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2 years ago

ΔABC is similar to ΔAXY by a ratio of 4:3. If BC = 24, what is the length of XY?

Mathematics

2 answers:

pogonyaev2 years ago

6 0

Answer:

Step-by-step explanation:

24/4 = 6 so....

4*6 is 24 and 3*6 is 18

faltersainse [42]2 years ago

3 0

Answer:

Length of XY is 18 units.

Step-by-step explanation:

Given,

$\triangle ABC\sim \triangle AXY$

By the ratio of 4 : 3

That is, the ratio of corresponding sides of triangles ABC and AXY is 4 : 3,

$\implies \frac{AB}{AX}=\frac{BC}{XY}=\frac{AC}{AY}=\frac{4}{3}$

We have, BC = 24 units,

$\frac{24}{XY}=\frac{4}{3}$

$72=4XY$

$\implies XY=\frac{72}{4}=18$

Hence, the length of XY is 18 units.

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Every day, a lecture may be canceled due to inclement weather with probability 0.05. Class cancelations on different days are in

andrezito [222]

<h3>(a)Probability of cancelling at least 4 classes is 0.0055.</h3><h3>(b)Probability of 10th class is third class that gets cancelled = 0.0031</h3>

Step-by-step explanation:

Here, the question is<u> incomplete</u>.

Every day, a lecture may be canceled due to inclement weather with probability 0.05. Class cancellations on different days are independent.

(a) There are 15 classes left this semester. Compute the probability that at least 4 of them get canceled.

(b) Compute the probability that the tenth class this semester is the third class that gets canceled.

Now, here:

The probability of cancelling each class = 0.05

Now, probability of cancelling at least 4 classes

= 1 - P(Cancelling at max 3 classes)

= 1 - P(0 ≤ x ≤ 3) = 1 - Binomial (15,0.05,3)

= 0.0055

Hence, probability of cancelling at least 4 classes is 0.0055.

(b) As given, 10th class is third class that gets cancelled.

So, the first and second classes that get cancelled in between 1 - 9.

P(2 class cancelled in 1st 9) = Binomial (15,0.05,3) = 0.0629

Also, as given P(10th class cancelled) = 0.05

⇒ P(10th class is third class that gets cancelled ) = 0.0629 x 0.05 = 0.0031

5 0

2 years ago

If 2x2 + y2 = 17 then evaluate the second derivative of y with respect to x when x = 2 and y = 3. Round your answer to 2 decimal

Vera_Pavlovna [14]

Answer:

y''=-1.26

Step-by-step explanation:

We are given that $2x^2+y^2=17$

We have evaluate the second order derivative of y w.r.t. x when x=2 and y=3.

Differentiate w.r.t x

Then , we get

$4x+2yy'=0$

$2x+yy'=0$

$yy'=-2x$

$y'=-\frac{2x}{y}$

Again differentiate w.r.t.x

Then , we get

$2+(y')^2+yy''=0$ $(u\cdot v)'=u'v+v'u)$

$2+(y')^2+yy''=0$

Using value of y'

$yy''=-2-(-\frac{2x}{y})^2$

$y''=-\frac{2+(-\frac{2x}{y})^2}{y}$

Substitute x=2 and y=3

Then, we get $y''=-\frac{2+(\frac{4}{3})^2}{3}$

$y''=-\frac{18+16}{9\times 3}=-\frac{34}{27}$

Hence,y''=-1.26

6 0

2 years ago

One of the factors of the polynomial x3 − 5x2 is x + 3. What is the other factor?

blondinia [14]

Answer:

C. x² − 8x + 24 − 72/(x+3)

Step-by-step explanation:

See attached picture for long division method.

Logically, we know x³ − 5x² factors to x² (x − 5). Since x + 3 isn't a factor, we know the remainder isn't 0. So we can narrow the options down to A or C.

One way to find the remainder is through long division. Or, since this is multiple choice, we multiply the options by x + 3 and see which one results in an answer of x³ − 5x².

(x + 3) (x² − 8x + 24 − 72/(x+3))

(x + 3) (x² − 8x + 24) − 72

x³ − 8x² + 24x + 3x² − 24x + 72 − 72

x³ − 5x²

6 0

1 year ago

6.5% of people in the U.S. Have A- blood type. You randomly select 6 Americans and ask them if their blood type is A-. a) Find t

Keith_Richards [23]

Answer:

a) 7.54189*10^-8

b) 0.99999999

c) E ( X ) = 0.39 , s ( X ) = 0.604

Step-by-step explanation:

Solution:-

- We will assume the proportion of people with A- blood group is independent and remains constant for a fairly small sample of n = 6 Americans selected at random.

- We will denote a random variable X = The number of americans out of 6 that have blood group type A-.

- The random variable is assumed to follow binomial distribution.

- The probability of success is the proportion of people in U.S that have blood group type A-, p = 0.065:

X ~ Bin ( 6 , 0.065 )

Where, r represents the number of americans out of selected 6 have blood group A-. The pmf of a binomial variate is given as:

P ( X = r ) = nCr * ( p ) ^r * ( 1 - p ) ^ ( n - r )

a) Find the probability that all 6 are type A-

- We will pmf given above and set r = 6. And evaluate the resulting probability:

P ( X = 6 ) = 6C6 * ( p )^6 * ( 1 - p ) ^ ( 0 )

= p^6

= ( 0.065 )^6

= 7.54189*10^-8

b) Find the probability that at most 4 of them are type A-

- We will pmf given above and evaluate the following expression:

P ( X ≤ 4 ) = 1 - P ( X = 5 ) - P ( X = 6 )

P ( X ≤ 4 ) = 1 - 6C5 * ( p )^5 * ( 1 - p ) ^ ( 1 ) - p^6

= 1 - 6*(0.065)^5 ( 0.935 ) - 0.065^6

= 1 - 6.50923*10^-8 - 7.54189*10^-8

= 0.99999999

c) Find the mean and standard deviation.

- The mean E ( X ) of the defined random variable distributed binomially is given by:

E ( X ) = n*p = 6*0.065 = 0.39 people

- The mean s( X ) of the defined random variable distributed binomially is given by:

s ( X ) = √n*p*q = √(6*0.065*0.935) = 0.604

5 0

2 years ago

As a result of a cyclone, the price of bananas rose 85% to $9.99 per kg. How much did bananas cost before the cyclone?

Karo-lina-s [1.5K]

The original price was $8.49 :)

7 0

2 years ago