Does a parallelogram always have four sides?

In ΔPQR, r = 870 cm, p = 410 cm and ∠Q=142°. Find ∠R, to the nearest degree.

lutik1710 [3]

Answer: 26

Step-by-step explanation:

8 0

3 years ago

A Geiger counter counts the number of alpha particles from radioactive material. Over a long period of time, an average of 14 pa

UkoKoshka [18]

Answer:

0.2081 = 20.81% probability that at least one particle arrives in a particular one second period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Over a long period of time, an average of 14 particles per minute occurs. Assume the arrival of particles at the counter follows a Poisson distribution. Find the probability that at least one particle arrives in a particular one second period.

Each minute has 60 seconds, so $\mu = \frac{14}{60} = 0.2333$

Either no particle arrives, or at least one does. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . So

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.2333}*(0.2333)^{0}}{(0)!} = 0.7919$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7919 = 0.2081$

0.2081 = 20.81% probability that at least one particle arrives in a particular one second period.

8 0

4 years ago

Please help with the questions in the image

Pavel [41]

Answer: f(x) = (x - 3)²

<u>Step-by-step explanation:</u>

Use the vertex formula: y = a(x - h)² + k

and input the vertex (h, k) = (3, 0) and the given point (x, y) = (4, 2) to solve for a

2 = a(4 - 3)² + 0

2 = a(1)²

2 = a

Now, input (h, k) = (3, 0) and a = 1 into the vertex formula:

y = 1(x - 3)² + 0 → y = (x - 3)²

****************************************************************************

Answer: g(x) = -(x + 1.25)² + 2.5625

<u>Step-by-step explanation:</u>

Use the vertex formula: y = a(x - h)² + k

and input the given points for (x, y) to create a system of equations, then solve for a, h, and k.

EQ1: 2 = a(-2 - h)² + k

2 = a(4 + 4h + h²) + k

2 - 4a - 4ah - ah² = k

EQ2: 1 = a(0 - h)² + k

1 = ah² + k

1 - ah² = k

EQ3: -2.5 = a(1 - h)² + k

-2.5 = a(1 - 2h + h²) + k

-2.5 -a + 2h + ah² = k

<u>Substitute</u> - set EQ1 = EQ2 and EQ2 = EQ3 to eliminate k

EQ1 = EQ2: 2 - 4a - 4ah - ah² = 1 - ah²

1 - 4a - 4ah = 0

EQ2 = EQ3: 1 - ah² = -2.5 - a + 2ah - ah²

3.5 + a - 2ah = 0

<u>Elimination:</u> - now solve the system for "a"

1 - 4a - 4ah = 0 → 1(1 - 4a - 4ah = 0) → 1 - 4a - 4ah = 0

3.5 + a - 2ah = 0 → -2(3.5 + a - 2ah = 0) → <u> -7 - 2a + 4ah = 0 </u>

-6 - 6a = 0

-6a = 6

Next, replace "a" with -1 into either of the equations to solve for "h"

1 - 4a - 4ah = 0

1 - 4(-1) - 4(-1)h = 0

1 + 4 + 4h = 0

5 + 4h = 0

4h = -5

Now, replace "a" with -1 and "h" with -1.25 into any of the original equations (EQ1, EQ2, or EQ3) to solve for k:

1 - ah² = k

1 - (-1)(-1.25)² = k

1 - (-1)(1.5625) = k

1 + 1.5625 = k

Now, input (h, k) = (-1.25, 2.5625) and a = -1 into the vertex formula:

y = -1(x - (-1.25))² + 2.5625 → y = -(x + 1.25)² + 2.5625

4 0

4 years ago

Find the length of each arc. Round your answer to the nearest tenth

Sauron [17]

Answer:

52 yd

Step-by-step explanation:

The formula for arc length is s = rФ, where r is the radius and Ф is the central angle in radians.

Here the central angle is 300° and the radius is 10 yd.

Convert 300° to radians:

π rad

Multiply 300° by the conversion factor ------------

180°

obtaining

(300/180)π = 5.2 rad

Then the arc length is s = rФ = (10 yd)(5.2 rad) = 52 yd

6 0

3 years ago

BRAINLIEST FOR RIGHT ANSWER!!! Which statements are always true about a system of linear equations?

allsm [11]

Answer:

Step-by-step explanation: ion kno

8 0

3 years ago