Answer:
-6i
Step-by-step explanation:
Complex roots have to come in conjugate pairs
So if we have 6i as a root, we must have -6i as a root
Answer:
-6i
Step-by-step explanation:
Hello, because this polynomial function has real coefficients and 6i is a zero, the conjugate of 6i is a zero as well. It means -6i is a zero.
The degree is 4 the number of zeroes is less or equal to 4 and we have already, 6, 4, 6i and -6i. So we have all the zeroes.
Thank you
The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,θ) . Select the correct equation in polar coordinates below.
x2+y2−4x=0
a. r=4 sinθ
b. r=4 cosθ
c. r cos2θ=4 sinθ
d. r sin2θ=4 cosθ
Answer:
B. r = 4cosθStep-by-step explanation:
Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).
x = rcosθ and y = rsinθ.
Substituting the value of x and y in their polar form into the given expression we have;
x²+y²−4x=0
( rcosθ)²+( rsinθ)²-4( rcosθ) = 0
Expand the expressions in parenthesis
r²cos²θ+r²sin²θ-4rcosθ = 0
r²(cos²θ+sin²θ)-4rcosθ = 0
From trigonometry identity, cos²θ+sin²θ =1
The resulting equation becomes;
r²(1)-4rcosθ = 0
r²-4rcosθ = 0
Add 4rcosθ to both sides of the equation
r²-4rcosθ+4rcosθ = 0+4rcosθ
r² = 4rcosθ
Dividing both sides by r
r²/r = 4rcosθ/r
r = 4cosθ
Hence the correct equation in polar coordinates is r = 4cosθ
I need help please, m bda =
And m bca =
Step-by-step explanation:
Exterior angle BOA = 250°
Interior angle BOA = 360°- 250° = 110°
Now,
(A) BDA = interior angle BOA / 2 = 55°( Property of circles)
(B) From the figure, we observe that AOBC is a cyclic quadrilateral (i.e. sum of opposite angles is 180°).
Therefore, BCA + BOA = 180°
BCA = 180° - 110° = 70°
Does artistic ability determine which type of operating system a person prefers? Suppose that a market research company randomly selected n=259 adults who used a desktop or laptop outside of the workplace (tablets and smartphones were excluded).
Answer:
Your question lacks some parts attached below is the complete question
Answer : 2.66
Step-by-step explanation:
The expected number ( E ) can be calculated using the formula below
[tex]E = \frac{row total * column total }{gross total}[/tex]
since we are computing the number of subjects that would prefer Linux operating system and are also rated as exceptional
The row total to be used = 53 ( row total of exceptional )
The column total to be used = 13 ( column total of Linux )
The gross total to be used = summation of row total of both exceptional and no-exceptional = 259
BACK TO THE EQUATION
E = [tex]\frac{53*13}{259}[/tex] = 689 / 259
E = 2.6602 ≈ 2.66
When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?
Answer:
Because it increases the risk of Type 1 error
Step-by-step explanation:
ANOVA is the analysis of the variance .
When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error .
For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test. Similarly to test 10 population mean would require 45 separate two sample t test.
This has two disadvantages .
First the procedure is too lengthy and tediuos.
Second the overall level of significance greatly increases as the number of t- tests increases.
The analysis of the variance compares two different estimates of variance using the F distributionto determine whether the population means are equal.
BRAINLEST Find the sum of the first 6 terms of the infinite series: 1 - 2 + 4 - 8+...
Answer:
-21
Step-by-step explanation:
1-2+4-8+16-32
=-21
Answer:
The sum of the first 6 terms of the infinite series will be - 21.
Step-by-step explanation:
In this case, the infinite geometric series 1 - 2 + 4 - 8 + ... is represented by the following summation,
[tex]\sum _{{k=0}}^{{n}}(-2)^{k}[/tex]
Therefore if we continue this pattern, the first 6 terms will be 1 - 2 + 4 - 8 + 16 - 32. Adding these terms,
1 - 2 + 4 - 8 + 16 - 32
= - 1 + 4 - 8 + 16 - 32
= 3 - 8 + 16 - 32 = - 5 + 16 - 32
= 11 - 32 = Solution : - 21
George's height is 1.75 meters and Martha's height is 160 centimeters. How much taller is George than Martha in millimeters?
