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3 years ago

*Need Help??!!

Mathematics

2 answers:

RoseWind [281]3 years ago

3 0

The probability of getting a country CD out of all the CDs is the number of country CDs divided by the total number of CDs in Dante's Collection.

The total number of CDs in Dante's collection is $6+12+8+4+10=40$ .

The total number of country CDs is 12.

So our required probability is $\frac{12}{40}= \frac{3}{10}$ .

In percentage this is 3 divided by 10, and then multiply by 100. We get 30%. Answer choice D is correct.

ANSWER: D

hjlf3 years ago

3 0

Answer: D.) 30%

Step-by-step explanation:

From the given pie chart, we have the number of country CD = 12

The total number of CD's= $12+8+4+6+10=40$

Now, the probability that a randomly chosen CD will be country is given by :-

$\text{P(country)}=\dfrac{\text{Number of country CD}}{\text{Total CDs}}\\\\=\dfrac{12}{40}=\dfrac{3}{10}=0.3$

In percent, $0.3\times100=30\%$

Hence, the probability that a randomly chosen CD will be country is 30%.

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Calculate the length of sides triangle pqr and determine weather or not triangle is a right angled. P(-4,6) q(6,1) r(2,9)

Tom [10]

$\bold{\huge{\underline{ Solution }}}$

<h3>Given :-</h3>

We have given the coordinates of the triangle PQR that is P(-4,6) , Q(6,1) and R(2,9)

We have to calculate the length of the sides of given triangle and also we have to determine whether it is right angled triangle or not

<h3>Let's Begin :-</h3>

Here, we have 

Coordinates of P =( x1 = -4 , y1 = 6)
Coordinates of Q = ( x2 = 6 , y2 = 1 )
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By using distance formula 

$\pink{\bigstar}\boxed{\sf{Distance=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}$

Subsitute the required values in the above formula :-

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$\sf{ = }{\sf\sqrt{ (6 - (-4))^{2} + (1 - 6)^{2}}}$

$\sf{ = }{\sf\sqrt{ (6 + 4 )^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ (10)^{2} + (- 5)^{2}}}$

$\sf{ = }{\sf\sqrt{ 100 + 25 }}$

$\sf{ = }{\sf\sqrt{ 125 }}$

$\sf{ = 5 }{\sf\sqrt{ 5 }}$

Length of QR

$\sf{ = }{\sf\sqrt{(2 - 6)^{2} + (9 - 1)^{2}}}$

$\sf{ = }{\sf\sqrt{(- 4 )^{2} + (8)^{2}}}$

$\sf{ = }{\sf\sqrt{16 + 64 }}$

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$\sf{ = }{\sf\sqrt{ (-4 - 2 )^{2} + (6 - 9)^{2}}}$

$\sf{ = }{\sf\sqrt{ (-6 )^{2} + (-3)^{2}}}$

$\sf{ = }{\sf\sqrt{ 36 + 9 }}$

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We have to determine whether the triangle PQR is right angled triangle

<h3>Therefore, </h3>

By using Pythagoras theorem :-

Pythagoras theorem states that the sum of squares of two sides that is sum of squares of 2 smaller sides of triangle is equal to the square of hypotenuse that is square of longest side of triangle

That is,

$\bold{ PQ^{2} + QR^{2} = PR^{2}}$

Subsitute the required values,

$\bold{ 125 + 80 = 45 }$

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From above we can conclude that,

The triangle PQR is not a right angled triangle because 205 ≠ 45 .

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2 years ago

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SashulF [63]

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