[tex]\frac{11z}{z+3}=13-i,z\in\mathbb{C}[/tex]
First, multiply both sides by [tex]z+3[/tex],
[tex]11z=(13-i)(z+3)[/tex]
[tex]13z+39-iz-3i=11z[/tex]
Collect terms and put z on the left,
[tex]2z-iz=3i-39[/tex]
[tex]z(2-i)=3i-39[/tex]
[tex]z=\frac{3i-39}{2-i}[/tex]
Division of complex numbers is defined by multiplying both denominator and numerator with complex conjugate of the denominator,
[tex]z=3\frac{(i-13)(2+i)}{(2-i)(2+i)}[/tex]
Multiply out,
[tex]z=3\frac{2i-1-26-13i}{5}[/tex]
[tex]z=3\frac{-11i-27}{5}[/tex]
The result is,
[tex]z=-\frac{81}{5}-\frac{33}{5}i[/tex]
Hope this helps :)
According to the U.S. National Center for Health Statistics, there is a 98% probability that a
20-year-old male will survive to age 30.
(a) Using statistical software, simulate taking 100 random samples of size 30 from this
population.
(b) Using the results of the simulation, compute the probability that exactly 29 of the 30 males
survive to age 30.
(c) Compute the probability that exactly 29 of the 30 males survive to age 30, using the
binomial probability distribution.
(d) Using the results of the simulation, compute the probability that at most 27 of the 30 males
survive to age 30.
(e) Compute the probability that at most 27 of the 30 males survive to age 30 using the
binomial probability distribution.
(f) Compute the mean number of male survivors in the 100 simulations of the probability
experiment. Is it close to the expected value?
(g) Compute the standard deviation of the number of
male survivors in the 100 simulations of the probability experiment. Compare the result to the
theoretical standard deviation of the probability distribution
Answer:
0.03398 or 3.398%
Step-by-step explanation:
-This is a binomial probability problem.
-Given p=0.24, n=100, the probability that exactly 30 people is calculated as:
Hence, the probability that exactly 30 people have hypertension is 0.03398
Use the information angle 8 is congruent to angle 11 to determine which lines are parallel.
A. p || q
B. l || m
C. m || n
D. l || n
Answer:
A
Step-by-step explanation:
based on line p and q
Answer: p || q
Or A
Step-by-step explanation:
good luck
if logx27 + logy4 =5
and logx27 - logy4 =1
find x and y
Answer:
Hello,
I have reply too quick in comments (sorry)
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}log_x (27)+log_y (4)=5\\log_x (27)-log_y (4)=1\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}2*log_x (27)=6\\2*log_y (4)=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}log_x (27)=3\\log_y (4)=2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x^{log_x (27)}=x^3\\y^{log_y (4)}=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}27=x^3\\4=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x=3\\y=2\\\end{array}\right.\\\\[/tex]
help please! willing to give brainly and 5 stars
Answer:
The answer is 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
2/5x-8/5y+x+½y
2/5(1)-8/5(-6)+1+½(-6)
2/5+48/5+1-3
10-2
8
a farmer produced 47581 2 oranges of one kind and 651 65 oranges of another kind He mixed these oranges and packed in 296 boxes how many oranges did he pack in a box?
Step-by-step explanation:
I am not sure the scanning of the text went well, as this has some strange gaps in the numbers.
I understand that we have 475812 oranges of one type and 65165 oranges of another type.
we have no information, if these types of oranges have significantly different sizes or weight. so, we have to assume that they are reasonably equal to each other.
therefore, the "different type" statement is just to confuse us. the text could have also said that these were 2 different truck loads of the same type.
we only need to deal with the total number of oranges.
so,
475812 + 65165 = 540977 total oranges
he packs them into 296 boxes.
that makes
540977 / 296 = 1827.625 oranges per box.
these are many oranges for one box in real life.
and it is not a round number, which is strange for a home work or test question if this type.
if the farmer truly put only the same number of oranges in every box, he would have
540977 - 1827×296 = 540977 - 540792 = 185
oranges left over.
in any case, these are all signs that there was probably something wrong with the text. but you see the principle up there. please do the same thing with the real numbers.
Numbers of one kind oranges=475812
No of other kind oranges=65165Total oranges
[tex]\\ \sf\longmapsto 475812+65165=540977[/tex]
Total boxes=296Oranges per box:-
[tex]\\ \sf\longmapsto \dfrac{540977}{296}=1827.6[/tex]
[tex]\\ \sf\longmapsto 1827(Approx)[/tex]
A principal of $4000 is placed in a savings account at 6% per annum compounded annually. How much interest is earned in the account after three years
The interest earned in the account after three years is $720.
The formula for simple interest= P×T × R/100
Principal (P) = $4000
Time( T) = 3 years
Rate(R) = 6%
interest(I)= 4000×3 × 6/100
I = 72000 ÷ 100
I = 720
Therefore, the interest earned in the account after three years is $720.
Learn more about simple interest here:
https://brainly.com/question/19705587
There was 1500ml of orange juice in the carton. Molly used 1/4litre at breakfast. How much orange juice was left in the carton.?
Answer:
1250ml
Step-by-step explanation:
1/4litre=250ml
1500-250
complete explanation please
Ken needs a total of $410 to buy a new bicycle. He has $35 saved. He earns $15 each week delivering newspapers. How many weeks will Ken have to deliver papers to have enough money to buy the bicycle?
Thanks so much! :D
Answer:
25 weeks
Step-by-step explanation:
Since we already know that he has $35 buck-a-roons saved, we can just subtract that from the cost of the bicycle to find the actual price—which would be 375. Then, we know that for every week, he gains $15 bucks. Therefore we know that 15 would be our variable so we can create the following equation:
15x + 35 = 410
15x = 375
15x/15 = 375/15
x = 25
After 25 weeks, Ken will have enough money to buy the bicycle.
Find the average rate of change of g(x) = 2x^3 - 5 from x= -4 to x= 2
Step-by-step explanation:
the average change rate is the change of the functional values from the beginning to the end of the interval, and then that divided by the length of the interval.
like with every average or mean value calculation.
g(-4) = 2×(-4)³ - 5 = -128 - 5 = -133
g(2) = 2×2³ - 5 = 16 - 5 = 11
so, on an interval of x values of 2- -4 = 6 units the function changes its values by 11 - -133 = 144 units.
the average charge rate for this x interval is therefore
144 / 6 = 24 = 24/1
for 1 unit change of x, g(x) changes in the average by 24 units.
Levi decides to examine the effect of fertilizer on the growth of tomato plants. He chooses four plants for his experiment and applies varying amounts of fertilizer to three of them. He does not apply fertilizer to one plant.
Over a 15-day period, the plants receive fertilizer on Days 1, 4, 7, 10, and 13. Levi measures the height of all of his plants with a meterstick on Days 3, 6, 9, 12, and 15. He also makes sure to hold all experimental factors constant except for the fertilizer.
What is the independent variable in Levi's experiment on tomato plants?
the days plant height was measured
the days fertilizer was applied
the amount of fertilizer given to the plants
the measurements of plant height
Answer:
Step-by-step explanation:
The measurement of the height is the dependent variable. The independent variable is the amount of fertilizer applied.
How to find joint and combined variation?
Step-by-step explanation:
Z will stay the same since the 2 will divide into 1
Which expression is equivalent to -80?
O -4.5
O-4.5
O 4/5
O 4.5
Answer:
-4/5
Step-by-step explanation:
When you divide -4 from 5 you get -0.80
Priya is buying raisins and almonds to make trail mix. Almonds cost $5.20 per pound and raisins cost $2.75 per pound. Priya spent $11.70 buying almonds and raisins. The relationship between pounds off almonds a, pounds of raisins r, and the total cost is represented by the equation 5.20a + 2.75r = 11.70.
How many pounds of raisins did Priya buy if she bought the following amount of almonds:
a pounds of almonds
Answer:
2.25 pounds of raisins
Step-by-step explanation:
What is the minimum value of the objective function, C with given constraints?
C=5x+6y
2x+y≤83 x+4 y≤17 x≥2 y≥1
A; 10
B; 16
C; 18
D; 19
Answer:
A 10
Step-by-step explanation:
10. What is the multiple zero and multiplicity of f(x) = (x - 3)(x - 3)(x + 5)?
Multiple zero is -3; multiplicity is 2
Multiple zero is 5; multiplicity is 1
Multiple zero is -5; multiplicity is 1
Multiple zero is 3; multiplicity is 2
Answer:
x=3, multiplicity of 2
x=-5, multiplicity of 1
Step-by-step explanation:
f(x) = (x - 3)(x - 3)(x + 5)
Rewriting
f(x) = (x - 3)^2(x + 5)
Setting equal to zero
0 = (x - 3)^2(x + 5)
Using the zero product property
(x-3)^2 = 0 x+5 = 0
x-3 = 0 x= -5
x=3 x-5
Since x-3 was squared, the multiplicity is 2
Answer:
x=3, multiplicity of 2
x=-5, multiplicity of 1
Step-by-step explanation
Simplify the expression (4r — 5r²) - (r — 2r²) what is the answer
The Junior class has raised
4/7
of the amount of money that is needed for the Junior-Senior
Prom, and the Senior class has raised 3/11 of the amount of money that is needed. Estimate
what portion of the money the two classes have already raised of the money
A.1/4 of the money
B.all of the money
C.1/2 of the money
D.3/4 of the money
Answer:
B. all of the money this is my answer
The wave speed is 500 m/s and the frequency is 5 Hz. What is the wavelength?
[tex]\pink{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: given \\ \sf \: speed \: \: v = 500 \: m {s}^{ - 1} \\ \\ \sf \: frequency \: \: f = 5 \: Hz \\ \\ \sf \: wavelenght \: \: \: \lambda \: = \: to \: find \\ \\ \bf \: we \: know \: that \\ \\ \sf \: v = f \lambda \\ \bf \implies \: \lambda = \frac{v}{f} \\ = \frac{500}{5} \\ = 100 \: m \\ \\ \therefore \sf \lambda \: = 100 \: m\end{array}}}}[/tex]
Rewrite the following using exponents.
5*5*5*5*5*5
O
25
(5) * (6)
056
Jamie kept track of the total hours and minutes she worked this week at the local health food store.
Monday - 3 hours
Thursday - 5 hours 30 minutes
Saturday - 3 hours 30 minutes
Sunday - 6 hours 45 minutes
How many decimal hours did Jamie work this week? (2 points)
17.11
18.05
18.75
Answer:
18.05
Step-by-step explanation:
The data recorded in following Table 1 shows the length of Medical checkup conducted by a Health & safety team, in meters,
20 25 33 47 39 41 21
39 33 32 38 41 37 49
59 60 31 28 48 36 60
b) Find the Mean and Median of the minutes.
c) Find Standard deviation also comment on the result.
d) Sketch Histogram and Frequency Polygon.
Answer:
yggnvfghg46777tuutyuyt6yffttgdfhurdvhu
how many ways can this be done. if a committee of 5 people from 7 men and 8 women?
Answer:
3003 ways
Step-by-step explanation:
(7+8)C5
= 15C5
= 15!/(5!10!)
= 3003
HELP HELP! I NEED URGENT HELP WITH THIS equashin.
Answer:
V = 1071.79 yd^3
Step-by-step explanation:
The volume of a cone is
V = 1/3 pi r^2 h where r is the radius and h is the height
We are given a diameter of 16 so the radius is 1/2 of the diameter or 8
The height is 16
V = 1/3 ( 3.14) (8)^2 ( 16)
V = 1071.78666 yd^3
Rounding to the nearest hundredth
V = 1071.79 yd^3
[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: of \: Cone \: = \: \pi \: {r}^{2} \: \frac{h}{3} }}}}}\end{gathered}[/tex]
[tex] \bf{\red{ \longrightarrow}} \tt \: r \: = \: \frac{Diameter}{2} \\ [/tex]
[tex]\bf{\red{ \longrightarrow}} \tt \: r \: = \: \frac{16 \: yd}{2} \\ [/tex]
[tex]\bf{\red{ \longrightarrow}} \tt \: r \: = \: \frac{ \cancel{16 \: yd} \: \: ^{8} }{ \cancel{2}} \\ [/tex]
[tex]\bf{\red{ \longrightarrow}} \tt \: \large{\bf{{{\color{navy}{r \: = \: 8 \: yd}}}}}[/tex]
[tex]\bf{\red{ \longrightarrow}} \tt \: \: \large{\bf{{{\color{navy}{h \: = \: 16 \: yd}}}}}[/tex]
[tex] \bf \large \longrightarrow \: \: 3.14 \: \times \: {8}^{2} \: \times \: \frac{16}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \:3.14 \: \times \: 64 \: \times \: \frac{16}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \:3.14 \: \times \: 64 \: \times \: \frac{ \cancel{16} \: \: ^{5.33} }{ \cancel{3}} \\ [/tex]
[tex]\bf \large \longrightarrow \: \:3.14 \: \times \: 64 \: \times \: 5.33[/tex]
[tex]\bf \large \longrightarrow \: \:200.96 \: \times \: 5.3[/tex]
[tex]\bf \large \longrightarrow \: \:1071.79[/tex]
Option (A) is the correct answer
Find the length of the arc.
A. 15π mi
B. 5400π mi
C. 135π mi
D. 125π16 mi
Answer:
A. 15π mi
Step-by-step explanation:
First find the circumference
C = 2*pi*r
C = 2 * pi*18
C = 36pi
The arc is 150 degrees
The fraction of the circle is
150/360 = 5/12
Multiply this by the circumference
5/12 * 36 pi
15 pi
1 gal/ml times 10ml what is mass
Answer:
Step-by-step explanation:
37854.11784
Determine what type of model best fits the given situation:
A. linear
B. exponential
O c. quadratic
D. none of these
Reset Selection
A: 28, 23,30, 25, 27
B: 22, 19, 15, 17, 20
The difference between the mean of the numbers in list A and the average of the numbers in list B is?
Answer:
8
Step-by-step explanation:
mean of A=28+23+30+25+27/5 = 26.6
average of B=22+19+15+17+20/5 = 18.6
now,
difference= 26.6-18.6
=8,,
Find the value of w
A. 141
B. 110
C. 80
D. 100
Answer:
141
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)
We know z+70 = 180 since they form a straight line
z = 110
z = 1/2 ( 79+w)
110 = 1/2 ( 79+w)
220 = 79+w
220-79 = w
141 =w
The value of w is found to be 141.
ChordWhat is chord of a circle?The line segment connecting any two locations on a circle's circumference is referred to as the chord of the circle.
It should be emphasised that the diameter is the circle's longest chord, which runs through its centre.
Relation between chord and arc:When two chords cross inside of a circle, the angle's measure is equal to the product of the lengths of the intersecting arcs and the vertical angle, divided by two.
Formula for chord angle:angle formed by two chords = 1/2 (sum of intercepted arcs)
Calculation for arc w:Estimate angle z by linear pair.
z + 70 = 180
z = 110
z is the angle formed between two chord of the circle.
Thus,
z = 1/2( 79 + w) {sum of intercepted arcs}
110 = 1/2( 79 + w)
Further solving,
w = 141
Therefore, the value of arc w comes out to be 141.
To know more about linear pair, here
https://brainly.com/question/8720873
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Which choice shows 30 + 10 + 20 rewritten correctly using the commutative property and then simplified correctly?
A.30 + 20 + 10 = 50 + 10 = 60.
B.30+10+10+10=40+10+10=50+10=60
C.30+20+10=50+30=80
D.30+10+10+10=40+10=50
Answer:
A. 30+20+10=50+10=60
Step-by-step explanation:
The commutative property is the property of which you can rearrange the numbers around but the answer stays the same. From the original equation, you moved 20 and 10 around and added 30+20=50 then, you add 10 plus that 50 since you haven't done anything to the 10 yet. So, 50+10=60.
Hope this helped! Please rate 5 stars and give Brainliest!
