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2 years ago

What is the missing pattern 7, 11, 2, 18, -7

1 answer:

8 0

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula $n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}$ , equivalent to the recurrence formula $a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}$ .

<h3>What is the missing element in a sequence?</h3>

A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:

$n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}$ (1)

Now we prove that given expression contains the pattern:

n = 0

n = 1

7 + (- 1)² · 2² = 7 + 4 = 11

n = 2

7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2

n = 3

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18

n = 4

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7

To learn more on patterns: brainly.com/question/23136125

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Answer:

$A' =(-y,x)$

Step-by-step explanation:

Given

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$A = (x,y)$

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When a point is rotated counterclockwise, we start by switching the positions of x and y as follows:

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3 years ago

A salesperson is paid an 8.25% commission on sales when the invoice is

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Answer:

The salesperson's commission for this month is $3,803

Step-by-step explanation:

Percentages

Let's call x to the sales volume, not including commission.

The salesperson is paid an 8.25% commission on sales, thus the total invoice is x + 8.25%x = x + 0.0825x = 1.0825x

We are given this total invoice, thus:

1.0825x = $49,900

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The salesperson's commission is

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The salesperson's commission for this month is $3,803

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2 years ago

The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated

statuscvo [17]

We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.

We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.

So we can define the proportion of coffee that Jeremiah has in his body as:

P(t) = 1*e^{k*t}

Such that:

P(4.8 h) = 0.5 = 1*e^{k*4.8}

Then, if we apply the natural logarithm we get:

Ln(0.5) = Ln(e^{k*4.8})

Ln(0.5) = k*4.8

Ln(0.5)/4.8 = k = -0.144

Then the equation is:

P(t) = 1*e^{-0.144*t}

Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:

P(t) = 0.6 = 1*e^{-0.144*t}

Again, we use the natural logarithm:

Ln(0.6) = Ln(e^{-0.144*t})

Ln(0.6) = -0.144*t

Ln(0.6)/-0.144 = t = 3.55

So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.

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2 years ago

Write an equation in slope-intercept

Finger [1]

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3 years ago

Read 2 more answers

Why does the formula for area of a triangle makes sense.

galben [10]

Answer: bh=4×5=20b, h, equals, 4, times, 5, equals, 20 square units, so the area of the triangle is \dfrac 12 bh = \dfrac 12 \times 4 \times 5 = 10

bh=

×4×5=10start fraction, 1, divided by, 2, end fraction, b, h, equals, start fraction, 1, divided by, 2, end fraction, times, 4, times, 5, equals, 10

Step-by-step explanation:

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2 years ago