You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?

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Work Shown:

Method 1

List out the first few powers of 'i', where [tex]i = \sqrt{-1}[/tex]

The process repeats every four terms. Divide the exponent by 4 to look at the remainder.

39/4 = 9 remainder 3

Ignore the quotient 9. The remainder is all we care about

Since we get remainder 3, this means i^39 = i^3 = -i

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Method 2

i^39 = i^(36+3)

i^39 = i^36*i^3

i^39 = i^(9*4)*i^3

i^39 = (i^4)^9*i^3

i^39 = (1)^9*i^3

i^39 = 1*i^3

i^39 = i^3

i^39 = -i

This is a bit longer method, but it helps confirm that i^39 = i^3 = -i we found earlier in the previous section.

Answer:

The car passed the truck after 60 minutes.

Step-by-step explanation:

We should first find how far the truck was from the entrance to the highway when the car entered (after 11 minutes). We know that the distance travelled is the product of the time and speed, therefore, the location of the truck is given by [tex]d = 60 * 11 = 660[/tex].

Now we can build functions representing the distance from the entrance of both vehicles, in respect to the time travelled.

Truck's Function
[tex]x_0 = 660m \\ v = 60mph \\ \to x(t) = 660m + 60t[/tex]

Car's Function
[tex]x_0 = 0m \\ v = 71mph \\ \to x(t) = 71t[/tex]

Finally, we can equalize both functions to find out at what time the car passed the truck (when their graphs intercepted):

[tex]660 + 60t = 71t \\ \to 660 = 11t \\ \to t = 60m[/tex]

Answer:

-3/4

Step-by-step explanation:

From a point on the graph, count down and count right until you get to a another point. For example, for this problem, you can use (0,-2) as a starting point. From here, if you go down 3 and go right 4, you get another point on the graph. So, the slope is -3/4.

Saying that the populations of the U.S. and India went up by 2.6 million and 15.8 million respectively is an absolute comparison.

The relative comparison of the populations of the U.S. and India from 2015 to 2016 would be 0.81% and 1.21% respectively.

In terms of population growth, an absolute comparison is made when the increase in population is denoted through the use of whole numbers. No percentages or fractions are used.

By simply mentioning that the U.S. population rose by 2.6 million and that of India rose by 15.8 million is therefore absolute.

The relative comparison is found as:

= Change in population / Population in 2015

For the United States:

= 2.6 million  / 320.7 million

= 0.81%

For India:

= 15.8 million / 1.31 billion

= 1.21%

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Answer: use your brain you can do it

Step-by-step explanation:

anything is possable with the power of imagination

A number system is defined as the representation of numbers by using digits or other symbols, one hundred twenty one thousand, two hundred eleven in base ten numerals is 10^5+2*10^4+10^3+2*10^2+10^1+1*10^0.

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner

one hundred twenty one thousand, two hundred eleven is

121211

This can be written in base ten numerals.

121211

=100000+20000+1000+200+10+1

=10^5+2*10^4+10^3+2*10^2+10^1+1*10^0

Therefore one hundred twenty one thousand, two hundred eleven  in base ten numerals is 10^5+2*10^4+10^3+2*10^2+10^1+1*10^0.

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Considering the definition of an equation and the way to solve it, the number is -3/7.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it. This is, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:

Being "x" a number, and knowing that eight more than six times a number is the same as two less than 8 times the numbe, the equation in this case is:

8 + 6x= 2 - 8x

Solving:

6x + 8x= 2-8

14x= -6

x= (-6) ÷ 14

x= -3/7

Finally, the number is -3/7.

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Answer:

Marcus Ran 1.25km farther than cindy

Step-by-step explanation:

After school, Marcus ran 3.2 km and Cindy ran 1.95 km. Who ran farther? How much farther? Marcus ran 1.25 km farther than Cindy.

So, the polynomial with the require properties is x⁵ + x⁴ - 3x³ - 5x² - 2x

A polynomial is an expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² + ... + a₂x² + a₁x + a₀ where aₙ are coefficients and n ≥ 2.

