Q: The circle graph above gives the distribution of salad dressing chosen by customers at a restaurant. If approximately 200 customers order salad 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?

I can’t determine the difference without the graph — please provide the percentages or angle measures for the Italian and Vinaigrette slices (or upload the circle graph). Explanation / How to compute once you give the data If you are given percentages: let $p_I$ and $p_V$ be the fractions (as decimals) choosing Italian and Vinaigrette. Then $$\text{difference}=200\cdot|p_I-p_V|.$$ Example: if Italian is $30\%$ and Vinaigrette is $18\%$, then difference $=200\cdot(0.30-0.18)=24$ customers. If you are given central angles (degrees): let $d_I$ and $d_V$ be the slice angles. Convert to fractions via $p=\dfrac{d}{360}$, so $$\text{difference}=200\cdot\left|\dfrac{d_I-d_V}{360}\right|.$$ Example: if $d_I=108^\circ$ and $d_V=65^\circ$, difference $=200\cdot\frac{43}{360}\approx23.9\approx24$ customers. Send the slice percents or angles (or the image) and I’ll compute the closest daily difference.

Q: 60 in spanish

The correct answer is: sesenta Explanation Sesenta is the Spanish cardinal number for 60. Pronunciation: /seˈsenta/ (roughly "seh-SEHN-tah"). Example: "Tengo sesenta años." = "I am sixty years old."

Q: .375 as a fraction

The correct answer is: $\frac{3}{8}$ Explanation 0.375 is a terminating decimal with three decimal places, so write it as a fraction over 1000 and reduce to lowest terms. Steps: First step: $$0.375=\frac{375}{1000}$$ Second step: Divide numerator and denominator by their greatest common divisor (125): $$\frac{375\div125}{1000\div125}=\frac{3}{8}$$ Final step: $$\frac{3}{8}=0.375$$ Therefore, $0.375=\frac{3}{8}$.

Q: 2 liters to oz

The correct answer is: $67.6280452\text{ fl oz}$ Explanation You convert liters to US fluid ounces using the factor $1\text{ L}=33.8140226\text{ fl oz}$. Steps: Conversion factor: $$1\text{ L}=33.8140226\text{ fl oz}$$ Multiply by 2 liters: $$2\text{ L}\times33.8140226\frac{\text{fl oz}}{\text{L}}=67.6280452\text{ fl oz}$$ Rounded (typical): $$\approx67.63\text{ fl oz}$$ Therefore, 2 liters ≈ $67.63\text{ fl oz}$. Note: This is for US fluid ounces. If you meant imperial (UK) fluid ounces, 2 L ≈ $70.40\text{ fl oz (imp)}$.

Q: 2. A radio station is giving away tickets to a play. They plan to give away tickets for seats that cost $10 and $20. They want to give away at least 20 tickets. The total cost of all the tickets they give away can be no more than $280. Use a graph to determine possible outcomes.

The correct answer is: All integer pairs (x,y) with x = number of $10 tickets and y = number of $20 tickets satisfying $y\in\{0,\dots,8\}$ and $20-y\le x\le 28-2y$. There are 45 possible outcomes. Explanation Let $x$ = number of \$10 tickets and $y$ = number of \$20 tickets. Constraints: At least 20 tickets: $x+y\ge20$. Total cost at most \$280: $10x+20y\le280$, which simplifies to $x+2y\le28$. $x,y\ge0$ and must be integers. Steps: Write the inequalities: $x+y\ge20$ $x+2y\le28$ Combine to bound $y$: Subtracting gives $y\le8$, so $y\le8$ and $y\ge0$, hence $y\in\{0,1,\dots,8\}$. For each integer $y$ in that range, $x$ must satisfy $20-y\le x\le 28-2y$ (and $x\ge0$, but the left bound already enforces positivity for these $y$). List (or compute) the integer solutions by plugging $y=0,\dots,8$: $y=0:\ x=20,\dots,28$ (9 values) $y=1:\ x=19,\dots,26$ (8 values) $y=2:\ x=18,\dots,24$ (7 values) $y=3:\ x=17,\dots,22$ (6 values) $y=4:\ x=16,\dots,20$ (5 values) $y=5:\ x=15,\dots,18$ (4 values) $y=6:\ x=14,\dots,16$ (3 values) $y=7:\ x=13,\dots,14$ (2 values) $y=8:\ x=12$ (1 value) Total integer outcomes: $9+8+\dots+1=45$. Geometric description (graph): the feasible region is the triangular region bounded by the lines $x+y=20$, $x+2y=28$, and the $x$-axis. Its

Question

Dawn and Emily each had the same length of ribbon. Both girls used their ribbons to make identical bows. Dawn made 12 bows and had 128 cm of ribbon left. Emily made 9 bows and had 176 cm of ribbon left. How many bows could Emily make with the ribbon she had left?

Accepted Answer

The correct answer is:$11$

Explanation

Let each bow use $x$ cm of ribbon and let the total ribbon length be $L$.

Steps:

Dawn: $L = 12x + 128$. Emily: $L = 9x + 176$.
Equate and solve: $$12x + 128 = 9x + 176$$ $$3x = 48$$ $$x = 16$$
Emily's leftover $176	ext{ cm}$ can make $$\frac{176}{16} = 11$$ bows.

Therefore, Emily could make 11 more bows with the ribbon she had left.

Dawn and Emily each had the same length of ribbon. Both girls used their ribbons…