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3 years ago

The average of 10 numbers is -5. A new number is added to the list making the average -6. What is the new number?

Mathematics

1 answer:

Shtirlitz [24]3 years ago

4 0

Answer:

- 16

Step-by-step explanation:

Average is calculated as

average = $\frac{total}{count}$

Thus for the given 10 numbers we have

$\frac{total}{10}$ = - 5 ( multiply both sides by 10 )

total = - 50

let the number added be x, then

$\frac{total+x}{11}$ = - 6 ( multiply both sides by 11 )

total + x = - 66, that is

- 50 + x = - 66 ( add 50 to both sides )

x = - 16

The new number is - 16

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A pendulum is set swinging. its first oscillation is through 30 and each succeeding oscillation is through 95% of the angle of t

Marat540 [252]

<u>Answer-</u>

<em>After 76 swings</em><em> the angle through which it swings less than 1°</em>

<u>Solution-</u>

From the question,

Angle of the first of swing = 30° and then each succeeding oscillation is through 95% of the angle of the one before it.

So the angle of the second swing = $(30\times \frac{95}{100})^{\circ}$

Then the angle of third swing = $(30\times (\frac{95}{100})^2)^{\circ}$

So, this follows a Geometric Progression.

$(30,\ 30\cdot \frac{95}{100},\ 30\cdot (\frac{95}{100})^2............,0)$

a = The initial term = 30

r = Common ratio = $\frac{95}{100}$

As we have to find the number swings when the angle swept by the pendulum is less than 1°.

So we have the nth number is the series as 1, applying the formula

$T_n=ar^{n-1}$

Putting the values,

$\Rightarrow 1=30(\frac{95}{100})^{n-1}$

$\Rightarrow \frac{1}{30} =(\frac{95}{100})^{n-1}$

Taking logarithm of both sides,

$\Rightarrow \log \frac{1}{30} =\log (\frac{95}{100})^{n-1}$

$\Rightarrow \log \frac{1}{30} =(n-1)\log (\frac{95}{100})$

$\Rightarrow -1.5=(n-1)(-0.02)$

$\Rightarrow 1.5=(n-1)(0.02)$

$\Rightarrow n-1=\dfrac{1.5}{0.02}$

$\Rightarrow n-1=75$

$\Rightarrow n=76$

Therefore, after 76 swings the angle through which it swings less than 1°

8 0

3 years ago

The temperature in Frederick decreased 8

velikii [3]

You find the overall change in temperature by adding them together.
-8 would be from were is decreased 8 degrees and +8 would be from where it increased 8 degrees
Like: -8+8=0

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3 years ago

5/2.35 = 12/x<br><br> what does x =

Maksim231197 [3]

Step-by-step explanation:

5 = 12 Cross multiply

2.35 x

5x = 28.2 Divide 5 on both sides to isolate the variable

x = 5.64

<h3><u><em>Hope this helps!!!</em></u></h3><h3><u><em>Please mark as brainliest!!!</em></u></h3>

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3 years ago

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andre [41]

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I hope this helps :)

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ivann1987 [24]

Answer:

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