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3 years ago

1. Solve for : 2(3x - 3) = -18

Mathematics

1 answer:

Murrr4er [49]3 years ago

5 0

Answer:

-2

Step-by-step explanation:

1. Rewrite the equation:

2(3x - 3) = -18

2. Use the distributive property:

2(3x - 3) = -18 ---> 6x - 6 = -18

3. Add 6 to both sides:

6x - 6 = -18 ---> 6x = -12

4. Divide both sides by 6:

6x = -12 ---> x = -2

Now we know our answer is -2, let's make sure it's correct:

2(3x - 3) = -18

2(3(-2) - 3) = -18

2(-6 - 3) = -18

-12 - 6 = -18

-18 = -18

This tells us our answer is true!

Hope this helps :D

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3 years ago

In Pant Science (May 2010), a group of Japanese environmental scientists investigated the ability of a hybrid tomato plant to pr

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Answer:

a) P(x > 120) = 0.03288

b) P(100 < x < 110) = 0.46777

c) value of a for which P(x < a) = 0.25

a = 99.91

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 105.3

Standard deviation = σ = 8.0

a) P(x > 120)

To work this, we first need To convert 120 go standardized/normalized/z-scores.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

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To determine P(x > 120) = P(z > 1.84)

We use the tables for these probabilities now.

P(x > 120) = P(z > 1.84) = 1 - P(z ≤ 1.84) = 1 - 0.96712 = 0.03288

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We normalize the two value in the inequality

For 100,

z = (x - μ)/σ = (100 - 105.3)/8.0 = -0.66

For 110,

z = (x - μ)/σ = (110 - 105.3)/8.0 = 0.59

To determine P(100 < x < 110) = P(-0.66 < z < 0.59)

We use the tables for these probabilities now.

P(100 < x < 110) = P(-0.66 < z < 0.59) = P(z < 0.59) - P(z < -0.66) = 0.72240 - 0.25463 = 0.46777

c) value of a for which P(x < a) = .25

Let the z-score of a be z'

z' = (x - μ)/σ = (a - 105.3)/8.0

P(x < a) = P(z < z') = 0.25

Using the table, z' = - 0.674

-0.674 = (a - 105.3)/8

a - 105.3 = -5.392

a = 105.3 - 5.392 = 99.91

Hope this Helps!!!

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Let MN be the midsegment of the trapezoid.

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