What is the correct form of the partial fraction decomposition for the expression StartFraction 13 x minus 7 Over (x + 2) (4 x minus 3) EndFraction?

StartFraction A Over x + 2 EndFraction + StartFraction B Over 4 x minus 3 EndFraction
StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over 4 x minus 3 EndFraction
StartFraction A Over (x + 2) (4 x minus 3) EndFraction + StartFraction B Over (x + 2) (4 x minus 3) EndFraction
StartFraction A Over (x + 2) (4 x minus 3) EndFraction + StartFraction B x + C Over (x + 2) (4 x minus 3) EndFraction

Answer:

h+r=34

r=34-h.....1

total surface area=2πr(r+h)

2992=2πr×34

2992/34=2πr

88/2=22/7×r

44×7/22=r

r=2×7=14cm

If the length of the confidence interval for the mean of a normal population is reduced by 1/3, the sample size needs to be increased.

When the population standard deviation is known, the formula for calculating the confidence interval for the mean is given by:

Confidence interval = mean ± (z * (σ/√n))

Where:

mean represents the sample mean

z is the z-score corresponding to the desired level of confidence

σ is the population standard deviation

n is the sample size

To reduce the length of the confidence interval, we need to decrease the value of (z * (σ/√n)).

Since the population standard deviation (σ) is known, the only way to decrease this value is by increasing the sample size (n).

By increasing the sample size, the standard error (σ/√n) decreases, resulting in a narrower confidence interval.

Therefore, the sample size needs to be increased to achieve a reduction in the length of the confidence interval.

To learn more about confidence interval click here: brainly.com/question/13067956

#SPJ11

Answer: b=2/5

Step-by-step explanation:

Step 1: Cross-multiply.

2b−1/2 = b−1/6

(2b−1)*(6)=(b−1)*(2)

12b−6=2b−2

Step 2: Subtract 2b from both sides.

12b−6−2b=2b−2−2b

10b−6=−2

Step 3: Add 6 to both sides.

10b−6+6=−2+6

10b=4

Step 4: Divide both sides by 10.

10b/10 = 4/10

b = 2/5

Samantha often talks on her cell phone while driving. this can be distracting and increases her chance of having an accident. Don't use the phone at all while driving.

What is rules of driving?

I will advise her to refrain from using her phone at all while driving.

Learn more about driving rules

brainly.com/question/10825924

#SPJ4

Answer:

y = 4.8

Step-by-step explanation:

Given that y is inversely proportional to x² then the equation relating them is

y = \(\frac{k}{x^2}\) ← k is the constant of proportion

To find k use the condition when x = 4, y = 7.5 , then

7.5 = \(\frac{k}{4^2}\) = \(\frac{k}{16}\) ( multiply both sides by 16 )

k = 16 × 7.5 = 120

y = \(\frac{120}{x^2}\) ← equation of proportion

When x = 5 , then

y = \(\frac{120}{5^2}\) = \(\frac{120}{25}\) = 4.8

Answer:

9.28

Step-by-step explanation:

Answer:

$13,000

Step-by-step explanation:

52 weeks in a year means 26 two week periods (fortnights, if you feel it is important in social studies). This means 2600 dollars per year. Multiplty by 5 to get $13,000. Hope this helps!

Answer:

Laila got 96 out of 120 questions wrong. Laila got 80% on the exam.  20% is the rate of the 24 questions you missed.

Step-by-step explanation:

Hope this helps u

When the coefficient matrix A is zero, the system of equations represented by A * X = B is either dependent (many solutions) or inconsistent (no solutions), depending on the values of b₁ and b₂.

In the given matrix equation A * X = B, where A is the coefficient matrix and X and B are column matrices representing variables and constants, respectively, it is stated that A = 0. Since A = 0, the coefficient matrix becomes: [0 0]; [0 0]. Now let's consider the system of equations represented by A * X = B: a₁x + a₂y = b₁; a₃x + a₄y = b₂. With A = 0, the equations become: 0x + 0y = b₁; 0x + 0y = b₂. These simplified equations reveal that regardless of the values of b₁ and b₂, the system becomes: 0 = b₁; 0 = b₂.

