Hey there :)

( a - b )( a² + ab + b² )
Let us distribute ( a - b ) into the other

a ( a² ) + a ( ab ) + a ( b² ) - b ( a² ) - b ( ab ) - b ( b² )
a³ + a²b + ab² - a²b - ab² - b³

We can further simplify
a²b - ab² = 0
ab² - ab² = 0

a³ - b³

You can see in the picture which I have attached. It is the 8th formula

7 0

3 years ago

Read 2 more answers

Which of the following is a verbal

wolverine [178]

Answer: Three less than a number

Step-by-step explanation: z-3 means the three is subtracted from the unknown number.

<em>An unknown quantity less than three. would be 3 - z or z < 3</em>

3 0

3 years ago

Read 2 more answers

Can anyone explain this question to me? My teacher solved it but I didn’t understand how she did it

Amiraneli [1.4K]

Step-by-step explanation:

To find the space a figure takes, we need to find the volume. Volume of a rectangular prism can be found by multiplying the length, width, and height of the figure.

We can start with the green block. The dimensions of this figure are 6cm, 3cm, and 3cm. The 5cm at the bottom is not a dimension of the green figure. Instead, it shows the total width of both blocks. We will use this later.

Back to the first block, we will find its volume by multiplying its dimensions together.

3 · 3 · 6 = 54

So, the volume of the first block is 54 cm³.

To this, we will add the volume of the blue block. We can find its dimensions with some simple deduction.

The picture shows that the height of the figure is 4cm less than the height of the green one, 6cm.

6 - 4 = 2

The height, then, is 2cm.

The width can be found by subtracting the width of the green block from the total width of both figures, 5cm.

5 - 3 = 2

So, the width is also 2cm.

We can see that the length of the blue block is equal to that of the green one, so we know that the length is 3cm.

Now, multiply all the dimensions we have found together.

2 · 2 · 3 = 12

The volume of the blue block is 12cm³.

We have found the volumes of both figures, so now we can add them both together to find the total.

54 + 12 = 66

So, the total volume is 66cm³.

I hope this was a satisfactory explanation ^^ Good luck, mate

7 0

2 years ago

A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new

faltersainse [42]

Answer:

The predictive value of a positive test is 18.2%.

Step-by-step explanation:

The population screened is 300.

The true prevalence value of the Lyme disease among clinic attendees is 10\% \Rightarrow 0.10.10% = 0.10.

The proportion that sensitivity is 60\% \Rightarrow 0.6060% = 0.60

The proportion of the specificity is 70\% \Rightarrow 0.70.70% = 0.70

Step 2 of 2

We have to calculate the probability value of the predictive value of positive test.

\begin{array}{c}\\\left( \begin{array}{l}\\{\rm{Positive Predictive }}\\\\{\rm{value}}\left( {PPV} \right)\\\end{array} \right) = \frac{{{\rm{Prevalence}} \times {\rm{Sensitivity}}}}{{\left( {{\rm{Prevalence}} \times {\rm{Sensitivity}}} \right) + \left( {{\rm{1 - Prevalence}} \times 1 - {\rm{Specificity}}} \right)}}\\\\ = \frac{{0.1 \times 0.60}}{{\left( {0.1 \times 0.60} \right) + \left( {1 - 0.1 \times 1 - 0.70} \right)}}\\\\ = \frac{{0.06}}{{0.33}}\\\\ = 0.181818\\\\ = 0.182{\rm{ }}\left( {{\rm{Round to 3 decimal place}}} \right)\\\end{array}

(Positive Predictive value, PPV) =

(Prevalence×Sensitivity)/Prevalence×Sensitivity +(1−Prevalence×1−Specificity)

= (0.1×0.60)/0.1×0.60 + (1−0.1×1−0.70)

= 0.06 /0.33

= 0.181818

(Positive Predictive value, PPV) = 0.182 (3decimals)

We have to convert the PPV into percentage,

\begin{array}{c}\\PPV = 0.182 \times 100\\\\ = 18.2\% \\\end{array}

PPV=0.182×100

= 18.2%

Therefore, the predictive positive value is 18.2%.

7 0

3 years ago