Answer:
[tex]n=-12[/tex]
Step-by-step explanation:
[tex]\text{When}~ n = -12,\\\\~~~~~-2(6x+2) = -12x-4\\\\\implies -12x -4 = -12x -4 \\\\\text{Since both sides are equal for all values of x, there are infinitely many solutions.}[/tex]
What are the fourth roots of 2√3 −2i? Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure.
By using the De Moivre's formula, the quartic roots of the complex numbers (in polar form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).
How to find the roots of a complex number
Complex numbers are numbers of the form a + i b, where a and b are the real and imaginary component, respectively. In other words, complex numbers are an expansion from real numbers. The n-th root of a complex number is found by using the De Moivre's formula:
[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n} \right) + i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for i = {0, 1, 2, ..., n - 1}.
Where:
r - Norm of the complex number.θ - Direction of the complex number, in radians.The norm of the complex number is found by Pythagorean theorem:
[tex]r = \sqrt{(2\sqrt{3})^{2}+(-2)^{2}}[/tex]
r = 4
And the direction is determined below:
[tex]\theta = \tan^{-1} \left(\frac{2\sqrt{3}}{-2} \right)[/tex]
θ = 2π/3 rad
Then, the quartic roots of the complex numbers (in polar form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).
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A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 23 times, and the man is asked to predict the outcome in advance. He gets 20 out of 23 correct. What is the probability that he would have done at least this well if he had no ESP
The probability that he would have done at least this well if he had no ESP is 0.99979
What is the probability of determining that he would have done well with no ESP?To determine the probability, we need to first find the probability of doing well with ESP.
The probability of having 20 correct answers out of 23 coin flips is:
[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]
Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:
[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]
There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.
Therefore, the probability of doing well with ESP is:
[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]
= 0.00021
The probability that he would have at least done well if he had no ESP is:
= 1 - 0.00021
= 0.99979
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I need help on this 1 question. Thank you.
Answer: 5/6, 3/4, 4/12
Step-by-step explanation:
Convert them all into a common denominator, 12.
5/6=10/12, 3/4=9/12, and 4/12 stays the same. 10>9, and 9>4
A certain television is advertised as a 95-inch tv (the diagonal length). if the width of the tv is 77 inches, how tall is the tv? round to the nearest tenth of an inch.
The height of the television given the length of its diagonal and its width is 55.6 inches
What the height of the tv?The height of the television can be determined using Pythagoras Theorem.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
√95² - 77² = 55.6 inches
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Answer: 55.6
Step-by-step explanation: 55.6 that's what I put in and got it right
liz wants to determine which sport students like to play the most at her school.which method will most likely produce a random example.
Answer:
Random sampling
Step-by-step explanation:
Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.
Find the volume of rectangular pyramid 5in 5 in 2 in
Answer:
16.67
Step-by-step explanation:
formula for a rectangular pyramid =
lengthxwidth= base area x height/3
2x5=10x5=50
50/3=16.67
Samuel can type 40 words per minute. How many hours would it take him to type
2.6 x 10^5 words?
Answer:
108 1/3 hours
Step-by-step explanation:
There are 60 minutes in 1 hours.
40 words/minute × 60 = 2400 words/hour
2.6 × 10^5 / 2400 = 108.3333... = 108 1/3
Answer 108 1/3 hours
The weight, w, that a horizontal beam can support varies inversely as the
length, l, of the beam. a beam measuring 5 meters in length can support
430 kilograms. how much weight can a beam measuring 2 meters
support?
A beam measuring 2 meters can support 172 kilograms
How to determine the weight?The variation is a direct variation.
So, we have:
w = kl
Where k is the constant of variation.
When l = 5, w = 430.
This means that:
430 = 5k
Divide both sides by 5
k = 86
So, we have:
w = 86l
When l = 2, we have:
w = 86 * 2
Evaluate
w = 172
Hence, a beam measuring 2 meters can support 172 kilograms
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Choose the graph below that matches the equation: =2/3 + 5
It is TRUE, so shade on the SAME side as (0,0)
Find the value of z if the volume of the cylinder is 1696.5m^3 use 3.14 for pi and round your answer to the nearest whole number.
Answer:
6 m
Step-by-step explanation:
The missing dimension can be found using the volume formula with the known values filled in. This gives an equation that can be solved for z.
The volume of a cylinder is given by the formula ...
V = πr²h
__
Using the given values, we have ...
1696.5 m³ = 3.14(z²)(15 m)
z² = (1696.5 m³)/(47.1 m) ≈ 36.0191 m² . . . . divide by 47.1 m
Taking the square root, we find z to be ...
z ≈ √(36.0191 m²) ≈ 6.00 m
The value of z is about 6 m.
1930 to the nearest 1000
Answer:
2000.
Step-by-step explanation:
The hundreds digit is 9 so we round up the 1 so the answer is 2000.
The diameter of a circle is 12 miles. What is the circle's area use 3.14
Step-by-step explanation:
Are of a circle is πr^2
to find the radius r=d/2
=12/2=6r
3.14x6x6
=169.56 cm^2
please mark as brainliest
Chris needs a clever pattern for Math class tomorrow. He comes up with this pattern: 8, 4, 12, 6, 16, 8, 20, 10, ___, __.
What is his rule for this pattern
A. each set of 4 numbers adds to 36.
B. each set of four numbers adds up to 30.
C. each set of 2 numbers makes up a prime number.
D. the first number in each set of 2 numbers is 4 more than the last first number, and the second number is ½ of the first.
Answer:
D
Step-by-step explanation:
can't really explain it just is the answer
hope this helps!
Part 1 - Application
If the length of an arc of a circle of radius 7 is approximately 10.99 cm. What is the measure of the central
angle associated with the arc? Use 3.14 for It. Give your answer in degrees and radians (approximate to two
decimals and exact).
The measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have a length of an arc of a circle of radius 7 is approximately 10.99 cm.
The radius r = 7 cm
The arc length l = 10.99 cm
We know,
l = rθ
θ is the central angle.
θ = l/r = 10.99/7 = 1.57 radians
To convert 1.57 radians into the degree multiply it by 180/π
θ = 89.95 degree
Thus, the measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
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Anyone mind helping me solve this inequality? Step by step
By decomposing the figure in simpler shapes, we will see that the total area is:
a = 180 cm²
How to find the area of the composite figure?
Remember that the area of a rectangle of width W and length L is:
A = L*W
And the area of a triangle with base B and height H is:
A = B*H/2.
Then, the upper part can be seen as a rectangle of length of 6cm and width of 6 cm, with two triangles on the sides, such that each triangle has a base of 3cm and a height of 6cm.
So the area of that part is:
A = 6cm*6cm + 2*(3cm*6cm/2) = 54cm²
Now, the bottom triangle has a base of 12 cm, and a height of:
15cm - 6cm = 9cm
Then its area is:
A' = 12cm*9cm/2 = 54cm²
This means that the total area of the figure is:
total area = 54cm² + 54cm² = 108cm²
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There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
5 blue, 4 red = 9 total
Probability (Blue, Blue) = 5/9 x 5/9 = 25/81 = 0.30864
Probability (Red, Red) = 4/9 x 4/9 = 16/81 = 0.19753
Probability (Blue,Blue) or (Red,Red) = 25/81 + 16/81 = 41/81 = 0.506173
Fraction answer = 41/81
Decimal answer = 0.506173 (round off as needed)
x+6/x+3 X x-6/x-3
A. 2x-12/x-3
B. x-12/x-6
C. x^2-12/x^2-6
D. x^2-36/x^2-9
d
Step-by-step explanation:
Consider triangle ABC. What is b?
Answer:
A triangle is equal to 540° so you do 112 add 37 which equals 149° then take it away from 540 which gives you 391° as your answer
Step-by-step explanation:
Your Welcome
1. You need a parking for your food truck, so you purchased 26 “parking hours” that you can use over the next month to park your food truck at the fair. Weekday hours cost $2/hour and weekend hours cost $10/hour. You spent a total of $220. How many weekday hours did you purchase?
2.If the weekday hours tripled but your budget of $220 for 26 parking hours remain the same. How many weekend hours can you purchase now that the weekday hours have increased?
The weekday hours you purchased is 5 hours.
The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.
What are the linear equations that represent the question?2a + 10b = 220 equation 1
a + b = 26 equation 2
Where:
a = number of hours for weekday parking b = number of hours for weekend parkingHow many weekday hours did you purchase?
Multiply equation 2 by 10
10a + 10b = 260 equation 3
Subtract equation 3 from equation 2
8a = 40
a = 5 hours
What is the weekend hours I can purchase?
(5 x 3) + b = 26
15 + b = 26
b = 26 - 15
b = 11 hours
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1.How many more pupils go to school by tricycle than bicycle?
A.4
B.5
C.3
D.2
2.what is the total number of pupils in grade 6 Simplicity?
A.33
B.28
C.29
D.30
3.what fraction of the pupil in grade 6 Simplicity walk to school?
A.8/33
B.12/33
C.10/33
D.3/33
4.what percentage of the pupil goes to school by walking?
A.24%
B.33%
C.9%
D.36%
How many more cubic inches are in the volume of a cylinder with a diameter of 12 inches and a height of 13 inches than in the volume of a cylinder with a diameter of 10 inches and a height of 11 inches?
Answer:
Approx. 606.02 cubic inches more.
Step-by-step explanation:
[tex]Volume=\pi *(\frac{diameter}{2})^2*height[/tex]
First, let's find the volume of the first cylinder (diameter=12, height=13).
[tex]V=\pi * (\frac{12}{2})^2 * 13\\V=\pi * (6)^2 * 13\\V=\pi * 36 * 13\\V=3.14*36*13\\V=113.04*13\\V=1469.52 in^3[/tex]
Now let's find the volume of the second cylinder (d=10, h=11).
[tex]V_{2}=\pi * (\frac{10}{2})^2*11\\V_{2}=\pi * (5)^2*11\\V_{2}=\pi * 25 * 11\\V_{2}=3.14*25*11\\V_{2}=78.5*11\\V_{2}=863.5in^3[/tex]
Lastly, we can subtract the volume of the second cylinder from the volume of the first cylinder.
This gets us a solution of 606.02 cubic inches.
Suppose you have the following null and alternative hypothesis
A type I error takes place if a given null hypothesis is rejected but is said to be true in the population such as the forecast shows it is snowing outside but actually it is isn't.
What is type 11 error?A type II error is known to be a statistical term that tells the error that takes place when one fails not to accept a null hypothesis that is said to be really false. A type II error create a false negative.
It known is known also as an error of omission. Example is the forecast shows that It is not snowing but it is actually snowing.Note that:
Type I error is false positive.Type II error is false negative.The power of the test shows that:
The Power is the likelihood of rejecting the null hypothesis even if it is false.Power is the likelihood of making the right decision that is to reject the null hypothesis even if the null hypothesis is false.Power is the likelihood of not making a Type II error and others.See full question below
Suppose you have the following null and alternative hypothesis:
H o: it is snowing.
H a: It is not snowing
(A) in the context of this problem, describe a Type-1 error
(B) Describe Type II error
(C)Describe power of the test
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In a group of 32 musicians, all play piano, guitar, or both. Of those musicians, 12 only play guitar and 16 play both How many of the musicians play only piano
Answer:
4 only play piano
Step-by-step explanation:
12 + 16 = 28
32 - 28 = 4
Consider the following histogram.
A histogram with 5 bars with intervals of equal width. The height of the first bar is 2. The height of the second bar is 5. The height of the third bar is 6. The height of the fourth bar is 5. The height of the fifth bar is 2.
© 2018 StrongMind. Created using GeoGebra.
Which answer correctly describes the shape of the data in the histogram?
left-skewed
right-skewed
symmetrical
uniform
Answer:
The shape of the data in the histogram is Symmetrical.
Step-by-step explanation:
This is because the distribution, or data set is the same to the left and right of the center point.
The tables show the battery lives (in hours) of two brands of laptops. Which brand's battery lives are more spread out? Explain
14 friends go out for dinner and the bill for food and drink comes to £130. The friends decided to add a 5% tip on the top of this total. If they divide this expense equally between them, How much does each friend pay?
The amount each friend does pay is £9.75
How to calculate the pay of each friend using fractions and arithmetic operations?We are going to find 5% of the total amount paid and divide it by the numbers of all the friends to determine the amount paid by each one of them.
From the given information:
The 5% of 130 = £6.5Total amount paid = £130 + £6.5 = £136.5Therefore, the cost of each friend is = [tex]\dfrac{136.5}{14}[/tex]
The cost of each friend = £9.75
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What is the exact value of x
Answer:
The value of x is 30 degrees.
Step-by-step explanation:
We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)
[tex]~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3[/tex]
Given quadrilateral A(2,-1) B(1,3) C(6,5) D(7,1), you want to prove that it is a parallelogram by showing opposite sides are parallel. What formula would you use?
Answer: Slope formula
Step-by-step explanation:
You could show the slopes of the opposite sides are equal, and thus they are parallel.
DO,K = (9, 6) (3, 2) The scale factor is
Using proportions, it is found that the scale factor of the transformation is of 1/3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, during the transformation, each coordinate was divided by 3, hence, applying the proportion, the scale factor of the transformation is of 1/3.
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helppp quickkkkkkk enough points
Answer:
[tex]a=2\\\\ b = 20\\\\ c = 47[/tex]
Step by step explanation:
[tex]a(x) = 2(x+5)^2 -3\\\\~~~~~~~=2(x^2 +2 \cdot 5 \cdot x +5^2) -3\\\\~~~~~~~=2(x^2 +10x+25) -3\\\\~~~~~~~=2x^2 +20x +50 -3 \\\\~~~~~~~=2x^2 +20x +47\\\\\text{By comparing}~ 2x^2 +20x +47~ \text{with the standard form}~ ax^2 +bx+c,\\\\a=2,~ b = 20,~ c = 47[/tex]
Answer:
A or 57 7/9ft3
Step-by-step explanation:
13/3x10/3x4/1 = 520/9=57 7/9