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4 years ago

Express in simplest a+bi form: Square root of 1b + Square root of -1b

Mathematics

1 answer:

Nimfa-mama [501]4 years ago

5 0

Express in simplest a+bi form: Square root of 1b + Square root of -1b

$\sqrt{1b} + \sqrt{-1b}$

Lets simplify $\sqrt{-b}$

We know $\sqrt{-1} = i$

$\sqrt{-b} =i\sqrt{b)$

We cannot simplify $\sqrt{1b}$

$\sqrt{1b} + \sqrt{-1b}$

$\sqrt{1b} + i\sqrt{b}$

So a + ib form is $\sqrt{1b} + i\sqrt{b}$

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two brothers marco and fernando are training for a marathon marco runs at a rate of 6miles per hor. Fernando funs at at a rate o

satela [25.4K]

We know that
speed=distance/time
solve for time
time=distance/speed

in this problem
Marco runs at a rate of 6 miles per hour.
Fernando funs at a rate of 7.2 miles per hour
Difference=7.2-6=1.2 miles/hour
so
speed=1.2 miles/hour
distance=0.3 miles
time=?
time=distance/speed-----> 0.3/1.2-----> 0.25 hour-----> 0.25*60=15 minutes

the answer is
0.25 hour (15 minutes)

Alternative Method
Let
x---------> Fernando's distance when Marco is 0.3 miles apart

Fernando funs at a rate of 7.2 miles per hour
for distance =x
time=x/7.2------> equation 1

Marco runs at a rate of 6 miles per hour.
for distance=x-0.30
time=(x-0.30)/6------> equation 2

equate equation 1 and equation 2
7.2*(x-0.3)=6x-----> 7.2x-2.16=6x
7.2x-6x=2.16------> x=2.16/1.2-------> x=1.8 miles

time=x/7.2-----1.8/7.2=0.25 hour

6 0

4 years ago

Someone help ASAP will give brainliest

bogdanovich [222]

The 3rd answer, is correct.

3 0

4 years ago

2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviati

Ket [755]

Answer:

$\sigma = 11.28$ --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Explain how the standard deviation is calculated.

Start by calculating the mean

To do this, we divide the sum of the products of grade and number of students by the total number of students;

i.e.

$\bar x = \frac{\sum fx}{\sum f}$

So, we have:

$\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}$

$\bar x = \frac{7531}{91}$

$\bar x = 82.76$

Next, calculate the variance using the following formula:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}$

i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset

So, we have:

$\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}$

$\sigma^2 = \frac{11580.6816}{91}$

$\sigma^2 = 127.26$

Lastly, take the square root of the variance to get the standard deviation

$\sigma = \sqrt{\sigma^2}$

$\sigma = \sqrt{127.26}$

$\sigma = 11.28$ --- approximated

Hence, the standard deviation is approximately 11.28

Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.

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3 years ago

Please help will mark Branliest!! DESPERATE!! Find the probability of the event. You flip a coin and get tails 62 times and head

nirvana33 [79]

Answer:

62\56

Step-by-step explanation:

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3 years ago

Dan was thinking of a number. Dan subtracts 2.6 from the number and gets an answer of 72.8. Form an equation with

nirvana33 [79]

Answer: x - 2.6 = 72.8

x is the number which Dan was thinking (x > 2.6)

we have:

x - 2.6 = 72.8

Step-by-step explanation:

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3 years ago