Maggie's brother is 3 years younger than twice her age. The sum of their age is 24. How old is Maggie?

y = 72.

Solving the System of Equations

To find the solution of the system of equations given by 2x - 2y = -38 and -5x - 4y = 23, we can use the method of elimination or substitution. In the method of elimination, we can multiple the first equation by 2 to make the coefficients of y the same, which would give us 4x - 4y = -76. Then, we could add this new equation to the second given equation (-5x - 4y = 23) to eliminate the y variable:

4x - 4y = -76 (First equation multiplied by 2)

-5x - 4y = 23 (Second given equation)

Adding these equations together, we get:
-1x + 0y = -53
or simply
-x = -53, from which x = 53.

Next, we can substitute x back into either of the original equations to solve for y. For example, using 2x - 2y = -38:

2(53) - 2y = -38

106 - 2y = -38

-2y = -38 - 106

-2y = -144

y = 72

Therefore, the solution to the system of equations is x = 53 and y = 72.

Andrew should determine the number of bookshelves and tables to make by using linear programming to solve for the variables given the constraints of his time, material costs, and profits. The optimal solution lies where the constraints intersect within the feasible region.

The student inquired about how many bookshelves and tables Andrew should make in order to maximize profit, given the constraints of time, material cost, and the profit from each item sold. This is a typical problem that can be solved using linear programming, a method in mathematics to achieve the best outcome given a series of linear constraints.

First, let us define two variables: x for the number of bookshelves and y for the number of tables. The constraints given by Andrew's situation are:

x + y \<= 18 (time constraint to make the furniture)

20x + 45y \<= 600 (cost constraint for materials)

Profit function to maximize: P = 60x + 100y

To maximize the profit P, we need to solve for x and y within the given constraints. After setting up the equations, we can graph the constraints and find the feasible region. The solution will be at a vertex of the feasible region, given by the intersection of the constraints. Andrew can use methods like the graphical method, the simplex method, or an algebraic method to find the optimal numbers of bookshelves (x) and tables (y) to maximize his profit.

Answer:

C)

Step-by-step explanation:

both of the equations equal y so, the two equations equal eachother

133=x + (x+5) + (x+14)

133 = 3x+19

3x=114

x= 114/3 =38

5+38 =43

38+14 =52

check: 38 +43 +52 = 133

3 sides are : 38, 43 & 52

The decimal form of the number 4 3/7 is, 4.43

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The number is,

⇒ 4 3/7

Now, We can change in decimal form as;

⇒ 4 3/7

⇒ 31 / 7

⇒ 4.43

Thus, We get;

⇒ 4 3/7 = 4.43

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Answer:

you can make 12 bouquets...each containing 5 roses, 7 daisies, and 2 lilies

Step-by-step explanation:

Answer:

standard form y = -x + b.

Step-by-step explanation:

Given : Graph and points (0,4)(4,0).

To find : Standard form of equation .

Solution : We have given that  points (0,4)(4,0).

Let [tex]x_{1}[/tex] = 0 ,   [tex]x_{2}[/tex] = 4

[tex]y_{1}[/tex] =4  ,      [tex]y_{2}[/tex] = 0.

Slope = [tex]\frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }[/tex].

Plugging values

Slope = [tex]\frac{0 - 4}{4 - 0}[/tex].

Slope = -1 .

Standard form y = m x + b

                        y = -1 x + b.

Plug (0,4)  

 4 = -1 ( 0)+ b

4 = b .

Now , plugging values b= 4 , m = -1.

y = -x + b.

Therefore, standard form y = -x + b.

Answer:

The probability is 42%

Step-by-step explanation:

The probability that A and B, two independent events, happens is given by:

P=P(A)*P(B)

In this case, lets call A the event in which there are sunny weather tomorrow and B the event in which Tara goes to the beach. Taking into account that they are independent, that means that one event doesn't affect the other, the probability P that it will be sunny tomorrow and Tara will go to the beach is:

P=0.7*0.6=0.42

Multiplying P by 100, we get:

P=42%

So, the probability that it will be sunny tomorrow and Tara will go to the beach is 42%

The number of gallons of paint to cover the entire wall will be 3 gallons of paint.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

If 1/2 gallon of paint covers 1/6 of a wall. Then the division of the numbers 1/2 and 1/6 will be given by putting a division sign between them. Then the number of gallons of paint is calculated as,

⇒ (1/2) / (1/6)

⇒ (1/2) x 6

⇒ 3

The number of gallons of paint to cover the whole wall will be 3 gallons of paint.

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To fit data to a normal distribution and estimate population percentages, calculate the mean and standard deviation for the data set, use these values to construct a normal distribution, and apply the empirical rule and confidence intervals to estimate population percentages.

To use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages, you will need to understand key statistical principles such as standard deviation, the mean, and the normal distribution curve.

The mean, which is an average of all the values in a data set, provides a central value. The standard deviation represents the spread of the data around this mean. A lower standard deviation indicates that the values are closer to the mean, while a higher standard deviation indicates a wider spread.

A normal distribution, also known as a bell curve, shows how values in a data set are dispersed around the mean. The properties of the normal distribution (68% of data within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations) are known as the empirical rule or the 68-95-99.7 rule.

To estimate population percentages using the mean and standard deviation, you construct a confidence interval. This range provides an estimate of where you expect the true population parameter to lie with a certain level of confidence. For example, a 95% confidence interval means that you can be 95% confident that the true population mean lies within this interval.

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Answer:

[tex]l=\frac{P}{2}-w[/tex]

Step-by-step explanation:

we know that

The formula for the perimeter of a rectangle is equal to

[tex]P=2(w+l)[/tex]

where

l is the length

w is the width

Solve for l

That means ----> Isolate the variable l

Divide by 2 both sides

[tex]\frac{P}{2}=\frac{2(w+l)}{2}[/tex]

Simplify right side

[tex]\frac{P}{2}=w+l[/tex]

Subtract w both sides

[tex]\frac{P}{2}-w=w+l-w[/tex]

Simplify right side

[tex]\frac{P}{2}-w=l[/tex]

Rewrite

[tex]l=\frac{P}{2}-w[/tex]

Answer:Solve P = 2l + 2w for w.

The first step is to isolate the variable term, 2w.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

To simplify a fraction by dividing both top and bottom by the same factor.

So,  pm/ pn equals to m/n .

If any variable or factor is present in both numerator and denominator. Then, these variables or factor are cancelled out each other.

In expression pm/pn , we observed that variable p is present in both numerator and denominator. So, variable p is cancelled out to each other.

Therefore,  pm/pn = m/n

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