Simplify the following expression:

( 4 + 5i ) / 4i
Select one:

a.
( 5 + 4i ) / 4


b.
( 5 - 4i ) / 4


c.
( 5i + 4i ) / 4


d.
( 5i - 4 ) / 4

The frequency distribution based on the information given is illustrated below.

A frequency distribution table is the

chart that summarizes all the data under two columns - variables/categories, and their frequency.

It should be noted that the distribution table has two or three columns and the first column lists all the outcomes as individual values or in the form of class intervals, depending upon the size of the data set.

Given the above information the frequency distribution table is:

Cost of living Number of states

85.0 - 94.9 9

95.0 - 104.9 5

105.0 - 114.9 0

115.0 - 124.9 2

125.0 - 134.9 2

135.0 - 144.9 1

145.0 - 154.9 1

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Answer: C. 5.4 Blocks

Step-by-step explanation:

Given information

5 bags = 3 blocks

Set variable

Let x be the number of blocks

Constructure proportional equation

[tex]\frac{3}{5} } ~=~\frac{x}{9}[/tex]

Cross multiply the fraction

[tex](3)~*~(9)~=~(5)~*~(x)[/tex]

[tex]27~=~5x[/tex]

Divide 5 on both sides

[tex]27~/~5~=~5x~/~5[/tex]

[tex]\Large\boxed{x=5.4~blocks}[/tex]

Hope this helps!! :)

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Answer:

oc

Step-by-step explanation:

5 times .6 equals 3

9 times .6 equals 5.4

The particle will stop at D.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

In pentagon ABCDE shown above, each side is 1 cm. If a particle starts at point A and travels clockwise 723 cm along ABCDE, then

Number of sides = 5

Let x be the one complete revolution.

5 x = 725

x = 145

Now, 145 - 2 = 143

Hence, it will stop at D which is 2 less than A.

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Answer:

d 1-12-3-5 is the answer

Answer:

For finding Percentage u have to multiply the number with 100

e.g.,

[tex] \frac{4}{50} \times 100[/tex]

[tex]4 \times 2 = 8\%[/tex]

Hopefully this helps u...

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Answer:

See below.

If the correct sum is 1155, then Ken had 495 stamps, and Henry had 660 stamps.

Step-by-step explanation:

Henry had h stamps.

Ken had k stamps.

After giving away 2/3 of his stamps, Henry ended up with 1/3 of his stamps, or h/3.

After giving away 3/4 of his stamps, ken ended up with 1/4 of his stamps, or k/4.

h/3 = k/4

h + k = 1156

4h = 3k

h = 1156 - k

4(1156 - k) = 3k

4624 - 4k = 3k

4624 = 7k

k = 4624/7

Stamps left: 0.25 × 4624/7 = 1156/7

h = 1156 - k

h = 1156 - 4624/7

h = 8092/7 - 4624/7

h = 3468/7 =495.43

Stamps left: 1/3 × 3468/7 = 1156/7

Total number of stamps left: 1156/7 + 1156/7 = 2312/7 = 330.29

The problem is solved correctly, but the numbers given must be incorrect since you cannot have a fraction of a stamp.

Answer:

-0.8, -0.2, 0.8, 1.6

Step-by-step explanation:

Answer:

10 mph

Step-by-step explanation:

speed of boat in still water = x

speed of current = 5

speed of boat with current (downstream) = x + 5

speed of boat against current (upstream) = x - 5

distance downstream = 9

distance upstream = 3

time = t

speed = distance/time

distance = speed × time

downstream:

9 = (x + 5)t

upstream:

3 = (x - 5)t

9 = xt + 5t

3 = xt - 5t

9 = xt + 5t

-3 = -xt + 5t

-----------------

6 = 10t

t = 0.6

9 = (x + 5)0.6

15 = x + 5

x = 10

The rate of the slower cyclist is 16 mph while the rate of the faster cyclist is 21 mph.

let us assume the following;

x = rate of slower cyclist

x + 5 = rate of faster cyclist

We know that formula for distance is;

distance = travel time*rate

Thus;

2x + 2(x + 5) = 74

Since the two cyclists are a distance of 74 miles apart after a time 2 hours. Thus;

2x + 2x + 10 = 74

4x + 10 = 74

4x = 74 - 10

4x = 64

x = 64/4

x = 16

Rate of faster cyclist = 16 + 5 = 21 mph

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Answer:

x = 1.086

Step-by-step explanation:

Formula

6^x = 7                     Take the log of both sides.