George should be 150 mm taller than Martha.
Calculation of the height in millimeters:
Since George's height is 1.75 meters and Martha's height is 160 centimeters.
So here we convert the meters to mm
So,
[tex]= 1.75\times 100\\\[/tex]
= 1750 mm
Now 160 cm to mm
So,
[tex]= 160\times 10[/tex]
= 1,600 mm
So, the difference should be
= 1,750 - 1,600
= 150 mm
Therefore, George should be 150 mm taller than Martha.
Learn more about height here: https://brainly.com/question/15810288
Jake’s dad is 6 more than 3 times Jake’s age. The sum of their ages is 42 . Find their ages. Use whole numbers.
Answer: Jake is 9 and his dad is 33.
Step-by-step explanation: 9x3=27+6=33 9+33=42
Answer:
Jake is 9 and Jake's dad is 33
Step-by-step explanation:
To solve this we need to create a equation where D is the age of Jake's dad and J is the age of Jake
J+D=42
3J+6=D
Solve by substitution
Find the missing side or angle.
Round to the nearest tenth.
Answer:
[tex] b = 2.7 [/tex]
Step-by-step explanation:
Given:
< C = 53°
< B = 80°
a = 2
Required:
Find b
Solution:
The question given suggests we are given measures for a ∆.
To find side b, which corresponds to angle B, first, we'd find angle A, which corresponds to side a, then apply the Law of sines to find side b.
=> A = 180 - (53 + 80) = 47°
Law of Sines: [tex] \frac{a}{sin(A} = \frac{b}{sin(B} [/tex]
Plug in the values into the formula
[tex] \frac{2}{sin(47} = \frac{b}{sin(80} [/tex]
Cross multiply
[tex] 2*sin(80) = b*sin(47) [/tex]
Divide both sides by sin(47) to make b the subject of formula
[tex] \frac{2*sin(80)}{sin(47} = b [/tex]
[tex] 2.69 = b [/tex]
[tex] b = 2.7 [/tex] (nearest tenth)
If 2( a^2 +b^2 ) = ( a+b)^2 , then
a. a+b =0
b. a =b
c. 2a =b
d. ab =0
Answer:
the answer is a=b
Step-by-step explanation:
The average salary of all assembly-line employees at a certain car manufacturer is $42,000 is it a sample or population
Answer:
Population parameters
Step-by-step explanation:
Population parameters usually find from the average values, in a simple way we can say that finding the average value comes in the Population Parameters.
In the given question, car manufacturing companies provide sample of average.
So, given scenario is a type of "Population parameters".
The radius of a circle measures 5 inches A central angle of the circle measuring 12 radians cuts off a sector
What is the area of the sector?
Enter your answer as a simplified fraction in the box
area =
inches squared
Answer:
25/4 square inches
Step-by-step explanation:
The area of a sector of a circle is given by the formula ...
A = (1/2)r²θ
where r is the radius and θ is the central angle in radians.
For your sector, the area is ...
A = (1/2)(5 in)²(1/2) = 25/4 in²
If 4 pounds of cherries cost $10, what is the unit price
Answer:
2.5$ per pound
Step-by-step explanation:
The cost of 4 pounds of cherries cost 10$
So to khow the price of 1 pound we must divide 10 by 4.
● 10/4 = 2.5
So 1 pound costs 2.5$
simplify -3(2g - 6) +4g
-3-2g+6+4g
3+2g
hope it helps
Answer:
-2g + 18
Step-by-step explanation:
-3(2g - 6) + 4g
First we use distributive property.
