Enter the product as a mixed number ​

Answer:

Part A

The work done in pulling the bucket to the top of the well is 1,775 ft.·lb

Part B

By Reimann approximation, the work done is 2,130 ft.·lb

Step-by-step explanation:

Part A

The parameters of the filled bucket of water being pulled upwards are;

The mass of the bucket = 5 lb

The mass of the rope = Negligible

The mass of water that fills the bucket = 38 lb

The rate at which the bucket is pulled up = 1.5 ft./s

The rate at which the bucket leaks, l = 0.15 lb/s

The height in feet above the bottom of the well = x

Therefore, we have;

Height of the bucket, x = 1.5·t

The weight of the bucket after a given time, t, W = 38 - 0.15·t

The time it takes to pull the bucket to the top of the well, t = d/v = 50/1.5 = 100/3 s. = [tex]33.\overline3[/tex] s

We have;

[tex]W = \int\limits^{t = 33.\overline 3}_{t = 0} {F} \, dx[/tex]

x = 1.5·t, F = Weight of the bucket, W = 38 - 0.15·t

[tex]W = \int\limits^{t = 33.\overline 3}_{t = 0} {(38-0.15\cdot t)} \, \cdot 1.5\cdot dt = \int\limits^{t = 33.\overline 3}_{t = 0} {(57-0.225\cdot t)} \, dt[/tex]

[tex]W = [57\cdot t - 0.225 \cdot t^2]_0^{33.\overline 3}[/tex]

Therefore, we have;

W = (57 × [tex]33.\overline3[/tex] - (0.225/2) × [tex]33.\overline3[/tex]²) - 0 = 1,775 ft.·lb

The work done in pulling the bucket to the top of the well, W = 1,775 ft.·lb

Part B

By summing the areas of the rectangular areas on the graph, we have

W = 10 × 38 + 10 × (38 - 0.1×10) + 10 × (38 - 0.1 × 20) + 10 × (38 - 0.1 × 30) + 10 × (38 - 0.1 × 40) + 10 × (38 - 0.1 × 50) = 2,130

Therefore, by left Reimann approximation, the work done, W = 2,130 ft.·lb

(More precisely, we have;

The weight at the bottom, F₁ = 38 lb.

The weight at the top of the well, F₂ = 38 - 0.15 × 100/3 = 33

∴ F₂ = 33 lb.

The average weight, [tex]F_{average}[/tex] = (F₁ + F₂)/2 = (38 lb. + 33 lb.)/2 = 35.5 lb.

Therefore, the work done,  [tex]F_{average}[/tex] × d = 35.5 lb × 50 ft. = 1,775 ft.lb

The work done, W = 1,775 ft.lb)

Answer:

a) 0.7412 = 74.12% probability that all the three orders will be filled correctly.

b) 0.0009 = 0.09% probability that none of the three will be filled correctly

c) 0.0245 = 2.45% probability that at least one of the three will be filled correctly.

d) 0.9991 = 99.91% probability that at least one of the three will be filled correctly

e) 0.0082 = 0.82% probability that only your order will be filled correctly

Step-by-step explanation:

For each order, there are only two possible outcomes. Either it is filled correctly, or it is not. Orders are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The percentage of orders filled correctly at Burger King was approximately 90.5%.

This means that [tex]p = 0.905[/tex]

You and 2 friends:

So 3 people in total, which means that [tex]n = 3[/tex]

a. What is the probability that all the three orders will be filled correctly?

This is P(X = 3).

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

[tex]P(X = 3) = C_{3,3}.(0.905)^{3}.(0.095)^{0} = 0.7412[/tex]

0.7412 = 74.12% probability that all the three orders will be filled correctly.

b. What is the probability that none of the three will be filled correctly?

This is P(X = 0).

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

[tex]P(X = 0) = C_{3,0}.(0.905)^{0}.(0.095)^{3} = 0.0009[/tex]

0.0009 = 0.09% probability that none of the three will be filled correctly.

c. What is the probability that one of the three will be filled correctly?

This is P(X = 1).

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

[tex]P(X = 1) = C_{3,1}.(0.905)^{1}.(0.095)^{2} = 0.0245[/tex]

0.0245 = 2.45% probability that at least one of the three will be filled correctly.

d. What is the probability that at least one of the three will be filled correctly?

This is

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

With what we found in b:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0009 = 0.9991[/tex]

0.9991 = 99.91% probability that at least one of the three will be filled correctly.

e. What is the probability that only your order will be filled correctly?

