Answers
Answer:
[tex]-i[/tex]
Step-by-step explanation:
Imaginary numbers
Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].
Given expression:
[tex]i^{31}[/tex]
Rewrite 31 as 30 + 1:
[tex]\implies i^{30+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies i^{30} \cdot i^1[/tex]
[tex]\implies i^{30}i[/tex]
Rewrite 30 as 2 · 15:
[tex]\implies i^{(2 \cdot 15)}i[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left(i^2\right)^{15}i[/tex]
[tex]\textsf{Apply\:imaginary\:number\:rule}\quad \:i^2=-1:[/tex]
[tex]\implies \left(-1\right)^{15}i[/tex]
As -1 to the power of an odd number is -1:
[tex]\implies -1 \cdot i[/tex]
[tex]\implies -i[/tex]
Related Questions
When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23. Find the value of the lesser integer.
Answers
The value of the lesser integer is 5.
According to the question,
We have the following information:
When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23.
Let's take the lesser integer to be x.
So, the next consecutive odd integer is (x+2).
Now, we have:
4(x+2)-x = 23
4x+8-x = 23
3x+8 =23
3x = 23-8
3x = 15
x = 15/3
(3 was in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 5
Hence, the lesser integer in the given situation is 5.
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hello, in the picture you can see a graph and my teacher said that the domain and range would be all real numbers possible. could you please help me because I don't understand why.
Answers
The domain is all the values of the independent variable (in this case, x) for which the function is defined.
In this case, as it is indicated with the arrows in both ends, the function continues for greater and smaller values of x.
As there is no indication that for some value or interval of x the function is not defined (a discontinuity, for example), then it is assumed that the function domain is all the real values.
Example function:
We have the function y=1/(x-2)
We can look if there is some value of x that makes the function not defined.
The only value of x where f(x) is not defined is x=2. When x approximates to 2, the value of the function gets bigger or smaller whether we are approaching from the right or from the left.
Then, the function is not defined for x=2. So, the domain of f(x) is all the real numbers different from x=2.
The domain is, by default, all the real numbers, but we have to exclude all the values of x (or intervals, in some cases like the square roots) for which f(x) is not defined.
Can you Convert 840 inches to cm. Use unit analysis to convert the rate.
Answers
we know that
1 in=2.54 cm
so
840 in
Applying proportion
1/2.54=840/x
x=(840*2.54)/1
x=2,133.6 cm
answer is
2,133.6 cmApplying unit rate or unit analysiswe have
2.54 cm/in
Multiply by 840 in
2.54*(840)=2,133.6 cm40/
A 90% confidence interval for a proportion is found to be (0.52, 0.58). What isthe sample proportion?
Answers
A 90% confidence interval for a proportion is given as (0.52,0.58).
It is required to find the sample proportion.
Recall that for confidence interval (x,y), the sample proportion is the midpoint:
[tex]c=\frac{x+y}{2}[/tex]Substitute x=0.52 and y=0.58 into the equation:
[tex]c=\frac{0.52+0.58}{2}=\frac{1.1}{2}=0.55[/tex]The answer is C.
33Select the correct answer from each drop-down menu.A75°B40°AoIn the figure, line segment AB is parallel to line segment CD.СDdegreesThe measure of angle Cisdegrees, and the measure of angles Dis>254075ResetNext
Answers
Answer:
Angle C = 40 degrees
angle D = 75 degrees
Explanation:
From the information given,
Angle A = 75 degrees
Angle B = 40 degrees
AB is parallel to CD. This means that AD and BC are transversals.
Angles A and D have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
angle D = 75 degrees
Angles B and C have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,
Angle C = 40 degrees
the table below shows the attendance and revenue at theme parks in the us
Answers
Let
y ------> the year
x ----> revenue
so
Plot the given ordered pairs
see the attached figure
(please wait a minute to plot the points)
In the graph the x-coordinate 0 represent year 1990
Find out the equation of the line
take two points
(1990, 5.7) and (2006, 11.5)
Find the slope m
m=(11.5-5.7)/(2006-1990)
m=5.8/16
m=0.3625
Find the equation of the line in slope intercept form
y=mx+b
we have
m=0.3625
point (1990, 5.7)
substitute and solve for b
5.7=(0.3625)(1990)+b
b=-715.675
therefore
y=0.3625x-715.675What is the answer to 6x + =5
Answers
Answer:
x = 5/6 or x = 0.83
Step-by-step explanation:
6x + =5
6x + 0 = 5
6x = 5
6x/6 = 5/6
x = 5/6 or x = 0.83
alex was late on his property tax payment to the county. he owed $6,915 and paid the tax 9 months late. the county charges a penalty of 5% simple interest. find the amount of the penalty. (round to the nearest cent as needed)
Answers
We have to use the simple interest formula.
