Answer:
[tex]\displaystyle z=\frac{5}{2}\biggr(\cos\frac{11\pi}{6}+i\sin\frac{11\pi}{6}\biggr)[/tex]
Step-by-step explanation:
A complex number in polar form is [tex]z=r(\cos\theta+i\sin\theta)[/tex] where [tex]r=\sqrt{x^2+y^2}[/tex] and [tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)[/tex], thus:
[tex]r=\sqrt{x^2+y^2}=\sqrt{(\frac{5\sqrt{3}}{4})^2+(-\frac{5}{4})^2}=\sqrt{\frac{75}{16}+\frac{25}{16}}=\sqrt{\frac{100}{16}}=\frac{10}{4}=\frac{5}{2}[/tex]
[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)=\tan^{-1}\biggr(\frac{-\frac{5}{4}}{\frac{5\sqrt{3}}{4}}\biggr)=\tan^{-1}\biggr(-\frac{\sqrt{3}}{3}\biggr)=\frac{11\pi}{6}[/tex]
Thus, the complex number in polar form is [tex]\displaystyle z=\frac{5}{2}\biggr(\cos\frac{11\pi}{6}+i\sin\frac{11\pi}{6}\biggr)[/tex]
How much money will you have in 8 years if you invest $4000 at 2% compounded quarterly
Answer:
If you invest $4000 at 2% compounded quarterly you will make 4,694$.
Step-by-step explanation:
Answer:
$4686.64
Step-by-step explanation:
here is the function 4000(1+0.02)^8
In a poll of Mr. Briggs’s math class, 67% of the students say that math is their favorite academic subject. The editor of the school paper is in the class, and he wants to write an article for the paper saying that math is the most popular subject at the school. Explain why this is not a valid conclusion and suggest a way to gather better data to determine what subject is most popular.
This is not a valid conclusion because the data was not randomly collected from various classes in the school but from a particular class.
Collection of data for a research workThe collection of data for a research work should be done in such a way as to include a good number of the test subjects.
The sampling methods that can be used to gather better data include the following:
Random sampling,Cluster sampling, andSystematic sampling methods.These methods will ensure that a good number of the test subjects are included in the research work in order to form a valid conclusion.
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Please help with my math!!!!!
By applying the point-slope formula, the linear function y = -x/3 - 4 has a slope of - 1/3 and passes through the point (-3, -3) seen on Cartesian plane.
How to determine the line equation by knowing its slope and a point
According to analytical geometry, we could know the equation of the line by means of the point-slope equation:
y - y₁ = m · (x - x₁) (1)
Where:
x - Independent variabley - Dependent variable(x₁, y₁) - Known pointm - SlopeIf we know that m = -1/3 and (x₁, y₁) = (-3, -3), then the line equation is:
y + 3 = -(1/3) · (x + 3)
y + 3 = -x/3 -1
y = -x/3 - 4
Lastly we proceed to graph the function by a graphing tool (i. e. Desmos).
By applying the point-slope formula, the linear function y = -x/3 - 4 has a slope of - 1/3 and passes through the point (-3, -3) seen on Cartesian plane.
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HURRY UP 10 MIN LEFT (100 points)!!!!!!!!!!!
Which of the following words is not a translation for "=?"
equals
similar
is
equal to
Answer:
similar
Step-by-step explanation:
Answer:
Similar
Step-by-step explanation:
For similarity or congruence we use ~ symbol not equal to
Is equal to also denote to =Equals is generally=Fatima wants to find the value of sine theta, given cotangent theta = four-sevenths. which identity would be best for fatima to use?
By using trigonometric relations, we will find that:
sin(θ) = (√33)/7 = √(33/49)
How to find the value of the sine?Remember that for a right triangle, we have the relations:
cos(a) = (adjacent cathetus)/(hypotenuse)
sin(a) = (opposite cathetus)/(hypotenuse).
Here we know that:
cos(θ) = 4/7
Then we can say that we have a triangle with an adjacent cathetus of 4 units and a hypotenuse of 7 units. Now we need to find the other cathetus.
opposite cathetus = √(7^2 - 4^2) = √33
Then we can write:
sin(θ) = (√33)/7 = √(33/49)
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Answer:
The answer is D.
Step-by-step explanation:
Edge 2022
The volume of Earth is approximately 1 x 10^12 cubic kilometers. The volume of Mercury is approximately 6 x 10^10 cubic kilometers. About how many times bigger is Earth’s volume than Mercury’s?
Answer:
Volume of the Earth is about 16.67 times bigger than Mercury's volume.