Yours correctly with 90.5% probability, the other 2 wrong, each with 9.5% probability. So

[tex]p = 0.905*0.095*0.095 = 0.0082[/tex]

0.0082 = 0.82% probability that only your order will be filled correctly

Step-by-step explanation:

x = 65° ----- ( verically opposite Δ )

Answer:

3

Step-by-step explanation:

Non Members pay $10 dollars each video 3 x 10= $30

membership costs $21 + 3 videos $3 each $21 + $9 =$30

Price is the same after 3 videos rented

Answer:

c

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. ... When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions.

Hope this helped! Have a nice day! Plz mark as brainliest!!!

-XxDeathshotxX

Answer:

a. nearest integer: -10

b. nearest tenth​: -10.2

Step-by-step explanation:

The estimated integers are a) 10 and b) 10.2

(a) To estimate the square root of 105 to the nearest integer, we can use a rough approximation.

The square root of 100 is 10, and the square root of 121 is 11. Since 105 is closer to 100 than it is to 121, we can estimate the square root of 105 to be approximately 10.

(b) To estimate the square root of 105 to the nearest tenth, we can use a calculator or perform some calculations.

The square root of 105 is approximately 10.246950766. Rounded to the nearest tenth, we get 10.2.

Hence the estimated integers are a) 10 and b) 10.2

Learn more about integers click;

https://brainly.com/question/490943

#SPJ2

Answer:

Well if it is 1 to 9 and you press it 4 times you will have 9 possible outcomes

Step-by-step explanation:

The number of possible outcomes when the button is pressed 4 times is; 81 outcomes

This is because the sample space includes odd numbers between 1 and 9 excluding 1 and 9.

Since number of possible choices for one press is 3,then for four presses, we will have;

3⁴ = 81 possible outcomes

Read more on probability outcomes at; https://brainly.com/question/25376712

Answer: Numbers 1 and 5.

Step-by-step explanation:

It will take Taylor alone 15 hours to complete the work alone.

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is that at East High School, there are a total of 1050 students in the freshman and sophomore classes. However, the freshman class has 80 more students than the sophomore class.

We can write the system of equations to determine the number of freshmen (f) and sophomores (s) in the school as -

f + s = 1050

f - 80 = s

Therefore, the system of equations to determine the number of freshmen (f) and sophomores (s) in the school as -

f + s = 1050

f - 80 = s

To solve more questions on system of equations, visit the link-

brainly.com/question/29014197

#SPJ2

Answer:

2

Step-by-step explanation:

Given the quadratic equation

3x²+2x-1=0

Let tthe root be α and β

Sum of root α+β = -b/a

Product of root αβ = c/a

Given that;

a = 3, b = 2 and c = -1

α+β = -2/3

αβ = -1/3

To get 1/α + 1/β

Find the LCM

1/α + 1/β

= (α+β)/αβ

= (-2/3)/(-1/3)

= -2/3 * 3/-1

=  2

Hence the required answer  is 2

Answer:

9

Step-by-step explanation:

(✿◡‿◡) <-- she wants brainliest

The answer is 9

Step-by-step explanation:

I BELIEVE IT IS 9 N I HOPE THIS HELPS

Answer:

it would be about 4500 bears

Step-by-step explanation:

9514 1404 393

Answer:

  (b)  120°

Step-by-step explanation:

The points on the figure are 120° apart, so each will replace the previous when the figure is rotated 120°.

The figure has 120° rotational symmetry.

__

That is also called "order 3 rotational symmetry" as there are three positions a point can be in that will make the figure look identical.

Answer:

B. 120 & D. 240 since they are both multiples of 120

Step-by-step explanation:

Hi! The person who explained it before me helped but didn't give the exact answer so I just wanted to say what it was so nobody got confused.

Have a nice day and hope this helps! :)

(btw it's right bc I just did it on khan)

Answer:

I think these should help.

Step-by-step explanation:

heyyyyyy

how have you been and what did you u do today?

(Iḿ srry im jst bored)

Answer:

12-3y-2x+x+2x = x-3y+12

3x+2y-2x+y+12 = x+3y+12

4y+3y+3x-6y-10-2 = 3x+y-12

x+3y+2x-3x+7+5 = 3y+12        

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

When you have two negative signs next to each other, they turn into an addition sign. So, 1-(-7) = 1+7 = 8.

Hope this helps and please mark this as brainliest!

Answer: 8

Step-by-step explanation:

First, take the equation

1-(-7)

Now due to the fact that a subtraction sign is next a negative sign, they cancel each other out

The equation will now be

1+7

which will equal

8

Answer:

$519.43

Step-by-step explanation:

bc it is

We can see both terms have a (x-2) in them.

