ind the amount in the account after $800 is invested for 1 year at 9ompounded monthly. (enter a number. round your answer to two decimal places.)

The equation of the line are :

(a) y = x + 1, (b) 4y = 3x - 1, (c) y = -x + 1, (d)  y = -2x + 1 and (e) y = 2x.

Slope intercept form of the line is y = mx + c, where m is the gradient and c is the y intercept.

Point slope of the line is (y - y') = m (x - x'), where m is the gradient and (x', y') is a point.

(a) Equation of the line through (2, 3) and gradient 1.

Substituting in point slope form,

y - 3 = 1 (x - 2)

y - 3 = x - 2

y = x + 1

(b) Equation of the line through (-1, -1) and gradient 3/4.

y - -1 = 3/4 (x - -1)

y + 1 = 3/4 x + 3/4

y = 3/4 x - 1/4

4y = 3x - 1

(c) Equation of the line through (1, 0) and (-2, 3).

Slope, m = (3 - 0) / (-2 - 1) = -1

y intercept = 1

y = -x + 1

(d) Equation of the line through (0, 1) and (-1, 3).

Slope, m = (3 - 1) / (-1 - 0) = -2

y - 1 = -2 (x - 0)

y = -2x + 1

(e) Equation of the line through (1, 2) and parallel to the line with gradient 2.

Two parallel lines have the same slope.

y - 2 = 2 (x - 1)

y = 2x

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Answer:

t = 3s

Step-by-step explanation:

The equation t = 3s can be used to calculate the total cost.

Answer:

40 1/4

Step-by-step explanation:

160 is a multiple of 4

160 / 4 = 40

40 1/4

Emile paid $3.96 for 4 songs, resulting in a unit rate of $0.99 per song. This means that each individual song costs $0.99.

To calculate the unit rate, we divide the total cost by the quantity. In this case, Emile paid $3.96 for 4 songs.

Unit Rate = Total Cost / Quantity

Substituting the given values:

Unit Rate = $3.96 / 4

Unit Rate = $0.99 per song

The unit rate of $0.99 per song means that for each individual song Emile purchased, he paid $0.99. This is the cost per unit or the price for one unit of the item, in this case, a song.

Understanding the unit rate is useful when comparing prices or quantities. It allows for a direct comparison between different quantities or sizes. In Emile's case, knowing that each song costs $0.99 helps determine the cost if he were to purchase a different number of songs.

In summary, Emile's purchase of 4 songs for $3.96 results in a unit rate of $0.99 per song, meaning that each individual song costs $0.99.

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Answer:

3,975.16 United States Dollar

Step-by-step explanation:

To find the displacement and total distance traveled by the object from t=0 to t=6, we need to integrate the velocity function over the given time interval.

The displacement can be found by integrating the velocity function v(t) with respect to t over the interval [0, 6]. The integral of v(t) represents the net change in position of the object during this time interval.

The total distance traveled can be determined by considering the absolute value of the velocity function over the interval [0, 6]. This accounts for both the forward and backward movements of the object.

Now, let's calculate the displacement and total distance traveled using the given velocity function v(t) = t^2 - (1/t) - 12 over the interval [0, 6].

To find the displacement, we integrate the velocity function as follows:

Displacement = ∫[0,6] (t^2 - (1/t) - 12) dt.

To find the total distance traveled, we integrate the absolute value of the velocity function as follows:

Total distance = ∫[0,6] |t^2 - (1/t) - 12| dt.

By evaluating these integrals, we can determine the displacement and total distance traveled by the object from t=0 to t=6.

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Yes the expressions are equivalent

Answer:

9

Step-by-step explanation:

no

Considering the given quadratic equation, it is found that the quickest way to find the maximum height is given by:

c. Complete the square.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The maximum height is at the vertex, which is found completing the squares, hence option c is correct.

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The number of students that are likely to be in the class will be 30 students.

From the information, it was stated that the classroom of students can be divided into two, three, and five groups, with no students left over.

Therefore, the number of students that are likely to be in the class will be:

= 2 × 3 × 5

= 30

Therefore, the number of students that are likely to be in the class will be 30 students.

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Answer:

Negative correlation

Step-by-step explanation:

You can draw a line of best fit the would go downhill from left to right which would be a negative slope. This means it has a negative correlation.

Answer:

D. (x2 + 3)(x+ 2)

Step-by-step explanation:

When x3 + 2x2 + 3x + 6 is grouped, it is simplified to (x2 + 3)(x + 2).

Answer: 55

Step-by-step explanation:

All the angles of a triangle added = 180 if you add 75 + 50 you get 125 and 180 - 125 you get 55 so the to check your answer you add it all 75 + 50 + 55 = 180 if you get 180 then you did the problem right hope this helps!

The required side length x is 14.86 units for the given right triangle.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The right triangle is given in the question, as shown.

