The interpretation for this interval is that we can be 98% confident that the population mean amount of syrup dispensed is between 1.092 and 1.104 fluid ounces.
A. The data collected in this situation is quantitative.
B. The parameter of interest in this situation is the population mean amount of syrup dispensed.
C. We know that the sample mean is normally distributed because the population of syrup content (fluid ounces) is assumed to be normally distributed with a standard deviation of 0.016 fluid ounces.
D. The appropriate critical value (z α/2 ) for a 98% confidence interval for population mean in this situation is 2.05.
E. Using the appropriate formula, the 98% (two-sided) confidence interval for the population mean amount of syrup dispensed is (1.092, 1.104).
F. The interpretation for this interval is that we can be 98% confident that the population mean amount of syrup dispensed is between 1.092 and 1.104 fluid ounces.
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1. Before you took this course, you probably heard many stories about Statistics courses. Oftentimes
parents of students have had bad experiences with Statistics courses and pass on their anxieties to their
children. To test whether actually taking AP Statistics decreases students' anxieties about Statistics, an
AP Statistics instructor gave a test to rate student anxiety at the beginning and end of his course.
Anxiety levels were measured on a scale of 0-10. Here are the data for 16 randomly chosen students
from a class of 180 students:
paired
t
SU
Pre-course anxiety level
Post-course anxiety level
Difference (Post - Pre)
7 6 9 5
4 3 7 3
-3 -3 -2 -2
6 7
4 5
-2 -2
5
4
-1
7 6 4
6 5 3
-1 -1 -1
3
2
-1
2 1
2 1
0 0
3
3
0
4
4
0
2
3
1
The assumptions include:
1. The observations are normally distributed.
2 The observertions are independent.
What are the test hypothesis?Test hypotheses include the null hypothesis that the anxiety level is same before after the course and the alternative hypothesis that the anxiety level derveases after taking the course.
The standard deviation is 1.1475. The value of to will be:
= -1.125 / (1.1475 / √16)
= 3.9212
Based on the p value, it should be noted that the null hypothesis is rejected.
In conclusion, the anxiety level decrease after the students take the course.
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Before you took this course, you probably heard many stories about Statistics courses. Oftentimes parents of students have had bad experiences with Statistics courses and pass on their anxieties to their children. To test whether actually taking AP Statistics decreases students' anxieties about Statistics, an AP Statistics instructor gave a test to rate student anxiety at the beginning and end of his course.
Anxiety levels were measured on a scale of 0-10. Here are the data for 16 randomly chosen students from a class of 180 students:
Do the data indicate that anxiety levels about Statistics decreases after students take AP Statistics? Test an appropriate hypothesis and state your conclusion.
2(-3x+5)+2(x+4) when x=2
Answer:
12
Step-by-step explanation:
p(x) = 2(-3x+5)+2(x+4)
Substitution :
p(2) = 2(-3(2) +5) + 2(2+5)
= 2(-6 + 5) + 2 (7)
= 2(-1) + 2(7)
= -2 + 14
= 12
11 + x = 7 - 4x what is x
Answer:
x = 6
Step-by-step explanation:
Solve for x
[tex]11+x=7-4x[/tex]
Add 7 on both sides
[tex]18+x=4x[/tex]
Subtract x on both sides (same as 1x)
[tex]18=3x[/tex]
Divide by 3
[tex]6=x[/tex]
I really need help with this math problem
Step-by-step explanation:
The area with the highest inches receives most rainfall 1¼
The area with the lowest inches received lowest rainfall 1/8
1¼ location will have highest frequency using the ⅛line plot. There are 10 of ⅛ in 1¼
Add all the inches
1/8 + 3/8 +1/8 + 1/8 + 3/4+ 3/4 + 1/4 + 1¼ + 1/4 +1
6/8 + 2¼ + 1
6/8 + 3¼
6/8 + 13/4 = 32/8
Total rain = 4inches
A(-1, 2) and C(3, 4) are opposite vertices of a rhombus ABCD. Find the coordinates of the points where the diagonals intersect
Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). The coordinates of the intersection point are (1,3).
