Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to complex numbers (1∕2 + 4i)².
Define complex numbers.Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the case of quadratic equations, the unknown roots are simplified using complex numbers if the roots are not real. In computer science and engineering, complex numbers are used. Both mechanical and civil engineering use complex numbers. Control systems employ complex numbers.
Given,
Complex numbers:;
(1/2 + 4i)²
(a +b )² = a² + b² + 2ab
Multiplying,
(1/2)² + (4i)² + 2(1/2)(4i)
1/4 + 16i² + 4i
i² = -1
1 - 64/4 + 4i
-63/4 + 4i
Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to (1∕2 + 4i)².
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i need help with finding the slope
HELP ASAP PLEASE PASA PLEH math yes math middle school math yeah it’s math ok I’ll stop now
The expression of the inequality is -0.96 ≤ 0.3x and the solution will be x ≥ -3.2 thus, option (D) is correct.
What is inequality?A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
As per the given,
-0.96 ≤ 0.3x
Divide by 0.3 into both sides of the above equation,
-0.96/0.3 ≤ x
x ≥ -3.2
The number line goes from -3.2 to the positive or greater than -3.2 in the last option.
Hence "The solution of the inequality -0.96 ≤ 0.3x is x ≥ -3.2".
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Determine the x-intercept of the line whose equation is given: y = 4 x + 2 a. (0, 2) b. (negative 2, 0) c. (0, negative one-half) d. (Negative one-half, 0) Please select the best answer from the choices provided A B C D
Answer:
D
Step-by-step explanation:
the x- intercept is the point where the line crosses the x- axis.
any point on the x- axis has a y- coordinate of zero.
let y = 0 in the equation and solve for x , that is
4x + 2 = 0 ( subtract 2 from both sides )
4x = - 2 ( divide both sides by 4 )
x = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex] ← x- intercept
coordinates of x- intercept = (- [tex]\frac{1}{2}[/tex], 0 )
How do i say uwu please tell me right now now right now
Answer: look it up how to pronounce the word
Step-by-step explanation: go to goggle translate or an app.
-3-10x=25+4x what’s the answer
Answer:
[tex] \: \: \: \: \: \: \: \: \: \: -3-10x=25+4x \\ ⇒ - 10x - 4x = 25 + 3 \\ ⇒ \: \: - 14x = 28 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⇒x = - \frac{ 28}{ 14} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⇒x = - 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]Step-by-step explanation:
Thank you
A salon wants to conduct a survey in order to study the consumption pattern of its consumers. The population mean spending on visiting salon per month is unknown with the population standard deviation is assumed to be $200. A random sample of 55 customers is selected and the sample mean spending on visiting salon per month is $800.
(a) Construct a 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month. (3 marks)
(b) It is suggested to do the second round inspection. This time, the sample size is 120. What is the sampling error at 95% confidence level? (2 marks)
a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows: (747, 853).
b) The sampling error at 95% confidence level is of: $35.78.
What is a z-distribution confidence interval?The bounds of the confidence interval are given as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The parameters for this problem are given as follows:
[tex]\overline{x} = 800, \mu = 200, n = 55, z = 1.96[/tex]
Hence the lower bound of the interval is of:
800 - 200 x 1.96/square root of 55 = 747.
The upper bound of the interval is of:
800 + 200 x 1.96/square root of 55 = 853.
The sampling error for a sample size of 120 is calculated as follows:
200 x 1.96/square root of 120 = $35.78.
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Andrew buys 8 bottles of cranberry juice at the corner store for a total cost of $5.68. If each bottle costs the same amount, how much is 6 bottles of juice?
Answer:
it is y=kx
Step-by-step explanation:
The cost of 6 bottle juice is $4.26.
What is cost?
A cost is the value of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.
Given:
Andrew buys 8 bottles of cranberry juice at the corner store for a total cost of $5.68.
So, the cost of each bottle is,
$5.68/8 = $0.71
Now to find the cost of 6 bottle of juice.
6 x $0.71 = $4.26
Hence, the cost of 6 bottle juice is $4.26.
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A school sells adult tickets and student tickets for a play. Adult tickets cost $8 each and student ticket cost $4 each. They collect $320 in total
Answer:
The answer is 8a + 4s = $320
Step-by-step explanation:
Let us take a for adult tickets and s for student ticket we get,
8a and 4s
They collect $320 in total
8a + 4s = $320
Thus, The equation represents this relationship is 8a + 4s = $320
what is an equation of the line that passes through the points (2,7) and (8,4)
Answer:
y = - 0.5x + 8
Step-by-step explanation:
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\frac{7-4}{2-8}[/tex]
[tex]\frac{3}{-6}[/tex]
[tex]-\frac{1}{2}[/tex]
m = - 1/2
y = - 1/2x + b
4 = - 0.5(8) + b
4 = - 4 + b
b = 8
y = - 0.5x + 8
Help!!!! Urgent pls!!!!
Answer: 34.44
Step-by-step explanation:
Answer:its d
Step-by-step explanation:
PLEASE HELP 50 BRAINLY POINTS IF YOU ANSWER THIS QUESTION CORRECTLY
A probability value is listed at the top of each column. Determine the probability for each situation, then drag and drop each situation into the column under its correct probability.
The list of all probabilities from first to last are 0.5, 0.5, 0.2, 0.4, 0.5,
and 0.2.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
There are a total of 6 possibilities when rolling a die and of which three are even numbers.
P(rolling an even number is) = 3/6 = 1/2 0.5.
There are two possibilities when flipping a coin,
∴ The probability of getting a head is (1/2) = 0.5.
There are a total of (1 + 1 + 3) = 5 possibilities of choosing a block out of which one is red, therefore the probability of choosing a red is = (1/5) = 0.2.
Total 10 marbles and 4 blue marbles, hence the probability of choosing a blue marble is (4/10) = 2/5 = 0.4.
There are a total of 8 balls out of which 4 are soccer balls, hence the probability of choosing a soccer ball is = 4/8 = 1/2 = 0.5.
Total 15 balls out of which 3 tennis balls hence the probability of choosing a tennis ball is = 3/15 = 0.2.
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What do the graphs indicate about (4, 4) ?
A. It is the only ordered pair that satisfies y = 1/4 * x + 3 it is also the only ordered pair that satisfies . y = 2x - 4
B. It is the only ordered pair that satisfies y = 4x + 3 it is also the only ordered pair that satisfies y = 1/2 * x - 4
C. It is the only ordered pair that satisfies both y = 1/4 * x + 3 and . y = 2x - 4
It is the only ordered pair that satisfies both y = 4x + 3
D. and y = 1/2 * x - 4
Point (4,4) is the only ordered pair that satisfies both equations y = (1/4) x + 3 and y = 2x - 4.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
In the given graph,
The point (4, 4) is the intersection point of the lines.
Since, the point (4, 4) is intersection point,
Therefore, this point will satisfy the equations of line.
From the options, take equations,
y = (1/4) x + 3
Substitute x = 4 and y = 4
4 = (1/4) 4 + 3
4 = 4
y = 2x - 4
Substitute x = 4 and y = 4
4 = 2 × 4 - 4
4 = 4
The point (4,4) satisfies both the equations.
Therefore, (4,4) is the only ordered pair that satisfies both equations y = (1/4) x + 3 and y = 2x - 4.
Option (C) is correct option.
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PLEASE HELP
Find the arc length and sector area for the following:
(Use pi=3.14...do not use the pi button on your calculator!)
arc length =
sector area =
The area of the sector and length of the arc are 4.7 unit squared and 3.14 units respectively.
How to find the area of a sector and arc length?A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them.
The area of sector of a circle is the amount of space enclosed within the boundary of the sector.
Therefore,
area of the sector = 1 / 2 r²∅
area of the sector = 1 / 2 × 3² × π / 3
area of the sector = 9π / 6
area of the sector = 3 / 2 × 3.14
area of the sector = 4.71 units²
Length of the arc = r∅
where
r = radius∅ = radianTherefore,
Length of the arc = 3 × π / 3
Length of the arc = π
Length of the arc = 3.14 units
Therefore, the area of the sector is 4.71 units² and the length of the arc is 3.14 units.
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I need this answer asap
Answer:
x=-8
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x= -8
Step-by-step explanation:
-------------------------
An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If
x engines are made, then the unit cost is given by the function C(x)-0.3x²-192x+47,470. How many engines must be made to minimize the unit cost?
Do not round your answer.
There are 320 engines must be made to minimize the unit cost.