We have to determine the side length x for the given triangle.

As we know that Pythagoras's theorem,

perpendicular² + base² = hypotenuse²

Substitute the known values in the above formula, and we get

10² + 11² = x²

100 + 121 = x²

x² = 221

x = √221

x = 14.86

Thus, the required side length x is 14.86 units.

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a) The initial population is \(N_0\) = 125 / \(e^{(2k)}\).

b) The exponential growth model for the bacteria population is N = \(N_0\) × \(e^{(kt)}\).

c) The number of bacteria after 8 hours is N = \(N_0\) × \(e^{(8k)}\).

d) After t = ln(25,000 / \(N_0\)) / k hours the bacteria count will be 25,000.

(a) To calculate the beginning population, we must first establish the bacterium population's exponential growth rate. Assume that the initial bacterial population is \(N_0\). The exponential growth model is given by:

N = \(N_0\) × \(e^{(kt)}\)

Where N is the number of bacteria at time t, \(N_0\) is the starting population, e is the natural logarithm base, k is the growth rate constant, and t is time in hours.

We have two data sets: N = 125 after two hours and N = 350 after four hours. We can solve using these two equations \(N_0\) and k.

(125) = \(N_0\) × \(e^{(2k)}\)

(350) = \(N_0\) × \(e^{(4k)}\)

Dividing the second equation by the first equation:

(350/125) = \(e^{(2k)}\)

Taking the natural logarithm of both sides:

ln(350/125) = 2k

Solving for k:

k = ln(350/125) / 2

Now that we have k, we can plug it into either equation and solve for it. \(N_0\):

\(N_0\) = 125 / \(e^{(2k)}\)

(b) The bacterium population's exponential growth model is:

N = \(N_0\) × \(e^{(kt)}\)

Where \(N_0\) = 125 / \(e^{(2k)}\) and k = ln(350/125) / 2

(c) To calculate the number of bacteria present after 8 hours, we use the exponential growth model with t = 8:

N = \(N_0\) × \(e^{(8k)}\)

(d) To calculate the time when the bacterium count reaches 25,000, enter N = 25,000 into the exponentially growing model and solve for t:

25,000 = \(N_0\) × \(e^{(kt)}\)

t = ln(25,000 / \(N_0\)) / k

However, in the absence of a specified growth rate constant (k) and starting population (\(N_0\)), we are unable to determine a precise value for t.

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The question is -

The number of bacteria in the culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.

(a) Find the initial population.

(b) Write an exponential growth model for the bacteria population. (Let t represent time in hours)

(c) Use the model to determine the number of bacteria after 8 hours.

(d) After how many hours will the bacteria count be 25,000?

To sort the numbers using a heap, we first insert all the numbers into the heap. Then we repeatedly remove the maximum element from the heap and add it to the sorted list until the heap is empty. Here are the steps to build the heap and sort the numbers:

1. Start with an empty heap.
2. Insert 94 into the heap. The heap now looks like this: [94].
3. Insert 53 into the heap. The heap now looks like this: [94, 53].
4. Insert 96 into the heap. The heap now looks like this: [96, 53, 94].
5. Insert 87 into the heap. The heap now looks like this: [96, 53, 94, 87].
6. Insert 43 into the heap. The heap now looks like this: [96, 53, 94, 87, 43].
7. Insert 75 into the heap. The heap now looks like this: [96, 75, 94, 87, 43, 53].
8. Insert 23 into the heap. The heap now looks like this: [96, 75, 94, 87, 43, 53, 23].
9. Remove the maximum element (96) from the heap and add it to the sorted list. The heap now looks like this: [75, 53, 94, 87, 43, 23].
10. Remove the maximum element (75) from the heap and add it to the sorted list. The heap now looks like this: [94, 53, 23, 87, 43].
11. Remove the maximum element (94) from the heap and add it to the sorted list. The heap now looks like this: [87, 53, 23, 43].
12. Remove the maximum element (87) from the heap and add it to the sorted list. The heap now looks like this: [53, 43, 23].
13. Remove the maximum element (53) from the heap and add it to the sorted list. The heap now looks like this: [43, 23].
14. Remove the maximum element (43) from the heap and add it to the sorted list. The heap now looks like this: [23].
15. Remove the maximum element (23) from the heap and add it to the sorted list. The heap is now empty.

Therefore, the sorted list in decreasing order is [96, 94, 87, 75, 53, 43, 23].

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Answer:

6 1/3  

Step-by-step explanation:

18 3/4 divided by 3 is 6 1/3

a. Drive Co.'s revenue function R(X) = (-x^2/5)-247x.

b. The price per drive when revenue is maximized is $370.6.

c. The maximum profit made from the sale of these drives if Drive Co. incurs production costs of $179 per drive and has fixed costs of $250 is $6030.

