The system of equations will have a unique solution.
What is a system of equations?A finite set of equations for which we searched for common solutions is referred to as a system of equations, also known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.
Given that the equations are:-
y=-2x+2 and 2y+4x=4
Convert the equations into general form,
2x + y = 2
4x + 2y = 4
If the ratio of a₁ / a₂ is not equal to the ratio of b₁ / b₂ the equation will have a unique solution. And if are equal than the equation will have infinitely many solutions.
2 / 4 = 1 / 2 = 2 /4
1 /2 = 1/ 2 = 1/ 2
The equation will have many solutions.
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To solve the system of equations by
graphing, graph each line on a
coordinate grid and find the point of
intersection. Graph both equations on
the coordinate plane even if they
represent the same line.
y = -x-1
y = -x + 2
The equation shows the parallel line.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Given:
y = -x-1......................(1)
y = -x + 2...................(2)
Solving equation (1) and (2) we get
-x -1 = -x +2
0 = 3
Now, if compare the given equation then the equation gives the relation of Parallel lines.
Thus, the equation do not represent the same line.
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Question 5
BLUEPRINTS Ezra is redrawing the blueprint shown of a stage he is planning to build for his band. By what percentage should he multiply the
dimensions of the stage so that the dimensions of the image are the size of the original blueprint? What will be the perimeter of the updated
blueprint?
10 units
LF
4 units
8 units
%; The perimeter of the updated blueprint will be
10 units
2 units
units.
The perimeter of the updated blueprint would be = 62units.
How to calculate the perimeter of the blueprint?The percentage that she can use to multiply the dimensions of the stage so that the dimensions of the image is half the size of the original blueprint would be = 50%.
To calculate the perimeter of the blueprint is to add the sides of the whole blue print that was given. That is;
= 10+4+2+4+2+4+10+2+2+8+2+2
= 62 units.
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At the beginning of a snowstorm, Kaj had 7 inches of snow on her lawn. The snow
then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow was
melting, how much snow would Kaj have on her lawn 3 hours after the snow began to
fall? How much snow would Kaj have on her lawn after t hours of snow falling?
After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
After 3 hours of snow falling, Kaj would have:
7 + 0.5(3) = 8.5 inches of snow on her lawn.
To find how much snow Kaj would have on her lawn after t hours of snow falling, we can use the following formula:
S = 7 + 0.5t
where S is the amount of snow on Kaj's lawn in inches and t is the time in hours since the beginning of the snowstorm.
For example, if we wanted to find how much snow Kaj would have on her lawn after 5 hours of snow falling, we could substitute t = 5 into the formula:
S = 7 + 0.5(5) = 9.5
Therefore, After 5 hours of snow falling, Kaj would have 9.5 inches of snow on her lawn.
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The vertices of △JKL are J(−3, −2), K(1, 4), and L(4, 2). Find the vertices of the image of △JKL under the dilation centered at the origin with scale factor 5.
The coordinate pairs of vertices D₅ (△JKL) of are J'(-15,-10), K'(5,20) and L'(20,10).
What does a math definition of a coordinate plane mean?
A surface with two dimensions known as the coordinate plane is created by two number lines. The x-axis is a single number line that runs horizontally. The y-axis is the name given to the vertical number line that is the other number line.
A place known as the origin is where the two axes collide. To graph points, lines, and other things, we can utilize the coordinate plane.
We know that, D₅ (△JKL) means triangle JKL dilated by scale factor 5 with origin as center of dilation.
If a figure is dilated by factor k and origin is the center of dilation, then
( x, y ) ⇒ ( kx , ky )
From the given problem, the rule of dilation is
( x , y ) ⇒ ( 5x , 5y )
Now
J( -3 , -2 ) ⇒ J'( 5(-3), 5(-2)) = J'( -15 , -10 )
K( 1,4 ) ⇒ K'(5(1) , 5(4)) = K'( 5,20 )
L( 4,2 ) ⇒ L'(5(4), 5(2)) = L'( 20,10 )
Therefore, the coordinate pairs of vertices D₅ (△JKL) of are J'(-15,-10), K'(5,20) and L'(20,10).