-3 × 2g = -6g
-3 × -6 = 18
now we have
-6g + 18 + 4g
Now we combine the like terms
-6g + 4g = -2g
Finally we have
-2g + 18
and they are not like terms so we leave them and the equation is solved.
how many solutions are there to this non-linear systems/graph a. one solution,b.two solutions,c.no solutions
Fill in the blanks and explain the pattern
0,1,1,2,3,5,__,__,21,34,55
Answer:
8,13
Step-by-step explanation:
Look at the pattern :
0,1,1,2,3,5,...,...,21,34,55.
As you see the number in the pattern was made by the sum of 2 numbers behind it. Then, the blanks must be filled by :
3 + 5 = 88 + 5 = 13So, the blanks must be filled by 8 and 13
Answer:
In the two blanks would be 8, 13.
The pattern is practically the Fibonacci Code.
Step-by-step explanation:
The Fibonacci Code is a mathematical sequencing in which you start with two numbers and add them together to make the third number, then you add the third number and the second number together. Practically you keep adding each new sum and the number before it in the sequence to find the next new sum.
After 55 in this pattern, the pattern would go 89, 144, 233, 377, 610, 987,...
Which phrase describes the algebraic expression 8f+7?
the product of 8 and 7 more than a number
the quotient of 8 and 7
8 times the sum of a number and 7
8 times a number plus 7
Answer:
8 times a number plus 7
Step-by-step explanation:
Let the number be f.
Simply, 8 f+7 is the expression.
Thank you!
Find the minimum sample size n needed to estimate for the given values of c, , and E. c, , and E Assume that a preliminary sample has at least 30 members.
Answer:
hello your question is incomplete below is the complete question
Find the minimum sample size n needed to estimate μ For the given values of c, σ, and E. c=0.98, σ=6.5, and E=22 Assume that a preliminary sample has at least 30 members.
Answer : 48
Step-by-step explanation:
Given data:
E = 2.2,
std ( σ ) = 6.5
c ( level of confidence ) = 0.98
To find the minimum sample size
we have to first obtain the value of [tex]Z_{a/2}[/tex]
note : a can be found using this relation :
( 1 - a ) = 0.98 ----- equation 1
a = 1 - 0.98 = 0.02
hence: a/2 = 0.01
This means that P( Z ≤ z ) = 0.99 the value of z can be found using the table of standard normal distribution. from the table the value of z = 2.33
P( Z ≤ 2.33 ) = 0.99
To obtain the sample size n
[tex]n = (\frac{std*z}{E} )^{2}[/tex]
n = [tex](\frac{6.5*2.33}{2.2} )^2[/tex] = (6.88409)^2
Therefore n ≈ 48
what is 90.125 written in expanded from?
Answer:
The answer is 90+0+0.1+0.02+0.005.
Step-by-step explanation:
The reason for my answer is because 90 is in the tens place. 90+0 is equal to 90 so that's why it is a +0 after the 90. Now, we have a decimal. After the decimal, we have 125. It is +0.1 because the 1 in 90.125 is in the tenths place. Next, it is +0.02 because the 2 in 90.125 is in the hundredths place. Last but not least, it is +0.005 because the 5 in 90.125 is in the thousandths place.
State whether each ratio forms a proportion.
1) 6:3, 18:9 2) 3:4, 30:40 3) 14/18,28/36 4) 2/5,5/2
Answer: Please Give Me Brainliest, Thank You!
#1, #2, #3 do, but #4 doesn't
Step-by-step explanation:
#1
18/9=2
6/3=2
#2
30/3=10
40/4=10
#3
28/14=2
36/18=2
Write each expression in a simpler form that is equivalent to the given expression. Let g be a nonzero number. 1/g^1 or 1/g-1
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
Apply rule : [tex]a^1 =a[/tex]
[tex]\displaystyle \frac{1}{g^1 } =\frac{1}{g}[/tex]
[tex]\displaystyle \frac{1}{g^{-1}}[/tex]
Apply rule : [tex]\displaystyle a^{-b}=\frac{1}{a^b}[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }[/tex]
Apply rule : [tex]\displaystyle \frac{1}{\frac{1}{a} } =a[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }=g[/tex]
Answer:
[tex]\frac{1}{g^1}[/tex]
= [tex]\frac{1}{g}[/tex]
[tex]\frac{1}{g - 1}[/tex]
= [tex]\frac{g^1}{1}[/tex]
= [tex]\frac{g}{1}[/tex]
= g
Hope this helps!
