Yamuna is getting ready to attend Wittenberg University in the fall. She needs 6 notebooks
at $2.19 each and a chromebook at $529.00. If she has $575 to spend, how much does
she have left for lunch?

Step-by-step explanation:

We need to break up the given expression into two separate fractions so that when they are added together, we will get the original expression.

Note that the denominator is made up of two factors, [tex](2x - 1)[/tex] and [tex](x^2 + 1).[/tex] But note that the 2nd factor is a 2nd order polynomial so as a rule, the numerator of the fraction containing this factor must be an (n - 1)-order polynomial, where n is the order. With that in mind, we can write the general form of the partial fractions as follows:

[tex]\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{Ax + B}{x^2 + 1} + \dfrac{C}{2x - 1}[/tex]

[tex]\:\:\:\:=\dfrac{2Ax^2 + Bx - Ax - B + Cx^2 + C}{(2x - 1)(x^2 + 1)}[/tex]

Here, we combined the two fractions to form the equation above. Next, we compare the numerators on either side. Note that we satisfy the equality if we impose the following conditions:

[tex]2A + C = 0\:\:\:\:\:\:\:\:\:\:\:\:\:\:(1)[/tex]

[tex]2B - \:A = 1\:\:\:\:\:\:\:\:\:\:\:\:\:\:(2)[/tex]

[tex]-B + C = 7\:\:\:\:\:\:\:\:\:\:\:\:\:\:(3)[/tex]

To find the values of the constants A, B and C, we need to solve this system of equations. We start by multiplying Eqn(3) by 2 and then adding it to Eqn(2) to get

[tex]-A + 2C = 15\:\:\:\:\:\:\:\:\:\:\:\:\:\:(4)[/tex]

Then, multiply Eqn(1) by -2 to get

[tex]-4A - 2C = 0\:\:\:\:\:\:\:\:\:\:\:\:\:\:(5)[/tex]

Add Eqn(4) to Eqn(5) and we will get

[tex]-5A = 15 \Rightarrow A = -3[/tex]

Now that we know the value of A, we can use this in Eqn(2) to get

[tex]2B - (-3) = 1 \Rightarrow B = -1[/tex]

Next, to solve for C, we use the value of A in Eqn(1) to get

[tex]2(-3) + C = 0 \Rightarrow C = 6[/tex]

Therefore, the given expression can be written as

[tex]\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{6}{2x - 1} + \left(\dfrac{-3x - 1}{x^2 + 1}\right)[/tex]

As a check, let's combine the two fractions together:

[tex]\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{6}{2x - 1} + \left(\dfrac{-3x - 1}{x^2 + 1}\right)[/tex]

[tex]= \dfrac{6x^2 + 6 - 6x^2 - 2x + 3x + 1}{(2x - 1)(x^2 + 1)}[/tex]

[tex]= \dfrac{x + 7}{(2x - 1)(x^2 + 1)}[/tex]

As expected, we got the original expression.

Using the principle of proportional relationship, the number of whole serving that can be made is 26.

Recall :

Total amount of aquafaba in ounces :

Amount of aquafaba required per serving of consomme :

1 serving = 6 oz

x servings = 160 oz

Cross multiply

6x = 160

Divide both sides by 6

x = 160/6

x = 26.667

Hence, the amount of whole serving that can be made is 26.

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Answer:

D) 1530

Step-by-step explanation:

I used Desmos :)

Answer:

RM1,600

Step-by-step explanation:

2000 * 0.20= 400

2000-400= 1600

Answer: 1326

Step-by-step explanation: There is no factorial for addition however the formula n (n+1)/2 works for this where n is the last number of your addition (in this case 51).

Would appreciate brainly <3

Using the Central Limit Theorem, the statement is false, as for the averages of  the data values for a sample group, the standard error is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], hence, the formula is:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

While for a single value, it is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Hence, the formulas are different, and for an average of the data values for a sample group it is:

[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

A similar problem is given at https://brainly.com/question/24663213

Answer:

f=25

Step-by-step explanation:

24+1=25

25-1=24

Answer:

$12

Step-by-step explanation:

Answer:

11

1

11 over 1

Step-by-step explanation:

Answer:

Simplifying

6r + r + -5r = 0

Combine like terms: 6r + r = 7r

7r + -5r = 0

Combine like terms: 7r + -5r = 2r

2r = 0

Solving

2r = 0

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Divide each side by '2'.

r = 0

Simplifying

r = 0

7r-5r < this is the answer

6r+r=7r

Answer:

Ok the answer is 200 feet

Answer:

3/10

Step-by-step explanation:

You have to make them the same fraction.

2/5 = 4/10

3/10 =3/10

3/10 + 4/10 = 7/10

10/10 - 10/10 =3/10

3/10 is the amount of tigers.

Answer:

4x+2=4x+4, no solution

Step-by-step explanation:

first, i'm assuming the flower bed is a square so that all 4 sides are x+1. next, to find the perimeter you have to add up the side lengths of each shape.

vegetables: x + x+1 + x + x+1 = 4x+2 so the perimeter of the vegetables must be 4x+2

flowers: x+1 + x+1 + x+1 + x+1 = 4x+4

since the two must be equal, we have 4x+2=4x+4, this is the equation Trent can use

next, to solve the equation, subtract 4x from both sides to get 2=4. this obviously isn't true so there is no solution

This is quite an interesting problem. I am not sure how high you are in math, but I am going to use calculus I techniques to solve it. First, we need to model an equation. Let P be the total profit and x be every time you increase the cost by $10. If you think about it hard enough you come up with the equation

[tex]P(x)=(200-5x)(250+10x)[/tex]

(200-5x) is the amount of plots you will be able to sell, and (250+10x) is the amount you charge for. So, at x =0

[tex]P(0)=(200-5(0))(250+10(0))=(200)(250)=$50,000[/tex]

This is the initial condition where if we sell 200 plots at $250/plot.

