Express 4 hours on seconds and leave answer in standard form

17 water jugs need 98.6 gallons of water.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Francisco who just got his driver’s license and wants to rent a car. The Platinum Car Rental Company charges $180 plus $92 per hour to rent a car. The Plastic Car Rental Company charges $250 plus $75 per hour.

Assume that after [x] number of hours the companies charge the same amount. We can write the equality equation as -

180 + 92x = 250 + 75x

92x - 75x = 250 - 180

17x = 70

x = 70/17

x = 4.12 hours

Therefore, for x = 4.12 hours the companies charge the same amount.

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Answer:

c=20

Step-by-step explanation:

Answer:9

Step-by-step explanation:

we have the expression

Let

x=3t-4

Change the variable

so

10x^2+9x-9=0

solve the quadratic equation using the formula

we have

a=10

b=9

c=-9

substitute

we have

x=3/5 and x=-3/2

Find the value of t

Remember that

x=3t-4

For x=3/5

3/5=3t-4

3t=3/5+4

3t=23/5

t=23/15

For t=-3/2

-3/2=3t-4

3t=-3/2+4

3t=5/2

t=5/6

therefore

the answer is

The area of the surface between the cylinders x2 + y2 = 1 and x2 + y2 = 4 for the hyperbolic paraboloid z = y2 - x2 is 3π√(17).

Hyperbolic paraboloid is a doubly ruled surface that can be described as a saddle-shaped surface that has hyperbolic curves in two different directions and parabolic curves in the third. It can be represented by the equation z = x2 - y2 or z = y2 - x2, depending on the orientation of the surface.Let's take the hyperbolic paraboloid z = y2 - x2, the part of the hyperbolic paraboloid that lies between the cylinders x2 + y2 = 1 and x2 + y2 = 4 is shown below:

Let's solve the problem now:

We can evaluate the surface area of this region using a double integral in cylindrical coordinates:

∫∫R √(1 + fx2 + fy2) dA, where f is the function z = y2 - x2, and R is the region of integration.

For this particular problem, R is the annular region between the cylinders x2 + y2 = 1 and x2 + y2 = 4, and it can be expressed as 1 ≤ r ≤ 2, 0 ≤ θ ≤ 2π. Therefore, we have:

∫∫R √(1 + fx2 + fy2) dA= ∫02π ∫12^2 √(1 + (−2x)2 + (2y)2) rdrdθ

= ∫02π ∫12^2 √(17) rdrdθ= √(17) ∫02π ∫12^2 rdrdθ

= √(17) ∫02π [r2/2]12^2 dθ= √(17) ∫02π (4 − 1)/2 dθ

= √(17) ∫02π 3/2 dθ= 3π√(17).

Therefore, the area of the surface between the cylinders x2 + y2 = 1 and x2 + y2 = 4 for the hyperbolic paraboloid z = y2 - x2 is 3π√(17).

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Answer:

3

Step-by-step explanation:

Evaluate F(x) = –x^2 – 4x by substituting -1 for x:

              F(-1) = –(-1)^2 – 4(-1)

This becomes:

               F(x) = –1 + 4  =  3

\(\huge\mathfrak\pink{Answer...}\)

+,- 17

\(\huge\mathfrak\purple{hope \: it \: helps..}\)

Step-by-step explanation:

Doesn't the line show where the median is? Then it would be class 1

by proving the base case and establishing the inductive step, we have shown that the recursive formula S(n) : Dn = nDn−1 + (-1)^n holds true for all positive integers n, using mathematical induction.

Base Case: For n = 1, the formula becomes D1 = 1*D0 + (-1)^1, which simplifies to D1 = D0 - 1. This is true since the number of derangements of a single element is 0, as there are no ways to arrange a single element such that it is not in its original position.

Inductive Hypothesis: Assume that the formula holds for some positive integer k, i.e., Sk: Dk = kDk−1 + (-1)^k.

Inductive Step: We need to show that the formula holds for k + 1, i.e., Sk+1: Dk+1 = (k + 1)Dk + (-1)^(k+1).

Using the recursive definition of derangements, we know that Dk+1 = (k + 1)(Dk + Dk-1). Substituting the inductive hypothesis Sk, we have Dk+1 = (k + 1)((k)Dk-1 + (-1)^k) + Dk-1. Simplifying this expression, we get Dk+1 = (k + 1)Dk + (-1)^k(k + 1) + Dk-1.

Now, we need to manipulate the right-hand side of the formula to match the desired form. Rearranging terms, we have Dk+1 = kDk + (-1)^k(k + 1) + Dk-1 + Dk.

