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2 years ago

The distance between B and C

Mathematics

1 answer:

alina1380 [7]2 years ago

5 0

Answer:

The answer is

<h2> $\sqrt{13} \: \: or \: \: 3.6055 \: \: units$ </h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

$d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

B ( 3 , 1 ) and C( 6 , 3)

The distance between them is

$|BC| = \sqrt{( {3 - 6})^{2} + ({1 - 3})^{2} } \\ = \sqrt{ ({ - 3})^{2} + ( { - 2})^{2} } \\ = \sqrt{9 + 4}$

We have the final answer as

$\sqrt{13} \: \: or \: \: 3.6055 \: \: units$

Hope this helps you

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An equation was created for the line of best fit from actual enrollment data. It was used to predict the dance studio enrollment

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Answer: First option is correct.

Step-by-step explanation:

Enrollment month Actual Predicted Residual

January 500 8 4

February 400 15 -1

March 550 15 -1

April 13 12 -1

May 16 17 -1

June 14 15 -1

Since we know that

Residual value = Actual value - Predicted value

Sum of residuals is given by

$4-1-1+1-1-1=1$

since we can see that sum of residual is more than 0.

So, it can't be a good fit .

Hence, No, the equation is not a good fit because the sum of the residuals is a large number.

Therefore, First option is correct.

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2 years ago

Which statements about the factors of the terms in the expression 20 a + 15 a b + 24 b are true? Select three options.

ExtremeBDS [4]

Answer:

Following are the true statements

2. The factors common to 20a and 15ab are 1, 5, and a.

3. The factors common to 20a and 24b are 1, 2, and 4.

5. The GCF of the expression is 1

Step-by-step explanation:

Expression is 20a + 15ab + 24b

Now lets have a look at each of the options provided!

1. The factors common to 20a and 15ab are 1, 5, a, and b.

False

As you can see there is no b in 20a term only 1,5,a are common hence it is false.

2. The factors common to 20a and 15ab are 1, 5, and a.

True

The terms 20a and 15ab are divisible by 1,5,a hence it is true.

3. The factors common to 20a and 24b are 1, 2, and 4.

True

The terms 20a and 24b are divisible by 1,2,4 hence it is true

4. The GCF of the expression is ab.

False

20a + 15ab + 24b

As you can see ab is not common in all of the terms hence it cannot be greatest common factor

5. The GCF of the expression is 1

True

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Factor of 15 are: 3,5,1

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2 years ago

Automobile repair costs continue to rise with the average cost now at $367 per repair (U.S. News & World Report website, Jan

tino4ka555 [31]

Answer:

$\mu = 367$

$\sigma = 88$

a. What is the probability that the cost will be more than $450?

We are supposed to find P(x > 450)

Formula : $z=\frac{x-\mu}{\sigma}$

$z=\frac{450-367}{88}$

$z=0.9431$

Refer the z table :

P(z<0.9431)=0.8264

P(z> 0.9431)=1-P(z<0.9431)=1- 0.8264= 0.1736

Hence the probability that the cost will be more than $450 is 0.1736

b)What is the probability that the cost will be less than $250?

We are supposed to find P(x<250)

Formula : $z=\frac{x-\mu}{\sigma}$

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Refer the z table :

P(z<-1.3295)=0.0934

Hence the probability that the cost will be less than $250 is 0.0934

c)What is the probability that the cost will be between $250 and $450?

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Hence the probability that the cost will be between $250 and $450 is 0.733

d) If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost?

p = 0.05

refer the z table

z = -1.65

Formula : $z=\frac{x-\mu}{\sigma}$

$-1.65=\frac{x-367}{88}$

$-1.65 \times 88=x-367$

$-145.2+367=x$

$221.8=x$

Hence If the cost for your car repair is in the lower 5% of automobile repair charges, so, cost is $221.8

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2 years ago

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Goshia [24]

Answer:

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$\frac{al+bm+cn}{\sqrt{l62+m^2+n^2}}=\frac{(3\times 0)+(2\times 1)+(-2)(1)}{\sqrt{3^2+2^2+(-2)^2}}=\frac{0+2-2}{\sqrt{17}}=0$

Distance between point (0,1,1) and (1) is zero. That is point 90,1,1) is lies on the line (1).

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2 years ago

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2 years ago