A recipe calls for 3 cups of sugar and 9 cups of water. How many cups of water should be used with 12 cups of sugar?
2 answers:
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Answer:
The dimensions of the box is 3 ft by 3 ft by 30.22 ft.
The length of one side of the base of the given box is 3 ft.
The height of the box is 30.22 ft.
Step-by-step explanation:
Given that, a rectangular box with volume of 272 cubic ft.
Assume height of the box be h and the length of one side of the square base of the box is x.
Area of the base is =
The volume of the box is = area of the base × height
Therefore,
The cost per square foot for bottom is 20 cent.
The cost to construct of the bottom of the box is
=area of the bottom ×20
cents
The cost per square foot for top is 10 cent.
The cost to construct of the top of the box is
=area of the top ×10
cents
The cost per square foot for side is 1.5 cent.
The cost to construct of the sides of the box is
=area of the side ×1.5
cents
cents
Total cost =
Let
C
Putting the value of h
Differentiating with respect to x
Again differentiating with respect to x
Now set C'=0
Now
Since at x=3 , C''>0. So at x=3, C has a minimum value.
The length of one side of the base of the box is 3 ft.
The height of the box is
=30.22 ft.
The dimensions of the box is 3 ft by 3 ft by 30.22 ft.
Answer:
a) There are 9 outcomes.
b) **i have attached the tree diagram**
c) 1/9
d) 1/9
Step-by-step explanation:
Both events (choosing a shirt and choosing pants) are not mutually exclusive (disjoint). Meaning that both events can occur at the same time.
a) For a sequence of two events in which the first event can occur <em>m</em> ways and the second event can occur <em>n</em> ways, the events together can occur a total of <em>m</em> • <em>n</em> ways. So for this problem, you would do 3 • 3 which equals 9.
b) **tree diagram is attached**
c) Because there are two different events occurring (choosing a shirt and choosing pants) you need to multiply using the Multiplication Rule for Independent Events : P(A and B) = P(A) * P(B)
The probability of event A occurring (choosing a red shirt) is 1/3 and the probability of event B occurring (choosing brown pants) is also 1/3.
1/3 * 1/3 = 1/9
d) You would do the same thing here as part c.
The probability of event A occurring (choosing a blue shirt) is 1/3 and the probability of event B occurring (choosing blue pants) is again 1/3.
1/3 * 1/3 = 1/9
I hope this was helpful!! :)
Start with the original expression.
Use the Distributive Property — multiply by both
and
.
Combine the like terms — add up all the constants.
Reorder the terms.
Amelia must substitute 8 for the variable using parentheses. To simplify, Amelia must multiply 8 by 6. 8 is not a solution of the equation.
<h3>What is algebraic expression?</h3>
Algebraic expression are the expression which consist the variables, coefficients of variables and constants.
The algebraic expression are used represent the general problem in the mathematical way to solve them.
Amelia is using substitution to determine if 8 is a solution to the equation. The equation which is Amelia is solving for a = 8 is,
First, Amelia must substitute 8 for the variable using parentheses as,
To simplify, Amelia must. multiply 8 by 6.
The left hand side of the eqqation is not equal to the right hand side. Thus, 8 is not a solution of the equation.
Thus, Amelia must substitute 8 for the variable using parentheses. To simplify, Amelia must multiply 8 by 6. 8 is not a solution of the equation.
Learn more about the algebraic expression here;