Find the measures of ∠X and ∠Y.

The sum of three consecutive numbers is 267.what is the largest number

iris [78.8K]

Rather than trial and error, you can do this with an equation.

x + x+1 + x+2 = 267 =>
3x+3 = 267
x = 264/3 = 88

So the numbers are 88+89+90. 90 is the largest number.

3 0

3 years ago

A fire company keeps two rescue vehicles. Because of the demand on the vehicles and the chance of mechanical failure, the probab

VashaNatasha [74]

Answer:

(a) P (Both vehicles are available at a given time) = 0.81

(b) P (Neither vehicles are available at a given time) = 0.01

(c) P (At least one vehicle is available at a given time) = 0.99

Step-by-step explanation:

Let A = Vehicle 1 is available when needed and B = Vehicle 2 is available when needed.

<u>Given</u>:

The availability of one vehicle is independent of the availability of the other, i.e. P (A ∩ B) = P (A) × P (B)

P (A) = P (B) = 0.90

(a)

Compute the probability that both vehicles are available at a given time as follows:

P (Both vehicles are available) = P (Vehicle 1 is available) ×

P (Vehicle 2 is available)

$P(A\cap B)=P(A)\times P(B)$

$=0.90\times0.90\\=0.81$

Thus, the probability that both vehicles are available at a given time is 0.81.

(b)

Compute the probability that neither vehicles are available at a given time as follows:

P (Neither vehicles are available) = [1 - P (Vehicle 1 is available)] ×

[1 - P (Vehicle 2 is available)]

$P(A^{c}\cap B^{c})=[1-P(A)]\times [1-P(B)]\\$

$=(1-0.90)\times (1-0.90)\\=0.10\times0.10\\=0.01$

Thus, the probability that neither vehicles are available at a given time is 0.01.

(c)

Compute the probability that at least one vehicle is available at a given time as follows:

P (At least one vehicle is available) = 1 - P (None of the vehicles are available)

$=1-[P(A^{c})\times P(B^{c})]\\=1-0.01.....(from\ part\ (b))\\ =0.99$

Thus, the probability that at least one vehicle is available at a given time is 0.99.

6 0

3 years ago

Triangle TRI has a base of m centimeters and a height of n centimeters. Rectangle RECT has a length of n centimeters and a width

Irina18 [472]

Answer: Triangle TRI has an area of mn/2 cm²( area of triangle 1/2× base×height= 1/2×m×n:mn/2) whereas rectangle RECT has an area of nm cm² ( area of rectangle is length×width= n×m:nm cm²)

8 0

4 years ago

The measures of two sides of a triangle are 11 and 20. Between what two numbers must be the third side fall?

Studentka2010 [4]

Answer:

Step-by-step explanation:

The largest number must be less than 31.

The smallest number must be greater than 9.

4 0

3 years ago

Suppose a farm has pens for raising insects. A pen is shaped as a rectangle that measures x meters wide and 2x meters long and h

Ludmilka [50]

Answer:

1.2 meters.

Step-by-step explanation:

Length of pen = 2x meters

width of pen = x meters

shape of pen is rectangular

we know that area of rectangle is given by length * width

Thus, area of the pen is x*2x = $2x^2$

It is also given that area of pen is 2.8 square meters.

Equating numerical value of area with area in terms of x, we have

$2x^2 = 2.88\\=> x^2 = 2.88/2\\=> x^2 = 1.44\\=> x = 1.2$

Thus value of x is 1.2 meters.

5 0

3 years ago