Solution

log 6^x = log 7         Bring the power down You are now dealing with log 6

x * log 6 = log 7        Divide by log 6

x = log 7/log 6

x = .8451 / .7782       Divide

Answer

x = 1.086

Using the normal distribution, there is a 0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 90, \sigma = 10[/tex]

The probability that’s a car picked at random is traveling at more than 100 km/hr is one subtracted by the p-value of Z when X = 100, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{100 - 90}{10}[/tex]

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587.

0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.

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Answer:

x-1 gave ggs is it correct

Answer:

123 soda and 87 hot dogs

Step-by-step explanation:

Let s = # soda and h = # hot dogs

s +  h = 210         s = h + 36  Substitute the h + 36 for s into the first equation

s + h = 210

(h + 36) + h = 210  

h + 36 + h = 210  Combine the h's

2h + 36 = 210  Subtract 36 from both sides

2h = 174  Divide both sides by 2

h = 87  This is the number of hot dogs.  Substitute this into either equation above to find the sodas.        

s + h = 210

s + 87 = 210

s = 123  

OR

s = h + 36

s = 87 + 36

s = 123

Using proportions, it is found that you would expected the white counter to be chosen 128 times.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of the white counter is given as follows:

p = 32/(32 + 18) = 32/50 = 0.64.

Hence, out of 200 trials, the number of trials in which the white counter is expected to be chosen is given by:

0.64 x 200 = 128 times.

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Step-by-step explanation:

1.

the expected sample mean is always the general mean : 168.5 pounds.

2.

the SD of a sample is the general SD / sqrt(sample size).

in our case

the sample SD = 68/sqrt(150) = 5.55217675...

3.

if we are looking for only the probability that any single woman is below 160 pounds, we would use the normal z calculation :

z = (x - mean)/SD = (160 - 168.5)/68 = -8.5/68

but we have here the question about the probability of the mean value of a whole sample of 150 women.

so, we need to adapt the z-calculation by the principle of 2) for the SD of a sample :

z = (x - mean)/(SD × sqrt(sample size)) =

= (160 - 168.5)/(68 × sqrt(150)) = -8.5/(68×sqrt(150)) =

= -0.010206207 ≈ -0.01

that gives us in the z-table the p-value 0.49601

this 0.49601 is the probability that a sample of 150 women has a mean value of below 160 pounds.

4.

similar to 3.

the z value we are looking for

z = (175 - 168.5)/(68 × sqrt(150)) = 6.5/(68 × sqrt(150)) =

= 0.007804747... ≈ 0.01

that gives us the p-value 0.50399.

that would be the probability of a sample mean of 175 or below.

to get above 175 we need to get the other side of the bell-curve :

1 - 0.50399 = 0.49601

so, this case has about the same probability as 3.

5.

as 3), just with the sqrt(200) instead of the sqrt(150).

z = -8.5/(68 × sqrt(200)) = -0.008838835... ≈ 0.01

so, the probability is still about the same as in 3) :

0.49601

6.

as 4) just with sqrt(200).

z = 6.5/(68 × sqrt(200)) = 0.006759109... ≈ 0.01

so, the probability is still about the same as for 4) :

0.49601

The answers are :

1) The expected mean for a sample of 150 women is 168.5 pounds.

2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.

3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.

4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.

5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.

6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.

What is probability ?

Probability is a measure of the likelihood of event to occur. The probability of all the events in a sample space adds up to 1.

1)

We know that the expected mean of a sample is always equal to general mean.

As per the question, mean weight is 168.5 pounds.

