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givi [52]
3 years ago
12

A large grandfather clock strikes its bell once at 1:00, twice at 2:00, three times at 3:00, etcetera. what is the total number

of times the bell will be struck in a day? use an arithmetic series to help solve the problem and show how you arrived at your answer.
Mathematics
2 answers:
erastovalidia [21]3 years ago
8 0
There is a formula for adding consecutive integers.
sum = (n * (n+1)) / 2
for summing 1 through 12 it is
sum = (12 * 13) / 2 = 156/2 = 78
The clock goes through two "12-hour cycles" in a day, so the answer is 2 * 78 or 156 times.


uranmaximum [27]3 years ago
7 0

Answer:

<h2>300 times per day.</h2>

Step-by-step explanation:

Basically, to solve this problem we just have to sum:

1+2+3+...+24

But, using an arithmetic series, we have to use this formula:

Sum=n(\frac{a_{1}+a_{n} }{2})

Where, n is the total number of elements (in this case is 24), a_{1} is the first element (1) and a_{n} is the last element (24), because a day has 24 hours.

So, replacing all variables, we have:

Sum=24(\frac{1+24}{2})\\Sum=24\frac{25}{2}=300

Therefore, the bell will be struck 300 times per day.

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6 0
2 years ago
The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% p
Stolb23 [73]

Answer:

First type of fruit drinks: 48 pints

Second type of fruit drinks: 32 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 55% pure fruit juice

Let's call B the amount of second type of fruit drinks. 80% pure fruit juice

The resulting mixture should have 65% pure fruit juice and 80 pints.

Then we know that the total amount of mixture will be:

A + B = 80

Then the total amount of pure fruit juice in the mixture will be:

0.55A + 0.8B = 0.65 * 80

0.55A + 0.8B = 52

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:

-0.8A -0.8B = -0.8*80

-0.8A -0.8B = -64

-0.8A -0.8B = -64

               +

0.55A + 0.8B = 52

--------------------------------------

-0.25A = -12

A = \frac{-12}{-0.25}

A = 48\ pints

We substitute the value of A into one of the two equations and solve for B.

48 + B = 80

B = 32\ pints

6 0
3 years ago
The measurement of the complement of an angle exceeds the measure of the angle by 25%. Find the measurement of the angle and its
tester [92]
Let the angles be A and C 

<span>Complimentary angles, therefor </span>
<span>A + C = 90 </span>

<span>The measurement of the complement of an angle exceeds the measure of the angle by 25% (you used a % sign so I'll use % instead of degrees) </span>
<span>C = 1.25A </span>

<span>Substitute </span>
<span>A + 1.25A = 90 </span>
<span>2.25A = 90 </span>
<span>A = 40º <----- </span>
<span>C = 50º <----- </span>
<span>------------------------------ </span>

<span>If you meant 25º </span>
<span>A + (A + 25) = 90 </span>
<span>2A + 25 = 90 </span>
<span>2A = 65 </span>
<span>A = 32.5º </span>
<span>C = 57.5º</span>
3 0
3 years ago
-27 - x = -51<br> ................
Katarina [22]

Answer:

24

Step-by-step explanation:

-27 - x = -51

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x = 24

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3 years ago
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Step-by-step explanation:

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