Luis’s cedar chest measures 4 feet long, 2 feet wide, and 2 ¼ feet high. What is the volume of the chest?

Answers

Answer 1

Answer:

[tex]4 {ft}^{3} [/tex]

Step-by-step explanation:

[tex]2 \times \frac{1}{4} = 0.5 \\ v = lbh \\ 4 \times 2 \times 0.5 \\ = 8 \times 0.5 \\ = 4 {ft}^{3} [/tex]

Answer 2

The volume of Luis’s cedar chest is 18 cubic feet.

The dimensions of Luis’s cedar chest are length=4 feet, width=2 feet and height=2 1/4 feet.

What is the formula to find the volume of the cuboid?

The volume of the cuboid is the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height. If we have a rectangular sheet and we go on stacking such sheets, we will end up getting a shape that has some length, breadth, and height.

The formula to find the volume of the cuboid is l×b×h.

Where, l=length, b=breadth or width and h=height.

Now, volume=4×2×2.25=18 cubic feet.

Therefore, the volume of Luis’s cedar chest is 18 cubic feet.

To learn more about the volume of the cuboid visit:

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Related Questions

Johnny and a robot standing 5 melo (units of length) apart (in a flat area) on the
planet Rote. They spot a flying object hovering in the sky at the same time. If the
angle of elevation from Johnny to the flying object is 29°, and the angle of elevation
from the robot to the flying object is 42°, find the distance from the flying object to
the ground. For this problem, assume that the heights of Johnny and the robot are
neligible. [8 marks]

Answers

Answer:

distance from the flying object to

the ground

= 7.2 melo(unit of measurement)

Step-by-step explanation:

The distance between the robot and Jo is 5 melo( unit Of measurement)

Let the distance between the flying object and the ground= y

Let's the remaining length of the closest between robot and Jonny and the ground be x.

Y/(x+5)= tan 29.... equation 1

Y/x= tan 42.... equation 2

Equating the value of y

Tan 29(x+5) = tan42(x)

Tan29/tan 42 = x/(x+5)

0.61562(x+5)= x

3.0781= x- 0.61562x

3.0781= 0.38438x

3.0781/0.38438= x

8.008= x

8= x

Y/x= tan 42

Y/8= 0.9004

Y= 7.203

Y= 7.2 melo (unit of measurement )

Use the two highlighted points to find the
equation of a trend line in slope-intercept
form.

Answers

Answer: y=(4/3)x+2/3

Step-by-step explanation:

Slope-intercept form is expressed as y=mx+b

First, find the slope (m):

m= rise/run or vertical/horizontal or y/x (found between the highlighted points)

m = 4/3

Second, find b:

Use one of the highlighted points for (x, y)

2=4/3(1)+b

6/3=4/3+b

2/3=b

b=2/3

Plug it into the equation:

You get y=(4/3)x+2/3 :)

A random sample of 1400 Internet users was selected from the records of a large Internet provider and asked whether they would use the Internet or the library to obtain information about health issues. Of these, 872 said they would use the Internet

1. The standard error ˆp SE of the proportion pˆ that would use the Internet rather than the library is:_______

a. 0.013.
b. 0.25.
c. 0.485.
d. 0.623.

2. If the Internet provider wanted an estimate of the proportion p that would use the Internet rather than the library, with a margin of error of at most 0.02 in a 99% confidence interval, how large a sample size would be required? (Assume that we don’t have any prior information about p).

a. 33
b. 3909
c. 2401
d. 4161

Answers

Answer:

1   [tex]\sigma_{\= x } = 0.0130[/tex]

2  [tex]n = 3908.5[/tex]

Step-by-step explanation:

From the question we are told that

     The  sample size is  [tex]n_p = 1400[/tex]

      The  number of those that said the would use internet is [tex]k = 872[/tex]

       The margin of error is  [tex]E = 0.02[/tex]

Generally the sample proportion is mathematically evaluated as

            [tex]\r p = \frac{k}{n_p}[/tex]

substituting values

            [tex]\r p = \frac{ 872}{1400}[/tex]

substituting values

           [tex]\r p = 0.623[/tex]