What is rhombus?
A rhombus is a special type of parallelogram in which all four sides are of equal length. Equivalently, a rhombus is a quadrilateral with four sides of equal length.
Since ABCD is a rhombus, its diagonals AC and BD are perpendicular bisectors of each other, and they intersect at their mutual midpoint M.
The midpoint M of AC is the average of the coordinates of A and C, namely:
M = ((-1+3)/2, (2+4)/2) = (1, 3)
Similarly, the midpoint of BD is the average of the coordinates of B and D. Since we don't know the coordinates of B and D, we need to find them first.
The other two vertices of the rhombus are obtained by reflecting A and C about the midpoint M, since opposite sides of a rhombus are parallel and equal in length. To do this, we subtract the coordinates of M from those of A and C, and then add them to M:
B = 2M - A = 2(1,3) - (-1,2) = (3,4)
D = 2M - C = 2(1,3) - (3,4) = (-1,2)
Now we can find the midpoint of BD:
N = ((3-1)/2, (4+2)/2) = (1, 3)
Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). Therefore, the coordinates of the intersection point are (1,3).
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What’s the answer to this
Answer: 45 ml/h
Step-by-step explanation: that is s/t graph
read in any point on the part of graph distance , and divide
it with time .
95:2 hours,
1. Use properties of logarithms with the given approximations to evaluate the expression. Use logb2=0.693 and/or logb6=1.792 to find logb12.2. Complete parts (a) and (b). a. Write the inverse of y=8x in logarithmic form. b. Graph y=8x and its inverse and discuss the symmetry of their graphs.3. 2log2^15 EVALUATEUse properties of logarithms with the given approximations to evaluate the expression.loga3≈0.477andloga5≈0.699.Use one or both of these values to evaluate loga27.Write as a single logarithm. Assume that variables represent positive numbers.5log2x+2log2zOn the basis of data for the years 1918 through1997, the expected life span of people in a country can be described by the functionf(x)=12.576ln x+17.088 years, where x is the number of years from1905 to the person's birth year. What does this model estimate the life span to be for people born in 1941?This model estimates that the life span for people born in1941 is
1. Use properties of logarithms with the given approximations to evaluate the expression. Use log2=0.693 and/or log6=1.792 to find log12.
Answer: log12 = log6 + log2 = 1.792 + 0.693 = 2.485.
2. Complete parts (a) and (b).
a. Write the inverse of y=8x in logarithmic form.
Answer: log8(y) = x.
b. Graph y=8x and its inverse and discuss the symmetry of their graphs.
Answer: The graph of y=8x and its inverse will have the same shape, but it will be flipped across the line y = x. This is known as the symmetry of their graphs.
3. 2log215 EVALUATE Use properties of logarithms with the given approximations to evaluate the expression. log3≈0.477 and log5≈0.699. Use one or both of these values to evaluate log27. Write as a single logarithm. Assume that variables represent positive numbers. 5log2x+2log2z
Answer: log27 = log5 + log3 = 0.477 + 0.699 = 1.176.
4. On the basis of data for the years 1918 through 1997, the expected life span of people in a country can be described by the function f(x) = 12.576ln x + 17.088 years, where x is the number of years from 1905 to the person's birth year. What does this model estimate the life span to be for people born in 1941?
Answer: This model estimates that the life span for people born in 1941 is 70.698 years.
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A sequence {an} is defined recursively, with a1 = -1, and, for n > 1, an = an-1 + (-1)n. Find the first five terms of the sequence.
