Given the similar figures above what is the value of w?

To find the work done in pumping the entire contents of the fuel tank into the tractor, we need to calculate the potential energy difference between the initial position of the gasoline in the truck's tank and its final position in the tractor's tank.

Given:

- Diameter of the cylindrical gasoline tank: 4 feet

- Length of the cylindrical gasoline tank: 5 feet

- Opening on the tractor tank is 5 feet above the top of the tank in the truck

First, let's calculate the volume of the cylindrical gasoline tank using the formula for the volume of a cylinder:

Volume = π * (radius^2) * height

The radius of the tank is half the diameter, so the radius is 4 feet / 2 = 2 feet.

Volume = π * (2^2) * 5 = 20π cubic feet

Since the entire contents of the fuel tank need to be pumped, the volume of gasoline to be pumped is 20π cubic feet.

To calculate the work done in pumping the gasoline, we need to find the vertical height through which the gasoline is lifted. This height is the sum of the height of the tank and the distance between the top of the tank and the opening on the tractor tank.

Height = 5 feet + 5 feet = 10 feet

The work done in pumping the gasoline can be calculated using the formula:

Work = Force × Distance

In this case, the force is the weight of the gasoline, and the distance is the height through which it is lifted. To calculate the weight of the gasoline, we need to know the density of gasoline. The density of gasoline can vary, but an average value is around 6.3 pounds per gallon.

Let's convert the volume of gasoline from cubic feet to gallons:

1 cubic foot = 7.48052 gallons (approximately)

Volume in gallons = 20π * 7.48052 ≈ 149.61π gallons

Weight of gasoline = Volume in gallons * Density of gasoline

Assuming the density of gasoline as 6.3 pounds per gallon:

Weight of gasoline = 149.61π * 6.3 ≈ 940.06π pounds

Finally, we can calculate the work done:

Work = Weight of gasoline * Height

Work = 940.06π * 10 ≈ 9400.6π foot-pounds

Therefore, the work done in pumping the entire contents of the fuel tank into the tractor is approximately 9400.6π foot-pounds.

Learn more about Work here:

https://brainly.com/question/29050812

#SPJ11

Answer:

1. e

2. d

3. b

4. c

Step-by-step explanation:

Hope This Helps!

Plz Mark Brainliest!

Answer:

32/24

Step-by-step explanation:

opposite/ adjacent

Answer:

32/24

Step-by-step explanation:

the value of the test statistic is -1.48. This indicates that there is a significant difference in gas expenses between diesel truck owners and regular gas truck owners, as the t value is negative and falls outside the range of values expected if there were no difference between the means.

In this scenario, we have two samples - one of diesel truck owners and one of regular gas truck owners - and we want to compare the mean gas consumption in one week between the two groups using an independent-samples t test.The mean gas consumption for diesel truck owners is $68 and for regular gas truck owners is $84. We can calculate the difference between the means as follows:
$84 - $68 = $16
The pooled variance can be calculated using the following formula:
pooled variance = [(n1-1)*s1^2 + (n2-1)*s2^2]/(n1+n2-2)
Substituting the values we have:
pooled variance = [(n1-1)*s1^2 + (n2-1)*s2^2]/(n1+n2-2)
pooled variance = [(n1-1)*(6.9)^2 + (n2-1)*(21.74)^2]/(n1+n2-2)
pooled variance = (4*(6.9)^2 + 4*(21.74)^2)/(8-2)
pooled variance = 232.80
The degrees of freedom total is simply the sum of the degrees of freedom for the two samples:
degrees of freedom total = n1 + n2 - 2
degrees of freedom total = 4 + 4 - 2
degrees of freedom total = 6
Now we can calculate the test statistic using the following formula:
t = (x1 - x2) / (sqrt(sp^2/n1 + sp^2/n2))Where x1 and x2 are the sample means, sp^2 is the pooled variance, and n1 and n2 are the sample sizes. Substituting the values we have:
t = (68 - 84) / (sqrt(232.80/4 + 232.80/4))
t = -16 / (sqrt(58.20 + 58.20))
t = -16 / (sqrt(116.40))
t = -16 / 10.79
t = -1.48 (rounded to two decimal places)

Learn more about  test statistic here:

https://brainly.com/question/31746962

#SPJ11

Answer:

$1.94 per square inch

The values of p, q, and r are p = 2, q = 5, and r = 3, respectively.

