Part 1 of 2
Challenge Josh plans to make birdhouses to sell at a craft fair. He has a sample of the wood he wants to use. The sample has area
square foot and weighs pound
The local hardware store sells the wood only by the square yard. There are 9 square feet in 1 square yard. What is the unit rate for pounds of the wood per square yard? If
Josh needs 3 square yards of the wood in all, how many pounds of the wood does he need?

An algebraic expression (w + 6) (w+8)  for the given rectangular sandbox represents the total area of the rectangular sandbox and cement walkway.

As given in the question,

For the given rectangular sandbox,

Let w represents the width of the rectangular sandbox.

Length of the rectangular sandbox is given by (w + 2 )foot

On the entire surrounding of the rectangular sandbox there is 3 foot wide cement walkway

Length of the rectangular sandbox including cement walkway

= w + 2 + 3 + 3

= w + 8

Width of the rectangular sandbox including cement walkway

= w + 3 + 3

= w + 6

Area of the rectangular sandbox including cement walkway is represented by the algebraic expression :

= Length × width

= (w + 6) (w+8)

Therefore, the given algebraic expression  (w + 6) (w+8) represents the area of the rectangular sandbox including cement walkway.

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For a set population, a parameter does not change. A parameter is a numerical value that describes some aspect of a population, such as the mean, median, or standard deviation.

It is a fixed value that represents the entire population and does not change as new data is collected.

If there are three different samples of the same size from a set population, it is possible to get three different values for the same statistic.

Because a sample is a subset of a population, the values of statistics calculated from samples will vary depending on the specific individuals or observations that are included in the sample. Even if the samples are of the same size, they will likely have different values for the statistics because of the randomness of sampling.

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The required value of k will the system of linear equations has infinite number of solutions is 8.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given set of equations is

kx + 4y = k - 4 ...(i)

16x + ky = k ...(ii)

We apply Cramer's rule to find the value of k.

Here,

D = k² - (16 × 4)

= k² - 64

= (k + 8) (k - 8)

D1 = k (k - 4) - 4k

= k² - 4k - 4k

= k² - 8k

= k (k - 8)

D2 = k² - 16 (k - 4)

= k² - 16k + 64

= (k - 8)²

= (k - 8) (k - 8)

For infinite number of solutions, we must have

D = 0 = D1 = D2

⇒ k = 8,

since (k - 8) is the common factor in D, D1 and D2.

∴ the required value of k is 8.

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Answer:

Step-by-step explanation:

The mistake that Sam made is that he tried to find the ratio of white to blue cars by combining the ratios of white to red cars and red to blue cars. However, this method does not work because the ratios are not independent of each other.

To find the correct ratio of white to blue cars, we need to use the fact that the ratio of red to blue cars is 5:2 and the ratio of white to red cars is 7:3. We can use these ratios to find the fraction of cars that are white and blue in the garage.

Firstly, we can find the fraction of red cars by taking the ratio of red to blue cars which is 5:2 and simplifying it to 5/7.

Now we can find the fraction of white cars by taking the ratio of white to red cars which is 7:3 and simplifying it to 7/10.

Now, to find the ratio of white to blue cars, we can subtract the fraction of red cars from the fraction of white cars.

So,

(7/10) - (5/7) = (7/10) - (5/7) * (3/3) = (7/10) - (15/21) = (721 - 1510) / (210) = (147 - 150) / 210 = -3/210

The correct ratio of white to blue cars is -3/210 which can be understood as NO white cars in the garage. Sam has made an error in his calculation.

The roots of the quadratic equation 3x^(2)+2x-1=0 are -1/3 and -1.

A quadratic equation is a type of polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The variable x is raised to the power of 2 (squared) in this equation, which gives the equation its name "quadratic", which comes from the Latin word "quadratum" meaning square.

Quadratic equations can have two solutions, known as roots or zeros, which can be found by using the quadratic formula: x = (-b ± √(b^2-4ac))/2a.

The solutions of a quadratic equation can also be found by factoring the equation or by completing the square method.

Quadratic equations are used in many areas of mathematics

The roots of the equation 3x^(2)+2x-1=0 are the values of x that make the equation true. To find the roots, we can use the quadratic formula: x = (-b ± √(b^2-4ac))/2a.