What is an expression?Expression in math's is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
The unit cost is given by the function,
⇒ C(x)= 0.3x²- 192x + 47,470
Now,
Since, The unit cost is given by the function,
⇒ C(x)= 0.3x²- 192x + 47,470
Hence, We get;
⇒ dC/dx = 0.6x - 192
Put dC/dx = 0
⇒ 0 = 0.6x - 192
⇒ 0.6x = 192
⇒ x = 320
And, d²C/dx² = - 192 < 0
Hence, This gives the maximum value.
So, The number of engines which must be made to minimize the unit cost = 320
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Please factor the following questions
Factor the following questions is.6 m(x+2 n+2),
What is factor?
In mathematics, an integer m that can be multiplied by another integer to create n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.
[tex]6 x m+12 m+12 m n[/tex]
Factor out common term[tex]$6 m$ : $6 m(x+2+2 n)$[/tex]
[tex]\begin{aligned}& =6 m(x+2+2 n) \\& =6 m(x+2 n+2)\end{aligned}[/tex]
[tex]13 r+r+9 x r[/tex]
Add similar elements: [tex]$13 r+r=14 r$[/tex]
[tex]=14 r+9 x r[/tex]
[tex]15 x y+45 y+3 m y[/tex]
Factor out common term [tex]3y: $\quad 3 y(5 x+15+m)$[/tex]
[tex]\begin{aligned}& =3 y(5 x+15+m) \\& =3 y(5 x+m+15)\end{aligned}[/tex]
[tex]$7 m n+13 m n+8 m n$[/tex]
Add similar elements: [tex]$7 m n+13 m n+8 m n=28 m n$[/tex][tex]$=28 \mathrm{mn}$[/tex]
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write the equation of the line shown on the graph 0,3 3,1
Answer:
write the equation of the line shown on the graph 0,3 3,1
Step-by-step explanation:
ano ba slope of variables
Find the measure of angle A.
Answer: 32
Step-by-step explanation:
Answer:
25 degrees
Step-by-step explanation:
sum of all three angles of a triangle equal 180
135+5x+4x=180
135+9x=180
-135. -135
9x=45
x=5
angle A is 5x
5(5)
25
hopes this helps please mark brainliest
1.
For a birthday party, Marissa bought three cartons of ice cream at $4.59 each and two packages of plastic
bowls at $3.00 each. If food is not taxed and non-emergency grocery items are taxed at the rate of 5%, what
was her total bill?
Answer:
$20.07
Step-by-step explanation:
You want Marissa's total bill when she bought three cartons of ice cream at $4.59 each and two packages of plastic bowls at $3.00 each, with the plastic being taxed at 5%.
Extended amountsThe amount for each item will be the product of the cost per unit and the number of units.
ice cream total = 3 × $4.59 = $13.77
plastic total = 2 × $3.00 = $6.00
TaxThe tax is applied only to the plastic, so the amount of tax is ...
5% × $6.00 = $0.30
Total billThe total bill is the sum of the item costs and the tax:
$13.77 +6.00 +0.30 = $20.07
Marissa's total bill was $20.07.
Sine, Cosine, Tangent question below
Answer:False
Its just simply incorrect
Two parallel lines are cut by a transversal, as shown. If m 21 = 114°, what is m 22?
help me asap
Answer:
∠ 2 = 66°
Step-by-step explanation:
∠ 1 and ∠ 2 are same- side interior angles and sum to 180° , then
∠ 2 + 114° = 180° ( subtract 114° from both sides )
∠ 2 = 66°
Could the average person lift the weight of $150 in quarters? HINT: The average quarter weighs 0.2 oz.
The solution is 120 ounces
An average man can lift the weight of $ 150 in quarters
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total weight an average man can lift be = A
Now , the weight of an average quarter = 0.2 ounces
Now , Number of quarters in $ 1 = 4 quarters
Let the total amount be = $ 150
So , the number of quarters in $ 150 is given by the equation
Number of quarters in $ 150 = 150 x 4
Substituting the values in the equation , we get
Number of quarters in $ 150 = 600 quarters
And , the weight of 600 quarters = 600 x weight of an average quarter
Substituting the values in the equation , we get
Number of quarters in $ 150 = 600 quarters
The weight of 600 quarters = 600 x 0.2
The weight of 600 quarters = 120 ounces
Therefore , the value of A is 120 ounces
Hence , an average man can lift the weight of $ 150 in quarters
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The equation of a line perpendicular to y=3x-1 and goes through (0,2)
Answer:
y = [tex]-\frac{1}{3}[/tex]x + 2
Step-by-step explanation:
Find the reciprocal change the sign of the gradient (m=3):
[tex]-\frac{1}{3}[/tex]
so
y = [tex]-\frac{1}{3}[/tex]x + c
The intersect is 2, so c = 2
Final answer: y = [tex]-\frac{1}{3}[/tex]x + 2
Explain why a selection of 10 students from your class can have marks that aren’t normally distributed when the marks of entire class are normally distributed.
