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Alchen [17]
2 years ago
12

A number sequence has nth term 6n + 3 (a) Write down the first four terms of this sequence.  1st term ..............., 2nd term

..............., 3rd term ..............., 4th term
Mathematics
2 answers:
aivan3 [116]2 years ago
7 0

Answer:

9, 15, 21, 27

Step-by-step explanation:

Given n=6n+3

When n=1, t= 6(1)+3 =9

When n=2, t=6(2)+3=15

When n=3, t=6(3)+3=21

When n=4, t=6(4)+3=27

SHORT TRICK :

Whenever the value of 'n' is given in the form of an algebraic expression the common difference of the Arithmetic Progrsiion (A.P) is the coefficient of 'n' in the given expression.

Ex: In this Problem,

Given that n=6n+3

The coeeficient of 'n' is '6'

If you obsereve the answer you will also see that the Common difference is also '6'

Zarrin [17]2 years ago
6 0

Step-by-step explanation:

fknfbflfhe them,......e.<em>.</em><em>t.</em><em>y</em>

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7^x=3^[x+4] solve x using logarithmic
Andrei [34K]

By taking advantage of the definition of <em>exponential</em> and <em>logarithmic</em> function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).

<h3>How to solve an exponential equation by logarithms</h3>

<em>Exponential</em> and <em>logarithmic</em> functions are <em>trascendental</em> functions, these are, functions that cannot be described <em>algebraically</em>. In addition, <em>logarithmic</em> functions are the <em>inverse</em> form of <em>exponential</em> functions. In this question we take advantage of this fact to solve a given expression:

  1. 7ˣ = 3ˣ⁺⁴     Given
  2. ㏒ 7ˣ = ㏒ 3ˣ⁺⁴      Definition of logarithm
  3. x · ㏒ 7 = (x + 4) · ㏒ 3     ㏒ aᵇ = b · ㏒ a
  4. x · ㏒ 7 = x · ㏒ 3 + 4 · ㏒ 3     Distributive property
  5. x · (㏒ 7 - ㏒ 3) = 4 · ㏒ 3      Existence of additive inverse/Modulative and associative properties
  6. x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3)     Existence of multiplicative inverse/Modulative property/Result

By taking advantage of the definition of <em>exponential</em> and <em>logarithmic</em> function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).

To learn more on logarithms: brainly.com/question/20785664

#SPJ1

4 0
1 year ago
Is 8.9 ml greater or less than 0.89 l
irina1246 [14]
It is less than.......
6 0
3 years ago
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Eduardo used fabric to make three costumes. he used 1/4 yard for first then 2/4 yard for the second and 3/4 yard for the third c
Dmitry [639]
 add the fractiosn together, since they all have the same denominator, simply add the numerators
1/4+2/4+3/4=6/4
or
1 1/2 yards of fabric (2/4 = 1/2)
6 0
3 years ago
In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean
Nastasia [14]

Answer:

a) \bar X =\frac{46+54}{2}=50

And the margin of error is given by:

ME= \frac{54-46}{2}= 4

The confidence level is 0.96 and the significance level is \alpha=1-0.96=0.04 and the value of \alpha/2 =0.02 and the margin of error is given by:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

We can calculate the critical value and we got:

z_{\alpha/2} = 2.05

And if we solve for the deviation like this:

\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}

And replacing we got:

\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45

b) ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor \sqrt{2}

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

\bar X represent the sample mean  

\mu population mean (variable of interest)  

\sigma represent the population standard deviation  

n=80 represent the sample size  

Solution to the problem

Part a

The confidence interval for the mean is given by the following formula:  

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

For this case we can calculate the mean like this:

\bar X =\frac{46+54}{2}=50

And the margin of error is given by:

ME= \frac{54-46}{2}= 4

The confidence level is 0.96 and the significance level is \alpha=1-0.96=0.04 and the value of \alpha/2 =0.02 and the margin of error is given by:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

We can calculate the critical value and we got:

z_{\alpha/2} = 2.05

And if we solve for the deviation like this:

\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}

And replacing we got:

\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45

Part b

For this case is the sample size is doubled the margin of error would be:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor \sqrt{2}

5 0
2 years ago
Help please 10 points
Mazyrski [523]
Im guessing it would be about 50 degrees
7 0
2 years ago
Read 2 more answers
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