Find the missing number of each unite rate 10/2=?/1 16/4= ?/1

Barack walks 2 kilometers south and then x kilometers east. He ends 5 kilometers away from his starting position. Find x

amid [387]

Answer:

4.6 km

Step-by-step explanation:

-This is a Pythagorean Theorem problem where the distances walked are effectively the base and height of the imaginary right triangle thereof.

#Apply Pythagorean theorem to solve:

$b^2+h^2=H^2\\\\2^2+x^2=5^2\\\\x^2=5^2-2^2=21\\\\x=\sqrt{21}\\\\x=4.58\ km$

$\approx 4.6\ km$

Hence, the distance x is 4.6 km

7 0

3 years ago

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

dexar [7]

Answer:

The value of the constant C is 0.01 .

Step-by-step explanation:

Given:

Suppose X, Y, and Z are random variables with the joint density function,

$f(x,y,z) = \left \{ {{Ce^{-(0.5x + 0.2y + 0.1z)}; x,y,z\geq0 } \atop {0}; Otherwise} \right.$

The value of constant C can be obtained as:

$\int_x( {\int_y( {\int_z {f(x,y,z)} \, dz }) \, dy }) \, dx = 1$

$\int\limits^\infty_0 ({\int\limits^\infty_0 ({\int\limits^\infty_0 {Ce^{-(0.5x + 0.2y + 0.1z)} } \, dz }) \, dy } )\, dx = 1$

$C\int\limits^\infty_0 {e^{-0.5x}(\int\limits^\infty_0 {e^{-0.2y }(\int\limits^\infty_0 {e^{-0.1z} } \, dz }) \, dy }) \, dx = 1$

$C\int\limits^\infty_0 {e^{-0.5x}(\int\limits^\infty_0{e^{-0.2y}([\frac{-e^{-0.1z} }{0.1} ]\limits^\infty__0 }) \, dy }) \, dx = 1$

$C\int\limits^\infty_0 {e^{-0.5x}(\int\limits^\infty_0 {e^{-0.2y}([\frac{-e^{-0.1(\infty)} }{0.1}+\frac{e^{-0.1(0)} }{0.1} ]) } \, dy }) \, dx = 1$

$C\int\limits^\infty_0 {e^{-0.5x}(\int\limits^\infty_0 {e^{-0.2y}[0+\frac{1}{0.1}] } \, dy }) \, dx =1$

$10C\int\limits^\infty_0 {e^{-0.5x}([\frac{-e^{-0.2y} }{0.2}]^\infty__0 }) \, dx = 1$

$10C\int\limits^\infty_0 {e^{-0.5x}([\frac{-e^{-0.2(\infty)} }{0.2}+\frac{e^{-0.2(0)} }{0.2}] } \, dx = 1$

$10C\int\limits^\infty_0 {e^{-0.5x}[0+\frac{1}{0.2}] } \, dx = 1$

$50C([\frac{-e^{-0.5x} }{0.5}]^\infty__0}) = 1$

$50C[\frac{-e^{-0.5(\infty)} }{0.5} + \frac{-0.5(0)}{0.5}] =1$

$50C[0+\frac{1}{0.5} ] =1$

$100C = 1$ ⇒ $C = \frac{1}{100}$

C = 0.01

3 0

2 years ago

Of his 94 compact discs, Raul plans to donate 17 to the thrift store. To the nearest tenth of a percent, what percent is this?

Masteriza [31]

For this case we can solve the problem by means of the following rule of three:
94 --------> 100%
17 --------> x
Clearing x we have:
x = (17/94) * (100)
x = 18,08510638%
To the nearest tenth of a percent:
x = 18.1%
Answer:
This is 18.1% of his compact discs.

6 0

3 years ago

The larger of two numbers is 5 less that twice the smaller if their sum is 70, find the numbers

Vikentia [17]

Let the number be x and 2x-5 from the above given condition

x+2x-5=70

or

3x=75 s0 x=25

Hence, the number are 25 and 45

6 0

3 years ago

What makes a function

Bas_tet [7]

A function is a expression that defines a relationship between one variable and another variable

4 0

3 years ago

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