The first five terms of the sequence given the definition are -1, 0, 1, 2 and 3
How to find the first five terms of the sequence.To find the first five terms of the sequence {an}, we can use the recursive definition of the sequence and compute each term one by one:
a1 = -1
For n = 2, we have:
a2 = a1 + (-1)² = -1 + 1 = 0
For n = 3, we have:
a3 = a2 + (-1)³ = 0 - (-1) = 1
For n = 4, we have:
a4 = a3 + (-1)⁴ = 1 + 1 = 2
For n = 5, we have:
a5 = a4 + (-1)⁵ = 2 - (-1) = 3
Therefore, the first five terms of the sequence {an} are:
a1 = -1
a2 = 0
a3 = 1
a4 = 2
a5 = 3
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At which point do the lines y=4x+1 and y=2x-1 intersect
The lines having linear equation y=4x+1 and y=2x-1 intersect at the point (-1, -3).
What is a linear equation, exactly?
A linear equation is an algebraic equation of the first degree that describes a line in a two-dimensional plane. It is an equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope represents the rate of change of y with respect to x, while the y-intercept represents the point at which the line crosses the y-axis
Now,
To find the point of intersection between the lines y=4x+1 and y=2x-1, we can set the two equations equal to each other or we can graph these and find the intersection point.
1.
4x+1 = 2x-1
Simplifying this equation, we get:
2x = -2
x = -1
Now, we can substitute this value of x into either equation to find the corresponding value of y:
y = 4x+1 = 4(-1)+1 = -3
Therefore,
the lines y=4x+1 and y=2x-1 intersect at the point (-1, -3).
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Watch help video Given f(x)=x^(3)+kx+9, and the remainder when f(x) is divided by x-3 is 27 , then what is the value of k ?
When f(x) is divided by x-3 is 27 , then what is the value of k is -3
What is remainder theοrem?Remainder Theοrem is an apprοach οf Euclidean divisiοn οf pοlynοmials. Accοrding tο this theοrem, if we divide a pοlynοmial P (x) by a factοr ( x – a); that isn’t essentially an element οf the pοlynοmial; yοu will find a smaller pοlynοmial alοng with a remainder.
When f(x) is divided by x - 3, the remainder is 27, which means that
f(3) = 27.
We can use this fact tο sοlve fοr k as fοllοws:
f(x) = x³ + kx + 9
f(3) = 27
Substituting x = 3 intο the expressiοn fοr f(x), we get:
f(3) = 3³ + k(3) + 9 = 27
Simplifying the left side, we get:
27 + 3k + 9 = 27
Cοmbining like terms, we get:
3k + 36 = 27
Subtracting 36 frοm bοth sides, we get:
3k = -9
Dividing bοth sides by 3, we get:
k = -3
Therefοre, the value οf k is -3.
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The temperature in Australia one morning was -5°C at 08:00 and increased by 2°C every hour until 12:00. What will the temperature be at 11:00
Answer:
3*C
Step-by-step explanation:
We can Frame an equation, taking the previous temperature as "x" and adding 2 by every hour.
Previous Temprature + 2 = New Temprature
Therefore by this equation:
at 8AM , the Temperature is -5 + 2 = -3*c
at 9AM , the Temperature is -3 + 2 = -1*c
at 10 AM, the Temperature is -1 + 2 = 1*c
Therefore at 11AM , the Temperature will be 1 + 2 = 3*c
Hope it helps.
The border of a susan b. Anthony dollar is in the shape of a regular polygon. How many sides does the polygon have what is the measure of each angle of the border round your answer to the nearest degree
The polygon has 12 sides and each angle has a measure of 30°.
The border of a Susan B. Anthony dollar is in the shape of a regular polygon. A regular polygon is a polygon with equal sides and equal angles. To calculate the number of sides and measure of the angles, the formula for finding the measure of the interior angles of a regular polygon is used. The formula is (n-2)180/n where n is the number of sides. For the Susan B. Anthony dollar, the number of sides is 12, so the measure of the interior angles is (12-2)180/12 = 30°. Therefore, the polygon has 12 sides and each angle has a measure of 30°, rounded to the nearest degree.
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The trinomial 2x2 + 13x + 6 has a linear factor of x + 6.
2x2 + 13x + 6 = (x + 6)(?)
