Given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i
Powers of complex number expressionsThe given complex number is z = -1 - i
[tex]z^3[/tex] means to raise z to the power of 3
[tex]z^3=(-1-i)^3[/tex]
Expand and simplify the expression:
[tex]z^3=(-1)^3+3(-1)^2(-i)+3(-1)(-i)^2+(-i)^3\\\\z^3=-1-3i-3i^2-i^3[/tex]
Note that:
[tex]i^2=-1\\\\i^3=-i[/tex]
Substitute these into the resulting expression
[tex]z^3=-1-3i-3(-1)-(-i)\\\\z^3=-1+3-3i+i\\\\z^3=2-2i[/tex]
Therefore, given z = -1 - i, the expression for [tex]z^3[/tex] is 2 - 2i
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The diameter of a pipe is normally distributed, with a mean of 0.8 inch and a variance of 0.0004. What is the probability that the diameter of a randomly selected pipe will exceed 0.84 inch? (You may need to use the standard normal distribution table. Round your answer to three decimal places.) . Hint: take the square root of the variance to find the standard deviation.
The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977
What is probability?Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events
How to determine the probability?The given parameters are:
Mean = 0.8
Variance = 0.0004
Calculate Standard deviation using
σ = √σ²
This gives
σ = √0.0004
Evaluate
σ = 0.02
Calculate the z-score at x = 0.84 using
z = (x - [tex]\bar x[/tex])/σ
This gives
z = (0.84 - 0.8)/0.02
Evaluate
z = 2
The probability is then represented as:
P(x > 0.84) = P(z > 2)
Next, we look up the value of the z table of probabilities
From the z table of probabilities, we have:
P(x > 0.84) = 0.977
Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977
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During an unusual storm, the temperature fell 8° C, rose 5° C, fell 4° C,
and then rose 6° C. If the temperature was 32° C at the outset of the storm,
what was it after the storm was over?
_ May Occur if the chosen sample is too small for a study.
a) Participation Bias
b) response Bias
c)non-response Bias
d) sampling Bias
e) Reasearcher Bias
The non response bias can happen if the chosen sample is too small for a study.
What is the non response bias?This is the term that is used to refer to the type of bias that happens in a research study because the some of the study participants could not participate in the study.
This type of bias is a very serious matter of concern while carrying out research.
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What is the area of a poster that is 1 1/2 feet by 2 1/2 feet?
The area of the poster is 28.75 feet square.
How to determine the areaNote that the area of a rectangle is given as;
Area = length × width
Length = 11. 5 feet
Width = 2. 5 feet
Area = 11. 5 × 2. 5
Area = 28. 75 feet square
Thus, the area of the poster is 28.75 feet square.
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The length of the major axis of the ellipse below is 14, and the length of the
red line segment is 3. How long is the blue line segment?
Answer:
11
Step-by-step explanation:
The focal length is 14, and thus the sum of the lengths of the blue and red segments is also 14.
Suppose that X is a Bernoulli random variable with success probability 0.8. (Note: If this number is not already rounded to two decimal places, round it to two decimal places before proceeding.)
Calculate the probability of failure.Round your answer to two decimal places and enter it as a decimal number (as opposed to a fraction percentage or a fraction).
Considering the probability of success of 0.8 in the Bernoulli trial, the probability of failure is of 0.2.
What is the probability of failure in a Bernoulli trial?
The probability of failure in a Bernoulli trial is one subtracted by the probability of a success.
In this problem, the probability of a success is of 0.8, hence the probability of failure is:
pF = 1 - 0.8 = 0.2.
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1!+2(2!)+3(3!)+...+n(n!)=(n+1)!-1
Step-by-step explanation:
OK, let's assume it this way:
Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!
Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+
Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+...+(n+1)!-n!=(n+1)!-1!=(n+1)!-1
and boom problem solved
What are the domain and range of g(x)=√x+4?
OD: [4, ∞) and R: [0, ∞)
OD: (-4, ∞) and R: (-∞, 0)
OD: [-4, ) and R: [0, ∞)
OD: (4,) and R: (-∞, 0)
Answer:
Domain [-4 , +∞)
Range [0 , +∞)
Step-by-step explanation:
the function g such that g(x)=√(x+4) ,is defined
for the values of x that verify :
x + 4 ≥ 0
⇔ x ≥ -4
Then
The domain of g is [-4 , +∞)
………………………………………………
Let x ∈ [-4 , +∞)
then x ≥ -4
then x + 4 ≥ 0
then g(x) = √(x+4) ≥ 0
Therefore, we can affirm that the range of g is [0 , +∞)
Fill in the missing term in the pair of equivalent ratios. *
5:30 15:
Your answer
The state low temperatures for five states are as follows: -42
On a piece of graph paper, plot the following points: A (3, 1), B (1, 5), C (9, 9), and D (11, 5). These coordinates will be the vertices of a quadrilateral. How would you use the distance formula and the slope formula to prove that this figure is actually a rectangle?
The given coordinates are actually a rectangle
How to determine the quadrilateral type?
The coordinates are given as:
A (3, 1), B (1, 5), C (9, 9), and D (11, 5).
Calculate the distance between the coordinates using:
[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(3 -1)^2 +(1-5)^2} =\sqrt {20[/tex]
[tex]BC = \sqrt{(1 -9)^2 +(5-9)^2} =\sqrt {80[/tex]
[tex]CD = \sqrt{(9 -11)^2 +(9-5)^2} =\sqrt {20[/tex]
[tex]DA = \sqrt{(11 -3)^2 +(5-1)^2} =\sqrt {80[/tex]
The above shows that the opposite sides are congruent
Next, we calculate the slopes using:
m = (y2- y1)/(x2- x1)
So, we have:
AB = (1- 5)/(3-1) = -2
BC = (5- 9)/(1-9) = 1/2
CD = (9- 5)/(9-11) = -2
DA = (5- 1)/(11-3) = 1/2
The slopes of adjacent sides are opposite reciprocals.
This means that the sides are perpendicular
Hence, the given coordinates are actually a rectangle
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Find the point of intersection for the pair of linear equations. A. (5.1, 2.6) B. (-3.1, 2.4) C. (3.6, 2.2) D. (-4.6, 4.1) √x+y=-0.7 y = 3x + 11.7
The point of intersection for the pair of linear equations is (-5.5, -4.8)
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the point of intersection for the pair?The pair of linear equations is given as:
x + y = 0.7
y = 3x + 11.7
Substitute y = 3x + 11.7 in x + y = 0.7
x + 3x + 11.7 = 0.7
Evaluate the like terms
2x = -11
Divide both sides by 2
x = -5.5
Substitute x = -5.5 in y = 3x + 11.7
y = 3*-5.5 + 11.7
Evaluate
y = -4.8
So, we have
x = -5.5 and y = -4.8
Express the above points as an ordered pair, to determine the point of intersection
(x, y) = (-5.5, -4.8)
Hence, the point of intersection for the pair of linear equations is (-5.5, -4.8)
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The amount of detergent dispensed into bottles of liquid laundry detergent bottles for a particular brand is normally distributed with a mean of 84.5 ounces with a standard deviation of 1.1 ounces. If seventeen bottles are randomly chosen from the factory, what is the probability that the mean fill is more than 84.8 ounces
The probability that the mean fill is more than 84.8 ounces is 0.39358
How to determine the probability that the mean fill is more than 84.8 ounces?From the question, the given parameters about the distribution are
Mean value of the set of data = 84.5Standard deviation value of the set of data = 1.1The actual data value = 84.8The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (84.8 - 84.5)/1.1
Evaluate the difference of 84.8 and 84.5
z = 0.3/1.1
Evaluate the quotient of 0.3 and 1.1
z = 0.27
The probability that the mean fill is more than 84.8 ounces is then calculated as:
P(x > 84.8) = P(z > 0.27)
From the z table of probabilities, we have;
P(x > 84.8) = 0.39358
Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358
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Math man fell from the top of a 500 meter building. The equation d = t squared * 0.25 describes math man's distance from the ground as he falls. How long does math man spend falling if he falls all the way from the top of the building to the ground? Round your answer to the nearest tenth.
