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3 years ago

Evaluate the expression 4+√−9 and write the result in the form a+bi

Mathematics

2 answers:

Katarina [22]3 years ago

6 0

Answer:

Step-by-step explanation:

4+√(-9) = 4 + √9√(-1)

= 4 + 3i

Natali5045456 [20]3 years ago

4 0

Answer:

4 + 3i

Step-by-step explanation:

i = sqrt(-1)

sqrt(-9) = 3 * sqrt(-1) = 3i

The 4 remains the same

4 + 3i

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8 hoses can fill a tank in 30 minutes. If I had 48 hoses, how long would it take?

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Answer:

120 minutes

Step-by-step explanation:

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3 years ago

Read 2 more answers

The opposite of 4x and -5 + 4x

Arlecino [84]

The opposite of 4x is -4x and the opposite of -5+4x is 5+-4x

5 0

3 years ago

The probability that a lab specimen contains high levels of contamination is 0.14. A group of 4 independent samples are checked.

Shtirlitz [24]

Answer:

a) 0.5470 = 54.70% probability that none contain high levels of contamination.

b) 0.3562 = 35.62% probability that exactly one contains high levels of contamination.

c) 0.4530 = 45.30% probability that at least one contains high levels of contamination.

Step-by-step explanation:

For each sample, there are only two possible outcomes. Either they contain high levels of contamination, or they do not. The samples are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

The probability that a lab specimen contains high levels of contamination is 0.14.

This means that $p = 0.14$

A group of 4 independent samples are checked.

This means that $n = 4$

(a) What is the probability that none contain high levels of contamination?

This is P(X = 0)

$P(X = 0) = C_{4,0}.(0.14)^{0}.(0.86)^{4} = 0.5470$

0.5470 = 54.70% probability that none contain high levels of contamination.

(b) What is the probability that exactly one contains high levels of contamination?

This is P(X = 1)

$P(X = 1) = C_{4,1}.(0.14)^{1}.(0.86)^{3} = 0.3562$

0.3562 = 35.62% probability that exactly one contains high levels of contamination.

(c) What is the probability that at least one contains high levels of contamination?

Either none of the samples contain high levels of contamination, or at least one does. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want to find $P(X \geq 1)$ . So

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.5470 = 0.4530$

0.4530 = 45.30% probability that at least one contains high levels of contamination.

8 0

3 years ago

Triangles 1 and 2 are both isosceles. They each have a 30 degree angle. Explain why these triangles don't have to be similar to

Vladimir79 [104]

Step-by-step explanation:

Triangle 1 can have 30°, 75° and 75° angles whereas Triangle 2 can have 30°, 30° and 120° angles.

Since they do not have all 3 congruent angles, they are not similar.

8 0

3 years ago

Maria is using 208 ounces of water to make some soup. Her recipe calls for 2 fluid ounces of olive oil for every 13 cups of wate

Otrada [13]

Answer:

4 ounces

Step-by-step explanation:

-We first convert the cup capacity into ounces.

$13 \ cups=8 \ oz\times 13\\\\=104 \ oz$

#We now know that for every 2 cups of olive oil, she uses 104 ounces of water.

-Let x be the amount of olive oil used. We then equate and cross multiply to solve for x:

$104\ oz= 2 \ \\208=x\\\\\therefore x=\frac{2\times 208}{104}\\\\=4\ oz$

Hence, 4 ounces of oil will be used for the soup.

6 0

3 years ago