There are 12 girls and 18 boys in the class what is the largest number of groups they can split into and have the same number of boys and girls on each team?

we know that

The button has the shape of a circle

the circumference of a circle is equal to

[tex]C=\pi D[/tex]

where

D is the diameter of a circle

Step [tex]1[/tex]

Find the circumference of the 1-inch button

In this case we have that the diameter is equal to

[tex]D1=1\ in[/tex]

substitute the value in the formula

[tex]C1=\pi*1= \pi\ in[/tex]

Step [tex]2[/tex]

Find the circumference of the 3/8-inch button

In this case we have that the diameter is equal to

[tex]D2=3/8\ in[/tex]

substitute the value in the formula

[tex]C2=\pi*3/8= 3\pi/8\ in[/tex]

Step [tex]3[/tex]

Find the difference of their circumferences

[tex]C1-C2=\pi-3\pi/8=5\pi/8\ in[/tex]

therefore

the answer is

[tex]5\pi/8\ in[/tex]

average for 4 months total needs to equal 55*4 = 220 minutes

43 + 62 + 57 = 162

220-162 = 58

 58 minutes

We want to make a table of ordered pairs for the given equation, and then graph two of these points to graph the equation.

We have the equation:

y = (-1/3)*x + 1

We can make the table:

[tex]\left[\begin{array}{ccc}x&y\\-1&\\0&\\1&\\3&\end{array}\right][/tex]

To complete the table, we just need to evaluate the given equation in these x-values. We will get:

y(-1) = (-1/3)*(-1) + 1 = 1/3 + 1 = 4/3

y(0) = (-1/3)*0 + 1 = 1

y(1) = (-1/3)*1 + 1 = 2/3

y(3) = (-1/3)*3 + 1 = 0

Now we just complete the table with the values that we got:

[tex]\left[\begin{array}{ccc}x&y\\-1&4/3\\0&1\\1&2/3\\3&0\end{array}\right][/tex]

Now to graph the equation, we can graph two of these points, for simplicity I will graph (0, 1) and (3, 0).

Once the points are graphed, we just need to draw a line that connects them. The graph can be seen below.

If you want to learn more, you can read:

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Answer:

0.71

Step-by-step explanation:

Final answer:

To solve the algebraic equation stated as 'six times the sum of a number and 7 equals 2,' we distribute, subtract 42 from both sides, and then divide by 6, leading to the solution x = -20/3 or approximately -6.67.

Explanation:

The question involves solving an algebraic equation to find an unknown number. When the problem states that six times the sum of a number and 7 equals 2, it can be represented mathematically as 6(x + 7) = 2. To find the value of x, you need to follow these steps:

First, distribute the 6 to both x and 7, which gives 6x + 42 = 2.

Next, to isolate the variable term (6x), you would subtract 42 from both sides of the equation, resulting in 6x = 2 - 42, which simplifies to 6x = -40.

Finally, to find the value of x, divide both sides by 6, giving x = -40 / 6, which simplifies to x = -20 / 3 or approximately x = -6.67.

Graph is a representation of data by using the vertices and edges to convert the data in easily understandable form. Graph contains two axis, a vertical axis and a horizontal axis. These axis are also denoted as x axis and y axis.

In the given question we have to find the value of k using the points of graph on x axis and y axis.

Given

The graph passes through [tex]\rm\:A (4, -80)[/tex]

Value of [tex]\rm\;x= 4[/tex]

Value of [tex]\rm y=-80[/tex]

The value of k can be determined by the graphical intersection of the points on x axis and y axis. By putting the value of x and y in the given equation we got:

                                      [tex]\begin{aligned}\rm\;y&=kx\\\\k(4)&=-80\\\\k&=\dfrac{-80}{4} \\\\k&=-20\end[/tex]

Therefore by putting the values of x and y we found that the value of [tex]\rm\:k=-20[/tex]

Learn more about graphs here:

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To find the enrollment this year, calculate 12% of last year's enrollment and add it to the enrollment from last year. The enrollment this year is 17,360.

To find the enrollment this year, we need to calculate 12% of last year's enrollment and add it to the enrollment from last year.

Therefore, the enrollment this year is 17,360.

A peptide bond forms between two amino acids by a dehydration synthesis reaction. The number of peptide bonds in a polypeptide is always one less than the total number of amino acids. Therefore, in a polypeptide with 45 amino acids, there would be 44 peptide bonds.

A peptide bond is a chemical bond that forms between two amino acids when a carboxyl group of one amino acid reacts with the amino group of the other amino acid, releasing a molecule of water. This is a dehydration synthesis reaction, and it is how amino acids are linked together to form a polypeptide.

In a polypeptide chain, the number of peptide bonds present is always one less than the total number of amino acids. This is because each amino acid has one peptide bond with the next amino acid in the chain, except the last one. Hence, for 45 amino acids, there would be 44 peptide bonds.

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Final answer:

There are a total of 93 musicians in both the String and Brass sections of the Symphony Orchestra, with 29 in the Brass and 64 in the String section.

Explanation:

To determine how many musicians are in both the String and Brass sections of the Symphony Orchestra, we start by noting that there are 29 musicians in the Brass section. Since there are 35 more musicians in the String section, we add 35 to the number of Brass musicians to find the total in the String section:

Answer:

Quadrant

Step-by-step explanation:

The probability that it will snow and Amy will be late for school is found by multiplying the individual probabilities of each event, which are 60% and 10% respectively, resulting in 6%.

The probability that both events (it snowing and Amy being late for school) will occur is found by multiplying the probabilities of each independent event. As Amy states, there is a 60% chance of snow (which can be expressed as a probability of 0.60) and a 10% chance she will be late for school (expressed as a probability of 0.10). To find the probability that both events happen, we calculate:

Probability(snow and late) = Probability(snow) × Probability(late)

Probability(snow and late) = 0.60 × 0.10 = 0.06

Therefore, the probability that it will snow tomorrow and Amy will be late for school is 6%.