 miles given it has already worked for over 10,000 miles (P(B|A)), we use the formula:

P(B|A) = P(B & A) / P(A)

However, since any battery that has functioned for more than 20,000 miles must have also functioned for more than 10,000 miles, P(B & A) = P(B), hence:

P(B|A) = 0.4 / 0.8 = 0.5

Therefore, if a new car battery is still working after 10,000 miles, the probability that its total life will exceed 20,000 miles is 0.5 or 50%.

Answer:

At least 95% of data falls between 4 and 20.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 12

Standard deviation = 4

At least what percent of data falls between 4 and 20?

4 = 12 - 2*4

So 4 is two standard deviations below the mean

20 = 12 + 2*4

So 20 is two standard deviations above the mean

By the Empirical Rule, at least 95% of data falls between 4 and 20.

Answer:

I would say No

Step-by-step explanation:

3/4 = .75

like 3 quarters

.75 about .963 no its not its about .2 away

There's no such concept as "close" in mathematics. Or at least, you have to specify when you consider two numbers to be "close".

All we can say is that, since 3/4=0.75, the two numbers are

[tex]0.963-0.75=0.213[/tex]

units apart. Is this small enough to consider them as "close"? Is this big enough to consider them not to be "close"?

You should clarify more what you mean so that a definitive answer can be given.

Answer:

Explanation below.

Step-by-step explanation:

For this case we have the following dataset:

46, 16, 41, 26, 22 ,33, 30, 22 ,36, 34,

63, 21, 26, 18, 27, 24, 31, 38, 26, 55,

31,  47, 27, 43 ,35, 22 ,64,40, 58, 20,

49, 37, 53, 25, 29, 32, 23, 49, 39, 40,

24, 56, 30, 51, 21, 45, 27, 34, 47, 35

So we have 50 values. The first step on this case would be order the dataset on increasing way and we got:

16, 18, 20, 21, 21, 22, 22, 22, 23, 24,

24, 25, 26, 26, 26, 27, 27, 27, 29, 30

30, 31, 31, 32, 33, 34, 34, 35, 35, 36,

37, 38, 39, 40, 40, 41, 43, 45, 46, 47,

47, 49, 49, 51, 53, 55, 56, 58, 63, 64

We can find the range for this dataset like this:

[tex] Range = Max-Min = 64-16 =48[/tex]

Then since we need 7 classes we can find the length for each class doing this:

[tex] W = \frac{48}{7}=6.86[/tex]

And now we can define the classes like this and counting how many observations lies on each interval we got the frequency:

  Class           Frequency      Midpoint           RF                   CF

________________________________________________

[16-22.86)              8               19.43         (8/50)=0.16           0.16

[22.86-29.71)         11              26.29        (11/50)=0.22          0.38

[29.71-36.57)         11               33.14         (11/50)=0.22          0.6

[36.57-43.43)         7               40.0          (7/50)=0.14           0.74

[43.43-50.29)        6               46.86        (6/50)=0.12          0.86

[50.29-57.14)         4               53.72        (4/50)=0.08         0.94

[57.14-64]               3               60.57        (3/50)=0.06           1.0

________________________________________________

Total                         50                                         1.00

RF= Relative frequency. CF= Cumulative frequency

The relative frequency was calculated as the individual frequency for a class divided by the total of observations (50)

The mid point is the average between the limits of the class.

And the cumulative frequency is calculated adding the relative frequencies for each class.

Answer:

For the first case we are going to assume that the order matters, on this case 6, H is not the same as H,6

The sampling space denoted by S and is given by:

S ={(1,H), (2,H),(3,H),(4,H),(5,H),(6,H),

     (1,T), (2,T), (3,T),(4,T),(5,T),(6,T),

     (H,1), (H,2),(H,3), (H,4),(H,5),(H,6),

     (T,1), (T,2),(T,3), (T,4), (T,5),(T,6)}  

If we consider that (5,H) is equal to (H,5) "order no matter" then we will have just 12 elements in the sampling space:

S ={(1,H), (2,H),(3,H),(4,H),(5,H),(6,H),

     (1,T), (2,T), (3,T) , (4,T), (5,T),(6,T)}  

Step-by-step explanation:

By definition the sample space of an experiment "is the set of all possible outcomes or results of that experiment".

