Solutions greatest to smallest for function
=2+5−7

The decomposition of the partial fraction is [tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]

The expression is given as:

[tex]\frac{4ax-a^2}{x^2+ax-2a^2}[/tex]

Expand the denominator

[tex]\frac{4ax-a^2}{x^2- ax+2ax-2a^2}[/tex]

Factorize

[tex]\frac{4ax-a^2}{x(x- a)+2a(x-a)}[/tex]

Factor out x - a

[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)}[/tex]

The denominator of the partial fraction is a product of two linear factors.

So, the decomposition can be represented as:

[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]

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The word problem that depicts this algebraic equation is;

The sum of the weight of my son and my daughter is 9 kg but the product of their weights is 14. Find the weights of each person.

We want to write a word problem with the equation;

x(9 - x) = 14

The word problem that depicts this algebraic equation is;

The sum of the weight of my son and my daughter is 9 kg but the product of their weights is 14. Find the weights of each person.

Now, the word problem above is correct because if we assume their weights are x and y, then we can say that;

x + y = 9

xy = 14

Now, y = 9 - x

Thus, equation 2 is;

x(9 - x) = 14

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The number whose sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed is 32

the number can be expressed as 10x + y

x + y = 5

(10x+y) - 9

= 10y+x

x + y = 5

9x - 9y = 9

x + y = 5

x - y = 1

Add the equations

2x = 6

x = 6/2

x = 3

substitute into

x + y = 5

3 + y = 5

y = 5 - 3

y = 2

Therefore, the unknown number is 32.

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The value of y in the triangle is B. 6✓3.

From the information given,

NU = 9

UM = 3

MN = 3 + 9 = 12

NT² = 9 × 12 = 108

NT = ✓108

NT = 6✓3

Therefore, y is 6✓3.

The value of y in the triangle is 6✓3.

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Answer:

B

Step-by-step explanation:

A geometric shapes that can be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.

It should be noted that geometric shapes are the figure of area that is closed by a boundary.

In this case, a geometric shapes that. an be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.

This is because all the sides in a square are equal.

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The given expression is a perfect square trinomial.

Here we have the expression:

[tex](x^2 - 16)^2[/tex]

Notice that we can rewrite it as:

[tex](x^2 - 4^2)^2[/tex]

Then we can see that inside the parenthesis we have a difference of squares, but it is squared, so if we define:

[tex]x^2 = a\\4^2 = b[/tex]

We will have:

[tex](a - b)^2 = a^2 + -2ab + b^2 = (x^2)^2 - 2*(4^2)*(x^2) + (4^2)^2[/tex]

Which is in fact, a perfect square trinomial.

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Work Shown:

m^2+9m=0

m(m+9)=0

m = 0 or m+9 = 0

m = 0 or m = -9

For more information, check out the topics about factoring and the zero product property.

Answer:

$4.50

Step-by-step explanation:

We can use the distributive property to solve this problem. 0.05(50+40) is the total sales tax. 0.05 being the percentage and 50 and 40 being the things we need to distribute 0.05 to. This becomes 2.5+2. This is 4.5.

Answer:

$0.45

Step-by-step explanation:

0.05(50 + 40) = 50 x 0.05 + 40 x 0.05 = 0.25 + 0.20 = 0.45

The volume of the figure to the nearest whole number = 756π m³.

The figure shown exists composed of a cone and a cylinder.

The volume of the figure = volume of cone + volume of the cylinder

Height of cone = 12 - 8 = 4

Radius (r) of cone = 18/2 = 9 m

The volume of the cone V = 1/3hπr²

= 1/3 [tex]*[/tex] 4π [tex]*[/tex] 9² = 108π

The volume of the Cylinder = πr²h

radius (r) = 18/2 = 9 m

height (h) = 8 m

Volume of cylinder = π [tex]*[/tex] 9² [tex]*[/tex] 8 = 648π m³

Volume of the figure = 108π + 648π = 756π

The volume of the figure to the nearest whole number = 756π m³.

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Answer:

3/8 or 0.375 or 37.5%

Step-by-step explanation:

So since the coin is tossed three times, it's not to hard to write out every scenario since there will only be 2^3  combinations or 8 combinations. But we can also use Binomial Distribution Formula.

Binomial Distribution Formula:

   [tex]P(x)=(^n_x)p^xq^{n-x}[/tex]

   Where p = probability of success and q=probability of failure, x=how many successes, and n=total number of trials

   Combination Formula:

       [tex](^n_x) = \frac{n!}{x!(n-x)!}[/tex]

So let's define the variable values, since it's a coin, the probability of heads/tails should be 50/50 so p=0.50 and q=0.50. Since we want 2 heads then x=2, and since the total number of trials is 3, n=3.