This implies that the system is either dependent (has many solutions) if b₁ = b₂ = 0, or inconsistent (has no solutions) if b₁ ≠ 0 or b₂ ≠ 0. In summary, when the coefficient matrix A is zero, the system of equations represented by A * X = B is either dependent (many solutions) or inconsistent (no solutions), depending on the values of b₁ and b₂.

To learn more about coefficient matrix click here: brainly.com/question/9879801

#SPJ11

Answer:

stop rushing me aaaaaaaaaahhhhhhhh

Step-by-step explanation:

Electrical potential  at any point along the x-axis is V = Q/2πε0(1/R1 − 1/R3) and V at x is Vx = 0.55Q/πε0a

Given info,

A square in the x-y plane in free space has a point charge of q at comer (a/2,a/2) and the comer (a/2,-a/2) and a point charge of -q at (-a/2, a/2) and (-a/2, -a/2).

Let,

V = Q/4πε0R1 + Q/4πε0R2 + −Q/4πε0R3 + −Q/4πε0R4

  = Q/2πε0(1/R1 − 1/R3)

With,

R1 = √[(x - a/2)² + (a/2)²]

R3 = √[(x + a/2)² + (a/2)²]

At x = a/2,

R1 = a/2

R3 = a√5/2

Vx = 0.55Q/πε0a.

Therefore, Electrical potential is V = Q/2πε0(1/R1 − 1/R3) and V at x is Vx = 0.55Q/πε0a

To learn more about Electrical potential click here:

brainly.com/question/12645463

#SPJ4

A price floor is a law that limits the minimum price at which a good, service, or factor of production can be sold while a price ceiling is a regulation that limits the maximum price at which a good, service, or factor of production can be sold

Price floors are commonly implemented to support producers, while price ceilings are typically put in place to protect consumers from higher prices that might result from shortages or monopolies.

Example of Price Floor:Agricultural subsidies are a common example of price floors. Government price floors ensure that farmers receive a minimum price for their crops.

If the market price of wheat falls below the government-established price floor, the government may buy the excess supply at the guaranteed price, ensuring that farmers are able to make a profit. If there is a price floor, the minimum price is set above the equilibrium price.

Learn more about price ceiling at:

https://brainly.com/question/2562066

#SPJ11

Answer: (x+ -4)^2=9

Step-by-step explanation: We compete the square by taking had of the coefficient of our x term is -8, half of it would be -4, and squaring it gives us 16 then simplify

The solution to the quadratic equation is x = 7 or x = 1 and the equation is given as ( x - 7 ) ( x - 1 ) = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

x² - 8x + 7 = 0  be equation (1)

On simplifying the equation , we get

x² - x - 7x + 7 = 0

Taking the common factors in the equation , we get

x ( x - 1 ) - 7 ( x - 1 ) = 0

Now , on factorizing the equation , we get

( x - 7 ) ( x - 1 ) = 0

So , when ( x - 7 ) = 0

Adding 7 on both sides of the equation , we get

x = 7

And , when ( x - 1 ) = 0

Adding 1 on both sides of the equation , we get

x = 1

So , the two solutions to the equation is x = 7 or x = 1

Hence , the equation is ( x - 7 ) ( x - 1 ) = 0

To learn more about quadratic equations click :

https://brainly.com/question/25652857

#SPJ2

The differential equation is: r(1 - r ln r) y'' + (1 + x² ln x) y' - (1 + r) y = (1 - x ln x)² e². To find the particular solution, let's assume a particular solution of the form: yp(x) = A e^(r + ln x - x ln x)