By using the property (-1)^k + (-1)^(k+1) = 0, we can simplify the equation further to Dk+1 = kDk + (-1)^(k+1) + Dk-1 + Dk. This expression matches the form of Sk+1, which completes the induction step.

Therefore, by proving the base case and establishing the inductive step, we have shown that the recursive formula S(n) : Dn = nDn−1 + (-1)^n holds true for all positive integers n, using mathematical induction.

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Answer:

If I'm correct W should equal 54 not 9.

Step-by-step explanation:

(-1,2)

(x+1)=0

x=-1

(y-2)=0

y=2

You need to just see what you can substitute in to make x and y in their respected brackets to equal zero, and that gives your coordinates. You may also rearrange to find the value of x or y in these types of questions to solve for the values of either coordinates, hence how I got -1 and 2.

Answer:

59.04°

58.31 inches

Step-by-step explanation:

The solution triangle is attached below :

Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;

Let the angle = θ

Tanθ = opposite / Adjacent

Tanθ = 50/30

θ = tan^-1(50/30)

θ = 59.036°

θ = 59.04°

The length of ladder can be obtained using Pythagoras :

Length of ladder is the hypotenus :

Hence,

Hypotenus = √(adjacent² + opposite²)

Hypotenus = √(50² + 30²)

Hypotenus = √(2500 + 900)

Hypotenus = 58.309

Length of ladder = 58.31 inches

Answer:

59°

58.3 inches

Step-by-step explanation:

Here is the full question :

A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.

Please check the attached image for a diagram explaining this question

The angle the ladder makes with the ground is labelled x in the diagram

To find the value of x given the opposite and adjacent lengths, use tan

tan⁻¹ (opposite / adjacent)

tan⁻¹  (50 / 30)

tan⁻¹ 1.667

= 59°

the length of the ladder can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

√(50² + 30²)

√(2500 + 900)

√3400

= 58.3 inches

Answer: The approximate number of particles of skin a human can shed in five hours can be written in the form a times 10^b, where a is 3 and b is 6 .

Step-by-step explanation:

Given: Humans shed about 3million particles of skin every 5 hours.

Since, 1 million = 1,000,000

Then 3 million = 3 x 1 million

\(= 3 \times1,000,000\)

\(= 3,000,000\)

\(=3\times10^6\)

On comparing to \(a\times 10^{b}\) , we get a = 3 and b=6

So, the approximate number of particles of skin a human can shed in five hours can be written in the form a times 10^b, where a is 3 and b is 6 .

Answer:

6

Step-by-step explanation:

First, write the approximate number of particles of skin a human can shed in five hours in scientific notation. This number is three million which can be written in the form a × 10b, where a is 3 and b is 6.

Each tray will have 18 pieces after they have been cut to the same size.

To find the number of pieces on each tray after they have been cut to the same size, we need to find the least common multiple (LCM) of 3, 6, and 9. This will give us the smallest number of pieces that all three trays can be divided into without any remainder.

The LCM of 3, 6, and 9 is 18. This means that all three trays can be divided into 18 equal-size pieces without any remainder.

So, each tray will have 18 pieces after they have been cut to the same size. It is important to note that this is the smallest number of pieces that all three trays can be divided into, and any larger number would also work.

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The complete question is -

One tray of granola bars was cut into 3 equal-size pieces. A second tray was cut into 9 equal-size pieces, and a third was cut into 6 equal-size pieces. Jan wants to continue cutting until all three trays have the same number of pieces. How many pieces will there be on each tray?

Answer:

Step-by-step explanation:

Answer:

The value of x is 69°

Step-by-step explanation:

In a right angle triangle, if m and n are the two acute angles on it, then

That means if sin(m) = cos(n), then m + n = 90°

Let us use these facts to solve the question

∵ sin(21°) = 0.358

∵ cos(x°) = 0.358

→ That means sin(21°) = cos(x°)

∴ sin(21°) = cos(x°)

→ By using the facts above

∴ 21 + x = 90°

→ Subtract 21 from both sides

∵ 21 - 21 + x = 90 - 21

∴ x = 69°

∴ The value of x is 69°

Answer:

x+ x=?

Step-by-step explanation:

To find the centroid for the quarter circle using polar coordinates, we need to first determine the equations for the centroid coordinates (r,θ).