What is the other linear factor?
pls tell me how to do the table thing
The trinomial( consists three different terms), 2x² + 13x + 6, has a linear factor of (x + 6) and the linear factor of (x+6) is equals to a (2x+1).
We have, a trinomial 2x² + 13x + 6 has a linear factor of x + 6 and we have to determine that linear factor of (x + 6). To determine the linear factor of (x + 6) either dividing the trinomial by (x+6) or factorization of this trinomial. Factoring a trinomial means expanding an equation into the product of two or more binomials. Here, middle term of trinomial, b = 13
last term, c = 6
Using spliting middle term method for factorization, 2x²+ 13x + 6 = 2x² + 12x + x + 6
=> 2x² + 13x + 6 = 2x( x + 6) + 1(x + 6 )
Common factor from binomials,
=> 2x² + 13x + 6 = (x + 6)(2x + 1)
Thus, the linear factor of (x+6) is (2x +1).
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Evaluate the function graphically. Find f (2)
Answer:
function not defined for x = 2
Step-by-step explanation:
The open circle at x = 2 shows that the function is not defined for x = 2.
Use a trigonometric ratio to solve for a. round to two decimal places image below giving brainliest to whoever gets it correct
A new park in the shape of a hexagon will have 6
sides of equal length.
On a scale drawing, the coordinates of the vertices of the park are (26.5, 12), (38.5, 7), (26.5, 2), (13.5, 2), (1.5, 7),
and (13.5, 12)
.
How long is each side of the park?
The length of each side of the hexagon is 13 units long, which is equal to length of the park.
What is the length of each side of the park?In order to determine the length of every side of the hexagon, it is necessary to compute the distance between each pair of neighboring vertices.
This can be accomplished by employing the distance formula, which is represented as follows:
d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² ).
To facilitate the process, we will designate the vertices as A, B, C, D, E, and F in sequence, with A being the vertex at the top.
Then, the length of side AB is calculated as follows:
|AB| = √((38.5-26.5)² + (7-12)²)
|AB| = √((12)² + (-5)²)
|AB| = √(144 + 25)
|AB| = √169
|AB| = 13
Similarly, we can calculate the length of each side:
|BC| = √( (26.5-38.5)² + (2-7)² ) = 13
|CD| = √( (13.5-26.5)² + (2-2)² ) = 13
|DE| = √( (1.5-13.5)² + (7-2)² ) = 13
|EF| = √( (13.5-1.5)² + (12-7)² ) = 13
|FA| = √( (26.5-13.5)² + (12-12)² ) = 13
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Answer:
13 units
Step-by-step explanation:
d^2 = (x2 – x1)^2 + (y^2 – y^1)^2
Now we calculate the distance between 2 points:
d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2
d^2 = 169
d = 13
Therefore the length of each side of the park is 13 units.
A jar contains 3 red marbles numbered 1 to 3 and 7 blue marbles
numbered 1 to 7. A marble is drawn at random from the jar. Find the
probability that the marble is blue AND even-numbered.
The probability of drawing the blue and even-numbered marble from the given jar is 3/10.
The given problem can be solved using the concept of Probability. Let's see how to solve it.
Step 1: Total Number of Marbles in the Jar
Number of red marbles in the jar = 3
Number of blue marbles in the jar = 7
Total number of marbles in the jar = 3 + 7 = 10
Step 2: Find the Probability of Marble is Blue and Even Numbered
Number of blue marbles which are even-numbered = 3 (Blue marbles numbered 2, 4, and 6 are even-numbered marbles)
Total number of marbles in the jar = 10
Probability of marble is blue and even-numbered = Number of blue marbles which are even-numbered / Total number of marbles in the jar = 3/10
So, the required probability of drawing the blue and even-numbered marble is 3/10.
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If point X (-4,5) was rotated 180 Degrees counterclockwise around the origin, what would the coordinates of X' be?
Answer:
(4,-5)
Step-by-step explanation:
(x,y) → (-x, -y)
(-4,5) → (4,-5)
Helping in the name of Jesus.