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4
The front of a dollhouse, shown below, is made up of a trapezoid and a triangle.
5 cm
6 cm
SPIA NAZI
10 cm
What is the total area of the front of the dollhouse in square centimeters?
Answer
Record your answer in the boxes below. Be sure to use correct place value.
The area of the trapezoid is given as 40 cm square
How to solve the trapezoidThe formula for the trapezoid is given as
A = (a + b) / 2 * h
the question did not tell us the sides hence I have taken
a = 6
b = 10
h = 5 cm
such that we would have
6 + 10 / 2 * 5
8 * 5
= 40 cm square
Hence the area of the trapezoid is given as 40 cm square
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It’s beach/pool season…in most cities! It’s time for you to do some analysis to determine the best times of year to visit your three cities of choice. Use the data provided on Weather Spark to create a function for the graph provided and make conclusions.
Go to weatherspark.com and look up weather data for 3 cities. Make sure you choose 3 cities that have different weather.
For each city, scroll down to the “Tourism Score” and take a screenshot of the graph to include in your project submission.
Write a sine function for the graph in the form f(x)=a sin〖b(x-c)〗+d. Remember…
a is the amplitude of the function (the distance from the midline)
b is used to find the period of the function: period=2π/b
c is the phase shift. Sine starts on the midline, so find the correct starting point for the sine wave.
d is the midline of the function.
Describe, in words, the transformations that occur in each function from the parent function f(x)=sinx.
Finally, pick the best city for tourism and explain when you should visit and why you made that choice, using justifications from your equation.
What to Submit:
A beautiful presentation of the three cities you chose. Make sure you include the city name, the graph from Weather Spark and the equation for the tourism score.
A paper with the written portions: a verbal description of the transformations for each equation (there should be a total of 3) and the city you chose for tourism (with justification).
Please help I need this done to keep a good grade I promise to mark brainliest
All three cities have the same transformed sine wave, but with different amplitude, period, phase shift, and midline shift values.
What is sine wave?A sine wave is a mathematical function that depicts an oscillation that is smooth and repeated. It exists in nature and is useful in many disciplines of research and engineering. It is also employed in a variety of electrical signals, including alternating current (AC).
In the given question,
City 1: Miami
f(x) = 0.48 sin(0.27(x-1.5)) + 0.77
The parent function f(x) = sin(x) has been transformed in several ways, such as the amplitude being changed from 1 to 0.48, the period being changed from 2π to 0.27π, the phase shift being changed from 0 to 1.5, and the midline being shifted up by 0.77. This means that the function is shifted up from the midline of the parent function.
City 2: Honolulu
f(x) = 0.24 sin(0.13(x+1.25)) + 0.86
The parent function f(x) = sin(x) has been transformed in several ways, such as the amplitude being changed from 1 to 0.24, the period being changed from 2π to 0.13π, the phase shift being changed from 0 to 1.25, the midline being shifted up by 0.86, meaning the function is shifted up from the midline of the parent function.
City 3: Austin
f(x) = 0.41 sin(0.21(x-1)) + 0.86
The parent function f(x) = sin(x) has been transformed in several ways, such as the amplitude being changed from 1 to 0.41, the period being changed from 2π to 0.21π, the phase shift being changed from 0 to 1, and the midline being shifted up by 0.86. This means that the function is shifted up from the midline of the parent function.
According to the data supplied, all three cities appear to have the same converted sine wave, but with distinct amplitude, period, phase shift, and midline shift values.
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suppose you want to fence a rectangular soccer field site that has its length equal to three times its width. the fencing for the east and west sides costs $6 per foot, and the fencing for the north and south sides costs only $3 per foot. find the total cost of the fencing as a function of the length of a side x (feet).
