Answer: 77
Step-by-step explanation:
Find the quotient of z1 by z2. .Express your answer in trigonometric form.
Answer:
[tex]\frac{z_1}{z_2} = 3(cos(240^o) + isin(240^o))[/tex]
Step-by-step explanation:
Given
[tex]z1 = 12(cos(320^o) + isin(320^o))[/tex]
[tex]z2 = 4(cos(80^o) + isin(80^o))[/tex]
Required
[tex]Quotient = \frac{z_1}{z_2}[/tex]
We have:
[tex]Quotient = \frac{12(cos(320^o) + isin(320^o))}{4(cos(80^o) + isin(80^o))}[/tex]
Divide 12 by 4
[tex]Quotient = \frac{3(cos(320^o) + isin(320^o))}{(cos(80^o) + isin(80^o))}[/tex]
Solve using the following rule:
[tex]\frac{(cos(a) + isin(a))}{(cos(b) + isin(b))} = \cos(a - b) + isin(a - b)[/tex]
So, we have:
[tex]Quotient = \frac{3(cos(320^o) + isin(320^o))}{(cos(80^o) + isin(80^o))}[/tex]
[tex]Quotient = 3(cos(320^o-80^o) + isin(320^o-80^o))[/tex]
[tex]Quotient = 3(cos(240^o) + isin(240^o))[/tex]
Hence:
[tex]\frac{z_1}{z_2} = 3(cos(240^o) + isin(240^o))[/tex]
Marley has marbles of the same size and shape in a bag. There are 2 green, 5
blue, and 3 red marbles in the bag. Marley picks two marbles without looking.
What is the probability he will pick two red marbles?
a) 3/15
b)1/15
c) 3/50
d) 1/4
Answer:
B.) 1/15
Step-by-step explanation:
10 total marbles3/10 - 1/1 = 2/93/10 × 2/9 = 1/15Let f (x) = 10/x-4
What is the average rate of change of f (x) from 2 to 8 ?
Enter your response as a decimal.
Answer:
1.875
Step-by-step explanation:
The rate of change is the derivative of the function.
[tex]f(x) = \frac{10}{x-4}\\\\f'(x)=10\times \frac {d}{dx}\frac{1}{x-4}\\\\f'(x)=\frac{-10}{(x-4)^{2}}\\\\f'(2) = \frac{-10}{(2-4)^{2}} =-2.5\\\\f'(8)= \frac{-10}{(8-4)^{2}} =-0.625\\[/tex]
So, the rate of change is
f'(8) - f'(2) = - 0.625 + 2.5 = 1.875
If the equation y = |x| is graphed and then
moved up 3 units on the y-axis, what will be
the equation of the new graph?
Answer:
Step-by-step explanation:
The new equation will be
y = abs(x) + 3
I have made a graph to show you this.
The red graph is y = abs(x)
The blue graph is y = abs(x) + 3
You need only look at the point 0,0 to see what happened. On the red graph (0,0) is the lowest point. When you add 3 to get the lowest point, you should notice that the lowest point is now (0,3)
Lines A and B are parallel
A
1/2
3/125°
B
5/6
7/8
m 6 = [ ?]
==============================================
The 125 degree angle and angle 6 are supplementary. This is because of the same side interior angles theorem.
Let x be the measure of angle 6. Add this to 125, set the sum equal to 180, and solve for x.
x+125 = 180
x = 180-125
x = 55
------------
Or you could approach it this way:
y = measure of angle 2
y+125 = 180
y = 55
angle 6 = angle 2 (corresponding angles)
angle 6 = 55 degrees
-------------
Yet another way you could solve:
z = measure of angle 3
z+125 = 180
z = 55
angle 6 = angle 3 (alternate interior angles)
angle 6 = 55 degrees
A similar approach using alternate interior angles would involve angle 5 = 125, and then noticing that x+125 = 180 solves to x = 55
What’s the answer and how do you figure these out?
A regression was run to determine if there is a relationship between hours of tv watched per day (x) and the number of situps a person can do (y).The results of the regression were:y=ax+ba=−1.077b=30.98r2=0.744769r=−0.863Use this to predict the number of situps a person who watches 13.5 hours of TV can do.
Answer:
The number of situps is: 16.4405
Step-by-step explanation:
Given
[tex]y = ax + b[/tex]
[tex]a =-1.077[/tex]
[tex]b=30.98[/tex]
[tex]r^2 = 0.74476[/tex]
Required
Predict y when [tex]x = 13.5[/tex]
In the result, we have:
[tex]y = ax + b[/tex]
[tex]a =-1.077[/tex]
[tex]b=30.98[/tex]
This implies that:
[tex]y = -1.077x + 30.98[/tex]
To make prediction when [tex]x = 13.5[/tex]
We have:
[tex]y = -1.077*13.5 + 30.98[/tex]
[tex]y = -14.5395 + 30.98[/tex]
[tex]y = 16.4405[/tex]
PLZ HELP WILL GIVE 50 POINTS - QUADRATIC APPLICATIONS
find how far away (ground distance) from the catapult will white bird be at its highest. (round to the nearest 2 decimal points)
h= -0.114x^2+2.29x+3.5
Answer:
The bird will be at a ground distance of 10.04 units away.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Equation for the height:
The height of the bird after x seconds is given by:
[tex]h(x) = -0.114x^2 + 2.29x + 3.5[/tex]
Which is a quadratic equation with [tex]a = -0.114, b = 2.29, c = 3.5[/tex].
When the bird is at its highest?
Quadratic equation with [tex]a < 0[/tex], and thus, at the vertex. The ground distance is the x-value of the vertex. Thus
[tex]x_{v} = -\frac{b}{2a} = -\frac{2.29}{2(-0.114)} = 10.04[/tex]
The bird will be at a ground distance of 10.04 units away.
The initial condition for a one-dimensional transient conduction problem is the specification of:_______.
A. the time at which the solution to the problem starts.
B. the properties at the start of the solution.
C. the temperature at the initial time throughout the domain.
D. None of the above
Answer:
C
Step-by-step explanation:
if a bag of rice weighs 55 kg find the weight of 123 bags of rice
Answer:
6765
Step-by-step explanation:
the answer is 6765
Answer: 6,765 kg
Step-by-step explanation:
55 x 123 = 6,765kg of Rice
please help I'll give brilliantist:)
Which best describes the relationship between the successive terms in the sequence shown?
9, -1, -11, -21,
The common difference is -10,
The common difference is 10
The common ratio is -9)
The common ratio is 9.
Answer:
the common difference is 10
What is -4.5 need help pls help fast I will give u a brilliant and thank
Answer:
its -4.5??? what is the question you're asking
A triangle has side lengths of
[tex] \sqrt{125} [/tex]
[tex] \sqrt{5} [/tex]
[tex] \sqrt{20} [/tex]
What is the perimeter of the triangle?
[tex]4 \sqrt{5} [/tex]
[tex]6 \sqrt{5} [/tex]
[tex]8 \sqrt{5} [/tex]
none of the answers are correct
Answer:
3 is the right one
Step-by-step explanation:
Simple math you know
A study records the lengths of pregnancy (in days) of 500 women. The data is normally distributed with a mean of 266 days and a standard deviation of 16 days. How many women in the study had a pregnancy between 250 days and 282 days in length?
Answer:
371 women had their pregnancy between 250 days and 282 days in length.
di po ako sure sa answer ko, but it is based on what I remembered.
Step-by-step explanation:
z=532-266
16
√500
= 371.74 or 371
Area of triangle with sides a=8, b= 10, c=7
Answer:
d equal 10 this is the answer
Which equation is written in factor form?
You weigh a random sample of adult golden retrievers and get the following results: 55, 64, 58, 61, 69, 64, 59, 69, 72, and 65. Which answer gives a 98% confidence interval for the mean of the population
Answer:
The 98% confidence interval for the mean of the population is (59, 68.2).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{55+64+58+61+69+64+59+69+72+65}{10} = 63.6[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(55-63.6)^2+(64-63.6)^2+(58-63.6)^2+(61-63.6)^2+(69-63.6)^2+(64-63.6)^2+(59-63.6)^2+(69-63.6)^2+(72-63.6)^2+(65-63.6)^2}{10}} = 5.142[/tex]
Confidence interval:
We have the standard deviation for the sample, and thus, we use the t-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.821
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.821\frac{5.142}{\sqrt{10}} = 4.6[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 63.6 - 4.6 = 59
The upper end of the interval is the sample mean added to M. So it is 63.6 + 4.6 = 68.2.
The 98% confidence interval for the mean of the population is (59, 68.2).
what is the value of b?
Answer:
24
Step-by-step explanation:
2b = b+24
2b-b = 24
b = 24
If you sleep 6 hours a day every day for a year you are sleeping of every year. If there are 365 days in a year, how
many days per year would you sleep? Simplify your answer and write it as a mixed number.
days
Answer:
Step-by-step explanation:
365 x 24 = 8,760
365 x 6 = 2,190
8,760 - 2,190 = 6,570
6,570 / 24 = 273 3/4
The person sleeps 91 (1/4) days per year.
What is multiplication?Multiplication is the process of adding a number up to a given number.
Given that, the person sleeps 6 hours a day.
The total hours of sleeping over a year are:
365 × 6
= 2190 hours per year
Since there are 24 hours in a day, divide 2190 by 24 to get the answer in days per hour:
2190/24
= 91 (1/4)
Hence, the person sleeps 91 (1/4) days per year.
To learn more about multiplication, click here:
https://brainly.com/question/11527721
#SPJ2
Let 0 be an angle such that sec0= -13/12 and cot0<0. Find the exact values of tan0 and sin0.
Answer:
tan 0 = -2.4
sin 0 = 0.42
Step-by-step explanation:
sec 0 = -13/12 => cos 0 = -12/13
cot 0 < 0 => tan 0 < 0
so, the angle is on second quadrant
=> tan 0 = -12/5 = -2.4
=> sin 0 = 5/12 = 0.42
Answer:
Solution given;
Sec θ=-[tex]\frac{13}{12}[/tex]
cotθ< 0,
It lies in second quadrant.
where sin and cosec is positive.
Now
[tex] \frac{1}{cosθ}=-\frac{13}{12}[/tex]
cosθ=[tex]\frac{12}{13}[/tex]
[tex]\frac{b}{h}[/tex]=[tex]\frac{12}{13}[/tex]
b=12
h=13
By using Pythagoras law
p=[tex] \sqrt{13²-12²}=5 [/tex]
Now
exact values of tan θ=[tex]\frac{p}{b}[/tex]=[tex]\frac{5}{12}[/tex]
since it lies in II quadrant
tan θ=-[tex]\frac{5}{12}[/tex]
and
sinθ=[tex]\frac{p}{h}[/tex]=[tex]\frac{5}{13}[/tex]
since it lies in II quadrant
sin θ=[tex]\frac{5}{13}[/tex]
If there are 8 people, and each person has 4 coins, there are ____ times as many coins as people.
Answer:
2 times
Step-by-step explanation:
Answer:
4 times
Step-by-step explanation:
8 x 4 = 32 total coins
32÷8 = 4
Therefore, there are 4 times as many coins as people.
Hope this helps! :)
I NEED HELP ASAP PLEASE
Answer:
A and E
Step-by-step explanation:
B and D is unchangeable, species of bears and types of vegetables that existed in the world never changed.
C only consist of one data, temperature of Chicago at noon yesterday only.
The average number of employees that call in sick for the day over the course of a year is 25. The number of employees that call in sick on 12 days are 25, 10, 16, 39, 27, 25, 32, 25, 25, 22, 28, and 14. Enter the sample mean and the population mean in the boxes
Answer:
sample mean (x with the bar on top) =24
Step-by-step explanation:
Take the mean of all the number of employees but divide by the number of days size: (25+10+16...)/12=25
population mean (mu) =11.52
The same goes for the other one but divide by the population which is 25
Given that is directly proportional to (p-1)2 and p is always positive, find the
value of p when q = 80 , if 9= 30 when p = 7
A) 4
B) 6
Ch 10.82
Answer:
p = 10.8
Step-by-step explanation:
Given that p is directly proportional to (p-1)² and p is always positive, then;
q = k (p-1)²
If q = 30 and p = 7
30 = k(7-1)²
30 = 6²k
30 = 36k
5 = 6k
k = 5/6
To get p when q = 80
q =k (p-1)²
80 = 5/6((p-1)²
480 = 5(p-1)²
480/5 = (p-1)²
(p-1)² = 96
p-1 = √96
p-1 = 9.8
p = 9.8 + 1
p = 10.8
B) 6
Ch 10.82
Click on the area of the square?
Answer:
The answer for this question is 64 square centimeters
Step-by-step explanation:
To find the area of square , the formula is :
side × side , so in this question we should do 8×8 , since one of the side is 8 cm .
8×8 = 64
Thus the answer of your question is 64
—————————————————
[tex]\mathrm{A = s²}[/tex]
[tex]\mathrm{A = (8 \: cm)²}[/tex]
[tex]\mathrm{A = (8 \: cm)(8 \: cm)}[/tex]
[tex]{\boxed{\mathrm\green{A = 64 \: cm²}}}[/tex]
༆ANSWER:—————————————————
[tex]\purple{\boxed{\boxed{\tt\pink{64 \: square \: centimeters}}}}[/tex]
Hence, the area of the square that has a side of 8 cm, is 64 cm².Remember!To find the area of a square, just use the formula "A = s²".write each verbal phrase as an algebraic expression.
1. the sum of 8 and t
2. the quotient of g and 15
3. the product of 5 and b
4. the difference of 32 and x
Answer:
1. 8 + t
2. g/15
3. 5b
4. 32 - x
Step-by-step explanation:
1. the sum of 8 and t
8 + t
2. the quotient of g and 15
g/15
3. the product of 5 and b
5b
4. the difference of 32 and x
32 - x
The zeros of a parabola are 6 and -5. If (-1, 3) is a point on the graph, which equation can be solved to find the
value of a in the equation of the parabola?
O3 = a(-1 + 6)-1-5)
O 3 = a(-1-6)(-1 +5)
O -1 = a(3+6)(3-5)
O-1 = a(3-6)(3+5)
Answer:
3 = a(-1-6)(-1+5).
Step-by-step explanation:
y = a(x - 6)(x + 5)
When x = -1, y = 3 so we have:
3 = a(-1-6)(-1+5).
Help pleaseeeee thanks
Answer:
We know that 3 l 3 = 3.3, so the values of the stem and leaf plot would be;
4 l 8, 9
5 l 1, 6, 8, 8, 9
6 l 8, 9, 9, 9, 9
7 l 0, 2, 2, 2, 5, 5
8 l 0, 9
Hope this helps!
If P is inversely proportional to Q and if pad when Q = 4. Find the value
of when Q = 3.
A) 7 B) 6 C) 12
Answer:
8
Step-by-step explanation:
If p is inversely proportional to Q and P is 6 when q = 4, then;
p = k/q
6 = k/4
k = 6*4
k = 24
To get P when q = 3
Recall;
p = k/q
p = 24/3
p = 8
Hence the required value of p is 8
Note that the value of initial Q was assumed