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3 years ago

5. Explain why the equation 6| x | + 25 = 15 has no solution?

1 answer:

4 0

$6|x|+25=15\ \ \ |-25\\\\6|x|=-10\ \ \ |:6\\\\|x|=-\dfrac{5}{3} < 0\\\\NO\ SOLUTION\to x\in\O$

$\text{For any}\ x\in\mathbb{R}\ \text{we have}\ |x|\geq0$

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2. It has been estimated that about 30% of frozen chickens are contaminated with enough salmonella bacteria to cause illness if

Darina [25.2K]

Using the binomial distribution, it is found that there is a 0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.

For each chicken, there are only two possible outcomes, either they are contaminated, or they are not. The chickens are independently selected, hence, the binomial distribution is used.

<h3>What is the binomial probability distribution formula?</h3>

The formula is:

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

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

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

About 30% of frozen chickens are contaminated, hence $p = 0.3$ .

Chickens are delivered to grocery stores in crates of 24, hence $n = 24$ .

The probability that a certain crate has more than 4 contaminated chickens is:

$P(X > 4) = 1 - P(X \leq 4)$

In which:

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

Then

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

$P(X = 0) = C_{24,0}.(0.3)^{0}.(0.7)^{24} = 0.0002$

$P(X = 1) = C_{24,1}.(0.3)^{1}.(0.7)^{23} = 0.0020$

$P(X = 2) = C_{24,2}.(0.3)^{2}.(0.7)^{22} = 0.0097$

$P(X = 3) = C_{24,3}.(0.3)^{3}.(0.7)^{21} = 0.0305$

$P(X = 4) = C_{24,4}.(0.3)^{4}.(0.7)^{20} = 0.0687$

Hence

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0002 + 0.0020 + 0.0097 + 0.0305 + 0.0687 = 0.1111$

0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.

You can learn more about the binomial distribution at brainly.com/question/24863377

6 0

3 years ago

What is the solution to the system of equation 2x-y=7 Y=2x+3

Veronika [31]

4x - y = -4
-y = -4 - 4x (subtract 4x from each side)
y = 4 + 4x (divide by -1)
y = 4x + 4 (commutative property of addition to get the x-value in front).

Now we must plug what we have gotten y to equal into the other equation. If we try to plug what we have rearranged back into the original equation, we don't get anywhere.

2x - y = -7
2x - 1(4x + 4) = -7 (substitution)
2x - 4x - 4 = -7 (distributive property with -1)
-2x - 4 = -7 (combine like terms)
-2x = -3 (add 4 to each side)
x = 3/2 (divide by -2).

You2x-y=7
Y=2x+3 have just solved for x! We can now plug what we have found for x into either equation to get what y equals. (If this is truly a system of linear equations, then it will not matter which one we use.)

2(3/2) - y = -7 (substitution)

6/2 - y = -7 (multiplication)
3 - y = -7 (division)
- y = -10 (subtraction)
y = 10 (division)

You have just found y! As a point, the solution to this system is (3/2, 10) with the x-coordinate first and the y-coordinate second. If we plug x and y into both equations, we will find that they will make the equations true. This is how we check ourselves. Using both equations:

4x - y = -4
4(3/2) - 10 = -4 (does the left half equal -4?)
12/2 - 10 = -4
6 - 10 = -4
-4 = -4 (it does);

2x - y = -7
2(3/2) - 10 = -7
3 - 10 = -7
-7 = -7.

7 0

4 years ago

A potato chip company produces a large number of potato chip bags each day and wants to investigate whether a new packaging mach

alexandr1967 [171]

Answer:

The conditions for the approximation have been met

Step-by-step explanation:

Random samples on both cases and

p∧o proportion of bags packaged on the old machine that are damaged

p∧n sample proportion of bags packaged on the new machine that are damaged

p∧c = ( p∧o + p∧n ) / (nO + nN )

p∧o = 15 % p∧o = 0,15 nO = 150

p∧o * nO = 0,15 *150 p∧o * nO = 22,5

p∧n = 8 % p∧n = 0,08 nN = 200

p∧n*nN = 0,08 * 200 p∧n*nN = 16

Both p∧n*nN and p∧o * nO are bigger than 5

Therefore both samples are big enough for the approximation of the binomial distribution to normal distribution

4 0

3 years ago

Please help me solve this problem

Stells [14]

Answer:

$180

Step-by-step explanation:

To solve, we can set up a proportion and solve.

You earn $45 for 7.5 hours of work, and you earn $ x for 30 hours of work

45/7.5=x/30

Cross multiply

45*30=7.5*x

1350=7.5x

To solve for x, we need to get x by itself. It is being multiplied by 7.5. To undo this, divide both sides by 7.5

1350/7.5=7.5x/7.5

180=x

So, for 30 hours of work, you would earn $180

5 0

3 years ago

Read 2 more answers

Banneker Middle School has 750 students. Lynn surveys a random sample of 50 students and finds that 27 of them have pet dogs. Ho

Alika [10]

Answer: 405 students

Step-by-step explanation:

From the question, Banneker Middle School has 750 students and we are told that Lynn surveys a random sample of 50 students and finds that 27 have pet dogs. The number of students at the school that are likely to have pet dogs goes thus:

Since out of 50 students surveyed, 27 have pet dogs, this means we multiply the fraction by 750. This can be mathematically written as:

= 27/50 × 750

= 27 × 15

= 405

This means 405 students are expecting to have pet dogs.

3 0

3 years ago