How much power is needed to get up the stairs, if I can do this with 30 Joules of work in 3 seconds?

To fidn the surface area of the grain tank you need to find the area of:

Cylinder (without one of the bases as there are just one base exposed), use the next formula:

You have for the given cylinder:

h=12ft

r: as the diameter is 8.4ft the radius is 8.4tf/2=4.2ft

Cone (without the base as the base is not exposed), use the next formula:

You have for the given cone:

r= 4.2ft

s= 5.5ft

The entire exposed surface of the tank is:

Answer:

let p be the number of pages in the entire book. If she read 70% of the book, that means she read .70p.

But the second sentence said she read 84 pages. Well that means these 2 quantities must be equal....so,

.70p = 84

a) A and B are independent events.

b) The outcome of each game is independent of the other games so, Rachel's loss = p.

c) The probability of all marbles being red is 4

a) Given that a first marble is red and the second marble is also red, such that

P(1) = P(2) = 0.2, P(3) = P(5) = P(6) = 0.1 and P(4) = 0.3 and die is thrown two times. Also given that:

A1 = red

B1 = red.

So, P(A) = [P(1, 1) + P(2, 2) + P(3, 3) + P(4, 4) + P(5, 5) + P(6, 6)]

= P(1).P(1) + P(2).P(2) + P(3).P(3) + P(4).P(4) + P(5).P(5) + P(6).P(6)

= 0.2 x 0.2 + 0.2 x 0.2 + 0.1 x 0.1 + 0.3 x 0.3 + 0.1 x 0.1 + 0.1 x 0.1

= 0.04 + 0.04 + 0.01 + 0.09 + 0.01 + 0.01 = 0.20

Now, B = [(4, 6), (6, 4), (5, 5), (5, 6), (6, 5), (6, 6)]

P(B) = [P(4).P(6) + P(6).P(4) + P(5).P(5) + P(5).P(6) + P(6).P(5) + P(6).P(6)]

= 0.3 x 0.1 + 0.1 x 0.3 + 0.1 x 0.1 + 0.1 x 0.1 + 0.1 x 0.1 + 0.1 x 0.1

= 0.03 + 0.03 + 0.01 + 0.01 + 0.01 + 0.01 = 0.10

A and B both events will be independent if

P(A ⋂ B) = P(A).P(B) …. (i)

And, here (A ⋂ B) = {(5, 5), (6, 6)}

So, P(A ⋂ B) = P(5, 5) + P(6, 6) = P(5).P(5) + P(6).P(6)

= 0.1 x 0.1 + 0.1 x 0.1 = 0.02

From equation (i) we get,

0.02 = 0.20 x 0.10

0.02 = 0.02

Therefore, we can say that A and B are independent events.

b) We know that the outcome of each game is independent of the other games. Rachel's loss = p. As per the given information, the games in the series are unrelated, indicating the application of the probability multiplication principle.

c) The probability of all marbles being red is 4

Let a be the probability that the first player (ultimately) wins if the two players are tied in wins. Let b be the probability that she wins if she is 1 ahead. And let c be the probability she wins if she is 1 behind. We have the equations

a = rb + 1 - r x c

b = r + 1 - r x a

c = r x a

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Answer:

10 lattes and 23 cappuccinos were sold.

Step-by-step explanation:

Given that one day, a café sells 3 more than twice the number of cappuccinos as they do lattes, and they sold a total of 33 cappuccinos and lattes together, to determine which equation could be used to find the number of lattes that were sold at the coffee the following calculation must be carried out:

Latte = X

Cappuccino = 2X + 3

X + 2X + 3 = 33

3X + 3 = 33

3X = 33 - 3

X = 30/3

X = 10

Latte = 10

Cappuccino = 2 x 10 + 3 = 23

Therefore, 10 lattes and 23 cappuccinos were sold.

Answer:

x = 15

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.

To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:

Maximize Z = 4x1 + 7x2 + x3 + LP

The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.

The initial constraints remain the same:

2x1 + 3x2 + x3 = 20

3x1 + 4x2 + x3 + x4 = 40

8x1 + 5x2 + 2x3 - x5 = 70

The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.

