The answer of the given question based on the changing the denominator of fraction the answer is the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
What is Formula?In mathematics, formula is mathematical expression or equation that describes relationship between two or more variables or quantities. A formula can be used to solve problems or make predictions about particular situation or set of data.
Formulas often involve mathematical symbols and operations, like addition, subtraction, multiplication, division, exponents, and square roots. They may also include variables, which are typically represented by letters, and constants, which are fixed values that do not change.
To change the denominator of the fraction a+3/6-2a to 2(a²-9), we need to factor the denominator of the original fraction and then use algebraic manipulation to rewrite it in the desired form.
First, we can factor the denominator of the original fraction as follows:
6 - 2a = 2(3 - a)
Next, we can rewrite the denominator using the difference of squares formula:
2(a² - 9) = 2(a + 3)(a - 3)
Now, we can use the factored form of the denominator to rewrite the original fraction:
(a + 3)/(6 - 2a) = (a + 3)/(2(3 - a)) = -(a + 3)/(-2(a - 3)) = (3 + a)/(2(a - 3))
Therefore, the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
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Can you help me with this question please.
Answer:
[tex]x = 4\sqrt{3}[/tex]
Step-by-step explanation:
The triangle is right-angled
In a right-angled triangle, the following equality holds
[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]
[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]
Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]
I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is the most appropriate sample space S for the possible outcomes? a. S-(red,red), (red,black), (black,red), (black,black) b. S - fred,black) c. S-(0, 1, 2) d. none of the above
The option a. S-(red,red), (red,black), (black,red), (black,black) is the most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards
The most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards and observing the color of each (26 cards in the deck are red and 26 are black) is given by option a. S-(red,red), (red,black), (black,red), (black,black).
Sample space S in probability theory denotes the set of all possible outcomes of an experiment.
In other words, the sample space S represents all possible outcomes of an experiment under consideration. For instance, in the current scenario,
These four possible outcomes are independent and equally likely events, and the sample space S for the possible outcomes is given by option a. S-(red,red), (red,black), (black,red), (black,black).
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Graph the line with slope 3 passing through the point (1,-5),
Can somebody help me
Answer:
Step-by-step explanation:
To graph the line with slope 3 passing through the point (1,-5), we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line.
Substituting the given values, we get:
y - (-5) = 3(x - 1)
Simplifying the equation, we get:
y + 5 = 3x - 3
Subtracting 5 from both sides, we get:
y = 3x - 8
Now we have the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Comparing this equation to the one we just found, we can see that the slope is 3 and the y-intercept is -8.
To graph the line, we can plot the y-intercept at (0,-8) and then use the slope to find other points on the line. Since the slope is 3, we can go up 3 units and to the right 1 unit to find another point on the line. We can repeat this process to find more points on the line, and then connect them to graph the line.
The ordering and transportation cost €C for components used in manufacturing process is approximated by the function below, where C is measured in thousands of dollars and is the order size in hundreds_ C(x) = s(x x+3 (a) Verify that C(3) C(6) _ c(3) (b) According to Rolle's Theorem, the rate of change of the cost must be for some order size in the interval (3 answer to the nearest whole number:) components Find that order size (Round vour Need Help? Ialkto Tutor
The value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
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Unit 7 polygons and quadrilaterals
Homework 7 trapezoids
** this is a 2-page document **
Directions: if each quadrilateral below is a trapezoid, find the missing measures
Angle L can be calculated as follows:
angle L = angle - 180 LMO stands for angle. MNO \sangle L = 180 - 150 - 30 degree angle L = 0
As a result, angle L is 0 degrees.
1. We know that sides AB and CD of trapezoid ABCD are parallel. We can use the tangent function to find the length of side AD because angle B is a right angle and angle ABD is 45 degrees:
AD/AB = tan(45)
AD=AB * tan(45) AD=AB
As a result, AD = 10.
2. We know that the sides PQ and RS of the trapezoid PQRS are parallel. We can use the sine function to find the length of side PS because angle Q is a right angle and angle PSQ is 60 degrees:
PS/QS sin(60) =
PS = sin * QS (60)
5 * sqrt = PS (3)
As a result, PS = 5*sqrt (3).
3. We know that the sides UV and WX of a trapezoid UVWX are parallel. We can use the cosine function to find the length of side WU because angle V is a right angle and angle WVU is 30 degrees:
WU/UV cos(30) =
UV * cos WU (30)
5 * sqrt(3) / 2 = WU
As a result, WU = (5/2)*sqrt (3).
