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3 years ago

Which value of x is in the solution set of the following inequality -3×+5>17

Mathematics

1 answer:

Sholpan [36]3 years ago

5 0

Answer:

x < -4

Step-by-step explanation:

To solve the inequality, use inverse operations.

-3x + 5 > 17

-3x > 17 - 5 Subtract 5 from both sides.

-3x > 12 Divide both sides by -3.

x < -4 Flip the inequality sign since you divided by a negative.

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Can someone help answer the first two?

Murljashka [212]

Answer:

below given!

Step-by-step explanation:

1) mean = (7.4 + 5.8 + 7.3 + 7 + 8.9 + 9.4 + 8.3 + 9.3 + 6.9 + 7.5 + 9 + 5.8 + 5.5 + 8.6 + 9.3 +3.8) / 16

mean = 7.47

5 0

3 years ago

f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

3 years ago

The búfalo children put all of their candy together and weighed it. It weighed 2 1/4 pound . They shared it amongst the five peo

ratelena [41]

Answer:

0.45 lbs

Step-by-step explanation:

2 1/4 can be converted to the decimal: 2.25

2.25÷5 is how you will set this problem up, because 2.25 lbs of candy is being divided amongst 5 people.

0.45 lbs is the answer

8 0

3 years ago

Match each compound inequality to the graph of its solutions on the number line.

jekas [21]

What are the Answer Choices?

3 0

3 years ago

Read 2 more answers

Shaquil needs to borrow $400. The loan company charges him $80 in fees for the loan. Shaquil calculates that the annual percenta

lesya [120]

Answer:

(B)

Step-by-step explanation:

PRINCIPAL AMOUNT(p) = $400

RATE (r)= 250% = 2.5

INTEREST = $80

t = time (in days) = t/365

By using the formula,

r = $\frac{i}{pt}$

2.5 = $\frac{80*365}{400*t}$

t = $\frac{364*80}{400*2.5}$

t = 29.2

t = 29 days (approx)

Hence option (B) is correct.

6 0

3 years ago

Read 2 more answers