Generally the standard error of  [tex]\r p[/tex] is mathematically evaluated as

           [tex]\sigma_{\= x } = \sqrt{\frac{\r p (1- \r p)}{n} }[/tex]

substituting values

              [tex]\sigma_{\= x } = \sqrt{\frac{0.623 (1- 0.623)}{1400} }[/tex]

              [tex]\sigma_{\= x } = 0.0130[/tex]

For  a  95% confidence interval the confidence level is  95%

Given that the confidence interval is 95% the we can evaluated the level of confidence as

                    [tex]\alpha = 100 - 99[/tex]

                   [tex]\alpha = 1\%[/tex]

                   [tex]\alpha = 0.01[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from normal distribution table (reference math dot  armstrong dot edu) , the value is  

         [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

Give that the population size is very large  the sample size is mathematically represented as

            [tex]n = [ \frac{Z_{\frac{\alpha }{2} ^2 * \r p ( 1 - \r p )}}{E^2} ][/tex]

substituting values  

             [tex]n = [ \frac{2.58 ^2 * 0.623 ( 1 -0.623 )}{0.02^2} ][/tex]

             [tex]n = 3908.5[/tex]

An operator wants to determine the standard deviation for a machine relative to its ability to produce windshield wipers conforming within their specifications. To do this, she wants to create a p-chart. Over a month's time, she tests 100 units every day and records the number of manufacturing defects. The average proportion of non-conforming windshield wipers is found to be 0.042. What is the standard deviation of this sample

Answers

Answer:

the standard deviation of the sample is less than  0.1

Step-by-step explanation:

Given that :

The sample size n = 100 units

The average proportion of non-conforming windshield wipers is found to be 0.042 which is the defective rate P-bar

The standard deviation of the machine([tex]S_p[/tex]) can be calculated  by using the formula:

[tex]S_p =\dfrac{ \sqrt{ \overline P \times (1 - \overline P)} }{n}[/tex]

[tex]S_p =\dfrac{ \sqrt{0.042 \times (1 -0.042)} }{100}[/tex]

[tex]S_p =\dfrac{ \sqrt{0.042 \times (0.958)} }{100}[/tex]

[tex]S_p =\dfrac{ \sqrt{0.040236} }{100}[/tex]

[tex]S_p =\dfrac{ 0.2005891323 }{100}[/tex]

[tex]S_p =0.002[/tex]

Thus , the standard deviation of the sample is less than  0.1

In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?

Answers

Answer:the mean is greater than the median

Step-by-step explanation:

The mean is less than the median. Then the correct option is A.

What are statistics?

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.

Half the students scored 87.  

The next highest score is 71.

Then the median will be

(71+ 87) / 2 = 79

A few students scored 52, so the mean is slightly lower than the mean of 71 and 87.

Thus, the mean is less than the median.

Then the correct option is A.

The missing options are given below.

A. The mean is less than the median.

B. The mean and the median is the same.

C. The mean is greater than the mode.

D. The mean is greater than the median.

More about the statistics link is given below.

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Can I have help with 43 and 44 I need to see how to do them thanks.

Answers

Answer:

see explanation

Step-by-step explanation:

(43)

3[tex]x^{5}[/tex] - 75x³ ← factor out 3x³ from each term

= 3x³(x² - 25) ← this is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , thus

x² - 25 = x² - 5² = (x - 5)(x + 5)

Thus

3[tex]x^{5}[/tex] - 75x³ = 3x³(x - 5)(x + 5)

(44)

81c² + 72c + 16 ← is a perfect square of the form

(ac + b)² = a²c² + 2abc + b²

Compare coefficients of like terms

a² = 81 ⇒ a = [tex]\sqrt{81}[/tex] = 9

b² = 16 ⇒ b = [tex]\sqrt{16}[/tex] = 4

and 2ab = 2 × 9 × 4 = 72

Thus

81c² + 72c + 16 = (9c + 4)²

1. 3x^5 -75x³

=3x³(x²-25)

=3x³(x²-5²)

=3x³(x-5)(x+5)

2. 81c²+72c+16

=81c²+36c+36c+16

=9c(9c+4)+4(9c+4)

=(9c+4)(9c+4)

=(9c+4)²

According to the Empirical Rule, 99.7% of scores in a normal distribution fall within 2 standard deviations of the mean.

a. True
b. False

Answers

Answer:

False

Step-by-step explanation:

Here, we want to check the validity of the given statement. The statement is false.

Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.

Please check attachment for diagrammatic representation of the empirical rule.

someone please help me

Answers

Answer:

3 mL

Step-by-step explanation:

The fluid level is called the concave meniscus. The adhesive force causes it to crawl up on the sides, but you should ignore that while reading the level.

The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700 t 11,000 The population before construction is 67,000. Determine the projected population 16 yr after construction of the park has begun. people

Answers

Complete question :

The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700√t + 11,000 The population before construction is 67,000. Determine the projected population 16 yr after the construction of the park has begun. people

Answer:

486,200

Step-by-step explanation:

Given that the rate of change in population is represented by the function:

f(t) = 5,700√t + 11,000

To get the original function, we take the integral of the rate function because the rate of change is obtained by taking the derivate of the original equation

f(t) = 5,700t^1/2 + 11,000

Taking the integral of f with respect to t:

∫(5,700t^1/2 + 11,000)

[5700t^(1/2 + 1)] / (1/2 + 1) + 11000t + C

[(5700t^3/2)/ 3/2] + 11000t + C

Where C = constant

If population before construction = 67000

Then C = 67000

t = time = 16 years

Substitute values into the original change equation:

[(5700(16)^3/2)/ 3/2] + 11000t + 67000

[(5700 * 64) / 1.5] + 11000(16) + 67000

243200 + 176000 + 67000

= 486,200

Put 0.9,0.1038,0.10299,0.1037 in order from least to greatest

Answers

Answer: 0.10299,0.1037  ,0.1038 ,0.9

Step-by-step explanation:

In all the numbers we could see that 0.9 is the greatest because it has the greatest tenth value. The rest three have the same tenth value which is one and the same hundredth value which is 0 so we will compare the numbers using  their thousandth values.

In the numbers 0.1038,0.10299, 0.1037   The first one has a thousandth value of 3, the second one has a thousandth value of 2, and the third one has a thousandth value of 3. Which means the first and the second have the same thousandths value so using their last numbers which is 8  and 7 , 8 is greater than 7  so  0.1038  is greater than 0.1037 and 0.10299.  The same way 0.1037 is greater than 0.10299.

So to order them from least to greatest,

0.10299 will be first

0.1037  will be second  

0.1038  will be the third  

0.9  will be the last.

(Least) 0.10299>0.1037>0.1038>0.9 (Greatest)

Shane biked 1 mile less than three times the number of miles Lissette biked. Shane biked a total of 7 miles. Write an equation to determine how many miles Lissette biked.

Answers

Answer:

2.67 miles (or 8/3 miles which is also 3 2/3 miles)

Step-by-step explanation:

S (shane) = 7

L (lissette) = ??

S = 3(L) - 1

7 = 3L - 1

8 = 3L

L = 2.67 miles

Find the vertex of this parabola:
y = x2 + 2x - 3​

Answers

Answer:

(-1,-4)

Step-by-step explanation:

The equation of a parabola os written as: ax^2+bx+c

This parabola's equation is x^2+2x-3

● a= 1

● b= 2

● c = -3

The coordinates of the parabola are: ( (-b/2a) ; f(-b/2a) )

● -b/2a = -2/2 = -1

● f(-b/2a) = (-1)^2+2×(-1)-3=1-2-3= -4

So the vertex coordinates are (-1,-4)

Answer:

-1+2X

Step-by-step explanation:

how many meters are in 250 centimeters

Answers

Answer:

2.5 meters

Step-by-step explanation:

a sheet metal worker earns $26.80 per hour after receiving a 4.5% raise. what was the sheet metal worker's hourly pay before raise? Round your answer to the nearest cent

Answers

Answer

$25.59

Step-by-step explanation:

subtract by percentage or you can also do:

100% - 4.5% = 95.5%

95.5% x $26.80 = $25.594

IF ROUNDED: $25.59

Answer:

$25.65

Step-by-step explanation:

Let the original hourly rate be r.  