[tex]A=P(1+rt)[/tex]Replacing the given information, we have.
[tex]\begin{gathered} A=6,915(1+0.05\cdot\frac{9}{12}) \\ A=6,915(1.0375) \\ A=7,174.31 \end{gathered}[/tex]The final amount is $7,174.31, where the penalty is $259.31.second number when the list is sorted from greatest to least
Answers
5.2% = 0.052
1/7 = 0.14
-11/5 = -2.2
From the greatest to least:
[tex]0.14>0.052>-0.8>-2.2[/tex]The second number is: 5.2%
Answer:
5.2%
I need help with this practice problem The subject is trigonometry
Answers
SOLUTION
The range of the function is given as:
[tex](-\infty,-9\rbrack\cup\lbrack5,\infty[/tex]The asymptote of the function is at points
[tex]x=0,x=2\pi[/tex]The function is shown in the graph below
Therefore, the equation of the session is
[tex]f(x)=7\csc (\frac{x}{2})-2[/tex]Identify the function rule from the values in the table.
Answers
we are given a table of inputs and ouputs of a function. We notice that each output is obtained by multiplying the input by -4:
[tex]\begin{gathered} (-2)(-4)=8 \\ (0)(-4)=0 \\ (1)(-4)=-4 \\ (3)(-4)=-12 \end{gathered}[/tex]Therefore, the right answer is A.
24. How many gallons of ethanol are in a 100 gal mixture that is 10%
ethanol?
Answers
By working with percentages, we will see that there are 10 gallons of ethanol in the mixture.
How many gallons of ethanol are in the mixture?We know that we have a mixture with a volume of 100 gallons, and 10% of that mixture is ethanol, so we just need to find the 10% of 100 gallons.
To work with percentages, we will use the equation:
Volume of ethanol = total volume*ratio of ethanol.
V = 100gal*(10%/100%)
V = 100gal*0.10 = 10 gal
There are 10 gallons in the mixture.
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I have the answers for 1 and 2 3. Use your answers from # 1 and # 2 to find the length of each arc between gondola cars . Use 3.14 for and round to the nearest hundredth . You must write out all the numbers you are multiplying together meaning show your work for full credit . ( 5 points ) Central angle = 8°Radius = 95 ft
Answers
The length of an arc = 13.26 ft
Explanation:The length of an arc is given by the formula:
[tex]\begin{gathered} l=\frac{\theta}{360}\times2\pi r \\ \end{gathered}[/tex]Substitute θ = 8°, r = 95 ft, and π = 3.14 into the formula
[tex]\begin{gathered} l=\frac{8}{360}\times2\times3.14\times95 \\ \\ l=13.26\text{ ft} \end{gathered}[/tex]The length of an arc = 13.26 ft
a carpentar has 16 1/2m of wood he cuts the wood into peices that are each 2 3/4m long PLSSSSS HURRY!!!!!!!!
Answers
The most appropriate choice for fraction will be given by
6 pieces of wood are cut by the carpenter
What is a fraction?
Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
Total length of wood = [tex]16\frac{1}{2}[/tex] m
= [tex]\frac{33}{2}[/tex] m
Length of one piece of a wood = [tex]2\frac{3}{4}[/tex] m = [tex]\frac{11}{4}[/tex]
Number of pieces of wood cut by carpenter = [tex]\frac{33}{2}[/tex] ÷ [tex]\frac{11}{4}[/tex]
= [tex]\frac{33}{2}[/tex] [tex]\times \frac{4}{11}[/tex]
= 6
6 pieces of wood are cut by the carpenter
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Hunter has $300 in a savings account. The interest rate is 8%, compounded annually.To the nearest cent, how much will he have in 3 years?
Answers
EXPLANATION
If Hunter has $300 in savings and the interest rate is 8%, compounded annualy, we can apply the following equation:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where, P=Principal=300, r=rate (in decimal form) = 8/100 = 0.08, n=number of compounded times = 1 and t = time = 3
Substituting terms:
[tex]A=300\cdot(1+\frac{0.08}{1})^{1\cdot3}[/tex]Adding numbers:
[tex]A=300\cdot(1.08)^3[/tex]Computing the powers:
[tex]A=300\cdot1.26[/tex]Multiplying numbers:
[tex]A=378[/tex]In conclusion, there will be 378.00 in three years
1. Are these ratios equivalent? 8:7 and 4:2
Answers
EXPLANATION
The answer is no, because 8:7 and 4:2 are different relationships.
The given pair of triangles are similar. Find X and Y.