The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:

x3 = 20

x4 = 40

The initial artificial variable LP's value is set to 0.

Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.

The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.

This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.

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ANSWER

EXPLANATION

To reflect the triangle over the x-axis, the x-coordinates of the vertices remain the same, and the y-coordinates change to their opposites. Thus, to draw the image, we have to draw auxiliary vertical lines across each vertex of triangle LMN and graph the image of each vertex at the same distance from the x-axis on the opposite side,

Answer:

Sure! Let’s solve this equation step by step.

(7000).03 + (x).05=830

First, we can simplify the left side of the equation:

210 + 0.05x = 830

Next, we can subtract 210 from both sides:

0.05x = 620

Finally, we can divide both sides by 0.05 to solve for x:

x = 12400

So the solution to the equation (7000).03 + (x).05=830 is x = 12400.

Answer:

Smallest perimeter setup is (6 by 6 rectangle)

Step-by-step explanation:

Given:

Total number of tile = 36

Find:

Smallest perimeter setup

Computation:

Perimeter = 2(a + b)

So,

Perimeter if (4 by 9 rectangle )

Perimeter if (4 by 9 rectangle ) = 2[4+9]

Perimeter if (4 by 9 rectangle ) = 2[13]

Perimeter if (4 by 9 rectangle ) = 26

Perimeter if (3 by 12 rectangle )

Perimeter if (3 by 12 rectangle ) = 2[3+12]

Perimeter if (3 by 12 rectangle ) = 2[15]

Perimeter if (3 by 12 rectangle ) = 30

Perimeter if (1 by 36 rectangle )

Perimeter if (1 by 36 rectangle ) = 2[1+36]

Perimeter if (1 by 36 rectangle ) = 2[37]

Perimeter if (1 by 36 rectangle ) = 74

Perimeter if (6 by 6 rectangle )

Perimeter if (6 by 6 rectangle ) = 2[6+6]

Perimeter if (6 by 6 rectangle ) = 2[12]

Perimeter if (6 by 6 rectangle ) = 24

So,

Smallest perimeter setup is (6 by 6 rectangle)

The dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: h = (36 - x^2) / 8x = (√3)/2 feet

Let the length and width of the base be x, and let the height be h.

The surface area of the top is x^2, and the surface area of the remaining four sides is \(2(xh + xh) = 4xh\).

The cost of the top is \(x^2\), and the cost of the remaining four sides is \(2(4xh) = 8xh\). Therefore, the total cost is:

\(C(x,h) = x^2 + 8xh\)

We know that the total cost is $36, so we have:

\(x^2 + 8xh = 36\)

Solving for h, we get:

\(h = (36 - x^2) / 8x\)

The volume of the box is given by:

\(V(x,h) = x^2h\)

Substituting h in terms of x, we get:

\(V(x) = x^2 ((36 - x^2) / 8x)\)

Simplifying, we get:

\(V(x) = (1/8) x (36x - x^3)\)

To find the dimensions of the box that will have the greatest volume, we need to find the value of x that maximizes V(x). We can do this by taking the derivative of V(x) with respect to x, setting it equal to 0, and solving for x:

\(V'(x) = (1/8) (36 - 3x^2) = 0\)

Solving for x, we get:

x = 2√3

Therefore, the dimensions of the box that will have the greatest volume are:

Length and width of the base: 2√3 feet

Height: \(h = (36 - x^2) / 8x\) = (√3)/2 feet

The volume of the box is:

\(V = x^2h\)= (2√3)^2 ((√3)/2) = 9√3 cubic feet

Note: To confirm that this value represents the maximum volume, we can check that V''(x) < 0, which indicates a maximum point. We have:

\(V''(x) = (1/8) (-6x) = -3x/4\)

At x = 2√3, V''(x) = -3(2√3)/4 = -3√3/2 < 0, so this is indeed a maximum point.

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The total area of the back and side walls that should be painted is 57 square meters.

