convert 12 hours = __________ seconds

Answer:

s=ut +atsq/2

120=4u+4sq

4u=104

u=26m/sec

Answer:

26 m/s

Step-by-step explanation:

Given

\(s = ut + \frac{1}{2} {at}^{2} \)

When a = 2 , s = 120 and t = 4

Then

\(120 = u \times 4 + \frac{1}{2} \times 2 \times {4}^{2} \\ 120 = 4u + 16 \\ 120 - 16 = 4u \\ 104 = 4u \\ u = \frac{104}{4} \\ u \: = 26

Hope it will help :)❤

Answer:

1. The area is found by using the formula for a rectangle

The area is 150 cm²

2. The area is found by the definite integral for the area between two points under a curve

3. The methods are different

The methods are different because the area of figure A is found by the multiplication between the dimensions, while the area of figure B is found by the difference between the values of the integral of the function between the points

Step-by-step explanation:

1. The area of the shaded figure A is found by multiplying the dimensions of the figure, which is the length multiplied by the breadth of the figure

From the question, we have;

The area of the rectangular figure, A = Length × Breadth

The length of the figure = 15 cm

The breadth of the rectangular figure = 10 cm

Therefore, we have;

A = 15 cm × 10 cm = 150 cm²

The area of the rectangular figure, A = 150 cm²

2. The bell shape of the figure B is obtained from a function f(x) as obtained from MIT mathematics website as follows;

\(f(x) = e^{-t^2}\)

Therefore the area of the shaded region in the bell shaped figure between the points 0 and 1 on the x-axis is found by integration as follows;

\(A = \int\limits^1_0 {e^{-t^2}} \, dt = \dfrac{1}{2} \cdot \sqrt{\pi} \times erf(t)\)

Using a graphing calculator, we have;

\(A = \int\limits^1_0 {e^{-t^2}} \, dt \approx 0.746824\)

3. The method of finding the area of figure A is different from the method of finding the area of the figure B

The methods are different because the area of figure A is the area of the whole figure of a geometric shape with known formula for area while the area of of the shaded region has no predefined formula but is calculated using the calculus for the area under a curve.

Answer:

The answer is D, E, F  or it is also D to F

Step-by-step explanation:

9514 1404 393

Answer:

  A and B

Step-by-step explanation:

Speed is the change in distance divided by the change in time. That is, it is the slope of the distance vs. time curve. A steeper slope corresponds to a greater speed.

Between A and B, the slope is (30-0)/(1-0) meters/time-unit = 30 m/u.

Between B and C, the slope is (30-10)/(4-1) = 20/3 = 6 2/3 m/u.

Between C and D, the slope is 0.

Between D and F, the slope is (50-10)/(10-6) = 40/4 = 10 m/u.

The greatest slope is between A and B.

The object has the greatest speed between points A and B.

Answer:

72.5m/hr

Step-by-step explanation:

Divide 870 by 12 to represent how many miles David drove in 1 hour.

\(870 \div 12=72.5\)

David drove 72.5 miles per hour.

Answer: -4

Step-by-step explanation: Hello! :) To get started we need to use the equation 7x+3=4x-9, First, we need to subtract 4x from both sides to get 3x+3=-9, then we need to subtract 3 on both sides to get 3x=-12, Finally, we need to divide both sides by 3 to get x = -4. So x = -4.

Hope this helps!

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Answer:

I believe it's  (5.7, 2.2)

I hope it's correct :)

c

Step-by-step explanation:

for the lazy people like me its c

Answer:

The vertex, a maximum, is (25, 2400). It reveals that the maximum profit will result when the tickets are $25, and then the profit will be $2400.

Explanation:

p(d) = -4d² + 200d - 100

Comparing it with quadratic function, ax² + bx² + c

Here given: a = -4, b = 200, c = -100

Using Vertex Formula: x = -b/2a = -200/2(-4) = 25

Then find y = -4(25)² + 200(25) - 100 = 2400

Solution Set : (x, y) → (25, 2400)

As a > 0, the vertex is maximum.

