Answer:
After solving we get [tex]\mathbf{i^3=-i}[/tex]
Option D is correct.
Step-by-step explanation:
We are given:
If [tex]i=\sqrt{-1}[/tex] we need to find the value of [tex]i^3[/tex]
Solving:
[tex]i=\sqrt{-1}[/tex]
Taking cube on both sides
[tex]i^3=(\sqrt{-1})^3\\[/tex]
We can write [tex]a^3= a^2.a^1[/tex] Using this for solving:
[tex]i^3=(\sqrt{-1})^2.(\sqrt{-1})\\We \ know \ (\sqrt{-1})^2 =- 1 \ and \ \sqrt{-1}=1 \\i^3=-1(i)\\i^3=-i[/tex]
So, after solving we get [tex]\mathbf{i^3=-i}[/tex]
Option D is correct.
A random sample of house sizes in major city has a sample mean of 1204.9 square feet and a sample standard deviation of 124.6 square feet. Use the Empirical rule to determine the approximate percentage of house sizes that lie between 955.7 and 1454.1 square feet. Round your answer to the nearest whole number (percent).
Answer:
95% of house sizes lie between 955.7 and 1454.1 square feet.
Step-by-step explanation:
The empirical rule formula states that:
68% of data falls within 1 standard deviations from the mean - between μ – σ and μ + σ .
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ
In the above question,
Mean (μ)= 1204.9 square feet
Standard deviation (σ) = 124.6 square feet.
We are to determine the approximate percentage of house sizes that lie between 955.7 and 1454.1 square feet.
Step 1
We have to find the number of standard deviation from the mean
μ – xσ
1204.9 - 124.6x = 955.7
1204.9 - 955.7 = 124.6x
249.2 = 124.6x
x = 249.2/124.6
x = 2
μ + xσ
1204.9 + 124.6x = 1454.1
124.6x = 1454.1 - 1204.9
124.6x = 249.2
x = 249.2/124.6
x = 2
Therefore from the calculation above, it is 2 standard deviations from the mean, hence: from the empirical formula above,
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ
Help me plzzz
A photograph measures eleven inches wide and fourteen inches long. The picture is enlarged to fit on a wall. If the new larger picture is 231 inches wide,how long is it?
-294 inches
-412.5 inches
-234 inches
-181.5 inches
Answer:
294 inches
Step-by-step explanation:
Similar figures have congruent corresponding angles and proportional corresponding sides.
The sum of 7 and the cube of a number.
Answer:
7+x3
Step-by-step explanation:
Sum means to add the addends together. A number is a word form of a variable, and you are cubing that number which is multiplying that number by itself three times.
.
There were 3 squirrels and 18 acorns on Josh's back porch. What was the ratio of squirrels to acorns? Enter your answer in reduced form.
Answer:
1 to 6
Step-by-step explanation:
the ratio is found by dividing 18 by 3 which is 6.
basically, one squirrel per 6 acorns
what is the slope of (0,0) , (3,3)
Answer:
The slope is 1
Step-by-step explanation:
[tex]\frac{3-0}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1
Solve the system of equations by substitution.
3x+y = 10
7x+ 2y= 24
A. (2,4)
B. (2,-6)
C. (4,-2)
D. (2,-4)
If you can, explain step by step please :)
Answer:
C
Step-by-step explanation:
3x+y=10---(1)
7x+2y=24---(2)
From(1)
3x+y=10
y=10-3x---(3)
Substitute(3)into(2)
7x+2y=24
7x+2(10-3x)=24
7x+20-6x=24
x+20=24
x=24-20
x=4
Substitute x=4 into (1)
3x+y=10
3(4)+y=10
12+y=10
y=10-12
y=-2
Solve for x. Round to the nearest tenth.
Answer:
x = 9.6
Step-by-step explanation:
In a certain Algebra 2 class of 24 students, 9 of them play basketball and 13 of them
play baseball. There are 2 students who play both sports. What is the probability that
a student chosen randomly from the class plays basketball or baseball?
The probability that a student who is chosen randomly from the class who plays basketball or baseball is 11/24.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that In a certain algebra 2 class of 24 students, 9 of them play basketball and 13 of them play baseball. There are 2 students who play both sports.
2+5+4 =11
Expect the 13 people/students who didn't play,
Total people 24
P = 24-13=11
P = 11/24
The probability will be equal to 11/24.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
Write the equation of the line that has a slope of 8 and passes through the point (9, -1).
Answer:
Y=8x-9
Step-by-step explanation:
Let v represent the value of a bank acount, in thousands of dollars, t yearsaftertye account is opend at the bank
Answer:
could you explain it more
Step-by-step explanation:
If you went to a store
and you paid 80% of the
price of a jacket, what
percent was the jacket
discounted?
Answer:
is it 20% I'm not really sure
Answer:
$71.74
Step-by-step explanation:
Given:
Old price of the jacket = $ 80
Discount = 15 %
Therefore, discounted price =
Now, sales tax = 5.5 % on discounted price =
Therefore, the new price of the jacket after discount and paying sales tax is given as:
New price = Discounted price + Sales tax
New price = $ 68 + $ 3.74 = $ 71.74
So, the new price of the jacket is $ 71.74.
