REDUCING RATIOS
1. 55:33
2. 1,000:100
3. 560:80
4. 20:340

The single complex number corresponding to each expression:

1. √(-9) = 3i

2. √(-16) = 4i

3. √(-6)√(-24) = 12

4. √(-3)√(-75) = 15

5. (2+√(-12))/2 = 1 + 3i

6. (4 + √(-20))/2 = 2 + 5i

We represent √(-1) as i which is an imaginary number. Complex numbers are numbers of the kind a + ib, where a and b are real numbers.

Hence all real numbers are also complex numbers (i.e., when b = 0).

Also we use some formula for square roots:

√(ab) = (√a )(√b)

Now, to find the single complex number corresponding to each expression:

1. √(-9) = √(9) x √(-1) = 3i

2.  √(-16) = √(16) x √(-1) = 4i

3. √(-6)√(-24) = √(-6 x -24) = √(144) = 12

4. √(-3)√(-75) = √(-3 x -75) = √(225) = 15

5.  (2+√(-12))/2 =  (2+√4√3√(-1))/2 =  (2+2 x (√3)i)/2  = 1+(√3)i

6. (4 + √(-20))/2 = (4 + √4√5√(-1))/2 = (4 + 2 x (√5)i )/2 = 2 + (√5)i

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The expression after applying the distributive property, the formula becomes 0.8 + 3.6.

Algebra is the study of mathematical symbols, while logic is the manipulation of those symbols.

Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To answer the problem properly and accurately, this rule is used.

When you combine the results of two or more arithmetic operations, the result is the same as when you multiply each addend individually by the quantity and then unite the resultant products.

Given below is the phrase.

= −0.4 (−2 + (−9))

Once the distributive property has been used, we have

= 0.8 + 3.6

The result of applying the distributive property will be the equation 0.8 + 3.6.

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The value of x of the Quadratic Equation, (x - 7)² = 36 when the right-hand side is positive is 13 and for the negative right-hand side, it is 1. So the value of x could be 13 and 1 both.

Split into two equations:

(x - 7)² = 36

(x- 7) = √36 or (x- 7) = -√36

For equation (x- 7) = √36 value of x:

x - 7 = √(6)²

x - 7 = 6

x = 13

For equation (x- 7) = -√36 value of x:

x - 7 = -√(6)²

x - 7 = - 6

x = 1

∴ value of x could be 13 and 1 both.

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Titanium is used in aerospace (jet engines, missiles, and spacecraft), military, industrial processes (chemicals and petrochemicals, desalination plants, pulp, and paper), automotive, agriculture (farming), medical prostheses, orthopedic implants, dental and endodontic instruments and files, dental implants, sporting goods, jewelry, cell phones, and other applications, titanium can be alloyed with iron, aluminum, vanadium, and molybdenum, among other elements. And it's half life as per question is [tex]A(t)=A(500)*0.5^{\frac{t}{6} }[/tex]

The chemical element titanium has atomic number 22 and the symbol Ti. A transition metal with a silver hue, low density, and high strength that is resistant to corrosion in sea water, aqua regia, and chlorine can be created by reducing the only form it is found in the nature—an oxide.

William Gregor found the titanium in Cornwall, Great Britain, in 1791. Martin Heinrich Klaproth gave the metal the Titans' name from Greek mythology. The element is found in practically all living organisms, as well as bodies of water, rocks, and soils. It is mostly found in the minerals rutile and ilmenite, which are widely distributed in the Earth's crust and lithosphere. The Kroll and Hunter procedures are used to separate the metal from its main mineral ores. Titanium dioxide, the most prevalent substance, is a well-liked photocatalyst and is utilized in the production of white pigments. In addition, there are other substances such titanium tetrachloride (TiCl4), which is used in smoke screens and catalysts, and titanium trichloride (TiCl3), which is a catalyst in the creation of polypropylene.

This equation can be used to calculate the quantity of unstable nuclei left after time t:

[tex]N(t)=N(0)*0.5^{\frac{t}{T} }[/tex]

where,

N(t) = remaining quantity of substance after time t has elapsed

N(0)=  initial quantity of this substance

T= half life

So, as per question,

[tex]A(t)=A(500)*0.5^{\frac{t}{6} }[/tex]

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Answer:

A = 500 (1-0.5)^t/6 =500 (0.5)^t/6

Step-by-step explanation:

Took the test, this is the correct answer

A(t)=P (1-decay rate)^t

P=initial amount

Decay rate = 1/2=0.5

t=time

Make sure use t in minutes for the next calculation

Cartesian Co-ordinate system is used to describe graph of a line along a plane to test independent variable vs dependent variable.

the answer is test points

Answer:

I believe the answer is $17.75

Step-by-step explanation:

As if you have a base fee of 13.75 then 0.10 for each additional mile. Then 40 miles x 0.10 is 4. Hope this helps.

Since we used x and x+2 as consecutive odd integers. "x" to represent Henry's age, Henry's age is 27. Since we used the expression "x+2" to represent Cameron's age, Cameron's age is "27+2" which is just 29.

So the consecutive odd integers, just means they're separated by a value of 2. This can be generally expressed as "a and a+2" where the these two values would be consecutive odd integers assuming "a" is an integer.

So let's express the Henry's age as the variable "x", since it's unknown. Since Cameron is older, and by definition of a consecutive odd integer, Cameron's can be expressed as "x+2"

So the equation we need to set up is 2(Cameron's age) + (Henry's age) = 85

So we can substitute variables we defined to express Cameron and Henry's age:

2(x+2)+x= 85

Distribute the 2:

2x+4+x

Add like terms:

3x+4=85

Subtract 4 from both sides:

[tex]3x= 81[/tex]

Divide both sides by 3:

x=27

Since we used "x" to represent Henry's age, Henry's age is 27. Since we used "x+2" to represent the Cameron's age, Cameron's age is "27+2" which is just 29.

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LET US FIND THE GRADIENT

[tex]m = \frac{y2 - y1}{x2 - x1 \\ \\ } \\ = \frac{6 - ( - 2)}{(3 - ( - 3)} \\ = \frac{6 + 2}{3 + 3} \\ = \frac{8}{6} \\ m= \frac{4}{3} [/tex]

I WILL USE THE POINTS (-3,-2) TO GET THE VALUE OF C

[tex] - 2 = \frac{4}{3} ( - 3) + c \\ - 2 = - 4 + c \\ - 2 + 4 = c \\ c = 2[/tex]

THEREFORE THE EQUATION IS

[tex]y = \frac{4}{3} x + 2[/tex]

ATTACHED IS THE SOLUTION

From the figure, we observe that,

Non-rigid motions are used to map figure 1 onto figure 2.

Here, resizing (stretching horizontally, vertically, or both ways) is a non-rigid transformation.

So, the answer is,

The figures are congruent because non-rigid motions are used to map figure 1 onto figure 2.

The point corresponding to point C is H.

P(A) given that A and B are independent is; 35%

P(A|B) is defined as a conditional probability and it means the probability of event A that depends on another event B. It is also known as "the probability of A given B"

Now, the formula to find P(A|B) is;

P(A|B) = P(A∩B) / P(B)

Where;

P(A∩B) = P(A) *  P(B)

Thus;

P(A|B) = (P(A) *  P(B))/(P(B)

Plugging in the relevant values gives;

0.35 = P(A)

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Answer:

x>3

Step-by-step explanation:

5-2x<11

subtract 5on both sides of the equation

-2x<11-5

-2x<6

divide through by n negative 2,and the equality will change

X>-3

Hello there! Let's solve this inequality for the required variable, which is x.

With the given inequality, it can't be done in just one step, however it can be done in a few steps, which are as follows:

[tex]\implies\boldsymbol{5-2x < 11}[/tex]

[tex]\implies\boldsymbol{-2x < 6}[/tex]

[tex]\underbrace{\implies\boldsymbol{x > -3}}_\sf{answer}}[/tex]

I hope it helps, feel free to reach out if you have any queries :)

Answer:

225

Step-by-step explanation:

number of 2 minutes in 30 minutes

= 30 ÷ 2 = 15

each 2 minutes produces 15 widgets , then

15 ( lots of 2 minutes ) produces 15 × 15 = 225 widgets

Answer:

A. would be a quotient of 34 and a remainder of 14

B. would be a quotient of 22 and a remainder of 10

C. would be a quotient of 20 and a remainder of 34

Answer:

es la b

Step-by-step explanation:

porque diego es good

:D

Considering the definition of an equation and the way to solve it, for 6 additional gigabytes of data the two companies would charge the same amount.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the number of miles driven, and knowing that:

If the price charged by each company is the same, the equation is:

Price of company A= Price of company B

20.40 +9.80x= 18.60 +10.10x

Solving:

20.40 - 18.60= 10.10x - 9.80x

1.8= 0.3x

1.8 ÷ 0.3= x

6= x

Finally, for 6 of additional gigabytes the two companies would charge the same amount.

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Answer:

Step-by-step explanation:

If Keesha walks 12 blocks to school and its 88 squares in the sidewalk then you multiply 12 by 88 and get 1056:)

hope this helps ^^

The complementary angle to 38° is 52°.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius.

Let the angle be x°

Then the compliment of the angle = (90-x)°

and supplement of the angle = (180-x)°

According to question, (180-x) + 14 = 3(90-x)

or, 180-x+14 = 270-3x

or, -x+3x = 270-194

or, 2x = 76

or, x = 76/2 = 38°

Hence, the complementary angle to 38° is = 90-38 = 52°

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If  She then flew to New York where the temperature was 67 degrees. The change in temperature from when Tina left Atlanta and arrived in New York is : D:15°.

Given :

Beginning temperature = 72 degrees

Increase in temperature = 21 degrees

Decrease in temperature = 11 degrees

Temperature outside Atlanta = 67 degrees

First step is to calculate the temperature in Atlanta using this formula

Temperature = (Beginning temperature + Increase in temperature - Decrease in temperature )

Let plug in the formula

Temperature =  72 + 21 -11

Temperature = 82 degrees

Second step is to calculate the change in temperature

Change in temperature = Temperature in Atlanta - Temperature in New York

Change in temperature = 82 degrees - 67 degrees

Change in temperature = 15 degrees

Therefore the correct option is D.

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Answer:

A. 6

B. 2

Step-by-step explanation:

28/4 = 6

4/2=2

The conditional statement that the Venn diagram represents is:

"If it is a rose, then it is a flower".

Here we have a Venn diagram, in it we can see that the set called "roses" is included in the set called "flowers".

So, the conditional statement is:

"if it belongs to the smaller set, then it belongs to the larger set"

This is kinda trivial.

For our case, it will be written as.

"If it is a rose, then it is a flower".

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Observing the given limit, as x approaches infinity, the quotient of two limits, f(x) and g(x) is equal to the constant

he definition therefore of the given is that it shows f(x) and g(x) grows at the same rate as x goes to infinity.

Answer:

Step-by-step explanation:

The triangles are congruent because they have the same shape and size. They are also related in another way that I can't remember.

The equation which represent the prize money given to each person is $1500/w.

For the given condition in question;

Let 'w' be the number of coworkers.

The total money given to buy raffle tickets and won $1500.

This cam be written as;

w worker -------> $1500.

For 1 worker, use unitary method.

Divide both side by w.

1 worker -------> $1500/w.

Thus, the prize money given to each worker is $1500/w.

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Answer:

If i'm correct and the symbol between the f and g is multiplication the answer is 0.

Step-by-step explanation:

I have linked how I got this answer in the image below, I hope this is what you were looking for.

Answer:

The absolute value is the distance between a number and zero on a number line. There are always two numbers on the number line that are the same distance from zero. For instance, the numbers 4 and -4 are each a distance of 4 units away from zero. represents the distance from 4 to zero, which equals 4.

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P ( All three are not caused by firmware ) = 8423 %

The probability that the entire batch will be accepted = 0.8423

We are told that out of the 6225 cases of heart pacemaker malfunctions, 346 were found to be caused by firmware.

Thus,

Cases not caused by firmware = 6225 - 346 = 5879

So, the probability of the first case not being affected by the firmware is;

P( first case not caused by firmware ) = 5879/6225

Also,

The probability of the second case not being affected by the firmware is given as;

P(second case not caused by firmware|first case not affected by firmware) = 5878/6224

Similarly,

The probability of the third case not being affected by the firmware is given as;

P(third case not caused by firmware | first and second not caused by firmware) = 5877/6223

Now that we have the three probabilities, it is clear that the occurrences are not independent because the likelihood of one event depends on the likelihood of the others.

Thus, we will make use of the general multiplication rule which is;

P(A & B) = P(B) × P(A|B)

Thus;

P( All three not caused by firmware ) = P(first case not caused by firmware ) × P( second case not caused by firmware | first case not affected by firmware) × P( third case not caused by firmware | first and second not caused by firmware)

Substituting the values,

P(All three not caused by firmware) = ( 5879/6225 ) × ( 5878/6224 ) × ( 5877/6223 )

P(All three are not caused by firmware) = 0.84232558432 = 84.23 %

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