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3 years ago

Solve the system of inequalities 1-12y<:3y+1; 2-6y>4+4y

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

8 0

For 1 - 12y < 3y+1; y > 15

For 2 - 6y > 4 + 4y; y < -0.2

The given inequalities are:

1 - 12y < 3y + 1

2 - 6y > 4 + 4y

For 1 - 12y < 3y + 1:

1 - 12y < 3y + 1

Collect like terms

-12y - 3y < 1 - 1

-15y < 0

Multiply both sides by -1

-1(-15y) > 0(-y)

15y > 0

Divide both sides by 15

y > 0/15

y > 15

For 2 - 6y > 4 + 4y

Collect like terms

-6y - 4y > 4 - 2

-10y > 2

Multiply both sides by -1

-1(-10y) < 2(-1)

10y < -2

y < -2/10

y < -0.2

Learn more here: brainly.com/question/11316045

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Which equality represents the proportion $10 is to 15 cans as $30 is to $45 cans?

Sladkaya [172]

Answer:

I'm guessing it's C because it's the only one that looks right

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4 years ago

The quadratic function fhas a vertex at (3,4) and opens upward. The quadratic function g is shown below.

Alecsey [184]

Answer:

Option (C)

Step-by-step explanation:

Equation of the quadratic function having vertex at (3, 4) and opening upwards,

So the the minimum point of the function is (3, 4).

Therefore, minimum value of the function is 4 at x = 3.

y = (x - h)² + k [Here, (h, k) is the vertex]

g(x) = 2(x - 4)² + 3

Vertex of the parabola is (4, 3).

Since, leading coefficient is positive, parabola will open upwards.

Therefore, vertex will be the minimum point.

Minimum value of the function will be 3 at x = 4.

Minimum value of the function 'f' is greater than the minimum value of the function 'g'.

Option (C) will be the answer.

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3 years ago

A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more ar

frutty [35]

Answer:

There is a probability of 76% of not selling the package if there are actually three dead batteries in the package.

Step-by-step explanation:

With a 10-units package of batteries with 3 dead batteries, the sampling can be modeled as a binomial random variable with:

n=4 (the amount of batteries picked for the sample).
p=3/10=0.3 (the proportion of dead batteries).
k≥1 (the amount of dead batteries in the sample needed to not sell the package).

The probability of having k dead batteries in the sample is:

$P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}$

Then, the probability of having one or more dead batteries in the sample (k≥1) is:

$P(x\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{4}{0} p^{0}q^{4}=1*1*0.7^4=0.2401\\\\\\P(x\geq1)=1-0.2401=0.7599\approx0.76$

8 0

3 years ago

Eric's class consists of 12 males and 16 females. If 3 students are selected at random, find the probability that they

Reptile [31]

Answer:

The probability that all are male of choosing '3' students

P(E) = 0.067 = 6.71%

Step-by-step explanation:

Let 'M' be the event of selecting males n(M) = 12

Number of ways of choosing 3 students From all males and females

$n(M) = 28C_{3} = \frac{28!}{(28-3)!3!} =\frac{28 X 27 X 26}{3 X 2 X 1 } = 3,276$

Number of ways of choosing 3 students From all males

$n(M) = 12C_{3} = \frac{12!}{(12-3)!3!} =\frac{12 X 11 X 10}{3 X 2 X 1 } =220$

The probability that all are male of choosing '3' students

$P(E) = \frac{n(M)}{n(S)} = \frac{12 C_{3} }{28 C_{3} }$

$P(E) = \frac{12 C_{3} }{28 C_{3} } = \frac{220}{3276}$

P(E) = 0.067 = 6.71%

<u><em>Final answer</em></u>:-

The probability that all are male of choosing '3' students

P(E) = 0.067 = 6.71%

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4 years ago

The average weight of a mature human brain is approximately 1400 grams. what is the equivalent weight in kilometers? In pounds?

Illusion [34]

635.0293 kilograms

3086.472 pounds

Hope this helps.

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3 years ago