Enter the next three terms in the geometric sequence. Round to the nearest tenth value. 36, 54, 81, 121.5, ...

Answers

Answer 1

Answer:

Answer:

The next three terms of the sequence are 182.3, 273.5 and 410.3 respectively (all rounded to the nearest tenth value)

Step-by-step explanation:

A geometric sequence is one in which successive members are multiples of a constant common ratio.

From the sequence, we can identify that;

First term a = 36

common difference = 2nd term/first term = 3rd term/second term = 4th term/3rd term

Hence, common difference d = 54/36 = 81/54 = 1.5

The next three terms of the sequence are the 5th, 6th and 7th term respectively.

For the 5th term, we have 4th term × common ratio = 121.5 × 1.5 = 182.3

For the 6th term, we have 5th term × common ratio = 182.3 × 1.5 = 273.5

For the 7th term, we have 6th term × common ratio = 273.5 × 1.5 = 410.3

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Simplify the expression

1/5v+3/10v

Answers

$\frac15v+\frac3{10}v=\frac2{10}v+\frac3{10}v=\frac5{10}v=\frac12v$

Simplify
8v+w+7-8v+2w
4c^2 +6c-3c^2-2c-3
Z^3+5z+3z^2+1-4-2z^2

Answers

1) 8v+w+7-8v+2w

=w+7+2w

=3w+7

-----------------------------

2) 4c^2+6c-3c^2-2c-3

=c^2+6c-2c-3

=c^2+4c-3

-------------------------------

3) z^3+5z+3z^2+1-4-2z^2

=z^3+z^2+5z+1-4

=z^3+z^2+5z-3

What is the equation in point-slope form for the line parallel to y = –2x + 10 that contains J(6, 8)?Choose one answer.
a. x – 8 = 2(y – 6)
b. y – 8 = 2(x – 6)
c. y + 8 = –2(x – 6)
d. y – 8 = –2(x – 6)

Answers

y-y1= m(x1-x2)
using this formula
the answer is d
because slope has to remain the same if its parallel

An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 334 people living in East Vancouver and finds that 43 have recently had the flu. Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.03. How large a sample should she take to achieve this?

Answers

Answer:

The sample should be as large as 480

Step-by-step explanation:

Probability of having a flu, p = 43/334

p = 0.129

Margin Error, E = 0.03

Confidence Interval, CI= 95%

At a CI of 95%, $z_(crit) = 1.960$

The sample size can be given by the relation:

$n = p(1-p)(z/E)^(2)$

$n = 0.129(1-0.129)(1.960/0.03)^(2) \nn = 479.59\nn = 480$

Final answer:

To determine the sample size needed to estimate the population proportion with a desired margin of error, we can use the formula n = (z^2 * p * (1-p)) / (E^2), where n is the required sample size, z is the z-score corresponding to the desired level of confidence, p is the estimated proportion of the population with the characteristic, and E is the desired margin of error. Plugging in the given values, the epidemiologist should take a sample size of approximately 3245 in order to achieve her desired margin of error.

Explanation:

To determine the sample size needed to estimate the population proportion with a desired margin of error, we can use the formula:

n = (z^2 * p * (1-p)) / (E^2)

Where:

n is the required sample size
z is the z-score corresponding to the desired level of confidence (in this case, 95% confidence)
p is the estimated proportion of the population with the characteristic (in this case, the proportion of people with the flu in East Vancouver)
E is the desired margin of error (in this case, 0.03)

Plugging in the given values:

n = (z^2 * p * (1-p)) / (E^2) = (1.96^2 * 0.129 * 0.871) / (0.03^2) ≈ 3244.42

So, the epidemiologist should take a sample size of approximately 3245 in order to achieve her desired margin of error.

Learn more about Calculating Sample Size here:

brainly.com/question/34288377

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Graph each quadratic function
Y=x to the power of 2+4x-4

Answers

Does this help? Or does it need to be more specific?

y = x² + 4x - 4
x² + 4x - 4 = 0
x = -(4) +/- √((4)² - 4(1)(-4))
2(1)
x = -4 +/- √(16 + 16)
2
x = -4 +/- √(32)
2
x = -4 +/- 4√(2)
2
x = -2 + 2√(2)
x = -2 + 2√(2) x = -2 - 2√(2)
y = x² + 4x - 4
y = (-2 + 2√(2))² + 4(-2 + 2√(2)) - 4
y = (4 - 4√(2) + 8) + (-8 + 8√(2)) - 4
y = 4 + 8 - 8 - 4 - 4√(2) + 8√(2)
y = 4√(2)
(x, y) = (-2 + 2√(2), 4√(2))
or
y = x² + 4x - 4
y = (-2 - 2√(2))² + 4(-2 - 2√(2)) - 4
y = (4 + 4√(2) + 8) + (-8 - 8√(2)) - 4
y = 4 + 8 - 8 - 4 + 4√(2) - 8√(2)
y = -4√(2)
(x, y) = (-2 - 2√(2), -4√(2))

The perimeter of Jonah's square backyard is 56 meters. What is the area of Jonah's backyard?