Differentiating yp(x), we have:yp'(x) = A e^(r + ln x - x ln x) * (r/x - ln x - 1)

yp''(x) = A e^(r + ln x - x ln x) * [(r/x - ln x - 1)^2 - 1/x]. Substituting these into the differential equation, we have:r(1 - r ln r) [A e^(r + ln x - x ln x) * [(r/x - ln x - 1)^2 - 1/x]] + (1 + x² ln x) [A e^(r + ln x - x ln x) * (r/x - ln x - 1)] - (1 + r) [A e^(r + ln x - x ln x)] = (1 - x ln x)² e². Simplifying and collecting like terms, we get: A e^(r + ln x - x ln x) [(r/x - ln x - 1)^2 - 1/x + (1 + x² ln x)(r/x - ln x - 1) - (1 + r)] = (1 - x ln x)² e². Expanding and simplifying, we have:A e^(r + ln x - x ln x) [r²/x - 2r ln x + (1 - x²) ln x] = (1 - x ln x)² e². For this equation to hold for all x, the coefficients of the terms on both sides must be equal. Therefore, we have:r²/x - 2r ln x + (1 - x²) ln x = (1 - x ln x)² e².  Simplifying and rearranging, we get:r²/x - 2r ln x + ln x - x² ln x + x ln x = (1 - x ln x)² e²

Further simplifying, we have: r²/x - x² ln x = (1 - x ln x)² e²

Unfortunately, we cannot obtain a specific value for r that satisfies this equation. Hence, we are unable to determine a particular solution using the given form. However, the general solution y(x) = C₁e + C₂ ln x + yp(x) is still valid, where C₁ and C₂ are arbitrary constants, and yp(x) represents the particular solution that we were unable to determine explicitly.

To learn more about differential equation click here: brainly.com/question/2273154

#SPJ11

Answer:

Step-by-step explanation:

subtract the divied

The function f(x, y) = x * sin(y) is evaluated at the given values as follows:
(a) f(6, 4) = 6 * sin(4) ≈ -5.89
(b) f(f(6, 3)) = f(6 * sin(3)) ≈ -1.92
(c) f(-9, 0) = -9 * sin(0) = 0
(d) f(9, 2) = 9 * sin(2) ≈ 7.65

To evaluate the function f(x, y) = x * sin(y) at specific values, we substitute the given values of x and y into the function and simplify the expression.
(a) For f(6, 4), we have:
f(6, 4) = 6 * sin(4)
Using a calculator or trigonometric table, we find that sin(4) ≈ 0.0698
Therefore, f(6, 4) = 6 * 0.0698 ≈ -5.89
(b) For f(f(6, 3)), we first evaluate f(6, 3):
f(6, 3) = 6 * sin(3)
Using a calculator or trigonometric table, we find that sin(3) ≈ 0.1411
Then, we substitute this value into the function:
f(f(6, 3)) = f(6 * 0.1411)
f(f(6, 3)) ≈ 6 * 0.1411 ≈ -1.92
(c) For f(-9, 0), we have:
f(-9, 0) = -9 * sin(0) = 0
(d) For f(9, 2), we have:
f(9, 2) = 9 * sin(2)
Using a calculator or trigonometric table, we find that sin(2) ≈ 0.9093
Therefore, f(9, 2) = 9 * 0.9093 ≈ 7.65
Hence, the evaluated values of the function f(x, y) = x * sin(y) are approximately -5.89, -1.92, 0, and 7.65 for the given inputs.

Learn more about function here
https://brainly.com/question/31062578



#SPJ11

Answer:

6

Step-by-step explanation:

add them all together which will get you 24

then divide by the number of months

24/4=6

Answer:

x = 0

r = 20

Step-by-step explanation:

9x - 7 = -7

add 7 to each side of the equation:

9x = 0

x = 0

-4 = (r/20) - 5

add 5 to each side of the equation:

1 = r/20

multiply both sides by 20:

r = 20

Answer:

the answer is b:-6

Step-by-step explanation:

hoped I helped:)

Answer:

75

if your teacher says

that it is wrong then tell him/her to study once again

Answer:

x = 75

Step-by-step explanation:

The angle vertically opposite 50° is also 50° ( congruent )

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 angles from 180° for x

x = 180° - (50 + 55)° = 180° - 105° = 75°

Answer:

Decimal--x= -1.39

Fraction--x= -139/100

Step-by-step explanation:

You want to get x by itself in this problem

You have to distribute the 3 into the parenthesis first

1.2/8=15x+21

Now you can do 2 of either things....you can either divide 1.2/8 and then subtract 21 from both sides or you can just subtract 21 from both sides without dividing. I will use option 2.

