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4 years ago

Find the 6th term of a geometric sequence with t1=5 and r = -1/2

1 answer:

5 0

In this item, we are to calculated for the 6th term of the geometric sequence given the initial value and the common ratio. This can be calculated through the equation,

An = (A₀)(r)ⁿ ⁻ ¹
where An is the nth term, A₀ is the first term (in this item is referred to as t₀), r is the common ratio, and n is the number of terms.

Substitute the known values to the equation,

An = (5)(-1/2)⁶ ⁻ ¹
An = -5/32

Hence, the answer to this item is the third choice, -5/32.

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Find the value of x in the isosceles triangle shown below.

Reptile [31]

Answer:

x=10

Step-by-step explanation:

We can use the Pythagorean theorem to find x

The height meets the base at a right angle

The base is bisected ( cut in half) so the base is 6 the height is 8

a^2 + b^2 = c^2

6^2 + 8^2 = x^2

36+64 = x^2

100 = x^2

Taking the square root of each side

sqrt(100) = sqrt(x^2)

10 = x

4 0

3 years ago

Read 2 more answers

The mean rent of a 3-bedroom apartment in Orlando is $1300. You randomly select 10 apartments around town. The rents are normall

lana [24]

Answer:

96.49% probability that the mean rent is more than $1100

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 1300, \sigma = 350, n = 10, s = \frac{350}{\sqrt{10}} = 110.68$

What is the probability that the mean rent is more than $1100?

This is 1 subtracted by the pvalue of Z when X = 1100. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{1100 - 1300}{110.68}$

$Z = -1.81$

$Z = -1.81$ has a pvalue of 0.0351

1 - 0.0351 = 0.9649

96.49% probability that the mean rent is more than $1100

7 0

4 years ago

Which glide reflection describes the mapping triangle ABC triangleDEF?

ZanzabumX [31]

In order to visualize the transformations, we must execute the transformation in the options

The first transformation would shift triangle ABC 3 units to the left and reflect it across x = 4. This will not map ABC unto DEF.

The second transformation would shift triangle ABC 7 units down and reflect it across x =4. This will map ABC unto DEF,

So, the answer is the second option.

5 0

3 years ago

kelly has $50 in her checking account. she wrote a check for $75.00 which means that she’s overdrawn by $25. if she deposits $13

Zarrin [17]

Answer:

$120.50

Step-by-step explanation:

50 - 75 = -25

135.50 - 25 = 120.50

3 0

3 years ago

What is 15 thousands 20 hundreds 5 ones=

Law Incorporation [45]

The answer is 152,005

4 0

3 years ago