Then 1.045r + $26.80/hr.

Dividing both sides by 1.045, we get:

      $26.80/hr

r = ------------------ = $25.65  This was the before-raise pay rate.

         1.045

please help me out! <3

Answers

Answer:

[tex]-1 \frac{3}{4}[/tex]

Step-by-step explanation:

Using this number line, we can plot our original number - [tex]\frac{3}{4}[/tex] (see picture attached)

Adding a negative is the same thing as subtracting - so we are subtracting [tex]2\frac{1}{2}[/tex] from  [tex]\frac{3}{4}[/tex].

To subtract this, we can break up [tex]2\frac{1}{2}[/tex]  into 3 parts: 1, 1, and [tex]\frac{1}{2}[/tex]. We can subtract each of these from the current number and see where we land up. (again see picture)

We land up at [tex]-1 \frac{3}{4}[/tex].

Hope this helped!

A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet.

Required:
Do the results support the manufacturer's claim?

Answers

Complete question is;

A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:

Do the results support the manufacturer's claim?

Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed

Answer:

We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

Step-by-step explanation:

For the first sample, we have;

Mean; x'1 = 1160 ft

standard deviation; σ1 = 32 feet

Sample size; n1 = 19

For the second sample, we have;

Mean; x'2 = 1130 ft

Standard deviation; σ2 = 30 ft

Sample size; n2 = 11

The hypotheses are;

Null Hypothesis; H0; μ1 = μ2

Alternative hypothesis; Ha; μ1 > μ2

The test statistic formula for this is;

z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]

Plugging in the relevant values, we have;

z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]

z = 2.58

From the z-table attached, we have a p-value = 0.99506

This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

How to find which ratio is largest

Answers

In order to check whether its greater than or less than, First You have to make denominator value equal of both ratio value. then we have to make denominator value equal i.e. After that you check which ratio Numerator value is greater.

20.) The area of a circle is given by the equation A = nr2. If the radius of a circle is equal to 6 centimeters,
which of the following is closes to the area of the circle? (Use it = 3.14.)

113.04
18.84
36
28.26

please provide explanation​

Answers

Answer:

113.04 cm^2

Step-by-step explanation:

The area of a circle is

A = pi r^2

We know the radius is 6 cm

A = 3.14 * 6^2

A = 3.14 * 36

A =113.04

If the solutions for a quadratic equation are -2 and 5 what is the equation

Answers

Answer:

f(x) = x^2 - 3x -10

Step-by-step explanation:

If the solutions are {-2, 5}, the factors of the quadratic are (x + 2) and (x - 5).

The equation is f(x) = (x + 2)(x - 5) = x^2 - 3x -10

Find the sum of 1 + 3/2 + 9/4 + …, if it exists.

Answers

Answer:

Option (4)

Step-by-step explanation:

Given sequence is,

[tex]1+\frac{3}{2}+\frac{9}{4}..........[/tex]

We can rewrite this sequence as,

[tex]1+\frac{3}{2}+(\frac{3}{2})^2.............[/tex]

There is a common ratio between the successive term and the previous term,

r = [tex]\frac{\frac{3}{2}}{1}[/tex]

r = [tex]\frac{3}{2}[/tex]

Therefore, it's a geometric sequence with infinite terms. In other words it's a geometric series.

Since sum of infinite geometric sequence is represented by the formula,

[tex]S_{n}=\frac{a}{1-r}[/tex]  , when r < 1

where 'a' = first term of the sequence

r = common ratio

Since common ratio of the given infinite series is greater than 1 which makes the series divergent.

Therefore, sum of infinite terms of a series will be infinite Or the sum is not possible.