Since we are given a polynomial with the following properties: fifth degree, −1 is a zero of multiplicity 3, 2 is the only other zero.

We have that it has zero at

⇒ x + 1 = 0 and x - 2 = 0

⇒ (x + 1) and (x - 2) are factors of the polynomial

We are told that the polynomial has a zero of -1 with multiplicity of 3. This implies that the factor (x + 1) is repeated 3 times. That is (x + 1)(x + 1)(x + 1)

So, multiplying all four factors we have a polynomial of fourth degree as p(x) = (x + 1)(x + 1)(x + 1)(x - 2)

= (x² + 2x + 1)(x + 1)(x - 2)

= (x³ + 3x² + 3x + 1)(x - 2)

= x⁴ + x³ - 3x² - 5x - 2

To obtain a polynomial of degree 5, we multiply through by x, so we have

g(x) =xp(x)

= x(x⁴ + x³ - 3x² - 5x - 2)

= x⁵ + x⁴ - 3x³ - 5x² - 2x

So, the required polynomial is x⁵ + x⁴ - 3x³ - 5x² - 2x

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Answer:

Answer: 3 + 7 + 12 - 2 = 20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: the sum of one interior angle and one exterior angle is 180. x+120=180. x=180-120. x=60°. sum of angles in a triangle is 180.

Answer:

24 goals

Step-by-step explanation:

40/100×60=Adrians goals(g)

g=2400/100

=24

Step-by-step explanation:

24 goals in total I think.

Answer:

y-intercept is -17

x-intercept is 17

Step-by-step explanation:

See attached

(A) 1.5 (IQR) is used to identify outliers in a set of data.

As it is given in the description itself, the interquartile range is the best tool to use to find all of your outliers (IQR).

Therefore, (A) 1.5 (IQR) is used to identify outliers in a set of data.

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The correct question is given below:
Which of the following is used to identify outliers in a set of data?

(A) 1.5(IQR)

(B) 1.5(range)

(C) 2(mean)

(D) 2(median)

The longest part is Part B, which is a little longer than Part A.

The length is the measure of distance or total time from one point to another.

For example, when measuring dimensions, the length also shows the longest side of an object, especially the rectangle.

Together with the width, the length can be used to determine the area of an object or its perimeter.

Part                         A          B          C          D

Length (IN.)          1²/₇        1.3         1.15      ²¹/₂₀

Convert all lengths (A and D) into decimals:

Part                         A                 B           C          D

Length (IN.)         1.29 (1²/₇)       1.3         1.15     1.05 (²¹/₂₀)

Part B's length is the most extended length, followed by Part A, Part C, and lastly, Part D.

Thus, the most extended length of the four parts is Part B.

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Part                         A          B          C          D

Length (IN.)          1²/₇        1.3         1.15      ²¹/₂₀

The weighted average is -33.

given,(2,8)(-4.-7)and their weighted average is 3:5

Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set. In calculating a weighted average, each number in the data set is multiplied by a predetermined weight before the final calculation is made.

(2,8)x5=10+40

           =50

(-4,-7)x3=-12-21

            =-33

therefoe, the weighted average is -33.

The average is the sum of all individual observations divided by the number of observations. In contrast, the weighted average is observation multiplied by the weight and added to find a solution.

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Correct answer is B. The zeros of the function g will be ( -6 and 7.)

(x-7) and (x + 6) are factors in a function g.

To locate: The function g's zeros.

Because x-a=0 x = a, we know that if (x-a) is a function's factor, then x-a is the function's zero.

The fact that (x - 7) and (x + 6) are factors in the function g is a given.

x-7=0

x = 7

Likewise, x+6=0

x = -6

As a result, the function g's two zeros are -6 and 7.

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Answer:

40

Step-by-step explanation:

Work from left to right.

24* (-2)*5/(-6)= -48*5/(-6)

-48*5/(-6)=-240/(-6)

-240/(-6)=40

The equation of the line in y = mx + c form is y = (-25/4)(x) + 5.

Here, we are given a line as shown in the figure.

Let us take 2 points that the line passes through. We can see that the line passes through (0, 5) and (0.8, 0)

Now, we have two points, we can find the slope of the line.

Slope is taken to be m. Thus,

m = (y2-y1)/ (x2-x1)

here, (x1, y1) = (0, 5)

and (x2, y2) = (0.8, 0)

Therefore,

m = (0-5)/ (0.8 -0)

m = -5/0.8

we can simplify this as follows-

m = -50/8

m = -25/4

Thus, the slope of the line is -25/4.

Now, we already know that  (0, 5) is a point on the line. Thus, the y intercept of the line is 5.

⇒ c = 5

Now, substituting the values in the equation we get-

y = (-25/4)(x) + 5

Thus, the equation of the line in y = mx + c form is y = (-25/4)(x) + 5.

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Answer:

Step-by-step explanation:

average rate = f(3) - f(0) / 3 - 0 = 24 - 0 / 3 - 0 = 24 / 3 = 8

Answer: 50 ft long and 6.25 ft wide

Step-by-step explanation:

Solution :  Distance between (-1/2, -1) , (5/8, -1) = .75

Distance Formula :

Distance between two points can be evaluated if we know the c

[tex]\sqrt{{(y2-y1)^{2} } +(x2-x1)^{2}][/tex] = XY

The difference between the x-axis coordinates gives the horizontal distance and the difference between the y-axis coordinates gives the vertical distance.

Distance between the points P and Q is calculated as follows:

S and T are the points on the x-axis which are endpoints of two parallel line segments PS and QT respectively.

⇒ PR = ST

Coordinates of S and T are (x1, 0) and  (x2, 0) respectively.

OS =  x1 and OT = x2

ST = OT – OS = x2 – x1 = PR

Similarly,

PS =  RT

QR = QT – RT = QT – PS = y2 – y1

By Pythagoras theorem,

PQ2 = PR2 + QR2

PQ = √[(x2– x1)2+ (y2– y1)2]

Therefore,

Distance between two points (x1,y1) and (x2,y2) is given by:

[tex]\sqrt{{(y2-y1)^{2} } +(x2-x1)^{2}][/tex]

distance between (-1/2, -1) , (5/8, -1)

[tex]XY = \sqrt{{(-1-(-1))^{2} } +(5/8-(-1/2))^{2}]\\\\\\\\\\\\XY = \sqrt{9/16}\\\\\\XY = 3/4\\XY = .75\\[/tex]

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Answer:

That's probably false.

Answer: Can u pls help me withe my question?

Step-by-step explanation:

We get the inequality as:

There is no image to refer. So, here answering in general way.

Given,

The boundary line, y = -3x - 4

We can have 4 cases:

1) A dashed line and the shaded part is above the line.

y > -3x - 4

2) A dashed line and the shaded part is below the line

y < -3x - 4

Here we have dashed lines because the values of the line are not solutions for the inequality.

3) A solid line and the shaded part is above the line.

y ≥  -3x - 4

4) A solid line and the shaded part is below the line.

y ≤  -3x - 4

Here we have solid lines because the values in the line itself are solutions.

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Based on the amount that Luis earns per week, and the state flat rate income tax, Luis's state income tax for the week is $11.66

First, find out what Luis's earnings for the week were:

= Number of hours worked for the week x Earnings per hour

= 28 x 11.90

= $333.20

The state income tax is therefore:

= Amount earned weekly x State tax rate

= 333.20 x 3.5%
= $11.66

In conclusion, the state income tax of Luis for the week comes to an amount of $11.66.

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Answer:  4.1

Step-by-step explanation: You would do 8.2 m/2 because since 1cm =2m the opposite would be 2m = 1 cm so 8.2 = 4.1 because 2/2 = 1