(4i+1)² can be simplified to 8i-15
What is Complex number?A complex number is a number of the form a + bi, where a and b are real numbers
Given expression is (4i+1)²
four times of i plus one whole square.
(4i+1)² can be expanded by using algebraic identity
(a+b)²=a²+b²+2ab
(4i+1)²
Now put a as 4i and b as 1
(4i+1)²=16i²+1+2(4i)(1)
Where i²=-1
=-16+1+8i
=8i-15
Hence (4i+1)² can be simplified to 8i-15
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(9 − 9i) − (−7+ 2i)
Simply
Step-by-step explanation:
Simplify Calculator. Step 1: Enter the expression you want to simplify into the editor. The simplification calculator allows you to take a simple or complex expression and see fro googlle bro
Answer:
16 - 11i
Step-by-step explanation:
When Adding or Subtracting any Complex Number
we Add or Subtract the Real Parts together and Add or Subtract the Imaginary Parts together
So for our Question
( 9 - 9i ) - ( -7 + 2i ) = ( 9 - (-7) ) + ( -9 - 2 )i = 16 - 11i
A group conducted a survey of 13,000 brides and grooms married in the united states and found that the average cost of a wedding is $23,858. assume that the cost of a wedding is normally distributed with a mean of $23,858 and a standard deviation of $5,900. (a) what is the probability that a wedding costs less than $20,000? (round your answer to four decimal places.) (b) what is the probability that a wedding costs between $20,000 and $32,000? (round your answer to four decimal places.) (c) what is the minimum cost (in dollars) for a wedding to be included among the most expensive 5% of weddings? (round your answer to the nearest dollar.)
The measures, using the normal distribution, are given as follow:
a) Probability that a wedding costs less than $20,000: 0.257 = 25.70%.
b) Probability that a wedding costs between $20,000 and $32,000: 0.659 = 65.90%.
c) Minimum cost of the most expensive 5% of weddings: $33,564
Normal Probability Distribution
The z-score of a measure X of a variable that has to mean symbolized by and standard deviation symbolized by is given by the rule presented as follows:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
The z-score represents how many standard deviations measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.
Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of measure X in the distribution.
The mean and the standard deviation for the wedding prices are given as follows:
μ = 23858, σ = 5900
a) The probability that a wedding costs less than $20,000 is the p-value of Z when X = 20000, hence:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Z = (20000 - 23858)/5900
Z = -0.65
Z = -0.65 has a p-value of 0.257.
The probability that it costs between $20,000 and $32,000 is the p-value of Z when X = 32000 subtracted by the p-value of Z when X = 20000, found above, hence:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Z = (32000 - 23858)/5900
Z = 1.38
Z = 1.38 has a p-value of 0.816.
0.916 - 0.257 = 0.659.
The minimum cost for a wedding to be in the most expensive 5% of weddings is the 95th percentile, which is X when Z = 1.645, hence:
1.645 = (X - 23858)/5900
X - 23858 = 1.645 x 5900
X = $33,564.
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How do you create a polynomial function from a word problem?
Attached below is the problem that I am stuck on.
Considering the volume of the rectangular prism given the dimensions, it is found that:
The expression is: V = w³ - 8w² + 15w.The degree is of 3, the number of terms is of 3, and the leading coefficient is of 1.How to obtain the volume of a rectangular prism?The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width w, the height h and the length l, that is:
V = l x w x h.
In this problem, the dimensions are given as follows:
Width w.Length w - 5.Height w - 3.Hence the polynomial expression for the volume of the prism is given as follows:
V = w(w - 5)(w - 3)
V = w(w² - 8w + 15)
V = w³ - 8w² + 15w.
The features of the polynomial function are given as follows:
Degree of 3, as the highest exponent of the function is of 3.Number of terms of 3, which are w³, 8w² and 15w.The leading coefficient is of 1, as it is the term multiplying w³.More can be learned about the volume of a rectangular prism at https://brainly.com/question/22070273
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Here are some numbers.
8
11
13
18
25
37
8,13,18is an arithmetic progression and the rule is to add 5.
Use three of the numbers to make a different arithmetic
progression.
Describe the rule.
The different arithmetic progression is [tex]11, 18, 25[/tex] and the rule is to add [tex]7[/tex].
What is an arithmetic progression?
A series of numbers known as an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
We have,
[tex]8, 11, 13, 18, 25, 37[/tex]
Given arithmetic progression is [tex]8, 13, 18[/tex] and the constant difference is [tex]5[/tex].
By using this phenomenon we can create new arithmetic progression like,
[tex]11, 18, 25[/tex]
Here the constant difference or rule is [tex]7[/tex].
Hence the new and different arithmetic progression is [tex]11, 18, 25[/tex].
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How do I solve this.
Answer:
Step-by-step explanation:
small airplane flew 104 miles in 50 minutes. At this rate, how many miles can it fly in 3 hours?
An airplane can fly 374.4 miles in 3 hours.
A small airplane flew 104 miles in 50 minutes.
So, the rate would be,
rate = distance / time
rate = 104/50
rate = 2.08 miles/minute
We need to find the distance the airplane can flay in 3 hours.
3 hours = 180 minutes
t = 180 minutes
r = d/t
2.08 = d/180
d = 2.08 * 180
d = 374.4 miles
Therefore, an airplane can fly 374.4 miles in 3 hours.
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a sock drawer contains 10 white socks, 6 black socks , and 8 blue socks if 2 socks are chosen at random, without replacement
calculate the probability she chooses 2 socks of the same colour
Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
calculate the probability she chooses 2 socks of the same colour ?I clarify this because the question uses plural “drawing white socks”. Ok, in our language practice one does usually say socks instead of sock because they usually come in pair.
If it means 1 draw of 1 sock then the probability is 6out of 21. Or about 28.57%
But if it is to draw twice with one sock being drawn in each draw to get a pair of white socks then the probability is 6/21 * /20 = 30/420 = 1/14 or about 7.14%
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solve the inequality write the solution in interval notation
-x/3 < 5
The inequality expression given as -x/3 < 5 has a solution of x > -15
How to solve the inequality?From the question, the inequality is given as
-x/3 < 5
The above inequality can be re-written as follows
-x/3 < 5
There is no constant to add or subtract in the expression
So, we start by multiplying both sides of the expression by a constant
Multiply both sides by 3
expression
-x < 15
Divide both sides by -1
So, we have the following representation
x > -15
Hence, the solution to the expression is x > -15
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P is inversely proportional to Q.
P= 10 when Q = 1.2
a) Work out the value of P when Q = 2.
b) Work out the value of Q when P = 1.25
Answer:
P = 10
Q=12
[tex]p = \frac{1}{q} [/tex]
a). p = 1/2 = 0.5
b). 1.25 = 1/Q
Q = 1/1.25 Q = 0.8
Answer:
P=6
Q= 9.6
Step-by-step explanation:
A)
y=k/x
substitute it in.
10=k/1.2
10×1.2=k
k=12
y=12/x
x=2
12/2=6
P=6.
B)
Since we know y=kx
we know k=12
you would do 12/1.25 to give u Q
12/1.25=9.6
Write down three different factors of
360 with a sum between 90 and 100.
Answer: 90 x 4 x 1
Step-by-step explanation:
90 x 4 x 1 = 360
Please thank and rate <3
Answer:
360
Step-by-step explanation:
2³x3²x5
Please thank you and rate
Solve the inequalityr divided by negative 2.5 is less than or equal to 8.7 for r.
Answer:
r ≤ -21.75
Step-by-step explanation:
Forming the equation,
→ r ÷ (-2.5) ≤ 8.7
Then the value of r will be,
→ r ÷ (-2.5) ≤ 8.7
→ r ≤ 8.7 × (-2.5)
→ r ≤ -21.75
Hence, value of r is -21.75.
The function g(x) = x2 – 10x + 24 is graphed on a coordinate plane. Where will the function cross the x-axis?
(–6, 0) and (–4, 0)
(–2, 0) and (–12, 0)
(4, 0) and (6, 0)
(12, 0) and (2, 0)
The x-intercepts of the quadratic function g(x) = x² - 10x + 24 are given as follows:
(4, 0) and (6, 0).
When does a function crosses the x-axis?A function crosses the x-axis when the numeric value of the function is of y = 0, hence these points are called the x-intercepts of the function.
In this problem, the definition of the function is given as follows:
g(x) = x² - 10x + 24.
This function can be simplified as follows:
g(x) = (x - 6)(x - 4).
Applying the inverse of the Factor Theorem, the x-intercepts are given as follows:
x - 6 = 0 -> x = 6.x - 4 = 0 -> x = 4.Hence the x-intercepts of the function are given by the third option, which is of (4, 0) and (6, 0).
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Answer: C
Step-by-step explanation: trust me
What equation is graphed in this figure?
y−4=−1/3(x+2)
y−3=1/3(x+1)
y+2=−3(x−1)
y−5=3(x−1)
The equation of the graph in point slope form is y + 2 = -3(x - 1)
How to find equation of a graph?The equation of the graph in point slope form can be represented as follows;
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are variableusing two point let's find the slope
(0, 1)(-1, 4)
Hence,
m = 4 - 1 / -1 - 0
m = 3 / -1
m = -3
Therefore, the slope of the line is - 3.
