What is the solution to the system of equations below?

Anybody knows the answer?

vladimir1956 [14]

The top and bottom faces are 3 inches by 3 inches.

Area = 3 in. * 3 in. * 2 = 18 in.^2

The front, back, right, and left faces are 3 in. by 6 in.

Area = 3 in. * 6 in. * 4 = 72 in.^2

Total surface area = 18 in.^2 + 72 in.^2 = 90 in.^2

Answer: B. 90 square inches

3 0

3 years ago

There are three power plants [X, Y, Z] that at any given time each one either generates electricity or idles. Event A is that pl

insens350 [35]

We're told that

$P(A\cap B)=0.15$

$P(A\cup B)^C=0.06\implies P(A\cup B)=0.94$

$P(B\mid A)=P(B^C\mid A)=0.5$

where the last fact is due to the law of total probability:

$P(A)=P(A\cap B)+P(A\cap B^C)$

$\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)$

$\implies 1=P(B\mid A)+P(B^C\mid A)$

so that $B\mid A$ and $B^C\mid A$ are complementary.

By definition of conditional probability, we have

$P(B\mid A)=P(B^C\mid A)$

$\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}$

$\implies P(A\cap B)=P(A\cap B^C)$

We make use of the addition rule and complementary probabilities to rewrite this as

$P(A\cap B)=P(A\cap B^C)$

$\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)$

$\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)$

$\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]$

$\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]$

$\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C$

$\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)$

By the law of total probability,

$P(B)=P(A\cap B)+P(A^C\cap B)$

$\implies P(A^C\cap B)=P(B)-P(A\cap B)$

and substituting this into $(*)$ gives

$2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]$

$\implies P(B)=P(A\cup B)-P(A\cap B)$

$\implies P(B)=0.94-0.15=\boxed{0.79}$

8 0

3 years ago

What is the result of increasing 50 by 30%?

kogti [31]

Answer:

50 increased by 30% is 65

Step-by-step explanation:

'Percent (%)' means 'out of one hundred':

p% = p 'out of one hundred',

p% is read p 'percent',

p% = p/100 = p ÷ 100.

30% = 30/100 = 30 ÷ 100 = 0.3.

100% = 100/100 = 100 ÷ 100 = 1.

Percentage increase = 30% × 50

New value = 50 + Percentage increase

Calculate

New value =

50 + Percentage increase =

50 + (30% × 50) =

50 + 30% × 50 =

(1 + 30%) × 50 =

(100% + 30%) × 50 =

130% × 50 =

130 ÷ 100 × 50 =

130 × 50 ÷ 100 =

6,500 ÷ 100 =

65

Or just find 30% of 50 (15) and add that

8 0

2 years ago

Cual es el resultado de (7.006×10⁴¹)×(5.09×10²²)<br><br>

Murljashka [212]

Answer:

El resultado de (7.006×10⁴¹)×(5.09×10²²)=3.566054*10⁶⁴

Step-by-step explanation:

La notación científica es una manera rápida de representar un número utilizando potencias de base diez.

Los números se escriben como:

a*10ⁿ

donde:

a es un número real mayor o igual que 1 y menor que 10.
n es un número entero, que recibe el nombre de exponente u orden de magnitud. Representa el número de veces que se desplaza la coma. Siempre es un número entero, positivo si se desplaza a la izquierda, negativo si se desplaza a la derecha.

Para realizar la multiplicación con notación científica, debes multiplicar las magnitudes afectadas por las potencias de 10 y, por separado, multiplicar las potencias de 10, recordando la propiedad:

Si dos bases son iguales (el mismo número o variable), y son los factores de una multiplicación, ambas bases quedan en una sola y sus exponentes son sumados: xᵃ*xᵇ= xᵃ⁺ᵇ

En este caso:

(7.006×10⁴¹)×(5.09×10²²)=(7.006*5.09)*(10⁴¹*10²²)=35.66054*10⁴¹⁺²²= 35.66054*10⁶³

Siguiendo el formato a*10ⁿ, debes ajustar el valor de la base a de manera que sea un número real mayor que 1 y menor que 10. Entonces, se mueve la coma decimal hacia la izquierda tantos espacios hasta llegar a la derecha del primer dígito. Y se escribe la base 10, al cual el exponente se suma la cantidad de espacios que se mueve la coma, que es un número positivo porque la coma se desplaza a la izquierda.

Entonces 35.66054*10⁶³= 3.566054*10⁶⁴

<u><em>El resultado de (7.006×10⁴¹)×(5.09×10²²)=3.566054*10⁶⁴</em></u>

4 0

3 years ago

Find the area of the trapezoid<br> 3cm, 3cm, 8cm

love history [14]

The area of the trapezoid is the amount of space on it, and the value of the area is 16.5 square cm

<h3>How to determine the area?</h3>

The given parameters are:

Parallel sides = 3cm and 8 cm

Height = 3cm

The area is then calculated using:

Area = 0.5 * (Sum of parallel sides) * Height

So, we have:

Area = 0.5 * (3 + 8) * 3

Evaluate

Area = 16.5

Hence, the area of the trapezoid is 16.5 square cm