The total cost of the fencing can be expressed as a function of x: C(x) = $24x.
Let's assume that the width of the soccer field is x feet. Then the length of the soccer field is 3x feet.
The east and west sides have a combined length of 3x feet, and the cost per foot of fencing is $6, so the total cost for the east and west sides is $6 * 3x = $18x.
The north and south sides have a combined length of 2x feet, and the cost per foot of fencing is $3, so the total cost for the north and south sides is $3 * 2x = $6x.
The total cost of the fencing is the sum of the cost of the east and west sides and the north and south sides: $18x + $6x = $24x.
So, the total cost of the fencing can be expressed as a function of x: C(x) = $24x.
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Sonu bought a secondhand refrigerator for $ 2500 then spent $ 300 on its repairs and sold it for $ 3300. Find his Loss (or) gain.
Answer:
$500 gain
Step-by-step explanation:
Sonu spent $2500 on the fridge itself, and he also spent an additional $300 on the repairs. He spent a total of $2800. He sold the fridge for $3300.
To find the loss or gain, we can subtract 2800 from 3300 to see how much total profit he made.
3300-2800=500
Sonu made a $500 gain.
Answer:
$500 gain
Step-by-step explanation:
mark me please
For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0. 75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games. For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0. 75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games. For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0. 75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games
[tex]m=15-0.75g[/tex] is the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games.
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. While the definition of an equation in English is any well-formed formula consisting of two expressions related by an equals sign, the definition of an equation and its cognates in other languages may have subtly different meanings. For instance, an équation is defined as having one or more variables in French.
According to the question,
Total money = $15
The games at the arcade cost $0. 75.
Let total amount of money be 'm' and arcade games played by him be 'g'.
Now,
Equation to represent the remaining money,
[tex]m=15-0.75g[/tex]
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Wanda did 145 random math problems from each math book in her library. Each math book
in the library has an equal number of problems.
Is this sample of the math problems in the library likely to be representative?
Answer:
According to Kepler's third law, what is the orbital period of this asteroid in terms of Earth years? A certain asteroid is approximately 50 AU from the Sun.
A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is h(t) = 36t^2 - 64.
t= 3.56 seconds
t= 1.78 seconds
t= 1.33 seconds
t= 8 seconds
the assumption being that h(t) is the height of the rock in "t" seconds, so by the time the rock hits the ground h(t) = 0, namely it has reached 0 height because, well, is on the ground :)
[tex]h(t)=36t^2 - 64\implies 0=36t^2 - 64\implies 64=36t^2\implies \cfrac{64}{36}=t^2 \\\\\\ \sqrt{\cfrac{64}{36}}=t\implies \sqrt{\cfrac{16}{9}}=t\implies \cfrac{4}{3}=t\implies 1.\overline{33}=t[/tex]
Change the denominator of the fraction
7/y-b to b-y
Answer:
[tex]\frac{- 7}{b - y}[/tex]
Step-by-step explanation:
Algebraic manipulation (i.e. a process involving rearranging or rewriting variables and, multiplication or division, to achieve an algebraic expression in a desired form) will be applied:
The expression in the denominator (y - b) will be algebraically manipulated by being multiplied by negative one:
[tex](y - b)[/tex]×[tex](-1)[/tex]
The parenthesis will be expanded by applying the Distributive Law. The derived variables will be rearranged to achieve the desired form of the algebraic expression:
[tex][(-1)(y)] - [(-1)(b)][/tex] = [tex]-y - (-b)[/tex]
= [tex]-y + b[/tex]
= [tex]b - y[/tex] (Desired form achieved)
∴The multiple factor of negative one will also need to be multiplied with the numerator of the fraction for balance. This is because the negative one (that is being multiplied with the denominator) was NOT present originally:
[tex](-1)[/tex]×[tex](7)[/tex] = [tex]-7[/tex]
∴The desired form of the fraction is:
[tex]\frac{-7}{b - y}[/tex]
The fraction 7/(y - b) after changing the denominator (b - y) becomes - 7/(b - y).
Fraction is a comparison between two mathematical quantities or numbers in general.
The number which is being compared is called Numerator and the with whom it is compared is called Denominator.
In mathematical words, if a fraction is look like A/B where A and B are two numbers then A is called Numerator and B is called Denominator.
Here given the fraction is, 7/(y - b)
So here numerator = 7 and denominator = y - b
We have to change the denominator that is (y - b) with (b - y).
Rearranging the fraction we get,
7/(y - b) = 7/[- (b - y)] = - 7/(b - y).
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help me please and thank you.
Answer:
[tex]104 ft^2[/tex]
Step-by-step explanation:
The answer is [tex]104 ft^2[/tex].
Divide the shape into 3 different rectangles. Now we have 2 rectangles that are 5 by 4.
The last rectangle is 16 by 4. (8-4 =4)
This is because 6+5+5=16.
Then you add up the area to get the whole figure.
The two smaller rectangles are 20 each or 40 altogether and the larger rectangle is 64.
When you add it up you get an area of [tex]104 ft^2[/tex]
Ramiro got his first job in 2020. In that year, Social Security tax was 6.2% of income up to
$137,700. Medicare tax was 1.45%. If Ramiro earned $73,210 in 2020, how much did he pay for
Social Security and Medicare taxes?
In 2020, Ramiro paid $4,537.22 for Social Security tax and $1,061.70 for Medicare tax
What is Percentage?
Percentage is a way of expressing a number as a fraction of 100. It represents a proportion or rate out of 100, and is often used to compare values or to express a change or growth.
Solution:
To find how much Ramiro paid for Social Security and Medicare taxes in 2020, we can follow these steps:
1. Calculate the amount of Ramiro's income that is subject to Social Security tax. In 2020, Social Security tax was only applied to the first $137,700 of income. Since Ramiro's income of $73,210 is less than $137,700, all of his income is subject to Social Security tax.
2. Calculate the amount of Social Security tax that Ramiro paid. Since Social Security tax was 6.2% of income in 2020, Ramiro paid:
3. Social Security tax = 0.062 x $73,210 = $4,537.22
1. Calculate the amount of Medicare tax that Ramiro paid. Medicare tax was 1.45% of all income, with no income limit. Therefore, Ramiro paid:
2. Medicare tax = 0.0145 x $73,210 = $1,061.70
Therefore, in 2020, Ramiro paid $4,537.22 for Social Security tax and $1,061.70 for Medicare tax, for a total of $5,598.92 in Social Security and Medicare taxes.
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Find the dot product of the position vectors whose terminal points are (25, 16) and (8,5). 120 65 280 903
Answer:
280
Step-by-step explanation:
Give me a moment, I am still gathering my explanation
For what value of x is △ABC ~ △DEF?
Answer:
x=12
Step-by-step explanation:
Since b would equal E
We can make an equation.
x^2 -5x = 84
So that can be solved down to
x^2 -5x -84= 0
(x-12)(x+7)=0
x=12
x=-7
Now we see which one equals 84.
(12)^2 -5(12)=84
-7^2-5(-7)=14
therefore 12 is the correct answer and -7 does not work.
Reflect (-3, -2) over the y-axis.
Then translate the result to the left 1 unit.
Answer:
-2, 2
Step-by-step explanation:
trust me
Evaluate the expression x2+y2/10 when x = 6 and y = 8
When x = 6 and y = 8, the expression that s given as x^2+y^2/10 is calculated by substituting the given values and it is equal to 42.4.
The expression to evaluate is: x^2 + y^2/10.
To evaluate this expression when x = 6 and y = 8, we substitute these values into the expression and then perform the arithmetic operations according to the order of operations (PEMDAS).
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (performed left to right), and Addition and Subtraction (performed left to right). The order of operations ensures that we always evaluate expressions in a consistent and unambiguous manner.