Based on the equation of the function of the height of the building, it takes the man 44.7 seconds to fall from the top
How to determine how long it takes the math man to fall?The function of the height where the man falls is a quadratic function, and the equation of the function is given as:
d = t^2 * 0.25
The height of the building is 500
This means that the value of d is 500.
So, we have;
d = 500
Substitute 500 for d in the equation d = t^2 * 0.25
500 = t^2 * 0.25
Divide both sides of the above equation by 0.25
500/0.25 = t^2 * 0.25/0.25
Evaluate the quotient in the above equation
t^2 = 2000
Take the square root of both sides in the above equation
√t^2 = √2000
Evaluate the exponent
t = 44.7
Hence, it takes the man 44.7 seconds to fall
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When the sum of a number and 3 is subtracted from 10 the result is 5 solve om algebraic equation?
Answer:
y = 2
Step-by-step explanation:
Algebraic Equation is an equation where alphabets are used to represent numbers.
Solving the above question,
Let the number = y
Therefore,
Sum of the number = y + 3
If it's subtracted from 10 it becomes
10 - ( y + 3 )
The result : 10 - y - 3 = 5
- y = 5 - 10 + 3
- y = -2
Therefore,
y = 2
The demand for a given product demand is formulated by the linear trend equation: y= 50 – 6t.
Based on this information, when would be the first period that there is NO demand at all for this product?
Answer:
t >= [tex]\frac{25}{3}[/tex] or 8.33333333333
Step-by-step explanation:
We need to set up an inequality where demand is less than or equal to 0. The inequality looks like this:
50 - 6t <= 0
50 <= 6t
t >= [tex]\frac{25}{3}[/tex] or 8.33333333333
Please Help! Multiple Choice
Using the z-distribution, the z-statistic would be given as follows:
c) z = -2.63.
What are the hypothesis tested?At the null hypothesis we test if the means are equal, hence:
[tex]H_0: \mu_D - \mu_C = 0[/tex]
At the alternative hypothesis, it is tested if they are different, hence:
[tex]H_1: \mu_D - \mu_C \neq 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:
[tex]\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086[/tex][tex]\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556[/tex]Hence, for the distribution of differences, they are given by:
[tex]\overline{x} = 12 - 14 = -2[/tex].[tex]s = \sqrt{0.6086^2 + 0.4556^2} = 0.76[/tex]What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
[tex]z = \frac{-2 - 0}{0.76}[/tex]
z = -2.63.
Hence option B is correct.
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;
Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the
difference between proportions of men and women who own smartphones. Assume that you want 99% confidence that your
error is no more than 0.035.
Click the icon to view the discussion of sample size.
The sample should include men and
(Type whole numbers.)
women.
The sample should include 2702 men and 2702 women.
Given that you want to be 99% sure your error doesn't exceed 0.035.
A sample is a group of people selected from a larger population to provide data to researchers. The number of members of the population included in the sample is called the sample size.
The significance level is the probability that the test statistic is in the critical range if the null hypothesis is actually true. The confidence interval is 99% or 0.99.
The level of significance α = 1-0.99 = 0.01
the margin of error, ME = 0.035
The Z-critical value at the 99% confidence level or at the significance level of 0.01 is 2.575 (from standard normal tables).
We will now use the formula:[tex]n=\frac{Z^2_{critical}}{2(ME)^2}[/tex].
Substitute the values in the above formula, we get
n = (2.575) ² / (2 × (0.035) ²)
n = 6.630625 / (2 × 0.001225)
n = 6.630625 / 0.00245
n = 2701.966
Therefore, the sample should include 2702 males and 2702 females with a 99% certainty that the error does not exceed 0.035
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Which statement is true about the function f(x) = 6x7?
The function is even because f(–x) = f(x).
The function is odd because f(–x) = –f(x).
The function is odd because f(–x) = f(x).
The function is even because f(–x) = –f(x).
Answer: The function is odd because f(–x) = –f(x).
Step-by-step explanation:
[tex]f(x)=6x^7\\\\f(-x)=6(-x)^7 = -6x^7\\\\\therefore f(x)=-f(-x)[/tex]
The function is odd because f(–x) = –f(x).