Answers
Given that the pair of triangles are similar, then their corresponding sides are in proportion, this means that:
[tex]\frac{\text{longer leg of the triangle on the left}}{\text{shorter leg of the triangle on the left}}=\frac{\text{longer leg of the triangle on the right}}{\text{shorter leg of the triangle on the right}}[/tex]Substituting with the information of the diagram:
[tex]\frac{27}{x}=\frac{x}{9}[/tex]Cross multiplying:
[tex]\begin{gathered} 27\cdot9=x\cdot x \\ 243=x^2 \\ \sqrt[]{243}=x \\ 15.58\approx x \end{gathered}[/tex]Considering the triangle on the left, and applying the Pythagorean theorem with c = y (the hypotenuse), a = 27, and b = x (the legs), we get:
[tex]\begin{gathered} c^2=a^2+b^2 \\ y^2=27^2+x^2 \\ y^2=729+243 \\ y^2=972 \\ y=\sqrt[]{972} \\ y\approx31.18 \end{gathered}[/tex]
15. I need help on this question. How do you do it?
Answers
Solution:
Given the expression:
[tex]-5^2[/tex]This expression is evaluated as
[tex]\begin{gathered} -5\text{ multiplied in 2 places} \\ \Rightarrow-5\times-5 \\ =25 \end{gathered}[/tex]Hence,
[tex]-5^2[/tex]is evaluated to be 25
Add or subtract. Simplify. Change the answers to mixed numbers, if possible.
Answers
Answer:
[tex]\begin{gathered} \frac{1}{8} \\ \\ \text{LCD = 8} \end{gathered}[/tex]Explanation:
Here, we start by finding the lowest common denominator
From what we have, the lowest common denominator is the lowest common multiple of both denominators which is equal to 8
We divide the first denominator by this and multiply the result by its numerator. We take the same step for the second denominator
Mathematically, we have it that:
[tex]\frac{11-10}{8}\text{ = }\frac{1}{8}[/tex]given the function r(t)=t^2, solve for r(t)=4
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
r(t)=t^2
r(t)=4
t = ?
Step 02:
r(t)=4
t ² = 4
t = √4
t = 2
The answer is:
t = 2
Answer: t=2
Step-by-step explanation:
Because we know that for some value of t, r(t)= 4, and for ALL values of t, r(t)= t^2, then we know for some value of t, that t^2 = 4.
Based off of this information, we can take the square root of both sides, resulting in this equation.
t = [tex]\sqrt{4}[/tex]
This can be simplified.
t=2
This graph shows the solution to which inequality?3.2)(-3,-5)O A. ys fx-2B. vfx-2O c. vfx-2OD. yzfx-2
Answers
First, find the equation of the line, given that the points (3,2) and (-3,-6) belong to that line. To do so, use the slope formula and then substitute the value of the slope and the coordinates of a point on the slope-point formula of a line:
[tex]y=m(x-x_0)+y_0[/tex]The slope of the line, is:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{(2)-(-6)}{(3)-(-3)} \\ =\frac{2+6}{3+3} \\ =\frac{8}{6} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, the equation of a line (using the point (3,2)) is:
[tex]\begin{gathered} y=\frac{4}{3}(x-3)+2 \\ =\frac{4}{3}x-\frac{4}{3}\times3+2 \\ =\frac{4}{3}x-4+2 \\ =\frac{4}{3}x-2 \end{gathered}[/tex]Since the colored region on the coordinate plane is placed above the line
y=(4/3)x-2, then the equation of the inequality is:}
[tex]undefined[/tex]the price of a gallon of unleaded gas has risen to $2.92 today. yesterday's price was $2.85. find the percentage increase. round to the nearest 10th of a percent
Answers
Given:
[tex]\begin{gathered} P_{\text{today}}=2.92,P_{today}=Price\text{ of a gallon of unleaded gas today} \\ P_{\text{yesterday}}=2.85, \\ P_{yesterday}=Price\text{ of a gallon of unleaded gas today} \end{gathered}[/tex]To Determine: The percentage increase round to the nearest 1oth of a percent
The formula for percentage increase is given below:
[tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ In\text{crease}=P_{final}-P_{in\text{itial}} \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} P_{\text{yesterday}}=P_{i\text{nitial}}=2.85 \\ P_{\text{today}}=P_{\text{final}}=2.92 \\ \text{Increase}=2.92-2.85=0.07 \end{gathered}[/tex][tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ P_{in\text{crease}}=\frac{0.07}{2.85}\times100\% \\ P_{in\text{crease}}=0.02456\times100\% \\ P_{in\text{crease}}=2.456\% \\ P_{in\text{crease}}\approx2.5\%(nearest\text{ 10th)} \end{gathered}[/tex]Hence, the percentage increase to the nearest 10th of a percent is 2.5%
3. The number line below represents the solution to which inequality of he 0 1 2 3 4 5 6 7 8 9 10
Answers
let x be the money daniel has. So we get that
[tex]x\ge72+15\rightarrow x\ge87[/tex]Daniel has at least $87
Please help asap will give Brainly!!!