So let's plug the values into the equation:

[tex]P(x)=\frac{3!}{2!}*(0.50)^2*(0.50)^1[/tex]

Rewrite 0.50 as a fraction

[tex]P(x)=\frac{3*2*1}{2*1}*(\frac{1}{2})^2*(\frac{1}{2})^1[/tex]

Cancel out values in fraction, and also square the fraction

[tex]P(x)=3*\frac{1}{4}*\frac{1}{2}[/tex]

Multiply fractions

[tex]P(x)=3*\frac{1}{8}[/tex]

Multiply the two values

[tex]P(x)=\frac{3}{8}[/tex]

This means the probability is 3/8 or 0.375 or 37.5%

I also provided a diagram on how to just draw out each scenario/combination

Add both

Put in first one

Find

The factored polynomial is given as follows:

(5x - 1)(6x² + 1)

Polynomials are factored placing the common factor in evidence, then dividing all terms by the common factor.

The polynomial is:

6x²(5x - 1) + (5x - 1).

The common factor is (5x - 1), hence:

[tex](5x - 1)\left(\frac{6x^2(5x - 1)}{5x - 1} + \frac{5x - 1}{5x - 1}\right) = (5x - 1)(6x^2 + 1)[/tex]

Hence the factored polynomial is given as follows:

(5x - 1)(6x² + 1)

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The quilt will be 10.99 inches wider and 9.01 inches shorter than the bed.

The first step is to determine the dimensions of the quilt.

Dimensions = √35 = 5.92 feet

Now convert the dimensions of the quilt to inches

1 feet = 12 inches

5.92 x 12 = 70.99 inches

Difference in the width of the bed and the quilt = 70.99 - 60 = 10.99

Difference in the length of the bed and the quilt = 80 - 70.99 = 9.01

 Here are the options:

A. The quilt will cover half of the surface of the bed.

O B. The quilt will match up with the length of the bed, but 20 inches will hang over the length. °

C. The quit will be 14.6 inches wider and 15.4 inches shorter than the bed. O D. The quilt will be 10.99 inches wider and 9.01 inches shorter than the bed.

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Induced pluripotent stem cells can be a valuable tool in science and medicine because: A. induced pluripotent stem cells can become any cell type in the body, but are from adults, avoiding the controversies associated with embryonic stem cells.

A cell can be defined as the fundamental functional, structural and smallest unit of life, which is typically found in all living organisms.  

In Science, all living organisms are broadly grouped into two (2) main categories according to cell type and these include the following;

Basically, the reason why induced pluripotent stem cells can be a valuable tool in science and medicine is simply because they can become any cell type within the body of a living organism, but are usually derived from adults that are avoiding the controversies associated with embryonic stem cells.

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Complete Question:

Induced pluripotent stem cells are cells from adults that have been reprogrammed to imitate embryonic stem cells. Why might induced pluripotent stem cells be a valuable tool in science and medicine?

A. Induced pluripotent stem cells can become any cell type in the body, but are from adults, avoiding the controversies associated with embryonic stem cells

B. Induced pluripotent stem cells are the only type of stem cell that's truly pluripotent.

C. Induced pluripotent stem cells may become any cell type in the body, but are fraught with ethical questions over their use.

D. Induced pluripotent stem cells are derived from adult cells and therefore may have DNA abnormalities, allowing scientists to understand the effects of sun exposure or toxins on DNA

The test statistic is 27.8484, the p-value is 0, and the final conclusion is that the null hypothesis H is rejected.

Given that 914 babies were born to parents who used the new method, and 877 of them were girls, the significance level to test the claim that the new method is effective in increasing the likelihood of a baby being a girl, is 0.01.

The following information is provided: the sample size is N = 914, the number of favorable cases is X = 877, and the sampling ratio is

pˉ = X / N

Pˉ = 877/914

pˉ = 0.9595 and the significance level is α = 0.01

(a) Hypothesis Zero and Alternative

The following null and alternative hypotheses should be tested:

null: p = 0.5

Alternative: p> 0.5

This is equivalent to a right-tailed test, which requires a z-test for a proportion of the population.