A group of researchers wants to develop an experiment to determine whether a new drug effectively treats high blood pressure. The researchers want to inject the drug in monkeys first to determine whether there are any potential serious side effects.
Part A: What are some possible ethical issues to this type of testing? (5 points)
Part B: While conducting the experiment, the researchers find that blood pressure levels return to normal, and they declare the drug is the cause of the change. Is this a good assumption? Explain. (5 points) (10 points)
The possible ethical issues of testing are given below.
What is drug?
Any chemical that, when consumed, alters the physiology or psychology of an organism qualifies as a drug. Usually, foods and other substances that support nutrition are distinguished from drugs.
(A)
Possible ethical problems: Since animals are able to perceive their surroundings, they have the right to exist free from human interference.
Therefore, animal research should not be done by humans. It is wrong to use animals only as stools to advance scientific understanding.
The right for an animal to live a full life without pain or suffering should be equal to that of humans.
Part B:
For the following reason, this is a bad assumption.
It does not follow that just because a drug causes the blood pressure levels in monkeys to return to normal after consumption that the drug will do the same for humans. This is because how humans and monkeys react to drugs differ.
Furthermore, it's unclear whether the drug's return to normal blood pressure was caused by it or by some other confounding variables that the researcher neglected to take into account.
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Please help asap will give BRAINLIEST
Solve 2 4/7 X 2/3
1 15/21
2 8/21
2 12/14
3 2/12
Answer:
12
X
7
Step-by-step explanation:
consider the following method, which is intended to return the product of 3 and the nonnegative difference between its two int parameters.
Answer: the answer is try hard and if you don’t succeed try try again
Step-by-step explanation:
Determine the type of basic curve the set of parametric equations represents.
x(t)=3cos(t)
y(t)=3sin(t)
Select the correct answer below:
ellipse
circle
hyperbola
line
parabola
Answer:
Then it is a circle!
Suppose you roll a six-sided die. What is the probability that a 2 or 5 is NOT rolled? (in fraction form)
A) 1/6
B)2/6
C) 3/6
D)4/6
On solving the provided question, we can say that the probability that a 2 or 5 is NOT rolled is - 1- 1/3 = 2/3
What is probability?A branch of mathematics called probability describes the likelihood that an event will occur or that a proposition is true. The probability of an event ranges from 1 to 1, with 1 indicating certainty and numbers in between indicating the difficulty of the event.
to determine the likelihood of rolling a die with a 2 or a 5 on it. The probability formula can be used to do this.
[tex]P(E) = (Number of times event occurs)/(Total number of trials)[/tex]
S = 1, 2, 3, 4, 5, 6 is a sample space of potential results when rolling a dice.
If the likelihood of rolling a die and having a result of 2 or 5 is event E.
Number of occurrences [n(E)] = 2
[n(S)] = 6 trials in all
[tex]P(E) = 2/6 = \frac{1}{3}[/tex]
So, the probability that a 2 or 5 is NOT rolled is - \
1- 1/3 = 2/3
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IX.
A sorting machine at an orange processing plant has to sort 720 tons of oranges to meet a
deadline. The machine can process 360 tons of oranges in 50 minutes. Determine how
long it will take the machine to sort 720 tons of oranges.
Proportionately, the sorting machine will take 100 minutes (1 hour and 40 minutes) to process 720 tons if it takes 50 minutes to process 360 tons.
What is proportion?Proportion is the ratio or numerical relationship that one quantity bears to another.
Proportions are equated to each other to find missing variables.
Proportions are fractional values, usually depicted as fractions, decimals, or percentages.
The total number of oranges to sort = 720 tons
Machine processing speed = 360 tons per 50 minutes
Proportionately, the machine can process 7.2 tons per minute (360/50).
The time to sort 720 tons = 100 minutes (720/360 x 50) or (720/7.2)
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