Martha made 5 out of 6 free throws, Mary made 7 out of 8. Who is the better
shooter? Explain completely?
Answer:
Mary
Step-by-step explanation:
just do it trust me
Find the missing length.
9)
?
5
14
(Click on the picture)
Can anyone please help me with the last question I’m struggling!
The equation is x=-6
Step-by-step explanation:
In standard form the equation is y=4
And this is a horizontal line so the perpendicular line will be a vertical line of the form x=a
so that is why the equation is x=-6
Answer:
= -5
Step-by-step explanation:
Which of the following best describes the graph of the polynomial function below ?
Answer:
Presumably when they refer to the number of zeros, they're talking about co-ordinates with a y value of zero. In that case, the answer is C, The graph has no zeros.
Find the inverse: f(x) = 4 + 4/5 x.
Answer:
f−1(x)=5x4−5
Step-by-step explanation:
To find the inverse, interchange the variables and solve for y.
How many solutions does the equation 4x + 8 = -2 - 2 + 5x have? (5 points)
Two
One
None
Infinitely many
Answer:
i believe it only has one solution, which would be x=12.
Step-by-step explanation:
Answer:
write Then finding matrix the system as a matrix equation, solve a matrix equation by the inverse of the coefficient , S 4X-5v=lle 25x-ley=19 X-ley= 19
Step-by-step explanation:
its in answer
if f(x) = x^2 + 2, which interval describes the range of this function
The interval which describes the range of the provided function x^2 + 2 is negative infinity to two (-∞,2).
What is domain and range of function?
Domain of a function is the set of all the possible input values which are valid for that function. Range of a function is the set of all the possible output values which are valid for that function.
The given function is,
[tex]f(x) = x^2 + 2[/tex]
The domain of this function is all real numbers. As the quadratic function has the constant value of 2. The vertex of the function is at 0,-2. Thus, the range of this function is,
[tex]y\in R, y\geq -2[/tex]
Thus, the interval which describes the range of the provided function x^2 + 2 is negative infinity to two (-∞,2).
Learn more about the range of the function here;
https://brainly.com/question/2264373
#SPJ2
Item 2
Find the area of the trapezoid.
b1=4,b2=8,h=2
ASAP TIMED WILL GIVE 35 POINTS>
Answer:
12 units squared.
Step-by-step explanation:
The formula for the area of a trapezoid is 1/2(base1+base2)*height. First, add the two bases together. 4+8=12. Then multiply that number by both 1/2 and the height, 2. 1/2*2*12 equals 12 units squared.
Which expression best estimates
– 184-2į?
O 18-3
-18-3
0-18-(-3)
O 18-(-3)
Click the photo to find the measure of each interior angle of the regular polygon
==============================================
Work Shown:
n = number of sides = 6
i = measure of interior angle
i = 180(n-2)/n
i = 180(6-2)/6
i = 180(4)/6
i = 720/6
i = 120
Each interior angle of this regular hexagon is 120 degrees.
-----------------
Alternative Approach:
E = exterior angle
E = 360/n
E = 360/6
E = 60
Each exterior angle of this regular hexagon is 60 degrees
i+E = 180
i = 180-E
i = 180-60
i = 120
We get the same answer.
The graph show the ratio of pencils to pens sold at the school bookstore. If the bookstore sells 15 pencils, how many pens does it sell?
just look at the graph fam its 18 pens
How to find inequalities
Answer:
Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.
Step 2 Simplify by combining like terms on each side of the inequality.
Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.
Hope that helped happy holidays!
Veronica is choosing between two health clubs. After how many months will the total cost for each health club be the same? Yoga studio A (Membership: $22.50 and monthly: $24.50) Yoga studio B (Membership: $47.00 and monthly: $18.25)
PLEASE ANSWER ASAP FOR 35 POINTS :)
Answer:
4 months
Step-by-step explanation:
Answer:
4 months
Step-by-step explanation:
determine whether the relationship is a function or not a function.
Answer
not a function
Step-by-step explanation:
Answer:
kk
Step-by-step explanation:
ok
Write the prime factorization of 12. Use exponents when appropriate and order the factors from least to greatest (for example,22•3•5)
Answer:
the answer is 2×2×3 I think
3. Find the annual salary for Kathy if she is paid $2.100 every other week.
Annual Salary = Biweekly Salary * 26
The Chin family is having new carpet installed in the dining room. The carpet costs $249 for installation and $9 for each square yard. It cost the Chin family $465 to carpet the dining room.
Answer:
The Chine family installed 24 square yards
Step-by-step explanation:
Make an equation:
$249 prior to installing carpet
$9: per square yard, 9 can be represented as 9x because we don't know how many square yards are being installed
$465: total spent
9x + 249 = 465
subtract 249 from 465
then divide 9 by whatever 249 - 465 equals
ok so i know that you want brainleist but pls answer first?!
Step-by-step explanation:
[tex]Expression: \frac{40}{y - 16} [/tex]
[tex]When \: y=20, \: the \: value \: of \: the \: expression \: is \: \frac{40}{4} = 10 [/tex]
SOMEONE PLEASEE SOLVE!!
4√-88
Answer:
37.5*i
Step-by-step explanation:
4√88*√-1
4*(9.4)*i
37,7*i