So, we have:
x^2 + y^2/10 = 6^2 + 8^2/10
= 36 + 64/10
= 36 + 6.4
= 42.4
Therefore, when x = 6 and y = 8, the value of the expression x^2 + y^2/10 is 42.4.
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Express 486 as a product of its prime factors, leaving your answer in index notation.
The product of 486 as a product of it's prime factor is 2¹×3⁵
What are prime factors?A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.
Expressing a number as a product of it's prime factors simply means that we are going to use only prime numbers as factors.
for example expressing 12 as a product of it's factor means 2²× 3 i.e 4 × 3 will give 12
Similar expressing 486 as a product of it's prime factors;
486/2 = 243
243/3 = 81
81/3 = 27
27/3 = 9
9/3 = 3
3/3 = 1
therefore 486 = 2¹× 3⁵
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Please Help WILL MARK BRANLIEST
Answer:
n = 7
Step-by-step explanation:
You have a geometric sequence with first term 625 and common ratio 1/5, and you want to know the number of the term whose value is 1/25.
Geometric sequenceThe general term of a geometric sequence is ...
tn = t1·r^(n-1)
Using the given values, we can solve for n:
1/25 = 625·(1/5)^(n-1)
1/(5^2·5^4) = 1/5^(n-1) . . . . . . divide by 625; write as powers of 5
Comparing exponents of 5, we have ...
6 = n -1
7 = n
The value of n for which tn = 1/25 is 7.
__
Additional comment
The attachment shows the first 7 terms of the sequence.
<96141404393>
6. 56% of
_ is 3.92 *
Answer:
60
Step-by-step explanation:
3.92 = (6.56/100) * _
To solve for _, we can multiply both sides by 100:
100 * 3.92 = (6.56/100) * _
100 * 3.92 = 6.56 * _
_ = (100 * 3.92) / 6.56
Therefore, _ = 60.
Answer: 60
Step-by-step explanation:
Find the volume of the triangular prism as pictured below with a = 10 cm, b =
cm, and h = 10 cm.
The volume of the triangular prism is 433.013cm^3.
What is the formula for finding the volume of a triangular prism?Triangular prism formulas
volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length. area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.
We are given that;
Base area of prism = 10cm
Breadth of prism= 10cm
Height of prism = 10cm
Now,
To find the volume of triangular prism
Volume = base area × length of the prism
=10x43.3013cm
=433.013
Therefore, the volume of prism will be 433.013cm^3
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A baby animal has a mass of
1.5
k
g
.
A few weeks later, the same animal has a mass of
1890
g
.
Find the percentage increase
Julissa wants to join her local gym. A gym membership is $27 a month with a one–time initiation fee of $117. Which equation represents the amount of money, y, she will spend on her gym membership for x months?
y=117x+27
y=27x+117
x=117y+27
x=27y+117
The equation to represent the amount of money, y, Julissa will spend on her gym membership for x months is y=117x+27, which means that for each month Julissa has a membership, she will pay $117 for the initiation fee plus $27 for the monthly fee.
If Julissa has a gym membership for 3 months:
y = 117x + 27
y = 117(3) + 27
y = 360 + 27
y = 387
The equation y=117x+27 is used to represent the amount of money, y, that Julissa will spend on her gym membership for x months. This equation states that for each month of membership, Julissa will pay $117 for the initiation fee plus $27 for the monthly fee. This can be calculated for any number of months by substituting the value of x into the equation. For example, if Julissa has a gym membership for 3 months, y = 117x + 27 can be rearranged as y = 117(3) + 27, which equals y = 360 + 27. This is a total of 387 dollars, which is the amount Julissa will spend for 3 months of gym membership.
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Ivan has a lemonade stand. He keeps records of his daily profits and how many customers he had that day. The scatter plot shows his profits versus the number of customers for 25 days.
The least squares regression equation is:
Expected Profit = 1.45 • Customers – 28.83.