The amount of storage required to represent a simple graph with n vertices and m edges can vary depending on the chosen representation. Here's the storage requirement for each representation:

a) Adjacency lists:

In an adjacency list representation, we typically use an array of size n to store the vertices, and for each vertex, we maintain a linked list or an array to store its adjacent vertices. The space complexity of this representation is O(n + m), where n is the number of vertices and m is the number of edges.

Each vertex requires constant space, and each edge is represented by a link or entry in the adjacency list.

b) Adjacency matrix:

In an adjacency matrix representation, we use a 2D matrix of size n x n to represent the graph. Each entry (i, j) in the matrix represents whether there is an edge between vertices i and j. The space complexity of this representation is O(n^2), as we need to store n^2 entries for the complete matrix. However, if the graph is sparse (few edges compared to vertices), the space complexity can be reduced to O(n + m) by only storing the entries corresponding to the existing edges.

c) Incidence matrix:

In an incidence matrix representation, we use a 2D matrix of size n x m, where n is the number of vertices and m is the number of edges. Each entry (i, j) in the matrix represents whether vertex i is incident to edge j. The space complexity of this representation is O(n * m), as we need to store n * m entries for the matrix.

Similar to the adjacency matrix, if the graph is sparse, the space complexity can be reduced to O(n + m) by storing only the entries corresponding to the existing edges.

In summary:

a) Adjacency lists: O(n + m)

b) Adjacency matrix: O(n^2) or O(n + m) for sparse graphs

c) Incidence matrix: O(n * m) or O(n + m) for sparse graphs

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Answer:

why isnt there a backround base? it wouldnt be area if isnt so

Step-by-step explanation:

The area is 960 m

because 48*15=720

and 10*24=240

720+240= 960

The two different antiderivatives of f = 5x4 are x5 + C and x5 + 2C.

The given function is f = 5x4.

The antiderivative of f is given by: F (x) = ∫f (x) dx = ∫5x4dx= 5 * ∫x4dxLet's apply the power rule of integration for the antiderivative of x4.

∫xndx = (x(n+1))/(n+1)So,∫x4dx = x5/5Thus, F(x) = 5x5/5 + C = x5 + C

Where C is a constant of integration.

Antiderivative 1 =  x5 + C

Antiderivative 2 = x5 + 2C (where 2C is another constant of integration).

So, the two different antiderivatives of f = 5x4 are x5 + C and x5 + 2C.

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Both \(x^5 + C\) and \((5/6)x^6 + D\) are valid antiderivatives of \(f = 5x^4\) the function.

A function's antiderivative, or F'(x) = f, is a function F(x) whose derivative is equal to f(x) (x). Since it represents a family of functions that differ by an integration constant, an antiderivative is often referred to as an indeterminate integral. This implies that we can compute definite integrals of a function over any interval if we can identify its antiderivative. On the other hand, if we are aware of the value of a definite integral, we can use it to calculate the difference between the antiderivative values at the interval's ends.

The given function is \(f = 5x^4\).

The derivative of \(x^5 + C\) with respect to x is \(5x^4\), which is the same as f.

The derivative of \((5/6)x^6 + D\) with respect to x is \(5x^4\), which is also the same as f.

Therefore, both \(x^5 + C\) and \((5/6)x^6 + D\) are valid antiderivatives of \(f = 5x^4\).

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Answer:

-4 , 0 would be the answer your looking for I believe

Using equivalent angles, the equivalent expression is:

\(-\sin{\frac{\pi}{12}}\)

--------------------

--------------------

Then:

\(\frac{13\pi}{12} - \pi = \frac{13\pi}{12} - \frac{12\pi}{12} = \frac{\pi}{12}\)

The equivalent expression is, considering that in the third quadrant and in the first quadrant, the sine has opposite signals.

\(-\sin{\frac{\pi}{12}}\)

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The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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The clerk walked approximately 0.371π meters during the 132 minutes of delivering along the hallway.

To find the number of 3-meter segments the clerk walked during the 132 minutes, we need to integrate the velocity function over the given time interval.

v(t) = 4π sin(t)

The clerk starts at one end and takes 13 minutes to finish deliveries, so the time interval is from t = 0 to t = 13.

To calculate the distance walked, we integrate the absolute value of the velocity function over the given interval:

Distance = ∫[0, 13] |v(t)| dt

Let's calculate the integral:

Distance = ∫[0, 13] |4π sin(t)| dt

Since the absolute value of sin(t) is positive for the given interval, we can simplify the integral to:

Distance = 4π ∫[0, 13] sin(t) dt

Using the integral of sin(t), which is -cos(t), the expression becomes:

Distance = -4π cos(t) |[0, 13]

Now we can evaluate the integral over the given interval:

Distance = -4π (cos(13) - cos(0))

Simplifying further:

Distance = -4π (cos(13) - 1)

Calculating the value:

Distance ≈ -4π (0.907 - 1)

Distance ≈ -4π (-0.093)

Distance ≈ 0.371π meters

Therefore, the clerk walked approximately 0.371π meters during the 132 minutes.

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Answer:

x=3

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

its impossable

The new volume of the cylinder is $100$ cubic feet.

Let the original radius and height of the cylinder be $r$ and $h$, respectively. Therefore, the original volume of the cylinder is given by $\pi r^2 h = 100$. After the radius decreases by $10%$ and the height increases by $10%$, the new radius and height become $0.9r$ and $1.1h$, respectively. The new volume of the cylinder can be calculated as $\pi (0.9r)^2 (1.1h) = 0.891\pi r^2 h$. Since $0.891\pi r^2 h = 100$, the new volume of the cylinder is $100$ cubic feet.

Therefore, the new volume of the cylinder is the same as the original volume, i.e., $100$ cubic fee

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The z-score that has 2.5% of the normal distribution below it is approximately 2.06.

To find the z-score that has 2.5% of the normal distribution below it, we need to use the standard normal distribution table (also known as the z-table or normal distribution table). This table shows the area under the standard normal curve to the left of a given z-score.

First, we need to find the area to the left of the desired z-score, which is 2.5%. Then, we need to find the corresponding z-score in the z-table.

Looking at the z-table, we find the row that contains the first digit(s) of the desired z-score, which is 2.5 in this case. Then, we find the column that corresponds to the second decimal place of the desired z-score, which is 0.00 in this case. The intersection of this row and column gives us the area under the standard normal curve to the left of the z-score.

In this case, we find that the area to the left of the z-score is 0.4938. To find the z-score that corresponds to this area, we look in the body of the table and find the closest value to 0.4938, which is 0.01. The corresponding z-score in the row and column headers is 2.06.

Therefore, the z-score that has 2.5% of the normal distribution below it is approximately 2.06.

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Answer:

False

Step-by-step explanation:

I am assuming this is the answer you are looking for and if not I am sorry. The sides of this equation are not currently equal. (-7=12) So the statement of the equation is false.

Answer:

The LCM of 25 and 200 is 200.

Explanation:

Find the prime factorisation of 25

25 = 5 × 5

Find the prime factorisation of 200

200 = 2 × 2 × 2 × 5 × 5

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM:

LCM = 2 × 2 × 2 × 5 × 5

LCM = 200

Answer:

the HCF of 25 and 200 is 25 because it divides both of them and is maximum factor of them.

LCM of 25 and 200 is 200 because it can be divided by both 200 and 25

The average number in line: 0.5 persons. Average number of persons in the system: 1 person. Average time spent in line: 2.5 minutes. Increased arrival rate will result in more people in the waiting line.

The average number in line can be calculated using the formula for the average number of customers in the system, Ls = λWs, where λ is the arrival rate and Ws is the average time a customer spends in the system. In this case, the arrival rate is 10 persons per hour and the time per player is 5 minutes. Converting the arrival rate to arrivals per minute, we have λ = 10/60 = 1/6 arrivals per minute. Plugging these values into the formula, we get Ls = (1/6) * 5 = 5/6 = 0.833, which can be approximated to 0.5 persons.

The average number of persons expected to be in the system includes both those in the line and those being served. Since the system follows a First-Come-First-Serve (FCFS) discipline, the number of people in line will be equal to the number of people in the system. Therefore, the average number of persons in the system is also 0.5 persons.