To calculate the total area of the back and side walls that need to be painted, we need the dimensions of the walls. Let's assume we have the following dimensions:

Back Wall:

Height = 3 meters

Width = 5 meters

Side Wall 1:

Height = 3 meters

Length = 8 meters

Side Wall 2:

Height = 3 meters

Length = 6 meters

To calculate the area of each wall, we multiply the height by the width/length:

Area of Back Wall = Height * Width = 3 meters * 5 meters = 15 square meters

Area of Side Wall 1 = Height * Length = 3 meters * 8 meters = 24 square meters

Area of Side Wall 2 = Height * Length = 3 meters * 6 meters = 18 square meters

To calculate the total area of the back and side walls that need to be painted, we add up the individual areas:

Total Area = Area of Back Wall + Area of Side Wall 1 + Area of Side Wall 2

          = 15 square meters + 24 square meters + 18 square meters

          = 57 square meters

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The Probable question may be:

What is the total area of the back and side walls that need to be painted if the dimensions are as follows?

Back Wall:

Height = 3 meters

Width = 5 meters

Side Wall 1:

Height = 3 meters

Length = 8 meters

Side Wall 2:

Height = 3 meters

Length = 6 meters

The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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Marquise ran 13/6 miles through the park.

To find out how many miles Marquise ran through the park, we need to calculate 2/3 of \(3\frac{1}{4}\) miles.

First, let's convert 3 1/4 miles to an improper fraction:

\(3\frac{1}{4}\)= (4 × 3 + 1) / 4 = 13/4

Now, we can calculate 2/3 of 13/4:

(2/3) × (13/4)

= (2 × 13) / (3×4)

= 26/12

We can divide the numerator and denominator by their greatest common divisor, which is 2:

(26/2) / (12/2)

= 13/6

Therefore, Marquise ran 13/6 miles through the park.

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The teacher could use a hypothesis test for a population mean in the following situation:

The teacher wants to determine if computer-based instruction has a statistically significant effect on the average test scores of students in the class. The teacher can collect a sample of test scores from students who received computer-based instruction and a sample of test scores from students who did not receive computer-based instruction. Then, the teacher can use a hypothesis test for the population mean to compare the mean test scores of the two groups and determine if the difference is statistically significant.

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Complete question:

teacher is experimenting with computer-based instruction In which situation could the teacher use a hypothesis test for a ifference in two population means?

O The teacher uses a combination of treditional methods and computer based instruction She asks students # they lked computer based instruction better She wants to determine if the maorty prete the computer-based instruction

O She gives each student a pretest Then she teaches a lesson using a computer program Afterwards, she gives each student a postest The teacher wants to see f the difference in scores willshow an improvement 。

She ran om y d des the class into t goups One gup ecerves computer based instruction The other group recen es tradit na n rete wit t copters Ahe rst eten een student ha to solve a single problem. The teachers wants to compare the proportion of each group who can solve the problem 。She gives each student a pretest he then randomly dvides the class mto two groups.

Ο e group receves compte based i struct . The other go p eceves tradtind rst cto with t computers After instruction each student takes a post test. The teacher compares the improvement in scores (post test minus pretest) in the two groups

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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Answer:

Step-by-step explanation:

Multiply the constants and the variables

(4*5)(x*y) = 20xy

Answer:

Step-by-step explanation:

a₃=a-(3-1)d

=a-2d=3⇒equation 1

a₁₁=

=a-10d=11⇒eq 2

by elimination method

eq2-eq1

-8d=8d=-1

substituding in eq1 a=1

hope this helps

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Answer:

The polygon has a total of 15 sides

Step-by-step explanation:

Mathematically, the sum of the interior angles of a polygon can be calculated using the formula

(n-2) 180

Now there are 6 right angles. A right angle refers to 90 degrees. 6 right angles will be 6 * 90 = 540 degrees

Now the remaining number of angles in the polygon will be n-6 with each of this equal to 200 degrees each

The total amount of the remaining angles will be 200(n-6) = 200n-1200

Now adding all the interior angles will give the sum of 180(n-2)

180(n-2) = 200n -1200 + 540

180n -360 = 200n -660

200n -180n = 660-360

20n = 300

n = 300/20

n = 15

Answer:

Answer:

The perimeter is 48

Step-by-step explanation:

