Which expression is equivalent to the given expression?

In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 &

sergejj [24]

66 is your answer if you need anything else ask someone

6 0

3 years ago

Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

Answer: The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

$L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.$

Then, the series will be convergent if L < 1 and divergent if L > 1.

For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

7 0

4 years ago

Read 2 more answers

Seven times a number is less than or equal to a quantity that is 24 less than that same

Ad libitum [116K]

Answer:

$7x\leq x-24$

Here, $x$ denotes the required number.

Step-by-step explanation:

Let $x$ denotes the required number that satisfies the following condition.

''seven times a number is less than or equal to a quantity that is 24 less than that same number''

Seven times a number is equal to $7x$

Quantity that is 24 less than that same number is equal to $x-24$

Now find the inequality.

As seven times a number is less than or equal to a quantity that is 24 less than that same number,

$7x\leq x-24$

6 0

3 years ago

A farm had 480 acres more wheat than corn. After the farmers collected 80% of the wheat and 25% of the corn, the area of the whe

Sergio [31]

The area covered by corn is x
The area covered by wheat is (x+480)
After 80% of wheat was collected, the new area was:
20/10(x+480)
=1/5(x+480)
After 25% of the corn was collected, the new area was:
75/100x
=3/4x
New area equation will be:
(3/4)x=1/5(x+480)+300
(3/4x)=(1/5)x+96+300
solving for x we get:
11/20x=396
x=720
thus the original area of corn was 720 acres
Original area of wheat was 720+480=1200 acres

7 0

3 years ago

marty has 1 1/3 jugs of apple juice. he uses 3/4 of the juice to make freeze pops. what fraction amount of a jus doe marty have?

Vedmedyk [2.9K]

Answer:

=2 $\frac{1}{12}$