You have to bake a lot of brownies for your 6th-grade fundraiser! Although you have plenty of flour, cocoa, milk, and oil, you only have 8 1/2 sticks of butter. You need to know how many batches you can make, based upon your limited amount of butter. You can cook partial batches to use up every bit of butter and make the most brownies possible. Each batch needs 3/4 of a stick of butter. 4 How many batches of brownies can you bake? Justify your answer using equations, models, and/or words to explain your mathematical reasoning.

To solve the equation y = 2mx + 9b for x, subtract 9b from both sides, and then divide by 2m. The result is x = (y - 9b) / (2m). This manipulation is emblematic of solving linear equations which are foundational in algebra.

The student is asking to solve the linear equation y = 2mx + 9b for the variable x. This type of problem involves algebraic manipulation to isolate the variable of interest. Here are the steps to solve for x:

In this case, y is the dependent variable, m is the slope of the line, and b would be the y-intercept if this equation were graphed on a coordinate plane. To better understand this concept, let's take the specific equation y = 9 + 3x as an example which is a linear equation with b set to 9 and m set to 3.

To visualize this equation, one can construct a table of values by selecting various x values and calculating the corresponding y values. Then, these points are plotted on a graph to show the linear relationship. This process is depicted in Table A1 and Figure A1, with the equation illustrated in a graph.

The general form of a linear equation is y = mx + b, where m represents the slope and b the y-intercept. In these exercises, understanding and manipulating this form helps us find relationships between variables and understand how changes in one variable affect another.

area of a square = S^2

 S^2 = 123

S = sqrt(123)

S = 11.0905

 rounded to nearest tenth = 11.1 feet

The width of the rectangle is 3 inches less than twice the length, which is represented by L. The algebraic expression for the width is W = 2L - 3.

The width of a rectangle is described in the problem as being 3 inches less than twice the length of the rectangle. If the length of the rectangle is denoted by L, the algebraic expression to represent the width (W) can be written as:

W = 2L - 3

To clarify, this expression means that whatever the length L is, you would double it (that's the 2L part), and then subtract 3 inches to find the width of the rectangle.

The solution to the given inequality problem is;

q < 56

We are given the equation;

q + 12 - 2(q - 22) > 0

Step 1; Using distributive property, distribute 6 to the numbers inside the bracket to get;

q + 12 - 2q + 44 > 0

Step 2; Combining similar terms on the left side and simplifying gives us;

56 - q > 0

Step 3; Using addition property of equality, add q to both sides;

56 - q + q > 0 + q

q < 56

Thus, the final solution is q < 56

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The statement given is

  The population of Vermont was estimated to be about 620,000 in 2008.

Exact population of Vermont in 2008

                   = 615,000 ≤ A number between ≤ 620,000

                    =[615000, 620000]

The equation 6(a+3) = 18+6a is an identity after canceling out like terms on both sides, which implies that the solution for 'a' is all real numbers.

To solve for a in the equation 6(a+3) = 18+6a, we begin by expanding the left side of the equation:

6a + 18 = 18 + 6a

We notice that there are terms on both sides of the equation that can be cancelled out. The 6a on the left side can be subtracted from both sides, as well as the constant 18.

After cancelling out these terms, we are left with:

0 = 0

This equation suggests that the original equation is an identity, meaning that the value of a can be any real number, as the original equation holds true for all values of a.

The possible range of numbers of cars Ken might have is 0 ≤ Ken ≤ 24.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Jed has 25 toy cars.

Kai has 32 you cars.

Since Ken has fewer cars than either Jed or Kai, the maximum number of cars Ken could have is 24 (if both Jed and Kai give him one car each).

The minimum number of cars Ken could have is 0 (if both Jed and Kai have more cars than Ken).

So the possible range of numbers of cars Ken might have is 0 ≤ Ken ≤ 24.

Hence,  the possible range of numbers of cars Ken might have is 0 ≤ Ken ≤ 24.

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Final answer:

The current I in the AC circuit equation V = IZ is found by complex division and is equal to 1/5 + 3/5i when V = 1+i and Z=2-i.

Explanation:

To find the current I in the equation V = IZ where V = 1+i and Z=2-i, we need to solve for I using complex division. This process involves conjugating the denominator and then performing standard multiplication of complex numbers.

Step-by-step solution:

Therefore, the current I is 1/5 + 3/5i.

The angular speed of the wheel is 3960 rad/min and the revolutions per minute is 630 rpm.

The velocity of the truck is 60 mph. We need to convert this speed to inches per minute.

1 mile = 63360 in, 1 hour = 60 minutes

Hence:

60 mph = (60 mile * 63360 in/mi) / (1 hr * 60 min/hr) = 63360 in/min

The diameter = 32 in, hence radius = 32/2 = 16 in

The angular speed = 63360 in/min ÷ 16 in = 3960 rad/min

Revolution per minute = 3960 rad/min ÷ 2π = 630 rpm

Hence the angular speed of the wheel is 3960 rad/min and the revolutions per minute is 630 rpm.

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The wheels make approximately  52.55  revolutions per minute.

To find the angular speed of the wheels in radians per minute, we first need to find the linear speed of a point on the edge of the wheel.

The formula to calculate the linear speed (v) is given by:

[tex]\[ v = r \times \omega \][/tex]

Where:

-  v  is the linear speed,

-  r  is the radius of the wheel, and

- [tex]\( \omega \)[/tex] is the angular speed in radians per second.

