Elena collects data to investigate the relationship between the number of bananas she buys at the store, , and the total cost of the bananas, . Which value for the correlation coefficient is most likely to match a line of best fit of the form for this situation?
Answers
The correlation coefficient that is most likely to match a line of best fit of the form y = mx + b for this situation is of:
0.9.
What is a correlation coefficient?The correlation coefficient is an index that measures correlation between two variables, assuming numeric values between -1 and 1.
If the correlation coefficient is positive, the relation is positive, that is, they are direct proportional. If the correlation coefficient is negative, they are inverse proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the two variables is classified as strong.
In the context of this problem, the variables are listed as follows:
Number of bananas bought.Total price of the bananas.The total price increases with the number of bananas bought, and there is a strong positive relationship between these two variables, hence the coefficient should be greater than 0.6 and the correct option is:
0.9.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Related Questions
Does anybody know how to help me??
Answers
Answer:
D? I'm not sure tho so don't be mad if it's wrong
A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
How much langer is the pygmy rabbit than the
wase?
Answers
Pygmy rabbit is 22.61-10 meters longer than the wasp.
Given:
A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
Pygmy rabbit longer than the wasp = size of pygmy rabbit - size of wasp.
= (24 - 1.39)-10meters
= 22.61-10 meters.
Therefore pygmy rabbit is 22.61-10 meters longer than the wasp.
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Rebecca wants to buy a new phone. She has already saved $110 and received a gift of $50 from her grandmother that she added to her savings. She plans to earn the rest by selling necklaces for $5 each. The phone she wants to purchase costs $485. Write an equation that represents how many necklaces Rebecca will need to sell in order to have enough money to get her phone.
Answers
Answer:
5x=325+160
Step-by-step explanation:
this was very easy but i guess with so many words it could confuse people
What is the equation in slope-intercept form of the line that passes through the point (2, -1) and is perpendicular to the line represented by y=x+4?
y=32-4
y=3x+4
y=-32-2
y=-3x+2
Answers
The slope-intercept form is
y = - x + 1
Given points are (2, - 1)
and y = x + 4
The product of slopes of perpendicular lines is - 1
so , m = - 1/1 = -1
y = mx + b-1 = (-1) (2) + b -1 = -2 + b-1 + 2 = b b = 1∴ y = -1 (x) + b
y = - x + 1
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You rent a bicycle for 20 plus per hour. What is the rate of change
Answers
The rate of change for cost is = $2 per hour .
In the question ,
it is given that
the fixed rent for the bicycle is =$20
per hour charge of the bicycle is = $2
let the number of hours we rent a bicycle is = x
and let the total cost for renting the bicycle is = y
So , the equation to represent the cost becomes
y = 20 + 2x
to find the rate of change we differentiate the equation with respect to x .
we get
dy/dx = 2
Therefore , The rate of change is $2 per hour .
The given question is incomplete , the complete question is
You rent a bicycle for $20 plus $2 per hour. What is the rate of change of Cost ?
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Use the graph of y=f(x) to graph the function g(x)=f(x + 1)-3.
y = f(x)
4
Choose the correct graph of g below.
OA
OC.
B.
O D.
Q
Answers
Function g(x) is a translation of one unit to the left and 3 units down of f(x), then the correct option for the graph of g is B.
which is the graph of the transformed function?Here we start with a function f(x), and we also have the graph of this function.
And we want to find the graph of the function defined as:
g(x) = f(x + 1) - 3
Notice that:
g(x)= f(x + 1)
Is a translation of one unit to the elft of f(x).
g(x) = f(x) - 3
Is a translation of 3 units down of the graph of f(x).
Then:
g(x) = f(x + 1)- 3
Is a translation of one unit to the left and 3 units down.
With that in mind, we can see that the correct option for the graph of g(x) is option B.
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During the WMS Presidential elections, candidate #1 received 75 votes whereas candidate #2, who
promised better lunches and longer seminar class times received 165 votes. What is the percentage
difference between the WMS Presidential Candidate # 1 and WMS Presidential Candidate # 2's total
number of votes?
Answers
Answer: candidate 2 has 90 votes
Step-by-step explanation:
165-75=90
The sum of a number and 4 times the number
Write two equivalent expressions for each statement.
