All categories

3 years ago

| 2 +r | ≥ 3 (lines are absolute value)

Mathematics

1 answer:

Alex777 [14]3 years ago

4 0

Answer:

r ≤ -5 and r ≥ 1

Step-by-step explanation:

The solution has two parts:

1) that derived from | 2 +r | ≥ 3 when (2 + r) is already positive. Then:

2 + r ≥ 3, or r ≥ 1

and

that derived from | 2 +r | ≥ 3 when (2 + r) is negative. If (2 + r) is negative, then

|(2 + r)| = -(2 + r) = -2 -r, which is ≥ 3. Therefore, -2 -r ≥ 3, or -r ≥ 5. To solve this for r, divide both sides by -1 and reverse the direction of the inequality sign: r ≤ -5

You might be interested in

Solve for X:

galben [10]

Answer:

A. -61/9

Step-by-step explanation:

(7x + 28) + (7x +28) = 5x - 5 . . . . . . . given equation

14x +56 = 5x -5 . . . . . . . . . . . . . . . . . collect terms

9x = -61 . . . . . . . . . . . . . . . . . . . . . . . . subtract 5x+56

x = -61/9 . . . . . . . . . . . . . . . . . . . . . . . . divide by the coefficient of x

4 0

3 years ago

Read 2 more answers

For a fair coin, suppose you toss the coin 100 times.

Natasha_Volkova [10]

Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with $\mu = np, \sigma = \sqrt{np(1-p)}$ .

For the binomial distribution, the parameters are given as follows:

n = 100, p = 0.5.

Hence the mean and the standard deviation of the approximation are given as follows:

$\mu = np = 100(0.5) = 50$ .

$\sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5$

Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is <u>one subtracted by the p-value of Z when X = 66.5</u>.

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

$Z = \frac{66.5 - 50}{5}$

Z = 3.3

Z = 3.3 has a p-value of 0.9995.

1 - 0.9995 = 0.0005.

0.0005 = 0.05%

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

6 0

2 years ago

How are the solutions to the inequality -3x>18 different from the solutions to -3x>18 ?

Novay_Z [31]

Answer:

x < -6

Step-by-step explanation:

-3x > 18

Divide both sides by -3

-3x/-3 < 18/-3

Note : in inequalities when both sides are divided by negative or minus, the inequality sign changes.

Therefore

x < -6

There's no difference as the equations are the same

I hope this was helpful, please rate as brainliest

3 0

3 years ago

1.A house worth $250,000 has an coinsurance clause of 90 percent. The owners insure the property for $191,250. They then have a

Arisa [49]

1. Multiply the value of the house by the percent:

250,000 x 0.9 = 225,000

Divide the amount the owner insured by the clause amount:

191,250/225,000 = 0.85

Multiply that by the amount of damage:

0.85 x 80,000 = 68,000

They will receive $68,000

2. Follow the same steps as above:

180,000 x 0.75 = 135,000

101,250 / 135,000 = 0.75

0.75 x 50,000 = 37,500

They will receive $37,500

8 0

3 years ago

Read 2 more answers

If 1 euro is priced at $1.25 and if 1 euro will also buy 88 Japanese yen (€1 = ¥88), in equilibrium, with no arbitrage opportuni

Alborosie

Answer:

So the exchange rate is that each dollar is worth 70.4 yens.

Step-by-step explanation:

We have that:

1 euro is priced at $1.25

1 euro will also buy 88 Japanese yen

This also means that:

$1.25 is priced at 88 Japanese yen

How much is the cross rate between the yen and the dollar (yen per dollar exchange rate)?

How much yens is 1 dollar?

This can be solved by a simple rule of three.

$1.25 - 88 yen

$1 - x yen

$1.25x = 88$

$x = \frac{88}{1.25}$

$x = 70.4$

So the exchange rate is that each dollar is worth 70.4 yens.

5 0

3 years ago