A bucket containing 5 2/5 gallons of water is 2/7 full. How many gallons of water is in one fully filled bucket?

 We are asked to make w the subject of the formula.

First, we rearrange the equation by to ensure w is on the right hand of the equation.

Then, divide both sides by r

Multiply both sides by y

The above equation can be rearranged into

Thus, the formula for finding the value of w is (x/ry)-(z/r).

The scatter plot showing the relationship between the number of absences in a semester and students’ final exam scores. The trend shows that as absences increase, exam scores decrease.

This represents a Negative Correlation because:

• When one variable (absences) increases, the other variable (exam score) decreases.
• The points on the scatter plot trend downward from left to right.

To find the required number of cups milk needed, we set a proportion equation with number of cups be numerator and cups of milk as denominator.

Let x be the number of cups of milk needed, then

The numbers of cups of milk required is 273/25, which when converted to mixed fraction becomes 10 23/25.

To find the amount of vanilla in mL, we set up an equation in a way the unwanted units cancel out and leave the wanted unit we are looking for. Then,

Thus, a recipe of 6 teaspoons equals 29.58 mL.

we find the value of x by applying the absolute conditions to the given equation.

First, add 2 to both sides of equation

Add 10 to both sides of the equation

Next, we apply the absolute rule:

If u=a, a>0, then u=a or u=-a

In this case a=5, which is greater 0.

The first condition becomes

Solving for x

The second condition becomes

Solving for x

Then, the value of x is -4/3 or 2.

we are asked to find the number of gallons a full tank can hold. A full tank is equivalent to 1.

Convert the mixed fraction into proper fraction as follows

If we let x be the number of gallons in full tank, and setting up the proportion equation with the number of gallons on the numerator and fraction of tank on denominator as follows.

Cross-multiply to find the value of x.

Converting 189/10 to a mixed fraction is 18 9/10. Thus, when the tank is full, it holds 18 9/10 gallons of water.

 the percentage change in weight is found by calculating change in weight over original multiplied by 100%.

First, find the change in weight over the 3 months

Change in weight lost= 1860-130=30 lb

Thus

The percent change in weight is 19% to the nearest whole number.

The probability of finding the probability of a yellow ball is given by

Total number of balls in the bag=2+3+7=12 balls

The probability of drawing a yellow ball from the bag is 7/12.

 Let the unknown length of the x. The resulting rectangle is shown below.

Then, we apply the Pythagoras theorem to find the value of x as:

The value of the unknown length is approximately 17.7 feet.

To estimate the total amount, round each price to the nearest dollar:

1. Hat: $19.49 → $19 (since 0.49 rounds down)
2. Shirt: $21.49 → $21 (since 0.49 rounds down)
3. Shoes: $59.99 → $60 (since 0.99 rounds up)

Now, add the rounded values:

19+21+60=10019 + 21 + 60 = 10019+21+60=100