If four is half of five and two thirds of six is nine. what is thirty-two?
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Let
x--------> <span>the number of sandwich lunch specials sold
y-------> </span><span>the number of wrap lunch specials sold
we know that
2x+3y=1470
Part 1) </span><span>Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
we know that
</span>the equation to slope-intercept form is of the form
y=mx+b
so
2x+3y=1470------> solve for y
3y=1470-2x-----> divide by 3 both sides
y=(-2/3)x+1470/3
y=(-2/3)x+490
the slope m=-2/3
the y-intercept is 490
Part 2) <span>Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
</span><span>the slope is -2/3 and the y-intercept is 490
Plot the point (0,490)------> the y-intercept.
With the slope count 3 squares to the right and 2 squares down and plot that point, which is (0+3,490-2)--------> (3,488)
Draw a line through the two points
Part 3) </span><span>Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
In function notation, the equation is:
f(x)=(-2/3)x+490
The graph of this function represents how the value of the function varies as the value of x varies. Looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470.</span><span>
Part 4) </span>Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology
using a graph tool
see the attached figure
Part 5) Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different
we have that
2x+3y=1593
3y=1593-2x--------> y=(-2/3)x+531
slope=(-2/3)
y intercept=531
therefore
similarities : same slope
differences : y intercepts are different.
<span>This is basically telling me that the lines are parallel lines because they have the same slope.
</span>
6) Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations
Select two points on the line and write down their coordinates
Let
A( 0,300) B (450,0)
a) find the slope
m=(y2-y1)/(x2-x1)----> m=(0-300)/(450-0)----> m=-2/3
b) with the slope m=(-2/3) and the point A (0,300)
y-y1=m*(x-x1)-----> y-300=(-2/3)*(x-0)----> y=(-2/3)x+300
the answer Part 6) is
y=(-2/3)x+300
x--------> <span>the number of sandwich lunch specials sold
y-------> </span><span>the number of wrap lunch specials sold
we know that
2x+3y=1470
Part 1) </span><span>Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
we know that
</span>the equation to slope-intercept form is of the form
y=mx+b
so
2x+3y=1470------> solve for y
3y=1470-2x-----> divide by 3 both sides
y=(-2/3)x+1470/3
y=(-2/3)x+490
the slope m=-2/3
the y-intercept is 490
Part 2) <span>Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
</span><span>the slope is -2/3 and the y-intercept is 490
Plot the point (0,490)------> the y-intercept.
With the slope count 3 squares to the right and 2 squares down and plot that point, which is (0+3,490-2)--------> (3,488)
Draw a line through the two points
Part 3) </span><span>Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
In function notation, the equation is:
f(x)=(-2/3)x+490
The graph of this function represents how the value of the function varies as the value of x varies. Looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470.</span><span>
Part 4) </span>Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology
using a graph tool
see the attached figure
Part 5) Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different
we have that
2x+3y=1593
3y=1593-2x--------> y=(-2/3)x+531
slope=(-2/3)
y intercept=531
therefore
similarities : same slope
differences : y intercepts are different.
<span>This is basically telling me that the lines are parallel lines because they have the same slope.
</span>
6) Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations
Select two points on the line and write down their coordinates
Let
A( 0,300) B (450,0)
a) find the slope
m=(y2-y1)/(x2-x1)----> m=(0-300)/(450-0)----> m=-2/3
b) with the slope m=(-2/3) and the point A (0,300)
y-y1=m*(x-x1)-----> y-300=(-2/3)*(x-0)----> y=(-2/3)x+300
the answer Part 6) is
y=(-2/3)x+300
Answer:
The standard deviation of car age is 2.17 years.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 7.5
(a) If 99.7% of the ages are between 1 year and 14 years, what is the standard deviation of car age?
This means that 1 is 3 standard deviations below the mean and 14 is 3 standard deviations above the mean.
So
I want to find
The standard deviation of car age is 2.17 years.
The cube has 6 sides, each a square with dimensions 3 by 3,
the area of any of these squares is 3*3=9 square units.
The total area of the cube is 6*9 square units=54 square units
The volume of a cube with side length a is given by :
, thus the volume of the cube-shaped cell is 3*3*3=27 cube units.
(surface area):(volume)=54:27 = 2:1 =2
Answer:
the ratio of the numerical values is 2
(their ratio including units is 2/unit
the area of any of these squares is 3*3=9 square units.
The total area of the cube is 6*9 square units=54 square units
The volume of a cube with side length a is given by :
(surface area):(volume)=54:27 = 2:1 =2
Answer:
the ratio of the numerical values is 2
(their ratio including units is 2/unit