How to determine the true statement?The function is given as:
f(x) = 6x^7
A function is odd if the following is true
f(-x) = -f(x)
Calculate f(-x)
f(-x) = 6(-x)^7
f(-x) = -6x^7
Calculate -f(x)
-f(x) = -6x^7
By comparison;
f(-x) = -f(x) = -6x^7
Hence, the function is odd because f(–x) = –f(x).
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The vertices of a quadrilateral are A(-3,-1), B(1,5), C(5,5), and D(5,-1). Select the statement that represents this quadrilateral. A. ABCD is a rectangle because it has exactly one pair of right angles. B. ABCD is a trapezoid because it has at least one pair of parallel sides. C. ABCD is a square because it has all equal sides. D. ABCD is a parallelogram because it has two pairs of parallel sides.
Answer:
B. ABCD is a trapezoid because it has at least
one pair of parallel sides.
Step-by-step explanation:
the two points A(-3,-1) and D(5,-1) have the same y-coordinates
Then
The line AD is parallel to the x-axis
On the other hand,
the two points B(1,5) and C(5,5) have the same y-coordinates
Then
The line BC is parallel to the x-axis.
We obtain :
• AD is parallel to the x-axis
• BC is parallel to the x-axis.
Therefore
AD // BC
Conclusion:
ABCD is a trapezoid because it has at least
one pair of parallel sides.
Answer:
b
Step-by-step explanation:
plato
can two equilateral triangles always be congrunet ? give resons
SOLUTION :
YES as well as NO , two equilateral ∆s can be congruent if any of their side matched to one another,
& CANNOT be congruent if any of their side didn't matched in terms of length (magnitude).
________________________________
MARK BRAINLIEST!
Johnny picks up a baseball and throws it to Rob who is exactly 130 feet away at a direction of 50 degrees. Rob then throws the ball to Patrick who is 50 feet from Rob in a direction of 30 degrees. Find the exact distance and direction that Patrick is from Johnny.
I need to sketch a triangle.
The exact distance and direction that Patrick is from Johnny is; 177.81 ft and 215.52°
How to utilize trigonometric ratios?Let the distance of Johnny to Patrick be x.
The angle opposite x would be; (90 - 50) + 90 + 30 = 160°
We will therefore use the cosine rule to find x;
X² = A² + B² - 2ABcosx
Where;
A and B are the distance of Johnny to Rob and Rob to Patrick respectively. Thus;
X² = 130² + 50² - 2(130)(50)cos160
X²= 16900 + 2500 + 12216.004
X² = 31616.004
X = 177.81 ft
To get the direction "y" we will use sine rule;
50/siny = 177.809/sin160
50/siny = 177.809/0.342
50/siny = 519.9094
Siny = 50/519.904
Siny = 0.09617
y = sin⁻¹(0.09617)
y = 5.52°
The bearing of Patrick from Johnny is;
5.52 + 30 + 180 = 215.52°
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A line passes through the point −8, 4 and has a slope of −3/4.
Answer:
y = (-3/4)x + 2
Step-by-step explanation:
y = m * x + b where m is the slope and b is the y-intercept
y = (-3/4)x + b substituting the slope
4 = 6 + b => b = 2 substituting the point given
y = (-3/4)x + 2
Solve the equation 5 (x + 1) = 5x
[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
an equation = [tex]\sf{5(x+1)=5x}[/tex]✏[tex]\bigstar\textsf{To\quad find:-}[/tex]
x = ?✏[tex]\bigstar\textsf{Solution \quad steps:-}[/tex] ✏
first use the distributive property
[tex]\sf{\longmapsto{ 5x+5=5x}[/tex]
subtract both sides by 5x
[tex]\sf{\longmapsto{0x+5=0}[/tex] (strange expression right)
[tex]\sf{\longmapsto 0=-5}[/tex] (whattt ?!)
the above statement's false, so the equation has no solutions
`hope that was helpful to u ~
Someone help quickly pls :(
Assignment
Practice finding solutions to systems of equations using
substitution.
The value of x in this system of equations is 1.
