2 years,18 month.express the first quantity as a percentage of the second quantity
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Since -4 = 4 exp(iπ), by DeMoivre's theorem and using the fact that cos and sin are both 2π-periodic,

[tex]z^4 = 4 \exp\left(i\pi\right) \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi + 2i\pi k\right)\right)[/tex]

where k = 0, 1, 2, or 3. Then the 4th roots of -4 are

[tex]k = 0 \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi+0\right)\right) = \sqrt2 \exp\left(i\dfrac\pi4\right)[/tex]

[tex]k = 1 \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi+2i\pi\right)\right) = \sqrt2 \exp\left(i\dfrac{3\pi}4\right)[/tex]

[tex]k = 2 \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi+4i\pi\right)\right) = \sqrt2 \exp\left(i\dfrac{5\pi}4\right)[/tex]

[tex]k = 3 \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi+6i\pi\right)\right) = \sqrt2 \exp\left(i\dfrac{7\pi}4\right)[/tex]

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 - 2 cannot be further simplified? No properties of exponents can be used due to already knowing the answer of the top of your head, it could be a mistype though, or I'm just very very d*mb.

Answer:

pushin p

Step-by-step explanation:

pushin p

Answer:

No. they have a difference in value

the first ans is 6 while the second gives 9.56

Answer:

14

Step-by-step explanation:

because both sides need to be equal so if u plug in the 14 in x it gives you the same number for both sides 107.

Answer:

[tex]y = \frac{2}{3} x + 2[/tex]

Step-by-step explanation:

Start by finding the slope of the given line.

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Slope of given line

[tex] = \frac{5 - ( - 1)}{ - 2 - 2} [/tex]

[tex] = \frac{5 + 1}{ - 4} [/tex]

[tex] = \frac{6}{ - 4} [/tex]

[tex] = - \frac{3}{2} [/tex]

A perpendicular bisector cuts through the line at its midpoint perpendicularly.

The product of the slopes of two perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

[tex] - \frac{3}{2} m = - 1[/tex]

[tex]m = - 1 \div ( - \frac{3}{2} )[/tex]

[tex]m = - 1 \times ( - \frac{2}{3} )[/tex]

[tex]m = \frac{2}{3} [/tex]

[tex]y = \frac{2}{3}x + c[/tex], where c is the y-intercept.

To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]

Midpoint of given line

[tex] = ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )[/tex]

[tex] =( \frac{0}{2} , \frac{4}{2} )[/tex]

= (0, 2)

[tex]y = \frac{2}{3} x + c[/tex]

When x= 0, y= 2,

2= ⅔(0) +c

2= 0 +c

c= 2

Thus, the equation of the perpendicular bisector is [tex]y = \frac{2}{3} x + 2[/tex].

Answer:

3x2 = 6

6-4x-7

(6-4x) - 7

2x - 7 = messi ok no xd

3.5-

Step-by-step explanation:

Answer:

[tex](3x-7)(x+1)[/tex]

Step-by-step explanation:

Use the slide-and-divide method:

[tex]3x^2-4x-7[/tex]

[tex]x^2-4x-21[/tex] <-- Multiply last term by the leading coefficient 3

[tex](x-7)(x+3)[/tex] <-- Factor

[tex](3x-7)(x+1)[/tex]

=====================================================

Work Shown:

Let x and y be the two numbers.

We're given x = 162 and the variable y is unknown.

We're also given LCM = 1134 and HCF = 18

So,

LCM = (x*y)/HCF

1134 = 162*y/18

1134 = (162/18)y

1134 = 9y

9y = 1134

y = 1134/9

y = 126

The other number is 126

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

Notice that

showing that 18 is the highest common factor (HCF) of the numbers 162 and 126. This partially confirms the answer.

Now let,

So,

We see that 1134 is in each list of multiples and the smallest such common item. So the lowest common multiple (LCM) of 162 and 126 is 1134. This helps fully confirm the answer.

Answer:

Remainder is 93

Step-by-step explanation:

Use synthetic division:

-9 | 1   -1    3

____ -9   90

     1 -10 | 93

Therefore, the remainder is 93

Answer:

0.75 liters

Step-by-step explanation:

1000ml in 1 liter so 0.75*1000=750ml

750ml > 350ml

Answer:

63-|-6| = 57

Step-by-step explanation:

63-|-6|

63-6

57

Answer:

57

Step-by-step explanation:

Substitute -6 for variable h.

[tex]63-|(-6)|\\63-6\\57[/tex]

The rate at which the water was drained from the tank is 6 gallons of water per minute (option A)

To know the speed at which the tank was drained, we must carry out the following operations:

Taking into account the information provided by the table we establish how much water has been drained from the tank in 20 minutes.

450 gallons - 330 gallons = 120 gallons.

Subsequently, we must divide the amount of water (120 gallons) that was drained by the time it was drained (20 minutes).

120 gallons ÷ 20 minutes = 6 gallons / minute.

According to the above, we can establish that the bath drain rate is 6 gallons / minute (option A).

Note: This question is incomplete because there is some missing information. Here is the complete information:

What is the rate at which the water was drained from the tank?

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Answer:

x=-10

Step-by-step explanation:

since there's a given 120 degrees, and it's a isosceles triangle, we know that the line adds up to 180 (where the 120 degrees is). so 120+x=180, the interior angle measures 60 degrees. That being said, the 3 angles measure 60 degrees also. now there's a right angle mark on top, so we find the angle of the smaller triangle (near angle 2) by doing 90-60=30 degrees.

angle 2 is said to be x+160, and there's a line, which tells us that they must add to 180.. so x+160+30=180

x+190=180

x=-10.