Therefore, using one coordinates(1, -2) from the graph, the equation of the graph in point slope form is y + 2 = -3(x - 1)
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15. Find mACB. help me please
The measure of the angle ACB is 87°.
What does the term angle mean?Angles produced by two beams are included in the plane that contains the rays. The intersection of two planes may also produce an angle. Dihedral angles are the name given to them. It is also possible to determine the angle between two crossing curves using the angle created by the rays that are perpendicular to each intersecting curve at that point.
An angle can also refer to a measurement of a rotation or an angle. This number represents the length-to-radius ratio of a circular arc.
When two crossing lines in a plane are not perpendicular to one another, Euclid defined a plane angle as the inclination between those intersecting lines.
In triangle ADE and triangle ACB, the triangles are similar.
So,
∠AED/ ∠ABC = ∠DAE/∠CAB
∠AED = ∠ABC
11x-2 = 6x + 13
11x - 6x = 13 + 2
5x = 15
x = 15/5
x = 3
So, the measure of angle ABC is
∠ ABC = 6(3)+13
∠ ABC = 18+13
∠ ABC = 31°
Now, consider triangle ABC, the sum of all angles = 180°
So, 62° + 31° + ∠ACB = 180°
∠ACB + 93° = 180°
∠ACB = 180° - 93°
∠ACB = 87°
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Find the x- and y-intercepts of the graph of -7x+10y=35. State each answer as an integer or an improper fraction in simplest form.
x-intercept
The x-intercept is where y=0.
[tex]-7x+10(0)=35\\\\-7x=35\\\\x=\boxed{-5}[/tex]
y-intercept
The y-intercept is where x=0.
[tex]-7(0)+10y=35\\ \\ 10y=35\\\\y=\boxed{7/2}[/tex]
$15,000 is deposited into an account that pays 6.25% annual interest, compounded weekly. Find the balance after 7 years.
Answer: (if A=P(1+rt) is your formula)
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6.25%/100 = 0.0625 per year.
Solving our equation:
A = 15000(1 + (0.0625 × 7)) = 21562.5
A = $21,562.50
The total amount accrued, principal plus interest, from simple interest on a principal of $15,000.00 at a rate of 6.25% per year for 7 years is $21,562.50.
Please help me (check the file attached)
According to the model, the value of -6(10b + 0.8) will be -60b - 4.8.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, this is illustrated as:.
= -6(10b + 0.8)
Open the parentheses
= -60b - 4.8
Therefore, the value is -60b - 4.8.
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a cellular telephone tower that is 110 feet tall is placed on top of a mountain that is 1300 feet above sea level. what is the angle (in degrees) of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 200 feet above sea level? (round your answer to two decimal places.)
The angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 200 feet above sea level will be 87.36 degrees.
What is angle?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.
Here,
The cell phone tower's peak will be at a height of 1300 + 110 = 1410 feet above sea level.
Assuming that the user of a cell phone is 200 feet above sea level, the distance between them is 1410 feet- 200 feet, or 1210 feet.
The distance between them horizontally is 5 miles, or 5 * 5280, or 26400 feet.
The opposite cathetus is 26400 feet away and the neighboring cathetus is 1210 feet away.
the angle is 87.376 degrees, or tan(angle) = 26400 / 1210 = 21.82
A cell phone user 5 horizontal miles away and 200 feet above sea level will be depressed at an angle of 87.36 degrees from the top of the tower.
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There are 24 students in mr. bonogofsky's math class, 5 - of these students earned an a on the geometry unit assessment. how many students earned an ap
Answer: 19
Step-by-step explanation:
help meeeeeeeeeeeeeeeeee please
Answer:
324 ft
Step-by-step explanation:
[tex]v=\sqrt{2gh}[/tex]
[tex]v^2=(\sqrt{2gh})^2[/tex]
[tex]v^2=2gh[/tex]
[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]
[tex]\frac{v^2}{2g}=h[/tex]
[tex]\frac{144^2}{2(32)}=h[/tex]
[tex]\frac{20736}{64}=h[/tex]
[tex]324=h[/tex]
Quadrilateral ABCD has vertices A(9, 9), B(—7, 9),
C(-8,-5), and D(4,-5). In terms of units, what is the
perimeter of quadrilateral ABCD?
Round your answer to the nearest tenth.
Answer:get a tutor
Step-by-step explanation:
its free
A triangular number is a number that can be represented by arranging the number of dots in rows to form a triangle. The first four triangular numbers are represented in the diagram. Find the mean, median and range of the first 6 triangular numbers.
mean =
Number
median =
Number
range =
Number
The mean of the triangular dots is 4, the median is 8 and the range is 6.