Nrite equations of the lines through the given point parallel to and perpendicular to the given li x+y=3,(-3,2)
Answer:
vfejwbjelkn
Step-by-step explanation:
4x-2+3x+14=180
Solve for x.
Answer: x = 24
Step-by-step explanation:
To solve for x, we need to simplify the left side of the equation first by combining like terms:
4x - 2 + 3x + 14 = 180
7x + 12 = 180
Next, we will isolate the variable by subtracting 12 from both sides:
7x + 12 - 12 = 180 - 12
7x = 168
Finally, we will solve for x by dividing both sides by 7:
7x/7 = 168/7
x = 24
Therefore, the solution to the equation 4x-2+3x+14=180 is x = 24.
Solve for y. Then find the values of y that correspond
to the given values of x for the linear equation.
y + 8x = -2 forx = 0, 1, 2
Answer:
no one can solve that because how you spelled it but good luck
Answer:
y= -2 when x is 0,y= -10 where x is 1 and y= -18 where x is 2
Step-by-step explanation:
when you equate x to 0 then you substitute to the equation give which is y+8x= -2, the same thing applies to the next numbers which is 1 and 2. to show it will look like is suppose to be in the form like when x is 0 it will be y+8(0)= -2
which will solve to get y+0=-2
which is the same as y=-2
You are designing an icon for a mobile app. Use the provided ruler to answer the following questions.
a. Find the perimeter and area of the icon in the scale drawing. Round the measurements for the length and the width to the nearest half centimeter to calculate your answers.
The perimeter in the scale is ___ centimeters
The area in the scale drawing is __ square centimeters.
b. Find the actual perimeter and area of the icon.
The actual perimeter is ___ millimeters.
The actual area is ___ square millimeters.
a. The perimeter in the scale is 36 centimeters
The area in the scale drawing is 80 square centimeters.
b. The actual perimeter is 40 millimeters.
The actual area is 937.5 square millimeters.
To find the perimeter of the icon in the scale drawing, you need to add up the length of all its sides. Using the ruler provided, measure the length and width of the icon and round them to the nearest half centimeter. Then, add up the length and width and multiply by 2 to get the perimeter.
a. Assuming the scale of the drawing is 1 cm : 2 units, the length of the icon in the drawing would be 2 x 5 = 10 units and the width would be 2 x 4 = 8 centimeters.
The perimeter in the scale drawing would be 2 x (length + width) = 2 x (10 + 8) = 36 cm (rounded to the nearest half-centimeter).
The area in the scale drawing would be length x width = 10 x 8 = 80 square cm.
b. Assuming the scale of the drawing is 1 cm : 2 units, the actual length of the icon would be 2.5 cm / 2 = 1.25 units and the actual width would be 1.5 cm / 2 = 0.75 units.
The actual perimeter would be 2 x (length + width) = 2 x (1.25 + 0.75) = 4 cm = 40 mm.
The actual area would be length x width = 1.25 x 0.75 = 0.9375 square cm = 937.5 square mm.
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Solve the system of equations.
x + y = 8
y = x2 – 4
a. (3, 5) and (–4, 12)
b. (–3, 11) and (4, 4)
c. (4, 4) and (5, 3)
d. (12, –4) and (7, 1)
The solution of the system of equation is (3, 5) and (–4, 12) [option A]
The given system of equations is:
x + y = 8
y = x² – 4
To solve for x and y, we can substitute the second equation into the first equation for y:
x + (x² - 4) = 8
Simplifying, we get:
x² + x - 12 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -12
x = (-1 ± √(1² - 4(1)(-12))) / 2(1)
x = (-1 ± √(1 + 48)) / 2
x = (-1 ± 7) / 2
Solving for x gives us two possible values: x = 3 or x = -4.
To find the corresponding values of y for each value of x, we can substitute them into either of the original equations. Using y = x² - 4:
When x = 3, y = 3² - 4 = 5
When x = -4, y = (-4)² - 4 = 12
Therefore, the solution to the system of equations is (3, 5) and (-4, 12), which is answer choice (a).
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The graph is a translation of one of the basic functions , , , . Find the equation that defines the function.
help plsss its due today
The equation of line is y = -3x + 2
Define equation of variable?An equation for two variables is a mathematical statement that relates two variables, typically represented by x and y, using mathematical symbols and operations such as addition, subtraction, multiplication, and division.
To find the equation of the line that passes through the given points (2, -4), (3, -7), (4, -10), and (5, -13), we can use the slope-intercept form of the equation of a line:
y = mx + b, where slope of the line is m and y-intercept is b.
First, let's find the slope of the line using two of the points, say (2, -4) and (3, -7). The slope, m, is given by:
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
= (-7 - (-4)) / (3 - 2)
= -3
we know the slope, we can use one of the points, say (2, -4), and the slope to find the y-intercept, b. Use the slope intercept to form the equation of a line:
y = mx + b, and substitute in the slope and coordinates of one of the points:
-4 = (-3)(2) + b
Simplifying this equation, we get:
b = -4 + 6
= 2
Therefore, the equation of the line that passes through the given points (2, -4), (3, -7), (4, -10), and (5, -13) is: y = -3x + 2
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Solve 7u²-56=0, where u is a real number.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Therefore, the solutions to the equation 7u² - 56 = 0 are u = 2.83 and u = -2.83 (rounded to the nearest hundredth).
Answer: u = 2.83, -2.83.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two sides separated by an equals sign (=). The expressions on both sides of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. The goal in solving an equation is to find the value or values of the variable(s) that make the equation true.
What is real numbers?The real numbers are a set of numbers that includes all rational and irrational numbers. Real numbers can be represented on the number line, where every point corresponds to a unique real number. The real number system is denoted by the symbol R.
In the given question,
To solve the equation 7u² - 56 = 0, we can start by isolating the variable u by adding 56 to both sides of the equation:
7u² - 56 + 56 = 0 + 56
Simplifying the left side, we get: 7u² = 56
Dividing both sides by 7, we get: u² = 8
Taking the square root of both sides, we get: u = ±√8
Simplifying the square root, we get: u = ±2.83
Therefore, the solutions to the equation 7u² - 56 = 0 are u = 2.83 and u = -2.83 (rounded to the nearest hundredth).
Answer: u = 2.83, -2.83.
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Reed's number cube numbered (1, 2, 3, 4, 5, 6) is rolled and a spinner with 4 sections (A, B, C, D) is spun. P(1 and A)
The probability of rolling a 1 and spinning section A on the spinner is 1/24.
To find the probability of rolling a 1 and spinning section A on the spinner, we need to first determine the total number of possible outcomes for the experiment. The number cube has 6 possible outcomes, and the spinner has 4 possible outcomes. Therefore, the total number of possible outcomes for the experiment is 6 x 4 = 24.
Next, we need to determine the number of outcomes that meet the criteria of rolling a 1 and spinning section A. Rolling a 1 has a probability of 1/6, and spinning section A has a probability of 1/4.
The probability of both events occurring simultaneously is the product of the two probabilities, which is (1/6) x (1/4) = 1/24.
This means that out of the 24 possible outcomes, only one outcome will result in rolling a 1 and spinning section A on the spinner.
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Complete Question:
A number cube numbered (1, 2, 3, 4, 5, 6) is rolled and a spinner with 4 sections (A, B, C, D) is spun. Find the probability of P(1 and A).
part B observe the graph at what point do the lines appear to insersect
Answer:
Step-by-step explanation:
UK pounds (£) are in direct proportion to euros (€).
£20 buys €21.70
How many euros will £48 buy?
Answer:
52.08 Euros
Step-by-step explanation:
21.70 euros / 20 uk pounds = 1.085 per pound
so 48 euro x 1.085 pounds = 52.08 euros
Help plsss
Determine if it’s linear