For the case described here: "Toss a coin and a six-sided die".

Assuming that we have a six sided die with possible values {1,2,3,4,5,6}

And for the coin we assume that the possible outcomes are {H,T}

For the first case we are going to assume that the order matters, on this case 6, H is not the same as H,6

The sampling space denoted by S and is given by:

S ={(1,H), (2,H),(3,H),(4,H),(5,H),(6,H),

     (1,T), (2,T), (3,T),(4,T),(5,T),(6,T),

     (H,1), (H,2),(H,3), (H,4),(H,5),(H,6),

     (T,1), (T,2),(T,3), (T,4), (T,5),(T,6)}  

If we consider that (5,H) is equal to (H,5) "order no matter" then we will have just 12 elements in the sampling space:

S ={(1,H), (2,H),(3,H),(4,H),(5,H),(6,H),

     (1,T), (2,T), (3,T) , (4,T), (5,T),(6,T)}  

Answer:

a) 50,000 bottles

b) x = 45

Step-by-step explanation:

We are given the following in the question:

The annual revenue of sun block depends on how much they sell.

Let x be the quantity of 5 oz. bottles of sun block that they make and sell each year measured in 1000 's of bottles.

For x = 10,

10,000 bottles were made and sell each year.

For x = 25,

25,000 bottles of sun block were made and sell each year.

a) x = 50

[tex]\text{Number of bottles} = 50\times 1000 = 50,000[/tex]

Thus, 50,000 bottles of sun block does Scura make and sell.

b) Scura produces and sells 45000 bottles of sunblock

We have to find the value of x

[tex]x = \displaystyle\frac{\text{Number of bottles}}{1000} = \frac{45000}{1000} = 45[/tex]

Thus, x = 45 if Scura produces and sells 45000 bottles of sunblock.

For Scura's Sunblock Sales, if x=50, they sell 50,000 bottles, and when Scura sells 45,000 bottles of sunblock, x equals 45.

a. If x=50, then according to the relationship given where x represents thousands of bottles, Scura makes and sells 50,000 bottles of sun block.

b. To determine what x is equal to when Scura produces and sells 45,000 bottles of sunblock, we take the total number of bottles and divide by 1000, since x is measured in 1000s. So, x=45 when Scura produces and sells 45,000 bottles of sunblock.

Answer:

There is no enough evidence to claim that the average cost of accesories is different from $3,000.

Step-by-step explanation:

The significance level for this test is α=0.05.

The classical method is based on regions of rejection of acceptance, according to the sample parameter. In this case, the standard deviation of the population is unknown.

The null and alternative hypothesis are:

[tex]H_0: \mu=3000\\\\ H_a: \mu\neq 3000[/tex]

This is a two-tailed test, with significance level of 0.05.

The t-value for this sample is:

[tex]t=\frac{x-\mu}{s/\sqrt{N}} =\frac{3256-3000}{2300/\sqrt{50}}=\frac{256}{325}=0.787[/tex]

The degrees of freedom are:

[tex]df=n-1=50-1=49[/tex]

For df=49 and α=0.05 (two-tailed test), the critical values are [tex]|t|>2.009[/tex], so the value t=0.787 is within the acceptance region.

The null hypothesis can not be rejected.

Answer:

It will take 50,000 years to accumulate 5 centimeters of clay.

Step-by-step explanation:

The relationship between millimeter and centimer is that:

1ml = 0.1cm

So

How many ml are 5 cm?

1 ml - 0.1cm

x ml - 5cm

[tex]0.1x = 5[/tex]

[tex]x = \frac{5}{0.1}[/tex]

[tex]x = 50[/tex] ml

Clay on the deep seafloor accumulates at a rate of about 1 millimeter per 1,000 years. How long would it take to accumulate 5 centimeters of clay?

5cm is 50 ml.

1 ml per 1000 years.

So

1 ml - 1000 years

50 ml - x years

[tex]x = 50*1000[/tex]

[tex]x = 50,000[/tex]

It will take 50,000 years to accumulate 5 centimeters of clay.

