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3 years ago

In Triangle LMN, < M is a right angle. If MN = 10 and LN = 20.4, determine m < N to the nearest degree.

Mathematics

1 answer:

UNO [17]3 years ago

6 0

cos θ = $\frac{adjacent}{hypotenuse}$

cos ∠N = $\frac{10}{20.4}$

∠N = cos⁻¹ $(\frac{10}{20.4})$

∠N = 60.65°

Answer: 61°

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Una heladeria dispone de 20 frutas distintas para elaborar sus malteadas. Si los clientes pueden elegir tres sabores para mezcla

Dahasolnce [82]

Answer:

Existen 6840 permitaciones de malteadas de tres sabores distintos que la heladería puede ofrecer.

Step-by-step explanation:

En este caso, el cliente que adquiere una malteada de tres sabores distintos sigue el siguiente procedimiento:

1) El primer sabor sale de cualquiera de las 20 frutas disponibles.

2) El segundo sabor es distinto al primer sabor, es decir, que sale de las 19 frutas restantes.

3) El tercer sabor es distinto al primer sabor y al segundo sabor, es decir, que sale de las 18 frutas restantes.

Puesto que existe una doble conjunción y que puede importar el orden según la preferencia del cliente, se habla matemáticamente de una permutación, definida como:

$n\mathbb{P}k = \frac{n!}{(n-k)!}$ (1)

Donde:

$n$ - Número de sabores disponibles, adimensional.

$k$ - Número de sabores escogidos, adimensional.

Si tenemos que $n = 20$ y $k = 3$ , entonces la cantidad de malteadas de tres sabores distintos es:

$n\mathbb{P}k = \frac{20!}{(20-3)!}$

$n\mathbb{P}k = \frac{20!}{17!}$

$n\mathbb{P}k = 20\cdot 19\cdot 18$

$n\mathbb{P}k = 6840$

Existen 6840 permitaciones de malteadas de tres sabores distintos que la heladería puede ofrecer.

5 0

3 years ago

Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switc

s344n2d4d5 [400]

Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter. If six neighbors with the same type of opener set their switches independently.The probability of at least one pair of neighbors using the same settings is 0.65633

Step-by-step explanation:

Step 1

In the question it is given that

Automatic garage door opener utilizes a transmitter control with four independent switches

So .the number of Combinations possible with the Transmitters =

2*2*2*2= 16

Step 2

Probability of at least one pair of neighbors using the same settings = 1- Probability of All Neighbors using different settings.

= 1- 16*15*14*13*12*11/(16^6)

Step 3

Probability of at least one pair of neighbors using the same settings=

= 1- 0.343666

Step 4

So the probability of at least one pair of neighbors using the same settings

is 0.65633

3 0

3 years ago

Simplify the following expression by combining like terms. Select the most simplified expression

Jet001 [13]

Answer:

It is D

Step-by-step explanation:

Distribute:

=(4)(5m)+(4)(3)+2m

=20m+12+2m

Combine Like Terms:

=20m+12+2m

=(20m+2m)+(12)

=22m+12

8 0

3 years ago

Use this picture to solve for X

Zepler [3.9K]

Answer:

x=2

Step-by-step explanation:

i would set up a system of equation using the pythagorean theorem:

1^2+x^2=z^2

4^2+x^2=y^2

Add up these equations to get:

17+2x^2=y^2+z^2

But notice that

y^2+z^2=5^2

So you can substitute

17+2x^2=25

2x^2=8

x^2=4

x=2

8 0

2 years ago

The formula for the perimeter (P) of a rectangle is

shutvik [7]

Answer:

174

Step-by-step explanation:

L = 68

W=19

Use the formula given:

2 x 68 + 2 x 19 = 174

4 0

3 years ago