How many times smaller is 1.2 × 106 than 1.38 × 107?

The simplified form of radical √18 . 3√5 = 9√10

In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher. When the radical symbol is used to denote any root other than a square root, there will be a superscript number in the 'V'-shaped part of the symbol.

For example, ³√(8) means to find the cube root of 8. If there is no superscript number, the radical expression is calling for the square root.

The term underneath the radical symbol is called the radicand.

Given radical

√18 . 3√5

⇒ √(9 × 2) . 3√5

⇒ 3√2 . 3√5

⇒ 9(√2.5)

⇒ 9√10

⇒ 28.46

Hence, The radical √18 . 3√5 can be simplified to 9√10 having value = 28.46

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A total of 12,000 dollars is made from the sale of 300 books at a price of $40 each. 25 fewer books are sold for every $5 increase in price.      R(x)=(40+5x)(300−25x) R ( x ) = ( 40 + 5 x ) ( 300 − 25 x )

Assumed in this instance is , At a price of 40 dollars apiece, [tex]$(300)(40 \$)=12,000 \$$[/tex] books generate $300 in revenue. The result is that 25 fewer books are sold if we raise the price of each book by $5. That's [tex]$(300-25 x)$[/tex]. Due to the fact that the price always rises by five times more than the number of books, the cost is [tex]$(40+5 x)$[/tex].

[tex]$R=(300-25 x) \cdot(40+5 x)$[/tex]

[tex]$R=12000+6000 x-1000 x-125 x^2$\\$R=-125 x^2+5000 x+12000$\\$R=125 x^2-5000 x-12000$[/tex]

The revenue R is expressed as a function of the number x as it approaches 5. R(x)=(40+5x)(30025x) is the necessary revenue function. R(x) = (40 + 5 x)(300 25 x) is the necessary revenue function.

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When ABCD is dilated by a factor of the coordinate of D' and the size of the coordinate point is, A"s coordinate would be (-6, -2) (-3, -1) .

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

The coordinate point's size is specified as (-3, -1).

The coordinate A' will be supplied as follows if the coordinate A is dilatable by a factor of two: A' = (2(-3), 2(-1)) = (-6, -2)

Consequently, A"s coordinate would be (-6, -2)

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Note that the resultant expression after simplifying simplify square root of 3y² if y<0 is: y√3

Note that we need to take a factor out of the square root:  √(3y²) , where y<0.

The given expression is  √(3y²)

Recall that to take out a factor out of the square root that factor must have a degree in multiple of 2 such as x², x⁴, (x-2)⁴, thus,

√(3y²)  = √3y²

⇒ √3 √y²

⇒  √3 (y²)[tex]^\frac{1}{2}[/tex]

⇒ √3 (y)[tex]^\frac{2}{2}[/tex]

= y √3

Thus, having simplified the expression √(3y²), the result is:  y √3.

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Answer:

Below

Step-by-step explanation:

csc x = 1/sinx    

so    sinx ( 1 + cscx )

     = sinx ( 1 + 1/sinx)

      = sinx + sinx /sinx

      = sin x + 1              Done .

The statement regarding the region of rejection for a 5% significance level would be true is the region of rejection lies between the z-scores -2 and 2.Option B is correct.

A collection of values for the test statistic for which the null hypothesis is rejected constitutes a critical zone, sometimes referred to as the region of rejection. For example, if the observed test statistic is in the critical range, the null hypothesis is rejected and the alternative hypothesis is accepted.

Further the rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it. The rejection area, for the right-tailed test, for instance, is any value bigger than the critical value, or c 1 .

Therefore, the interval that causes the null hypothesis H 0 to be rejected in a hypothesis test is known as the region of rejection and is measured in the sampling distribution of the statistic under examination.

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Answer:

D. 1 5/16

Step-by-step explanation:

mark brainliest

If the sum of three numbers is 50, it forms a linear equation that is x + y + z = 50. By solving this equation we can get the value of x, y and z.

The Equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. There are different types of equations like linear, quadratic, cubic, etc. There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. The most basic and simple algebraic equations consist of one or more variables in math.

The sum of three number is 50 the first number is twice the second number the third number is half the first number.

x + y + z = 50

x = 2y

z = x / 2

Here we form a linear equation. A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. By solving this linear equation we can get the value of x, y and z.

