Response:
Her brother catches up to her at 11 am + 4 hours = 15 p.m
Detailed explanation:
Provided information;
Ariel's speed = 45 mph
She departed at 9 a.m
Her brother's speed = 60 mph
He began at 11 a.m
Inferred from the question: Since Ariel's speed is 45 mph, after two hours she is ahead by 90 miles.
Meanwhile, her brother travels at 60 mph, hence he is traveling (60 - 45) = 15 mph faster
Therefore, with this speed, he will catch up to her in 
= 4 hours.
So her brother catches up with her at 11 am + 4 hours = 15 p.m
Answer:
There is a probability of 24.51% that the weight of a bag exceeds the maximum permitted weight of 50 pounds.
Step-by-step explanation:
Problems dealing with normally distributed samples can be addressed using the z-score formula.
For a set with the mean 
and a standard deviation 
, the z-score for a measure X is calculated by
Once the Z-score is determined, we consult the z-score table to find the related p-value for this score. The p-value signifies the likelihood that the measured value is less than X. Since all probabilities total 1, calculating 1 minus the p-value gives us the probability that the measure exceeds X.
For this case
Imagine the weights of passenger bags are normally distributed with a mean of 47.88 pounds and a standard deviation of 3.09 pounds, thus 
What probability exists that a bag’s weight will surpass the maximum allowable of 50 pounds?
That translates to 
Thus
has a p-value of 0.7549.
<pthis indicates="" that="" src="https://tex.z-dn.net/?f=P%28X%20%5Cleq%2050%29%20%3D%200.7549" id="TexFormula10" title="P(X \leq 50) = 0.7549" alt="P(X \leq 50) = 0.7549" align="absmiddle" class="latex-formula">.
Additionally, we have that
There is a probability of 24.51% that the weight of a bag will exceed the maximum allowable weight of 50 pounds.
</pthis>
Respuesta:
La altitud del globo por encima del nivel del suelo es de 449,6 metros.
Explicación paso a paso:
El enunciado no está completo. El texto completo es: "Un globo se desplaza entre las ciudades A y B, que se encuentran a 1.500 m de distancia. Los ocupantes del globo observan la ciudad A con un ángulo de depresión de 27°, mientras que, para la ciudad B, el ángulo es de 36°. ¿Cuál es la altura aproximada del globo con respecto al suelo?"
El diagrama que ilustra esta situación está en el archivo adjunto. Para calcular la altura del globo, se pueden emplear las funciones trigonométricas, siendo recomendable hacer uso de la función tangente para los ángulos de depresión mencionados:
Ciudad A
Ciudad B
Donde 
y 
representan la altura desde el suelo y la distancia horizontal desde la ciudad A.
Luego, se igualan las alturas en ambas ecuaciones para calcular la distancia horizontal del globo en relación a la ciudad A:
Por último, la altura del globo sobre el suelo se calcula como:
La altura del globo respecto al nivel del suelo es 449,6 metros.
<span>The likelihood of both selected students being sophomores is 6/20, which simplifies to 3/10.
The expression for the probability that both chosen students are sophomores is (6c1) (5c1) /(20c2)
</span>
