Help plssssss!!!!!!!!!!

Get the general term for the sequence being your t3 = 11 and the t20 = 244.2

marusya05 [52]

Answer:

nth term = $t_{n} = 7.639(1.2)^{n - 1}$

Step-by-step explanation:

Let us assume that the given sequence is a G.P.

Now, if the first term of the G.P. is a and the common ratio is r, then

Third term = $t_{3} = ar^{2} = 11$ .......... (1) and

20th term = $t_{20} = ar^{19} = 244.2$ ........... (2)

Now, dividing equation (2) with equation (1) we get

$\frac{ar^{19} }{ar^{2} } = \frac{244.2}{11} = 22.2$

⇒ $r^{17} = 22.2$

⇒ r = 1.2.

Hence, from equation (1) we get

a(1.2)² = 11

⇒ a = 7.639 (Approx.)

Therefore, the general term of the sequence i.e. nth term = $t_{n} = 7.639(1.2)^{n - 1}$ (Answer)

5 0

3 years ago

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 oun

sveticcg [70]

Answer:

a. $f_X(x) = \dfrac{1}{3.5}8.5$

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. 86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

$f_X(x) = \dfrac{1}{B-A}A$

where A and B are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x) = \dfrac{1}{12-8.5}8.5$

$f_X(x) = \dfrac{1}{3.5}8.5$

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

$F(x) = \dfrac{x-A}{B-A}$

$F(10) = \dfrac{10-8.5}{12-8.5}$

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

$P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx$

$P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}$

$P(X\geq11) = {\dfrac{1}{3.5}} (12-11)$

$P(X\geq11) = {\dfrac{1}{3.5}} (1)$

$P(X\geq11) = 0.2857$

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)$

$P(9.5 \leq X\leq11.5) =0.2857* (2)$

$P(9.5 \leq X\leq11.5) =0.5714$

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

$P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx$

$P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}$

$P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)$

$P(X \geq 9) = {\dfrac{1}{3.5}}(3)$

$P(X \geq 9) = 0.2857*}(3)$

$P(X \geq 9) = 0.8571$

NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

3 0

3 years ago

An airplane travels 6032 kilometers against the wind in 8 hours and 7312 kilometers with the wind in the same amount of time. Wh

Vladimir79 [104]

Answer:

The rate of plane in still air is 834 km/hr and the rate of wind is 80 km/hr.

Step-by-step explanation:

The airplane travels 6032 km in 8 hours against the wind.

So, $u -v = \frac{6032}{8} = 754$ ........ (1) {Where u is the speed of plane in still air and v is the wind speed}

Again, the airplane travels 7312 km in 8 hours with the wind.

So, $u +v=\frac{7312}{8} =914$ ........ (2)

Now, adding equations (1) and (2) we get,

2u = 1668

⇒ u = 834 km per hour.

So, from equation (1), we get

v = u - 754 = 834 - 754 = 80 km per hour.

Therefore, the rate of the plane in still air is 834 km/hr and the rate of wind is 80 km/hr. (Answer)

3 0

3 years ago

A wheel with a diameter of 21 inches is rolling on a farm. After 100 revolutions, approximately how many inches has the wheel tr

makvit [3.9K]

Answer:69420

Step-by-step explanation:

if you go 21 inches down a 100 inch slope you will be 79 inches

6 0

3 years ago

Read 2 more answers

Write a phrase for expression 7hb

amm1812

This is all I got for an answer. I hope it helps!

7 and anuber times a number

3 0

2 years ago