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4 years ago

Geometry distance formula

Mathematics

1 answer:

viktelen [127]4 years ago

8 0

A(-4, 2) and B(3, -2).

I will do number 2.

Let d(A, B) = distance between the two points.

d(A, B) = sqrt{(3 -(-4))^2 + (-2-2)^2}

d(A, B) = sqrt{(3 + 4))^2 + (-2-2)^2}

d(A, B) = sqrt{(7)^2 + (-4)^2}

d(A, B) = sqrt{49 + 16}

d(A, B) = sqrt{65}

Done!

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An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made t

solniwko [45]

Answer:

B) Method 2 will increase the standard deviation of the students' scores.

Step-by-step explanation:

Given that an instructor in a college class recently gave an exam that was worth a total of 100 points.

The average score for his students was 43 and the standard deviation of the scores was 5 points.

And now he is considering two different strategies for rescaling the exam results of which:

Method 1 = Add 17 points to everyone's score.

Method 2 = Multiply everyone's score by 1.7 .

And we have to check what will be the impact of these methods on the standard deviation of the students' scores.

For this let us consider a simple example to understand this:

Firstly, Formula for calculating Standard Deviation = $\sqrt{\frac{\sum (X-Xbar)^{2}}{n-1}}$

Suppose,

X X - Xbar $(X - Xbar)^{2}$

3 3 - 6 = -3 -3 * -3 = 9

5 5 - 6 = -1 -1 * -1 = 1

10 10 - 6 = 4 4 * 4 = 16

Mean of above data, Xbar = $\frac{3+ 5+10}{3}$ = 6

Standard Deviation of data = $\sqrt{\frac{26}{3-1} }$ = 3.6055

Now let us suppose that we multiply each value of above data with 2 so the new data will be:

X X - Xbar $(X - Xbar)^{2}$

3*2 = 6 6 - 12 = -6 -6 * -6 = 36

5*2 = 10 10 - 12 = -2 -2 * -2 = 4

10*2 =20 20 - 12 = 8 8 * 8 = 64

Mean of new data, Xbar = $\frac{6+ 10+20}{3}$ = 12

Standard Deviation of new data = $\sqrt{\frac{104}{3-1} }$ = 7.2111

Hence, we see that when we multiply any value to the data the standard deviation will increase and in other words it will multiplied by that value which value we multiplied with each data value i.e. when we multiply each data value with 2 the standard deviation also get multiplied by as

3.6055 * 2 = 7.2111

Therefore option B is correct that Method 2 will increase the standard deviation of the students' scores.

And on the other hand Similarly by adding any constant to the data the Standard Deviation will remain same. Therefore Method 1 will have no impact on standard deviation of the students' scores.

8 0

4 years ago

PLEASE HELP ASAPPP !! Instructions: State what additional information is required in order to know that the triangles are congru

Svetllana [295]

<h3>Answer: angle T = angle W</h3>

Explanation:

We are given the sides are congruent due to the tickmarks. Specifically

TU = WV (single tickmarks)

TV = WX (double tickmarks)

So we just need the "A" of "SAS". The A is between the two S letters, so the angle is between the two sides. For triangle TUV, the angle T is between the two sides with the tickmarks. Similarly, angle W is between the tickmarked sides of triangle WVX.

If we know that angle T = angle W, then we have enough information to use SAS.

5 0

4 years ago

Match each expression written in standard form to the equivalent expression in factored form

den301095 [7]

Answer:

1. 15x^7y^2 + 4x^3 => x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x => 3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy => 3xy(5x^6y + 2)

4. 15x^7 + 10y^2 => 5(3x^7 + 2y^2)

Step-by-step explanation:

To obtain the answer to the question, first let us factorise each expression. This is illustrated below:

1. 15x^7y^2 + 4x^3

Common factor is x^3, therefore the expression is written as:

x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x

Common factor is 3x, therefore the expression is written as:

3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy

Common factor is 3xy, therefore the expression is written as:

3xy(5x^6y + 2)

4. 15x^7 + 10y^2

Common factor is 5, therefore the expression can be written as:

5(3x^7 + 2y^2)

4 0

3 years ago

Can someone check my math homework? Please I need it to be checked.

dmitriy555 [2]

I have to say this is wrong because you subtracted 3 and 3 is the variable term. So what you need to do is to add 9 to both side to get 3x by it self. Then divide by 3 and then x=6

6 0

3 years ago

Please help being timed for test !

balu736 [363]

Answer:

I think it B or C but hope I can help :)

Step-by-step explanation:

3 0

3 years ago