Answer:

It will take 50000 years to accumulate 5 centimeters of clay.

Step-by-step explanation:

Clay on the deep seafloor accumulates at a rate of about 1 millimeter per 1,000 years. To determine the amount of time it will take to accumulate 5 centimeters of clay, we would convert 5 centimeters to millimeters.

1 centimeter = 10 millimeters

5 centimeters = 5 × 10 = 50 millimeters

Therefore,

If 1 millimeter = 1000 years,

Then, 50 millimeters = 50 × 1000 =

50000 years.

Answer:

The Absolute Error is the difference between the actual and measured value.

[tex]Absolute \:error = |Actual \:value - Measured \:value|[/tex]

The Relative Error is the Absolute Error divided by the actual measurement.

[tex]Relative \:error = \frac{Absolute \:error}{Actual \:value}[/tex]

We know that the actual value is 102.0 mg/dL.

To find the absolute error and relative error for each measurement made by the glucose monitor you must use the above definitions.

a) For a concentration of 104.5 mg/dL the absolute error and relative error are

[tex]Absolute \:error = \left|102-104.5\right|\\Absolute \:error =\left|-2.5\right|\\Absolute \:error =2.5[/tex]

[tex]Relative \:error = \frac{2.5}{102.0}=0.0245[/tex]

b) For a concentration of 96.2 mg/dL the absolute error and relative error are

[tex]Absolute \:error = \left|102.0-96.2\right|\\Absolute \:error =\left|5.8\right|\\Absolute \:error =5.8[/tex]

[tex]Relative \:error = \frac{5.8}{102.0}=0.0569[/tex]

c) For a concentration of 102.2 mg/dL the absolute error and relative error are

[tex]Absolute \:error = \left|102.0-102.2\right|\\Absolute \:error =\left|-0.2\right|\\Absolute \:error =0.2[/tex]

[tex]Relative \:error = \frac{0.2}{102.0}=0.00196[/tex]

d) For a concentration of 98.3 mg/dL the absolute error and relative error are

[tex]Absolute \:error = \left|102.0-98.3\right|\\Absolute \:error =\left|3.7\right|\\Absolute \:error =3.7[/tex]

[tex]Relative \:error = \frac{3.7}{102.0}=0.0363[/tex]

e) For a concentration of 101.8 mg/dL the absolute error and relative error are

[tex]Absolute \:error = \left|102.0-101.8\right|\\Absolute \:error =\left|0.2\right|\\Absolute \:error =0.2[/tex]

[tex]Relative \:error = \frac{0.2}{102.0}=0.00196[/tex]

Answer:

[tex]$ \frac{\textbf{1.55}}{\textbf{1}} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{x}}{\textbf{3.5}} $[/tex]

Step-by-step explanation:

Let us assume that the total cost of the grapes = x $.

Given that it costs 1.55 $ for one pound. We are asked to determine how much it would cost for 3.5 pounds.

note that for one pound you pay 1.55 so how much should you pay for 3.5 pounds? Clearly, the cost increases with the increase in weight of the item.

This is equal to [tex]$ \frac{1.55}{1} \times 3.5 = x $[/tex]

[tex]$ \iff \frac{1.55}{1} = \frac{x}{3.5} $[/tex]

Hence, the answer.

Final answer:

To find the work needed to pump all of the water to the top of the tank, we need to calculate the potential energy at the half-full level and the top of the tank. By using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height, we can calculate the potential energy for each level and find the difference. The work needed is approximately 41 million mega-joules.

Explanation:

To calculate the work needed to pump all the water to the top of the tank, we need to find the potential energy of the water at the half-full level and the potential energy of the water at the top of the tank. The potential energy of an object is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

Given that the tank is half full, the height of the water column is 18/2 = 9 meters. The radius of the tank is 4 meters, so the volume of the water is πr^2h = π(4^2)(9) = 144π cubic meters. The mass of the water is density × volume = 1000 × 144π = 144,000π kg.