Step-by-step explanation:

convert kg into grams

1kg=1000g

1.5kg/350g=1.5×1000g/350

1500/350=300/70

=30/7

ratio will be 30:7

answer is 4.2g

The answer to the ratio is:

4.2g

First of all, we need to convert the kg to g

This can be done by multiplying the Kg by 1000

1.5kg x 1000= 1500g

Next, we solve the ratio since they are in the same parameters

This would be 1500g:350g

1500/350= 30/7.

Therefore, the ratio would be 30:7

Finally when further broken down, it would be 4.2g

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Answer:

30 are present 10 are absent

Step-by-step explanation:

75%=3/4

so 3/4 of them are absent

3/4(40)=30

and 40-30=10 are absent

Answer:

S 32, W 128, M 96

Step-by-step explanation:

W = 4S

S = 1/3M, or 3S = M

S + W + M = 256

Substitute

S + 4S + 3S = 256

8S = 256, S = 32

S = 32

W = 4S = 128

M = 3S = 96

Answer:

2,017

Step-by-step explanation: 2 meters= 2,000

So, 2,000+17= 2,017

2017 millimeters are in 2 meters, 17 millimeters as per the given unit conversion rate.

A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

Given, 1 meter is equal to 100 centimeters or 1,000 millimeters.

To calculate the total number of millimeters in 2 meters, 17 millimeters.

Since,

millimeters in 1 meter = 1000

Thus,

millimeters in 2 meter = 2000

millimeters in 2 meters, 17 millimeters = 2017

Therefore, there is 2017 mm in 2meteres, 17 mm as per the given unit conversion.

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Step-by-step explanation:

hope it will help you...

Answer:

c) G(x) = (x + 1)**2

Step-by-step explanation:

A function left shift is x + shift and a right shift is x - shift.

Answer: measure of the central angle

Step-by-step explanation: trust

Answer:

measure of the central angle

Step-by-step explanation:

Using the binomial distribution, it is found that there is a 0% probability that fewer that 5 in a sample of 20 pills will be acceptable.

For each pill, there are only two possible outcomes, either it is acceptable, or it is not. The probability of a pill being acceptable is independent of any other pill, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that fewer that 5 in a sample of 20 pills will be acceptable is:

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.96)^{0}.(0.04)^{20} = 0[/tex]

[tex]P(X = 1) = C_{20,1}.(0.96)^{1}.(0.04)^{19} = 0[/tex]

[tex]P(X = 2) = C_{20,2}.(0.96)^{2}.(0.04)^{18} = 0[/tex]

[tex]P(X = 3) = C_{20,3}.(0.96)^{3}.(0.04)^{17} = 0[/tex]

[tex]P(X = 4) = C_{20,4}.(0.96)^{4}.(0.04)^{16} = 0[/tex]

0% probability that fewer that 5 in a sample of 20 pills will be acceptable.

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Answer:

5.3

Step-by-step explanation:

8^2 - 6^2 = x^2

64 - 36 = x^2

28 = x^2

Square root of 28 is approx 5.3

Answer:

a perpendicular line from a point on ab

The number of tables with 4 chairs are 39.

We have a café which has 60 tables. 35% of the tables have 2 chairs at each table. The remaining 65% of the tables have 4 chairs at each table.

We have to determine the number of tables having 4 chairs.

The 10% of 250 will be -

[tex]\frac{10}{100} \times 250[/tex] = 25

According to question, we have -

Percentage of tables with 2 chairs = 35%

Percentage of tables with 4 chairs = 65%

Total number of tables = 60

Therefore -

Number of tables with 2 chairs = [tex]\frac{35}{100} \times 60[/tex] = 21

Therefore, number of tables with 4 chairs will be = 60 - 21 = 39

Hence, the number of tables with 4 chairs are 39.

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There are 39 tables that have 4 chairs.

i.e. the number  of tables with 4 chairs is: 39.

Here, we have to find the number of tables that have 4 chairs, we first need to calculate how many tables have 2 chairs, and then subtract that number from the total number of tables.

Given that 35% of the tables have 2 chairs, we can calculate the number of tables with 2 chairs as follows:

Number of tables with 2 chairs = 35% of 60 tables

Number of tables with 2 chairs = 0.35 * 60

Number of tables with 2 chairs = 21 tables

Now, to find the number of tables with 4 chairs:

Number of tables with 4 chairs = Total number of tables - Number of tables with 2 chairs

Number of tables with 4 chairs = 60 tables - 21 tables

Number of tables with 4 chairs = 39 tables

So, there are 39 tables that have 4 chairs.

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It will take 2 hours for the ambulance to pass the police car.

Given that a police car leaves a crime scene heading east directly towards the hospital at 72 kilometers per hour, and an ambulance leaves a quarter of an hour later and also heads directly east towards the hospital at 81 kilometers per hour, to determine how long will it take for the ambulance to pass the police car, the following calculation must be performed:

Therefore, it will take 2 hours for the ambulance to pass the police car.

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Answer:

they had 112 cookies

Step-by-step explanation:

14×8 = 112

Answer:

149(13/32)

Step-by-step explanation:

4781/32 and then take the remainder to make it an improper fraction

71.8

71.841:

The 4 represents the number that we'll be looking at since 4 is the next position to the right of 8, 8 is in the Tenths place. 4 is in the Hundredths place, and 4 will be the only number that could round up the 8.

In order to round, we need to remember how to round numbers:

First, 4<5, meaning that 4 is less than 5.

#1 above is stating that the number to the left of 4 stays the same.

If we use that rule:

71.8 is our answer.