In this case, a = 3, b = 2, and c = -1, so we have:

x = (-2 ± √(2^2-43(-1)))/2*3

Simplifying the above expression we get:

x = (-2 ± √(4+12))/6

x = (-2 ± √(16))/6

x = (-2 ± 4)/6

This gives two possible solutions:

x = (-2+4)/6 or x = (-2-4)/6

x = 2/6 or x = -6/6

x = 1/3 or x = -1

So the roots of the equation 3x^(2)+2x-1=0 are: x = 1/3 or x = -1

Therefore, The roots of the quadratic equation 3x^(2)+2x-1=0 are -1/3 and -1.

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The exact amount of grass will depend on the size of the backyard, how large the pool and walkway will be, and any other features that will need to be included.

The amount of grass the Thompson family will need to plant in their backyard will depend on the size of their backyard, as well as the size of the pool and walkway they plan to install. The larger the backyard, the more grass they will need. The size of the pool and walkway will also factor into the equation, as these will take up space in the backyard and reduce the amount of grass that can be planted. Additionally, any other features, such as a patio or deck, will also need to be taken into account, as these will also reduce the amount of grass that can be planted. Ultimately, the exact size of the grass area in their backyard will depend on all of these factors and can only be determined once these details are known.

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The length of the hypotenuse of one of the triangles would be = 28 cm

A triangle is defined as the polygon that has three sides with the total angle of 180°.

The paper that was cut by Kaylee has a side of 20 cm by 20 cm. Using the Pythagorean formula the hypotenuse can be calculated as follows:

c² = a² + b²

where c = hypotenuse = X

a = 20

b = 20

C² = 20² + 20² = 400+400 = 800

c = √800

c = 28cm (approximately)

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Answer:

Step-by-step explanation:

Let's call the number of women in the club "W", the number of men in the club "M", and the number of children in the club "C".

We may deduce from the facts provided that:

The club has a membership of 60 people.

Because women make up half of the club's membership, W = 60 / 2 = 30.

Because there are three times as many women as males in the club, W = 3M.

The remaining members of the club are youngsters, therefore C = 60 - W - M

The male-to-child ratio is n:1.

We know that W=30 from the first equation.

We may use the second equation to replace in the value of W to get 3M = 30. So, M = 30/3 = 10.

We can calculate the number of children in the club by inserting the values of W and M: C = 60 - W - M = 60 - 30 - 10 = 20

Now we may calculate the child-to-male ratio: C:M = 20:10 = 2:1. As a result, the value of n is 2.

Answer:

n=2

Step-by-step explanation:

Total 60 people in the club

Half are women ==> number of women = 60/2 = 30

Rest are are  men and women so rest = 30

This number is 3 times number of men

Number of men = 30/3 = 10

Number of children = 30 -10 = 20

Ratio of children to men: 20:10 or 2:1

So n= 2

A variable's value that, when substituted into the equation, results in a true assertion is known as the solution. The process of finding the solution to an equation is called solving the equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                      Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

To insert a value into an equation, what does that mean?

By solving for one variable, you can then enter that expression into the other equation using the substitution approach.

                         Making sure you are always substituting equivalent values is crucial in this situation. For instance: Sean is five years older than his daughter, who is his son's age.

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Answer:

m<1=41°

Step-by-step explanation:

m<1 and m<4 are vertically opposite angles, making them equal. We know m<4=41°, so we can say m<1=41° too.

Answer: 17

Step-by-step explanation:

Two negatives make a positive

[tex]-6+23[/tex]

Which is the same as

[tex]23-6=17[/tex]

Answer:

Step-by-step explanation:

The answer will be 17:

So since -6 is multiplied to -23 the negative rule needs to be applied ( a - (-b = a+b) so -6 - (-23) will now turn into -6 + 23.

Answer:

Volume of a sphere is 268.08yd³

Step-by-step explanation:

To Find the volume of a sphere we apply the given formula,

[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]

In the given information the radius is 4

Hence the volume of the sphere is,

[tex]Volume=\frac{4}{3} X3.14X4^{3}[/tex]

[tex]Volume = 268.08yd^{3}[/tex]

The binomial formula to find the coefficient of the t^17q^2 term in the expansion of (t+2g) ¹⁹ is 32.06.

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Answer:

y=3x+18

Step-by-step explanation:

the slope is 3

y-6=3(x+4)

y-6=3x+12

y=3x+18

The first step in solving a system of equations is to solve one of the equations with a variable.

A collection of one or more linear equations containing the same variables is known as a system of equations. When the graphs do not meet, there is no solution to a system of linear equations. When the graphs of the equations overlap at all locations, there can be an endless number of solutions or just one when they do not.

