Lana has $60. She spends 80% of the money. She then invests the remaining amount and earns a profit of 80%. How much money does she now have?

from the given estimations, we can find the actual addition of the numbers and see a trend the student utilizes to find their estimates. The exact sum is as follows

24+190=214

151+319=470

974+1022=1996

From the above evaluation, we can clearly see the students approximates the value in the ones values. So, in the problem we need to approximate 452+5017.

452+5017=5469

We can approximate 5469 based on the provided choices to 5470.

To find the least common denominator (LCD) of the fractions 1/2, 2/3, and 4/5, follow these steps:

Step 1: Identify the denominators

The denominators are 2, 3, and 5.

Step 2: Find the least common multiple (LCM)

The LCM of 2, 3, and 5 is the smallest number that all three denominators divide into evenly.

• Prime factorization:
  • 2=2
  • 3=3
  • 5=5

Since 2, 3, and 5 are all prime numbers, their LCM is:

2×3×5=30

The best way to display the frequency of each day of the week when students get up after 8 a.m. is by using a bar graph. Bar graphs are well-suited for representing categorical data, where each day of the week is a separate category, and the height of each bar corresponds to the count or frequency of students waking up late on that specific day.

Note: Histograms, on the other hand, are more appropriate for visualizing continuous or numerical data and are not ideal for categorical data like days of the week.Histograms are useful for understanding the distribution of data, identifying patterns, and assessing the shape of the data distribution, such as whether it's normally distributed, skewed, or has multiple modes.

As you can see below, the Histogram is used to depict a pattern/continuous/rangedata. While a bar graph does just fine even with discrete data.

To simplify the expression:

12+3×4−1+23

Step 1: Follow the order of operations (BODMAS)

Multiplication first:

3×4=12

23 = 2×2×2=8

Now the expression becomes:

12+12−1+8

Step 2: Perform addition and subtraction from left to right

• 12+12=24
• 24−1=23
• 23+8=31

The correct answer is 31.

the question requires we find the cost of two syringes.

If we let x be the cost of two syringes, then we set up a proportion equation with cost as numerator and number of syringes as denominator. The proportion equation becomes

Cross-multiply to solve for x

Rearranging the above

Divide both sides by 35

The cost of 2 syringes is $32.

in the given problem, we use the calculator to find 1.3*0.47=0.611

The length of the unknown side of the rectangle can be found by using the Pythagoras theorem. We label the triangle from the given data as shown below

Let the unknown length be x.

Applying the Pythagoras theorem, the value of x is found as:

\(a ^2 +b ^2 =c ^2\)

The unknown length of the triangle is approximately 8.9 feet.

The initial step is to establish the relationship between area of a circle and the radius. The area of the circle is given by the formula

Now, substituting the 49 π in2 in place of A in the equation above becomes:

We want to find r, therefore, we rearrange the equation as

Divide both sides by

Take square root both sides of the equation

The radius of the circle is 7 in, and the circumference of the circle is determined as follows

Substituting the value of r=7 becomes

Thus, the circumference of a circle whose area is 49  in2 is 14