if [tex]i = \sqrt{-1}, what is i^3[/tex]i^3 equal to?

Answer:

43

Step-by-step explanation:

800 × 8% × (8/12)

Answer:

n - 4 = - 15

Step-by-step explanation:

Hope this helps :)

Answer:

In equation form it should be: (6-x) -11

Step-by-step explanation:

BOOM!!! Your Welcome

Answer:

Step-by-step explanation:

What are you trying to find? If you want to find x then:

5x = 134 - 9

5x = 125

x = 25

if you want square root then,

x = √625    or

x = 5^2

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

An empty set is subset of each and every possible set, as it has no elements in it, which is why the given statement is " True "

Answer: 9x^2-9x-10 ==> D

Step-by-step explanation:

(3x+2)(3x-5)=

3x*3x + (-5)(3x) + 2*3x + (-5)(2)=

9x^2 - 5(3x) + 6x - 5(2)=

9x^2-15x+6x-10=

9x^2-15x+6x-10= 9x^2-9x-10 ==> D

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

Explanation:

Let's make

y = 3x+2

So we can replace the (3x+2) with y

We go from (3x+2)(3x-5) to y(3x-5)

Distribute that y term through

y(3x-5)

y(3x) + y(-5)

3xy - 5y

Then plug in y = 3x+2 and distribute two more times

3xy - 5y

3x( y ) - 5( y )

3x( 3x+2 ) - 5( 3x+2 )

3x(3x) + 3x(2) - 5(3x) - 5(2)

9x^2 + 6x - 15x - 10

9x^2 - 9x - 10

which seems to point to choice D assuming the -9 in the middle is supposed to be -9x

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

Side note: Alternative methods are the FOIL rule and the box method.

Answer:

LCM = 240

GCF = 8

Step-by-step explanation:

Least common multiple (LCM) is the smallest number that both 40 and 48 go into

Greatest common factor (GCF) is the largest number that can go into 40 and 48.

Yes, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

Here,

The differential equation (1-xy)y' = y^2

And,  y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2.

What is Differential equation?

A differential equation is a mathematical equation that relates some function with its derivatives.

Now,

To show y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2, we have to find the solution of differential equation.

The differential equation is;

[tex](1-xy)y'=y^2\\\\\\\\[/tex]

[tex](1-xy) \frac{dy}{dx} = y^2[/tex]

[tex]\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }[/tex]

It is form of  [tex]\frac{dx}{dy} + Px = Qy[/tex],

Where, P is the function of y and Q is the function of x.

Hence, Integrating factor = [tex]e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y[/tex]

The solution is;

[tex]x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c[/tex]

[tex]xy = lny + c[/tex]

Take c = 0, we get;

[tex]xy = lny\\\\y = e^{xy}[/tex]

Hence, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

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The domain q is a set of real numbers as(0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50).

The range is going to be a set of real numbers from 0 to 6.

The domain of a function is the set of input values that we are allowed to plug into our function. This set is the x-values in a function.

The range of a function is the set of output values that the function assumes.

Now, we are told that there is a set of ordered pairs (q, T), where T is the total value of q quarters in dollars, up to $1.50 in quarters

Now, from conversions, we know that 1 quarters is equal to 0.25 dollar.

Thus, the domain q is a set of real numbers as(0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50).

The maximum output value will be; 1.5/0.25 = 6

Meanwhile, the range is going to be a set of real numbers from 0 to 6.

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Answer:It means you would have spent $36 below zero and now you owe the bank some money

Step-by-step explanation:

The circumference of a circle with radius, r = 9.5m is 19π

What is circumference of circle?

The perimeter of a circle or ellipse is its circumference. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

What does a circle's circumference mean?

The complete length of a circle's arc is known as its circumference. The circumference of the circle is another name for it. The radius of the circle is the distance measured from any point on the circle to its center.

Given,

radius of the circle = 9.5m

The formula to calculate the circumference is -

C = 2πr

where r = radius of the circle

⇒ 2 × π × 9.5

⇒ 19π

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Answer:

B

Step-by-step explanation:

Answer B is the result of simplifying

The transformed equation is:

F(x) = G(x + 2) = (x + 2)^2

So we can se that the correct option is D.

We know that the graph of F(x) has the same shape of G(x) = x^2, but shifted to the left 2 units.

Remember that for a random function f(x), a shift of 2 units to the left is written as:

h(x) = f(x + 2).

Then, in this case, we can write:

F(x) = G(x + 2)

Replacing G(x), we can get the transformed equation:

F(x) = G(x + 2) = (x + 2)^2

So we can se that the correct option is D.

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Answer:

54 as a percentage of 216% is 116.64.

Step-by-step explanation:

100% of 54 is 54 so 54 x 2 would be 108. We have solved 200% of it now for the 16%. The percentage of 54 of 16% would be 8.64. Now add up all we have learned.

108 + 8.64 = 116.64

Answer:

n = -0.4, or n = -2/5.

Step-by-step explanation:

They are the same btw.

True, ax=b requires only one solution to be homogeneous. If ax=b is consistent, the ax=b solution set is acquired by translating the ax=0 solution set.

A two-linear equation system can have one solution, an infinite number of solutions, or even no solution. The number of solutions distinguishes equation systems.

Some key features regarding the consistent are-

Therefore, if the equation ax=0 has a trivial solution, the columns of the a matrix A are linearly independent.

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The polynomial function will be y = (x⁴-14x³+70x²-144x+104)

2 and 5+i are the roots of the given polynomial and the multiplicity of 2 and 5+i are 2 and 1 respectively.

Thus, the general form of the polynomial will be given as:

y = (x-2)² (x-(5+i)) (x-(5-i))                                  [as (5-i) is conjugate of (5+i)]

y = (x²+4-4x) (x-5-i) (x-5+i)

y = (x²-4x+4) (x²-5x+xi-5x+25-5i-xi+5i-i²)

y = (x²-4x+4) (x²-10x+25+1)                                            [as i²= -1]

y = (x²-4x+4) (x²-10x+26)  

y = (x⁴-10x³+26x²-4x³+40x²-104x+4x²-40x+104)

y = (x⁴-14x³+70x²-144x+104)

Thus, the polynomial is y = (x⁴-14x³+70x²-144x+104)

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The equation for the parabola Is; y = -²/₅[(x + 5)(x - 1)]

We are given the following;

x-intercepts = (-5,0) and (1,0)

y - intercept = (0, 2)

We know that the x-intercepts are the roots of the quadratic equation while the y-intercept is the value of y when x is zero.

Thus;

(x + 5) and (x - 1) are factors of the given quadratic equation.

f(x) = a(x + 5)(x - 1)

At y-intercept of (0,2), we have;

a(0 + 5)(0 - 1) = 2

a = -2/5

Thus we can write the equation for the parabola as;

y = -²/₅[(x + 5)(x - 1)]

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We get the values of m as 1 and n as 0.

We are given a function:

f(x) = m / (x - 1) + n

We are also given that:

f (-2) = 1 and f (4) = 3

We have to find the value of m and n.

f (-2) = m (2 - 1) + n

1 = m + n

n = 1 - m

f (4) = m / (4 - 1) + n

3 = 3 m + n

3 = 3 m + 1 - m

3 = 2 m + 1

2 m = 3 - 1

2 m = 2

m = 2 / 2

m = 1

m + n = 1

1 + n = 1

n = 0.

Therefore, we get the values of m as 1 and n as 0.

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The correct family is option D.

To understand this problem we must be aware of the concept of addition and subtraction and also BODMAS rules which applies in an linear equation.

The numbers given here are 4,2 and 6.

We can see here that on adding 4 and 2 we get 6;

4+2=6

And on subtracting 2 from 6 we get 4;

6-2=4

Also we can see here that on subtracting 4 from 6 we get 2;

6-4=2.

These three relations are true for the given numbers.

And we can see that option D clearly fits the answer.

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Please check the image attached aside with the graph of the quadratic equation.

In this problem we have a quadratic equation, of which we should plot the graph by matching five points. We can make use of its vertex, two roots, y-intercept and other point. First, determine the vertex of the quadratic function:

- x² - 12 · x - (35 + y) = 0

x² + 12 · x + (35 + y) = 0

12² - 4 · 1 · (35 + y) = 0

144 - 4 · (35 + y) = 0

144 - 140 - 4 · y = 0

4 · y = 4

y = 1

- x² - 12 · x = 36

x² + 12 · x + 36 = 0

(x + 6)² = 0

x = - 6

The vertex of the quadratic equation is (x, y) = (- 6, 1).

Second, calculate the roots of the quadratic equation:

- x² - 12 · x - 35 = 0

x² + 12 · x + 35 = 0

(x + 5) · (x + 7) = 0

The roots of the quadratic equation are (x, y) = (- 5, 0) and (x, y) = (- 7, 0).

Third, determine the y-intercept of the quadratic equation:

y = - 0² - 12 · 0 - 35

y = - 35

The y-intercept of the quadratic equation is (x, y) = (0, - 35).

And fourth, find another point by evaluating the quadratic equation:

y = - 1² - 12 · 1 - 35

y = - 48

The remaining point is (x, y) = (1, - 48).

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Answer:

20 m/s

Step-by-step explanation:

speed = 100m /5s = 20 m/s

  = 72 km/hr

  = 72 km / hr *  1 mile / 1.609 km = 44.7 mph

The percentage increase in the student's height is 10.52%.

Here we are given that a student's height increases from 1.52m to 1.68m.

Thus, the absolute increase in the student's height will be-

1.68 - 1.52 = 0.16 meters.

Now, we need to find the percentage increase in the student's height.

The formula for calculating percentage increase is given by-

Percentage increase = change in value/ initial value * 100

Here, the change in value is 0.16 meters and the initial value is 1.52 meters.

Thus, percentage increase in height = 0.16 / 1.52 *100

= 1600/ 152

= 400/ 38

= 200/ 19

= 10.52%

Thus, the increase in the student's height is 10.52%.

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Answer:

9/7

Step-by-step explanation:

9 red for every 7 blue can't be reduced

The number of weeks that it will take Jason to have coins from all 195 countries is 24 weeks.

It should be noted that an equation is simply used in Mathematics to show the relationship the exist between different variables.

Let the number of weeks be represented by w.

Therefore, based on the information, the appropriate equation will be:

99 + (4 × w) = 195

99 + 4w = 195

4w = 195 - 99

4w = 96

Divide

w = 96/4

w = 24

Therefore, based on the calculation illustrated above, the number of weeks that it will take Jason to have coins from all 195 countries is 24 weeks.

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The correct option is A) The 99% confidence interval ranges from 53.73 to 56.27 hours.

The 99% confidence interval for the mean hours devoted to social networking in January ranges from 53.73 to 56.27 hours.

In statistics, a confidence interval denotes the likelihood that a population parameter would then fall between two specified values.

sample size 'n' =200

Mean 'x'  = 55 hours

Standard deviation (Population) = 7 hours

For 99% confidence level

Z critical value = 2.58

Margin of error = ±2.58(std error)

Now, compute the standard error

Standard error = 7/√n

              =7/√200

               = 0.495

Thus, margin of error = ±0.495(258) = 1.28

Now, calculate the Confidence interval;

Confidence interval = (55 - 1.28, 55 + 1.28)

                                  = (53.72, 56.28)

Confidence interval = (53.73, 56.27) [approx.]

Therefore, the confidence level lies between 53.73, 56.27) [approx.]

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The correct question is-

In a sample of 200 households, the mean number of hours spent on social networking sites during the month of January was 55 hours. In a much larger study, the standard deviation was determined to be 7 hours. Assume the population standard deviation is the same. What is the 99% confidence interval for the mean hours devoted to social networking in January?

A) The 99% confidence interval ranges from 53.73 to 56.27 hours.

B) The 99% confidence interval ranges from 7 to 55 hours.

C) The 99% confidence interval ranges from 54.51 to 55.49 hours.

D) The 99% confidence interval ranges from 55 to 60 hours.

The option that would complete the given expression is; Option B: 10 to the fourth power

We are told that Juliana wants to write the number twenty thousand, one hundred ninety in expanded notation.

This can be broken down as;

20,190

This can be broken further down into;

20000 + 100 + 90

Writing in expanded notation gives;

(2 * 10⁴) + (1 * 10²) + (9 * 10¹)

Thus, we can say that the option that would complete the given expression is; Option B: 10 to the fourth power

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