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LiRa [457]
3 years ago
8

You borrow money for 4 years. The total amount that you repay is $7,840, which includes $840 in simple interest. How much was th

e principal? What was the annual interest rate?
Mathematics
1 answer:
Lina20 [59]3 years ago
6 0

Answer:

  • principal: $7000
  • interest rate: 3%

Step-by-step explanation:

amount repaid = principal + interest

$7840 = principal + $840

$7000 = principal . . . . . . . . subtract $840 from both sides of the equation

___

I = Prt

840 = 7000·r·4

840/(4·7000) = r = 0.03 = 3%

The principal was $7000; the interest rate was 3%.

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5) In a certain supermarket, a sample of 60 customers who used a self-service checkout lane averaged 5.2 minutes of checkout tim
Ne4ueva [31]

Answer:

\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643

S_p=2.940

t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751

df=60+72-2=130

p_v =P(t_{130}

Assuming a significance level of \alpha=0.05 we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

Step-by-step explanation:

Data given

Our notation on this case :

n_1 =60 represent the sample size for people who used a self service

n_2 =72 represent the sample size for people who used a cashier

\bar X_1 =5.2 represent the sample mean for people who used a self service

\bar X_2 =6.1 represent the sample mean people who used a cashier

s_1=3.1 represent the sample standard deviation for people who used a self service

s_2=2.8 represent the sample standard deviation for people who used a cashier

Assumptions

When we have two independent samples from two normal distributions with equal variances we are assuming that  

\sigma^2_1 =\sigma^2_2 =\sigma^2

The statistic is given by:

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

And t follows a t distribution with n_1+n_2 -2 degrees of freedom and the pooled variance S^2_p is given by this formula:

\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}

System of hypothesis

Null hypothesis: \mu_1 \geq \mu_2

Alternative hypothesis: \mu_1 < \mu_2

This system is equivalent to:

Null hypothesis: \mu_1 - \mu_2 \geq 0

Alternative hypothesis: \mu_1 -\mu_2 < 0

We can find the pooled variance:

\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643

And the deviation would be just the square root of the variance:

S_p=2.940

The statistic is given by:

t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751

The degrees of freedom are given by:

df=60+72-2=130

And now we can calculate the p value with:

p_v =P(t_{130}

Assuming a significance level of \alpha=0.05 we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

5 0
3 years ago
the mass of mars is approximately 100000000000000000000000 kilograms and that of neptune is about 100000000000000000000000000 ki
rusak2 [61]
Mars-10^23
Neptune-10^26
4 0
3 years ago
The zeroes are quadratic functions<br> are 6 and -4 which of these could be the functons.
LenaWriter [7]

Answer:

6 is the answer of your question

4 0
3 years ago
Read 2 more answers
Someone plz help me I will give brainliest
makvit [3.9K]

Answer:

2. 3/4 x 5/9 = 3x5/4x9 = 15/36 = 5/12

4. 4/7 x 1/2 = 4x1/7x2 = 4/14 = 2/7

6. 4/9 x 2/3 = 4x2/9x3=8/27

Step-by-step explanation:

Hope it helps!

5 0
3 years ago
Read 2 more answers
Write each repeating decimal using bar
SVETLANKA909090 [29]

Answer:

*The bar is supposed to go on top of the number, but I will put it at the bottom because I don't know how to do it at the top*

a) 0.<u>5</u>

b) 0.<u>13456</u>

Step-by-step explanation:

a) The 5 is repeating so you put the bar on top of the 5

b) The number 13456 is repeated so you put the bar on top of the 13456

6 0
3 years ago
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