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kkurt [141]
3 years ago
10

Simplify(5+2i)(1+3i)

Mathematics
1 answer:
hichkok12 [17]3 years ago
3 0
(5 + 2i)(1 + 3i)

5 * 1 = 5

5 * 3 = 15i

2i * 1 = 2i

2i * 3i = 6i^2

So we have...

5 + 15i + 2i + 6i^2

5 + 17i + 6i^2

In order....

6i^2 + 17i + 5
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Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation o
Mumz [18]

Answer:

0% probability that the mean of the sample taken is less than 2.2 feet.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 2.5 feet and a standard deviation of 0.2 feet.

This means that \mu = 2.5, \sigma = 0.2

Sample of 41

This means that n = 41, s = \frac{0.2}{\sqrt{41}}

Find the probability that the mean of the sample taken is less than 2.2 feet.

This is the p-value of Z when X = 2.2 So

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

By the Central Limit Theorem

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

Z = \frac{2.2 - 2.5}{\frac{0.2}{\sqrt{41}}}

Z = -9.6

Z = -9.6 has a p-value of 0.

0% probability that the mean of the sample taken is less than 2.2 feet.

6 0
3 years ago
A force of 12 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching i
sattari [20]

Answer:

Work done in stretching the spring = 7.56 lb-ft.

Step-by-step explanation:

Normal length of the spring = 8 in or \frac{8}{12} ft

= \frac{2}{3} ft

If the spring has been stretched to 11 inch then the stretched length of the spring is = 11 in

= \frac{11}{12} ft

Force applied to stretch the spring = 12 lb

By Hook's law,

F = kx [where k is the spring constant and x = length by which the spring is stretched]

12 = k(\frac{2}{3})

k = 18

Work done (W) to stretch the spring by \frac{11}{12} ft will be

W = \int\limits^\frac{11}{12} _0 {kx} \, dx

    = \int\limits^\frac{11}{12} _0 {(18x)} \, dx

    = 18[\frac{x^{2}}{2}]^{\frac{11}{12}}_0

    = 9(\frac{11}{12})²

    = 7.56 lb-ft

6 0
3 years ago
harry invests £6000 in a savings account. the account pays 3.4% compound interest per year. work out the value of his investment
Nataly_w [17]

Invested amount (P0 = £6000.

Rate of interest (r) = 3.4% = 0.034.

We know compound interest formula

A = P(1+r)^t

We need work out the value of his investment per year.

So, we need to plug t=1 and plugging values of P and r in the formula above, we get

A = 6000(1+0.034)^1

A = 6000(1.034)

A = 6204.

<h3>Therefore, the value of his investment per year is £ 6204.</h3>

Now, we need to work out the value of his investment after 3 years.

So, we need to plug t=3.

A = 6000(1+0.034)^3

A = 6000(1.034)^3

1.034^3=1.105507304

A = 6000 × 1.105507304

A = 6633.04

<h3>Therefore, the value of his investment after 3 year is  £ 6633.04.</h3>
6 0
3 years ago
Determine the unknown side of the similar triangle.<br> A) 8 <br> B) 12 <br> C) 18 <br> D) 24
blsea [12.9K]

Answer:

B-12

Step-by-step explanation:

Since 24÷12=2 you have to do 6×2 to find the ? and 6×2=12

8 0
3 years ago
4/7 - x = 6/35 what is x? how do I determine the answer?
vivado [14]
4/7 - x = 6/35

You're trying to get x by itself, so you have to subtract 4/7 from both sides.

-x = 6/35 - 4/7

You need both of the fractions to the right of the equal sign to have the same denominator so that we could simplify them, so multiply 5/5 to -4/7.

-4 /7 × 5/5 = -20/35

So, our new equation is :

-x = 6/35 - 20/35

Simplify.

-x = -14/35

Divide both sides by -1.

x = 14/35

Divide by 7.

x = 2/5

~Hope I helped!~
7 0
3 years ago
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