Answer:
blank space=[tex]\frac{31}{2}[/tex]+[tex]\frac{13i}{2}[/tex]
The empty boxes which make the equation true are (22 -3i) - (15 + 9i)
= 7 - 12i.
What are complex numbers?As the name suggests it is a combination of real numbers and imaginary numbers.
A complex number (a + ib) where a is the real part and b is the imaginary part.
'i' here is called iota and i = √-1, i² = - 1, i³ = - i and i⁴ = 1.
Given, (_ -3i) - (15+_i) = 7 - 12i.
Assuming the real number to be 'a' and the imaginary number to be 'b'.
∴ (a - 3i) - (15 + bi) = 7 - 12i.
a - 3i - 15 - bi = 7 - 12i.
On comparing the real and imaginary parts we get,
a - 15 = 7.
a = 22,
- 3i - bi = - 12i.
- bi = - 9i.
b = 9.
learn more about complex numbers here :
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what is 5 cm in mm. i need a simple answer. NO LINKS
50 millimeters
keystrokes
Evaluate the indicated limit algebraically. Change the form of the function where necessary. Please write clearly with description of each step, thank you very much.
3x^2+4.5
________
x^2-1.5
lim
x → ∞
Answer:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]
Step-by-step explanation:
We want to evaluate the limit:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}[/tex]
To do so, we can divide everything by x². So:
[tex]=\displaystyle \lim_{x\to \infty}\frac{3+4.5/x^2}{1-1.5/x^2}[/tex]
Now, we can apply direct substitution:
[tex]\Rightarrow \displaystyle \frac{3+4.5/(\infty)^2}{1-1.5/(\infty)^2}[/tex]
Any constant value over infinity tends towards 0. Therefore:
[tex]\displaystyle =\frac{3+0}{1+0}=\frac{3}{1}=3[/tex]
Hence:
[tex]\displaystyle \lim_{x\to \infty}\frac{3x^2+4.5}{x^2-1.5}=3[/tex]
Alternatively, we can simply consider the biggest term of the numerator and the denominator. The term with the strongest influence in the numerator is 3x², and in the denominator it is x². So:
[tex]\displaystyle \Rightarrow \lim_{x\to\infty}\frac{3x^2}{x^2}[/tex]
Simplify:
[tex]\displaystyle =\lim_{x\to\infty}3=3[/tex]
The limit of a constant is simply the constant.
We acquire the same answer.
Jenny is dog sitting for 13 dogs. One runs away, and she is not sure which one. There were 3 Labradors (L), 2 Golden Retrievers (G), 3 Dalmatians (D), 4 terriers (T), and 1 bulldog (B) in the original group.
What is the size of the population of dogs that could have run away from Jenny?
1
5
11
13
Answer:
5
Step-by-step explanation:
It is 5 because she originally had 13. There are 5 types of dogs she was dog-sitting. There are 5 possible types of dogs that ran away.
What’s the answer to this question ?
Step-by-step explanation:
112=35+d
112-35=d
d=77
hope it helps u
(Photo is part one)Malik also adds the following ingredients. How many cups of each
did he add? Show each step of your solution.
• 28 tablespoons of sugar
• 6 tablespoons of cocoa powder
Answer:
Step-by-step explanation:
what are we looking for?/
It cost 5.50 for parking, plus an additional $8 for each concert ticket purchased. If joe starts off with a 50 dollar bill and buys 3 concert tickets and a 10$ T-shirt, how much money will he have left? PLEASE HELP
Answer:
$10.50
Step-by-step explanation:
50-[5.50+8(3)+10] =
50-39.50=
10.50
Answer:
$6.00
first multiply eight and three then add the two things joe bougth. then the answer minus 50
Check the pic please
With steps please
Answer:
Angle BOD = 75⁰
Step-by-step explanation:
Answer attached...
Hope it helps :)
If x3=125 and y3=8, what is the value of y−x
Answer:
X= 5
Y= 2
Y-X= 2-5= -3
PLEASE HELP ASAP ???
Answer:
-1
Step-by-step explanation:
help pls pls pls シ
And thanks!
Answer:
the answer the 10.25 u move both decimals over and move it up to the top and divide like normal
Three triangles are drawn on the same piece of paper such that no two sides are on the same line. What is the maximum number of points of intersection of the three triangles?
Answer:
6
Step-by-step explanation:
Write the log equation as an exponential equation. You do not need to solve for x. log(5x+2)=3
Answer:
So happy you are with brainly
Step-by-step explanation:
34
Please help I’ll mark you as brainliest if correct
Answer:
I think it is 75
Step-by-step explanation:
because you divide 45 by 3 to get 15 then 15 x 5 is 75:)
2- Describe the cross section
The cross-section cut by the plane yields a quadrilateral with length and width equal to the length and width of the face that is parallel to the plane.
What is the quotient of (x^3 + 8) divided by (x + 2)?
Answer:
(x^3 +8)/(x+2) = x^2 -2x +4
Step-by-step explanation:
pls help im so confused find m
Answer:
i think it is 47
Step-by-step explanation:
In a study of academic procrastination, the authors of a paper reported that for a sample of 451 undergraduate students at a midsize public university preparing for a final exam in an introductory psychology course, the mean time spent studying for the exam was 7.74 hours and the standard deviation of study times was 3.10 hours. For purposes of this exercise, assume that it is reasonable to regard this sample as representative of students taking introductory psychology at this university.
(a) Construct a 95% confidence interval to estimate μ, the mean time spent studying for the final exam for students taking introductory psychology at this university. (Round your answers to three decimal places.) TWO VALUES
(b) The paper also gave the following sample statistics for the percentage of study time that occurred in the 24 hours prior to the exam.
n = 451 x = 43.78 s = 21.96
Construct a 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam. (Round your answers to three decimal places.)
Answer:
a) The 95% confidence interval to estimate μ is (7.435, 8.045) hours.
b) The 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam is (41.079%, 45.481%).
Step-by-step explanation:
Question a:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{3.3}{\sqrt{451}} = 0.305[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 7.74 - 0.305 = 7.435 hours
The upper end of the interval is the sample mean added to M. So it is 7.74 + 0.305 = 8.045 hours.
The 95% confidence interval to estimate μ is (7.435, 8.045) hours.
Question b:
90% confidence interval means that [tex]Z = 1.645[/tex]
The margin of error is:
[tex]M = 1.645\frac{21.96}{\sqrt{451}} = 1.701[/tex]
43.78 - 1.701 = 41.079%
43.78 + 1.701 = 45.481%
The 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam is (41.079%, 45.481%).
Kathy bought 5 pencils for the price of $6.30. Which equation represents r, the cost, in dollars, of each pencil?
A.r=6.30+5
B.r = 6.30÷5
C.r=6.30×5
D.r=6.30−5
9514 1404 393
Answer:
B. r = 6.30÷5
Step-by-step explanation:
The cost per pencil is found by dividing the cost by the number of pencils.
Here, the cost is $6.30 and the number of pencils is 5. Then the cost per pencil (r) is ...
r = 6.30 ÷ 5
Pay the bill using the fewest possible bills/coins
Answers:
Open the pdf below and youll find what you need. also do the largest bills you can.
Write 3 ratios equivalent to 2/5
Answer:
4/10, 6/15, 8/20
Step-by-step explanation:
help please thanks plsss
Answer:
A
area = 256 inches²
side = √256 = 16 inches
B
0.0063 inch = 6.3 × 10^-3
The average weekly salary of two employees is $5250. One makes $500 more than the other. Find their salaries.
Answer: thier salaries are $5000 and $5500
Step-by-step explanation:
Let the average weekly salary of one employee be =x
And that of the other employee be = x+500
Such that if thier average of their salaries= $5250
So, their total salary= $5250 x 2=10,500
The equation to solve each employee salary becomes
x+x+500=10,500
2x+500=10,500
2x=10,500-500
2x=10,000
x=10,000 /2
x= first employee salary =$5000
second employee = x+500 =$5500
The ratio of the diameters of two similar cylinders is 4/5 What is the ratio of their surface areas? of their volumes?
Answer:
yo
Step-by-step explanation:
jy
Rewrite as an exponential equation.
In7 = y
What is equivalent to -2(x-5)?
Answer:
-2x+10
Step-by-step explanation:
-2(x-5)
Distribute
-2*x -2*-5
-2x+10
Plz help me well mark brainliest if you are correct!
Which of the following is false about the figure?
a. m CUD = m VUM
b. M AUV + m DUA = 180
c. m MUC - m MUD = mzCUD
d. m PUD + m VUP = m PUM + m_CUA
Answer:
d.
Step-by-step explanation:
Let's examine each statement:
Option A: m<CUD = m<VUM (CORRECT)
Rationale: vertical angles are congruent to each other.
Option B: m<AUV + m<DUA = 180 (CORRECT)
Rationale: angles on a straight line
Option C: m<MUC - m<MUD = m<CUD (CORRECT)
Rationale:
m<MUC = m<MUD + m<CUD
Subtract m<MUD from each side
m<MUC - m<MUD = m<CUD
Option D is FALSE
Rationale:
m<PUD + m <VUP = 180° (angles on a straight line)
m<PUM + m<CUA ≠ 180°
Therefore,
m<PUD + m<VUP = m<PUM + m<CUA IS FALSE.
Peter buried a treasure chest on a remote island and is.making a map so he can find it later. One of the key landmarks in the area is a small rectangle hut, 5m by 8m
Is this linear, exponential growth, exponential decay, or neither?
Answer:
exponential decay
Step-by-step explanation:
the y coordinates are getting smaller while x gets bigger so for 1x y is .5 then .25 then .125 etc..
What type of angles are <5 and <6?
A. Vertical angles
B. Alternate exterior angles
C. Supplementary angles
D. Alternate interior angles
Answer:
C
Step-by-step explanation:
Supplementary angles because their sum is 180 degrees