Solving one of the equations for one of the variables in terms of the other variable is the first step in solving a system of equations by substitution. In order to eliminate one of the variables and generate a more straightforward equation that can be solved for the remaining variable, this expression can then be added to the other equations.

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Answer:

a. 2

b. 12

c. 15

d. See below

Step-by-step explanation:

It  takes 6 people 20 days to paint 4 houses  [A]

More the people less for same number of houses ==> less the time
More the people working for same time ==> more the number of houses

a. 3 people working for 20 days can finish only half of 4 houses = 2 houses

b. To paint 4 houses in 10 days will require twice the manpower which is 2 x 6 = 12 people

c. For 8 people to paint 4 houses, number of days = 6/8 x 20 = 15

d

People                                Days                            Houses

6                                           20                                    4

1                                            120  (2 x 20)                    4    

1                                              30  (  120/4)                    1

6                                             60                                  12  (3 x 20)

4                                             60                                   8   (4/6 x 12)  

Use the following info to complete the table

1 person will take 6x20 = 120 days to paint 4 houses

To paint 1 house, this time will be 1/4th = 120/4 = 30 days

So it takes 1 person 30 days to paint 1 house

Answer: 340

There's 7 days in a week. Meaning that you have to do 45 x 7 which is 315. since theres a 25 dollar gps fee you have to add 315 to 25 which is equal to 340

Answer: 144 took the quiz

Step-by-step explanation:

Answer: 408 length

Step-by-step explanation:

528 inches of the kitchen subtract the width which is 120inches and you get 108 so add the width an length and you get 528

It would take them 2/W hours, or approximately 1 hour and 36 minutes, to mow the lawn working together.'

What is rate ?

The rate is a measure of how much of a quantity is completed or changed per unit of time. It is often represented as a ratio of the amount of work done to the amount of time it takes to complete the work. For example, in the context of mowing a lawn, the rate could be expressed as the amount of lawn mowed per hour.

Let's call the amount of work required to mow a lawn "W".

Molly can do it in 3 hours, so her rate of work is W/3.

Her little brother can do it in 6 hours, so his rate of work is W/6.

When they work together, their combined rate of work is (W/3) + (W/6) = W/2.

So, working together, they can mow the lawn in W/2 hours, or 2/W hours.

Therefore, it would take them 2/W hours, or approximately 1 hour and 36 minutes, to mow the lawn working together.

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It would take them 2/W hours, or approximately 1 hour and 36 minutes, to mow the lawn working together.'

The rate is a measure of how much of a quantity is completed or changed per unit of time. It is often represented as a ratio of the amount of work done to the amount of time it takes to complete the work. For example, in the context of mowing a lawn, the rate could be expressed as the amount of lawn mowed per hour.

Let's call the amount of work required to mow a lawn "W".

Molly can do it in 3 hours, so her rate of work is W/3.

Her little brother can do it in 6 hours, so his rate of work is W/6.

When they work together, their combined rate of work is (W/3) + (W/6) = W/2.

So, working together, they can mow the lawn in W/2 hours, or 2/W hours.

Therefore, it would take them 2/W hours, or approximately 1 hour and 36 minutes, to mow the lawn working together.

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when two values are multiplied together, the result will be a new value that is the sum of the two original values multiplied by each other. Therefore, the product of XA and X+b is X2 + Xb.

The product of XA and X+b is XA(X+b).

XA(X+b) = X(A)(X+b) = X2 + Xb

The product of XA and X+b can be expressed as XA(X+b). This is the same as X(A)(X+b), which can be further expanded to X2 + Xb. This means that when two values, XA and X+b, are multiplied together, the result is a new value that is the sum of X2 and Xb. In other words, the product of XA and X+b is the sum of X multiplied by itself and X multiplied by b. This means that when two values are multiplied together, the result will be a new value that is the sum of the two original values multiplied by each other. Therefore, the product of XA and X+b is X2 + Xb.

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Answer:

Step-by-step explanation:

x represents the numbers of months and y represents the insect

population.

We are told that:

  1) we start with 125 insects, and

 2) the rascals double each month

Lets use m for months they double from the start of 125 insects.).

We can form an equation that will predict the insect population as a function of the numbers of months, m, from the start (125 insects).

Month 0 is 125

Month 1 would be 125*(1+1) or 125*2

 We can rewrite this as 125*2^1

Month 2                 125*2^2  [It dounbes again]

Month 3                  125^3     [It dounbes yet again]

Month 4                  125^4     [And again]

Month 5                  125^5     [And so on to Infinity and Beyond]

The pattern is 125*(2)^m. where m is months since the starting month of 0.

