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Kisachek [45]
2 years ago
15

Please answer with steps​

Mathematics
1 answer:
egoroff_w [7]2 years ago
7 0

9514 1404 393

Answer:

  n = 99

Step-by-step explanation:

The sum of logarithms is the log of a product. Here, the sum of terms is ...

  log(2/1) +log(3/2) +log(4/3) + ... +log((n+1)/n)

  = log((2/1)(3/2)(4/3)×...×((n+1)/n)) = log(n+1)

So, the question reduces to ...

  log(n+1) = 2

Taking antilogs, we have ...

  n +1 = 10^2 = 100

  n = 99

The value of n that makes the sum 2 is 99.

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Please help!! Thank you so much!!
Olenka [21]

Answer:

AC, AB, BC

Step-by-step explanation:

3x-13+2x-20+x+15=180

6x-18=180

6x=198

x=33

<a 86

<b 46

<c48

3 0
2 years ago
In a random sample of 26 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a sta
Rainbow [258]

Answer:

The critical value that should be used in constructing the confidence interval is T = 1.316.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 26 - 1 = 25

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.8}{2} = 0.9. So we have T = 1.316

The critical value that should be used in constructing the confidence interval is T = 1.316.

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.316\frac{0.23}{\sqrt{26}} = 0.059

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.059 = 2.741 pounds

The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.059 = 2.859 pounds.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

4 0
2 years ago
Lola and Brandon had a running race. They ran 3/10 of a mile. Lola was in the lead for 4/5 of the distance. For what fraction of
Kruka [31]

Answer:

Lola was in lead for \frac{6}{25} of a mile.

Step-by-step explanation:

We have been given that Lola and Brandon had a running race. They ran 3/10 of a mile. Lola was in the lead for 4/5 of the distance.

To find the fraction of a mile for which Lola was in the lead, we need to find 4/5 of 3/10 as:

\text{Fraction for which Lola was in lead}=\frac{3}{10}\times\frac{4}{5}

\text{Fraction for which Lola was in lead}=\frac{3}{5}\times\frac{2}{5}

\text{Fraction for which Lola was in lead}=\frac{3\times2}{5\times5}

\text{Fraction for which Lola was in lead}=\frac{6}{25}

Therefore, Lola was in lead for \frac{6}{25} of a mile.

7 0
3 years ago
an experiment consists of flipping a fair coin 4 times. What is the probability of obtaining at least one head?
Dvinal [7]
\mathbb P(X\ge1)=1-\mathbb P(X=0)

The probability of getting 0 heads in 4 tosses (or equivalently, 4 tails) is \dfrac1{2^4}=\dfrac1{16}.

So the desired probability is

1-\dfrac1{16}=\dfrac{15}{16}
7 0
3 years ago
Write a linear function that relates y to x <br><br> y=
son4ous [18]

y=x-2

hope this helped :)

7 0
2 years ago
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