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3 years ago

Write the following expression as a trinomial in standard form. 3(x+3)2 – 2(x + 3) +4

Mathematics

1 answer:

cestrela7 [59]3 years ago

4 0

Answer:

4(x+4)

Step-by-step explanation:

multiply the numbers

3(x+3)×2 - 2(x+3) +4

collect like terms

6(x+3) - 2(x+3) +4

Factor the expression

4(x+3)+4

Add the numbers

4x + 12 +4

4x + 16

4(x+4)

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Answer:

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adell [148]

Answer:

$76 \: {in}^{2}$

Step-by-step explanation:

Area of the figure = Are of square with side 8 in + 2 times the area of one triangle with base (8 - 5 = 3) 3 in and height 4 in

$= {(8)}^{2} + 2 \times \frac{1}{2} \times 3 \times 4 \\ \\ = 64 + 12 \\ \\ = 76 \: {in}^{2}$

3 0

3 years ago

1. A report from the Secretary of Health and Human Services stated that 70% of single-vehicle traffic fatalities that occur at n

Nuetrik [128]

Using the binomial distribution, it is found that there is a 0.7215 = 72.15% probability that between 10 and 15, inclusive, accidents involved drivers who were intoxicated.

For each fatality, there are only two possible outcomes, either it involved an intoxicated driver, or it did not. The probability of a fatality involving an intoxicated driver is independent of any other fatality, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

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

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

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:

70% of fatalities involve an intoxicated driver, hence $p = 0.7$ .

A sample of 15 fatalities is taken, hence $n = 15$ .

The probability is:

$P(10 \leq X \leq 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)$

Hence

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

$P(X = 10) = C_{15,10}.(0.7)^{10}.(0.3)^{5} = 0.2061$

$P(X = 11) = C_{15,11}.(0.7)^{11}.(0.3)^{4} = 0.2186$

$P(X = 12) = C_{15,12}.(0.7)^{12}.(0.3)^{3} = 0.1700$

$P(X = 13) = C_{15,13}.(0.7)^{13}.(0.3)^{2} = 0.0916$

$P(X = 14) = C_{15,14}.(0.7)^{14}.(0.3)^{1} = 0.0305$

$P(X = 15) = C_{15,15}.(0.7)^{15}.(0.3)^{0} = 0.0047$

Then:

$P(10 \leq X \leq 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.2061 + 0.2186 + 0.1700 + 0.0916 + 0.0305 + 0.0047 = 0.7215$

0.7215 = 72.15% probability that between 10 and 15, inclusive, accidents involved drivers who were intoxicated.

A similar problem is given at brainly.com/question/24863377

5 0

3 years ago

The base of a right pyramid is a regular hexagon with sides of length 12 m. The altitude is 6 m. Find the total surface area of

Eva8 [605]

Answer:

806.12 m

Step-by-step explanation:

Step 1: Write the data

Side (s) = 12

Altitude (h) = 6

Step 2: Write the formula for surface area of right hexagonal pyramid

Area = 3√3/2*s² + 3*s*√(h²+3s²/4)

Step 3: Substitute values of 's' and 'h'

Area = 3√3/2*(12)² + 3*(12)*√[6²+3(12)²/4]

Area = 806.12 m

Therefore, the total surface area of the pyramid is 806.12 m.

4 0

3 years ago