The average amount of time a person spends in line can be calculated using Little's Law, which states that the average number of customers in a stable system is equal to the arrival rate multiplied by the average time a customer spends in the system. In this case, the average number of customers in the system is 0.5 persons and the arrival rate is 10 persons per hour. Converting the arrival rate to arrivals per minute, we have λ = 10/60 = 1/6 arrivals per minute.

Plugging these values into the formula, we get 0.5 = (1/6) * Ws. Solving for Ws, we find Ws = 3 minutes. Since the average time spent in the system includes both waiting time and service time, and the service time is 5 minutes per player, the average time spent in line is Ws - service time = 3 - 5 = -2 minutes. However, a negative waiting time is not meaningful in this context. Therefore, we can approximate the average time spent in line to 2.5 minutes.

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Answer:

100 - 6n

Step-by-step explanation:

each book costs 6 and there are n books.

their total price is 6n

Answer:

a) A(x)  = 90*x/2  -  x²/2

b) A(max) = 1012.5 m²

Step-by-step explanation:

L = 90 meters of fencing

Rectangular area is

A(r) = x*y .            where  x  and  y  are the sides of the rectangle

the perimeter is  ( we are going to fence only 3 sides, then)

x + 2*y = 90    or .    y  = ( 90  - x ) /2

Area as a function of x is:

A(x)  = x * ( 90 - x)/2

A(x)  = 90*x/2  -  x²/2

Tacking derivatives on both sides of the equation:

A´(x) =45  -  2*x/2         A´(x) =45  - x

A´(x) = 0 .      45  - x = 0 .      x  = 45 . meters

and . y   =  ( 90  - x ) 2

y = ( 90- 45 )/2  

y = 22.5 meters

A(max) =  45*22.5  m²

A(max) = 1012.5 m²

If we get the second derivative of A(x) .  A"(x) = - 1       A"(x) < 0

Then A(x) has a maximum for x = 45

Answer:

p - w = $25 OR w + $25 = p

Step-by-step explanation:

pencil = p

pen = w

p - w = $25 OR w + $25 = p

Since absolute value represents the separation between any two points on a number line, it can be used to determine distances between any two points on a coordinate plane.

A coordinate plane is a two-dimensional plane that is created when two number lines cross. These number lines include the x-axis, a horizontal number line, and the y-axis, a vertical number line. These two number lines cross perpendicularly to form the coordinate plane.

The reason the plane is referred to as two-dimensional is that each point on it to which you may put your finger will require two measurements to determine its location: its distance from the x-axis and its distance from the y-axis.

No matter if a point is zero or not, absolute values will determine the distance between any two points.

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Answer:

Hope this helps have a good day! :)

Step-by-step explanation:

Exact form = 10/3

Decimal form = 3.3

Mixed number form = 3 1/3

the solution for x is x = 10/3 or approximately x = 3.33.

To solve for x in the equation 8x - 2 - 5x = 8, we need to simplify and combine like terms, then isolate x on one side of the equation.

Let's start by combining the x terms on the left side:

(8x - 5x) - 2 = 8

Simplifying further:

3x - 2 = 8

Next, we want to isolate the x term. We can do this by adding 2 to both sides of the equation:

3x - 2 + 2 = 8 + 2

Simplifying the equation:

3x = 10

Finally, to solve for x, we divide both sides of the equation by 3:

(3x) / 3 = 10 / 3

The division yields:

x = 10/3

Therefore, the solution for x is x = 10/3 or approximately x = 3.33.

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It will take approximately 17.3 years for the population to double if the growth rate per year is 4% of the current population.

The population of a country growing at a rate proportional to its population is modeled by the exponential growth equation:

P(t) = P0 e^(rt)

Where P(t) is the population after time t, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.

In this case, the growth rate per year is 4% of the current population, so r = 0.04. We want to find how long it will take for the population to double, which means we want to find t such that P(t) = 2P0.

Substituting into our equation, we get:

2P0 = P0 e^(0.04t)

Dividing both sides by P0 and taking the natural logarithm of both sides, we get:

ln(2) = 0.04t

Solving for t, we get:

t = ln(2)/0.04

≈ 17.3 years

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Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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