Maya is interning at a law firm over the summer and is paid b the hour. If her hourly wage is $52 which represents the proportional relationship between the wages she earns (w) and the number of hours (h)?
Answer: [tex]w= 52 h[/tex] .
Step-by-step explanation:
Given: Maya is interning at a law firm over the summer and is paid per hour.
Total wages = (Hourly wage) x (Number of hours worked)
If her hourly wage is $52, then the total wages(w) = 52 x (Number of hours(h))
i.e. w= 52 h
Hence, the proportional relationship between the wages she earns (w) and the number of hours (h) described by [tex]w= 52 h[/tex] .
The Rogers family drove 220 miles in 5.5 hours. How many miles would they drive at this same rate in 4 hours? A. 88 mi B. 147 mi C. 160 mi D. 179 mi Please show ALL work! <3
Answer:
160 miles
Step-by-step explanation:
We can use a ratio to solve
220 miles x miles
--------------- = ----------------------
5.5 hours 4 hours
Using cross products
220 *4 = 5.5x
880 = 5.5x
Divide each side by 5.5
880/5.5 = x
160 miles
Answer:
[tex]\large \boxed{\mathrm{C. \ 160 \ miles}}[/tex]
Step-by-step explanation:
We can solve this problem by ratios.
Let x be the missing value.
[tex]\displaystyle \frac{220}{5.5} =\frac{x}{4}[/tex]
Cross multiply.
[tex]5.5 \times x = 220 \times 4[/tex]
[tex]5.5x=880[/tex]
Divide both sides by 5.5.
[tex]\displaystyle \frac{5.5x}{5.5} =\frac{880}{5.5}[/tex]
[tex]x=160[/tex]
1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going to the river. Each monkey had 1 tortoise in each hand.
How many animals were going to the river?
Answer:
91 animals
Step-by-step explanation:
Because every elephant saw 3 monkeys, there were 9 * 3 = 27 monkeys and because every monkey had 1 tortoise in each hand and we know that monkeys have 2 hands, there were 27 * 2 = 54 tortoises. To find the total number of animals that were going to the river, we can calculate 1 + 9 + 27 + 54 = 91 animals.
Answer:
10
Step-by-step explanation:
Only the rabbit and the 3 monkeys are described as going to the river. The tortoises seem to be going to the river by virtue of being taken there by the monkeys. Those on the path to the river were ...
1 rabbit
3 monkeys
6 tortoises
A total of 10 animals.
15+9=? (5+3) What number is missing from the expression?
Answer:
[tex] \boxed{ \boxed{ \bold{ \mathsf{3}}}}[/tex]Step-by-step explanation:
Let the missing number be 'x'
⇒[tex] \mathsf{15 + 9 = x(5 + 3)}[/tex]
Distribute x through the parentheses
⇒[tex] \mathsf{15 + 9 = 5x + 3x}[/tex]
Swap the sides of the equation
⇒[tex] \mathsf{5x + 3x = 15 + 9}[/tex]
Add the numbers
⇒[tex] \mathsf{5x + 3x = 24}[/tex]
Collect like terms
⇒[tex] \mathsf{8x = 24}[/tex]
Divide both sides of the equation by 8
⇒[tex] \mathsf{ \frac{8x}{8} = \frac{24}{8} }[/tex]
Calculate
⇒[tex] \mathsf{x = 3}[/tex]
Hope I helped!
Best regards!
Sketch a graph to envision the following scenario. Place time on the x-axis. A rock climber is 25 feet above sea level. After 8 seconds he is at sea level. (He did not fall). What is the slope of the line depicted (no units)
Answer:
Please refer to the attached graph.
Slope = -3.125
Step-by-step explanation:
Given
Time is placed on x axis.
Initially, height of rock climber is 25 feet above sea level.
