Solve for w in the equation below.

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.

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

We follow the order of operations to solve the given expression.

First, we start with the numerator and solve it as follows

[3(2+6*4)]

We start with multiplication in inner brackets, 6*4=24. The expression becomes

[3(2+24)]

Then, we conduct the addition of 2+24=26. Then, the expression becomes

[3(26)]=3*26=78

Now, we solve for denominator, which is 26/2=13.

Thus, the expression is reduced into

\(\frac{[3(2+6\ast4)]}{(26\div2)}=\frac{78}{13}=6\)

The expression reduces into 6.

The final price of the stock on Thursday can be found by finding the price on the previous day taking into account the price changes as follows.

The price of the stock on Monday was $33.65

On Tuesday the price of the stock went up by $1.23 from Monday’s price. Then, Tuesday’s price was $(33.65+1.23)=$34.88

The price of the stock on Wednesday decreased by $0.97 from Tuesday’s price. The price on Wednesday became $(34.88-0.97)=$33.91

Thursday’s price increased by $2.75 from Wednesday’s price, which was $(33.91+2.75)=$36.66

Therefore, the final price of the stock on Thursday was $36.66.

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.

To find the area of the room, we form an equation of find an equation relating the length and width of the rectangle. If we let the width of the room to be w, then

Width of the rectangle= w

Length of rectangle=(w+8)

Area of the rectangle, A= Length*width=(w+8)*w

A=w(w+8)

Thus, the area of the rectangular room is w(w+8).

To round 24.375 kg to the nearest tenth (0.1 place), follow these steps:

1. Identify the tenth place in 24.375:
   • Tenth place: 3 (24.375)
   • Hundredths place: 7 (the next digit after the hundredths place)
2. Apply rounding rules:
   • If the hundredths place is 5 or greater, round up the tenth place.
   • Since 7 is in the hundredths place, round 24.3 up to 24.4.

We are asked to determine John’s uncle’s age relating to John’s age.

First, express John’s uncle’s age in terms of John’s age as follows

John’s age=k

John’s uncle’s age, u = 5k-12.

Thus, the relationship between Japheth’s uncle’s age to that of Japheth is u=5k-12.

 we need determine the radius of the circle before we can find the circumference of the circle from the given area.

Let r be the radius of the circle, then

Substituting the value of area

Dividing both sides by pi and taking square root on both sides yields

Now, the radius of the circle is 8 in. and the circumference of the circle is given by the relation:

To determine the number of sophomore students, follow these steps:

1. Identify the total number of students:

1,276

1. Identify the percentage of sophomores:

29%

1. Calculate the number of sophomores:

(29%×1,276) = (29/100× 1,276) = 370.04

1. Round to the nearest whole number:

370