So, this equation makes sense.

Now, let's maximize using the first derivative of the function.

Let's get it into an easily differentiable form.

[tex]P(x)=(200-5x)(250+10x)=-50x^2+2000x-1250x+50000\\=-50x^2+750x+50000[/tex]

From here, differentiate the problem.

[tex]P'(x)=-100x+750[/tex]

Now, set it equal to zero and solve for x.

[tex]P'(x)=-100x+750=0\\x=7.5[/tex]

This a critical point of the function. Let's plug back into the original equation to see what it gives us.

[tex]P(7.5)=(200-5(7.5))(250+10(7.5))=(162.5)(325)=52,812.50[/tex]

You cant sell half a plot, so we need to see what happens if we sell 162 plots and 163 plots, and then compare which one gives us more money.

In order to sell 162 plots

[tex]200-5x=162\\x=7.6[/tex]Plug back into P(x) to see the profit

[tex]P(7.6)=(200-5(7.6))(250+10(7.6))=(162)(326)=52,812[/tex]

Now, do the same for 163 plots

[tex]200-5x=163\\x=7.4\\P(7.4)=(200-5(7.4))(250+10(7.4))=(163)(324)=52,812[/tex]

As we can see, they are the same. So, you can charge either $324 or $326 in rent. But, if your teacher is not looking for a logical answer and you can somehow sell half a plot, you can charge $325 in rent for the maximum profit.

Answer:

if its me then i will bye the store. but the answer is 50%

Step-by-step explanation:

Answer:

7:1

Step-by-step explanation:

The original ratio was 6:42. To simplify this, we can find the greatest common factor for 6 and 42 by listing out their factors.

6: 1, 2, 3, 6

42: 1, 2, 3, 6, 7, 14, 21, 42

6 is the greatest common factor they share. We now need to divide each side by this number. This leaves us with 1:7. Since they want us to write the ratio in yellow triangles to blue triangles instead of blue triangles to yellow, we just need to flip the ratio to 7:1.

Answer:

No

But it us Near though

Step-by-step explanation:

9/15 or 3/5 =60%

Answer:

what answer

Step-by-step explanation:

?????????????

Answer:

A.

Step-by-step explanation:

All choices show the first original equation.

Each choice shows a different second equation.

Take the second original equation:

6x + 5y = 30

Multiply both sides by -5.

-30x - 25y = -150

Answer: A.

It takes 20 seconds for the cheetah to catch up to the antelope

Speed is the ratio of distance to time taken. It is given by:

Speed = distance / time

Let d represent the distance covered by the cheetah at time t, hence:

30 = d / t

t = d / 30

The antelope is 100 yards away, hence:

25 = (d - 100) / t

t = (d - 100)/25

d/30 = (d - 100)/25

25d = 30d - 3000

d = 600 yards

t = d/30 = 600/30 = 20 seconds

It takes 20 seconds for the cheetah to catch up to the antelope

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Answer:

Step-by-step explanation:

321

This can be represented by the exponential function:

[tex]P=378(2)^\frac{t}{36}[/tex]

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the factor.

Let P represent the population of the bacteria after t minutes.

Since the bacteria starts with a population of 378, hence a = 378. The bacteria doubles every 36 minutes, This can be represented by:

[tex]P=378(2)^\frac{t}{36}[/tex]

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The statement is true: the area under the graph line made with the x-axis

represents the change in position of the object on a velocity versus time

graph.

Reasons:

[tex]\displaystyle Velocity = \frac{Dislacement}{Time}[/tex]

The area under the velocity time graph is given by the integration of the function for the velocity over the time interval.

A constant velocity is an horizontal line and the integration of a constant with time, gives the product of time and the constant, which is area under the rectangular graph.

Therefore, the area under the graph line made with the x-axis represents the change in position of the object on a velocity versus time graph.

Learn more here:

https://brainly.com/question/18910091

Answer: True

Step-by-step explanation:

Answer:

Accrued expenses are those liabilities that have built up over time and are due to be paid. Accrued expenses are considered to be current liabilities because the payment is usually due within one year of the date of the transaction. Accounts payable are current liabilities that will be paid in the near future.

Answer:

Wages expense, Interest expense

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distance:

Speed:

Time:

Answer:

Step-by-step explanation:

Answer:

X=5

Step-by-step explanation:

Collect like terms then move the terms. Then collect liked terms. Calculate and Chang signs

Answer:

X = 5

Remember, x has a hidden one behind it, so it would be 1x

3x - 2(x + 1) = 2x - 7

Use the distributive property to multiply −2 by x+1.

3x−2x−2=2x−7

Combine 3x and −2x to get x

x−2=2x−7

Subtract 2x from both sides

x−2−2x=−7

Combine x and −2x to get −x

−x−2=−7

Add 2 to both sides

−x=−7+2

Add −7 and 2 to get −5

−x=−5

multiply both sides by -1

x=5

Answer:

7

Step-by-step explanation:

To find what 1/8 of 56 is, we can multiply it by 1/8. This makes it 56/8. Dividing 56 by 8 gives 7.

The element which should be used to help clarify a complicated idea in a text is ; A research question.

According to the question;

A research question is the best fit which should be used to help clarify a complicated idea in a text.

This is so because; a research question provides a basis for accessing all perspectives there is to the complicated idea.

Read more:

https://brainly.com/question/18675306

Answer:

D:) a research question.

Step-by-step explanation:took the test

Answer:

There will be 10 students in each van, and only 8 in one van

Step-by-step explanation:

26 + 32 = 58