The potential energy at the half-full level is PE = mgh = 144,000π × 9 × 9.8 = 12,931,200π joules. The potential energy at the top of the tank is PE = mgh = 144,000π × 18 × 9.8 = 25,862,400π joules. Therefore, the work needed to pump all the water to the top of the tank is the difference in potential energy = 25,862,400π - 12,931,200π = 12,931,200π joules. To convert to mega-joules, divide by 1,000,000, so the work needed is approximately 41 million mega-joules.

Answer:

Let's make a couple of assumptions to clarify the situation.  First, the coin flipping is fair, that is, each flip is independent of all the others and for each flip, the probabilities of heads and tails are both 1/2.  Second, you have enough money to pay me no matter how many tails are flipped before the first head.

Under those assumptions, the expected amount of money I will win in infinite.  

In decision theory, utility is often used to make decisions rather than money. If my utility is proportional to expected monitory payoff, I should pay whatever I can scrape up, my total assets.  For some reason, economists often assume utility functions have deminishing returns, and eventually flatten out.

In that case, the expected amount of utility payoff will be lower than the maximum utility.  What does that mean for this game?  It means it won't matter to me whether I get some large quantity of money like a trillion dollars, or any larger quantity of money, like a quadrillion dollars.  All my needs are met by a trillion dollars.  That's 240 dollars.  So I certainly shouldn't pay more than $40 to play the game.  As the utility function starts to flatten out earlier, perhaps $30 would come out to be a fair payment.

Answer:

addition tioin multiplication

Step-by-step explanation:

Using the given data, the coefficient of variation is 30% which matches option b.

Complete Question :

The hourly wages of a sample of 130 system analysts are given below. mean = 60 range = 20 mode = 73 variance = 324 median = 74. The coefficient of variation equals a. 0.30%. b. 30% O c. 5.4% d. 54%.

Answer: area = 5,456

Answer:

5456 sq. inches

Step-by-step explanation:

Let width = w,

Then length = w + 26

Perimeter = 2[length + width]

2[(w +26) + w] = 2[2w + 26] = 4w + 52

Perimeter given is 300

So, 4w + 52 = 300

4w = 248

w = 248/4 =62

length = 62 + 26 = 88

Area = length × width

Area = 88 × 62 = 5456 sq. inches

Answer:

a. The price that should be charged if the demand is 40 million gallons is $20.25.

b. The demand decreases by 16 millions of gallons.

Step-by-step explanation:

We know that the price-demand equation for gasoline is given by

[tex]0.1 x + 4 p = 85[/tex]

where

p is the price per gallon in dollars and

x is the daily demand measured in millions of gallons.

a. To find what price should be charged if the demand is 40 million gallons you must

Solve for p,

[tex]0.1x\cdot \:10+4p\cdot \:10=85\cdot \:10\\x+40p=850\\40p=850-x\\p=\frac{850-x}{40}[/tex]

We know that the demand is 40 million gallons (x = 40). So,

[tex]p=\frac{850-40}{40}=\frac{81}{4}=20.25[/tex]

b. To find how much does the demand decrease when the price increases by $0.4 you must

Solve for x,

[tex]0.1x\cdot \:10+4p\cdot \:10=85\cdot \:10\\x+40p=850\\x=850-40p[/tex]

We know that the price increases by $0.4. So,

[tex]-40\left(0.4\right)=-16[/tex]

The demand decreases by 16 millions of gallons.

When the demand is 40 million gallons, the price per gallon should be $20.25. The impact of a $0.4 price increase on the demand can be calculated by substitifying p in the equation, solving for x, and subtracting the original x value.

The subject of this question is algebra, specifically dealing with the use of equations representing real-world scenarios. In this case, the equation represents price-demand dynamics for gasoline.

a. To find the price that should be charged when the demand is 40 million gallons, substitute x with 40 in the equation, which gives 0.1 * 40 + 4p = 85. By simplifying this, we get 4 + 4p = 85. Further solving for p, we get 4p = 81, therefore p = 81 / 4, which is $20.25 per gallon.

b. When the price increases by $0.4, substitute p with p + 0.4 in the equation. This gives 0.1x + 4(p + 0.4) = 85. Solving this for x, and then subtracting the original x value, gives us the decrease in demand due to the increase in price.

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Answer:

The variance is 2.5.

Step-by-step explanation:

Let X = number of visitors in a museum.

The random variable X has an average of  5 visitors per 2 minutes.

Then in 1 minute the average number of visitors is, [tex]\frac{5}{2} =2.5[/tex]

The random variable X follows a Poisson distribution with parameter λ = 2.5.

The variance of a Poisson distribution is:

[tex]Variance=\lambda[/tex]

The variance of this distribution is:

[tex]V(X)=\lambda=2.5[/tex]

Thus, the variance is 2.5.

Answer:

The question is lacking the image of the histogram, but the file attachment to this answer contains the complete question and histogram image.

The percentage of the rats that navigated the maze in less than 5.5 minutes is 84%

Step-by-step explanation:

First of all let us compute the total frequency which represents the total number of rats in the experiment.

from the information given in the question, we are told that the total number of rats involved in the experiment are 25 rats and this makes up the total frequency.

To calculate the percentage of rats that navigated the maze in less than 5.5 minutes, you will first of all need to identify the 5.5 minute point on the histogram and add all the frequencies below that point. This gives the total number of rat that navigated in less than 5.5 minutes. These frequencies from 0 to <5.5 are; 3, 8, 6, and 4. And the total is given as the sum of these frequencies shown below:

Total number of rats that navigated in less than 5.5 minutes = 3 + 8 + 6 + 4 = 21. Hence, a total of 21 rats navigated the maze in less than 5.5 minutes.

Now to find the percentage of the number of rats that navigated in less than 5.5 minutes, we have to find out what percentage of 25 (total number of rats) is 21 (number of rats that navigated in less than 5.5 minutes). This is calculated thus:

[tex]\frac{21}{25}[/tex] × 100 = 0.84 × 100 = 84 %.

Therefore 84% of the total number of rats navigated the maze in less than 5.5 minutes in the experiment.

To find the percentage of rats that navigated the maze in less than 5.5 minutes, locate the bar on the histogram that represents that interval and calculate the percentage based on the number of rats in that interval compared to the total number of rats.

The histogram shows the times required for 25 rats to navigate a maze. To find the percentage of rats that navigated the maze in less than 5.5 minutes, we need to look at the data on the histogram. The histogram is divided into various time intervals, and the bars represent the number of rats that fall into each interval. You need to locate the bar that corresponds to the interval less than 5.5 minutes and calculate the percentage of rats represented by that bar.

Let's say the bar for the interval less than 5.5 minutes represents 10 rats. To calculate the percentage, we divide the number of rats in that interval (10) by the total number of rats (25) and multiply by 100:

(10/25) x 100 = 40%

Therefore, 40% of the rats navigated the maze in less than 5.5 minutes.

Answer:

The probability that of the 3 households randomly selected at least 1 owns a sports car is 0.1956.

Step-by-step explanation:

Let X = number of household owns a sports car.

The probability of X is, P (X) = p = 0.07.

Then the random variable X follows a Binomial distribution with n = 3 and p = 0.07.

The probability function of a binomial distribution is:

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

Compute the probability that of the 3 households randomly selected at least 1 owns a sports car:

[tex]P(X\geq 1)=1-P(X<1)\\=1-P(X=0)\\=1- {3\choose 0}(0.07)^{0}[1-0.07]^{3-0}\\=1-0.8044\\=0.1956[/tex]

Thus, the probability that of the 3 households randomly selected at least 1 owns a sports car is 0.1956.

Answer:

two-thirds

Step-by-step explanation:

In 2015, there was a campaign for the accumulation of households in the United States of America. Most of the citizens tried their best possible to acquire property in terms of buildings and other facilities. In the last quarter of the year, approximately two-thirds of the home in the United States of America were owned by households.

The given points

[tex](-3, 0)[/tex]

[tex](-2, 2)[/tex]

[tex](0, 1)[/tex]

[tex](1, -2)[/tex]

Imply that

[tex]f(-3)=0[/tex]

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

[tex]f(0)=1[/tex]

[tex]f(1)=-2[/tex]

Answer:

f(2) = -1.

Step-by-step explanation: