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3 years ago

The first term in this sequence is -1. Write the function that represents the sequence

Mathematics

1 answer:

sattari [20]3 years ago

3 0

Answer:

$a_{n}$ = 2n - 3

Step-by-step explanation:

Note the difference in consecutive terms is constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2

This indicates that the terms are an arithmetic sequence with

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 2, thus

$a_{n}$ = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

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Vika [28.1K]

Answer:

Step-by-step explanation:

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2 years ago

A researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic

Delvig [45]

Answer:

90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

Step-by-step explanation:

We are given that a researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic meter with a standard deviation of 0.093.

Firstly, the pivotal quantity for 90% confidence interval for the population mean iron concentration is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean iron concentration = 0.802 cc/cubic meter

s = sample standard deviation = 0.093

n = number of water samples = 27

$\mu$ = population mean

Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.706 < $t_2_6$ < 1.706) = 0.90 {As the critical value of t at 26 degree of

freedom are -1.706 & 1.706 with P = 5%}

P(-1.706 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 1.706) = 0.90

P( $-1.706 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $1.706 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ , $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ]

= [ $0.802 -1.706 \times {\frac{0.093}{\sqrt{27} }$ , $0.802 +1.706 \times {\frac{0.093}{\sqrt{27} }$ ]

= [0.771 , 0.832]

Therefore, 90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

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3 years ago

30PTS ASAP: BRAINLEST FOR BEST ANSWER! im stupid xD

Elena L [17]

Answer: $200-$75=$125

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2 years ago

Read 2 more answers

Place these events on the probability

Aleksandr [31]

Answer:

P(tails)=1/2
P(5)=1/6

Not sure of the rest but hope this helps

8 0

3 years ago

4. Diego is thinking of two positive numbers. He says, "If we triple the first number and

aleksandr82 [10.1K]

Answer:

3x + 2y = 34. and two possible pairs of positive numbers are (x, y) = (10, 2) and (x, y) = (4, 11).

Step-by-step explanation:

Let the First positive number be x and second positive number be y.

Triple of first number = 3x

double of second number = 2y

According to question,

3x + 2y = 34

Therefore, the equation is 3x + 2y = 34

So the two possible pair of numbers Diego would be thinking of must satisfy the equation 3x + 2y = 34

Now, 3x + 2y = 34

3x = 34 - 2y

Let x = 10 and by substituting its value in above expression,

$3 \times 10 = 34 - 2y$

$30 = 34 - 2y$

$2y = 34 - 30$

$2y = 4$

$y = 2$

Therefore first pair (x, y) = (10, 2)

In the same way put x = 4 then,

3x = 34 - 2y

$3 \times 4 = 34 - 2y$

$2y = 34 - 12$

$2y = 22$

$y = 11$

Therefore first pair (x, y) = (4, 11)

Therefore, (x, y) = (4, 11) and (x, y) = (10, 2) are the two possible pairs of numbers Diego could be thinking of as these both values satisfy the equation 3x + 2y = 34.

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2 years ago