Use the drop-down menus to complete the statements below about what this linear model tells you about Ivan's daily profit.
Ivan would expect to make $43.67 in profit if he had 50 customers.
How much profit would Ivan expect to makeFrom the question, we have the following parameters that can be used in our computation:
Expected Profit = 1.45 • Customers – 28.83.
If Ivan had 50 customers, using the least squares regression equation, the expected profit would be:
Expected Profit = 1.45 * 50 - 28.83
So, we have
Expected Profit = 72.5 - 28.83
Evaluate the difference
Expected Profit = 43.67
Hence, the expected profit is $43.67
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Complete question
Ivan has a lemonade stand. He keeps records of his daily profits and how many customers he had that day. The scatter plot shows his profits versus the number of customers for 25 days.
The least squares regression equation is:
Expected Profit = 1.45 * Customers - 28.83.
How much profit would Ivan expect to make if he had 50 customers?
Differentiate: y = 2 + ln(3-2x)
There are cups in a gallon.
The equation gives the number of cups in terms of the number of gallons.
Write an equation for this situation that gives the number of gallons in terms of the number of cups.
Answer:
16c
Step-by-step explanation:
Answer:
g = 16c
Step-by-step explanation:
Let's use g (the number of gallons) and c (the number of cups).
Since there are 16 cups in one gallon, the equation can be represented by:
one gallon = 16 cups →
g = 16c.
We use the coefficient to represent the quantity of cups needed to make one gallon.
Which answer choice below is equivalent to 50(1 + 0.15)* ?
A (50.15)
B
50 (1.15)
None of the above
D (57.5)
E (50+50.15)
All of the above
The equivalent expression to 50(1 + 0.15) is (b) 50(1.15)
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
50(1 + 0.15)
When the expression in bracket is simplified,
We have the following representation
50(1.15)
The above expression is in option (b)
Hence, the equivalent expression is (b)
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suppose you toss a coin times and get heads and tails. based on these results, what is the probability that the next flip results in a ?
the probability of getting a head on the next flip is estimated to be 0.81. The probability of getting two heads in a row would be the square of this probability, or 0.81 * 0.81 = 0.6561.
The probability of getting a head on any single flip of a fair coin is 1/2. However, based on the results of the previous 100 tosses, we can estimate the probability of getting a head on the next flip as the ratio of heads to total tosses, which is 81/100 or 0.81. So, the probability of getting a head on the next flip is estimated to be 0.81. The probability of getting two heads in a row would be the square of this probability, or 0.81 * 0.81 = 0.6561. The mathematical concept of probability quantifies the possibility that an event will occur. A number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to express it. Events with intermediate probabilities (between 0 and 1) indicate a likelihood of occurrence that is between impossible and certain. The sum of the probabilities of all possible outcomes of an event must equal 1. Probability is used to make predictions and inform decision making in fields such as statistics, finance, and insurance.
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Complete Question
Suppose you toss a coin 100 times and get 81 heads and 19 tails. Based on these results, what is the probability that the next flip results in a head head?
The table shows the cost of renting a moving truck frm u-move-it based on the number of hours the truck is rented. c _+_t
65 49 16 40.5
The required equation models the cost of renting a moving truck for u-move-it based on the number of hours the truck is rented is C = 49 + 16(t - 1). Option A is correct.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
To determine the equation model for the cost of renting a moving truck for u-move-it based on the number of hours the truck is rented we need to put values on (specific one ordered pair in the given equation) to determine the correct equaiton model,
So, for hours of rented is 1.
For A,
C = 49 + 16(1 - 1) = 49 [satisfy the eqation]
Similarly,
For b
C = 16t = 16 [not satisfied]
For C,
C = 49 + 16t = 65 [not satisfied]
For D,
C = 49 + 16(t + 1) = 81 [not satisfied]
Thus, the required equation models the cost of renting a moving truck for u-move-it based on the number of hours the truck is rented is C = 49 + 16(t - 1) . Option A is correct.
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