Option (4) will be the answer.

Find the general solution of the following differential equation. Primes denote derivatives with respect to x.(x+2y)y'=2x-yleft parenthesis x plus 2 y right parenthesis y prime equals 2 x minus y

Answers

Answer:

[tex]-[ln(x^2-yx-y^2)] = K\\[/tex]

Step-by-step explanation:

Given the differential equation [tex](x+2y)y'=2x-y[/tex], this can also be written as;

[tex](x+2y)\frac{dy}{dx} =2x-y[/tex]

On simplification

[tex](x+2y)\frac{dy}{dx} =2x-y\\\\\frac{dy}{dx} = \frac{2x-y}{x+2y} \\\\let \ y = vx\\\frac{dy}{dx} = v+x\frac{dv}{dx}[/tex]

The differential equation becomes;

[tex]v+x\frac{dv}{dx} =\frac{ 2x-vx}{x+2vx}\\\\v+x\frac{dv}{dx} = \frac{ x(2-v)}{x(1+2v)}\\\\v+x\frac{dv}{dx} = \frac{2-v}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v}{1+2v} - v\\\\x\frac{dv}{dx} = \frac{(2-v)-v(1+2v)}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v-v-2v^2}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-2v-2v^2}{1+2v}[/tex]

[tex]\frac{dx}{x} = \frac{1+2v}{2-2v-2v^2}dv\\\\integrating\ both \ sides\\\\[/tex]

[tex]\int\limits \frac{dx}{x} = \int\limits \frac{1+2v}{2-2v-2v^2}dv\\\\lnx = \frac{1}{2} \int\limits \frac{1+2v}{1-v-v^2}dv\\\\lnx + C = -\frac{1}{2}ln(1-v-v^2)[/tex]

[tex]C = -\frac{1}{2}ln(1-v-v^2) - lnx \\\\ -ln(1-v-v^2) - 2lnx = 2C\\\\-[ln(1-v-v^2) + lnx^2] = 2C\\\\-[ln(1-v-v^2)x^2] = 2C\\since\ v = y/x\\\\- [ln(1-y/x-y^2/x^2)x^2] = K\\\\-[ln(x^2-yx-y^2)] = K\\[/tex]

Hence the solution to the differential equation is [tex]-[ln(x^2-yx-y^2)] = K\\[/tex]

Does anyone know the answers to the graded activities on plato?

Answers

Answer:

Explanation

There are some activities in Courseware content that report scores and some that just report mastery and/or completion status.

Resolution

Dynamic vs. Non-dynamic mastery tests

Mastery tests give mastery status if the score is 80% or higher, but not all tests report a score. There are two types of mastery tests in Courseware content:

Non-dynamic tests: Those that do report a score, such as those in the Writing Process and Practice titles, in the Grammar and Mechanics modules, give the same number of questions each time; these are non-dynamic tests. For example, Splitting Fused Run-ons: Mastery Test presents ten questions. Even if the Learner answers the first three questions incorrectly and is, at that point, no longer able to answer eight correctly to achieve mastery, the remaining seven questions are presented.

Dynamic tests: Mastery tests from some content titles, such as Essential Reading Skills, however, are dynamic, which means they adapt to the Learner's responses. These tests do not always give the maximum number of questions; instead, they will end sooner if 80% is either achieved or no longer achievable. These tests show mastery if 80% or better was achieved, but do not show a score. For example, in Essential Reading Skills, Pronouns: Mastery Test, the maximum number of questions presented is five; mastery requires four questions are answered correctly. The test will end early if the student answers the first four correctly or two incorrectly out of the first four. Mastery is still based on achieving 80% or better, but the score is not fully determined, so no score is reported, by design.

Step-by-step explanation:

Six people attend the theater together and sit in a row with exactly six seats.
a. How many ways can they be seated together in the row?
b. Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people be seated together in the row with the doctor in an aisle seat?
c. Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row?

Answers

Answer

A. 720 ways

B. 240 ways

C. 6 ways

There are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.

What is a permutation?

A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.