1.2/8-21=15x+21-21

So now you cancel out the 21 on the right side and get...

-20.85=15x

Now divide by 15

-1.39=x in fraction form -139/100=x

Hope this helped!

To determine the sample size necessary for this study, we use the formula: n = (Z^2 * p * q) / E^2. The necessary sample size is approximately 1091.

Where:
- n = sample size
- Z = Z-score for the desired confidence level (98% confidence level corresponds to a Z-score of 2.33)
- p = estimated proportion (based on the information given, p = 0.8)
- q = 1 - p
- E = desired margin of error (3 percentage points)

Plugging in the values:

n = (2.33^2 * 0.8 * 0.2) / 0.03^2
n = 806.67

Rounding up to the nearest whole number, we get a sample size of 807. Therefore, the researcher needs to survey at least 807 women to be 98% confident that the proportion of women who wear shoes that are too small is within 3 percentage points of the true proportion.

To determine the necessary sample size for this study, we can use the formula for sample size calculation in proportion estimation:

n = (Z^2 * p * q) / E^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, q is the complement of the proportion (1 - p), and E is the margin of error.

In this case, we have:
- Confidence level: 98%, which corresponds to a Z-score of 2.33 (from the standard normal distribution table)
- Estimated proportion (p): 80% or 0.80
- Complement of the proportion (q): 1 - 0.80 = 0.20
- Margin of error (E): 3 percentage points or 0.03

Now, we can plug these values into the formula:

n = (2.33^2 * 0.80 * 0.20) / 0.03^2
n ≈ 1090.65

Since we need to round to the nearest whole number, the necessary sample size is approximately 1091.

Learn more about Z-score at: brainly.com/question/31871890

#SPJ11

Answer:

-67.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

I don't know if I did this right, but I ended up with 30√2 - 45√6

Sorry If it isn't right, have a nice day and keep learning

Using it's concept, the rate of change between point C and point D is of 2.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

\(r = \frac{f(b) - f(a)}{b - a}\)

Considering the points of the given linear function, we have that:

Hence the rate of change between point C and point D is given by:

r = (4 - 2)/(2 - 1) = 2.

More can be learned about the average rate of change of a function at https://brainly.com/question/24313700

#SPJ1

Answer:

I think it’s false, for example if I have -7 and -2 on a number line, -7 is less. The difference is +5 because if you add -7+5 that gets you -2.

Step-by-step explanation:

Answer:

Simone is correct

Step-by-step explanation:

Given

Line 1:

\((x_1,y_1) = (-2, 7)\)

\((x_2,y_2) = (3, 0)\)

Line 2:

\((x_1,y_1) = (2, 1)\)

\((x_2,y_2) =(12, -13)\)

Required

Is Simone correct?

Slope (m) is calculated using:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

For Line 1

\(m = \frac{0 - 7}{3 - (-2)}\)

\(m = \frac{0 - 7}{3 +2}\)

\(m = \frac{-7}{5}\)

\(m = -\frac{7}{5}\)

For Line 2:

\(m = \frac{-13 - 1}{12 -2}\)

\(m = \frac{-14}{10}\)

Divide by 2/2

\(m = \frac{-14/2}{10/2}\)

\(m = \frac{-7}{5}\)

\(m = -\frac{7}{5}\)

By comparison, both lines have the same slope.

Hence, Simone is correct

Answer:

hey you..................