If the width is W

AT first , Length is 10 +w

According to the question,

\((w+8) (10+w+4) = 135\\(w+8) (w+14) = 135\\\\w^{2} + 14w + 8w + 112- 135 = 0\\\\ w^{2} + 22w - 23 = 0\\(w+23) (w-1) = 0\\\\w+ 23 = 0 w-1=0\\\\w= -13 or w = 1\)

Expended width will be  w +8 = 1+8 = 9

Length is 10+w+4 = 15

So the perimeter is

= i2 x (9+15)

= 2x 24

= 48

The Solution to the problem of the rectangle is given below

For Part A:

For Part B

Meaning of Perimeter

The perimeter of any shape can be defined as the total sum of the sides of the shape.

For Part A

equation model= (14 + w) * (w +8) = 135

14w + 112 + 8w + \(w^{2}\) = 135

\(w^{2}\) + 22w - 23 = 0

solving the quadratic equation

w = -23 or 1

Because we are dealing with a physical quantity we will make use of the value 1

lenght of original rectangle = 10 + 1 = 11

Part B

Perimeter= 2(length) * 2 (breadth) = 2(11 + 4) * 2 (1 + 8)

Perimeter = 48

In conclusion, The Solution to the problem of the rectangle is given above.

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The values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.

We can use the logarithm properties to find the value of log57 given that log75 is 0.83.

One of the logarithm properties states that:

log(a * b) = log(a) + log(b)

Using this property, we can express log57 in terms of log75:

log57 = log(5 * 3 * 19)

Now, we can use the fact that log75 is 0.83 to find log5, log3, and log19, and then add them together to get the value of log57:

log57 = log(5 * 3 * 19)

log57 = log5 + log3 + log19

However, since the values of log5, log3, and log19 are not provided, we cannot determine the exact value of log57 without this information.

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The equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.

To find log57 using the given information log75 = 0.83, we can use the change of base formula:  

if log75 = 0.83, then log57 ≈ 0.827. To find log57 using the given information log75 = 0.83, we can use the change of base formula:log_b(a) = log_c(a) / log_c

Here, we want to find log57 (log_7(5)) using the given information log75 (log_5(7)).

We can rewrite the change of base formula as:log_7(5) = log_x(5) / log_x(7)We know that log_5(7) = 0.83,

so we can substitute this value into the equation:log_7(5) = log_x(5) / 0.83

Now we can use any common base, like base 10 or base e, to find the value of log_7(5). Let's use base 10:log_7(5) = log_10(5) / log_10(7)Now

we can calculate the values of log_10(5) and log_10(7) using a calculator:log_10(5) ≈ 0.69897log_10(7) ≈ 0.84510

Now substitute these values back into the equation:log_7(5) = 0.69897 / 0.84510Now divide to get the value of log_7(5):log_7(5) ≈ 0.82706So, if log75 = 0.83, then log57 ≈ 0.827.

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Answer = 1.8

Step 1) 3 ÷ 2.7 = 0.900

Step 2) 0.900 x 2 = 1.8

Time taken by the person to walk the boardwalk to the end and back is 0.9 hours.

Given that, The Coney Island Boardwalk is 2.7 miles long.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

A person walks at the average speed of 3 mph.

We know that, speed = Distance/Time

= 2.7/3

= 0.9 hours

Hence, time taken by the person to walk the boardwalk to the end and back is 0.9 hours.

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Legend

The term that refers to the labels at the right of the graph indicating how each subcategory is represented is the Legend.

The Legend is a key that indicates what the different colors, lines, or other symbols in a graph represent. It is usually located at the right or bottom of the graph and provides a clear explanation of the different subcategories.

The Legend is an essential component of a graph, as it helps the viewer understand the information presented in the graph. Without the Legend, the graph can be confusing and difficult to interpret. It is important to ensure that the Legend is clear and easy to understand so that the viewer can quickly identify the different subcategories represented in the graph.

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Answer:

3.451, 3.452, 3.453, 3.454, 3.455, 3.456, 3.457, 3.458, 3.459, 3.460

Answer:

3 gallons, i think

Step-by-step explanation:

1+1=2

1/4+3/4=4/4

2 4/4= 3

Answer:

d should be correct

Step-by-step explanation: