The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is 520[cos(18) + isin(18)]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Complex number is in the form z = a + bi, where a and b are real numbers.
The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is:
z = 65 * 8 [cos(14 + 4) + isin(14 + 4)] = 520[cos(18) + isin(18)]
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which unit of measure would be appropriate for the area of a bulletin board that is 2 meters tall and 6 meters wide
Answer:The entire area would be 12 square meters.
Step-by-step explanation:
2 x 6 square meters = 12 square meters. which is the entire area.
If x1 = 4, then x² + 1/x² =
Answer:
257/16
Step-by-step explanation:
Given :
x¹ = 4Then :
x² + 1/x²(x¹)² + 1/(x¹)²(4)² + 1/(4)²16 + 1/16257/16The diagram shows triangles ABC and PQR. ABC is mapped to PQR by combining two single transformations
Which polynomial function could be represented by the graph below?
A. [tex]f(x) = x^2 - 4x[/tex]
B. [tex]f(x) = x^2 + 4x[/tex]
C. [tex]f(x) = -x^2 - 4x[/tex]
D. [tex]f(x) = -x^2 + 4x[/tex]
Answer:
[tex]f(x) = {x}^{2} + 4x[/tex]
Step-by-step explanation:
The graph is concave up, this means that the leading term x^2 is positive.
[tex]f(x) = {x}^{2} + 4x[/tex]
[tex]y = {x}^{2} + 4x[/tex]
For the x intercept, let y = 0[tex] {x}^{2} + 4x = 0[/tex]
[tex]x(x + 4) = 0[/tex]
[tex]x = 0 \: \: \: or \: \: \: \: x = - 4[/tex]
The x intercepts are:
(0 , 0) and (-4 , 0)
For the y intercept, let x = 0
[tex]y = {0}^{2} + 4(0) = 0[/tex]
y intercept :(0, 0)
For the turning point:[tex]t.p = \frac{x1 + x2}{2} [/tex]
[tex]t.p = \frac{0 + ( - 4)}{2} = - 2[/tex]
[tex]f( - 2) = {( - 2)}^{2} + 4( - 2) = - 4[/tex]
Turning point:(-2 , -4)
If you connect all these coordinates you will get the parabola shown in the picture.
What effect does the circled point have on the standard deviation of the residuals? This point will increase the value of the standard deviation of the residuals because it has a large positive residual. This point will increase the value of the standard deviation of the residuals because it has a large negative residual. This point will not affect the value of the standard deviation of the residuals because it has a large positive residual. This point will decrease the value of the standard deviation of the residuals because it has a large negative residual.
The effect of this circled point is that: A. it will increase the value of the standard deviation of the residuals because it has a large positive residual.
What is the standard deviation of residuals?The standard deviation of residuals is also referred to as root mean square deviation and they are typically used in statistics to calculate the rate at which data points spread around a given regression line.
By critically observing the scatter plot shown in the image attached below, we can infer and logically deduce that the circled point will increase the value of the standard deviation of the residuals because it has a large positive residual.
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Complete Question:
A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. What effect does the circled point have on the standard deviation of the residuals?
Is renters insurance a fixed or variable expense?
[tex]\huge\purple{Hi!}[/tex]
renters insurance is a Fixed expenses
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
to determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
The correlation coefficient between the student's height and the distance they were able to jump is 0.86.
What is the correlation coefficient?The correlation coefficient is a number that ranges from -1 to 1. It shows the strength of the relationship between two variables. It also shows the direction of the relationship.
Positive correlation is when the two variables move in the same direction. If one variable increases, the other variable also increases. Negative correlation is when two variables move in different direction. If one variable increases, the other variable decreases. Zero correlation is when there is no relationship between the variables.
The correlation coefficient is calculated using a financial calculator.
Here is the complete question:
A group of students want to determine if a person's height is linearly related to the distance they are able to jump.
To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.
Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.
Enter the correlation coefficient. Round your answer to the nearest hundredth.
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Answer:
It's 0.92
Step-by-step explanation:
I took the test already
How can I solve this:
Simplify
Answer:
see the attachment photo!
Answer:
the answer is 7! hope this helps
Step-by-step explanation:
A shop has 4 fruits (bananas, oranges, apples, and grapes) and 2 dips (peanut butter and caramel).
Zeke's mom randomly buys 1 fruit and 1 dip for his lunch.
What is the probability that she selects his favorite option: bananas and peanut butter?
Answer:
total fruits and dips=4+2=6
P(select banana&peanut butter)=banana+peanut /total fruits and d
Step-by-step explanation:
total fruits and dips=4+2=6
P(select banana&peanut)=banana+peanut/total fruits and dips
P(select banana&peanut)=1+1=2/6
=1/3
please help !!!! and please answer every question not just one part.
Answer:
1) C. x-1 tells us that it has decreased by a value
2) original number of apples
3) 4(x-1)=28. Divide by 4, then take the 1 over
the simplification lf (x^3+2x-3)-(x^2-2x+4)
Answer:
x³ - x² + 4x - 7
Step-by-step explanation:
(x³ + 2x - 3) - (x² - 2x + 4)
remove first parenthesis and distribute second parenthesis by - 1
= x³ + 2x - 3 - x² + 2x - 4 ← collect like terms
= x³ - x² + 4x - 7 ← in standard form
To predict the outcome of the vote for the town budget, the town manag assigned random numbers and selected 12F registered voters. He then called these vote and asked how they planned to vote. Is th town manager's sample representative of population? Explain.
The town manager's sample is not representative of population as he only picked females.
What is a sample representative?It should be noted that a sample representative simply means a subset of a population which seeks to reflect the characteristics of the larger group.
In this case, the town manager's sample is not representative of populationas he only picked females. The males too ought to be given an equal chance.
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math 7 grade eog 2022 ansers
Write in point-slope form an equation of the line that passes through the given point and has the given slope. Point: (4, 8); m = 3/4
Answer:
[tex]\mathsf{y-8=\cfrac{3}{4}(x-4)}[/tex]
Step-by-step explanation:
Hi student, let me help you out!
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ..... ........ ...... ... ......... .... ....
First, let's recall the point-slope form equation: ↪ [tex]\mathrm{y-y_1=m(x-x_1)}[/tex].
where: y₁ = y-coordinate of the point (the second coordinate), m=slope, x₁=x-coordinate (the first coordinate).
Let's stick in the values accordingly. We obtain the following: [tex]\mathrm{y-8=\cfrac{3}{4}(x-4)}[/tex], which is our point-slope form equation.
Hope this helped you out, ask in comments if any queries arise.
Best Wishes!
[tex]\star\bigstar\overline{\overline{\underline{\underline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{4}}[/tex]
Any ideas for this question
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Explanation:
Let x = length of side BC
This is the height of the cylinder. Think of a can that is laying on its side. The radius of this can or cylinder is CD
If point B has x coordinate of 12, and BC is 12 units long, this must mean point C has x coordinate of 12-x. This is plugged into the function to show that CD has a length of exactly [tex]\sqrt{12-x}[/tex]
This is the radius of the cylinder
The volume of a cylinder is [tex]V = \pi*r^2*h[/tex]
Plug in the radius and height mentioned to get this function in terms of x
[tex]V = \pi*\left(\sqrt{12-x} \ \right)^2*x[/tex]
That simplifies to
[tex]V = \pi(12-x)x[/tex]
or
[tex]V = \pi(12x-x^2)[/tex]
Ignore the pi portion for now.
We wish to maximize the function f(x) = 12x-x^2
Use either calculus (specifically derivatives) or a graphing calculator to find that the vertex is at (6, 36)
This means x = 6 leads to the largest f(x) value being 36.
Therefore, the volume V is maxed out when x = 6 and we get a max volume of 36pi cubic units.
How to find a fraction from a decimal
Answer:
0.6= 6/10
[tex]0.6 = 6 \div 10[/tex]
Step-by-step explanation:
To convert a decimal to a fraction
place the decimal number over its place value
For example
in 0.8 the 8is in the tenths place,
so we place 6 over 10 to create the equivalent fraction, 8/10.
example 2
=6.25
625/100
25/4
Please help y’all I’ll do anything!!
Answer:
555
Step-by-step explanation:
If each side of a square is 15 miles, we can find the total distance travelled by finding how many sides of squares were travelled.
You could either count the boxes, or, as I'm going to do, you could calculate the length of each straight line.
I switch between the y axis and the x axis, because we are travelling in different directions (if moving up/down we pay attention to y-axis, if moving right/left we pay attention to x-axis)
From 'Home' to the 'Restaurant', we are travelling from 6 to -7 on the grid. So, if we want to know the distance between them, we need to figure out how far apart they are. This is similar to figuring how far apart any two numbers are--we find the difference. (6) - (-7) [6 + 7] = 13. So, the amount of squares travelled from home to the restaurant is 13.
[I pay attention to the values along the x-axis for these two points because we are considering the distance along the x-axis]
[y-axis because it is vertical travel]
Restaurant (at -5) to campground (at 2) has a distance of : 7
[x-axis because it is horizontal travel]
Campground (at -7) to Rest Area (at -3) has a distance of : 4
[y-axis travel]
Rest Area (at 2) to the endpoint of that line segment (at 8) has a distance of: 6
[x-axis travel]
Endpoint of line segment (at -3) to endpoint below destination (at 3) has a distance of : 6
[y-axis travel]
Endpoint below destination (at 8) to destination (at 9) has a distance of : 1
We can then add all of the distance travelled:
13 + 7 + 4 + 6 + 6 + 1
= 37
37 sides of boxes were travelled, so we can multiply:
37 x 15
= 555
because each box length is 15 miles.
So, the family travelled 555 miles
Write the following ratio using two other notations.
[tex] \frac{1}{3} [/tex]
Answer:
1:3
1 to 3
Step-by-step explanation:
The other notations a ratio [tex]\frac{a}{b}[/tex] can be written in are a:b and a to b.
