Review the equation used in writing a partial fraction decomposition.

StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction

or, [tex]\frac{-15x+10}{(5x-2)^2} = \frac{A}{5x-2} + \frac{B}{(5x-2)^2}[/tex]


Which system of equations can be used to determine the values of A and B?
(answer choices in attached image)

Answer:

x^-3

Step-by-step explanation:

1 / (x^3)     =   x^(-3)  

The 2-digit number is 26:

26 - 1 = 25 is a square number.

26 + 1 = 27 is a cube number.

Here we want to find a 2-digit number N, such that:

To do that, we can just create a list of cubic and square numbers of 2 digits, these are:

Square numbers:

4*4 = 16

5*5 = 25

6*6 = 36

etc...

Cube numbers:

3*3*3 = 27

4*4*4 = 64

etc...

Now, we can see that 25 is a square number and 27 is a cube number, then our 2-digit number can be 26.

Because:

26 - 1 = 25 is a square number.

26 + 1 = 27 is a cube number.

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The  total trash that will be produced over the next 8 years will be 107 trash

Given the function that represents the amount of trash, in tons per year, produced by a town has been growing linearly, and is projected to

continue growing according to the formula P(t) = 75 + 4t

The total trash that will be produced over the next 8 years is expressed as:

p(8) = 75 + 4(8)

p(8) = 75 + 32

p(8) = 107

Hence the  total trash that will be produced over the next 8 years will be 107 trash

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Answer:

25.3 lb

Step-by-step explanation:

We can multiply the whole by the percentage to find the part. Since 15.9% is equal to 0.159, the weight of fat is 159*0.159 = 25.281. Round this to the nearest tenth, and we get 25.3 pounds.

The perimeter of the rectangle as a function of its base is P = 2(b + 235/b)

The perimeter of a shape is the sum of the side lengths of the shape For all regular quadrilaterals, you add up the side lengths to determine the area

The given parameters are

Area = 235 sqare inches

The area of a rectangle is calculated using

Area = Base * Height

Note that the area of a shape is the amount of space on the shape

Recall that the area of a rectangle is calculated using

Area = Base * Height

Rewrite the above equation as

A = bh

So, we have

bh = 235

Make h the subject of the formula

h = 235/b

The perimeter of the rectangle is

P = 2(b + h)

So, we have

P = 2(b + 235/b)

Hence, the perimeter of the rectangle as a function of its base is P = 2(b + 235/b)

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Answer:

its the same as increasing x by 5 percent

Answer:

1.05x is the answer

Step-by-step explanation:

Step-by-step explanation:

when means of more than two groups are to be compared, ANOVA is perferred

Answer: 319.74 square mm

Step-by-step explanation:

[tex]6(7.3)^2=319.74[/tex]

66877383

Step-by-step explanation:

I made a single dad be single of ⅝

Using the given linear function, the formula underestimates the median weekly earnings in 2013 by $3.

The function that estimates the median weekly earnings n years after 1980 is given by:

W = 13n + 231.

2013 is 2013-1980 = 33 years after 2000, hence the estimate is given by:

W = 13 x 33 + 231 = 660.

Since 657 < 660, the formula underestimates the median weekly earnings in 2013 by $3.

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Answer:

OA

Step-by-step explanation:

Step-by-step explanation:

60000÷ 10 = 600 and 600 ÷ 3 =20

The total sales realized by the company was $20,000,000.

percentage, a relative value indicating hundredth parts of any quantity.

Let x be the total sales realized by the company.

Maria's pay is 3% of the total profits, which is 3% of 10% of total sales

0.03(0.1x) = 0.003x.

Her total income is given as $60,000, so we have:

0.003x = 60000

Solving for x:

x = 60000/0.003 = 20,000,000

Therefore, the total sales realized by the company was $20,000,000.

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Step-by-step explanation:

It is said A=B I have drawn the Venn diagram of A=B

Answer:

3.25 years (nearest hundredth)

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 4916=4000\left(1+\frac{0.064}{4}\right)^{4t}[/tex]

[tex]\implies \sf 4916=4000\left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \dfrac{4916}{4000}=\left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \dfrac{1229}{1000}=\left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=\ln \left(1.016\right)^{4t}[/tex]

[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=4t \ln \left(1.016\right)[/tex]

[tex]\implies \sf t=\dfrac{\ln \left(\frac{1229}{1000}\right)}{4\ln \left(1.016\right)}[/tex]

[tex]\implies \sf t=3.247594892...[/tex]

Therefore, it will take 3.25 years (nearest hundredth) for the account to grow to $4916.

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The value of x according to the equation in the task content is; -5.35 or -10.65.

The equation given in the task content is; (x + 8)² -7 = 0.

Hence, the equation can be solved as follows;

(x + 8)² - 7 = 0

x² + 16x +64 -7 = 0

x²+ 16x +57 = 0

By solving by means of the quadratic formula, we have;

x = -5.35

x = -10.65

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Using it's concept, it is found that the probabilities are given as follows:

a) 0.1431 = 14.31%.

b) 0.7910 = 79.10%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Item a:

The number of people is:

23 + 44 + 28 + 39 = 134.

