The Venn diagram shows the number of students playing instruments. How many students play both the guitar and

Two digits are selected with replacement from the digits 1, 2, 3, and 4.

Helen [10]

6 and 8 I believe is the answer

6 0

2 years ago

The following data are the distances between a sample of 20 retail stores and a large distribution center. The distances are in

sesenic [268]

Answer:

Variance = 1,227.27

Standard deviation = 35.03

Step-by-step explanation:

To calculate these, we use the following formulas:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

Standard deviation = Variance^0.5

Where;

n = number of values = 20

x = each value

Therefore, we have:

Sum of the values = 29 + 32 + 36 + 40 + 58 + 67 + 68 + 69 + 76 + 86 + 87 + 95 + 96 + 96 + 99 + 106 + 112 + 127 + 145 + 150 = 1,674

Mean = 1,674 / 20 = 83.70

Variance = ((29-83.70)^2 + (32-83.70)^2 + (36-83.70)^2 + (40-83.70)^2 + (58-83.70)^2 + (67-83.70)^2 + (68-83.70)^2 + (69-83.70)^2 + (76-83.70)^2 + (86-83.70)^2 + (87-83.70)^2 + (95-83.70)^2 + (96-83.70)^2 + (96-83.70)^2 + (99-83.70)^2 + (106-83.70)^2 + (112-83.70)^2 + (127-83.70)^2 + (145-83.70)^2 + (150-83.70)^2) / (20 - 1) = 23,318.20 / 19 = 1,227.27

Standard deviation = 1,227.27^0.5 = 35.03

5 0

2 years ago

Vanessa deposits $24,000 into each of two savings accounts. Account I earns 2. 4% interest compounded annually. Account II earns

ikadub [295]

The sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)

<h3>How to calculate compound interest's amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

$CI = P(1 +\dfrac{R}{100})^T - P$

The final amount becomes:

$A = CI + P\\A = P(1 +\dfrac{R}{100})^T$

<h3>How to calculate simple interest amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

$I = \dfrac{P \times R \times T}{100}$

For the considered case, we're given that:

Initial amount in both accounts deposited = $24,000 = P
Type of interest: Compound interest in first account and simple interest in second account
Unit of time: Annually
Rate of interest = 2.4% annually = R
Total unit of time for which amount is to be calculated: 5 years = T

In first account, the final amount at the end of 5 years is evaluated as:

$A = 24000(1 + \dfrac{2.4}{100})^4 = 24000(1.024)^4 \approx 27021.59\: \rm (in \: dollars)$