A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 350 nails. The contractor bought 3 more small boxes than large boxes, which altogether had 2950 nails. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.

Answer:

  the value of hi changes from 58 to 0:

  h(t) = -4.9t^2 +19.8t

Step-by-step explanation:

If the initial height changes, then the term in the equation that represents that height will change. The initial height term is hi, so it changes from 58 to 0.

  \(h(t)=-4.9t^2+19.8t+0\\\\\boxed{h(t)=-4.9t^2+19.8t}\)

The complete response x(t), with initial conditions and input, can derived using Laplace transform and inverse Laplace transform techniques.

To derive the complete response x(t), we first take the Laplace transform of the given differential equation, applying the initial conditions to obtain the transformed equation in the Laplace domain.

Next, we solve the transformed equation for the Laplace transform X(s) of x(t) using algebraic manipulations and inverse Laplace transforms

We consider the input u(t) = 5t, and take its Laplace transform U(s) to express it in the Laplace domain.

By substituting X(s) and U(s) into the transformed equation, we solve for X(s) to obtain the Laplace transform of the complete response.

Finally, we use inverse Laplace transform techniques to find the time-domain expression for x(t), the complete response of the system.

Sketching the response x(t) involves plotting the function x(t) with respect to time, considering the given initial conditions and input.

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Given the following trinomial:

Since the given trinomial is quadratic, there are two factors in this equation.

Step 1: Determine the factors of the first term, 2x².

There are no other possible factors of 2x² but 2x and x.

Therefore, we can now generate the initial factors.

Let A and B represent the unknown constants of the factors to be able to get the product of 2x² + 7x + 4.

Step 2: Let's determine A and B.

Let's think of possible constants of A and B that have a product of 4 and a sum of 7x when adding A multiplied by x and B multiplied by 2x.

Let's list down possible pairs.

TABLE

Sum of 4 (A and B) Sum of 7x

1 and 4 1(x) + 4(2x) = x + 8x = 9x

2 and 2 (2)(x) + 2(2x) = 2x + 4x = 6x

4 and 1 4(x) + 1(2x) = 4x + 2x = 6x

-1 and -4 -1(x) - 4(2x) = -x - 8x = -9x

-4 and -1 -4(x) - 1(2x) = -4x - 2x = -6x

None of the possible factors are possible to complete the equation, therefore, we can say that the given trinomial is not a perfect square and is not factorable.

If we are tasked to factor the trinomial by completing the square, we get:

The constant must be 3 and not 4 for it to be factorable and will

give you (2x + 1)(x + 3) = -1.

Answer:

Allison will owe $10,888.50 in 3 years

Step-by-step explanation:

FV=PV(1+r/n)^nt

Where,

PV=$7000

r=15%=0.15

n=quarterly=4

t=3 years

FV=PV(1+r/n)^nt

=7000(1+0.15/4)^4*3

=7000(1+0.0375)^12

=7000(1.0375)^12

=7000(1.5555)

=10,888.50

To 2 decimal places=$10,888.50

Allison will owe $10,888.50 in 3 years

Answer:

$10,888.20

Step-by-step explanation:

Order of Operations: BPEMDAS

Compounded Interest Rate Formula: A = P(1 + r/a)ᵃᵇ

A = Final Amount

P = Initial Amount

r = rate

a = Compounded number

b = time

Step 1: Define

P = 7000

r = 15% = 0.15

a = 4

b = 3 years

Step 2: Solve for A

At the end of the 3 years that elapsed, Allison will have to pay a final debt of $10,888.20.

DFS and BFS are two algorithms that are used to traverse graphs. BFS, unlike DFS, visits all vertices at a given distance from the start vertex before continuing. Similarly, DFS visits all vertices along a path before returning to the beginning.

The given labeled graph is: The process of both Depth-First Search and Breadth-First Search are explained below:

Depth-First Search:

Step 1: First, start with vertex 9 and mark it as visited.

Step 2: Choose an unvisited vertex that is adjacent to the current vertex 9 and mark it as visited.

Step 3: Continue the above step until you reach a dead end and backtrack until you find an unvisited vertex.

Step 4: Repeat steps 2 and 3 until all vertices are visited.

Step 5: The graph can be represented as a rooted spanning tree where vertex 9 is the root node.

The Rooted Spanning Tree for the DFS approach with root 9 is as follows: Breadth-First Search:

Step 1: First, start with vertex 9 and mark it as visited.

Step 2: Choose all the vertices that are adjacent to vertex 9 and mark them as visited.

Step 3: Add the adjacent vertices to the queue.

Step 4: Dequeue the vertex and select all its adjacent vertices and mark them as visited.

Step 5: Continue the above steps until all vertices are visited.