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well, our origin amount will be 80, so 80 is the 100% or all papers, now, she has graded 60, so what's leftover is 20, what's 20 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 80 & 100\\ 20& x \end{array} \implies \cfrac{80}{20}~~=~~\cfrac{100}{x} \\\\\\ 4 ~~=~~ \cfrac{ 100 }{ x }\implies x=\cfrac{100}{4}\implies x=25[/tex]

The largest prime number that divides the quantity is the largest prime number less than 5.5e+22.

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number that divides a quantity is a prime number that is a factor of that quantity.

We can start by computing the values of the factorials, and then use the property of modular arithmetic to find the prime divisors of the quantity.

0! = 1

1! = 1

2! = 2

3! = 6

...

50! = 30414093201713378043612608166064768844377641568960512000000000000

Now we can write the expression as

(0! + 1x1!) + (2x2!) + (3x3!) + ... + (50x50!)

We can notice that the number is very large, and it's impractical to factorize it using traditional methods.

We can use the property that if n is not divisible by a prime number p, then n! is not divisible by p^2. So we can eliminate all the powers of 2 and 5 from the expression, since 2 and 5 are the only prime factors of the factorials.

The next step would be to check if the remaining number is divisible by any prime numbers.

Since it's impractical to check for all the prime numbers, we can use the fact that the largest prime number is less than the square root of the number in question. Therefore, we can check for all primes less than √(50!) = √(30414093201713378043612608166064768844377641568960512000000000000)

Which is approximately 5.5e+22.

Therefore, the largest prime number that divides the quantity is the largest prime number less than 5.5e+22.

It's important to note that this is a very large number and checking for all prime numbers less than it would take a long time. And thus, answer cannot be given.

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Solving for x and y intercepts when given an equation:

X-intercept:

[tex]2x-5(0)=20[/tex]

[tex]2x=20[/tex]

[tex]x=10[/tex]

x-intercept occurs at (10,0)

Y-intercept

[tex]2(0)-5y=20[/tex]

[tex]-5y=20[/tex]

[tex]y=-4[/tex]

y-intercept occurs at (0,-4)

Answer:

8.5 hrs? direct variation

Step-by-step explanation:

60 per hour is 600 for 10 hours so 70 per hour to go 600 miles is 8.57142857143 in the calculator

600/60 =10

600/70 = 8.5

and its direct variation because on a graph 8.5 8.5 squares up for ever 1 square going over every time and the graph does curve but I haven't learned this stuff in years so I'm not 100% sure

here in equation function, John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.

To create an equation, multiplying and dividing are used to separate constants and variables. In an equation, terms in various forms on each side of the equality sign are equal. John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.To create an equation, multiplying and dividing are used to separate constants and variables.

so we have,

John had paid $8.00 an hour and waits tables

Therefore,

In 29 hours, he earns -

[tex]= 40 X 8\\= 320 $[/tex]

Via tups, he earned 210.50$

So, in total he earns

[tex]= 320 + 210.50\\= 530.50 $[/tex]

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3 and 2/3 as a mixed number will be 11/3.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold  Z.

A mixed number is a combination of a whole number and a fraction. It represents a number that is greater than zero but less than the next whole number. A mixed number is written with the whole number followed by a space and then the fraction.

[tex]=3+2/3[/tex]

[tex]=(3*3+2)/3[/tex]

[tex]=(9+2)/3[/tex]

[tex]=11/3[/tex]

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Answer:

4444/1000

You take the number of decimal points and turn them into zeros for the denominator

Only Erica's equation (y = -0.5x) is proportional

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the Erica equation:

y = -0.5x

The slope is -0.5, hence it is a negative slope and the intercept is at 0, hence it passes through the origin and is proportional

Given the Aliyah equation:

y = 2.5x - 8

The slope is 2.5, hence it is a positive slope and the intercept is at -8, hence it does not pass through the origin and is not proportional

Both equations are linear equations

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The longest angle is the straight line, or 180 degrees. To find it, draw two lines so that they form a straight line. Then measure the angle between the two lines using a protractor.

Angle is a figure formed by two lines or rays intersecting each other. It is measured in degrees, and is generally represented by the symbol ∠. The lines or rays that form the angle can be extended indefinitely, and the angle can be either acute, obtuse, right, reflex, or full. An acute angle is one that is less than 90°, an obtuse angle is one that is greater than 90°, a right angle is one that is exactly 90°, a reflex angle is one that is greater than 180°, and a full angle is one that is 360°.

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Answer:

y- intercept = 0

Step-by-step explanation:

the linear function can be expressed in slope- intercept form, that is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁ , y₁ ) = (4, - 4) and (x₂, y₂ ) = (- 2, 2) ← 2 ordered pairs from the table

m = [tex]\frac{2-(-4)}{-2-4}[/tex] = [tex]\frac{2+4}{-6}[/tex] = [tex]\frac{6}{-6}[/tex] = - 1

the line crosses the y- axis at (0, 0 ) ⇒ c = 0

y = - x + 0, that is

y = - x ←  is the linear function defining the ordered pairs in the table

A numerical equation using addition as the only operator, for instance, is 2 + 17.

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The halfway between the number is -1/4 on the number line.We can find halfway by using midpoint formula.

If the given number is positive mark it on the right side of the origin. If it is a negative number mark it on the left side of zero.Then divide each unit into the values equal to the fraction's denominator.

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.

Now

Using midpoint formula

[tex]x_{1}[/tex]+[tex]x_{2}[/tex]/2 =-5/6 +1/3 divide 2

Find common denominator and write the numerators above common denominator

-5+2/12 =-3/12

            =-1/4

Hence we find midpoint between numbers.

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The vertex and axis of symmetry of the graph is shown in image.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ f (x) = 1/4 (x + 6)² - 5

Now,

Since, The function is,

⇒ f (x) = 1/4 (x + 6)² - 5

Hence, The points corresponds to x = - 2 and - 4 are;

For x = - 2;

⇒ f (x) = 1/4 (x + 6)² - 5

⇒ f (x) = 1/4 (-2 + 6)² - 5

⇒ f (x) = 1/4 (4)² - 5

⇒ f (x) = 4 - 5

⇒ f (x) = - 1

For x = - 4;

⇒ f (x) = 1/4 (x + 6)² - 5

⇒ f (x) = 1/4 (-4 + 6)² - 5

⇒ f (x) = 1/4 (2)² - 5

⇒ f (x) = 1 - 5

⇒ f (x) = - 4

Thus, The points are;

⇒ (- 2, - 1) , (- 4, - 4)

And, The vertex of the function is,

⇒ ( - 6, - 5 )

And, The axis of symmetry of the graph is,

⇒ x = - 6

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10L  fuel does Asma's car use per 100 km of highway driving

In this question, we have to use the unitary method

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

What is a unitary in math?

a unitary state. (mathematics, of an algebra) That contains an identity element. (mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.

So from the unitary method, we can solve it

12 L of gasoline per 100 km

so for 5/6

12 L * 5/6

= 10 L

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To tell if a log graph is a growth or decaying, look at the slope of the line. If the slope is positive, then it is growth; if the slope is negative, then it is decay.

A positive slope indicates that the value is increasing over time, while a negative slope indicates that the value is decreasing over time. To find the slope, take two points on the line and calculate the change in the y-value divided by the change in the x-value.

If the answer is positive, the graph is growth; if the answer is negative, the graph is decay. Additionally, you can look at the y-intercept of the graph, which is the value where the line meets the y-axis. If the y-intercept is positive, the graph is growth; if the y-intercept is negative, the graph is decay.

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Answer:

6

Step-by-step explanation:

The growth factor is the number that is raised to an exponent.

Answer: 6

Therefore ,this maxima of the preceding problem is 2 ≥ 0 , which leads to x²+90=> f(x) ≥ 9 , indicating that there is no maxima.

The maxima & minima of the a function are its maximum and minimum points within or across a given range, and these points are collectively referred to as extrema in mathematical analysis. The highest value of the variable. The maximum amount, level, etc. The variable can only take a maximum of 2. Maximum refers to a peak (plural maxima). The lowest position is referred to as minimal (multiple minimum). Extremum is a phrase for the largest or least of anything (multi-extremum). Peaks (or minima) are used if there are better (or worse) sites available elsewhere but they are not nearby.

Here,

Given :

=> f(x) = x²+9 20

=> x²+9>0 and

=> f(x) 9,

maxima are not possible.

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The linear equation 3x – 2y = 6 has one real solution. To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.

For example, you can solve for y to get y = (6 + 3x)/2, and then substitute this into the equation to get 3x – 2((6 + 3x)/2) = 6, which you can then solve for x. Doing this will give you x = 3, which means that the solution is (3, 3).

The linear  equation 3x – 2y = 6 has infinitely many solutions. To find them, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable

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Answer:

8,960.66

Step-by-step explanation:

In general, the length of the billing cycle is at least 15 days and no longer than 90 days.

The finance charge for a billing cycle is 960.66.

The new opening balance in the following billing cycle is 8,960.66.