Insect Population(m) = 125*(2)^m

See the attached graph.

To determine the separation between two points in a coordinate plane, we analyze the distance formula. We can use this to study the connections between points and resolve mathematical issues.

A mathematical method called the distance formula is used to determine how far apart two points in a coordinate plane are from one another. The Pythagorean Theorem, which states that the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, is the source of the formula. We must first ascertain the coordinates of each point in order to compute the distance between them. The first point's coordinates are (x1, y1), and the second point's coordinates are (x2, y2). then, the separation between The formula d = (((x2-x1)2 + (y2-y1)2) can be used to identify the two points. This formula can be applied to several mathematical issues, including the analysis of point relationships.

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Answer:

Shorter leg of triangle: 4cm

Step-by-step explanation:

So, we are told   is the longer leg, let's say this is a. [tex]4\sqrt{15} = \sqrt{240}[/tex], the Pythagorean theorem is [tex]a^2+b^2=c^2[/tex] , we'll say b = shortest leg, which is what we're solving for.

Since the hypotenuse (c), is 4 times b I changed it to 4b in my equation. [tex]\sqrt{240} + b =4b[/tex], square this to get [tex]240 + b^2 = 16b^2[/tex], -b^2 on both sides, [tex]240 = 15b^2[/tex]  then divide by 15. [tex]16=b^2[/tex] , use square root and you get 4 = b. To find hypotenuse, which isn't needed for your answer multiply by 4.

Hypotenuse: 16 cm

Shorter leg: 4 cm

The value of k if one of the zeroes of the quadratic polynomial kx2 kx 1 is 3 is -2 or 2.

A quadratic polynomial is a polynomial of degree 2, meaning it has the form ax^2 + bx + c, where a, b, and c are constants and a is not equal to zero. It is also known as a second-degree polynomial. This type of polynomial is commonly used for modelling physical phenomena, such as the trajectory of a projectile or the vibration of a spring. A quadratic polynomial can also be used to solve equations that involve x2, such as the quadratic formula.

The quadratic equation kx2 kx 1 0 has two solutions, or zeroes, which are given by the quadratic formula: x = (k ± √(k2 - 4))/2. If one of the solutions is 3, then we can substitute 3 in for x and solve for k.

3 = (k ± √(k2 - 4))/2

6 = (k ± √(k2 - 4))

6 - (k ± √(k2 - 4)) = 0

k2 - 4 ± k - 6 = 0

k2 ± k - 2 = 0

k ± 2 = 0

k = -2 or k = 2.

Therefore, the value of k if one of the zeroes of the quadratic polynomial kx2 kx 1 is 3 is -2 or 2.

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Segment QS is not a radius of Circle P because it is diameter.

x + y = 1

2x - y = 4

The answer is: (5/3; -2/3)

The value of the expression  0.3k - 4m is 14. 14 is a constant term.

What is an expression?

There are numerous branches of mathematics. Arithmetic is the branch of mathematics that deals with numbers and their operations. Arithmetic taught us how to add, subtract, multiply, and divide two or more numbers.

An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4a - 5 is an expression in which the terms 4m and 5 are separated by the arithmetic sign - and a is the variable of the given expression.

Given expression is  0.3k - 4m.

To find the value of  0.3k - 4m, when k =20 and m =-2 put the values in the given expression.

Putting k =20 and m =-2 in  0.3k - 4m

0.3k - 4m

= 0.3 × 20 - 4 × (-2)

=6.0 + 8

= 14

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The diapers of brand B that cost $39.99 for 100 diapers is a better buy that the diapers of brand A that cost $24.94 for 60 diapers.

We must utilize the unitary method in this elementary algebra issue, which is nothing more than figuring out the price per diaper in both of the cases. The cost per diaper from Brand A which has 60 diapers worth $24.94 is to be determined. As a result, since 60 diapers cost $24.94, 1 diaper must cost $24.94/60, or around 42 cents per diaper. When we repeat the job for the Brand B, we see that 100 diapers cost $39.99, making 1 diaper cost $39.99/100, or 40 cents per diaper. Now that each diaper costs less when bought from Brand B, it turns out to be a superior purchase.

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18 3/4 because 600/32

Answer:

C) 75

Step-by-step explanation:

Put the set of number in order from biggest to smallest.

Then you will see that your two middle numbers are 75 and 75. Add 75 + 75= 150 then divide that by 2. Which equals 75.