Step-by-step explanation:
Given:
[tex]V_E = 1 \times 10^{12} \text{ km}^3\\V_M = 6 \times 10^{10} \text{ km}^3[/tex]
[tex]V_E[/tex] is the volume of the Earth and [tex]V_M[/tex] is the volume of the Mercury.
Divide volume of the Earth with the volume of Mercury.
[tex]\frac{V_E}{V_M} = \frac{1 \times 10^{12} \text{ km}^3}{6 \times 10^{10} \text{ km}^3} = \frac{1 \times 10^{2}}{6} = \frac{100}{6} = \frac{50}{3} \approx 16.67[/tex]
Volume of the Earth is about 16.67 times bigger than Mercury's volume.
Which graph has a slope of 1/3?
Answer: the one on the bottom left
Step-by-step explanation:
please how do i do this?
Answer:
4
Step-by-step explanation:
The figure can be split into 2 triangles, the larger one is the whole figure with base 18 and height 9. while the other small triangle has base 8 and height h. Since they are both right angled triangles with a shared angle, they are similar.
With similar triangles, we get the ratio of base : height = 8 : 8+10 = h : 9
Hence, 8 : 18 can be simplified to 4 : 9, which is also equal to h : 9. From here, we get h = 4.
Answer:
4
Step-by-step explanation:
The figure can be split into 2 triangles, the larger one is the whole figure with base 18 and height 9. while the other small triangle has base 8 and height h. Since they are both right angled triangles with a shared angle, they are similar.
Use the graph to find the cost of 6 show tickets.
Cost of Show Tickets
110
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4 5 6 7 8 9 10 11
Number of tickets
A. The cost of 6 show tickets is $50.
B. The cost of 6 show tickets is $5.
O C. The cost of 6 show tickets is $30.
O D. The cost of 6 show tickets is $6.
Cost ($)
C. The cost of 6 show tickets is $30.
bottom of graph represents number of tickets, look for 6 then go up till you hit the dot now go to the other side of the graph ( costs) and see which number the line hit which is 30
The distribution of the number of words in text messages between employees at a large company is skewed right with a mean of 8.6 words and a standard deviation of 4.3 words. If a random sample of 39 messages is selected, what is the probability the sample mean is more than 10 words?
0.0210
0.2454
0.3724
0.9790
Using the normal distribution and the central limit theorem, the probability the sample mean is more than 10 words is of 0.0210.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the parameters are given as follows:
[tex]\mu = 8.6, \sigma = 4.3, n = 39, s = \frac{4.3}{\sqrt{39}} = 0.6885[/tex]
The probability that the sample mean is more than 10 words is one subtracted by the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{10 - 8.6}{0.6885}[/tex]
Z = 2.03.
Z = 2.03 has a p-value of 0.979.
1 - 0.979 = 0.021.
The probability the sample mean is more than 10 words is of 0.0210.
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A bag contains 5 black marbles, 7 blue marbles, 3 green marbles, 4 red marbles, and 1 white marble. A marble is selected and then replaced. What is the probability of selecting a black marble?
Answer:
1/4
Step-by-step explanation:
5 black marbles out of 20 total is 5 /20 = 1/4
help I don't know what to put on it
Answer:
377.2 cm³
Step-by-step explanation:
Applied Formula :
Volume (cylinder) = πr²h
============================================================
Given :
⇒ r = 3.1 cm
⇒ h = 12.5 cm
=============================================================
Solving :
⇒ V = 3.14 x 3.1 x 3.1 x 12.5
⇒ V = 9.734 x 38.75
⇒ V = 377.2 cm³ (nearest tenth)
Volume
V=πr²h
π(3.1)²(12.5)3.14(3.1)²(12.5)377.2cm³Done!
I swear this always stress me out can someone help me
The approximate perimeter of the given shape is; 33.70cm.
What is the approximate perimeter of the shape?It follows Fromm the task content that the perimeter of the shape can be determined by determining the length of the curved surface and the the other three outer surfaces as follows;
Curves surface = 3.14 × (10/2) = 15.70cmThe perimeter of thee other three sides is; 4 + 4 + 10 = 18cmThe perimeter of the shape is therefore; 18 + 15.70 = 33.70cm.
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What is area of the figure?
Answer:
88
Step-by-step explanation:
can someone explain the proses of solving this? I don't need the answer but a step-by-step explanation would be super helpful!
Part 1
Focus on triangle ABC.
Since AB is a diameter of the circle, this means angle ACB is 90 degrees. Refer to Thale's Theorem. Or you could use the inscribed angle theorem. Thale's theorem is a special case of the inscribed angle theorem.
Minor arc CB is 48 degrees. Use the inscribed angle theorem to see that angle CAB is 48/2 = 24 degrees.
Therefore, angle CBA = 90 - (angle CAB) = 90 - 24 = 66 degrees
Answer: 66========================================================
Part 2
Inscribed angle CBA was found to be 66 degrees back in part 1.
This doubles to 132 degrees to represent minor arc AC.
Or you could note that:
minor arc AC = 180 - (minor arc CB) = 180 - 48 = 132
Inscribed angle BCD is 48 degrees. This doubles to 96 degrees when using the inscribed angle theorem, and this is the measure of minor arc CBD.
-----------
Here's what we know about the arc measures of the circle
minor arc AC = 132 degreesminor arc CB = 48 degreesminor arc BD = 96 degreesThese three arcs, along with minor arc AD, will add up to get a full 360 degree circle. Check out the diagram below.
Adding those 3 pieces gets us 132+48+96 = 276
This means minor arc AD has to be 360 - 276 = 84 degrees
Then use the inscribed angle theorem one more time to divide the minor arc AD in half to get the inscribed angle ACD
84/2 = 42
Answer: 42Please Help!! DUE SOON!! I'LL MARk BRAInLiEAST!! HIGH POintS!!
Answer:
Step-by-step explanation:
A store has clearance items that have been marked down by 50%. they are having a sale, advertising an additional 30% off clearance items. what percent of the original price do you end up paying
Answer:
20%
Step-by-step explanation:
50+30=80
100-80=20
so you would pay 20%
2. The diameter of sphere is 10 cm. Find the volume.
3. Juice is sold in aluminum cans that measure 7 inches in height and 4 inches in diameter. How many cubic inches of juice are contained in a full can?
4. The square pyramid has a volume of
297 cm3. The area of the base is 81 cm2. What is the height?
5. A glass is 10 cm deep and 8 cm wide. How much liquid can the glass hold?
6. A glass pyramid has a height of 6 inches. Its rectangular base has a length of 4 inches and a width of 2.5 inches. Find the volume of the glass.
7. A cylinder made of quartz has a volume of 5.8 cm3. If the radius is 2 cm, find the height.
8. Find the volume of a cone with a diameter of 10 meters and a height of 5.1 meters.
9. What is the volume of a sphere with a diameter of 18 ft?
10. Find the volume of a pyramid with a rectangular base measuring 6 cm by 4 cm and height 11 cm.
answer pls
The volume of the sphere will be V = 1570.79 cubic cm.
What is volume?The Volume of the sphere is the amount of quantity, which is obtained in the 3-dimensional space. A sphere is a circular ball type three dimensional object.
Given that:-
The diameter of the sphere is 10 cmThe volume of the sphere will be calculated as:-
V = 4 π r³
V = 4 x π x ( 5)³
V = 1570.79 cubic cm
Therefore the volume of the sphere will be V = 1570.79 cubic cm.
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does anyone know the width the length the height of this tissue box pls someone tell me Asap.
Answer:
Hey!
Well based on my knowledge it usually says that on the tissue box itself.... (in fine print)
i may be wrong.... but do check...
[tex]\huge\color{yellow}\underline \colorbox{violet} {\color{red}{QUESTION}}[/tex]
Direction:Find the volume of each solid figure below.
correct answer=brainles
nice answer=rate 5 star
explanation=heart
incorrect=report
no explanation=report
Explanation:
Volume of rectangular prism: Length * Width * Height
Solve:
1)
Volume: 9 * 9 * 9 = 9³ = 729 cm³
2)
Volume: 7 * 3 * 2 = 42 m³
3)
Volume: 7 * 7 * 7 = 7³ = 343 cm³
find the mid point of the line segment.
can you upload a less blury picture
Answer:
(-3/2, 0)
Step-by-step explanation:
The midpoint of a line segment is the average of the end point coordinates.
M = (A +B)/2
__
For end points A(-5, 5) and B(2, -5), the midpoint is ...
((-5, 5) +(2, -5))/2 = (-5+2, 5-5)/2 = (-3, 0)/2 = (-3/2, 0)
The midpoint of the segment is (-3/2, 0).
Please help, it’s due tomorrow
Answer:
The largest interger that satisfies the equation is 3
Step-by-step explanation:
If we subtract 10 from each side, we get 7x<=21
Then, we divide 7 on each side to get x<=3.
So the largest interger to satisfy the equation is 3
(Btw, <= means less than or equal to)
Hope this helped you, and have a great day!
Answer:
x<=3
Step-by-step explanation:
minus 10 fom both sides
7x + 10-10<=31-10
restate as
7x<=21
divid both side by same factor
7x/7 and 21/7
restate as
x<=3
Simplify
[tex]\sqrt{25-10\sqrt{3} +3}[/tex]
Answer:
The given equation is expansion of (a-b)²= a²-2ab+b²
[tex]\sqrt{25-10\sqrt{3} +3} \\ \sqrt{ {(5 - \sqrt{3})}^{2} } \\ (5 - \sqrt{3})[/tex]
A train left a station at noon going at 40 mph. A second train left at 3 pm going in thte same direction at 6o mph. At what time iwll the second train catch up with the first
Answer:
9PM
Step-by-step explanation:
3pm - 40x3=120 Miles Travelled (Noon Train)
3pm - 60x0=0 Miles Travelled (3pm Train)
4pm - 40x4=160 Miles Travelled (Noon Train)
4pm - 60x1=60 Miles Travelled (3pm Train)
5pm - 40x5=200 Miles Travelled (Noon Train)
5pm - 60x2=120 Miles Travelled (3pm Train)
6pm - 40x6=240 Miles Travelled (Noon Train)
6pm - 60x3=180 Miles Travelled (3pm Train)
7pm - 40x7= 280 Miles Travelled (Noon Train)
7pm - 60x4=240 Miles Travelled (3pm Train)
8pm - 40x8 = 320 Miles Travelled (Noon Train)
8pm - 60x5=300 Miles Travelled (3pm Train)
9pm - 40x9 = 360 Miles Travelled (Noon Train)
9pm - 60x6= 360 Miles Travelled (3pm Train)
A state tourist guide provides information on summer vacation towns. Some of the towns and related information are
given in the table below.
Average
Number
Town
Beach
Access?
Temp
(°F)
Location
of Hotels
Spring Haven
73.2
12
yes
West
Based on the information given in the table, the discrete quantitative variable would be the number of hotels.
What is a discrete quantitative variable?This refers to a variable in a distribution that can only take on a specific value that is countable.
This means that the number does not go on forever. Examples of these are the number of fingers and toes you have.
The discrete quantitative variable from the options would therefore be the number of hotels that there are.
________________________________________________________
The rest of the question is:
Which of the variables is a discrete quantitative variable?
A:average temperature
B:number of hotels
C:beach access
D:location
________________________________________________________
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What is sum of the geometric series?
Answer:
Sn=a1(1−rn)1−r,r≠1 C.
please answer asap! 20 points!!
A new car is purchased for 23,900 dollars. The value of the car depreciates at a rate of 6.4% per year. Which equation represents the value of the car after 4 years?
1) V= 23,900(0.936)(0.936)(0.936)(0.936)
2) V=23,900(1+0.064)⁴
3) V= 23,900(1−0.064)(1−0.064)
4) V= 23,900(0.064)⁴
Answer:
1) V= 23,900(0.936)(0.936)(0.936)(0.936)
Step-by-step explanation:
Each year, the car depreciates to 1 -0.064 = 0.936 of its previous value. After 4 years, the original value has been multiplied by this factor 4 times:
__
depreciated value = 23,900(0.936)(0.936)(0.936)(0.936)
_____
This could be represented by ...
V = 23,900(1 -0.064)⁴ . . . . . . not an answer choice
The diagonal of the rectangle is 10 inches long and the height of the rectangle is 8 inches. What is the perimeter of the rectangle in the inches?
Basic perimeter is really easy to understand;
Step-by-step explanation:
10 x 8 = 80 in.
80 in. is your answer! Please mark brainliest and have a great day! :D
I need help with all of these questions you see on the top. there the red squares. please someone smart. this is one of the problems I need to finish this tonight.
Answer:
490.1 in^3
Step-by-step explanation:
In order to find the volume of a cylinder, you would multiply the area of the base b the height, so a cylinder with base [tex]26 \pi in^{2}[/tex] and height 6 in would be [tex]26\pi \times 6[/tex]
This multiplies to 490.08845396 when put in a calculator, and rounded to the nearest tenth, the answer is 490.1 in^3
What percentage of the large circle does the small circle take up?
Please please help
Answer:
25 percent.
Step-by-step explanation:
To begin we want to find the area of the small circle. That would be pi(r)^2 or 9pi after plugging in the 3 for the radius. We can only assume that the large circle is double the radius of the smaller circle so it would be 6. Plug 6 in and get 36pi for the area of that circle. 9pi/36pi will equal 0.25 and that will be your percentage. I hope this helped.