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sveta
1 month ago
6

A car with an initial cost of $23,000 is decreasing in value at a rate of 8% each year. Write the exponential decay function des

cribed in this situation. Then use your function to determine when the value of the car will be $15,000, to the nearest year.
Mathematics
1 answer:
tester [12.3K]1 month ago
3 0

Answer:

Step-by-step explanation:

We will utilize the exponential decay formula described as

A = P(1 - r/n)^(nt)

Where

A symbolizes the value after a time period t.

n refers to the timeframe for value loss calculation

t indicates the number of years.

P stands for the population value.

r indicates the rate of decrease.

Based on the provided data,

P = 23000

r = 8% = 8/100 = 0.08

n = 1

Thus, the exponential decay function fitting this situation is

A = 23000(1 - 0.08/n)^1)^ t

A = 23000(0.92)^t

If A = 15000, it follows that

15000 = 23000(0.92)^t

0.92^t = 15000/23000 = 0.6522

Taking logarithm of both sides to base 10

Log(0.92^t) = log(0.6522)

t log(0.92) = log(0.6522)

- 0.036t = - 0.1856

t = - 0.1856/- 0.036

We find t = 5 years rounded to the nearest year

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J.J.Bean sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet.
babunello [11817]

The 99% confidence interval for the actual mean difference between average mail-order and internet purchase amounts falls within [$(-31.82), $12.02].

Step-by-step clarification:

We know a random sample of 16 mail-order sales receipts shows a mean sale amount of $74.50 and a standard deviation of $17.25.

For internet sales, a random sample of 9 receipts gives a mean sale amount of $84.40 with a standard deviation of $21.25.

The pivotal value utilized for constructing a 99% confidence interval for the true mean difference is given by;

                      P.Q.  =  

 ~

where,

= sample mean of mail-order sales = $74.50 \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }t__n_1_+_n_2_-_2

= sample mean of internet sales = $84.40

\bar X_1 = standard deviation for mail-order sales = $17.25

\bar X_2 = standard deviation for internet sales = $21.25

s_1 = number of mail-order sales receipts = 16

= number of internet sales receipts = 9s_2

Furthermore,  

 =  n_1 = 18.74

n_2

The actual mean difference between average mail-order and internet purchases is denoted by (s_p =\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }\sqrt{\frac{(16-1)\times 17.25^{2}+(9-1)\times 21.25^{2} }{16+9-2} }

).

Thus, the 99% confidence interval for (\mu_1-\mu_2) is expressed as;

      = \mu_1-\mu_2 Here, the t critical value at the 0.5% significance level with 23 degrees of freedom is 2.807.           =

          = [$-31.82, $12.02](\bar X_1-\bar X_2) \pm t_(_\frac{\alpha}{2}_) \times s_p \times \sqrt{\frac{1}{n_1} +\frac{1}{n_2}}

Therefore, the 99% confidence interval for the true mean difference between average mail-order and internet purchases is [$(-31.82), $12.02].

(74.50-84.40) \pm (2.807 \times 18.74 \times \sqrt{\frac{1}{16} +\frac{1}{9}})

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2 months ago
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3 months ago
Write a subtraction fact with the same difference as 16-7
PIT_PIT [12445]
Subtracting seven from sixteen results in nine
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8 0
2 months ago
Read 2 more answers
The yearly income for an individual with an associate’s degree in 2001 was $53,166 and in 2003 it was $56,970. What is the ratio
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Response:

8861: 9495

Detailed explanation:

The income ratio for the years 2001 to 2003:

53,166: 56,970

To simplify, divide both sides by 6:

8,861: 9,495

This can't be simplified further, so that is the final result!

8861: 9495

I hope this helps! Have a great day:)

6 0
2 months ago
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Respuesta:

P = 2/7 = 0.2857 o 28.57%

Explicación paso a paso:

En primer lugar, sabemos que hay 15 bolas y necesitamos identificar cuáles son pares y superiores a 10.

Por lo tanto, debemos calcular inicialmente la probabilidad de que el número obtenido sea par.

Los números pares son 2, 4, 6, 8, 10, 12, 14

Contamos 7 números de 15 ---> P(B) = 7/15

De esos números, solo dos son mayores a 10, que son 12 y 14, así que: P(A|B) = 2/15

Para encontrar la probabilidad de obtener un número par mayor que 10:

P(A/B) = P(A|B) / P(B)

P(A/B) = 2/15 / 7/15 = 2/7 = 0.2857

Para calcular el porcentaje: 0.2857 * 100 = 28.57%.

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