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What is a formula for the nth term of the given sequence? 36, 24, 16...

SpyIntel [72]

Answer:

The formula to find the nth term of the given sequence is 54 · $\frac{2}{3} ^{n}$

Step-by-step explanation:

The formula for nth term of an geometric progression is :

$a_{n} = \frac{a_{1}(r^{n})}{r}$

In this example, we have $a_{1}$ = 36 (the first term in the sequence) and

r = $\frac{2}{3}$ (the rate in which the sequence is changing).

Knowing what the values for r and $a_{1}$ are, now we can solve.

$a_{n} = \frac{a_{1}(r^{n})}{r}$ = $\frac{36 (\frac{2}{3} ^{n}) }{\frac{2}{3} }$ = 54 · $\frac{2}{3} ^{n}$

Therefore, the formula to find the nth term of the given sequence is

54 · $\frac{2}{3} ^{n}$

3 0

3 years ago

Suppose a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%. A cell phon

leva [86]

Answer:

We conclude that the actual percentage of households is equal to 30%.

Step-by-step explanation:

We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.

Their marketing people survey 150 households with the result that 43 of the households have three cell phones.

Let p = proportion of households that have three cell phones NOT known.

So, Null Hypothesis, $H_0$ : p = 30% {means that the actual percentage of households is equal to 30%}

Alternate Hypothesis, $H_A$ : p $\neq$ 30% {means that the actual percentage of households different from 30%}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of households having three cell phones = $\frac{43}{150}$ = 0.29

n = sample of households = 150

So, the test statistics = $\frac{0.29-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }$

= -0.27

The value of z test statistic is -0.27.

Also, P-value of the test statistics is given by;

P-value = P(Z < -0.27) = 1 - P(Z $\leq$ 0.27)

= 1 - 0.6064 = 0.3936

Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the actual percentage of households is equal to 30%.

4 0

3 years ago

How to find the area of each face of a prism

tatiyna

If the face is a square, then (l*l)

If the face is a triangle, then (b*h)(1/2)

If the face is a rectangle, then (l*w)

If the face is a circle, then (r²)(3.14)

You can then add all these faces up to get the total surface area of the prism.

3 0

3 years ago

Which sequence could be described by the explicit definition: t_n=2^n+1t n = 2 n + 1

yuradex [85]

Answer:

2. 27

3. Option C. 3, 5, 9, 17, 33, ...

Step-by-step explanation:

2. The sequence is defined by the explicit function $t_{n} = 2^{n} - n$

Therefore, the 5th term i.e. $t_{5}$ of the sequence.

$t_{5} = 2^{5} - 5 = 32 - 5 = 27$ (Answer)

3. The explicit definition is $t_{n} = 2^{n} + 1$

Hence, $t_{1} = 2^{1} + 1 = 3$

$t_{2} = 2^{2} + 1 = 5$

$t_{3} = 2^{3} + 1 = 9$

$t_{4} = 2^{4} + 1 = 17$

Therefore, the option C is the right sequence. (Answer)

4 0

3 years ago

Read 2 more answers

What is 3/7 in words

Marrrta [24]

Three sevenths !!!!!!

4 0

2 years ago