(b) Critical Value

Based on the information provided, the significance level is α = 0.01, so the critical value for this right-tailed test is Zc = 2.3263. This can be found using Excel or the Z distribution table. Region of rejection

The rejection area for this test on the right side is Z> 2.3263

Test statistics

The z-statistic is calculated as follows:

[tex]\begin{aligned}Z&=\frac{\bar{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\ &=\frac{0.9595-0.50}{\sqrt{\frac{0.5(1-0.5)}{914}}}\\ &=\frac{0.4595}{0.0165}\\ &=27.8484\end[/tex]

(c) The p-value

The p-value is the probability that the sample results are extreme or more extreme than the sample results obtained, assuming the null hypothesis is true. In this case,

the p-value is p = P (Z> 27.8484) = 0

(d) The decision on the null hypothesis

Using the traditional method

Since we observe that Z = 27.8484> Zc = 2.3263, we conclude that the null hypothesis is rejected.

Using the p-value method

Using the approximation of the P-value: the p-value is p = 0, and since p = 0≤0.01 we conclude that the null hypothesis is rejected.

(e) Conclusion

It is concluded that the null hypothesis H is rejected. Therefore, there is sufficient evidence to state that the population proportion p is greater than 0.5, at the significance level of 0.01.

Hence, for 914 babies born to parents using the new method, of which 877 were girls, the test statistic is 27.8484, the p-value is 0, and the final conclusion is that the null hypothesis is rejected.

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Answer:

A

Step-by-step explanation:

I. False. Consider y = 3 and x = 4.

II. False. Consider x = 1.

III. False. Consider x = -2.

Answer:

b = (a - 6)/2h

Step-by-step explanation:

a = 2bh + 6 (subtract 6 from both sides)

a - 6 = 2bh (divide both sides by 2)

(a - 6)/2 = bh (divide both sides by h)

(a - 6)/2h = b

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The carbon dioxide that is produced from the vampire energy used by the office computer is 1042.8 kWh.

Based on the information given, the number of hours that the computer is plugged on a day will be:

= 20/7

= 2.857 hours

Therefore, the power consumption in a year will be:

= 2.857 × 365

= 1042.8 kWh

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Answer:

130,000 -:- by 30 x 0.3 x 12 = 15,600.

Step-by-step explanation:

(I hope its right, Im not good at math)

Answer:

5.9512

Step-by-step explanation:

1. Convert the percentage to decimal

8% = 8/100 = 0.08

2. Multiply the decimal by the quantity to be extracted

(0.08)(74.39) = 5.9512

Hope this helps

Answer:

There are about 80 students age 15 and above take a car to school.

Step-by-step explanation:

1. For all the columns the total has been given.

2. Bus is taken as 60 as walk/bike has been given 65 under age 15.

3. 195 row total Age 15 and above has been provided and updated.

4. Walk/Bike 152, 65 is already given Age 15 and above difference is 87.

5. Bus 60 under age 15 is already given total 110 difference is 50.

6. Age 15 and above 65,50,195 (Total) is already given row difference is 80.

7. Car is Age 15 and above is 80 and Total column is 98 difference is 18.

8. Age 15 and above take car is 80.

Answer:

its 41%

Step-by-step explanation:

i took the test

The graph isn't bipartite because it isn't possible to assign either Blue or Red to each vertex, without having connected vertices with the same color.

The bipartite graph theorem states that a graph is considered to be bipartite only if it's possible to assign either Blue or Red to all the vertex, such that no two (2) connected vertices would have the same color.

By critically observing the image after assigning the colors to each vertices (see attachment), we can logically deduce that the graph isn't bipartite because it isn't possible to assign either Blue or Red to all the vertex, without having connected vertices with the same color.

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The amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.

Given mean of 112 inches, standard deviation of 14 inches.

We are required to find the amount that separates the lowest 20% ofthe means of yearly snowfall in the past 10 years from the highest 80%.

a) Bottom 20% would have a z score of -0.8416.

b) Top 80% would have a z score of 0.842.

Use the z formula to find the raw score.

z=(X-m)/sd

X=the raw score

m= mean

sd=standard deviation

Putting the value of low score.

-0.8416=(X-112)/14

X=-11.7824+112

=100.2176

Putting the values of high score.

0.842=(X-112)/14

X=123.788

The amount that seprates the lowest from highest is 123.788-100.2176

=23.57 inches.

Hence the amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.

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a) The exponential function that models the number of cells is: [tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]

b) There will be 1292 cells after 10 hours.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]

In which:

For this problem, the parameters are:

A(0) = 200, r = 0.75, n = 3.

