Probability and Cost Calculations

The probability of an event is the likelihood that the event will occur. It is expressed as a fraction, decimal, or percentage.

Experimental probability is based on the results of an experiment or a series of trials. It is calculated by dividing the number of times an event occurs by the total number of trials.

Based on 65 selections where a white marble was selected 41 times and a yellow marble 24 times, the probability of selecting a white marble next is 41/65, which is roughly 63%.

A linear equation is an equation that represents a straight line when graphed. It is usually written in the form y = mx + b, where m is the slope and b is the y-intercept.

An equation that represents the price (p) of a watermelon based on its weight (w) can be found using the information given. For example, if the price of a 7.3 pound watermelon is $4.38, we can use the formula p = 0.60w to calculate the price. This formula is found by dividing the price by the weight (4.38 / 7.3 = 0.60).

To find the total cost of Omar's repair, we use the original cost of $1000 and subtract the $80 coupon, then subtract 15% of the remaining amount. For Caleb, we first subtract 15% from $1000 then subtract $80. Caleb pays less, by $12.

To calculate the cost of 1 3/4 pounds of milk chocolate at $12.80 per pound, multiply the amount and price (1.75 * 12.80). To calculate the cost of 1 4/3 pounds of caramels at $9.28 per pound, multiply (1.33 * 9.28). The difference between these two costs is roughly $3.80.

Given 266 out of 350 visitors stopped at the gift shop, we can set up a proportion to find the estimated number out of 2300 visitors: 266/350 = x/2300. Solving for x gives us approximately 1674 visitors.

The total cost of the pictures is $85.75 minus the shipping fee of $3.25, or $82.50. Dividing the total cost by the cost per picture ($82.50 / $7.50) tells us that Todd ordered 11 pictures.

To find the average speed, we divide the distance by the time (30.15 miles / 2/3 hours). This equals 45.225 mph.

In the second month, the company received 25% more calls than the first month's 4264. This means they received 0.25 * 4264 = 1066 more calls. The second month's total was 4264 + 1066 = 5330 calls. The third month, with 6396 calls, saw an increase of 6396 - 5330 = 1066 calls. The percent increase is 1066/5330 * 100%, which rounds to 20%

Susan spends $12.36 * 2 = $24.72 on chicken, $1.98 * 1/2 = $0.99 on broccoli, and $3.49 on milk. This totals $29.20. She paid $29.20 + $0.80 = $30.00.

If the worker used 30 cups on the first day, and 90 cups on the second day, this means the worker used a total of 90 + 30 = 120 cups. Since the worker used 15% of the remaining cups on the second day, the number of cups remaining after the first day was 90 / 0.15 = 600 cups. Therefore, the original number of cups was 600 + 30 = 630 cups.

The expression 3^(0.1 * 5) / 7^(2/21) can be simplified to 3^(0.5) / 7^(1/21). Since 3^(0.5) is the square root of 3 and 7^(1/21) is a fractional root, we cannot simplify further without a calculator.

The coach wants to order hats that cost $9.95 each with a $5 shipping fee. The total must be less than $125. This setup can be represented as 9.95h + 5 < 125, where h is the number of hats.

The probability that the next person will purchase more than one item of artwork is 9 divided by the total number of visitors, which is 117 + 24 + 9 = 150 visitors. The probability is therefore 9/150, which simplifies to 3/50.

2(x + 7) - 18x + 54 can be simplified by distributing the 2: 2x + 14 - 18x + 54. Then combine like terms: -16x + 68. This simplifies to 16x + 74.

The final value will be zero when the amount gained equals the amount lost or when equal values are added and subtracted. Of the given choices, this only occurs when a person buys an item for $2.25 and then sells it for $2.25.

To get a representative sample of the student body, it's best to survey randomly selected students from every homeroom. This ensures a diverse group representing different grade levels and sections.

Manny spends $4.25 on shoes and $2.50 per game. If he has $25, we can set up the inequality 4.25 + 2.5x <= 25, where x is the number of games. This represents the total cost being less than or equal to his budget.

To find the value that makes the equation true, we need to isolate x. The equation is 2.1 * ? = 1.21. Dividing both sides by 2.1 gives us ? = 1.21 / 2.1 = 0.6.

Danielle's model is 2 inches by 1 inch, but the scale is 1 inch = 47 feet. The actual dimensions are 2 * 47 = 94 feet by 1 * 47 = 47 feet. The area of the base is then 94 * 47 = 4418 square feet.

The expression 7a - 8 - (12a + 4) can be simplified by distributing the negative sign: 7a - 8 - 12a - 4. Then combine like terms: -5a - 12

The ratio of boys to girls in Mr. Johnson's club is 4:12, which simplifies to 1:3. In Ms. Greene's club, with 6 boys, the number of girls can be found by setting up a proportion: 1/3 = 6/x. Solving for x gives us 18 girls.

