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Ber [7]
3 years ago
8

Phyllis invested 50000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 7

percent per year. After one year the total interest earned on these investments was 2720 dollars. How much money did she invest at each rate?
Mathematics
1 answer:
Elodia [21]3 years ago
5 0

Answer:

The amount invested at 5% was $39,000 and the amount invested at 7% was $11,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

I=P(rt)

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x-----> the amount invested at 5%

50,000-x -----> the amount invested at 7%

so

t=1\ year\\ I=\$2,720\\r_1=0.05\\r_2=0.07\\P_1=\$x\\P_2=\$(50,000-x)

substitute in the formula above

2,720=x(0.05*1)+(50,000-x)(0.07*1)

solve for x

2,720=0.05x+3,500-0.07x

0.07x-0.05x=3,500-2,720\\0.02x=780\\x=\$39,000

(50,000-x)=\$11,000

therefore

The amount invested at 5% was $39,000 and the amount invested at 7% was $11,000

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Find their respective z-scores.

 Who had the more convincing victory?

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B. Karen a more convincing victory because of a higher z-score.

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Answer:

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Step-by-step explanation:

From the question we are told that

  The mean of the current year  is  \mu_c =  186.32 \  minutes

   The standard deviation is  \sigma_c  =  0.305 \  minutes

   The time taken by  the winning car for the current year  is  x =  185.85 \ minutes

  The mean of the previous  year  is  \mu_p =  110.7 \  minutes

   The standard deviation the previous  year  is  \sigma_p  = 0.115  \  minutes

 The time taken by  the winning car for the previous year  is  y =   110.48 \ minutes    

Generally the z-score for current year is mathematically evaluated as

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=>     z_c  =  \frac{ 185.85- 186.32}{0.305 }

=> z_c  = -1.536

Generally the z-score for previous year is mathematically evaluated as

     z_p  =  \frac{y- \mu_p}{\sigma_p }

=>     z_p  =  \frac{ 110.48-110.7}{0.115  }

=> z_p  = -1.913

From the value obtained we see that  z_p  <  z_c , Hence  Karen had a more convincing victory because of the lower z -score.

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