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3 years ago

Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence.

Mathematics

2 answers:

Korvikt [17]3 years ago

7 0

Answer:

B. an = -4 *(-2)^n-1;-64

mr_godi [17]3 years ago

6 0

The sequence: a 1 = - 4, a 2 = 8, a 3 = -16,...
a 2 = a 1 * r
8 = - 4 * r
r = 8 : ( - 4 )
r = - 2
a n = a 1 * r^(n-1)
a 5 = - 4 * ( - 2 ) ^4 = - 4 * 16 = - 64
Answer:
The fifth term in the sequence is - 64.

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The function f(x)= (x-8) (x+2) (x+3) has which zeros

ArbitrLikvidat [17]

Answer:

(8, 0)

(-2, 0)

(-3, 0)

Step-by-step explanation:

x - 8 = 0

x = 8

x + 2 = 0

x = -2

x + 3 = 0

x = -3

4 0

2 years ago

Read 2 more answers

What is mAngleMHJ? HELP pLEASE 35° 50° 72.5° 92.5°

telo118 [61]

Answer:

50°

Step-by-step explanation:

1) Opposite angles are the same. Therefore,

2x-20=x+15

2x-x=15+20

x=35

2) Put x back in the equation for angle mhj

2(35)-20=50

6 0

3 years ago

Show the difference of the two sets

Rudik [331]

There is 8 fruits in set A and 7 in set B

6 0

2 years ago

In Δ,∠=70°,∠=50° ∠ . ℎ ∠.

AveGali [126]

Answer:

100°

Step-by-step explanation:

A triangle is a polygon shape with three sides. Triangles are of different types such as obtuse, scalene, equilateral, isosceles etc.

In triangle ABC:

70° + 50° + ∠C = 180° (sum of angles in a triangle)

120 + ∠C = 180

∠C = 180 - 120

∠C = 60°

Since ∠C is bisected into ∠ACD and ∠BCD, hence:

∠ACD = ∠BCD = ∠C / 2

∠ACD = ∠BCD = 60 / 2

∠ACD = ∠BCD = 30°

In triangle ACD:

∠A + ∠ACD + ∠ADC = 180° (sum of angles in a triangle)

50 + 30 + ∠ADC = 180

∠ADC + 80 = 180

∠ADC = 100°

6 0

3 years ago

You estimated the average rental cost of a 2 bedroom apartment in Denton. A random sample of 16 apartments was taken. The sample

Zigmanuir [339]

Answer:

The new sample size required in order to have the same confidence 95% and reduce the margin of erro to $60 is:

n=28

Step-by-step explanation:

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".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma=160)$

And the distribution for $\bar X$ is:

$\bar X \sim N(\mu, \frac{160}{\sqrt{n}})$

We know that the margin of error for a confidence interval is given by:

$Me=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The next step would be find the value of $\z_{\alpha/2}$ , $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$

Using the normal standard table, excel or a calculator we see that:

$z_{\alpha/2}=\pm 1.96$

If we solve for n from formula (1) we got:

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

$n=(\frac{z_{\alpha/2} \sigma}{Me})^2$

And we have everything to replace into the formula:

$n=(\frac{1.96(160)}{78.4})^2 =16$

And this value agrees with the sample size given.

For the case of the problem we ar einterested on Me= $60, and we need to find the new sample size required to mantain the confidence level at 95%. We know that n is given by this formula:

$n=(\frac{z_{\alpha/2} \sigma}{Me})^2$

And now we can replace the new value of Me and see what we got, like this:

$n=(\frac{1.96*160}{60})^2 =27.32$

And if we round up the answer we see that the value of n to ensure the margin of error required $Me=\pm 60$ $ is n=28.

5 0

2 years ago