From what we are given, a = 1 and b = 3, so in the form a:b, the ration would be 1:3 and in the form a to b it would be 1 to 3.
What is the name of the numeral system we use today?.
For what value of x does 4 superscript x baseline = (one-eighth) superscript x 5?
An equation is formed of two equal expressions. The value of x for which 4ˣ=(1/8)ˣ⁺⁵ is 3.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The value of x for which 4ˣ=(1/8)ˣ⁺⁵ is,
4ˣ=(1/8)ˣ⁺⁵
(2²)ˣ = (2⁻³)ˣ⁺⁵
2²ˣ = 2⁽⁻³ˣ⁺¹⁵⁾
2x = -3x + 15
5x = 15
x = 3
Hence, the value of x for which 4ˣ=(1/8)ˣ⁺⁵ is 3.
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I need help in this question if highly appreciate it if someone can help me solve this problem
Answer:
The one you chose is correct.
Step-by-step explanation:
The scale factor is 1.5. We know QP is 5. QP is the corresponding side to KJ. So, we multiply 5 with 1.5 and get 7.5 which is equal to 15/2
I found the scale factor by dividing LK which was 9 and QR which was 6.
9/6=1.5.
Hope this helps
Johnni guessed on all 8 questions of a multiple-choice quiz. each question has 4 answer choices. what is the probability that she got exactly 3 questions correct? round the answer to the nearest thousandth. p (k successes) = subscript n baseline c subscript k baseline p superscript k baseline (1 minus p) superscript n minus k. subscript n baseline c subscript k baseline = startfraction n factorial over (n minus k) factorial times k factorial endfraction 0.004 0.208 0.422 0.792
The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.
What is Probability ?Probability can be defined as the likeliness of
If you use the formula P(r)=[tex]^nC_r P^rq^{n-r}[/tex]
P is the probability of success = 3/4 = .25
the total number of questions is n = 8
the total number of questions that Johnni got correct is r = 3
the probability of getting an answer wrong is q = 1-0.25 = 0.75
Substituting all of these values
[tex]^8C_3 P^3 (0.75)^{8-3}[/tex]
= .208.
The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.
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Answer:
B. 0.208
Step-by-step explanation:
edge 2023
Solve the system of equations x + y = 14 and 5x - 3y = 38 by combining equations. +y = 14) -3y =38) (5x X +y = 14 5x -3y = 38 try 0x0y= You must answer all questions above in order to submit.
Answer:
6x+2y=52
Step-by-step explanation:
If you just drop down the answers, like for the first set x+5x=6x, so thats the first term and so on.
What is the slope of the line containing (-3, 1) and (1, -2)?
O A
OB.
O C.
O D.
314
413
-
314
43
Slope:-
m=y2-y1/x2-x1m=-2-1/1+3m=-3/4The slope of the given function is -3/4.
What is a slope?Slope is a value that describes the steepness and direction of a line.
Given are the points that lie on line, we need to find the slope of the line,
So,
m = y₂ - y₁ / x₂ - x₁
The ordered pairs are :-
(-3, 1) and (1, -2)
So, the slope (m) = -2-1 / 1+3 = -3/4
Hence, the slope of the given function is -3/4.
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HELP ASAP
A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.
The swimmer is underwater for 12 seconds.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The swimmer dives into the water 12 seconds after the timer was started.
The correct true statement is the swimmer comes back up 9 seconds after the timer was started.
Maximum height of a functionThe maximum height of a function is the point where the velocity the body is zero.
Given the function that represent the height of the swimmer as h(t)=t^2−12t+27
If the velocity of the function is zero, hence;
h'(t) = 2t - 12
0 = 2t - 12
2t = 12
t = 6secs
Substitute t = 6 into the function as shown:
h(6) = 6^2−12(6)+27
h(6) = 36 - 72 + 27
h(6) = -36 + 27
h(6) = -9 feet
Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.
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Anyone know how to do this?
Answer:
the tangent ratio should be the length of the leg opposite to angle D to the length of the leg adjacent to angle D
Step-by-step explanation:
tangent is opposite over adjacent
What is the slope of the line that passes through the pair of points?
(5, 8), (9,-3)
Answer:
-11/4
Step-by-step explanation:
slope = [tex]\frac{-3-8}{9-5} =\frac{-11}{4}[/tex]
Hope this helps
Answer:
-11/4
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (-3 - 8)/(9 - 5) = -11/4
Solve 2x + 5y = −13
3x − 4y = −8
(4, 1)
(−4, 1)
(4, −1)
(−4, −1)
Answer:
Step-by-step explanation:
6x + 15y = -39
-6x + 8y = 16
23y = -23
y = -1
2x - 5 = -13
2x = -8
x = -4
(-4, -1)
Option 4
Answer:
(−4, −1)
Step-by-step explanation:
I got it right on the test
solve for x.
2-[x+4(6-x)+16]-10=38-8x
Exact form is x = 86/11
Mixed number form is x = 7 whole number 9/11
please answer, much appreciated!!!!!
Answer:
i don't understand your question
Step-by-step explanation: