1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
uranmaximum [27]
3 years ago
11

There is a mountain with 45 bat caves in a row. Every cave has at least 2 bats and there are 490 bats in all. Any 7 caves in a r

ow contain exactly 77 bats. Suppose the first cave has 7 times more bats than the last cave. What is the greatest possible number of bats in the 30th cave?
Mathematics
1 answer:
zhannawk [14.2K]3 years ago
8 0

Answer:

12

Step-by-step explanation:

The first cave has 7 times more bats than the last cave.  So if the 45th cave has b bats, then the first cave has 7b bats.

There are 77 bats in every row of 7 caves.  So if there are 7b bats in the first cave, then there are 77−7b bats in caves 2 through 7.

Since there are also 77 bats in caves 2 through 8, that means cave #8 must have 7b bats.  Repeating this logic:

#1 = 7b

#2-#7 = 77−7b

#8 = 7b

#9-#14 = 77−7b

#15 = 7b

#16-21 = 77−7b

#22 = 7b

#23-28 = 77−7b

#29 = 7b

So the first 29 caves have 5(7b) + 4(77−7b) = 308 + 7b bats.

Now we do the same thing from the other end.  If cave #45 has b bats, then caves #39-#44 have 77−b bats.  And since caves #38-44 have 77 bats, then cave #38 has b bats.  Therefore:

#45 = b

#39-44 = 77−b

#38 = b

#32-37 = 77−b

#31 = b

So caves 31 through 45 have 3b + 2(77−b) = 154 + b bats.

Adding that to the first 29 caves, plus x number of bats in cave #30:

308 + 7b + x + 154 + b = 462 + 8b + x

We know this equals 490.

490 = 462 + 8b + x

28 = 8b + x

x is a maximum when b is a minimum, which is b = 2.

28 = 8(2) + x

x = 12

There are at most 12 bats in the 30th cave.

You might be interested in
A window in the shape of a parallelogram has the dimensions given.
devlian [24]

Answer:

A. 20ft

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Using your knowledge of exponential and logarithmic functions and properties, what is the intensity of a fire alarm that has a s
Ierofanga [76]

Option B:

I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}

Solution:

Given sound level = 120 decibel

To find the intensity of a fire alarm:

$\beta=10\log\left(\frac{I}{I_0} \right)

where I_0=1\times10^{-12}\ \text {watts}/ \text m^2}

Step 1: First divide the decibel level by 10.

120 ÷ 10 = 12

Step 2: Use that value in the exponent of the ratio with base 10.

10^{12}

Step 3: Use that power of twelve to find the intensity in Watts per square meter.

$10^{12}=\left(\frac{I}{I_0} \right)

$10^{12}=\left(\frac{I}{1\times10^{-12}\ \text {watts}/ \text m^2} \right)

Now, do the cross multiplication,

I=10^{12}\times1\times\ 10^{-12} \ \text {watts}/ \text m^2}

I=1\times\ 10^{12-12} \ \text {watts}/ \text m^2}

I=1\times\ 10^{0} \ \text {watts}/ \text m^2}

I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}

Option B is the correct answer.

Hence I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}.

5 0
3 years ago
Points E, F, and G are collinear. If EF = 8 and EG = 12, which point cannot lie between the other two?
Dima020 [189]
Point G can not be between
3 0
3 years ago
What is the value of x in the equation 3x-4y=65, when y equals 4?
andreev551 [17]

Answer:

x = 27

Step-by-step explanation:

3x - 4y = 65

3x = 65 + 4y

<em><u>Find x, when y = 4</u></em>

3x = 65 + 4 (4)

3x = 65 + 16

3x = 81

x = 27             [ \ x = \frac{81}{3}\ ]                    

5 0
3 years ago
A bus travels 300 miles in six hours. How far does the bus travel in one hour
babunello [35]

Answer:

50

Step-by-step explanation

The reason why is because you have to divide. 300 / 6 and you will get 50.

6 0
3 years ago
Other questions:
  • Simplify the expression 6(x+4)+1 and 5+8(3+x)<br><br> Thanks
    6·2 answers
  • Given that,
    12·2 answers
  • A tortoise traveled 1/6 kilometer in 7/8 hour. What was its average speed in kilometers per hour?
    10·1 answer
  • 50 BIG POINTS! Help me on math please!  @ Apologiabiology, @ Bookishfairy73
    8·2 answers
  • F(x)=-x^2+8x-20 find the min/max value
    5·1 answer
  • Write an expression to show how you could calculate the total amount David paid.
    15·2 answers
  • At the movie theatre, child admission is $5.20 and adult admission is $8.80. On Saturday, 123 tickets were sold for a total sale
    6·1 answer
  • A glass vase is shaped like a cylinder and has a radius of 2.5 inches. The vase holds 170 cubic inches of water. How tall is the
    11·2 answers
  • Try the numbers 22, 23, 24, 25 in the equation 4/3 = 32/d
    9·1 answer
  • Identify the domain of the function shown in the graph
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!