4. We know that the sides LM and NO of the trapezoid LMNO are parallel. We can use the sine function to find the length of side MO because angle L is a right angle and angle MNO is 30 degrees:
MO/NO sin(30) =
MO = 4 / 2 MO = NO * sin(30)
As a result, MO = 2.
Because angles MNO and LMO add up to 180 degrees, we can calculate angle LMO as follows:
LMO angle = 180 - angle LMO MNO angle = 150 degrees
Finally, because angle N is a right angle, we can calculate angle L as follows:
angle L = angle - 180 LMO stands for angle. MNO\sangle L = 180 - 150 - 30 degree angle L = 0
As a result, angle L is 0 degrees.
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What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
assistants please --------> The members of a weight loss support group just collectively weighed in at 1,519 pounds, which is 2% lighter than their previous weight. How much did the group weigh last time?
Work Shown:
x = previous total weight
2% of x = 0.02x = amount of weight lost
x - 0.02x = 0.98x = current total weight
0.98x = 1519
x = 1519/0.98
x = 1550 pounds
Check:
2% of 1550 = 0.02*1550 = 31
The group collectively lost 31 pounds.
1550-31 = 1519
The answer is confirmed.
Note that 98% of 1550 = 0.98*1550 = 1519
you have spent $2,500 on liquor for your bar. your bar sales have been $12,890. what is your cost of sales for liquor, expressed as a percentage?
The cost of sales for liquor, expressed as a percentage is 19.39%.
What is the cost of sales for liquor in percentage?To compute for the cost of sales for liquor, expressed as a percentage given that you have spent $2,500 on liquor for your bar and your bar sales have been $12,890, you can use the formula:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
where, Cost of Goods Sold (COGS) = Beginning Inventory + Purchases - Ending Inventory (or the total cost of goods sold during the period)
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
Let's compute for the COGS first:
COGS = Beginning Inventory + Purchases - Ending Inventory
= $0 + $2,500 - $0
= $2,500
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
= $12,890 - $0 - $0
= $12,890
Cost of sales is obtained as follows:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
= ($2,500 / $12,890) × 100
= 19.39%.
Therefore, the cost of sales for liquor, expressed as a percentage is 19.39%.
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What shape is this cross-section?
The crοss-sectiοn in the image shοwn appears tο be a trapezοid.
What is trapezοid?A quadrilateral with at least οne pair οf parallel sides. In this crοss-sectiοn, the tοp and bοttοm sides are parallel, while the οther twο sides are nοt parallel is trapezοid. There are times when people define trapezoids as having at least one pair of opposite sides that are similar, and other times they say there is just one pair.
The parallelogram satisfies the "at least one" interpretation of the definition because it has two pairs of opposite sides that are similar, which qualifies it as both a trapezoid and a parallelogram. The parallelism does not support the "one and only one" interpretation of the description. How students respond to this depends on how they describe themselves.
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Determine the number of 15 boxes in kilograms
Answer:
Step-by-step explanation:
150
Identify the slope and y intercept for the equation y = 2x + 3
How many sides has a polygon if the sum of its
interior angles is 1440⁰
Answer:
10 sides
Step-by-step explanation:
We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:
S = (n - 2) x 180 degrees
If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:
1440 = (n - 2) x 180
Dividing both sides by 180, we get:
8 = n - 2
Adding 2 to both sides, we get:
n = 10
Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.
Select the correct answer.Adam constructed quadrilateral PQRS inscribed in circle O. How can he prove PQRS is a square?A.He needs to show only that the diagonals are perpendicular.B.He needs to show only that the diagonals are perpendicular and congruent.C.He needs to show only that the diagonals are perpendicular and bisect each other.D.He needs to show that the diagonals are perpendicular, congruent, and bisect each other.
Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.
To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.
One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.
If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.
If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.
If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.
Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.
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Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.
Now, let's create another linear function using points B and C:
slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1
y-intercept (b) = y - mx = 4 - 1 * 3 = 1
Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:
2 = 1 + 1
This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.
In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.
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42 Développer chaque produit, puis réduire les expres-
sions obtenues.
A= 5x-3(x+12)
C = 2x² + x(4x - 5)
B=3x-6+7(2x+4)
D=4x²-x+x(5x-9)
2(2x-5)=-18 solve the equation algebraically. show all work
Answer:
Step-by-step explanation:
2(2x-5) = 18 (FOIL)
4x-10=18
4x = 28
x= 7
Answer:
x = -2
Step-by-step explanation:
2(2x - 5) = -18
Divide both sides by 2.
2x - 5 = -9
Add 5 to both sides.
2x = -4
Divide both sides by 2.
x = -2
For what values of the variables must ABCD be a parallelogram?