[tex]t_1 =0\ sec[/tex]
[tex]h_1[/tex] = 25 feet
After 8 seconds, he is at sea level.
[tex]t_2 =8\ sec[/tex]
[tex]h_2[/tex] = 0 feet
To find:
Graph of the given points and Slope of the line depicted.
Solution:
Kindly refer to the attached graph.
Here, we have been given two points to be plotted on the xy coordinate plane.
1st point is (0, 25): Time is 0 and height above sea level is 25 ft
2nd point is (8, 0): Time is 8 seconds and height above sea level is 0 ft (i.e. he comes to sea level)
First of all, mark these points and join them with a straight line.
Please refer to attached graph.
Slope of a line is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex]y_2 = 0\\y_1 = 25\\x_2 = 8\\x_1 = 0[/tex]
Using the formula:
[tex]m=\dfrac{0-25}{8-0}\\\Rightarrow m=-\dfrac{25}{8} = \bold{-3.125}[/tex]
x power 8 + x power 4 + 1
factorize
Answer:
[tex]1(x {}^{8} + x {}^{4} + 1)[/tex]
Step-by-step explanation:
[tex]x {}^{8} + {x}^{4} + 1 =1( x {}^{8} + x {}^{2} + 1)[/tex]
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.
2(cos20∘+isin20∘))3=__________
Answer:
After solving the power:
[tex]\bold{2(cos60^\circ+isin60^\circ)}[/tex]
Rectangular form:
[tex]\bold{1+i\sqrt3}[/tex]
Step-by-step explanation:
Given the complex number:
[tex]2(cos20^\circ+isin20^\circ)^3[/tex]
To find:
The indicated power by using De Moivre's theorem.
The complex number in rectangular form.
Rectangular form of a complex number is given as [tex]a+ib[/tex] where a and b are real numbers.
Solution:
First of all, let us have a look at the De Moivre's theorem:
[tex](cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )[/tex]
First of all, let us solve:
[tex](cos20^\circ+isin20^\circ)^3[/tex]
Let us apply the De Moivre's Theorem:
Here, n = 3
[tex](cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ[/tex]
Now, the given complex number becomes:
[tex]2(cos60^\circ+isin60^\circ)[/tex]
Let us put the values of [tex]cos60^\circ = \frac{1}{2}[/tex] and [tex]sin60^\circ = \frac{\sqrt3}{2}[/tex]
[tex]2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }[/tex]
So, the rectangular form of the given complex number is:
[tex]\bold{1+i\sqrt3}[/tex]
Which given answer is correct and how do you solve for it?
Answer:
b
Step-by-step explanation:
What is the probability that a student who has no chores has a curfew ?
Answer:
15/22
Step-by-step explanation:
Of the 66 students who have no chores, 45 have a curfew. So the probability is 45/66 = 15/22.
Find the missing probability. P(A)=7/20,P(A∪B)=191/400,P(A∩B)=49/400 ,P(B)=? A. 7/8 B. 1/4 C. 117/400 D. 19/40
Answer:
B
Step-by-step explanation:
P(AUB)=P(A)+P(B)-P(A∩B)
191/400=7/20+P(B)-49/400
P(B)=191/400+49/400-7/20=240/400-7/20=12/20-7/20=5/20=1/4
The value of P(B) is 1/4.
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
For an experiment having q number of outcomes, the number of favorable outcomes can be denoted by p. The formula to calculate the probability of an event is as follows:
Probability(Event) = Favorable Outcomes/Total Outcomes = p/q
Given data as :
P(A) = 7/20,
P(A∪B) = 191/400,
P(A∩B) = 49/400 ,
P(AUB) = P(A) + P(B) - P(A∩B)
Substitute the values of P(A), P(A∪B) and P(A∩B) in formula,
191/400 = 7/20 + P(B) - 49/400
Rearrange the terms in the equation,
P(B) = 191/400 + 49/400 - 7/20
P(B) = 240/400 - 7/20
P(B) = 12/20 - 7/20
P(B) = 5/20
P(B) = 1/4
Hence, the value of P(B) is 1/4.
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