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Katen [24]
3 years ago
10

√−100 = ___ +_____i ...

Mathematics
1 answer:
Natalija [7]3 years ago
7 0

Answer:

Step-by-step explanation:

Rewrite this as

\sqrt{(-1)(100)}

Knowing that i-squared = -1:

\sqrt{(i^2)(100)}

Both i-squared and 100 are perfect squares, so this simplifies to

±10i

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An equation is shown 3/4x=15. What is the value of x
uysha [10]
3/4x=15 you flip 3/4 to 4/3 and cancel it out on one side leaving x by itself then you multiply 4/3 by 15 and you get 60/3 and that equals 20 x=20 
7 0
3 years ago
There are nine empty seats in a theater, and six customers need to find places to sit. How many different ways can these six sea
dybincka [34]

Answer: 60480

Step-by-step explanation:

Given : The number of empty seats in a theater = 9

The number of customers need to find places to sit =6

Since order matters here, so we use permutations

The permutations of n things taking r at a time is given by :-

^nP_r=\dfrac{n!}{(n-r)!}

Then, the number of ways to arrange 6 seat in 9 seats :-

^9P_6=\dfrac{9!}{(9-6)!}=\dfrac{9\times8\times7\times6\times5\times4\times3!}{3!}\\\\=60480

Hence, the number of ways to arrange 6 seat in 9 seats = 60480

3 0
3 years ago
For a particular diamond mine, 81% of the diamonds fail to qualify as "gemstone grade". A random sample of 92 diamonds is analyz
Fed [463]

Answer:

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 92, p = 0.81

So

\mu = E(X) = np = 92*0.81 = 74.52

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{92*0.81*0.19} = 3.76

Find the probability that more than 79% of the sample diamonds fail to qualify as gemstone grade.

This is 1 subtracted by the pvalue of Z when X = 0.79*92 = 72.68. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{72.68 - 74.52}{3.76}

Z = -0.49

Z = -0.49 has a pvalue of 0.3121

1 - 0.3121 = 0.6879

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

4 0
3 years ago
Help plssss I’m trying to finish this diagnostics test
Allushta [10]

Answer: 5 Seconds

Step-by-step explanation: Given the equation of the height expressed ad;

h(t) = - 16t^2 + initial height

Given that initial height = 400feet

h(t) = - 16t^2 + 400

The waste will hit the ground at when h(t) = 0

substitute

0 =  - 16t^2 + 400

16t^2 = 400

t² = 400/16

t² = 25

t = √25

t = 5secs

4 0
3 years ago
kathi starts with a number. she adds 3 to her number, then doubles the result. finally, she subtracts 7. if she ended with 9 wha
11111nata11111 [884]
An equation is:
2(x+3)-7=9
Distribute the 2
2(x)+2(3) -7=9
2x+6-7=9
Combine like terms
2x-1=9
Add one to both sides
2x-1+1=9+1
2x=10
Divide both sides by two to isolate the variable.
2x/2=10/2
x=m

6 0
3 years ago
Read 2 more answers
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