Q: Write the name of the period that has the digits 913.

Answer: Thousands Explanation: In the context of place value in the decimal number system, each group of three digits is referred to as a "period." The periods are named from right to left as units, thousands, millions, etc. The digits 913 fall in the thousands period. Steps: Identify the Place Value System: The decimal system is organized in groups of three digits, each called a period. Determine the Period Name: The first period from the right is the units (or ones) period. The second period is the thousands period. The third period is the millions period, and so on. Locate the Digits 913: Since 913 is typically placed in the second group from the right in a larger number, it belongs to the thousands period. Thus, the name of the period that has the digits 913 is the thousands period.

Q: 32. Based on the measurements shown on △ABC, AB must be: A. less than 7 ft B. between 7 and 10 ft C. between 10 and 17 ft D. greater than 17 ft A 47° B 68° C 7 ft 10 ft

Answer: B. between 7 and 10 ft Explanation: To find the length of $ AB $ in $\triangle ABC$, we can use the Law of Cosines. This theorem relates the lengths of the sides of a triangle to the cosine of one of its angles. Given the sides $ AC = 10 $ ft, $ BC = 7 $ ft, and angle $ C = 68^\circ $, we can find $ AB $. Steps: Law of Cosines Formula: \[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \] where $ c $ is the side opposite angle $ C $. Substitute the Known Values: \[ AB^2 = 10^2 + 7^2 - 2 \cdot 10 \cdot 7 \cdot \cos(68^\circ) \] Calculate: \[ AB^2 = 100 + 49 - 140 \cdot \cos(68^\circ) \] Find $\cos(68^\circ)$: \[ \cos(68^\circ) \approx 0.3746 \] Continue Calculation: \[ AB^2 = 149 - 140 \cdot 0.3746 \] \[ AB^2 = 149 - 52.444 \] \[ AB^2 = 96.556 \] Solve for $ AB $: \[ AB = \sqrt{96.556} \approx 9.82 \text{ ft} \] Since $ AB \approx 9.82 $ ft, it falls between 7 and 10 ft. Thus, the correct answer is B. between 7 and 10 ft.

Q: How does 2025 minus 1943 work?

Answer: 82 Explanation: To find the difference between 2025 and 1943, you subtract the smaller number from the larger number: \[ 2025 - 1943 = 82 \] This calculation shows that 2025 is 82 years after 1943.

Q: • The circle graph above gives the distribution of salad dressing chosen by customers at a restaurant. If approximately 200 customers order each day at the restaurant. Which of the following is closest to the difference per day between the number who choose Italian dressing and the number who choose vinaigrette dressing? Blue cheese 20% French 5% Italian 45% Vinaigrette 30%

Answer: 30 Explanation: To find the difference between the number of customers choosing Italian dressing and those choosing vinaigrette, we need to calculate the number of customers for each dressing type based on the percentages given in the circle graph. Then, subtract the number of vinaigrette customers from the number of Italian dressing customers. Steps: Identify the percentages: Italian dressing: 45% Vinaigrette dressing: 30% Calculate the number of customers for each dressing: Total customers per day = 200 Italian dressing customers = $ 200 \times \frac{45}{100} = 90 $ Vinaigrette dressing customers = $ 200 \times \frac{30}{100} = 60 $ Find the difference: Difference = Italian dressing customers - Vinaigrette dressing customers Difference = $ 90 - 60 = 30 $ Thus, the difference per day between the number who choose Italian dressing and the number who choose vinaigrette dressing is 30.

Q: Math Question from Image

Answer: Yes, Diego's statement is correct. The answer is $ \frac{6}{5} $ or $ 1 \frac{1}{5} $. Explanation: To find how many groups of $ \frac{5}{6} $ are in 1, we need to divide 1 by $ \frac{5}{6} $. This involves the concept of dividing fractions, which is done by multiplying by the reciprocal. Steps: Set up the division problem: \[ 1 \div \frac{5}{6} \] Convert the division to multiplication by the reciprocal: \[ 1 \times \frac{6}{5} \] Perform the multiplication: \[ 1 \times \frac{6}{5} = \frac{6}{5} \] Convert the improper fraction to a mixed number: \[ \frac{6}{5} = 1 \frac{1}{5} \] Thus, there are $ \frac{6}{5} $ or $ 1 \frac{1}{5} $ groups of $ \frac{5}{6} $ in 1.

Question

What is the number who chose Italian dressing?

Accepted Answer

Answer: The number of customers who chose Italian dressing is 90.

Explanation:  This problem involves understanding the distribution of salad dressing choices among customers, which is represented by a circle graph (pie chart). The key concepts involved are percentage calculations and proportions. The problem asks to find the difference in the number of customers choosing Italian dressing and vinaigrette dressing, given the total number of customers and the percentage distribution.

The method involves:

Calculating the number of customers for each dressing based on the percentage.
Finding the difference between the two numbers.

Steps:

Identify the total number of customers:

Total customers = 200

Determine the percentage for Italian dressing:

From the table, Italian dressing = 45%

Calculate the number of customers who chose Italian dressing:

$$
   \text{Number of Italian dressing customers} = \frac{45}{100} \times 200 = 0.45 \times 200 = 90
   $$

Determine the percentage for Vinaigrette dressing:

Vinaigrette = 30%

Calculate the number of customers who chose Vinaigrette dressing:

$$
   \frac{30}{100} \times 200 = 0.30 \times 200 = 60
   $$

Find the difference between Italian and Vinaigrette dressing customers:

$$
   90 - 60 = 30
   $$

Question asks for the difference between the number who chose Italian dressing and the number who chose vinaigrette dressing:

The difference is 30.

Note: The question also mentions the number who chose vinaigrette dressing, but the main calculation is to find the number for Italian dressing, which is 90.