A 15-inch candle is lit and steadily burns until it is burned out. Let b represent the burned length of the candle (in inches) a
nd let r represent the remaining length of the candle (in inches).
a. Write a formula that expresses r in terms of b.When 3.1 inches have burned from the candle, the remaining length of the candle is inches.
b. Graph the relationship between a and b
a. Write a formula that expresses r in terms of b.When 3.1 inches have burned from the candle, the remaining length of the candle is inches.
b. Graph the relationship between a and b
1 answer:
Answer:
(a)r=15-b
11.9 Inches
(b)See attached
Step-by-step explanation:
Length of the candle =15 inch
Let b represent the burned length of the candle (in inches)
Let r represent the remaining length of the candle (in inches).
Therefore:
(a) r+b=15
r=15-b
When b=3,1 Inches
Remaining Length, r=15-3.1=11.9 Inches
(b)The graph showing te relationship between r and b is shown below.
r is plotted on the y-axis while b is plotted on the x-axis as labelled.
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1)Define the variables you will use in your model.
Let
x------->total pounds of the fruit
y-------> the total number of granola bars
TC----> total cost
Tf------> total cost of the fruit
Tg----> total cost of the granola bars
2) Write an inequality representing the total cost of your purchase. (3 points)
a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1
Tf=4*x
b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.
Tg=1*y--------> Tg=y
c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.
TC=Tf+Tg
TC=4*x+y
inequality------->
3. Write the inequality that models the number of granola bars you need to buy.
You need at least 10 granola bars
so
4. Describe in words what each of your inequalities means
inequality 1
the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars
inequality 2
5. Graph your system of inequalities.
using a graph tool
see the attached figure
6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution.
Let
A-------> one point on the graph that represents a viable solution
B-------> one point on the graph that does not represent a viable solution
A(4,20)
x=4-------> total pounds of the fruit
y=20------> the total number of granola bars
check point A
substitute the values of x and y in the inequality 1
-------> is ok
substitute the values of x and y in the inequality 2
--------> is ok
the point A represents a viable solution, because satisfies both inequalities
B(10,30)
x=10-------> total pounds of the fruit
y=30------> the total number of granola bars
check point B
substitute the values of x and y in the inequality 1
-------> is not a viable solution
substitute the values of x and y in the inequality 2
--------> is ok
the point B is not a viable solution because does not satisfy the inequality 1
Answer:
And the critical value for the significance level used is:
Since the calculated value is less than the critical value we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the College graduation status and cola preference are independent
Step-by-step explanation:
For this case we want to test the following hypothesis:
Null hypothesis: College graduation status and cola preference are independent
Alternative hypothesis: College graduation status and cola preference are dependent
For this case we got a calculated statistic of:
And the critical value for the significance level used is:
Since the calculated value is less than the critical value we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the College graduation status and cola preference are independent
The height of Radon plant is 6.3 meters
<em><u>Solution:</u></em>
Given that, Allies plant has a height of 6 meters
Radon’s plant grows meters higher
To find: Height of Radon plant
From given information,
Height of Allies plant = 6 meters
Height of radon plant = + Height of Allies plant
Substituting the known value,
Thus Radon plant grows to height of 6.3 meters