Given that the lowest common multiple (LCM) of A and B is 2250, and the prime factorization of A is A = 2 × p × q¹, and the prime factorization of B is B = 2 × p² × q², we can compare the prime factorizations to determine the values of p, q, and r.

From the prime factorization of 2250 (2 × 3² × 5³), we can observe the following:

The prime factor 2 appears in both A and B.

The prime factor 3 appears in A.

The prime factor 5 appears in A.

Comparing this with the prime factorizations of A and B, we can deduce the following:

The prime factor p appears in both A and B, as it is present in the common factors 2 × p.

The prime factor q appears in both A and B, as it is present in the common factors q¹ × q² = q³.

From the above analysis, we can conclude:

p = 2

q = 5

r = 3.

For similar question on lowest common multiple.

https://brainly.com/question/16054958  

#SPJ8

Answer:

35 and 37

Step-by-step explanation:

hope it helps :)))

Answer:

35+37

Step-by-step explanation:

Basic odd numbers go as shown

1,3,5,7,9,11....

Let the first number be x and the second number be x + 2

x+ (x+2) =72

2x+2=72

2x=72-2

2x=70

x=70/2

x=35

Add 2 to find the other number or simply subtract 35 from 70

Anyway this gives you 37

Making your 2 answers 35 and 37

Answer:

c x=3

Step-by-step explanation:

I did the math for it

The candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.

The given table shows the height of a candle as it burns continuously over time. The first column represents time in hours, ranging from 0 to 1, while the second column represents the corresponding height in centimeters.

From the data, we can observe that the candle starts at a height of 25 centimeters when the time is 0 hours. As time progresses, the height of the candle decreases gradually. Specifically, for every hour that passes, the candle burns 0.625 centimeters.

Therefore, the main answer is that the candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.

Learn more about Height

brainly.com/question/21982748

#SPJ11

Answer:

Answer: (1,-7)

Step-by-step explanation:

since the translation is under (x + 4, y - 2)

the symbols (+ and -) would change so the translation to use would be

(x - 4, y + 2)

so you plug in (5, -9) to the new translation and you get your answer which is (1,-7)

Answer:

x = 8

Step-by-step explanation:

a² + b² = c²

x² + 15² = 17²

x² + 225 = 289

x² = 289 - 225

x² = 64

\(\sqrt{x^2} =\sqrt{64}\)

x = 8

Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Learn more about multiplication at https://brainly.com/question/10873737

#SPJ1

Answer:

1/18

Step-by-step explanation:

1/6 * 1/3

1 *1 = 1

6 * 3 = 18

1/18

Answer:

0.05555555555555

Step-by-step explanation:

You can try rounding it

Answer: No although the expressions are equivalent by the distribute property, it is not in simplest form because when we combine 6.5x and 3.25x as they are like terms the simplified expression is 9.75x + 6.5

Step-by-step explanation: hope this helps

Answer:

19

Step-by-step explanation:

-8+8=0

0+19=19

Hope it helps.

Answer:

19

Step-by-step explanation:

I just took the quiz

Answer:

who's asking?

Step-by-step explanation:

Answer:

Step-by-step explanation:So we know x + y = 21 and 5x +10y = 165 We line them up in columns    x +   y =   21  5x +10y = 165 To eliminate the x variable, I'll multiply every element in the 1st equation by -5. -5x + -5y = -105  5x + 10y =  165 Now we combine (add) the equations, which eliminates x altogether.  5y = 60   ...   y = 12 From there, x + 12 = 21  ...  x = 21-12  ...  x = 9 You should double check.  Do 9 nickles and 12 dimes equal $1.65? A very important thing to remember using this method is to do the same thing to each element in the equation that you change! I hope that helps.

The solution for x in the equation is x = 2b/(2a - c)

The equation is given as

2ax - b = cx + b

Collect the like terms in the above equation

So, we have the following equation

2ax - cx = b + b

Evaluate the like terms in the above equation

So, we have the following equation

2ax - cx = 2b

Factor out x from the equation

x(2a - c) = 2b

Divide both sides by 2a - c

x = 2b/(2a - c)

Hence, the solution for x is x = 2b/(2a - c)

Read more about subject of formula at

https://brainly.com/question/10643782

#SPJ1

If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two

When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.

Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .

To know more about linear regression, click here

https://brainly.com/question/32505018

#SPJ11

The success rates of the three treatments in preventing cardiac events are approximately 90.91% for the stress management program, 79.41% for the exercise program, and 70% for usual heart care.

a. Two-way table:
| Treatment | Cardiac Events | No Cardiac Events |
|-----------|-----------------|----------------------|
| Stress Management | 3 | 30 |
| Exercise | 7 | 27 |
| Usual Care | 12 | 28 |
b. The success rates of the three treatments in preventing cardiac events can be calculated as the percentage of people in each group who did not experience a cardiac event.
- Stress management: 90.9% success rate (30/33)
- Exercise: 79.4% success rate (27/34)
- Usual care: 70% success rate (28/40)
Therefore, the stress management program had the highest success rate in preventing cardiac events, followed by the exercise program and then usual care.

Stress management and its impact on reducing heart attacks. Let's analyze the study results and create a two-way table, as well as calculate the success rates of the three treatments in preventing cardiac events.
a. Two-way table:
| Treatment          | Cardiac Events | No Cardiac Events | Total |
|--------------------|----------------|-------------------|-------|
| Stress Management  | 3              | 30                | 33    |
| Exercise Program   | 7              | 27                | 34    |
| Usual Heart Care   | 12             | 28                | 40    |
| Total              | 22             | 85                | 107   |
b. Success rates of the three treatments in preventing cardiac events:
1. Stress Management:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (30 / 33) * 100
Success rate ≈ 90.91%
2. Exercise Program:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (27 / 34) * 100
Success rate ≈ 79.41%
3. Usual Heart Care:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (28 / 40) * 100
Success rate = 70%

Visit here to learn more about cardiac events:

brainly.com/question/27524618

#SPJ11

Answer:

1a. y= -6x+30

1b. y= -6x-22

2a. y= 3x+2

2b. y= -1x+4

The probability that Ella's 10th roll is her last roll is 31/108, or approximately 0.2870.

To find the probability that Ella's 10th roll is her last roll, we need to consider the following:

The last roll must be a repeat of the previous roll, so the previous roll cannot be the first roll or the 6th roll, because there is no previous roll in those cases.

Ella must not have rolled the same number on consecutive rolls before her 10th roll.

The probability of rolling the same number on consecutive rolls is 1/6, so the probability of not rolling the same number on consecutive rolls is 5/6.

Let's break down the probability of Ella's 10th roll being her last roll by considering the different cases:

Case 1: Ella's 8th roll is the first roll of a pair, and her 9th roll is the second roll of that pair.

In this case, Ella cannot roll the same number on consecutive rolls, so the probability of her 10th roll being her last roll is simply 1/6.

Case 2: Ella's 8th roll is the first roll of a pair, but her 9th roll is not the second roll of that pair.

In this case, Ella must roll a number different from her 9th roll, and then roll the same number as her 9th roll on her 10th roll.

The probability of rolling a different number on her 9th roll is 5/6, and the probability of rolling the same number on her 10th roll is 1/6.

Therefore, the probability of her 10th roll being her last roll in this case is (5/6)*(1/6) = 5/36.

Case 3: Ella's 8th roll is not the first roll of a pair, but her 9th roll is the second roll of a pair.

In this case, Ella must roll a number different from her 8th roll, and then roll the same number as her 8th roll on her 9th roll.

The probability of rolling a different number on her 8th roll is 5/6, and the probability of rolling the same number on her 9th roll is 1/6.

Therefore, the probability of her 10th roll being her last roll in this case is (5/6)*(1/6) = 5/36.

Case 4: Ella's 8th roll is not the first roll of a pair, and her 9th roll is not the second roll of a pair.

In this case, Ella must roll a number different from both her 8th and 9th rolls, and then roll the same number as her 9th roll on her 10th roll.