This implies :

The expected mean for a sample of 150 women is :

= 168.5 pounds

2)

The standard deviation (SD) of the mean for a sample of 150 women is :

= 68 / (√150)

= 5.55

3)

The probability of 150 women having a sample mean below 160 pounds will be represented by z and will be :

z = ( x - mean) / ( SD × (√sample size))

= (160 - 168.5) / (68 × √150)

= 0.01

If we use the z table then the probability will be :

= 0.49601

4)

Similarly as part 3 :

z = (175 - 168.5) / (68 × √150)

z  = 0.01 (approximately)

The probability of 150 women having a sample mean below 175 pounds will be :

= 0.50399

And the probability of 150 women having a sample mean above 175 pounds will be :

= 1 - 0.50399

= 0.49601

5)

Here , we have to find probability of 200 women , so 150 in formula of z in 3rd part will be replaced by 200.

i.e.,

z = (160 - 168.5) / (68 × √200)

z = 0.01 ( approximately)

and probability will be :

= 0.49601

6)

Here , we have to find probability of 200 women , so 150 in formula of z in 4th part will be replaced by 200.

z = (175 - 168.5) / (68 × √200)

z = 0.01

And probability equal to :

= 0.49601

Therefore , the answers are :

1) The expected mean for a sample of 150 women is 168.5 pounds.

2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.

3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.

4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.

5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.

6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.

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Answer:

160

Step-by-step explanation:

22 + 18 = 25 percent

40 = 25 percent

100 / 25 = 4

40 x 4 = 160.

Answer:

(3+3) x (3+1)

Step-by-step explanation:

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

Using the z-distribution, it is found that since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.

At the null hypothesis, it is tested if the proportion is still of 44%, that is:

[tex]H_0: p = 0.44[/tex]

At the alternative hypothesis, it is tested if the proportion is now different of 44%, that is:

[tex]H_1: p \neq 0.44[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]p = 0.44, n = 1360, \overline{p} = \frac{626}{1360} = 0.4603[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.4603 - 0.44}{\sqrt{\frac{0.44(0.56)}{1360}}}[/tex]

z = 1.51

Using a z-distribution calculator, for a two-tailed test, as we are testing if the proportion is different of a value, with z = 1.51, the p-value is of 0.1310.

Since the p-value is greater than 0.05, there is not enough evidence to conclude that there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes.

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Answer:

4900

Step-by-step explanation:

When rounding a number such as 4928 to the nearest hundred, we use the following rules:

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

In this case, Rule B applies and 4928 rounded to the nearest hundred is:

4900

Answer:

Step-by-step explanation:

4,928, look at the last two numbers 28 if they are above 50 you round up, if below 50 round down,

The answer is 4,900

The value of f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].

Given a function f(x)=4-2x+6[tex]x^{2}[/tex].

We are told to find out the value of f(a), f(a+h) and [f(a+h)-f(a)]/hwhere h≠0.

Function is like a relationship between two or more variables expressed in equal to form.The value which we entered in the function is known as domain and the value which we get after entering the values is known as codomain or range.

f(a)=4-2a+6[tex]a^{2}[/tex] (By just putting x=a).

f(a+h)==[tex]4-2(a+h)+6(a+h)^{2}[/tex]

=4-2a-2h+6([tex]a^{2} +h^{2} +2ah[/tex])

=4-2a-2h+6[tex]a^{2} +6h^{2} +12ah[/tex]

=[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]

[f(a+h)-f(a)]/h=[[tex]6a^{2} +6h^{2}-2a-2h+12ah[/tex]-(4-2a+6[tex]a^{2}[/tex] )]/h

=[tex](6a^{2} +6h^{2} -2a-2h+12ah)/h[/tex]

=[tex](6h^{2} -2h+12ah)/h[/tex]

=6h+12a-2.

Hence the value of function f(a)=4-2a+6[tex]a^{2}[/tex], f(a+h) is [tex]6a^{2} +6h^{2} -2a-2h+12ah[/tex] , [f(a+h)-f(a)]/h is 6h+12a-2 in the function f(x)=4-2x+6[tex]x^{2}[/tex].

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Carey's weekly salary before tax is  $1300.