The number of people that prefer Pepsi is:

23 + 28 = 51.

Hence, for the two people, the probability is:

p = 51/134 x 50/133 = 0.1431 = 14.31%.

Item b:

There are 23 + 44 = 67 females, and 39 males who prefer Coke, hence the probability is:

p = (39 + 67)/134 = 0.7910 = 79.10%.

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The  given pics are your answers... Thank you

As per the question seems, the expected value can be  positive, negative or zero.

The given question is of probability, which cannot be negative so don't get confused between expected values and probability, expected value and be negative, positive or zero.

What is probability?

Probability can be defined as the ration of favorable outcomes to the total number of events.

If person playing different games in casino , the probability of that person winning could be varying from 0/7 to 7/7 which implies that person can win from zero games to all games. If that person wins all the 7 games that mean he the gain in values, but if the loses 1 games or more games there than he supposed have gain or have loosen expected values so it can be positive, negative or zero. however the person loosen every game their is certain negative expected values.

Thus, The expected value can be  positive, negative or zero.

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The equation for the profit from selling the items is P =  40x-0.5x²-300. The values of x are 10 and 70.

We have the cost function in this question to be

Cx = 60x+300

Revenue = 100x−0.5x²

A. The revenue function is stated as the revenue - cost

= (100x−0.5x²)-60x+300

We have to open the equation

40x-0.5x²-300

B. when profit is 50 dollars

50 = 40x-0.5x²-300

We have to multiply both sides by 10

500 = 400x - 5x² - 3000

We have to collect like terms and form a quadratic equation

5x² - 400x - 3500 = 0

We have to solve the quadratic equation above using a quadratic calculator.

Hence

x = 10, 70

So the two values that would create a profit of 50 dollars is 10 and 70.

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The formula for the number of bacteria at time t is 1000 x (2^t).

The number of bacteria after one hour is 2828

The number of minutes for there to be 50,000 bacteria is 324 minutes.

The exponential function that can be used to determine the number of bacteria with the passage of time is:

initial population x (rate of increase)^t

1000 x (2^t).

Population after 1 hour : 1000 x 2^(60/40) = 2828

Time when there would be 50,000 bacteria : In(FV / PV) / r

Where:

In (50,000 / 1000)

In 50 / 1  = 3.91 hours x 60 = 324 minutes

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[tex]\displaystyle\\\binom{52}{3}=\dfrac{52!}{3!49!}=\dfrac{50\cdot51\cdot52}{2\cdot3}=22100[/tex]

Answer: x-7

Step-by-step explanation:

[tex]f(x)+g(x)=-3x-5+4x-2=\boxed{x-7}[/tex]

Answer:

116.5027

Step-by-step explanation:

degree/360 *pie * radius^2

We can actually deduce here that the ordered pairs that make both inequalities true are:

An inequality is known to be an expression that shows that certain variables or values are not equal to each other. It is usually seen in an inequality expression as:

We see the attached image that shows the graph of inequality and which completes the question.

The options that complete the question are:

A. –2, 2

B. (0, 0)

C. (1,1)

D. (1, 3)

E. (2, 2)

When we insert the values of each axes into the inequality expressions given, we will discover that the ordered pairs that the inequalities true is (1,1) and (2, 2).

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The first negative term of the sequence is -2

The terms of the sequence which is the first negative term can be calculated as follows:

The sequence with nth term is 150 - 4n.

The first negative term will be the first term you will multiply by 4 that will be greater than 150.

Therefore,

nth term with first negative number = 150 - 4(38)

nth term with first negative number = 150 - 152

nth term with first negative number = -2

Therefore, the first negative term of the sequence is -2

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3x^3 x 4x^2 = 12x^5

3x^3 x 1 = 3x^3

2x^2 x 4x^2 = 8x^4

2x^2 x 1 = 2x^2

1x x 4x^2 = 4x^3

1x x 1 = 1x

12x^5 + 3x^3 + 8x^4 + 2x^2 + 4x^3 + 1x

Simplify

12x^5 + 7x^3 + 8x^4 + 2x^2 + 1x

Thus, answer is B

Hope this helps!

The rate is 50gtt per minutes.

From the information, out of the total hours of 8 hours, four hours were used.

The volume will be:

= 1000 - 400

= 600ml

Time = 4 × 60 = 240 minutes

Drop factor = 20

Therefore, the growth rate will be:

= 600/240 × 20

= 50gtt/min

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Answer:

x = 3

Step-by-step explanation:

We can use the following equation to solve for x:

[tex]315=9x-27+8x+24+5x-17+2x+23\\315=(9x+8x+5x+2x)+(-27+24-17+23)\\315=24x+3\\312=24x\\13=x[/tex]

Step-by-step explanation:

1) 3 + 4 = 7

2) 6 - 6 = 0

3) 1 + 3 = 4

4) 6 + 9 = 15

5) 10 - 14 + 2 = -2

6) 2 + 3 - 5 = 0