The probability of rolling a different number on her 8th roll is 5/6, the probability of rolling a different number on her 9th roll, given her 8th roll, is 4/6, and the probability of rolling the same number as her 9th roll on her 10th roll is 1/6.

Therefore, the probability of her 10th roll being her last roll in this case is (5/6)(4/6)(1/6) = 5/54.

To find the total probability, we need to sum the probabilities from each case:

1/6 + 5/36 + 5/36 + 5/54 = 31/108.

For similar question on probability.

https://brainly.com/question/27774105

#SPJ11

Answer:

Gradient=¾

Step-by-step explanation:

Write the equation in slope-intercept form y=mx+c

3x-4y=24

-4y=24-3x

y=24/-4-3x/-4

y=-6+¾x

y=¾x-6

The gradient is therefore ¾

The y-intercept of the line occurs at(0,-6)

The x-intercept of the line occurs at(8,0)

Finding the midpoint of the two intercepts

{(x1+x2)/2,(y1+y2)/2}

M={0+8/2,(-6+0/2)}

M={8/2,-6/2}

M=(4,-3)

As you can see, the other information was not required to solve it

Given the polynomial function h(x) = 3x³ - 7x² - 22x+8a) Possible rational zeroes of h(x)When the polynomial is written in descending order, its leading coefficient is 3. We write down all the possible rational roots in the form of fractions:± 1/1, ± 2/1, ± 4/1, ± 8/1, ± 1/3, ± 2/3, ± 4/3, ± 8/3

The denominators are factors of 3, and the numerators are factors of 8.b) Finding all the zeros. The rational root theorem states that if a polynomial function has a rational root p/q, where p is a factor of the constant term and q is a factor of the leading coefficient, then p/q is a zero of the polynomial function. Using synthetic division, we get the following information:3 | 3 - 7 - 22 8| 1 - 2 - 8 03 | 1 - 2 - 8 | 0 - 0This means that x = -1, 2, and 8/3 are the zeros of the polynomial function h(x).Therefore, all the zeros of h(x) are -1, 2, and 8/3.

To know more about polynomial visit :-

https://brainly.com/question/11536910

#SPJ11

25463 grams radioactive kind of americium will be left after 2160 years.

We know that Half Life Formula will be,

\(N=I(\frac{1}{2})^{\frac{t}{T}}\)

where N is the quantity left after time 't'; 'T' is the half life of the substance and 'I' is the initial quantity of the substance.

Given that the initial quantity of the substance (I) = 814816 grams

Half life of the radioactive kind of americium is (T) = 432 years

The time elapsed (t) = 2160 years

Now we have to find the quantity left that is the value of N for the given values.

N = \(814816\times(\frac{1}{2})^{\frac{2160}{432}}=814816\times(\frac{1}{2})^5\) = 814816/32 = 25463 grams.

Hence 25463 grams radioactive kind of americium will be left after 2160 years.

To know about half life formula here

https://brainly.com/question/25750315

#SPJ1

The radius of the cylindrical shaped soup can is r = 3.3 cm

Given data ,

A company is designing a soup can that is in the shape of a right circular cylinder. The height of the can will be 3 times the radius of the can. The volume of the can will be 350 cubic centimeters

Now , Volume of Cylinder = πr²h

where h = 3r

On simplifying , we get

350 = πr²3r

350 = 3πr³

Divide by 3π on both sides , we get

r³ = 37.13615

Taking cube root on both sides , we get

r = 3.3 cm

Hence , the radius of soup can is r = 3.3 cm

To learn more about cylinder click :

https://brainly.com/question/16134180

#SPJ1

Answer:

first graph: m = 3

second graph:

m=-5/2

Step-by-step explanation:

You can pick out nice points from the graph, any two points and calculate slope:

m = y-y / x-x

see image. For first graph.

But you can also SEE the slope (and just count squares) look for those nice points on the graph and count how far up(or down) and how far over to the next nice point.

On the first graph, find a nice point. Then see it is 3UP and 1OVER to the next point. 3UP1OVER gets you to the next point and the next.

3UP1OVER is the slope 3/1. This is the slope m = 3.

On the second graph, from one point to the next is 5DOWN2OVER.

5DOWN2OVER is the slope -5/2.

Lines with negative slope go down from left to right.