To calculate the price of 4 1/2 pounds of apples on sale at a 10% discount from the original price of $1.60 per pound, first find the discount: $1.60 * 0.10 = $0.16. The sale price is $1.60 - $0.16 = $1.44 per pound. The total cost is 4.5 * $1.44 = $6.48.

To find the sale price of an item originally priced at p dollars with a 20% discount, we can use Expression B (0.8p) or Expression E (p - 0.2p). Both represent reducing the original price by 20%, resulting in the same sale price.

Out of 200 name tags, 35% are blue, so there are 200 * 0.35 = 70 blue tags. 3/8 of the name tags are yellow, which is 200 * (3/8) = 75 yellow tags. The number of red tags is then 200 - 70 - 75 = 55.

Given a temperature decrease of 12°C from midnight to 6:00 am, starting at 12°C, the expression to represent this is 12 - 12. This represents subtracting the decrease from the original temperature.

To calculate the average amount of water Shawnte drinks per hour, we divide the total amount she drinks (1/2 of a 6-ounce glass) by the time (3/2 hours): (1/2 * 6) / (3/2) = 3 / (3/2) = 2 ounces per hour.

The tip is 17% of the lunch cost of $13.00, which is 0.17 * $13.00 = $2.21. Adding the tip to the original cost gives us the total cost of $13.00 + $2.21 = $15.21.

The decimal equivalent of 7/12 can be found by dividing 7 by 12. This gives you 0.58333.... Rounded to the nearest thousandth, it's 0.583.

A box contains 160 pencils per box, so the total number of pencils (y) can be represented by multiplying the number of boxes (x) by 160: y = 160x. If x = 12, then the total number of pencils is 160 * 12 = 1920 pencils.

Scott's discounted sofa costs $460, and the 8% tax is $460 * 0.08 = $36.80. So, including tax, he pays $460 + $36.80 = $496.80. To find out how much he saves compared to the original price, we need to know the original price (which is not given) and then subtract the final price from it.

To solve the equation 1/2(x - 9) = 9 1/3, first simplify the fraction on the right to 28/3. Then, multiply both sides by 2 to get x - 9 = 56/3. Add 9 to both sides: x = 83/3, or approximately 27.67.

The final value will be zero when the amount gained equals the amount lost or when equal values are added and subtracted. This occurs when a person bikes 3.1 miles to school and then bikes 3.1 miles back home. The total distance traveled is 3.1 + 3.1 = 6.2 miles, but the net change in position is zero.

Mario surveyed 120 customers, and 42 said they'd buy children's shoes. Since he has 440 customers per month, we can set up a proportion: 42/120 = x/440. Solving for x gives us approximately 154 customers who would buy children's shoes.

To find the value of 2% of (1/5) ^ 4, first calculate (1/5) ^ 4 = 1/625. Then multiply by 0.02 (which is 2%): 0.02 * (1/625) = 0.000032.

There are a total of 100 + 250 + 150 = 500 paper clips. The probability of selecting a small or medium paper clip is the number of small or medium clips (100 + 250 = 350) divided by the total number of clips (500): 350/500 = 7/10.

The expression 7a - 8 - (12a + 4) can be simplified by distributing the negative sign: 7a - 8 - 12a - 4. Then combine like terms: -5a - 12

The ratio of boys to girls in Mr. Johnson's club is 4:12, which simplifies to 1:3. In Ms. Greene's club, with 6 boys, the number of girls can be found by setting up a proportion: 1/3 = 6/x. Solving for x gives us 18 girls.

To calculate the price of 4 1/2 pounds of apples on sale at a 10% discount from the original price of $1.60 per pound, first find the discount: $1.60 * 0.10 = $0.16. The sale price is $1.60 - $0.16 = $1.44 per pound. The total cost is 4.5 * $1.44 = $6.48.

To find the sale price of an item originally priced at p dollars with a 20% discount, we can use Expression B (0.8p) or Expression E (p - 0.2p). Both represent reducing the original price by 20%, resulting in the same sale price.

Out of 200 name tags, 35% are blue, so there are 200 * 0.35 = 70 blue tags. 3/8 of the name tags are yellow, which is 200 * (3/8) = 75 yellow tags. The number of red tags is then 200 - 70 - 75 = 55.

Given a temperature decrease of 12°C from midnight to 6:00 am, starting at 12°C, the expression to represent this is 12 - 12. This represents subtracting the decrease from the original temperature.

To calculate the average amount of water Shawnte drinks per hour, we divide the total amount she drinks (1/2 of a 6-ounce glass) by the time (3/2 hours): (1/2 * 6) / (3/2) = 3 / (3/2) = 2 ounces per hour.

The tip is 17% of the lunch cost of $13.00, which is 0.17 * $13.00 = $2.21. Adding the tip to the original cost gives us the total cost of $13.00 + $2.21 = $15.21.