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nika2105 [10]
2 years ago
13

Learning Task 3:

Mathematics
2 answers:
padilas [110]2 years ago
6 0

Answer:

Area = x^2- 25

Area =9x^2 +24x + 16

Length = (3x -2)

Speed = \left(y^2-3y+1\right)

Product = 3m^3 + 6m^2 - 6m

Step-by-step explanation:

Solving (1):

Length = (x + 5)

Width = (x - 5)

Required

Calculate Area

Area = Length * Width

Area = (x + 5) * (x - 5)

Area = x^2 + 5x - 5x - 25

Area = x^2- 25

Solving (2):

Given

Length = (3x + 4)

Required: Calculate Area

Area =Length * Length

Area =(3x + 4) * (3x + 4)

Area =9x^2 + 12x + 12x + 16

Area =9x^2 +24x + 16

Solving (3):

Area = 3x^2 + 7x - 6

Width = x + 3

Required: Calculate Length

Area = Length * Width

Length = \frac{Area}{Width}

Length = \frac{3x^2 + 7x - 6}{x + 3}

Factorize the numerator

Length = \frac{3x^2 + 9x -2x - 6}{x + 3}

Length = \frac{3x(x + 3) -2(x + 3)}{x + 3}

Length = \frac{(3x -2) (x + 3)}{x + 3}

Divide by x + 3

Length = (3x -2)

Solving (4):

Distance = (2y^3 - 7y^2 + 5y -1)

Time = 2y - 1

Required: Determine the average speed

This is calculated as:

Speed = \frac{Distance}{Time}

Speed = \frac{2y^3 - 7y^2 + 5y -1}{2y - 1}

Factorize the numerator

Speed = \frac{\left(2y-1\right)\left(y^2-3y+1\right)}{2y - 1}

Speed = \left(y^2-3y+1\right)

Solving (5):

Multiply (m^2 + 2m - 2) by sum of (m + 3) and (2m - 3)

First, calculate the sum:

Sum = m + 3 + 2m - 3

Sum = m +  2m+3 - 3

Sum = 3m

Then, the product

Product = (m^2 + 2m - 2)(3m)

Product = 3m^3 + 6m^2 - 6m

Verizon [17]2 years ago
3 0

Answer:

Step-by-step explanation:

Solving (1):

Required

Calculate Area

Solving (2):

Given

Required: Calculate Area

Solving (3):

Required: Calculate Length

Factorize the numerator

Divide by x + 3

Solving (4):

Required: Determine the average speed

This is calculated as:

Factorize the numerator

Solving (5):

Multiply  by sum of  and  

First, calculate the sum:

Then, the product

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a yes udjwjwjwjwjwjwjwjwjw

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2 years ago
The Corporate Lawyer, a magazine for corporate lawyers, reported that out of 200 firms with employee stock ownership plans, 150
tiny-mole [99]

Answer:

The 90% confidence interval for the population proportion of all such firms with this as the primary motivation is (69.96%, 80.04%).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The Corporate Lawyer, a magazine for corporate lawyers, reported that out of 200 firms with employee stock ownership plans, 150 indicated that the primary reason for setting up the plan was tax related.

This means that n = 200, \pi = \frac{150}{200} = 0.75

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.}{2} = 0.975, so Z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.645\sqrt{\frac{0.75*0.25}{200}} = 0.6996

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.645\sqrt{\frac{0.75*0.25}{200}} = 0.8004

As percent:

0.6996*100% = 69.96%

0.8004*100% = 80.04%.

The 90% confidence interval for the population proportion of all such firms with this as the primary motivation is (69.96%, 80.04%).

6 0
3 years ago
Find the length of a segment with an endpoint of (2, 1) and a midpoint of (–2, –1).
Travka [436]

Answer:

Length of segment =4\sqrt5 units = 8.94 units

Step-by-step explanation:

Given:

End point of line: (2,1)

Midpoint of line: (-2,-1)

To find length of line segment.

Solution:

Distance from endpoint to midpoint is half the length of segment as the midpoint divides the line into equal halves.

Distance from end point to mid point can be found out using distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2)

Plugging in points for end point (2,1) and midpoint(-2,-1).

d=\sqrt{(-2-2)^2+(-1-1)^2)

d=\sqrt{(-4)^2+(-2)^2)

d=\sqrt{16+4)

d=\sqrt{20}

d=2\sqrt{5}

Length of half segment =2\sqrt{5} units

∴ Length of segment = 2\times length\ of\ half\ segment= 2\times 2\sqrt5=4\sqrt5 units

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2 years ago
Simplify the following expression:<br> (2a - 3) + (-a + 5)<br> PLEASE HELP ME
Feliz [49]

Answer:

(a+2)

Soo you could solve by removing the parenthesis, then combining all like terms. Then subtract.

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2 years ago
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What 82*1million................
ipn [44]
<span><span>ur answer is

(82)</span><span>(1000000)

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2 years ago
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