What is a function?

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.

Drive Co. sells portable 905 hard drives when the price is $66/drive and can sell 800 hard drives when the price is $87/drive.

Let p be the price of hard drive and x be the number of hard drives.

When x = 905, then p = 66.

So, (x1,p1) = (905,66)

Similarly, when x = 800, then p = 87.

So, (x2,p2) = (800,87)

So, the equation of line between x and p is given as -

p-p1=[(p2-p1)/(x2-x1)}(x-x1)

Plugging in the values -

p-66=[(87-66)/(800-905)](x-905)

p-66=(21/-105)(x-905)

-105p+6930=21x-19005

-105p-21x=-19005-6930

-105p-21x=-25935

p=(-21x/105)-247

p=(-x/5)-247

So, the price function p(x) = (-x/5)-247.

Now, derive the revenue function -

Revenue = Number of drives × price per drive

Revenue = x · p(x)

Revenue = x · (-x/5)-247

Revenue = (-x^2/5)-247x

Therefore, the revenue function R(x) = (-x^2/5)-247x.

For maximum revenue -

dR/dx = R'(x) = 0 and R''(x)<0

dR/dx = -2x/5-247 = 0

-2x/5 = 247

x = -1235/2

x = -617.5

Therefore, the number of drives at maximum revenue is 618 drives.

The price per drive is -

p(618) = {-618/5}-247

p(618) = -370.6

Therefore, the price per drive is $370.6.

Now, the profit S(x) = Revenue R(x) - Total Cost C(x)

C(x) = fixed cost + variable cost

Variable cost = number of drives × price per drive

C(x) = 250 + 179x

Substituting the values -

S(x) = [(-x^2/5)-247x] - [250+179x]

S(x) = (-x^2/5)-68x-250

In order to get maximum profit differentiate the equation and equate it to 0.

dS/dx = 0

dS/dx = -2x/5-68 = 0

-2x/5 = 68

x = 340/-2

x = -170

d^2S/dx^2 = -2/5<0

So, maximum profit will be at x = 170.

S max = S(170) = [(170)^2 /5] - 68 (170) - 250

= 5780 - 11560 - 250

= -6030

Therefore, the maximum profit earned is $6030.

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Answer:the annual medical expenses for a typical 20 yr old

Step-by-step explanation:

The total simple interest earned by Liz at the end of 5 years is found as: $28.5

A straightforward but effective idea. Very simply: interest is the benefit for saving - and the penalty of borrowing.

Principal P = $570

Interest r = 1%

Time t = 5 years.

SI = P*R*t / 100

SI = 570*1*5 / 100

SI = 28.5

Thus, the total simple interest earned by Liz at the end of 5 years is found as: $28.5.

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The complete question is-

Liz spent her summer break working at Wild Lakes waterpark. At the end of the summer, she put $570 of her earnings into a savings account that earns 1% interest each year. Find her simple interest after 5 years.

Answer:

Square and Equilateral Triangle: same as length

Step-by-step explanation:

For a Square/equilateral triangle  it would be the same as length

Answer:

34 pounds

Step-by-step explanation:

hi again!

so if three students have 10.2 to wash, we can find how many pounds the 3 students have in total by multiplying 10.2*3, because that is the same as doing 10.2+10.2+10.2. this gives us a result of 30.6 points for the three students.

now if the fourth student has 3.4 pounds, we just add that to 30.6

thus we have 30.6+3.4 which equals your answer, 34.

Answer:

The correct answer is number 2.

The given statement is is not correct because if you round the answer to the nearest tenth it would not make it a close answer.

According to the statement

we have to search out that the given statements are the proper or not, and if they're correct then we've got explain the explanation for this.

So, For this purpose, we all know that the

From the given information:

The statement which is given are:

Miguel received a $50 gift card to a bookstore. He would love to shop for 3 books that cost $15.75 each including tax. He estimates that he cannot buy all three books because each book costs about $20, and every one three books would cost $50.

And now after analyzing this, we are able to say that the

no,his answer isn't correct because if you around the answer to the closest tenth it'd not make it an in depth answer.

3*15.75 = 47.25

which is a smaller amount than the 50 dollars.

So, The given statement is is not correct because if you round the answer to the nearest tenth it would not make it a close answer.

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The answer is 237.55

Define Percentage

A ratio or figure stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

Given expression is,

125.8% of £188.83

Rewrite it as,

⇒ 125.8 / 100 * 188.83

⇒ 1.258 * 188.83

⇒ 237.54814

⇒ 237.55 (rounded to 2 Decimal places)

Hence, the answer is 237.55

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Answer:

Answer is below

Step-by-step explanation:

Answer:

u just multiply7×5t

=35t

Answer:

4

Step-by-step explanation:

six times four equals twenty four

Answer:

A

Step-by-step explanation:

26÷6=4