It is assumed that six people will attend the theater together and sit in a row of six.

The following are the various ways they can be seated in a row together:

⇒ 6!

⇒ 6 × 5 × 4 × 3 × 2 × 1

⇒ 720

If the doctor sits in the aisle seat, the remaining 5 persons can sit in the remaining 5 seats 5! ways

The total possibilities are as follows:

⇒ 5 × 4 × 3 × 2 × 1

= 120

Consider that the six persons are made up of three married couples.

In addition to the aforementioned, divide the six chairs into three groups of two seats each.

There is one choice in each block for the husband to be placed on the left and the wife to be positioned on the right and the 3 couples can be seated in the 3 blocks in 3! ways.

⇒ 3 × 2 × 1

The required answer is 6.

Thus, there are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.

Learn more about permutation here:

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A box is dragged across 20 meters with a force of 60 Newtons, which are kg*m/s^2

Answers

Answer:

Mass= 6kg

Acceleration= 10 ms^-2

Work done = 1200Nm

Step-by-step explanation:

kg*m/s^2 represent the force.

The kg represent the mass

The m/s^2 represent the acceleration

The acceleration here will be due to gravity force= 10 ms^-2

Then the mass= 60/10

Mass= 6 kg

The force = 60 Newton

Distance covered in the direction of the the force= 20 Meters

The work done in the direction of the force= force* distance

The work done in the direction of the force=60*20

The work done in the direction of the force=1200 Nm

Answer: 20 • 60

Step-by-step explanation:

A shopping centre wants to examine the amount of space required for parking. Studies indicated that 50% of staff and shoppers use public transportation. A survey of 1002 was taken, and 483 responded that they used public transportation. At 5% level of significance, is it reasonable to conclude that the survey results indicate a change?

Answers

Answer:

The survey result doesn't indicate the change

Step-by-step explanation:

Previous study result is 50%

Survey result:

483/1002 = 0.482 = 48.2%

Comparing with previous result:

50% - 48.2% = 1.8% < 5%

Since this result is within 5% level of significance, it can be concluded that the survey result doesn't indicate the change

The isotope of plutonium 238Pu is used to make thermoelectric power sources for spacecraft. Suppose that a space probe was launched in 2012 with 4.0 kg of 238Pu.

Required:
a. If the half-life of 238Pu is 87.7 yr, write a function of the form Q(t)= Q0e- kt.to model the quantity Q(t) of 238Pu left after t-years.
b. If 1.6 kg of 238Pu is required to power the spacecraft's data transmitter, for how long will scientists be able to receive data?

Answers

Answer:

A) Q(t) = 4e^-(0.0079t)

B) t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

Step-by-step explanation:

a)

to write a function of the form Q(t)= Q₀e⁻^kt to model the quantity Q(t) of ²³⁸Pu left after t-years.

so given that; half-life of ²³⁸Pu is 87.7 years,

∴ t =  87.7 years , Q(t) = 0.5Q₀

Now we substitute these value in the form  Q(t)= Q₀e⁻^kt

Q(t)= Q₀e⁻^kt

0.5Q₀ = Q₀e^ -(87.7k)

0.5 = e^ -(87.7k)

now we take the natural logarithm of both sides

In(0.5) = Ine^ -(87.7k)

Now using the property logₙnᵃ = a

-87.7k = In(0.5)

k = - In(0.5) / 87.7

k = 0.0079

ALSO it was given that Q₀ = 4.0 kg

Therefore , model quality Q(t) of ²³⁸pu left after t years is:

Q(t) = 4e^-(0.0079t)

b)

to find the time left after 1.6kg of ²³⁸pu

we simple substitute  Q(t) = 1.6 into Q(t) = 4e^-(0.0079t)

so we have

1.6 = 4e^-(0.0079t)

e^-(0.0079t) = 1.6/4

e^-(0.0079t) = 0.4

again we take the natural logarithm of both sides,

Ine^-(0.0079t) = In(0.4)

again using the property logₙnᵃ = a

-0.0079t = In(0.4)

t = - in(0.4) / 0.0079

t = 115.99 ≈ 116

Therefore scientist will be able to receive data after 116 years

A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.6. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.Required:a. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state?b. What is the probability that in the long run the traffic will not be in the delay state?c. An important assumption of the Markov process model presented here has been the constant or stationary transition probabilities as the system operates in the future. Do you believe this assumption should be questioned for this traffic problem? Explain.