Hence the equation is:

[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]

[tex]A(t) = 200(1 + 0.75)^{\frac{t}{3}}[/tex]

[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]

The number of cells after 10 hours is:

[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]

[tex]A(10) = 200(1.75)^{\frac{10}{3}}[/tex]

A(10) = 1292.

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The sample should include 2702 men and 2702 women.

Given that you want to be 99% sure your error doesn't exceed 0.035.

A sample is a group of people selected from a larger population to provide data to researchers. The number of members of the population included in the sample is called the sample size.

The significance level is the probability that the test statistic is in the critical range if the null hypothesis is actually true. The confidence interval is 99% or 0.99.

The level of significance α = 1-0.99 = 0.01

the margin of error, ME = 0.035

The Z-critical value at the 99% confidence level or at the significance level of 0.01 is 2.575 (from standard normal tables).

We will now use the formula:[tex]n=\frac{Z^2_{critical}}{2(ME)^2}[/tex].

Substitute the values ​​in the above formula, we get

n = (2.575) ² / (2 × (0.035) ²)

n = 6.630625 / (2 × 0.001225)

n = 6.630625 / 0.00245

n = 2701.966

Therefore, the sample should include 2702 males and 2702 females with a 99% certainty that the error does not exceed 0.035

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Answer:

51 Adult tickets were sold that day.

Step-by-step explanation:

Let c = child and a = adult

c + a = 148                      5.50c + 9.00a = 992.50

Change the first equation so that it is either in the form c = or a =and then plug that number into the second equation.

I am going to change the first equation to c = by subtracting a from both sides

c = 148 - a

Now I am going to plug 148 -a for c in the second equation.

5.5(148 - a) + 9a = 992.5 Next distribute the 5.5

814 - 5.5a + 9 a = 992.5 Add the a terms together

814 + 3.5a = 992.5 Subtract 814 from both sides

3.5a = 178.5  Divide both sides by 3.5

a = 51

Answer:

males = 7

females = 43

Step-by-step explanation:

whilst it may seem intuitive to simply subtract 36 from 50, it is not saying "there are 36 males, how many females?" but instead, "the difference between the number of males and females is 36".

You can solve this equation most easily algebraically. For example:

Number of males = x

number of females = y

the question states that the total number of people = 50

therefore we can say that the total number of males (x) + the total number of females (y) = 50 people

therefore: x + y = 50

similarly, the question says that the number of males (x) + 36 = the total number of females (y)

therefore: x + 36 = y

we now have two equations:

x + y = 50

x + 36 = y

whilst both equations have two unknowns (x and y), therefore we can't simple solve for x or y, with the combination, we can see a pattern.

focusing on the second equation: x + 36 = y

we can add x to both sides, because you can pretty much do anything to the equation as long as you do it to both sides.

x + 36 + x = y + x

now this may seem very random, but you now see that one side of the equation equals y + x, and remember from the other equation, x + y = 50. Therefore we can substitute x + y in the second equation for 50.

our two equations:

x + 36 + x = y + x

x + y = 50

therefore:

x + 36 + x = 50

for the sake of clarity, we can combine like terms...

x + x = 2x

therefore:

x + 36 + x = 50

2x + 36 = 50

solve for x by subtracting 36 from both sides, then dividing both sides by 2

2x + 36 - 36 = 50 - 36

2x = 14

2x / 2 = 14 / 2

x = 7

now remember:

Number of males = 7 (we now know x = 7)

now that we've solved for x, we can go back to our original equation:

x + 36 = y

and substitute x...

7 + 36 = y

43 = y

Now remember:

Number of females = 43 (we now know y = 43)

therefore there are 7 males and 43 females. we can proof this by adding 7 and 43, and you'll see you reach 50, which is the correct total number of people.

hope this helps :)

A piece-wise function that has domain of all real numbers and range of [tex][-3, \infty)[/tex] is f(x) = |x| - 3, as:

[tex]|x| - 3 = x - 3, x \geq 0[/tex]

[tex]|x| - 3 = -x - 3, x < 0[/tex]

A piece-wise function is a function that has different definitions, depending on the input.

One example is the absolute value function, defined as follows:

[tex]|x| = x, x \geq 0[/tex]

[tex]|x| = -x, x < 0[/tex]

The function is defined for all real values, with a range of [tex][0, \infty)[/tex]. Shifting it down 3 units, it will have the desired range, as follows:

[tex]|x| - 3 = x - 3, x \geq 0[/tex]

[tex]|x| - 3 = -x - 3, x < 0[/tex]

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i think this is the answer