Answer:
$9 for 36
Step-by-step explanation:
To find the unit price, divide the total cost by the number of items. Here are the costs per item for each option:
1. $0.54
2. $0.43
3. $0.31
4. $0.28
5. $0.25
The best deal is $9 for 36 pens as it results in the lowest price of $0.25 per pen.
Answer and explanation:
Algebra revolves around the fundamental idea of using letters known as variables to represent quantities, which allows for solving for unknown values. Essentially, algebra involves transitioning from what is known to what is unknown to ascertain those unknown results. For instance, if we know a specific item was purchased twice but we're unsure of its price, we can denote this unknown price as 2a or 2p, depending on the selected variable. If the total spending for those items is, say, $50, we can set up the equation 2a = $50, which leads us to find that the cost per item is $25.
Algebra can also manifest itself in expressions, commonly referred to as algebraic expressions, which can be incorporated into equations, such as the previously mentioned 2a = $50. These expressions may take forms like 2a + 3b, where a and b designate the costs of different products that were acquired in quantities of 2 and 3, respectively.
1,107 cc
The scanning consists of 10 intervals:
[0,1.5), [1.5,3), [3,4.5), [4.5,6), [6,7.5), [7.5,9), [9,10.5), [10.5,12), [12,13.5), [13.5,15)
To estimate the volume using the Midpoint Rule, n should be set to 10.
Given that we will use n=5, we will split the range [0,15] into five intervals of lengths 3 each:
[0,3], [3,6], [6,9], [9,12], [12,15] and calculate their midpoints:
1.5, 4.5, 7.5, 10.5, and 13.5.
Next, we will determine the volume V from the five cylinders, where each has a height h=3 and the base area A corresponds to the calculated midpoints' intervals:
Cylinder 1
Midpoint=1.5, corresponding to the 2nd interval
A = 18, V= height * area of the base = 18*3 = 54 cc
Cylinder 2
Midpoint=4.5, corresponding to the 4th interval
A = 78, V= height * area of the base = 78*3 = 234 cc
Cylinder 3
Midpoint=7.5, corresponding to the 6th interval
A = 106, V= height * area of the base = 106*3 = 318 cc
Cylinder 4
Midpoint=10.5, corresponding to the 8th interval
A = 129, V= height * area of the base = 129*3 = 387 cc
Cylinder 5
Midpoint=13.5, corresponding to the 10th interval
A = 38, V= height * area of the base = 38*3 = 114 cc
Thus, the estimated volume is
54 + 234 + 318 + 387 + 114 = 1,107
Beth travelled the remaining distance with an average speed of 52 mph
Solution:
Given, Beth drives 200 miles in 4 hours.
The equation for distance speed is expressed as:
--- eqn 1
Calculating time spent for 18 miles:
She completes the initial 18 miles at an average speed of 36 mph.
Distance here equals 18 miles
speed equals 36 mph
Substituting values into eqn 1 yields,
Determining average speed for the remaining journey:
The distance left to cover is = 200 miles – 18 miles = 182 miles
The time spent on the remaining trip equals the total time minus the duration for the first 18 miles
Inserting values into eqn 1 gives us
This confirms that the average speed for the rest of the journey is 52 mph
Given that x y is parallel to z w and x z serves as a transversal that crosses both x y and z w, it follows that ∠ x z w equals ∠ z x y, which are alternate interior angles because x y is parallel to z w. Also, v is where x z intersects y w, therefore ∠ x v y is congruent to ∠ z v w due to vertically opposite angles. Consequently, this yields triangle Δ x y v being similar to triangle Δ z w v based on the angle-angle similarity.