3x + y = 9
y=-4x+10
1. Substitute the value of y in the first equation:
2. Combine like terms:
3. Apply the subtraction property of equality:
4. Apply the division property of equality:
What is the value of y?
y=
3x + (-4x+10) = 9
-x+10=9
-x=-1
x=1
Answer:
y = 6
Step-by-step explanation:
Solving system of linear equation using substitution method:3x + y = 9 ---------------(I)
y = -4x + 10 -----------------(II)
Substitute y = -4x + 10 in equation (I)
3x - 4x + 10 = 9
Combine like terms,
-x + 10 = 9
Subtract 10 from both sides. (subtraction property of equality)
-x = 9 - 10
-x = -1
Divide both sides by (-1). {Division property of equality}
[tex]\sf \dfrac{-x}{-1}=\dfrac{-1}{-1}\\\\ \boxed{x = 1}[/tex]
Now, substitute x = 1 in equation (II) and find the value of y.
y = -4*1 + 10
= -4 + 10
[tex]\sf \boxed{\bf y = 6}[/tex]
What is the measure of
I need help figuring out any details that are in this graph and what you can make of it.
The graph shows the comparison of the human welfare and ecological footprints.
What is a graph?A graph simply means a diagram that shows the relationship between variables.
From the graph, it can be seen that countries such as Norway, Canada, USA, and Australia meet the minimum criteria for sustainability.
The graph also shows that Sierra Leone is the least developed country among the countries compared as it has the lowest human development index.
The threshold for high human development as given as 0.8. Most African countries had a human development index of 0.5 and below.
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Can you guys show me what process you would use for this? I mostly need the process
The value of the expression for the given values of the variables is 1/9
Evaluating an ExpressionFrom the question, we are to determine the value of the expression for the given values of the variables
The given expression is
[tex](\frac{4x^{3} -2y-2z^{3} }{4y^{2}-16x^{2} }) ^{2}[/tex]
From the given information,
x = 2
y = -5
z = 3
Putting the values of the variables into the expression
[tex](\frac{4(2)^{3} -2(-5)-2(3)^{3} }{4(-5)^{2}-16(2)^{2} }) ^{2}[/tex]
[tex](\frac{4(8) +10-2(27) }{4(25)-16(4) }) ^{2}[/tex]
[tex](\frac{32 +10-54 }{100-64 }) ^{2}[/tex]
[tex](\frac{-12 }{36 }) ^{2}[/tex]
[tex](\frac{-1 }{3 }) ^{2}[/tex]
[tex]= \frac{1}{9}[/tex]
Hence, the value of the expression for the given values of the variables is 1/9
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Andy is preparing the company's income statement. His first line item is the company's service revenue. What will he deduct from this line item to obtain the net income?
Andy needs to subtract _______ from the service revenue.
Fill in the blank
Andy needs to subtract cost from the service revenue.
What does Andy need to subtract?
Revenue is the total income earned before any deductions are made. Net income is the total revenue less total expenses or cost.
Net income = total revenue - cost
For example, if a company sold 100 loaves of bread for $100 dollars. The cost of making the bread is $50. The revenue is $100 and the net income is $50 (100 - 50).
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What is the equation of the line that is parallel to line R, y = 2x + 5, and passes through the
point (-2, 2)?
Answer:
y = 2x + 6
Step-by-step explanation:
We are given the line R, which is y=2x+5, and we want to find the equation of the line that is parallel to this line, and that also passes through the point (-2, 2).
Parallel lines have the same slope, yet different y-intercepts.
So, we should first find the slope of y=2x+5.
The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.
As 2 is in the place of where m (the slope) should be, 2 is the slope of the line.
It is also the slope of the line parallel to it.
We can write the equation of the new line in slope-intercept form as well; here is the equation so far, with what we know:
y = 2x + b
We need to find b.
As the equation passes through the point (-2, 2), we can use its values to help solve for b.
Substitute -2 as x and 2 as y.
2 = 2(-2) + b
Multiply.
2 = -4 + b
Add 4 to both sides.
6 = b
Substitute 6 as b.
y = 2x + 6
Which function is graphed?
Answer: [tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]
Step-by-step explanation:
By inspection, we know the equation of the parabola is [tex]y=x^2 +4[/tex] and the equation of the line is [tex]y=-x+4[/tex].
Since there is an open hole at x=3 for the parabola and a closed hole at x=3 for the line, the function is
[tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]