The formula for the centroid coordinates are:
r = (1/A) ∫∫ r^2 sin(θ) dr dθ
θ = (1/A) ∫∫ 0.5r^2 cos(θ) dr dθ
where A is the area of the lamina, which is given as π/4 in this problem.
For the quarter circle, we know that the radius (r) ranges from 0 to R (where R is the radius of the circle) and the angle (θ) ranges from 0 to π/2. Therefore, we can rewrite the integrals as follows:
r = (1/π/4) ∫0^(π/2) ∫0^R r^2 sin(θ) dr dθ
θ = (1/π/4) ∫0^(π/2) ∫0^R 0.5r^2 cos(θ) dr dθ
Simplifying these integrals and solving for r and θ, we get:
r = (4/πR^4) ∫0^(π/2) (1-cos^3(θ)) dθ
θ = (2/πR^4) ∫0^(π/2) (1-cos^2(θ)) sin(θ) dθ
Evaluating these integrals, we get:
r = (8R/9π)
θ = (4R/3π)
Therefore, the centroid coordinates (r,θ) for the quarter circle are:
r = (8R/9π)
θ = (4R/3π)
Note that these coordinates are relative to the origin of the polar coordinate system. To find the absolute centroid coordinates, we need to add the coordinates of the center of the circle to these values.

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Answer:

The expression below, 4x=20 when x=5.

Step-by-step explanation:

4(5)=20

The amount will become zero after 400 months.

Given that, Mr. Tallchief have $400,000 in his account after his retirement,

He intends to withdraw 4,000 from the account every month after the retirement,

We need to find the equation that represents the amount in the account n months after his retirement.

So,

f(n) = 400,000 - 4000n

This equation will give the withdrawal of money each month,

Now, when the account will have no money in it,

A = 0,

0 = 400,000 - 4000n

400,000 = 4000n

n = 400

Hence, the amount will become zero after 400 months.

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Answer: the answer is the second choice .

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Step-by-step explanation: as the second one is bigger than the first one .

In project management, a control chart is a tool used to monitor and track a project's progress over time. It provides a graphical representation of a project's performance, allowing project managers to quickly identify any deviations from the plan.

For more complex projects, statistical analysis can be applied to the control chart to identify potential causes of schedule deviation.

By analyzing the control chart data using statistical methods, project managers can determine whether the schedule deviation is due to random variation or a systematic cause. If the deviation is due to a systematic cause, the statistical analysis can help identify the root cause of the problem.

Once the root cause is identified, project managers can take corrective action to get the project back on track. The use of statistical analysis on control charts is a powerful tool for project management, enabling project managers to make data-driven decisions and minimize the risk of schedule delays and cost overruns.

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The formula for the balance b, in dollars, in the account after t weeks:
b = 710 - 35t

The formula takes into account the starting balance of $710 and the fact that you're withdrawing $35 every week. The same amount every week, you can simply multiply the number of weeks by 35 to get the total amount that you've withdrawn. Subtracting that total from the starting balance gives you the formula for the balance after t weeks.
The balance b in the account after t weeks, we can use the following formula:

b = initial_balance - (withdrawal_amount * t)
In this case, the initial_balance is $710 and the withdrawal_amount is $35 per week. So the formula for the balance after t weeks would be:
b = 710 - (35 * t)

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Answer:

3x+10y

Step-by-step explanation:

3x+2y(5) =

3x+2(5)y =

3x+2*5y = 3x+10y

The correct statement regarding the solution of the expression is given as follows:

Miguel made no mistakes.

The expression for this problem is defined as follows:

32/[2(2³ - 4)].

The parenthesis has precedence, and inside the parenthesis, the cube has precedence, hence:

32/[2(8 - 4)] = 32/[2(4)]

Multiplying in the denominator and then dividing the numerator by the denominator, the result is given as follows:

32/[2(4)] = 32/8 = 4.

Meaning that no mistake was made.

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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Answer:

The answer is below

Step-by-step explanation:

a) Cost of hiring the bicycle for 14 days is:

Cost = 65 * 14 days + 44 = 954 riyals

b) The number of days the bicycle is hired is to be the same as the number of days the bicycle is to be hired. Let us assume that the bicycle and helmet is to be hired for x days, hence:

Cost of bicycle = 65 * x + 14 = 65x + 44

Cost of helmet = 12.5 * x = 12.5x

Total cost = 65x + 44 + 12.5x = 77.5x + 44

Since 750 riyals is available, hence:

750 = 77.5x + 44

77.5x = 706

x = 9.11

Therefore the maximum number of days is 11. The total cost for 11 days is:

Total cost = 77.5(9) + 44 = 741.5 riyals

Money not spent = 750 riyals - 741.5 riyals = 8.5 riyals

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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