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3 years ago

A geometric sequence has a common ration(s) of 3 and the 8th term (a8) is 13,122. What

Mathematics

1 answer:

nikdorinn [45]3 years ago

3 0

Answer:

First term a = 6

Step-by-step explanation:

a (first term) = ?

r (common ratio) = 3

T₈ (8th term) = 13122

The nth term of a geometric progression gp is

Tn = arⁿ⁻¹

T₈ = ar⁸⁻¹

T₈ = ar⁷

13122 = a * 3⁷

13122 = a * 2187

a = 13122 / 2187

a = 6.

The first term a = 6

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17. Solve the following:<br> x – 3y = 5<br> 5x – 2y = -1

Phantasy [73]

Answer:

(- 1, - 2 )

Step-by-step explanation:

Given the 2 equations

x - 3y = 5 → (1)

5x - 2y = - 1 → (2)

Rearrange (1) expressing x in terms of y by adding 3y to both sides

x = 5 + 3y → (3)

Substitute x = 5 + 3y in (2)

5(5 + 3y) - 2y = - 1 ← distribute left side

25 + 15y - 2y = - 1

25 + 13y = - 1 ( subtract 25 from both sides )

13y = - 26 ( divide both sides by 13 )

y = - 2

Substitute y = - 2 in (3) for corresponding value of x

x = 5 + (3 × - 2) = 5 - 6 = - 1

Solution is (- 1, - 2 )

8 0

3 years ago

What is the volume of the prism

Softa [21]

Answer:

600

Step-by-step explanation:

multiply w l h

10 x 5=50

50 x 12=160

5 0

2 years ago

The ration of girls to boys in a marching band is 10to8 if there are 32 boys in the marching band how many of the students in th

daser333 [38]

Answer:

40 girls

Step-by-step explanation:

if there r 32 than u know 8 times 4 equals 32. Then u have to multiply 4 on the other side as well. So 10 times 4 equals 40 girls

5 0

3 years ago

This person did something wrong and I do not know what it is :( Please help this is for points!

Arlecino [84]

Answer:

0.4 cm

Step-by-step explanation:

The magnifying glass basically zooms into smaller objects. If the insect appears to be 2cm, then it is actually smaller than this. It cannot be 10 cm.

If the scale factor is 5, then this means that the insect is zoomed in 5 times through the magnifying glass. Use the following ratio:

$\frac{2}{5}$

This fraction can also be seen as division, so:

$2$ ÷ $5=0.4$

The insect is actually 0.4 cm long.

(or 4 millimeters)

:Done

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3 years ago

g Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distrib

algol13

Answer:

The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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 $s = \frac{\sigma}{\sqrt{n}}$ .