Given that the diameter of the wheels is 32 inches, the radius (r ) is half of the diameter, so [tex]\( r = \frac{32}{2} = 16 \)[/tex] inches.

We are given the speed of the truck,  v = 60  mi/h. To convert this to inches per minute, we need to convert miles to inches and hours to minutes:

[tex]\[ 60 \text{ miles/h} = 60 \times 5280 \text{ inches/60 minutes} = 5280 \text{ inches/minute} \][/tex]

Now, we can rearrange the formula to solve for [tex]\( \omega \):[/tex]

[tex]\[ \omega = \frac{v}{r} \][/tex]

Substituting the known values:

[tex]\[ \omega = \frac{5280 \text{ inches/minute}}{16 \text{ inches}} \]\[ \omega = 330 \text{ radians/minute} \][/tex]

So, the angular speed of the wheels is 330 radians per minute.

Now, to find the number of revolutions per minute (rpm), we need to convert the angular speed from radians per minute to revolutions per minute. Since [tex]\( 2\pi \)[/tex] radians is equal to one revolution, we have:

[tex]\[ \text{Revolutions per minute (rpm)} = \frac{\omega}{2\pi} \][/tex]

Substituting the value of [tex]\( \omega \):[/tex]

[tex]\[ \text{rpm} = \frac{330}{2\pi} \]\[ \text{rpm} \approx \frac{330}{6.28} \approx 52.55 \][/tex]

So, the wheels make approximately  52.55  revolutions per minute.

To answer the question, first, multiply the total leftover dip by the portion that Jim divided. Then, divide this result by the number of friends. Therefore, each friend gets 3/10 of a cup of dip.

The subject of this question clearly falls under the category of Mathematics, more specifically, the concept of fractions. The problem here is to find out how much dip each friend gets if 4/5 of the 3/4 cup of leftover dip is divided equally between two friends.

To solve this, we need to perform multiplication of fractions, and then division by the number of friends. Step 1: Multiply 3/4 (leftover dip) by 4/5 (portion that Jim divided). Doing this, we get (3/4) * (4/5) = 12/20, which simplifies to 3/5 cup. This is the amount of dip Jim divided.

Step 2: Divide this result by 2 (number of friends). So, (3/5) / 2 = 3/10. Hence, each friend gets 3/10 of a cup of dip.

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divide the total gallons by the number of containers

40.8 / 8 = 5.1 gallons each

Answer:

Step-by-step explanation:

[tex]6x^2-17x+5[/tex]

This can be written as

[tex]6x^2-15x-2x+5[/tex]

Because -15-2=-17 and also (-15)(-2)=30

so now we have two pairs

[tex](6x^2-15x)+(-2x+5)[/tex]

Take out GCF from each pair

[tex]3x(2x-5)-1(2x-5)[/tex]

since (2x-5) is now the common factor so final factored form

[tex](3x-1)(2x-5)[/tex]

Answer:

The first steps in the solution to the equation [tex]\log_2 x + \log_2 (x-6) = 4[/tex] is, [tex]\log_2 x(x-6) = 4[/tex]

Step-by-step explanation:

Given the equation:  [tex]\log_2 x + \log_2 (x-6) = 4[/tex]

Using logarithmic laws;

[tex]loa_b x + \log_b y = \log_b (xy)[/tex]

then;

[tex]\log_2 x(x-6) = 4[/tex]

Therefore, the first steps in the solution to the equation [tex]\log_2 x + \log_2 (x-6) = 4[/tex] is, [tex]\log_2 x(x-6) = 4[/tex]

Answer: log2(x(x-6))=4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To me, it seems like 14 is just telling u something.....and 15. a)30% b)75%

hope this helps :)

Answer: 1,900 street tacos and 510 Cuban sandwiches.

Explanation:

Alexi=20*80=1,600

Tony = 17*30=510   3x00 = 300 street tacos

1,600 + 300 = 1,900 street tacos and 510 Cuban sandwiches.

since the thousands place is a 3 which is lower than a 5

 it would be rounded to 20,000

Answer:

Nearest ten thousands 20000,

Step-by-step explanation:

Given  :23,569

To find : Rounded to the nearest ten thousands

Solution: We have given that 23,569

We can write it as 23,569

Step 1 : Identify the ten thousands digit 2 in 23,569

Step 2: Identify the next smallest place value 3 in 23,569

Step 2: We can the digit less  than five, so it would be rounded down

Step 3 : The ten thousands remain same   and Every digit after becomes a zero.

Step 4 : Number become 20000.

Therefore,  nearest ten thousands 20000,

The total cost of the haircut including the tip is $20.70. 18*15%=2.70+18=20.7.

Hope this helps:)

Answer:

$20.70

Step-by-step explanation:

Turn the % to a decimal.

15%= 15/100 = 0.15

Multiply the total and decimal.

18.00 x 0.15

= 2.70

Add the total to the sum.

18.00 + 2.70

= 20.70

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The number that fits all the given criteria is 3955, where all digits are odd, the last two add to 10, the first and last to 8, and the first two to 12.

To find a number where all digits are odd, the last two digits add up to make ten, the first and last digits add up to eight, and the first two digits add up to twelve, we can use a process of elimination and reasoning.

Therefore, the number is 3955.