Answers
Let the number be n.
Then the expression is:
The sum of a number and 4 times the numbersum = n + 4nsum = 5nAnswer:
4x + x5xStep-by-step explanation:
Forming the expression,
→ 4x + x
Let's solve the expression,
→ 4x + x
→ 5x
Hence, the answer is 5x.
Question 7
Let f (x) = -2x³ + ax² +2. You are told that f (2) = 14, what is the value of a ?
a=9
a=8
a=7
a=6
Answers
Answer:
a = 7
Step-by-step explanation:
Substitute x for 2 and f(x) for 14
14 = -2(2³) + a(2²) + 2
14 = -16 + 4a + 2
14 = -14 + 4a
14 + 14 = 4a
28 = 4a
4a = 28
Divide both sides by 4
4a/4 = 28/4
a = 7
Alternative:
Since from the question, you're already told that f(2) = 14, you just have to find the number that can be multiplied by 2 with a resultant of 14; that number is 7. To confirm, substitute a for 7 in the equation.
The cost to attend a public university in a recent year is $16,241. The circle graph to
the right shows the percentage of that cost for tuition/fees, room, board, and
computer costs. Determine the cost, in dollars, for each category.
The cost of tuition and fees is $.
(Round to the nearest cent as needed.)
The cost of room is $.
(Round to the nearest cent as needed.)
The cost of board is $.
(Round to the nearest cent as needed.)
The computer costs are $
(Round to the nearest cent as needed.)
Cost to Attend a Public University
Tuition/Fees 36.9%
Room 31.5%
Board 24.9%
Computer costs 6.7%
Answers
Answer:
Tuition and Fees = $5,992.93
Room = $5,115.92
Board = $4,044.01
Computer Costs = $1,088.15
Warren likes to draw pictures of people and animals. In his notepad, he has drawn 2 pictures of people for every 5 pictures of animals.
If Warren has drawn 18 more pictures of animals than people in his notepad, how many pictures of animals has he drawn
Answers
By solving a linear equation, it is obtained that Warren has drawn 30 pictures of animals
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let Warren has drawn 5x pictures of animals and 2x pictures of people
Warren has drawn 18 more pictures of animals than people in his notepad
By the problem,
5x - 2x = 18
3x = 18
x = [tex]\frac{18}{3}[/tex]
x = 6
Number of pictures of animals Warren has drawn = [tex]5 \times 6 = 30[/tex]
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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer. (2 points)
Part B: Write a function to represent the data. Show your work. (4 points)
Part C: Determine the average rate of change between day 2 and day 4. Show your work. (4 points)
Answers
A) The data modelling is an exponential function.
B) The explicit funciton that will be used to represent the data is;
f(n) = 2(2)^(n - 1)
C) The average rate of change here is; 7
How to model a function?A) We are given the coordinates as;
(1, 2), (2, 4), (3, 8), (4, 16)
From the given coordinates, we can observe a pattern which is that when x increases by 1, then y is multiplied by 2.
Thus, we can see that as the quotient between consecutive terms is the same, the data is a geometric sequence which is an exponential function.
B) The explicit formula that will be used for a geometric sequence with common ratio r and first term a is given by:
f(n) = ar^(n - 1)
Since first term ; a = 2
and common ratio r = 2, then we can say that;
f(n) = 2(2)^(n - 1)
C) The formula for average rate of change here is;
dy/dx = (y₂ - y₁)/(x₂ - x₁)
The coordinates of the 2nd and 4th day are;
(2, 4) and (4, 16)
Thus;
dy/dx = (16 - 4)/(4 - 2)
dy/dx = 14/2 = 7
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Distance in Feet
1. Earlier this week the famous "Live Cannonball” - Gunter Money was shot from a cannon at the Austin Expo.
Gunter flew to a height of 70 feet and traveled a distance of 160 feet only to land perfectly in a safety net.
Assume (0, 0) was the starting point for Gunter's flight and that he landed in the net at (160, 0).
(a) Use matrices to find the equation for Gunter Money's path.
(b) Write the equation for Gunter Money's path in vertex form.
(c) device a method to estimate the angle at which Gunter money takes off
Answers
The 160 feet range and 70 feet height of the path of Gunter Money which can be described with a quadratic equation, gives;
(a) The path is; y = -1.09375×10²·x² + 1.75·x
(b) The vertex form of the equation is; y = -1.09375·(x - 80)² + 70
(c) The angle at the start is approximately 60.3°
What is quadratic equation?A quadratic equation is a single variable polynomial equation of the second degree.
The points in the path which is a path of a projectile and has a shape of a parabola are;
(0, 0), (80, 70), and (160, 0)
The equations are;
y₁ = a·x₁² + b·x₁ + c
y₂ = a·x₂² + b·x₂ + c
y₃ = a·x₃² + b·x₃ + c
Plugging in the coordinates of the three points in the path gives;
0 = a·0² + b·0 + 1·c70 = a·80² + b·80 + 1·c0 = a·160² + b·160 + 1·cThe matrix becomes;
[tex]A = \begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}[/tex]
[tex]X = \begin{bmatrix}a \\b \\c\end{bmatrix}[/tex]
[tex]Y = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]
We have;
A·X = Y, which gives;
[tex]\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}\cdot \begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]
[tex]X = \dfrac{Y}{A} = A^{-1}\cdot Y[/tex]
Where;
A⁻¹ = The inverse of the matrix A
[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \frac{ \begin{bmatrix}0 \\70 \\0\end{bmatrix}}{\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}} = \begin{bmatrix}\dfrac{1}{12800} & -\dfrac{1}{6400} & \dfrac{1}{12800} \\\\-\dfrac{3}{160} &\dfrac{1}{40} & -\dfrac{1}{160} \\\\1 &0 &0 \\\end{bmatrix}\bullet \begin{bmatrix}0\\ \\70\\ \\0\end{bmatrix}=\begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]
[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]
[tex]a = -\dfrac{7}{640}[/tex]
[tex]b = \dfrac{7}{4}[/tex]
c = 0
The equation for Gunter Money's path is therefore;
[tex]y = -\dfrac{7}{640} \cdot x^2 + 1\dfrac{3}{4} \cdot x + 0 = -1.09375\times 10^2 \cdot x^2 + 1.75\cdot x[/tex]
(b) The vertex of the path is (h, k) = (80, 70)
The vertex form of a quadratic equation is; y = a·(x - h)² + k
The equation of Gunter Money's path in vertex form is therefore;
[tex]y = -\dfrac{7}{640} \cdot \left(x - 80)^2 + 70 = -1.09375\times 10^2\cdot (x - 80)^2+70[/tex]
(c) The angle of the parabolic path of Gunter Money's motion at a point is given by the value of the arctangent of the differentiation of the function for the motion at the point as follows;
[tex]y' = -\dfrac{7\times 2}{640} \cdot x + 1\dfrac{3}{4}[/tex]
At the point Gunter Money takes off, (0, 0), we have;
[tex]tan(\theta) = y' = -\dfrac{7\times 2}{640} \times 0 + 1\dfrac{3}{4} = 1\dfrac{3}{4} = 1.75[/tex]
[tex]\theta = arctan(1.75) \approx 60.3^{\circ}[/tex]
The angle is approximately 60.3°
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Tritium is a radioactive isotope of hydrogen that decays by about 5% per year. A large bottle of water that contained 856,000 tritium atoms remained undisturbed for 13 years. How much tritium does the bottle contain now?
If necessary, round your answer to the nearest whole number.
tritium atoms
Answers
The amount of Tritium that bottle contains now will be 439,421.
What is an exponent?Consider the function:
y = a (1 - r)ˣ
Where x is the number of times this decay occurs, a = initial amount, and r = fraction by which this decay occurs.
Tritium is a radioactive isotope of hydrogen that rots by around 5% each year. An enormous container of water that contained 856,000 tritium iotas stayed undisturbed for a very long time.
Then the amount of Tritium that bottle contains now will be given as,
y = 856,000 (1 - 0.05)¹³
Simplify the equation, then we have
y = 856,000 (1 - 0.05)¹³
y = 856,000 (0.95)¹³
y = 856,000 (0.51334)
y = 439,421
The amount of Tritium that bottle contains now will be 439,421.
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David is three time as old as Joseph after 3 years David will be only twice as old as process will be there find their present ages
Answers
Answer:
Joseph's present age=3 yrs
David's present age=9 yrs
Step-by-step explanation:
Let Joseph's present age be x.
David's present age=3x
__________________
Ater 3 yrs,
Joseph's age=x+3
David's age=2(x+3)
Also, we can add 3 to David's present age to get age After 3 yrs. So, David's age after 3 yrs would also be 3x+3.
Now, balance them.
3x+3=2(x+3)
3x+3=2x+6
x=3
D"s prsent age=9
J's present age=3
The equation
Ax+By=−18
A
x
+
B
y
=
−
18
goes through the coordinates (-3, 10) and (6, -2).
Answers
By solving a system of equations, we will see that the equation is:
-4*x - 3*y = -18
How to find the equation?We know that the linear equation:
A*x + B*y = -18
We know that this linear equation passes through the points (-3, 10) and (6, -2), then replacing these values in the equation we will get two equations:
A*-3 + B*10 = -18
A*6 + B*-2 = -18
So we have a system of equations:
-3A + 10B = -18
6A - 2B = -18
if we add the two times the first equation and the second one we get:
2*(-3A + 10B) + 6A - 2B = 2*(-18) - 18
18B = -3*18
B = -3
by replacing that value of B in one of the equations we will be able to solve it for A.
6*A - 2*(-3) = -18
6*A + 6 = -18
6*A = -18 - 6 = -24
A = -24/6 = -4
The equation is:
-4*x - 3*y = -18
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Created a painting with an area of 48 in.² and a length of 6 inches they create a second painting with an area of 64 in.² it has the same width as the first painting what is the length of the second painting
Answers
The length of the second rectangle is 8 in
How to find the length of the second painting?Since we have painting with an area of 48 in.² and a length of 6 inches, since it is a rectangle, its area is A = LW where
L = length of rectangle = 6 in and W = width of rectangleSo, making Wsubject of the formula, we have
W = A/L
Since
A = 48 in² and L = 6 inSubstituting these into the equation, we have
W = A/L
W = 48 in²/6 in
W = 8 in
Now, since the second painting with an area of 64 in.² it has the same width as the first painting, since it is also a rectangle, its area is A = LW where
L = length of rectangle and W = width of rectangleSo, making L subject of the formula, we have
L = A/W
Since
A = 64 in² and W = 8 inSubstituting these into the equation, we have
L = A/W
L = 64 in²/8 in
L = 8 in
So, the length of the second rectangle is 8 in
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The resistance of a thermistor, a device used to monitor the temperature inside an engine, changes with temperature. The resistance of the thermistor is given by R(t) = t3 + 5, where R is measured in ohms and t is the temperature in °C. What is the average rate of change of resistance per degree of temperature change between 0°C and 2°C?
A.
4 ohms/°C
B.
8.5 ohms/°C
C.
11 ohms/°C
D.
17 ohms/°C
Answer: In photo below
You're Welcome :)
Answers
The average rate of change of the resistance of the thermistor for each degree change in the temperature, when the temperatures changes from 0 °C and 2 °C is A. 4 ohms/°C
What is the average of a set of values?The average is calculated by adding the values in the dataset then dividing the result by the count of the numbers or values in the set. The average is also known as the arithmetic mean.
The function for finding the resistance of the thermistor is; R(t) = t³ + 5
The unit of the R = Ohms
The unit of t = Degrees Celsius, °C
The resistance of the thermistor when the temperature is t = 0 °C is found as follows;
R(0) = 0³ + 5 = 5
Therefore;
When the temperature is 0 °C the resistance of the thermistor is 5 Ohms
When the temperature is t = 2 °C, we have;
R(2) = 2³ + 5 = 13
The resistance of the thermistor at t = 2 °C is 13 Ohms
The average rate of change of a function, f(x), is found using the formula;
[tex]A(x) = \dfrac{f(x_2) - f(x_1) }{x_2-x_1}[/tex]
The average rate of change of the resistance per degree change in the temperature, between the temperature interval of 0 °C and 2 °C is therefore;
[tex]A(x) = \dfrac{R(2) - R(0)}{2 - 0}[/tex]
Which gives;
[tex]A(t) = \dfrac{13 -5}{2 - 0}= 4[/tex]
The average rate of change of the resistance of the thermistor between the temperatures of t = 0 °C and t = 2 °C is 4 Ohms/°C
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The weight, in pounds, of a newborn baby t months after birth can be modeled by the equation W=1.75t+6. What is the slope of the equation and what is its interpretation in the context of the problem?
Answers
Answer:
the slope is 1.75
Step-by-step explanation:
Interpretation: The weight of newborn is 6 lb at birth, and every month baby gained 1.75 lb. You replace x with month you want to know the weight. For example you can calculate the weight after 4 month : w= 1.75(4)+6= 13 lb
Given m || n
find the value of x and y.
(6x+19)° (2y+1)⁰
(3x+8)°
m
n
Answers
A value for x is therefore represented by the first number in an ordered pair, and a value for y is represented by the second.The x- and y-coordinates are the names given to these values.
Find the value of x and y ?The Method of Elimination
To ensure that the two equations have the same leading coefficient, multiply each equation by a reasonable number in step one.
Step 2: Reverse the first equation and subtract the second one.
Step 3: Find y using this new equation.
Step 4: Change Equation 1 or Equation 2 above to y = 2 and then solve for x.
multiply the equation y = x - 6 by -6.
You will then get the equation: 6y = -6x + 36
The two equations will be:
6y = -6x + 36
y = 6x - 19
And you can see that if you add them, you will be able to eliminate x. answer is -6.
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Linear regression question 8
Use graph below using all the points on the graph to figure out the line of best fit and the estimate of Carter’s weight 15 weeks into his diet.
Answers
The linear regression equation from the given scatter plot is:
y = -1.62x + 215.64.
Using this function, the estimate of his weight 15 weeks into the diet is:
191.34 pounds.
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the scatter plot of the situation into a linear regression calculator.
From the given scatter plot, the points are given as follows:
(0,216), (1,214), (2,213), (3,210), (4,210), (5,207), (6,206), (7,202), (8,203), (9,202), (10,200)
Inserting these points into a calculator, the line of best fit is given as follows:
y = -1.62x + 215.64.
The estimate weight at the 15th week of the diet is the numeric value of the function when x = 15, that is, the lone instance of x in the function is replaced by 15, as follows:
y = -1.62(15) + 215.64 = 191.34 pounds.
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When we add any two multiples of 5 and 10 we sometimes,always or never get a number ending in 2.
Sometimes
Never
Always
Answers
Answer:
Never
Because for example; 25(the multiple of 5) + 20(the multiple of 10) equals 45
Answer:
Step-by-step explanation:
never
REMEMBER 4. What is the difference in length? Carrot 14 cm Show the difference in length two ways. Write an equation for each. The difference in length is Pea pod 5 cm cm.
Answers
The difference in lengths is 9 cm and the length of the carrot is 9 cm longer than the pea pod.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have to determine the difference in lengths
The length of the carrot = 14 cm
The length of the pea pod = 5 cm
The difference in lengths = maximum length - minimum length
The difference in lengths = 14 cm - 5 cm
Apply the subtraction operation, and we get
The difference in lengths = 9 cm
We conclude that the length of the carrot is 9 cm longer than the pea pod.
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SOMEONE HELP ME.
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building.
Answers
The dimension of the rectangular room in the actual building are 55 feet by 30 feet.
How to find the dimension of the rectangular room in the actual building?Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building.
The dimensions of this rectangular room in the actual building can be found as follows:
let's find the length of the actual room
1 inches = 10 feet
3 inches = ?
cross multiply
length = 30 ft
Let's find the width of the room
1 inches = 10 feet
5.5 inches = ?
cross multiply
width = 55 ft
Therefore, the width and length of the room are 55 feet and 30 ft respectively.
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PLS HELP QUICK!! IL MARK YOU BRAINLIEST
A cooler is filled with containers of yogurt. Some of the containers have low-fat yogurt and some have non-fat yogurt. There are three flavors for each type of yogurt, as shown in the table. Sophie chooses a container at random. What is the probability that she chooses low-fat yogurt?
Answers
Answer:
Step-by-step explanation 2/3 is the answer :
The required probability, that she chooses low-fat yogurt is 2/3.
Given that, a cooler is filled with containers of yogurt. Some of the containers have low-fat yogurt and some have non-fat yogurt. There are three flavors for each type of yogurt, as shown in the table.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
From the given,
Sample space = 24
Low Fat =16
Non-fat = 8
The probability that she chooses low-fat yogurt
= 16/24
= 2/3
Thus, the required probability, that she chooses low-fat yogurt is 2/3.
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On a banquet table, 8 different dishes of food will be placed in a row. There are 4 vegetarian dishes and 4 meat dishes.
They will be placed alternating between the two types of dishes. A vegetarian dish will be first. How many ways are
there to place the dishes on the table?
Answers
If a vegetarian dish will be first. The number of different ways that are there to place the dishes on the table is 576.
How to find the number of different ways?There are 4 vegetarian dishes = P4 = 4!
There are 4 meat dishes =P4 =4!
Now let find the number of different ways
Number of different ways = 4! × 4!
Number of different ways = 24 × 24
Number of different ways = 576 different ways
Therefore the number of different ways is 576.
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which is the correct answer for this ??????
Answers
The given system of linear equations has no solution. By solving the equations using substitution method we get (11, 0) where no solution exists.
How many solutions can a system of linear equation can have?
A system of linear equations is usually a set of two linear equations with two variables.
The solution to a system of linear equations is the point at which the lines representing the linear equations intersect.
With linear systems of equations, there are three possible outcomes in terms of number of solutions:
One solutionInfinitely many solutionsNo solutionHow to identify the number of solutions?
Rewrite both equations in slope-intercept form, y = mx + b.
Compare the slopes of the lines, m, and their y-intercepts, b, to determine the number of solutions.
If the two equations have different m-values, then the system has one solution.If the two equations have the same m-value but different b-values, then the system has no solution.If the two equations have both the same m-value and the same b-value, then the system has infinitely many solutions.According to the given question:
Given system of linear equation are: y = -x + 11 and -4x -4y = 44
Rewriting the equations in slope-intercept form
y = -x + 11 ---- 1)-4y = -4x + 44Simplifying further by dividing the equation with -4 on both side
y = x - 11 ------ 2)
Clearly, both the equation have different m-values.
Hence the system of equation have one solution.
Now solving by substitution method
Substituting 2) in 1)
x - 11 = -x + 11 (since y = x -11 from 2))
2x = 22
∴ x = 11
Now substituting x = 11 in equation 2) to get the value of y
y = 11 - 11
∴ y = 0
So, the system of equation has no solution at (11, 0).
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Find x in this equation.
3/8 = 15/5x - 2
Answers
Answer:
x=19/24
Step-by-step explanation:
3/8=15/5x-2
3/8= 3x -2 |*8
3=24x-16
24x=19
x=19/24
Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 24 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Answers
Step-by-step explanation:
Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 24 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Looking at your chart:
cost/length in inches
6/100 = $0.06 per inch
8.1/135 = $0.06 per inch
9.6/160 = $0.06 per inch
10.8/180 = $0.06 per inch
So the rate stays at a constant rate of $0.06 per inch.
Andy needs 24 feet or 288 inches at a constant rate of $0.06 per inch.
= 288 * $0.06
= $17.28
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Emily needs 15 yards or 540 inches at a constant rate of $0.06 per inch.
= 540 * $0.06
= $32.40
A plumber who is just starting out offers low rates to attract new customers. He charges $35 to visit a client's home, plus an additional $20 per hour. If the plumber charges a customer $45 for a visit, how long was it?
Answers
If the plumber charges a customer $45 , then the visit was 0.5 hours long .
In the question ,
it is given that
the fixed charge to visit a client's home is = $35
additional per hour charge of plumber is = $20 .
let the time taken by plumber in the customer house be "x" .
So , according to the question
the equation for total charge is
total charge = 35 + 20x
given the customer paid $45 ,
So , 45 = 35 + 20x
20x = 45 - 35
20x = 10
x = 10/20 = 0.5
Therefore , If the plumber charges a customer $45 , then the visit was 0.5 hours long .
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