Answer:
assuming it's a perfect world and that the fish lives in a 1 cubic meter fish tank 1*1.4422 will increase the volume my a factor of 3
If two marbles are selected at random with replacing between draws, what is the probability that the outcome is red then yellow? (round your answer to four decimal places. )
The probability that the outcome is red then yellow is 0.036.
Given that in a jar there are 8 red marbles, 1 yellow marble and 6 green marbles.
We are required to find the probability of obtaining a red then yelow marble if two marbles are drawn and replacement is used.
Probability is the calculation of finding the chance of happening a event among all the events possible. It lies between 0 and 1.
Probability=Number of items/ Total items.
Number of red marbles=8
Number of yellow marble=1
Number of green marbles=6
Total marbles=15
Probability of obtaining red marble=8/15
Probability of obtaining yellow marble=1/15 (Because replacing is there so the number of total marbles do not decrease)
Required probability=8/15*1/15
=8/225
=0.035555
After rounding off we will get 0.036.
Hence the probability that the outcome is red then yellow is 0.036.
Question is incomplete. The following line should be included in question:
A jar contains 8 red marbles , a yellow marble and 6 green marbles.
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What is the answer of the fractions 9 and 1/6 multiplied by 1 and 1/11? Then, that answer simplified into simplest form?
The simplest form is 10.
We can find simplest as form:
Given, fractions are [tex]9\frac{1}{6}[/tex] and [tex]1\frac{1}{11}[/tex]
[tex]9\frac{1}{6}\times 1\frac{1}{11}[/tex]
[tex]\frac{55}{6}\times \frac{12}{11}[/tex]
[tex]=\frac{55\times 12}{6\times 11}[/tex]
=10
Hence, simplest form of given fraction is 10.
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For each of the number lines, write an absolute value equation that has the following solution set. 26 and m
On a number line, an absolute value equation that has the given solution set is |m - 4| = 2.
How to write the absolute value equation?By critically observing the given question, we can infer and logically deduce that the solution sets for this absolute value equation is given by:
m = {2, 6}
Next, we would calculate the mean of the solution sets as follows:
m₁ = (2 + 6)/2
m₁ = 8/2
m₁ = 4.
Also, we would calculate the difference in the solution sets as follows:
m₂ = (6 - 2)/2
m₂ = 4/2
m₂ = 2.
Mathematically, the absolute value equation is given by:
|m - m₁| - m₂ = 0
|m - 4| - 2 = 0
|m - 4| = 2.
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find the value of n:
[tex]\frac{n}{11} = \frac{3.5}{7}[/tex]
The value of n from the given expression is 5.5
Solution to linear equation and fractionsFractions are expression written as a ratio of two integers. The linear equation on the other hand has a leading degree of 1.
Given the equation below;
n/11 = 3.5/7
Simplify to have
n/11 = 1/2
Cross multiply the given result to have:
11 = 2n
Swap
2n = 11
Divide both sides by 2 to have;
2n/2 = 11/2
n = 5.5
Hence the value of n from the given expression is 5.5
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Alan is arranging 3 different stuffed toys in a row on a shelf. create a sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e).
The sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt
How to create the sample space?The given parameters are
Stuffed toys, n = 3
Toys to arrange, r = 3 i.e. teddy bear (t), a kitten (k), and an elephant (e).
The number of arrangement is calculated as;
Ways = nPr
Substitute the known values in the above equation
Ways = 3Pr
Apply the permutation formula
Ways = 3!/0!
0! =1
So, we have
Ways = 3!/1
This gives
Ways = 3!
Expand
Ways = 3 * 2 * 1
Evaluate
Ways = 6
This means that the sample size is 6
Hence, the sample space for the arrangement of a teddy bear (t), a kitten (k), and an elephant (e) is tke, tek, kte, ket, etk and ekt
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QUICK!!!
The total arm and blade of a windshield wiper is 12 in. long and rotates back and forth through an angle of 90 degrees. The shaded region in the figure is the portion of the windshield cleaned by the 9-in. wiper blade. What is the area of the region cleaned?
answer with the last three decimal places (no rounding)
The area of the region is: 63.585 square inches.
What is the area of the region cleaned?If we have a circle of radius R, the area of said circle is:
A = pi*R^2
Particularly, if we have a section of the circle defined by an angle θ, the area of that region is:
A = (θ/2pi)*pi*R^2 = (θ/2)*R^2
In this case we have:
θ = 90° = pi/2
R = 9in
Replacing that we get:
A = (pi/4)*(9in)^2 = (3.14/4)*(9in)^2 = 63.585 in^2
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Select the correct answer. which of these organizations provides help to the friends and families of an alcoholic? a. national clearing house for alcohol and drug information b. american council on alcoholism c. alateen
Answer: C
Step-by-step explanation:
What is the solution to the system of equations?
[tex](\frac{3}{2},\frac{5}{2})[/tex]
Step-by-step explanation:The first equation can be rearranged by subtracting y from both sides. This gives you x = 4 - y.
The second equation is x = y - 1
Therefore, as both equations are equal to x, you can say that they are equal to each other, so 4 - y = y - 1.
If you add 1 to each side, you get 5 - y = y
If you add y to each side, you get 5 = 2y
Divide both sides by 2 to get y = 5/2
Now you can substitute 5/2 for y. For example, the second equation becomes x = 5/2 - 1
x is therefore 3/2
This can be written as [tex](\frac{3}{2},\frac{5}{2})[/tex], which is the final answer.
Which shows the following expression after the negative exponents have been eliminated?
Answer:
[tex]\frac{a^3b^4}{ab^2}[/tex] which is the last choice in the question
Step-by-step explanation:
Simplify
[tex]\frac{a^3b^{-2}}{ab^{-4}} = \frac{a^3}{a}\frac{b^{-2}}{b^{-4}}[/tex]
Using the fact that [tex]\frac{x^m}{x^n} =x^{m-n}[/tex]
We get
[tex]\frac{a^3}{a} = a^{3-1} = a^2[/tex]
[tex]\frac{b^{-2}}{b^{-4}} = b^{-2-(-4)} = b^2[/tex]
So
[tex]\frac{a^3b^{-2}}{ab^{-4}} =a^2b^2[/tex]
Multiplying numerator and denominator by [tex]ab^2[/tex] gives
[tex]a^2b^2 \frac{ab^2}{ab^2}[/tex]
= [tex]\frac{a^3b^4}{ab^2}[/tex] ANSWER
Hint:
We can eliminate first choice since negative exponents still remain
We can eliminate third choice because the expression has a minus sign which is not possible
That just leaves second and fourth choices to work with
Mary wants to hang a mirror in her room. the mirror and frame must have an area of 7 square feet. the mirror is 2 feet wide and 3 feet long. which quadratic equation can be used to determine the thickness of the frame, x? square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. arrow on the bottom frame with an x and an arrow on the right frame with an x. x2 14x − 2 = 0 2x2 10x − 7 = 0 3x2 12x − 7 = 0 4x2 10x − 1 = 0
The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.
The correct option is D.
What is a quadratic equation ?A quadratic equation is an algebraic equation of the second degree in x.. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
According to the given information:Total area = 7 square feet
and,
Total area = Length x Width
So,
7 = (2x + 3)(2x + 2)
7 = 4x2 + 4x + 6x + 6
7 = 4x2 + 10x + 6
4x2 + 10x + 6 - 7 = 0
4x2 + 10x - 1 = 0
Hence,
The quadratic equation use to determine the thickness of the frame, x is 4x² + 10x - 1 = 0.
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I understand that the question you are looking for is:
Mary wants to hang a mirror in her room. the mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x. Which quadratic equation can be used to determine the thickness of the frame, x?
A. x² + 14x - 2 = 0
B. 2x² + 10x - 7 = 0
C. 3x² + 12x - 7 = 0
D. 4x² + 10x - 1 = 0
A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse? startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 5 2nd row y = startfraction 14 over 81 endfraction (x minus 2) squared minus 6 endlayout startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 25 2nd row y = startfraction 14 over 81 endfraction (x minus 2) squared minus 6 endlayout startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 5 2nd row y = negative startfraction 14 over 81 endfraction (x 7) squared 8 endlayout startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 25 2nd row y = negative startfraction 14 over 81 endfraction (x 7) squared 8 endlayout
The system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:
y = (2/7)(x - 2)^2 - 6(x - 1)^2 + (y - 2)^2 = 5^2What are equations?The equation is described as the state of being equal and is commonly represented as a math expression with equal values on either side, or it refers to an issue in which many factors must be considered. 2+2 = 3+1 is an example of an equation.To find the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse:
The vertex form of a quadratic function is given by: f(x) = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola, a is constant.