Answers

Answer:

a) 0.36

b) 0.3

c) Yes

Step-by-step explanation:

Given:

Probability of no traffic delay in one period, given no traffic delay in the preceding period = P(No_Delay) = 0.9

Probability of finding a traffic delay in one period, given a delay in the preceding period = P(Delay) = 0.6

Period considered = 30 minutes

a)

Let A be the probability that for the next 60 minutes (two time periods) the system will be in the delay state:

As the Probability of finding a traffic delay in one period, given a delay in the preceding period is 0.6 and one period is considered as 30 minutes.

So probability that for the next two time periods i.e. 30*2 = 60 minutes, the system in Delay is

P(A) = P(Delay) * P(Delay) =  0.6 * 0.6 = 0.36

b)

Let B be the probability that in the long run the traffic will not be in the delay state.

This statement means that the traffic will not be in Delay state but be in No_Delay state in long run.

Let C be the probability of one period in Delay state given that preceding period in No-delay state :

P(C) =  1 - P(No_Delay)

        = 1 - 0.9

P(C) = 0.1

Now using P(C) and P(Delay) we can compute P(B) as:

P(B) = 1 - (P(Delay) + P(C))

      = 1 - ( 0.6 + 0.10 )

      = 1 - 0.7

P(B) = 0.3

c)

Yes this assumption should be questioned for this traffic problem because it implies that  traffic will be in Delay state for the 30 minutes and just after 30 minutes, it will be in No_Delay state. However, traffic does not work like this in general and it makes this scenario unrealistic. Markov process model can be improved if probabilities are modeled as a function of time instead of being presented as constant (for 30 mins).

PLEASE HURRY! i walked north 8 miles, the west 4 miles, and finally south 5 miles, at the end how far was i from where i started

Answers

Answer:

5 miles away

Step-by-step explanation:

If you walked north 8 miles, then west 4 miles, then south 5 miles, you have, in total, travelled 4 miles west and [tex]8-5=3[/tex] miles north.

This creates a triangle, in which we can find the the length of the hypotenuse to find how far away you are now.

We can use the Pythagorean theorem since this is a right triangle.

[tex]a^2+b^2=c^2\\3^2+4^2=c^2\\9+16=c^2\\25=c^2\\c=5[/tex]

Hope this helped!

Answer:

5 miles away

Step-by-step explanation:

How many solutions does the following equation have? -14(z-5)=-14x+70

Answers

Answer:

Infinite amount of solutions

Step-by-step explanation:

Parallel lines have no solution

Same lines have infinite solutions

Intersecting lines have 1 solution

Step 1: Write out equation

-14(x - 5) = -14x + 70

Step 2: Distribute -14

-14x + 70 = -14x + 70

Here we see that we have 2 exact same lines. Therefore, we have infinite amount of solutions.

Alternatively, we can plug in any number x and it would work. So then we would have infinite amount of solutions as well.

Find out the Time Zone for UAE and its neighboring countries. Express them as positive or negative rational numbers with reference to Greenwich Mean Time. Note down the time of few of your daily activities such as breakfast, school time, lunch time, etc. Compare the same time with GMT.anyone please answer this.

Answers

Answer:

UAE is in the Gulf Standard Time zone.

It is GMT + 4

Breakfast: 7 am; GMT 3 am

School time 8 am: GMT 4 am

Lunch time: 12:30 pm; GMT 8:30 am

Step-by-step explanation:

UAE is in the Gulf Standard Time zone.

It is GMT + 4

Breakfast: 7 am; GMT 3 am

School time 8 am: GMT 4 am

Lunch time: 12:30 pm; GMT 8:30 am

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