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LUCKY_DIMON [66]

3 years ago

13

Thomas has an album that holds 600 baseball cards each page of the album holds 6 cards. If 45% of the album is empty, how many p

ages are filled with baseball cards

1 answer:

My name is Ann [436]3 years ago

3 0

Answer:

55 pages

Step-by-step explanation:

Knowing that the <em>book holds 600 cards and 6 cards/page</em>, we can tell that there are <em>100 pages</em>.

From that, we know that 45% are empty, which means <em>55% of all of the pages have cards</em>.

55% of 100 is 55. Therefore, 55 pages have baseball cards.

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The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

3 years ago

Determine the values of a, b, and c for the quadratic equation<br><br> 3x2−5x+6=0

sweet-ann [11.9K]

Answer:

The values of a, b, and c for the quadratic equation

a=3

b=-5

c=6

7 0

3 years ago

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The water in the reservoir decreases by 47% during a drop period before the drought the reservoir had 44,580 acre feet of water

Ket [755]

47 * 44,580
--------------
100

8 0

3 years ago

A square has the same area as a

gogolik [260]

Answer:

10

Step-by-step explanation:

rectangle area: 100

√100 is 10 therefore 10 is length of square

7 0

3 years ago

Read 2 more answers

What is the answer? Thank you, :)

sergiy2304 [10]

One litter is 1000 milliliters

if each friend wants 400 milliliters, and there are ten friends, samantha needs 4000 milliliters of lemonade

since each pitcher can hold 2 liters, or 2000 milliliters, she’ll need to refill it 2 times

this is because 4000/2000 is 2

final answer: 2 times

hope this helped!!

4 0

2 years ago