The for the values of the variables x = 7 and y = 10, the given must be a parallelogram.
What is parallelogram?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base and height of the parallelogram determine its area.
For the given quadrilateral to be parallelogram the opposite sides need to be parallel and equal.
For the given quadrilateral we have:
2y - 16 = y - 6
2y - y = -6 + 16
y = 10
Also,
2x + 2 = y + 6
Substitute the value of y = 10:
2x + 2 = 10 + 6
2x = 16- 2
2x = 14
x = 7
Hence, the for the values of the variables x = 7 and y = 10, the given must be a parallelogram.
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find the number of outcomes in the complement of the given event. out of 344 high school students in their senior year, 175 are left-handed.
There are 169 outcomes in the complement of the given event.
To find the number of outcomes in the complement of the given event, which is that out of 344 high school students in their senior year, 175 are left-handed, you need to follow a few steps. So, let's get started. To find the number of outcomes in the complement of the given event, you will first find the total number of students that are right-handed, which can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169Therefore, there are 169 right-handed students.
Next, to find the number of outcomes in the complement of the given event, you will need to subtract the number of outcomes in the given event from the total number of possible outcomes. Since the number of possible outcomes is equal to the total number of students, the number of outcomes in the complement of the given event can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169 Therefore, there are 169 outcomes in the complement of the given event.
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Find the probability of
drawing a spade, then
drawing a face card out of a
deck
The likelihood of pulling a spade followed by a face card from a deck is 3/52, or roughly 0.0588. (rounded to four decimal places).
What is the probability?The probability of drawing a spade from a deck of 52 cards is 13/52, or 1/4, since there are 13 spades in the deck.
Once a spade has been drawn and not returned to the deck, there are now 51 cards left in the deck, of which 12 are face cards (the Jack, Queen, and King of each suit). Therefore, the probability of drawing a face card given that a spade has already been drawn is 12/51.
To find the probability of both events happening together (drawing a spade and then a face card), we can multiply the probabilities of each event:
P(drawing a spade, then drawing a face card) = P(drawing a spade) x P(drawing a face card given that a spade has been drawn)
= (1/4) x (12/51)
= 3/52
Therefore, the probability of drawing a spade, then drawing a face card out of a deck is [tex]3/52[/tex] , or approximately [tex]0.0588[/tex] (rounded to four decimal places).
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The Tire Rack, America’s leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, the Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The following data show survey ratings (1 to 10 scale with 10 the highest rating) for 18 maximum performance summer tires (Tire Rack website, February 3, 2009). The variable Steering rates the tire’s steering responsiveness, Tread Wear rates quickness of wear based on the driver’s expectations, and Buy Again rates the driver’s overall tire satisfaction and desire to purchase the same tire again. (Data is in TireRack file)
1. Develop an estimated regression equation that can be used to predict the Buy Again rating given based on the Steering rating. At the .05 level of significance, test for a significant relationship. Interpret the coefficients (Say what they mean in terms of change in you corresponding to a change in x)
2. Did the estimated regression equation developed in part (a) provide a good fit to the data? Explain.
3. Develop an estimated regression equation that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating.
4. Is the addition of the Tread Wear independent variable significant? Use 0.05 level of significance.
1 Tire Steering read WeaBuy Again 2 Goodyear 8.9 8.5 8.1 3 Michelin F89 9 8.3 4 Michelin H 8.3 8.8 8.2 5 Dunlop SI 8.2 8.5 7.9 6 Goodyear 7.9 7.7 7.1 7 Yokoham 84 8.2 8.9 8 Yokoham 7.9 7 7.1 9 Kumho P 7.9 7.9 8.3 10 Goodyear 7.6 5.8 4.5 11 Hankook 7.8 6.8 6.2 12 Michelin E 7.4 4.8 13 IMichelin N7 14 Michelin S 6.9 15 Kumho 776.6 16 Dunlop SI 6.2 4.2 17 Bridgestof 5.7 5.5 18 Goodyear 5.7 5.4 19 Dunlop SI57 5 5 34 3.6 2.9 3.3
Tire Steering Tread Wear Buy Again
Goodyear Assurance TripleTred 8.9 8.5 8.1
Michelin HydroEdge8.9 9 8.3
Michelin Harmony 8.3 8.8 8.2
Dunlop SP 60 8.2 8.5 7.9
Goodyear Assurance ComforTred 7.9 7.7 7.1
Yokohama Y372 8.4 8.2 8.9
Yokohama Aegis LS4 7.9 7 7.1
Kumho Power Star 758 7.9 7.9 8.3
Goodyear Assurance 7.6 5.8 4.5
Hankook H406 7.8 6.8 6.2
Michelin Energy LX4 7.4 5.7 4.8
Michelin MX4 7 6.5 5.3
Michelin Symmetry 6.9 5.7 4.2
Kumho 722 7.2 6.6 5
Dunlop SP 40 A/S 6.2 4.2 3.4
Bridgestone Insignia SE200 5.7 5.5 3.6
Goodyear Integrity 5.7 5.4 2.9
Dunlop SP20 FE 5.7 5 3.3
Show transcribed image text
The survey ratings provide valuable feedback for drivers who are looking for quality tires for their vehicles. These ratings can give insight on steering responsiveness, how quickly a tire wears, and overall customer satisfaction. Drivers can also see how their tire of choice stacks up against other tires, making it easier to make an informed decision when shopping for tires.
The Tire Rack is America’s leading online distributor of tires and wheels. They conduct extensive testing to ensure that customers are provided with the most suitable tires for their vehicles, driving styles, and driving conditions. They also use an independent consumer survey to help drivers gain insight on long-term tire experiences.
The following data show survey ratings on a 1-10 scale, with 10 being the highest rating, of 18 maximum performance summer tires, as of February 3, 2009 (Tire Rack website). The variables are Steering (steering responsiveness), Tread Wear (quickness of wear), and Buy Again (overall tire satisfaction and desire to purchase the same tire again). The Yokohama Aegis LS4 has a Steering rating of 7.9, Tread Wear rating of 7, and Buy Again rating of 7.1. The Dunlop SP20 FE has a Steering rating of 5.7, Tread Wear rating of 5, and Buy Again rating of 3.3.
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-5y+3x=3, -8y+9x=-12
Answer:
x = -4
y = -3
Step-by-step explanation:
-5y + 3x = 3
-8y + 9x = -12
Time the first equation by -3
15y - 9x = -9
-8y + 9x = -12
7y = -21
y = -3
Now put -3 in for y and solve for x
-5(-3) + 3x = 3
15 + 3x = 3
3x = -12
x = -4
Let's Check
-5(-3) + 3(-4) = 3
15 - 12 = 3
3 = 3
So, x = -4 and y = -3 is the correct answer.
60 mi / 1 hr = ? mi / 5 hr
Answer: 300 minuets
Step-by-step explanation:
Answer:
350
Step-by-step explanation:
60 miles is 1 hr. all it is, is a ratio. multiply 60 by 5 to get your answer; 350
What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
Answer:
Step-by-step explanation:
120
I want you to put Ronaldo in this cartesian plane it has to be measured!! The best one wins 45pt and I will rate you best ! Send me your worked document in the answers
Love you guys!
Answer:
Step-by-step explanation:
what?
what is (2x+45)° x° = what?
Answer:
x = 45.
Step-by-step explanation:
Given a straight line with the equation.
First collect like terms:
2x + x = 180 - 45
Then calculate:
3x = 135
Finally after dividing both sides by 3:
x = 45
Maggie crochets squares to make a blanket. She has 6 squares made. She then makes 6 squares each hour for 3 hours. Determine which of the following represent the linear relationship described.
The linear relationship of Maggie crocheting squares is y = 6 + 6x graph (b)
How to determine the linear relationshipLet x be the number of hours Maggie spends crocheting squares, and let y be the total number of squares she has made.
Initially, Maggie has 6 squares made,
so y = 6 when x = 0.
For each hour that she spends crocheting squares, Maggie makes 6 more squares.
Therefore, the relationship between x and y is:
y = 6 + 6x
This is a linear relationship with a slope of 6, which means that Maggie is crocheting squares at a rate of 6 squares per hour.
This is represented by graph (b)
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Rosa wants to Invest $1400 a savings account that pays 4.4% simple Interest. How long will take for this investment to double In value? Round your answer to the nearest tenth.
Answer: 31.8 years
Step-by-step explanation:
The formula to calculate the simple interest is:
I = Prt
where:
I = Interest
P = Principal amount
r = Rate of interest
t = Time (in years)
We want to know how long it will take for the investment to double in value. That means the interest earned should be equal to the principal amount. So, we can write:
2P = P + I
Simplifying:
P = I
Now, we can substitute the values given in the problem:
1400 = 14000.044t
Simplifying:
t = 1400/(1400*0.044) = 31.82 years
Therefore, it will take approximately 31.8 years for the investment to double in value.
a college student takes the same number of credits each semester. before beginning college, the student had some credits earned while in high school. after 2 semesters, the student had 45 credits, and after 5 semesters, the student had 90 credits. if c(t) is the number of credits after t semesters, write the equation that correctly represents this situation.
The equation that correctly represents this situation is c(t) = 45 + 45(t-2). This equation states that the total number of credits the student will have after t semesters is equal to 45 (the number of credits they had before beginning college) plus 45 times the number of semesters after two (t-2).
To explain this equation in more detail, we need to break it down. First, the student had some credits earned while in high school, so the equation starts off with c(t) = 45, which is the number of credits the student had before beginning college.
Next, 45(t-2) represents the number of credits earned in the additional semesters since college began. The t-2 part of the equation means that the total number of credits earned in the additional semesters starts at zero for t = 2. Then, for each additional semester, 45 credits are added. So, for example, when t = 5, 45 credits are added to the initial 45 credits the student had before beginning college, resulting in 90 credits.Therefore, the equation c(t) = 45 + 45(t-2) correctly represents this situation.
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given the augmented matrix in row-reduced form, assume that it is equivalent to an augmented matrix of a system of linear equations. for each matrix: determine the number of equations and number of variables in the corresponding system of linear equations. determine if the system is underdetermined or overdetermined.
System : [ 1 ¼ -1/4 | 1]
[ 0 0 0 | 0]
find the solution(s) to the system, if it exists. state the solution as a point (be sure to use parentheses), use parameter(s) and if needed. if the system is inconsistent, then state no solution.
The given augmented matrix is equivalent to a system of linear equations with 1 equation and 3 variables. The system is underdetermined and the solution to the system is [tex](x, y, z)[/tex]= (0, 0, 0).
The given augmented matrix is in row-reduced form and is equivalent to a system of linear equations. The matrix has 3 columns and 1 row, so there is 1 equation and 3 variables in the corresponding system of linear equations. Since there is only one equation, the system is underdetermined and has infinitely many solutions.
The solution to the system can be stated as: (x, y, z) = (0, 0, 0). The solution is a point where all the variables are equal to zero. Since the matrix is in row-reduced form, this is the only solution to the system. If the augmented matrix was not in row-reduced form, then the solution would be stated as a parameter, such as (x, y, z) = (0, 0, t), where t is a parameter.
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Answer:
1 equation, 3 variablesunderdetermined(x, y, z) = (1 -s +t, 4s, 4t)Step-by-step explanation:
For the given augmented matrix, you want to know the number of equations and variables it represents, whether the system is under- or over-determined, and the solution, using parameters as required.
[tex]\left[\begin{array}{ccc|c}1&\dfrac{1}{4}&-\dfrac{1}{4}&1\\\vphantom{\dfrac{T}{q}}0&0&0&0\end{array}\right][/tex]
Augmented matrixEach column of the augmented matrix is the coefficient of the variable in a linear equation represented by the row. The first row of the matrix represents the equation ...
[tex]1x +\dfrac{1}{4}y-\dfrac{1}{4}z=1[/tex]
The second row of the matrix represents the tautology ...
0x +0y +0z = 0
It contributes no information about the relationships between the variables.
The matrix represents 1 equation in 3 variables.
SolutionFor there to be a unique solution to a linear system, there must be as many consistent and independent equations as there are variables. Here, there are fewer equations than variables. This system is underdetermined.
The solution to an underdetermined system can be written in terms of parameters of free choice. We will need as many parameters as there are missing equations: 2.
Here, the coefficients of y and z suggest we choose parameters that let us represent those values as multiples of 4.
Parameters: s, t
Let y = 4s, z = 4t. Then the equation becomes ...
x +1/4(4s) -1/4(4t) = 1
x +s -t = 1
x = 1 +t -s
Now, the solution can be written as ...
(x, y, z) = (1 +t -s, 4s, 4t)
uessing on an exam: in a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers. what is the probability that: (please round all answers to four decimal places)
In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977
How to calculate the probability?In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers.
The probability of guessing on an exam can be calculated by using the formula:n(C)/(n(T))where n(C) is the number of favorable events and n(T) is the total number of events. Let's solve the given problem:
Probability of getting the first question correct: P (1st) = 1/4 Probability of getting the second question correct: P (2nd) = 1/4Probability of getting the third question correct: P (3rd) = 1/4 Probability of getting the fourth question correct: P (4th) = 1/4Probability of getting the fifth question correct: P (5th) = 1/4 The probability of guessing all questions correctly can be calculated by multiplying the probability of each question together. P (all) = P (1st) * P (2nd) * P (3rd) * P (4th) * P (5th)= 1/4 * 1/4 * 1/4 * 1/4 * 1/4= 1/1024Therefore, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977. (rounded to four decimal places)Answer: 0.000977
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