Step 6: The graph can be represented as a rooted spanning tree where vertex 9 is the root node.

The Rooted Spanning Tree for the BFS approach with root 9 is as follows: Conclusion: The Rooted Spanning Tree for the DFS approach with root 9 is{9, 7, 6, 4, 5, 2, 1, 3, 8}

The Rooted Spanning Tree for the BFS approach with root 9 is{9, 7, 8, 6, 3, 5, 2, 4, 1}.

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Answer:

If the roots of any equation are equal then it means that their Discriminant = 0

So, b²-4ac = 0

We have given the equation 2x² + kx + 2, where,

a = 2

b = k (we have to find the value)

c = 2

Then, b²-4ac=0

b² - 4(2)(2) = 0

b² - 16 = 0

b² = 16

√16 = 4

Hence the vue of k is 4.

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Step-by-step explanation:

hope it helps you ( ◠‿◠ )

Answer:

Step-by-step explanation:

To solve this inequality, you can start by subtracting 24 from both sides to isolate the variable p on one side:

3p > 24

3p - 24 > 24 - 24

3p - 24 > 0

Then, you can divide both sides by 3 to solve for p:

(3p - 24)/3 > 0/3

p - 8 > 0

p > 8

The solutions to the inequality are all values of p that are greater than 8. This means that the correct answers are B: p = 10, C: p = 11, and all values of p greater than 11.

I hope this helps! Let me know if you have any questions.

Answer: The answer is 24

Step-by-step explanation: because it's the same line and it's only telling you half of the line so you just double it

The null hypothesis implied that cars 20 years or older do not pass safety inspection ≤  30%.

The alternative hypothesis implied that cars 20 years or older do not pass safety inspection >  30%

The local county officials are testing a hypothesis about the proportion of cars 20 years.

And older that do not pass their annual safety inspection at the service station.

The null hypothesis and alternative hypothesis can be stated as follows,

Null hypothesis,

The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station ≤  30%.

Alternative hypothesis,

The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station > 30%.

The null hypothesis assumes that the service station is not allowing cars with known violations to pass the safety inspection.

And that the rejection rate of 30% is consistent .

With the true rate of cars 20 years and older that do not pass their annual safety inspection at the service station.

The alternative hypothesis suggests that the service station is allowing cars with known violations to pass the safety inspection.

And that the rejection rate is lower than the true rate of cars 20 years .

And older that do not pass their annual safety inspection at the service station.

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Answer: 18.6

Step-by-step explanation: 9.3 is one side of the diagonal and the other side will be 9.3 as well, so you add 9.3+9.3=18.6

If the amount of budget for media and sales combined is $25,000,000. Then the total annual budget will be $125,000,000.

The complete question is attached below.

The quantity of anything is stated as though it were a fraction of a hundred.

The pie chart below shows how the annual budget for a certain company divided by department.

If the amount of budget for media and sales combined is $25,000,000.

Then the total annual budget will be

Let x be the total annual budget.

17% + 3% = 25,000,000 / x

       20% = 25000000 / x

      0.20 = 25000000 / x

            x = $125,000,000

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On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

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this is so easy it's: 1015

your welcome

According to the above, to draw a 1:2 scale we must divide the figure in 2.

The scale model is a way of drawing a figure that is smaller or larger in size. In this case, the size would be smaller, 1:2 means that for each unit of measurement (cm) of the original figure, there are 2 units on the scale.

According to the above, if the circle has a 12cm radius, then the scale model would have a 6cm radius, that is, it would be smaller than the original as shown in the second image.

Note: This question is incomplete. Here is the complete information:

Draw a scale of 1:2 of the following figure:

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Answer:

$12,000

Step-by-step explanation:

Use the simple interest formula: P = A(1 + rt)

P = final balance (?)

A = starting balance (10,000)

r = interest rate (0.05)

t = years (4)

P = 10,000(1 + 0.05 · 4)

P = 10,000(1 + 0.2)

P = 10,000(1.2)

P = 12,000

The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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The blocks in this design are c. the four different litters. The pigs within each litter were grouped together as a block, and the three dietary supplements were randomly assigned to the two pigs within each block.

This helps control for any variation between litters that could affect the results of the feed trial. The 24 identical pens are not the blocks in this design, but rather the units where the treatments were applied.

A litter is defined as the live birth of several young at once in an animal from the same mother and typically from the same pair of parents, especially three to eight young. The term is most frequently used to refer to the offspring of mammals, although it can also refer to any animal that bears numerous offspring.

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Answer:

Yes

Step-by-step explanation:

Answer: Equation 1, sum of the numbers: x + y = 53. Equation 2, difference of the numbers: x - y = 25. System of equations: x + y = 53. x - y = 25. 2x = 78.

Step-by-step explanation:

there you go

Answer:

x = 80

Step-by-step explanation:

∡KJL = 180 - (60 + 40)

∡KJL = 80

∡XJK + ∡KJL = 180  (they are a linear pair of angles)

x + 20 + 80 = 180

x + 100 = 180

x = 80  

Answer:

33.33%

Step-by-step explanation:

8 out of 24 hours is equivalent to 1/3 which equals to 33.33%

Answer:

8/24 converted to a percentage = 33.333333333333%

Answer:

A.-4-4i

Step-by-step explanation:

You can just substitute c with 3-4i in c-d=7

so the equation now looks like this:

3-4i-d=7

Now move 3 and -4i to the other sides:

-d=4+4i

Divide by -

Which is -4-4i

So the answer is A.-4-4i

Hope this helps!

An inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint : 150c + 750t ≥ 12000

Let the number of chairs sold = c

Let the number of tables sold = t

the price for each chair = $150

the price for each table = $750

The inequality that could represent the number of tables and chairs sold will be:

(150 × c) + (750 × t) ≥ 12000

150c + 750t ≥ 12000

Therefore,  an inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint : 150c + 750t ≥ 12000

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Answer:

5 miles

Step-by-step explanation:

1 Day =1 mile

5 Days = 5×1= 5 miles

Answer:

D

Step-by-step explanation:

Option 4.

The vertex form of a parabola is

where, a is a constant (h,k) is the vertex.

The given function is

The vertex of the function is (0,0) and it goes through (-2, 4) and (2, 4).

It is given that the vertex of function g(x) is at (5,2).

Substitute h=5 and k=2 in the equation.

g(x) is passed through (3, 6).

 Divide both sides by 4.

Substitute a=1 in equation (2).

The function g(x) is g(x) =(x-2)2+5) .

Therefore, the correct option is 4.

hope this helps

Answer:

D

Step-by-step explanation:

After combining like terms to create equivalent expression we get (-1.9 + 1.2) + (5.1 - 3.6)t. Simplifying further, we get: -0.7 + 1.5t.

To combine like terms, we add or subtract the coefficients of the same variables. In this case, the variables are t and the constant terms (without variables) are -3.6, -1.9, and 1.2.

So the equivalent expression after combining like terms is:

(-1.9 + 1.2) + (5.1 - 3.6)t

Simplifying further, we get:

-0.7 + 1.5t

A coefficient is a numerical factor that is multiplied by a variable in an algebraic expression. It tells you how many times the variable appears in the expression. For example, in the expression 3x + 2, the coefficient of x is 3. Variables are symbols used to represent unknown quantities in mathematical equations or expressions. They can take on different values, and their value can be solved for using algebraic techniques. Equivalent expressions are expressions that have the same value for all possible values of the variables involved. For example, 2x + 4 and 4 + 2x are equivalent expressions since they simplify to the same value. Equivalent expressions can be useful in simplifying and solving algebraic equations.

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Complete Question

Combine like terms to create an equivalent expression. −

3. 6−1. 9+1. 2+5. 1 −3. 6−1. 9t+1. 2+5.

Recursive algorithm for minimum number of bills needed to make an amount, given n and k denominations:Calculate the minimum number of bills by considering each denomination and recursively reducing the remaining amount

Here's a description and analysis of a recursive algorithm that computes the minimum number of bills needed to make an amount n using a system of k denominations:

Algorithm: MinimumBills(n, denominations)

If n is zero, return 0 (no bills needed).

If n is negative, return infinity (impossible to make the amount).

If n is a value that has already been computed and stored, return the stored value.

Set minBills to infinity.

For each denomination d in the k denominations:

a. If n is greater than or equal to d, recursively call MinimumBills(n - d, denominations) and store the result in numBills.

b. If numBills is less than minBills, update minBills to numBills.

Store minBills for the value of n.

Return minBills.

Analysis:

The recursive algorithm computes the minimum number of bills needed to make the amount n using the given denominations. The algorithm explores all possible combinations of denominations to find the optimal solution.

Time Complexity: The time complexity of the algorithm depends on the values of n and k denominations. Since the algorithm explores all possible combinations, the worst-case time complexity is exponential, \(O(k^n)\).

However, if the denominations are limited and n is relatively small, the algorithm can run in polynomial time.

Space Complexity: The space complexity of the algorithm is determined by the recursion depth, which is equal to n. Therefore, the space complexity is \(O(n).\)

Note: To optimize the algorithm and avoid redundant calculations, you can use memoization by storing the results for previously computed values of n in a lookup table. This can significantly reduce the number of recursive calls and improve the overall performance.

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