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kiruha [24]
2 years ago
5

For the past three months, grace used her cell phone for 43 minutes, 62 minutes, and 57 minutes. How many minutes would she have

to use her cell phone Thur month for the average usage over the four months to be 55 minutes
Mathematics
2 answers:
chubhunter [2.5K]2 years ago
7 0

The answer is 55 minutes.

lubasha [3.4K]2 years ago
3 0

Answer: She have to use her cell phone for 58 minutes in the fourth month.

Step-by-step explanation:

Since we have given that

Number of minutes Grace used her cell phone are as follows :

43 minutes, 62 minutes, 57 minutes, x.

Average = 55 minutes

As we know the formula for "Average":

Average=\dfrac{43+62+57+x}{4}\\\\55=\dfrac{162+x}{4}\\\\55\times 4=162+x\\\\220-162=x\\\\58=x

Hence, She have to use her cell phone for 58 minutes in the fourth month.

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Jane invested £4000 for 3 years with an interest rate of 1.5%. What was her investment worth at the end of this period?
ddd [48]

Answer:

$4182.7

Step-by-step explanation:= 4000*(1.5%)*3

Year 1= 4000*(100%+1.5%)= 4060

Year 2= 4060*(100%+1.5%)= 4120.9

Year 3= 4120.9*(100%+1.5%)= 4182.7

6 0
2 years ago
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Prove that (sec 12A-1)/(sec 6A-1)=tan 12A/tan 3A
adelina 88 [10]

Let x=3A. Recall the following identities,

\cos^2\theta=\dfrac{1+\cos2\theta}2

\sin^2\theta=\dfrac{1-\cos2\theta}2

\sin2\theta=2\sin\theta\cos\theta

Now,

\dfrac{\sec12A-1}{\sec6A-1}=\dfrac{\sec4x-1}{\sec2x-1}

=\dfrac{\cos2x(1-\cos4x)}{\cos4x(1-\cos2x)}

=\dfrac{2\cos2x\sin^22x}{\cos4x(1-\cos2x)}

=\dfrac{2\cos2x\sin^22x(1+\cos2x)}{\cos4x(1-\cos^22x)}=\dfrac{2\cos2x\sin^22x(1+\cos2x)}{\cos4x\sin^22x}=\dfrac{2\cos2x(1+\cos2x)}{\cos4x}

=\dfrac{4\cos2x\cos^2x}{\cos4x}

=\dfrac{4\cos2x\cos^2x\sin4x}{\cos4x\sin4x}=\dfrac{4\cos2x\cos^2x\tan4x}{\sin4x}

=\dfrac{4\cos2x\cos^2x\tan4x}{2\sin2x\cos2x}=\dfrac{2\cos^2x\tan4x}{\sin2x}

=\dfrac{2\cos^2x\tan4x}{2\sin x\cos x}=\dfrac{\cos x\tan4x}{\sin x}

=\dfrac{\tan4x}{\frac{\sin x}{\cos x}}=\dfrac{\tan4x}{\tan x}=\dfrac{\tan12A}{\tan3A}

QED

5 0
2 years ago
Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all of the headphones and music players in identical pack
tiny-mole [99]

Answer:

he can make 4 packages hope this helps

8 0
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The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of vi
baherus [9]

Answer: 2185

Step-by-step explanation:

Let p be the proportion of visitors are campers.

Given : The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state.

The prior proportion of visitors are campers : p=0.35

Allowable error : E= 2%= 0.02

We know that the z-value for 95% confidence = z_c=1.96

Then by Central Limit Theorem , the required sample size would be :

n=p(1-p)(\dfrac{z_{c}}{E})^2

\Rightarrow\ n=0.35(1-0.35)(\dfrac{1.96}{0.02})^2\\\\ n= 0.35(0.65)(9604)

Simply , we get

n=2184.91\approx2185  [Rounded to the next whole number.]

Hence, the smallest sample size to estimate the population proportion of campers =2185

7 0
2 years ago
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