The mathematical operation that would be used to determine the required value is division. Division is a mathematical operation that entails grouping a number into equal parts using another number.

In order to determine Carey's weekly salary before tax, divide the yearly salary by the number of weeks in a year.

Carey's weekly salary before tax = yearly salary / number of weeks in a year

$67,600 / 52 = $1300

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the minimum amortization is given as 20300 dollars

We have the value of A to be $3235000

while we have the value of B to be $3474000

Of these two values the greatest or the highest is that of the option B.

Next we have to find the corridor value using 10 percent

0.10 * 3474000

= 347400

$505740 -  347400

= 158340

The number of years = 7.8

minimum amortization = 158340/7.8

= 20300 dollars

Hence the minimum amortization is given as 20300 dollars

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The expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰

From the question, we are to determine the expression that represents the number of reams of paper the company produced during the second year

From the given information,

During the first year of operation,

The company produced 8.4 × 10⁹ reams of paper

And

During the second year,

the company produced 5.6 times the number of reams of paper that it produced during the first year.

Thus,

The number of reams of paper the company produced during the second year = 5.6 × 8.4 × 10⁹ reams of paper

The number of reams of paper the company produced during the second year = 47.04 × 10⁹ reams of paper

= 4.704 × 10¹ × 10⁹ reams of paper

= 4.704 × 10¹⁰ reams of paper

Hence, the expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰

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a. This information is given to you.

b. We want to find

[tex]\mathrm{Pr}\{X > 8.9\}[/tex]

so we first transform [tex]X[/tex] to the standard normal random variable [tex]Z[/tex] with mean 0 and s.d. 1 using

[tex]X = \mu + \sigma Z[/tex]

where [tex]\mu,\sigma[/tex] are the mean/s.d. of [tex]X[/tex]. Now,

[tex]\mathrm{Pr}\left\{\dfrac{X - 10.5}2 > \dfrac{8.9 - 10.5}2\right\} = \mathrm{Pr}\{Z > -0.8\} \\\\~~~~~~~~= 1 - \mathrm{Pr}\{Z\le-0.8\} \\\\ ~~~~~~~~ = 1 - \Phi(-0.8) \approx \boxed{0.7881}[/tex]

where [tex]\Phi(z)[/tex] is the CDF for [tex]Z[/tex].

c. The 76th percentile is the value of [tex]X=x_{76}[/tex] such that

[tex]\mathrm{Pr}\{X \le x_{76}\} = 0.76[/tex]

Transform [tex]X[/tex] to [tex]Z[/tex] and apply the inverse CDF of [tex]Z[/tex].

[tex]\mathrm{Pr}\left\{Z \le \dfrac{x_{76} - 10.5}2\right\} = 0.76[/tex]

[tex]\dfrac{x_{76} - 10.5}2 = \Phi^{-1}(0.76)[/tex]

[tex]\dfrac{x_{76} - 10.5}2 \approx 0.7063[/tex]

[tex]x_{76} - 10.5 \approx 1.4126[/tex]

[tex]x_{76} \approx \boxed{11.9126}[/tex]

Answer:

0.28

Step-by-step explanation:

Depreciation Expense per mile:

= (Cost of delivery truck - Salvage value) ÷ Expected miles driver

=(33000-2760)÷108000=0.28 per mile

Using proportions, it is found that the correct option for when the machine will stop running the algorithm is:

B) 9 P.M. on Saturday.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The algorithm runs for 972 hours. Each day has 24 hours, hence we apply the proportion to find the number of days as follows:

972/24 = 40.5 days.

The remainder of the division of 40.5 by 7, as a week has 7 days, is of 5.5, which means that the code will finish running 5.5 days after the 9 A. M. Monday, that is at 9 P. M. on a Saturday, which means that option B is correct.

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Answer:

Step-by-step explanation:

If it is not Monday, then there are students in the gym.

Negation: It is not Monday and there are not students in the gym.

Statement: It is Monday or there are students in the gym.

Equivalent: If there are not students in the gym, then it is Monday.

Neither: There are not students in the gym or it is not Monday.