In a seventh grade class, 14 out of 30 students are boys. In simplest terms, what is the ratio of the number of boys to the number of girls in this grade?

Final answer:

The inequalities that accurately model the situation where Adam needs fewer than 30 cones, with at least a dozen large ones, are y≥12, x+y≤30, and x≥0. These inequalities represent the constraints on large cones, total cones, and the feasibility of small cones respectively.

Explanation:

The student asks about modeling a situation with inequalities where Adam needs both small and large cones for soccer practice, with fewer than 30 cones total and at least a dozen large ones. The variables x represent the number of small cones and y represent the number of large cones. To accurately model this scenario, the following inequalities are correct:

   y≥12: Adam needs at least a dozen large cones.

   x+y≤30: The total number of cones, both small and large, is less than or equal to 30.

   x≥0: The number of small cones can be zero but not negative, as you can't have a negative number of cones.

Thus, the inequalities that model this situation are y≥12, x+y≤30, and x≥0. These inequalities account for the constraints on the number of large cones needed, the total limit on cones, and the feasibility of the number of small cones respectively.

Equation in slope intercept form will be 5x + 20.

It is given that to join a online learning community, startup fee is $ 20 and the monthly fee is $ 5.

We have to write an equation in slope-intercept form.

What is the equation for slope intercept form ?

Equation for slope intercept form is y = mx + c.

Let's assume ;

y = total cost

x = months

c = startup fee

∵ equation in a slope intercept form is y = mx + c.

Putting the values , we get ;

y = 5x + 20

Thus the equation in slope intercept form will be y = 5x + 20.

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The smallest odd number from the list provided (6, 4, 3, 8) is 3, as it is the only number that is not divisible by 2 and is therefore classified as an odd number.

The question asks to identify the smallest odd number from a given list of numbers: 6, 4, 3, and 8. We start by defining what an odd number is. An odd number is an integer which is not divisible by 2, meaning it cannot be evenly divided into two equal whole numbers. With this definition in mind, we can examine each number in the list.

Gathering only the odd numbers from the list, we have just one, which is the number 3. Since this is the only odd number, it is by default also the smallest odd number from the list.

Answer:

Step-by-step explanation:

This question wants us to write the given line in a slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. We already know the slope, which is 5, so just insert 5 in for m. We get y = 5x = b. We're not done, however, we still need to solve for b. (3,13) equals 5(3)+b=13. This gives us our final result of b=-2. insert this into the equation for b, and the equation becomes y = 5x -2.

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x = long piece

y = short piece

 x = 2y+1

2y +1 +y =16

3y +1 = 16

3y =15

y = 15/3 =5

 y = 5

x = 2(5) +1 = 11

short piece is 5 feet

long piece is 11 feet

The value of x is 4/5 in the given equation 6x-5=7-9x

Two or more expressions with an Equal sign is called as Equation.

The given equation is  6x-5=7-9x

Six times of x minus five equal to seven minus nine times of x

Take all the variables terms on one side and constants on other side.

6x+9x=7+5

15x=12

Divide both sides by 15

x=12/15

The GCF of 12 and 15 is 3

So divide numerator and denominator by 3

x=4/5

Hence, the value of x is 4/5 in the given equation 6x-5=7-9x

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The solution of expression is, r = 1

We have to give that,

An expression to solve,

14 = 8 - 6r

Now, Simplify the expression by combining the like terms as,

14 = 8 - 6r

Add 6r on both sides,

14 + 6r = 8 - 6r + 6r

14 + 6r = 8

Subtract 14 on both sides,

6r = 8 - 14

6r = 6

Divide into both sides by 6,

r = 6/6

r = 1

Therefore, The solution is, r = 1

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Final answer:

The item with an original price of $480 is marked down twice, first by 10%, reducing it to $432, and then by another 20%, making the final sale price $345.60.

Explanation:

The original price of the item is $480. The first markdown of 10% reduces the price by $48 (10% of $480), which makes the new price $432. After six months, the item is marked down again by 20%, which is $86.40 (20% of $432). The final sale price of the item after both markdowns is $432 - $86.40 = $345.60.

Answer: 11cm, 11cm, 16.5cm, 16.5cm

Step-by-step explanation:

To find the length of each side of a rectangle in ratio of 3:2, set up the equation for the perimeter and solve for the sides using algebraic manipulation.

To find the length of each side of the rectangle, we must solve for the sides using the given ratio. Let's assume the ratio is 3x:2x, where x is a common factor. The perimeter of a rectangle is equal to 2 times the length plus 2 times the width. So, we can set up the equation: 2(3x) + 2(2x) = 55 cm. Simplifying the equation, we get 6x + 4x = 55. Combining like terms, 10x = 55, and dividing both sides by 10, we find x = 5. Therefore, the length of each side is 3x = 3(5) = 15 cm, and the width is 2x = 2(5) = 10 cm.

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Jessica will receive a $12.5 change back.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

The total cost of all purchased items

cereal for $3.75, milk for $1.50, and bread for $2.25

So,

3.75+1.50+2.25 = $7.5

Jessica paid $20

She will get back = 20 - 7.5 = $12.5

Hence "Jessica will receive a $12.5 change back".

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Answer:

the greatest common factor is 3

Step-by-step explanation:

375: 1, 3, 5,11, 15, 25, 75, 125, 375

66: 1, 2, 3, 6, 11, 22, 33, 66

333: 1, 3, 9, 37, 111, 333

The factor in the expression 12+5(-3n-8) is (-3n-8).

In the expression 12+5(-3n-8), the part (-3n-8) is a factor.

A factor is a number or expression that divides another number or expression evenly. In this case, the expression (-3n-8) is being multiplied by 5, making it a factor of the overall expression.

For example, if we let n=2, the expression (-3n-8) becomes (-3*2-8) = (-6-8) = -14. So, the factor (-3n-8) in the given expression becomes 5*(-14) = -70.

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The factor of the expression 12 + 5(-3n - 8) is -3n - 8.

In the expression 12 + 5(-3n - 8), the factor is the term being multiplied by 5. In this case, the expression -3n - 8 is the factor.

So, the factor of the expression is -3n - 8.

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The equation 10y-3x+6=11 in standard form is represented as -3x + 10y = 5.

To write the equation 10y-3x+6=11 in standard form, we need to rearrange the terms. Standard form is usually given as Ax + By = C, where A, B, and C are integers and A and B are not both 0.

First, we should move the term containing 'x' and the term containing 'y' to the left side of the equation, and the constant term on the right side of the equation. The resulting expression would be 3x - 10y = -5.

The standard form is not negative, we will multiply through by -1. So, our final equation in standard form is -3x + 10y = 5.

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