Explain how you know the right triangles are similar

Two cars are driving towards an intersection from perpendicular directions. The first car's velocity is 101010 meters per second

guajiro [1.7K]

Answer:

D(L)/dt = 407,6 m/s

Step-by-step explanation:

Let call A the intersection point.

As the cars are driving from perpendicular directions, they form with a coordinates x and y, a right triangle, and distance between them is the hypotenuse (L), then

L² = x² + y²

Taking derivatives with respect to time we have:

2*L* D(L)/dt = 2*x *D(x)/dt + 2*y* D(y)/dt (1)

In this equation we know: At a certain time

x = 444 m and D(x)/dt = 10 m/s

y = 333 m and D(y)/dt = 666 m/s

And L = √(x)² + (y)² ⇒ L = √ (444)² +( 333)² ⇒ L = √197136 + 110889

L = √308025

L = 555 m

Thn plugin these values in euatn (1) we get

2* 555 * D(L)/dt (m) = 2* 444* 10 + 2*333*666 (m*m/s)

D(L)/dt = ( 4440 + 221778)/555 (m/s)

D(L)/dt = 407,6 m/s

6 0

4 years ago

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let

HACTEHA [7]

Answer:

(a) The value of P (X ≤ 2) is 0.8729.

(b) The value of P (X ≥ 5) is 0.0072.

(c) The value of P (1 ≤ X ≤ 4) is 0.7154.

(d) The probability that none of the 25 boards is defective is 0.2774.

(e) The expected value and standard deviation of X are 1.25 and 1.09 respectively.

Step-by-step explanation:

The random variable X is defined as the number of defective boards.

The probability that a circuit board is defective is, p = 0.05.

The sample of boards selected is of size, n = 25.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={25\choose x}0.05^{x}(1-0.05)^{25-x};\ x=0,1,2,3...$

(a)

Compute the value of P (X ≤ 2) as follows:

P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)

$P(X\leq =x)=\sum\limits^{2}_{x=0}{{25\choose x}0.05^{x}(1-0.05)^{25-x}}\\=0.2774+0.3650+0.2305\\=0.8729$

Thus, the value of P (X ≤ 2) is 0.8729.

(b)

Compute the value of P (X ≥ 5) as follows:

P (X ≥ 5) = 1 - P (X < 5)

$=1-\sum\limits^{4}_{x=0}{{25\choose x}0.05^{x}(1-0.05)^{25-x}}\\=1-0.9928\\=0.0072$

Thus, the value of P (X ≥ 5) is 0.0072.

(c)

Compute the value of P (1 ≤ X ≤ 4) as follows:

P (1 ≤ X ≤ 4) = P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)

$=\sum\limits^{4}_{x=1}{{25\choose x}0.05^{x}(1-0.05)^{25-x}}\\=0.3650+0.2305+0.0930+0.0269\\=0.7154$

Thus, the value of P (1 ≤ X ≤ 4) is 0.7154.

(d)

Compute the value of P (X = 0) as follows:

$P(X=0)={25\choose 0}0.05^{0}(1-0.05)^{25-0}=1\times 1\times 0.277389=0.2774$

Thus, the probability that none of the 25 boards is defective is 0.2774.

(e)

Compute the expected value of X as follows:

$E(X)=np=25\times 0.05=1.25$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{np(1-p)}=\sqrt{25\times 0.05\times (1-0.05)}=1.09$

Thus, the expected value and standard deviation of X are 1.25 and 1.09 respectively.

8 0

4 years ago

Algebra 1 Prerequisites

frozen [14]

No solution

explanation:

5 0

3 years ago

What is the length of the line segment that is graphed from (3, 1) to (8, 1)?

tia_tia [17]

A.4 units
D.9 units
id go with 9 units hope this helps

7 0

4 years ago

Read 2 more answers

Here are some of the lowest tempatures recorded in the last 2 centuries for some US cities. Tempatures are in degrees Farhrenhei

oksian1 [2.3K]

Answer:

wouldn't it be A?

Step-by-step explanation:

4 0

3 years ago