How many triangles will there be in the 7th term of the following

The table shows the results of a poll of 200 randomly selected juniors and seniors who were asked if they attended prom. Find th

Zielflug [23.3K]

Answer:

(a) $\frac{7}{25}$

(b) $\frac{19}{116}$

(c) $\frac{28}{125}$

Step-by-step explanation:

Number of juniors who attended prom,n(J)=28

Number of seniors who attended prom,n(S)=97

Total of those who attended prom=125

Number of juniors who did not attend prom,n(J')=56

Number of seniors who did not attend prom,n(S')=19

Total of those who attended prom=75
Total Number of students=200

(a) P (a junior who did not attend prom)

$P(J')=\frac{56}{200}= \frac{7}{25}$

(b)

$P(Senior)=\frac{116}{200}$

$P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}$

(c)P (junior | attended prom)

$P(Senior)=\frac{84}{200}$

$P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}$

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Explorers on a planet with a thin atmosphere want to measure the acceleration of gravity at its surface. So they use a spring gu

Murljashka [212]

Answer:

The value of $g_s$ is $g_s=\frac{30}{21} \:\frac{m}{s^2}$ .

Step-by-step explanation:

We know that the position function is given by

$s(t)=30t-\frac{g_s}{2} t^2$

Velocity is defined as the rate of change of position. Therefore,

$v(t)=\frac{d}{dt}(s(t))$

So, the velocity function is

$v(t)=\frac{d}{dt}(s(t))\\\\v(t)=\frac{d}{dt}(30t-\frac{g_s}{2} t^2)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(30t\right)-\frac{d}{dt}\left(\frac{g_s}{2}t^2\right)\\\\v(t)=30-g_st$

When a body reaches a vertical velocity of zero, this is the maximum height of the body and then gravity will take over and accelerate the object downward. Thus,

$v(t)=30-g_st=0\\\\g_s=\frac{30}{t}$