Answers
The following completes the proof: D. The Alternate Interior Angles Theorem shows that the angles BAC and DCA are congruent.
The Alternate Interior Angles Theorem: What is it?
According to the alternate interior angles theorem, when a transversal cuts over two (2) parallel lines, the alternate interior angles that are created are congruent.
We can infer and logically derive from the Alternate Interior Angles Theorem that the sentence that correctly concludes the proof is that angle BAC and angle DCA are congruent.
Segment AB is parallel to segment DC, while segment BC is parallel to segment AD, according to the information provided. Create the diagonals A and C using a straight edge. By virtue of the Reflexive Property of Equality, it is congruent to itself.
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20 P1: a For two events, A and B.P(B) -0.5, P(AB) -0.4 andPAB) = 0.4.Calculatei PAB)ii P(A)ili P(AUB)iv P(AB)(8 marks)b Determine, with a reason, whetherevents A and B are independent ornot.(2 marks)probabilityStatistics and
Answers
We have two events A and B.
We know that:
P(B) = 0.5
P(A|B) = 0.4
P(A∩B') = 0.4
i) We have to calculate P(A∩B).
We can relate P(A∩B) with the other probabilities knowing that:
[tex](A\cap B)\cup(A\cap B^{\prime})=A[/tex]So we can write:
[tex]P(A\cap B)+P(A\cap B^{\prime})=P(A)[/tex]We know P(A∩B') but we don't know P(A), so this approach is not useful in this case.
We can try with the conditional probability relating P(A∩B) as:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]In this case, we can use this to calculate P(A∩B) as:
[tex]\begin{gathered} P(A\cap B)=P(A|B)P(B) \\ P(A\cap B)=0.4*0.5 \\ P(A\cap B)=0.2 \end{gathered}[/tex]ii) We have to calculate P(A) now.
We can use the first equation we derive to calculate it:
[tex]\begin{gathered} P(A)=P(A\cap B)+P(A\cap B^{\prime}) \\ P(A)=0.2+0.4 \\ P(A)=0.6 \end{gathered}[/tex]iii) We have to calculate P(A∪B).
We can use the expression:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=0.6+0.4-0.2 \\ P(A\cup B)=0.8 \end{gathered}[/tex]iv. We can now calculate P(A|B') as:
[tex]\begin{gathered} P(A)=P(A|B)+P(A|B^{\prime}) \\ P(A|B^{\prime})=P(A)-P(A|B) \\ P(A|B^{\prime})=0.6-0.4 \\ P(A|B^{\prime})=0.2 \end{gathered}[/tex]b) We now have to find if A and B are independent events.
To do that we have to verify this conditions:
[tex]\begin{gathered} 1)P(A|B)=P(A) \\ 2)P(B|A)=P(B) \\ 3)P(A\cap B)=P(A)*P(B) \end{gathered}[/tex]We can check for the first condition, as we already know the value:
[tex]\begin{gathered} P(A|B)=0.4 \\ P(A)=0.6 \\ =>P(A|B)P(A) \end{gathered}[/tex]Then, the events are not independent.
Answer:
i) P(A∩B) = 0.2
ii) P(A) = 0.6
iii) P(A∪B) = 0.8
iv) P(A|B') = 0.2
b) The events are not independent.
The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
Answers
Ticket price as a function of time. If you write the number [tex]2040[/tex] where you see [tex]x[/tex] in this function and take the value where you see [tex]y[/tex], you will reach the correct answer.
[tex]y=1.83(2040)-2225.5[/tex][tex]y=1507.7[/tex]Solve 39 - 5 = 13 for q.q=
Answers
We are given the following equation:
[tex]3q-5=13[/tex]We are asked to solve for "q". To do that, we will first add "5" on both sides, like this:
[tex]\begin{gathered} 3q-5+5=13+5 \\ 3q=18 \end{gathered}[/tex]Now we will divide by 3 on both sides, like this:
[tex]\begin{gathered} \frac{3q}{3}=\frac{18}{3} \\ q=6 \end{gathered}[/tex]Therefore, the value of q is 6.
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Oaks Hardware purchases an extension ladder list priced at $120. It is available at a 15% discount. What is the available price?
Answers
A 15% discount means that the retail price is 85% of the original price.
To calculate said retail price, we'll use a rule of three:
Thereby,
[tex]x=\frac{120\cdot85}{100}\rightarrow x=102[/tex]Therefore, we can conclude that the available price is $102
the product of (2-x)and (1-x)is equal to x^2-3x+2
Answers
So the product of (2-x) and (1-x) is equal to x^2 - 3x + 2
The function, f. is drawn on the accompanying set of axes. On the same set of axes, sketch the graph of f-?, the inverse of f
Answers
We are given the following graph:
The inverse of the graph is shown below: