Tamara's claim that raising the complex number i to any integer power results in either -1 or 1 is incorrect. The powers of i follow a cyclic pattern which includes i, -1, -i, and 1.
Explanation:I must disagree with Tamara's statement that raising the complex number i to any integer power results in either -1 or 1. The powers of i actually follow a recurring pattern: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1, and then the pattern repeats.
For i to the power of 1, the result is just i itself.For i to the power of 2 (i^2), the result is indeed -1.For i to the power of 3 (i^3), the result is -i.For i to the power of 4 (i^4), the result is back to positive 1.So, while -1 and 1 are indeed in the sequence of results, they're not the only possibilities. Specifically, -i and i are also possible results of raising i to an integer power.
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(x 2 + 2x - 1)(x 2 + 2x + 5) Please help asap!
Your school drama club is putting on a play and hopes to raise $600 from ticket sales. They sell adult tickets for $8 each and student tickets for $5 each. Let x represent the number of adult tickets and y represent the number of student tickets. The equation to represent the number of tickets sold to reach their goal, 8x+ 5y = 600, is graphed below. If 40 adult tickets are sold, how many student tickets must be sold to reach their goal?
Diagram can be shown here:
https://static.k12.com/eli/bb/343/3_23939/2_15013_4_23943/d7066d09bfa7bf4e8df2b2c0b508a3e8ba21c76d/media/b1cd8381087979f1dffbcd6f3efef158a61fbd57/mediaasset_649354_1.gif
A bike ramp has a slope of 3/4. What is the angle the ramp makes with the ground?
There are seven black marbles and nine white marbles in a bag what is the aprroximate probability of drawing two black marbles and then a white marble without replacement
The approximate probability of drawing two black marbles and then a white marble without replacement is 9/80.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Number of black marbles = 7
Number of white marbles = 9
The event of drawing two black marbles from seven black marbles is
⇒ [tex]\frac{7C_{2} }{16C_{2} }[/tex]
[tex]7C_{2} =\frac{(7)(6)}{(1)(2)}[/tex]
⇒ 21
[tex]16C_{2}=\frac{(16)(15)}{(1)(2)}[/tex]
⇒ 120
Now, [tex]\frac{7C_{2} }{16C_{2} }=\frac{21}{120}[/tex]
Total number of balls, after drawing 2 black balls without replacement is
⇒ 16 - 2 = 14
The event of drawing a white marble without replacement from nine white marbles is
[tex]\frac{9C_{1} }{14C_{1} } = \frac{9}{14}[/tex]
Thus, the approximate probability of drawing two black marbles and then a white marble without replacement is
P(E) = [tex](\frac{21}{120}) (\frac{9}{14} )[/tex]
⇒ 9/80
Hence we can conclude that the approximate probability of drawing two black marbles and then a white marble without replacement is 9/80.
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Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall. He found a plane with an incline of 12 degrees that he could climb until he could get to an altitude of 100 m. How far should Galileo walk up the inclined plane? Round your final answer to the nearest hundredth.
Galileo walk 480.97 meters up the inclined plane if Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have:
Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters.
Let's suppose Galileo walked x meters up the inclined plane.
The plane with an inclined a 12°
As we can see in the right angle triangle the sin ratio:
[tex]\rm sin24\° = \frac{100}{x}[/tex]
[tex]\rm x = \frac{100}{sin24\°}[/tex]
x = 480.97 meters (Sin12° = 0.20791)
Thus, Galileo walk 480.97 meters up the inclined plane if Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
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helpppppppppppppppppppppppppp
Match each angle measure in degrees with its equivalent measure in radians
Answer:
Hm..
Step-by-step explanation:
PLEASE HELP ASAAAAPPPPPP
The following table gives the science scores and times spent studying for 10 students:
Name Scores (%) Time Spent
Studying (hrs)
Angela 90 4
Brad 70 2
Curt 80 3
Dozer 60 1
Enda 50 1
Frank 40 2
Gill 100 4
Hailey 100 3
Intra 50 1
John 80 3
Describe the correlation between the score and time spent studying.
As per the table, the given science scores and time data for studying about 10 hours are given.
A positive correlation can be seen between the number of hours spent studying and the scores. This states that the no. of hours of studying could be on the independent and the score would be the dependent quantity. When on the graph with the time studying on the x-axis and the y-axis gives you the graph the line seems to be going up hence a positive correlation.Learn more about the gives the science scores and times spent studying.
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Can someone please help me out on this?
32 to 28 is what percentage of what change an increase or decrease
PLEASE HELP ME ON THIS
The mean of the data set is 18 what’s the missing number 21,11,blank,27,22,13,16
9514 1404 393
Answer:
16
Step-by-step explanation:
The sum of the 7 numbers needs to be 7·18 = 126.
Then the missing number is ...
126 -21 -11 -27 -22 -13 -16 = 16
AC is tangent to circle O at A. If mBY =24, what is m
5. Write a conditional statement. Write the converse, inverse and contrapositive for your statement and determine the truth value of each. If a statement’s truth value is false, give a counterexample.
What is the correct definition of the third quartile of a data set?
A. The third quartile is all the numbers of the data set added together and divided by 3. B. The third quartile is the difference between the maximum and median. C. The third quartile is the median of the upper half of data in the data set. D. The third quartile is the mode of the upper half of data in the data set.
Option: C is the correct answer.
C. The third quartile is the median of the upper half of data in the data set.
Step-by-step explanation:We know that our data is divided into three quartiles:
1)
First quartile or lower quartile--
It is the median of the lower set of the data.
2)
Middle quartile or Median--
Median is the central tendency of the data and it always exist in the middle of the data set.
3)
Third quartile or upper quartile--
It is obtained by finding the median of the upper set of the data.
Hence, the answer is: Option: C
Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for what other family of functions?
Exponential
Linear
Rational
Polynomial
Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for the exponential family of function.
This comes from the definition of logarithm itself which says that a logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Let us illustrate this by way of an example. We know that 100 can be represented as [tex] 10^2 [/tex]. Here 10 is the base, 2 is the power and 100 is the given number. Therefore,
[tex] 10^2=100 [/tex]
Likewise, we can represent 1000 as [tex] 1000=10^3 [/tex]
Now, if we multiply [tex] 10^2 [/tex] and [tex] 10^3 [/tex] we will get: [tex] 10^2\times 10^3=10^{2+3}=10^5 [/tex]. We added the powers. Therefore, the logarithm of [tex] 10^5 [/tex] to the base 10 is 5.
Let us see if we will get the same result by using the rules of logarithms.
[tex] log(10^2\times 10^3)=log(10^2)+log(10^3)=2log(10)+3log(10)=2+3=5 [/tex]
As we can see we got the same result by using the logarithm and the exponential rule, thus, verifying our answer. Similar results can be obtained for other operations of the logarithmic rule.
The measure of a minor arc is equal to the measure of __________
A grocery store sells chili peppers at $2.04 for a dozen. At this rate, what's the cost per pepper? A. $0.17 B. $1.70 C. $0.07 D. $1.07
What is the vertex of the graph of y = x2 + 4x?
(–2, –12)
(–2, –8)
(–2, –6)
(–2, –4)
Answer:
(-2, -4)
Step-by-step explanation:
Let's remember how to calculate the vertex of a parabola:
If we have the equation of the parabola given in the form y = ax^2 + bx + c, the x-coordinate of the vertex is x = -b/2a. For the y-coordinate we just replace the x of the equation with -b/2a and do the calculation.
In this case, a = 1, b = 4, c = 0.
The x-coordinate of the vertex is x = -4/2*1 = -2
The y-coordinate is y = (-2) ^2 + 4*(-2) = 4 - 8 = -4
Therefore, the vertex is (-2, -4)
Line AB intersects line DF. Which statement shows that the two lines are perpendicular?
Line AB and line DF are on the same plane.
Line AB and line DF intersect only once.
Line AB and line DF intersect at a 90° angle.
Line AB and line DF intersect at a 180° angle.
what is the measure of AC?
Factor completely x2 - 8x + 16
A. (x+4)(x+4)
B. (x-4)(x-4)
C. (x+4)(x-4)
D. (x-2)(x-8)
Does anyone know what the system of equations for this would be?
Please help will give Brainliest!! 1.Find the length of line segment AB when A=(2, 0) and B=(2, 6)
2.Find the length of CD: C(12, -10) and D(0, -6)
3.Find the length of EF: E(-3, 2) and F(6, 2)
PLEASE HELP ME ON THIS
QUICKLY!!!!!!!!!!!!!!!!!
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Convert the fraction to decimal and decimal into the fraction 10.222
Answer:
10 and 222/1000
Step-by-step explanation:
A recipe calls for 1 1/2 cups of sugar. Alexis only has measuring cups that measuring cups that measure 1/4 cup. how many times will alexis have to fill the measuring cup?
Please help ASAP!! Super appreciated!!! <3
The table below shows the data collected on the number of car washes, y, each day since the Auto Spa opened, x.
Days Since Auto Spa Opened 0 20 40 60 80 100
Number of Car Washes 29 35 18 31 28 14
The owner of the new Auto Spa created a line of best fit for the data that can be modeled by the following equation.
y = -0.12x + 31.76
Match the slope and y-intercept with the correct description for the given situation.
titles
the number of cars washes on the day the Auto Spa opened
the ratio of car washes to the number of days since the Auto Spa opened
the number of car washes
the total number of days since the Auto Spa opened
the ratio in the number of days since the Auto Spa opened to the total profit
pair
y-intercept
slope
Answer:
The slope is the ratio of car washes to the number of days since Auto Spa opened; and the y-intercept is the number of car washes on the day the Auto Spa opened.
Step-by-step explanation: