Suppose a system of equations has 3 equations and 5 variables. additionally, suppose the coefficient matrix for the system has 3 pivot columns. Based on the information provided, it is consistent.
The number of pivot columns in the coefficient matrix of a system of equations determines the rank of the matrix, which is a measure of the number of linearly independent rows or columns. A system of equations is consistent if and only if the rank of the coefficient matrix is equal to the number of unknowns in the system.
In this case, the system has 3 equations and 5 variables, so it is not immediately clear if the rank of the coefficient matrix is equal to the number of unknowns. Additionally, the number of pivot columns alone is not enough to determine the consistency of the system, as there may be additional relationships between the variables that affect the rank.
So, Based on the information provided, it is consistent.
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Write an explicit formula for a_na n , the n^{\text{th}}n th term of the sequence 19, 13, 7,
An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 19 - 6(n - 1).
How to write an explicit formula for the arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we have the following parameters:
First term, a₁ = 19
Second term, a₂ = 13
Next, we would determine the common difference as follows:
Common difference, d = a₂ - a₁
Common difference, d = 13 - 19
Common difference, d = -6
Substituting the parameters into the mathematical expression, we have;
aₙ = 19 + (n - 1)(-6)
aₙ = 19 - 6(n - 1).
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Which rectangular prism has the largest volume?
Answer:
The first one is largest volume: 27
Step-by-step explanation:
1) 3*3*3=27
2)4*4*1=16
3)2*4*2=16
4)1*6*2=12
lisle and linda walk in opposite directions from the same point. lisle walks 0.8 kilometers every 10 minutes, and linda walks 2.8 kilometers every 30 minutes. how far apart are they after 1 hour?
The total distance between lisle and Linda will be 10.4 kilometers.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that lisle and Linda walk in opposite directions from the same point. lisle walks 0.8 kilometers every 10 minutes, and Linda walks 2.8 kilometers every 30 minutes.
lisle's distance in an hour:-
0.8 x 6 = 4.8 Km
Linda's distance in an hour:-
2.8 x 2 = 5.6 Km
Total distance = 4.8 + 5.6 = 10.4 Km
Therefore, there will be 10.4 kilometers between Lisle and Linda overall.
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Hexagon HEXAGZ has vertices H(3,0), E(1, -2), X(-1, -2), A(-3,0), G(-2,2), and Z(1,2). What are the coordinates of the image of HEXAGZ for a dilation with center (0,0) and a scale factor of 3.5?
Answer: ion know
Step-by-step explanation: 1 + 2 = 3
HELP THIS IS FOR EXTRA CREDIT AND ITS DUE TODAY
You spin a spinner that is equally divided into 11 parts. 3 parts are green, 3 parts are speckled, 2 parts are white, and 3 parts are yellow.
What is the probability of the spinner not stopping at a white section? Write your answer as a decimal rounded to the nearest hundredth.
Answer: The probability of the spinner stopping at a green section and then rolling a 3 is 1/22
Step-by-step explanation: A spinner stopping at a green section
B: rolling a 3
the spinner is divided into 11 parts, 3 of them are green, then:
P(A) = 3/11
the number cube has 6 numbers, then:
P(B) = 1/6
The two events are independent, then:
P(A∩B) = P(A)*P(B) = 3/11 * 1/6 = 1/22
the first box has two white balls. the second box has two black balls. the third box has a white and a black ball. all boxes are labeled but all labels are wrong! you are allowed to open one box, pick one ball at random, see its color and put it back into the box without seeing the color of the other ball. how many such operations are necessary to correctly label the boxes?
To correctly label the boxes, you need to perform two operations. In the first operation, you can choose to open any of the three boxes. Regardless of which box you open, you will be able to determine the color of one ball.
Then, you can use that information to deduce which of the other two boxes must contain two balls of the same color and which must contain one ball of each color. In the second operation, you can choose to open the box which contains two balls of the same color. The color of the ball you take out will tell you the correct label of the box. By performing these two operations, you can correctly label the boxes with only two ball selections.
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(2x+5)
(4y -1)
(3x-33)
Answer: (38, 25) or x = 38 and y = 25
Step-by-step explanation:
We will use the measurement of a straight line and vertical angles to help us solve.
First, vertical angles are congruent. We will set up an equation and use inverse operations to isolate the x variable.
Given:
(3x - 33) = (2x + 5)
Add 33 and subtract 2x from both sides of the equation:
x = 38
Next, we know a straight line is equal to 180 degrees. We can substitute the value we found above for x. Then we will simplify and use inverse operations to isolate the y variable.
Given:
(2x + 5) + (4y - 1) = 180
Substitute for x:
(2(38) + 5) + (4y - 1) = 180
Simplify:
81 + (4y - 1) = 180
Subtract 80 (81 - 1) from both sides of the equation:
4y = 100
Divide both sides of the equation by 4:
y = 25
the number of new cases of a disorder in a population that emerge in a particular time interval is called the:
The number of new cases of a disorder in a population that emerge in a particular time interval is called the incidence.
About incidenceIncidence refers to the rate at which a new event occurs in a population. Incidence takes into account the variable time period during which a disease-free individual becomes at risk of spreading the disease.
In incident calculations, the quantifier is the number of events that have occurred in a given time. Then the quantifier of the denominator is the population that is at risk of experiencing the event during this period.
Simply put, incidence refers to new cases and is used to determine the etiology of the disease. While prevalence is more widely used to refer to health status in certain populations.
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An item is regularly priced at $30. Maria bought it on sale for 80% off the regular price. How much did Maria pay?
Answer:
$24
Step-by-step explanation:
30 times .80=24
Do the following lengths form a right triangle?
The lengths form a right triangle are Triangle 2,3 and 4.
Side lengths a , b , c form a right triangle if, and only if, they satisfy a² + b² = c² . We say these numbers form a Pythagorean triple.
About Pythagorean theoremThe Pythagorean theorem reads:
"In a right triangle, the square of the hypotenuse equals the sum of the squares of the other sides."
Thus the three sides of a right triangle have an interrelated relationship.
This theorem has two mandatory properties, namely it only applies to right triangles and you must know at least two sides first to be able to determine the other side.
While the purpose of this theory is basically to determine the length of one side of a right triangle. Whereas for a right triangle it is actually very easy because one of the characteristics of a right triangle is that it has one of the 90° angles.
However, this theory can also be used to calculate the length of the diagonal of a square or beam and cube which also looks like a right triangle.
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Write x^4 +5x^2-8 in quadratic form, if possible
Writing x^4 + 5x^2 - 8 in quadratic form will result to
y² + 5y - 8How to write the equation in quadratic formQuadratic equation involves having the variables to be in exponents of 2 as the maximum. That is making the equation degree 2
The equation x^4 + 5x^2 - 8 is rewritten by say
x² = y
then we have
y² + 5y - 8
The equation in quadratic form is y² + 5y - 8
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Calculate the area of the figure below using the following information:
Area of triangle ABC = 7.95 square units
Area of triangle ACD = 9.8 square units
Area of triangle AED = 8.75 square units
Image of irregular pentagon with vertices points A, B, C, D, and E starting at upper left moving clockwise. Two dotted diagonal lines, one connecting vertices A and C, and the second connecting vertices A and D.
The area of figure ABCDE is 26.5 square units.
What is a Triangle?Three angles, three sides, and three vertices make up the closed shape of a triangle. It is one of the most fundamental geometric shapes, and the symbol for it is.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape
Given:
Area of triangle ABC = 7.95 square units
Area of triangle ACD = 9.8 square units
Area of triangle AED = 8.75 square units
To calculate the area of the figure we have to add the area of the individual triangles together.
So, Area of figure ABCDE
= Area of triangle ABC + Area of triangle ACD + Area of triangle AED
= 7.95 + 9.8 + 8.75
= 26.5 square units
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suppose the 99% confidence interval for the mean sat scores of applicants at a business college is given by [1,692, 1,842]. this confidence interval uses the sample mean and the sample standard deviation based on 25 observations. what are the sample mean and the sample standard deviation used when computing the interval?
The upper bound is 1842 and lower bound is 1692. By using these boundaries and t-table, the sample mean is 1767 and sample standard deviation = 133.98.
Here, the two boundaries are 1692 and 1842.
Mean = (1692+1842) /2 = 1767
Here the degree of freedom, df = (n-1) = 25-1 =24
Margin of error = (1842-1692)/2 = 75
Confidence level = 99%
From the t table, value of T with confidence level 99% and df= 24 is 2.80
The equation for margin of error is M = Ts/√n
M= 75 , T= 2.80, n =25
75 = (2.80 × s) / √25
75 = 2.80s/ 5
s = (75×5)/2.80 = 133.928 = 133.93
So the sample mean is 1767 and the standard deviation is 133.93.
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10 m
55 m
60 m
90 m
20 m
15 m
Whats the perimeter
The perimeter of the polygon is 250m
What is polygon? what its perimeter?A polygon is a closed, straight-sided two-dimensional plane shape in geometry. There are no curves on the polygon's surface. The polygon can be divided into two different types, such as regular polygons and irregular polygons, depending on its sides and angles.
The total of a polygon's sides is referred to as the polygon's perimeter. If a polygon has regular sides, its perimeter may be calculated using the formula Perimeter of Regular Polygon = (Number of Sides) x (Polygonal Side Length) units.
Given the sides of the polygon are 10 m, 55 m, 60 m, 90 m, 20 m and 15 m.
The perimeter of the polygon = sum of all sides
The perimeter of the polygon = 10m + 55m + 60m + 90m + 20m + 15 m.
The perimeter of the polygon = 250m
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what is the probability that a standard normal random variable will be between .3 and 3.2?
0.3814 is the probability that a standard normal random variable .
What is the probability equation?
The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula.
P(E) = positive outcomes/total outcomes is how it's expressed mathematically. The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula. Mathematically speaking, it seems as follows: P(E) stands for positive outcomes/total outcomes.
P(0.3 < z < 3.2)
= P(z < 3.2) - P(z < 0.3)
= 0.9993 - 0.6179
= 0.3814
Probability = 0.3814
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9 units to the left, 7 units up
The Equation of parabola is .y = a(x + 9)² + 7
What is Equation of Parabola?The general equation of a parabola is: y = a(x – h)² + k where (h,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.
Given:
The general equation of a parabola is given by
y = a(x – h)² + k
Here (h, k) denotes the vertex.
We have 9 units to the left which is represented by '+9' and 7 units up which is represented by '+7'
So, the Equation of parabola is
y = a(x – h)²
y = a(x + 9)² + 7
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find the value of angle x
Answer:
72⁰
Step-by-step explanation:
180-36= 144 (angles in a triangle=180)
144/2=72 (parallel lines are equal)
Select the trigonometric equation that can be used to find x.
Answer:
tan(64)= x/11
Step-by-step explanation:
if we make 64 degrees are central angle then that means the side along the right angle is the adjacent and side x is the opposite
since tan∅ = opposite/adjacent
we know angle is 64 and adjacent is 11
thus,
tan 64 = x/11
A coral reef is located near to a chemical plant. Scientists measure the number of colonies of coral over a period of 20 years. Each year, the
number of colonies is 5 times the previous year.
Which equation shows the number of colonies, c after t years?
c=5-25²
c=25-3²
c=25-5²
c=25+3t
c=25-20¹
SCALE:
0 - 1 - 2 - n
25-125-625-n
Find out which equation best suits N on the scale.
Answer:
c = 25 * 5^t
Step-by-step explanation:
c = 25 * 5^t
This equation best suits N on the scale as it follows the pattern of the number of colonies being 5 times the previous year.
if there are 250 members of the 8th grade class, then what percent prefer either tennis or football? (the tennis is 20 and the football is 14)
The percentage of preference of tennis or football is, 13.6%
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
The total number of students who prefer tennis is 20.
And the total number who prefer football is 14,
so the total number who prefer either tennis or football is
⇒ 20 + 14
⇒ 34
To find the percentage of students who prefer either tennis or football, we can divide the number of students who prefer either by the total number of students and multiply by 100:
(34 / 250) x 100 = 13.6%
So, approximately 13.6% of the 8th grade class prefer either tennis or football.
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Help with thisss pleasseeeee
Answer:
y[tex]\geq[/tex]2x-3
Step-by-step explanation:
y intersect is -3
slop is 2, which eliminates option 2 and 4
when plugging in the point 2,2 in the equation- its a true solution for option 3.
y[tex]\geq[/tex]2x-3
2[tex]\geq[/tex]4-3
2[tex]\geq[/tex]1 True.
A 20-minute TV program consists of two commercials, each 13 over 4 minutes long, and three equal-length entertainment segments. How long is each entertainment segment? Enter your answer as a decimal. ( read the question in the picture instead its easier to understand)
Answer:
6.0 min
Step-by-step explanation:
20/3=6 remain 2 = 2 x 1min commercial
6 mins long
Year 9 students from a school were asked to choose one language to study. The table shows information about their choices. Students in maths class 9s1 were told to draw a pie chart to ultralight
zelma is 18 years older than her son. she was three times older as old as he was last year. how old are they now?
Zelma is 28 years old and her son is 10 years old. We brought this conclusion with the help of algebra.
Let x = son's age now
Then, x+18 = Zelma's age now
x-1 = son's age one year ago
x+17 = Zelma's age one year ago
x+17 = 3(x-1)
x+17 = 3x-3
2x = 20
x = 10
Algebra is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables as if they were numbers and is therefore essential in all applications of mathematics.
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The graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been changed somewhat. Which of the following could be the equation of F(x)?
A possible equation for F(x) is given as follows:
A. F(x) = 0.4x² + 1.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.From this graph, function f(x) is moved up one unit, hence:
F(x) = ax² + 1.
The function f(x) was also vertically compressed, meaning that a < 1, hence:
F(x) = 0.4x² + 1.
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which variable is the dependent variable--the variable that responded to or depended on the treatment, and was measured by the researchers?
The dependent variable is the variable that responds to or depends on the treatment and is measured by the researchers.
The dependent variable is also known as the outcome variable, response variable, or dependent measure. The dependent variable is the result that the researchers are interested in observing and understanding the relationship with the independent variable, which is the variable that the researchers manipulate or control in the study. The dependent variable is what the researchers are trying to explain or predict based on the independent variable.
In other words, the value of the dependent variable is dependent on the independent variable.
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Solve for x on the diagram below
Answer:
x = 60°
Step-by-step explanation:
the 'x' angle and the adjacent 120° angle form a straight line
a straight line consists of 180°
what is the unit of measurement for coding the length of lacerations? a. square inches b. inches c. square centimeters d. centimeters
The unit of measurement for coding the length of lacerations d)centimeters.
Centimeters are the most common unit of measurement used to code the length of lacerations. This is because they are a small enough unit of measurement that they can accurately describe even the smallest of lacerations.
Centimeters are also the most commonly used metric unit of length, making them the most useful when coding lacerations for medical records. In addition, centimeters are a more precise unit of measurement than inches and are accepted internationally as a unit of measurement, making them the best choice when coding lacerations.
Finally, centimeters are consistent units of measurement, making it easy to compare laceration lengths between different patients and different medical records.
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AC = 3x + 3, AB= -1 + 2x, and BC = 11.
The value of x is 7.
What are Collinear Points?Collinear points are the points which are formed on a straight line, whether they are close or far away.
Figure representing the question is given below.
From the figure, we have,
AB + BC = AC
(-1 + 2x) + (11) = 3x + 3
2x + 10 = 3x + 3
Like terms adding together,
2x - 3x = 3 - 10
-x = -7
x = 7
Hence the value of x is 7.
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I need help on this problem
The distance of Main Street is given by the equation D = 319.25 feet
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the distance of Main Street be D
Now , let the triangle be represented as ΔABC
The base of the triangle BC = 300 feet
The hypotenuse of the triangle AC = distance between First avenue and Canal street
The measure of angle ∠BAC = 70°
From the trigonometric relations , we get
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin 70° = 300 / D
Multiply by D on both sides of the equation , we get
D ( sin 70° ) = 300
Divide by sin 70° on both sides , we get
D = 300 / ( sin 70° )
On further simplification , we get
D = 300 / 0.939692
D = 319.2535
D = 319.25 feet
Hence , the distance is 319.25 feet
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