How to determine the Measures of central tendency?
A measure of central tendency is defined as a single value that attempts to describe a set of data by identifying the central position within the given set of data.
From the question, the parameters are dots that will form triangle as
.
. . .
. . . . .
. . . . . . .
Total mumber of dots is 1+3+5+7=16
These parameters are represented as follows:
The mean is the average of all the dots that formed the triangle
Mean value of the set of data = [tex]\frac{16}{4} =4[/tex]
The median is the middle number when arranged in ascending or descending order of magnitude
The median is [tex]\frac{16}{2} =8[/tex]
The range is the highest value minus the lowest value in the dots
The range is 7-1=6
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alice passes through four traffic lights on her way to work, and each light is equally likely to be green or red. independent of the others. (a) what is the pmf, the mean, and the variance of the number of red lights that alice encounters?
The value for the number of red lights that Alice encounters are found.
Mean = 2; Var = 1; PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾What is meant as the independent events?The set of findings from an experiment is thought to as events in probability. There are numerous sorts of events, including independent, dependent, and mutually exclusive ones.X = no of red lights crossed by Alice.
X is Binomial distributed
In which n=4, p=0.5, q = 0.5
Mean value is found by the formula,
Mean = np
Mean = 4×0.5
Mean = 2
And, variance = npq
Var = np(1-p)
Var = 4×0.5×0.5
Var = 1
PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾
Thus, the value for pmf, the mean, and the variance of the number of red lights that Alice encounters are found.
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For triangle XYZ, m∠X = (5g + 18)° and the exterior angle to ∠X measures (8g + 32)°. Find the measure of ∠X and its exterior angle. Interior angle = 68°; exterior angle = 112° Interior angle = 112°; exterior angle = 68° Interior angle = 73°; exterior angle = 105° Interior angle = 105°; exterior angle = 73°
The interior angle and the exterior angle of triangle XYZ is 68° and 112° respectively.
What is a triangle?
A triangle is a plane shape that has three sides.
Recall that, the sum of a interior angle and an exterior angle of a triangle is 180°.
Using the formula,
a+b = 180°............ Equation 1Where:
a = interior angle b = exterior angle.From the question,
Given:
a = m∠X = (5g + 18)° b = ∠X = (8g + 32)°Substitute these values into equation 1
(5g + 18)+ (8g + 32) = 180Solve for g
13g + 50 = 18013g = 130g = 130/13g = 10Hence, interior angle of X = (5×10)+18 = 50+18 = 68° and exterior angle of X = (8×10)+32 = 80+32 = 112°
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Answer: I belive the answer is A
Step-by-step explanation: i could be wrong
find the value of x in each case
potatoes cost $0.85 per pound. Luke bought 2.75 pounds of potatoes. How much did he pay for the potatoes. Round to the nearest cent
Answer:
$2.34
Step-by-step explanation:
2.75 x 0.85 = $2.3375
Since we are rounding, it will round up to $2.34.
Answer:
Step-by-step explanation:
Cost of 2.75 pounds of potato =.
2.75x0.85
= $2.3375
9x – 17 = -17 + 9x help me pls
Answer:
Step-by-step explanation:
um ok so
Answer:
x=0
Step-by-step explanation:
the rest of this is so i can reach twenty characters.
Trevor is a high school quarterback. On
average, out of each 16 attempts, he
completes 5 out of 8 passes and throws 1
pass that is intercepted. If Trevor passes
40 times, how many completions would
he be expected to make? (setting up proportions )
The total number of completions Trevor be expected to make is 25.
Define the term proportions?Proportion is mostly discussed using ratios and fractions. A fraction is written as a/b, while a ratio is represented as a:b, and a proportion implies that two ratios remain equal. In this case, a and b can be any two integers. According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios and fractions are equivalent.For the given question.
Let the number of completion by Trevor be 'x'.
Trevor completes 5 out of 8 passes.
Total passes are 40
Then, proportions set up is-
5/8 = x/40
x = 25
Thus, the total number of completions Trevor be expected to make is 25.
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1/2v + 8 = 3 – 1/3v plss
Answer:
v = -6
Step-by-step explanation:
½v + 8 = 3 - ⅓v
Collect like terms
½v + ⅓v = 3 - 8
⅚v = -5
Divide both sides by ⅚
⅚v/⅚ = -5/⅚
v = -5 × 6/5
v = -30/5
v = -6
Please help,
Will mark as brainliest
Answer: D
Step-by-step explanation:
5 x 3 = 15
8 x 3 = 24
the multipliers are both 3
so they are "similar shapes".
The other options don't have the same multipliers so they aren't right :)