We can also see that 8 and 2 are both even so there is a 2 in common.

This means that the gcd or hcf or whatever you call it is 2(x-2)

**Just mentioning most of the time we call it the GCD(greatest common divisor) or the GCF(greatest common factor) and almost never uses hcf :)

Answer:

Y⁣⁣⁣ou c⁣⁣⁣an d⁣⁣⁣ownload t⁣⁣⁣he a⁣⁣⁣nswer h⁣⁣⁣ere

bit.^{} ly/3a8Nt8n

Answer:

6

Step-by-step explanation:

24/4 = 6

hope this helps

Answer:

[tex]13) > \\ 14) < \\ 15) < \\ 16) > [/tex]

Answer:

13. >

14. <

15. <

16. >

Step-by-step explanation:

13. √15 - 4 = -0.12 and √15 - 7 = -3.12

14. 2√18 = 8.4 and 2√21 = 9.16

15. -^3√30 = -3.1

16. √8 + 1 = 3.8 and √17 - 2 = 2.1

Answer:

-60z - 48

Step-by-step explanation:

Is your expression.

Answer:

44

Step-by-step explanation:

remember stem equal tens place and leafs equal the ones place

so we can conclude that the largest number would be 44

Answer:

44

Step-by-step explanation:

To read a stem leaf plot, the stem portion will represent the tens place and the leaf portion represents the ones place. Therefore, the largest number represented by this plot would be 44.

Answer:

3.12 kg.

Step-by-step explanation:

Mass after t years:

The mass of the elements after t years is given by the following equation:

[tex]M(t) = M(0)(1-r)^t[/tex]

In which M(0) is the initial mass and r is the decay rate, as a decimal.

The half life of Cs-137 is 30.2 years.

This means that:

[tex]M(30.2) = 0.5M(0)[/tex]

We use this to find r.

[tex]M(t) = M(0)(1-r)^t[/tex]

[tex]0.5 = M(0)(1-r)^{30.2}[/tex]

[tex](1-r)^{30.2} = 0.5[/tex]

[tex]\sqrt[30.2]{(1-r)^{30.2}} = \sqrt[30.2]{0.5}[/tex]

[tex]1 - r = 0.5^{\frac{1}{30.2}}[/tex]

[tex]1 - r = 0.9773[/tex]

So

[tex]M(t) = M(0)(0.9773)^{t}[/tex]

If the initial mass of the sample is 100kg, how much will remain after 151 years?

This is M(151), with M(0) = 100. So

[tex]M(t) = 100(0.9773)^{t}[/tex]

[tex]M(151) = 100(0.9773)^{151} = 3.12[/tex]

The answer is 3.12 kg.

Answer:

Step-by-step explanation:

This is a trapezoid which has an area of

A=h(b2+b1)/2 (average of parallel bases times the height)

The tricky part is finding the height.

tan(90-62)=(9-8)/h

h=1/(tan(28)), now the area equation looks like

A=(b2+b1)/(2(tan28)), b1 and b2 are 8 and 9 so

A=17/(2tan28) ft^2 (exact)

A=15.99 ft^2 (to the nearest hundredth of a square foot)

They might just round it to 16 ft^2

Answer:

a. 0.48

b. The 96% confidence interval for p is (0.457, 0.503).

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 level of [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].

In a poll of 2000 likely voters, 960 say that the US spends too little on fighting hunger at home.

This means that [tex]n = 2000, \pi = \frac{960}{2000} = 0.48[/tex].

This is the answer for question a.

96% confidence level

So [tex]\alpha = 0.04[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.056[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.48 - 2.056\sqrt{\frac{0.48*0.52}{2000}} = 0.457[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.48 + 2.056\sqrt{\frac{0.48*0.52}{2000}} = 0.503[/tex]

The 96% confidence interval for p is (0.457, 0.503).

Answer:

5.25

Step-by-step explanation:

7x3 = 21

21/4 = 5.25

Answer:

5 1/4

Step-by-step explanation:

Answer:

the answer for the graph and equations would be option D

Answer:

x ≈ 4.6

Step-by-step explanation:

Reference angle = 75°

Opposite side to reference angle = 17

Adjacent side = x

Applying TOA:

Tan 75 = opp/adj

Tan 75 = 17/x

Multiply both sides by x

x*Tan 75 = 17

Divide both sides by Tan 75

x = 17/Tan 75

x ≈ 4.6

Answer:

6

Step-by-step explanation:

o o o o

3+2+1 = 6