For the sailboat we have vertex: (h, k) = (2, -6) and one point: (-7, 8) that is f(-7) = 8.
f(x) = a(x - 2)^2 - 6We will find a using f(-7) = 8:
f(-7) = a(-7-2)^2 - 6f(-7) = 49a - 649a - 6 = 849a = 14a = 14/49a = 2/7The quadratic function for the sailboat is given by:
f(x) = (2/7)(x - 2)^2 - 6 or y = (2/7)(x - 2)^2 - 6The equation for a circle with a radius of 5 and center (1, 2) is:
(x - 1)^2 + (y - 2)^2 = 5^2Therefore, the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:
y = (2/7)(x - 2)^2 - 6(x - 1)^2 + (y - 2)^2 = 5^2Know more about equations here:
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The correct form of the question is given below:
A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?
(6+q)-xy pllease help this question turn in words
In words (6 + q) - xy is six added to a number subtracted from the product of two numbers
The problem is a algebraic expression
What is an algebraic expression?A algebraic expression a mathematical expression containing one or more variables used to express a word problem
We want to convert the algebraic expression (6 + q) - xy into a word problem.
First, we have 6 + q which is six added to a number.Next, we have xy which is the product of two numbersSince (6 + q) is subtracted from xy, we have (6 + q) - xy as six added to a number subtracted from the product of two numbersSo, (6 + q) - xy in words is six added to a number subtracted from the product of two numbers
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What are the coordinates of point J'? (-2,-4) (-2,-6) (Negative nine-halves, negative 4) (Negative nine-halves, negative 9)
The coordinates of point J' in the quadrilateral F'G'H'J' is J'(-2, -4)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.
Quadrilateral FGHJ is dilated according to the rule Do,Two-thirds(x,y) to create the image quadrilateral F'G'H'J', which is not shown. Quadrilateral FGHJ has points F(-5, -4), G(-3, -2), H(-1, -4) and J(-3, -6).
The coordinates of point J' in the quadrilateral F'G'H'J' is J'(-2, -4)
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Answer:
(-2,-4)
Step-by-step explanation:
Geometry B E2020!! :3
A school administrator believes that the mean class gpas for a given course are higher than the preferred mean of 2.75 at a significance level of 0.05 , and checks a randomly chosen sample of 50 classes. create a histogram, and calculate , the -statistic, and the -value.
The mean GPA is greater than 2.75.
What is GPA?A grade point average is a figure that represents the average of the final grades obtained in courses over time. A student's grade point average, sometimes known as a GPA, is computed by adding all accumulated final grades and dividing the total by the number of grades granted.To find the GPA:
GPA is calculated and could be utilized by the college to tell choices, which include the subsequent educational progression.Divide the total range of grade factors earned with the aid of the total number of letter-graded units undertaken.Mean GPA = total/50= 2.75.Therefore, the mean GPA is greater than 2.75.
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the value of digit 7 in 906.7
The answer is tenths
Step-by-step explanation:
According to the place value chart of decimals,the first number after the decimal point starts from tenths and continues.so the answer is tenths
Hi :)
Remember Place value in decimal numbers
———————————[tex]\large\boldsymbol{\hfill\stackrel{hundreds}{9}~\hfill\stackrel{tenths}0~\hfill\stackrel{ones}6.\hfill\stackrel{tenths}{7}}[/tex]
Then
The place-value of [tex]\boldsymbol{7}[/tex] is [tex]\boldsymbol{tenths}[/tex].
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
Sami cuts out a rectangle that has a perimeter of 48 inches and a length of 13 inches. they cut out another rectangle that is the same length and twice as wide. what is the perimeter of the new rectangle?
Answer:
70 inches
Step-by-step explanation:
the width of the original rectangle:
48/2 - 13 = 24 - 13 = 11
the new rectangle:
length: 13
width: 2(11) = 22
perimeter: 2(13+22) = 2(35) = 70
The perimeter of the new rectangle is 70 inches.
What is Area of Rectangle?The area of Rectangle is length times of width.
The perimeter of a rectangle is given by the formula P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
The first rectangle has a perimeter of 48 inches and a length of 13 inches.
48 = 2(13 + w)
24 = 13 + w
w = 11
So the first rectangle has a length of 13 inches and a width of 11 inches.
The second rectangle has the same length of 13 inches and twice the width of the first rectangle, which means it has a width of 22 inches.
P = 2(13 + 22)
= 2(35)
= 70
Therefore, the perimeter of the new rectangle is 70 inches.
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If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?
Formula for finding area of rhombus: [tex]\frac{d1 * d2}{2}[/tex]
d₁ = 16 yd
Area = 72 yd²
Rhombus Area =>
[tex]\frac{16 * d2}{2} = 72[/tex]
16*d₂ = 144
d₂ = 9
AC = 9 yd
Hope it helps!
Determine what type of model best fits the given situation: water leaking from a local reservior at the rate of 500 gallons per hour.
The type of model that best fits the given situation is; A linear equation Model
What is the model of the equation?Right inside the local reservoir we will have an initial amount of water A.
Now, for every hour that passes by, the amount of water in the reservoir decreases by 500 gals.
Thus, after t hours, the amount of water in the reservoir is expressed as:
W = A - 500gal * t
This is clearly a linear equation model and so we can conclude that the model that fits best in the given situation is a linear model.
The domain of this model is restricted because we can't have a negative amount of water in the reservoir, and as such the maximum value of t accepted is: W = 0 = A - 500gal*t
t = A/500 hours
Therefore, the domain of this linear relation is: t ∈ {0h, A/500 }
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Given MTS and SQP, find sq
The measure of the side SQ from the given diagram is 19/6
Similar shapesSimilar shapes are shapes that has equal length and equal side measures and angles.
From the given diagram, the measure of the sides TSis congruent to SP and the measure of MS is congruent to SQ.
Using the expression below to determine the value of x
MS/ST = SQ/SP
Given the following parameters
MS =30
ST = 10
SQ = 6x-1
SP = 3 - 2x
Substitute the given parameters into the formula to have:
30/10 = 6x-1/3-2x
Cross multiply
10(6x-1) = 30(3-2x)
Expand
60x - 10 = 90 - 60x
60x + 60x = 90 + 10
120x = 100
x = 10/12
x = 5/6
Determine the measure of SQ
SQ = 6x - 1
SQ = 5(5/6) - 1
SQ = 25/6 - 1
SQ = 19/6
Hence the measure of the side SQ from the given diagram is 19/6
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Match each scenario with the type of correlation it shows.
the time spent practicing and the
number of free throws made
the number of items bought and the
checking account balance
the height of baseball player and the
number of hits made.
000
negative correlation
no correlation
positive correlation
The time spent practicing and the number of free throws made has a positive correlation. The number of items bought and the checking account balance has a negative correlation. The height of baseball player and the
number of hits made has no correlation.
About positive correlation:
Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation.
About negative correlation:
A negative or inverse relationship between two variables in statistics exists when higher values of one variable tend to be correlated with lower values of the other. Such scenarios have negative correlation.
About no correlation:
When two events or variables are unaffected by each other or are not inter-related, they are said to possess no correlation.
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Answer:
option 1 is positive option 2 is negative option 3 is none
Step-by-step explanation:
Enginuity said so
PLEASE ANSWER QUICKLY
Answer:
1st option
Step-by-step explanation:
to find f(g(x)) substitute x = g(x) into f(x) , that is
f(g(x))
= f(4x - 5)
= 2(4x - 5) + 1 ← distribute parenthesis
= 8x - 10 + 1
= 8x - 9
The area of a painting is 4081 c m squared.
If the width of the painting is 53 cm, what is its length, in centimeters?
Type your numerical answer below (without units). If necessary, round to the nearest integer.
Answer:
49,2
Step-by-step explanation:
i dont practice math in english so the variables might be a little different!! The little L with the squiggly is supposed to represent length
The length of the painting is 77 cm if the area of the painting is 4081 sq cm and the width is 53 cm.
The area of a rectangle is the product of the length and width of the same rectangle.
Given that:
The area of the painting, A = 4081 cm².
The width of the painting, b = 53 cm.
To find the length of the painting, use the following formula to obtain the area of the rectangle:
Area = length × breadth
Let the length of the painting is l, then
A = l × b
4081 = l × 53
l = [tex]\frac{4081}{53}[/tex]
l = 77
Thus, the length of the painting is 77 cm.
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The numbers of questions answered correctly by various students on a 1010-question quiz are an example of which type of data?
The numbers of questions answered correctly by various students on a 10 question quiz are an example of discrete data.
What is discrete data?Discrete data is the type of data that has clear spaces between values.
As a result, the test-scores are discrete data. Although most discrete data, refers to things we can count easily, it does not have to be numeric. Non-numeric categories could be described as discrete data.
Discrete data is a count that involves integers — only a limited number of values is possible. This type of data cannot be subdivided into different parts. Discrete data includes discrete variables that are finite, numeric, countable, and non-negative integers.
Discrete data is a type of quantitative data that includes figures and statistics of non divisible, single points of data that you can count. You typically write discrete data points as numbers that represent exact values, and discrete data usually represents single events that have already occurred. When reviewing discrete data, companies analyze exact figures like units that were sold on a given day or the hours that an employee worked during a certain week.
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Evaluate the expression under the given conditions. tan(2); cos() = 5 13 , in quadrant i
The solution to given expression tan(2θ) is 22.615°
For given question,
We have been given an expression tan(2θ)
Given that cos(θ) = 5/13, and θ is in quadrant 1.
We know that the trigonometric identity
sin²θ + cos²θ = 1
⇒ cos²θ = (5/13)²
⇒ sin²θ = 1 - 25/169
⇒ sin²θ = 169 - (25/169)
⇒ sin²θ = 144/169
⇒ sin(θ) = 12/13
We know that the identity cos(2x) = cos²x - sin²x
⇒ cos(2θ) = cos²θ - sin²θ
⇒ cos(2θ) = 25/169 - 144/169
⇒ cos(2θ) = -119/169
And sin(2x) = 2sin(x)cos(x)
⇒ sin(2θ) = 2sin(θ)cos(θ)
⇒ sin(2θ) = 2 × 12/13 × 5/13
⇒ sin(2θ) = 120/169
We know that, tan(x) = sin(x)/cos(x)
⇒ tan(2θ) = sin(2θ)/cos(2θ)
⇒ tan(2θ) = (120/169) / (-119/169)
⇒ tan(2θ) = 120 / (-119)
⇒ tan(2θ) = -1.008
Since θ is in quadrant 1, tan(2θ) = 1.008
⇒ 2θ = arctan(1.008)
⇒ 2θ = 45.23
⇒ θ = 22.615°
Therefore, the solution to given expression tan(2θ) is 22.615°
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Find the area of this triangle. Round to the nearest tenth.
The area of the triangle rounded to the nearest tenth is 33.3 squared inches.
What is the area of the triangle?
Given the data in the diagram;
Angle B = 133°Side a = 7Side c = 13Side b = ?Angle C = ?First we find the dimension of side b.
From the rule of cosines.
b = √[ a² + c² - 2acCosB ]
We substitute into the formula.
b = √[ 7² + 13² - ( 2 × 7 × 13 × cos( 133° ) ]
b = √[ 49 + 169 - ( 182 × cos( 133° ) ) ]
b = √[ 218 - 182×cos( 133° ) ]
b = √[ 342.1237 ]
b = 18.5
Next, we find angle C.
From rule of cosines.
cosC = [ b² + a² - c² ] / 2ba
cosC = [ 18.5² + 7² - 13² ] / [ 2 × 18.5 × 7 ]
cosC = [ 342.25 + 49 - 169 ] / [ 259 ]
cosC = [ 222.25 ] / [ 259 ]
cosC = [ 0.8581 ]
C = cos⁻¹[ 0.8581 ]
C = 30.9°
Now, we can find the area of the triangle.
Area = [ ab × sinC ] / 2
Area = [ 7 × 18.5 × sin( 30.9 ) ] / 2
Area = [ 129.5 × 0.51354 ] / 2
Area = 66.5 / 2
Area = 33.3 in²
The area of the triangle rounded to the nearest tenth is 33.3 squared inches.
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When measuring variables, it is often preferable to use a small sample size because:______.
When measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.
