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3 years ago

3. 3(2x - 1) + 4 = 3 - 5(1 - x)

Mathematics

2 answers:

yarga [219]3 years ago

8 0

Answer:

= -3

Step-by-step explanation:

Svetradugi [14.3K]3 years ago

4 0

Answer:

x = -3

Step-by-step explanation:

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In ΔDEF, the measure of ∠F=90°, the measure of ∠D=73°, and FD = 27 feet. Find the length of EF to the nearest tenth of a foot.

aliya0001 [1]

Answer:

88.3

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A study of the US clinical population found that 24.5% are diagnosed with a mental disorder, 14% are diagnosed with an alcohol-r

Keith_Richards [23]

Answer:

Part (A) The probability that someone from the clinical population is diagnosed with a mental disorder, knowing that the person is diagnosed with an alcohol-related disorder is 0.286

Part (B) The probability that someone from the clinical population is diagnosed with an alcohol-related disorder, knowing that the person is diagnosed with a mental disorder is 0.163.

Step-by-step explanation:

Consider the provided information.

A study of the US clinical population found that 24.5% are diagnosed with a mental disorder, 14% are diagnosed with an alcohol-related disorder, and 4% are diagnosed with both disorders.

P(M) = P(Mental disorder) = 24.5% = 0.245

P(A) =P(Alcohol-related disorder) = 14% = 0.14

P(M and A) =P(Both disorder) = 4% = 0.04

Part (A) What is the probability that someone from the clinical population is diagnosed with a mental disorder, knowing that the person is diagnosed with an alcohol-related disorder?

$P(\text{Mental disorder}\mid\text{alcohol-related disorder})=\frac{P(M\ and\ A)}{P(A)}$

$P(\text{Mental disorder}\mid\text{alcohol-related disorder})=\frac{0.04}{0.14}=0.286$

Hence, the required probability is 0.286.

Part (b) What is the probability that someone from the clinical population is diagnosed with an alcohol-related disorder, knowing that the person is diagnosed with a mental disorder.

$P(\text{alcohol-related disorder}\mid\text{Mental disorder})=\frac{P(M\ and\ A)}{P(M)}$

$P(\text{alcohol-related disorder}\mid\text{Mental disorder})=\frac{0.04}{0.245}=0.163$

Hence, the required probability is 0.163.

8 0

3 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$