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3 years ago

Solve the inequality. Show your work. |4r + 8| ≥ 32

2 answers:

8 0

$|4r+8|\geq32\iff4r+8\geq32\ \vee\ 4r+8\leq-32\ \ \ |-8\\\\4r\geq24\ \vee\ 4r\leq-40\ \ \ |:4\\\\r\geq6\ \vee\ r\leq-10$

$Answer:\ r\geq6\ \vee\ r\leq-10\to r\in\left(-\infty;\ -10\right>\ \cup\ \left< 6;\ \infty\right)$

S_A_V [24]3 years ago

7 0

|4r + 8| ≥ 32

Split this expression into two expressions:

First ⇒ 4r + 8 ≥ 32 and second ⇒ 4r + 8 ≤ - 32

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First expression: 4r + 8 ≥ 32

Subtract 8 from both sides.

4r ≥ 24

Divide both sides by 4.

r ≥ 6

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Second expression: 4r + 8 ≤ - 32

Subtract 8 from both sides.

4r ≤ -40

Divide both sides by 4.

r ≤ -10

---

Your answer is $\boxed {r \geq 6~or~ r \leq -10}$

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I need help on this questions. These sequences are hard.<br>

marissa [1.9K]

Step-by-step explanation:

1. "List the first 9 terms of the sequence defined recursively by

Sₙ = Sₙ₋₂ · (Sₙ₋₁ − 1)

with S₁ = 2 and S₂ = 3"

The first two terms are provided. To find the third term, substitute n = 3:

S₃ = S₃₋₂ · (S₃₋₁ − 1)

S₃ = S₁ · (S₂ − 1)

S₃ = 2 · (3 − 1)

S₃ = 4

Repeating this process, we get that the first nine terms of the sequence are:

2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784

2. "Compute the value of ∑(k=1 to 8) Sk, where Sk is the same sequence as in the previous question."

All we have to do here is add up the first 8 terms:

2 + 3 + 4 + 9 + 32 + 279 + 8896 + 2481705

= 2490930

3. "Is the sequence from question 1 arithmetic, geometric, or neither? Explain how you reach your conclusion."

If the sequence were arithmetic, it would have a common difference. But the difference between 3 and 4 is not the same difference between 4 and 9.

If the sequence were geometric, it would have a common ratio. But the ratio between 2 and 3 is not the same ratio between 3 and 4.

So the series is neither arithmetic nor geometric.

4. "Find the sum of the first 200 terms of the arithmetic sequence that begins: 12, 18, 24..."

The sum of the first n terms of an arithmetic sequence is:

S = n (a₁ + aₙ) / 2

where a₁ is the first term and aₙ is the nth term.

The nth term of an arithmetic sequence is:

aₙ = a₁ + d (n − 1)

where d is the common difference.

Here, the first term is 12, so a₁ = 12. The common difference is 18 − 12 = 6. So the 200th term is:

a₂₀₀ = 12 + 6 (200 − 1)

a₂₀₀ = 1206

The sum of the first 200 terms is:

S = 200 (12 + 1206) / 2

S = 121800

4 0

3 years ago

What is the solution for X in the equation 4x - 3 + 5 = 2x + 7 - 8x

PolarNik [594]

Answer:

C. X = 1/2

Step-by-step explanation:

4x - 3 + 5 = 2x + 7 - 8x

4x +2 = - 6x + 7

4x + 6x = 7 - 2

10x = 5

x = 1/2

5 0

2 years ago

What is the answer 19=3s+4

krok68 [10]

Answer:

Step-by-step explanation:

hello :

19=3s+4

19-4 = 3s+4-4

3s=15

s=15/3

s=5

5 0

3 years ago

Read 2 more answers

A manufacturer of processing chips knows that 2\%2%2, percent of its chips are defective in some way. Suppose an inspector rando

kipiarov [429]

The data in the question seems a bit erroneous. I am writing the correct question below:

A manufacturer of processing chips knows that 2%, percent of its chips are defective in some way. Suppose an inspector randomly selects 4 chips for an inspection. Assuming the chips are independent, what is the probability that at least one of the selected chips is defective? Lets break this problem up into smaller pieces to understand the strategy behind solving it.

Answer:

The probability that at least one of the selected chips is defective is 0.0776.

Step-by-step explanation:

The question states that the probability of defective chips is 2% i.e. 0.02. Let p denote the probability of selecting a defective chip so, p = 0.02

An inspector selects 4 chips, which means n=4 and we need to compute the probability that at least one of the selected chips is defective. Let X be the number of defective chips selected. We need to compute P(X≥1) which means either 1, 2, 3 or 4 chips can be defective.

We will use the binomial distribution formula to solve this problem. The formula is:

where n = total no. of trials

p = probability of success

x = no. of successful trials

q = probability of failure = 1-p

we have n=4, p=0.02 and q=1-0.02=0.98.

We need to compute P(X≥1) which is equal to:

P(X≥1) = P(X=1) + P(X=2) + P(X=3) + P(X=4)

A shorter method to do this is to use the total probability theorem:

P(X≥1) = 1 - P(X<1)

= 1 - P(X=0)

= 1 - ⁴C₀ (0.02)⁰(0.98)⁴⁻⁰

= 1 - (0.98)⁴

= 1 - 0.9224

P(X≥1) = 0.0776

4 0

3 years ago

PLS HELP!! WILL MAKE BRAINLIEST!!!!

poizon [28]

Answer:

(86.2,0) is the x-intercept.

Step-by-step explanation:

You can use the slope formula to figure this one out:

Just use two of the points on the table, any of them will work:

$(33,-22)\\(52,-33)$

$\frac{-22-33}{33-52} =\frac{-55}{-19}=\frac{55}{19}$

Now you have the slope of the equation, now using the y-intercept equation you can substitute the variables for point of the table and the new slope.:

$(71,-44)\\y=mx+b\\-44=\frac{55}{19} (71)+b$

Now just solve for b to get the y intercept:

$-44=\frac{55}{19}(71)+b\\-44= \frac{3905}{19} +b\\(-\frac{3905}{19})-44=\frac{3905}{19} +b(-\frac{3905}{19})\\ -\frac{4741}{19}=b$

Now you have the y-intercept so you just have to plug in 0 to the y spot and it will calculate the x-intercept.

$0=\frac{55}{19}x-\frac{4741}{19}\\(+\frac{4741}{19})0=\frac{55}{19}x-\frac{4741}{19}(+\frac{4741}{19})\\\\\frac{4741}{19}=\frac{55}{19}x\\\frac{\frac{4741}{19}}{\frac{55}{19} }= \frac{\frac{55}{19} x}{\frac{55}{19} } \\\frac{431}{5} =x\\or\\86.2=x$

And that's the x-intercept.

5 0

2 years ago

Read 2 more answers