What are variables?A variable is defined as any property, number, or amount that can be measured or counted. A variable is also known as a data item. Variables include age, business revenue and expenses, country of birth, capital expenditure, class grades, eye color, and vehicle type. A variable in research is essentially a person, place, object, or phenomenon that you are attempting to quantify in some way. The simplest way to comprehend the distinction between a dependent and independent variable is to consider what the words tell us about the variable in question. When measuring variables, small sample size is frequently preferred because the smaller the sample, the greater the likelihood of a misleading result.Therefore, when measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.
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Write the equation for a circle centered at the origin with x-intercepts of (-9,0) and (9,0).use ^2 for squared, ^3 for cubed,
The equation of the circle can be shown as, x² + y² = 9², or, x² + y² = 81.
The equation of a circle, with the center at the origin and the radius r units, is given as x² + y² = r².
In the question, we are asked to write the equation for a circle centered at the origin with x-intercepts of (-9, 0) and (9, 0).
We can find the radius of the circle using the distance formula,
D = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁, y₁) and (x₂, y₂) are the endpoints of a line segment.
Radius is the distance between the center and any point on the circle.
Thus, taking (x₁, y₁) as (0, 0), the origin, for the center, and (x₂, y₂) as (9, 0), for any point on the circle, we get the radius as:
r = √((9 - 0)² + (0 - 0)²),
or, r = √(9² + 0²),
or, r = √9² = 9.
Thus, the radius of the circle is r = 9 units.
Thus, the equation of the circle can be shown as, x² + y² = 9², or, x² + y² = 81.
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i need help with my algebra assignment
Answer:
[tex]Question 1\\1+i\\-1-i\\Question 2\\\\-1+i\\1-i[/tex]
Step-by-step explanation:
Complex Numbers:
Complex numbers can generally be expressed in the form: [tex]a+bi[/tex] where a and b are both real numbers, with the a part representing the real part of the complex number, and the bi representing the imaginary part.
We can also graph these numbers using the complex plane. The complex plane has the real axis where the x-axis would normally be, and the imaginary axis where the y-axis would normally be. So by this definition the "a" is what determines the horizontal position or the position on the real axis and the "b" is what determines the vertical position or the position on the imaginary axis.
I attached a diagram of the complex plane, and it's essentially the same as a normal graph, with a=x, and b=y.
Question 1:
So when a complex number lies above the real-axis, that means the imaginary part is greater than 0. When a complex numbers lies to the right of the imaginary axis, that means the real part is greater than 0.
This means we have the form: [tex]a+bi \text { where } a > 0 \text{ and } b > 0[/tex]. You can literally plug in any number for a and b, so long as it fits this. For example we can just do: [tex]1+i[/tex]
So when a complex number lies below the real-axis, that means the imaginary part is less than 0. when a complex numbers lies to the left of the imaginary axis, the real part is less than 0.
This means we have the form: [tex]a+bi \text { where } a < 0\text{ and }b < 0[/tex]. You can plug in any real number that lies within this restriction. An example would be:
[tex]-1-i[/tex]
Question 2:
Above real axis and to the left of the imaginary axis means: b>0 and a<0. So we can plug in any number into the standard form that fits this restriction. an example would be: [tex]-1+i[/tex]
Below real axis and to the right of the imaginary axis means: b<0 and a>0. So we can plug in any number into the standard form that fits this restriction. An example would be: [tex]1-i[/tex]
A juggler is performing her act using several balls. she throws the balls up at an initial height of 4 feet, with a speed of 15 feet per second. this can be represented by the function h(t) = −16t2 15t 4. if the juggler doesn't catch one of the balls, about how long does it take the ball to hit the floor? 7.52 seconds 1.15 seconds 0.47 seconds 0.22 seconds
The ball will take 1.15 seconds to hit the floor.
It is given that,
A juggler is performing her act using several balls. The height as a function of time is given by :
[tex]h(t) =-16t^{2} + vt +s[/tex].............(1)
where,
v is the speed of the ball
s is initial height
t is time taken
Putting h(t) = 0 and solving equation (1)
[tex]-16t^{2} + vt +s = 0[/tex]
[tex]-16t^{2} + 15t +4 = 0[/tex]
On solving above equation using graphing calculator and solving for t we get, t = 1.154 second.
Hence, the correct option is (b) " 1.15 seconds ".
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Tickets to the movies cost $24 for 1 adult. The price of 1 child was 2/3 of that price. How much did a family with 2 adults and 2 children have to pay?