Can someone check over these math problems that I did? Please?
1. The bloodhound, a type of dog, has 4.0 X 10^9 (10 to the ninth power) scent receptors in its nose. A human has 1.2 X 10^7 scent receptors. How many times more scent receptors does a bloodhound have than a human. round to nearest whole number. ---------- I got 333 is that right?
2.
Last year, 65 pounds of hamburger patties were cooked to serve between 250 and 300 people. this year the school expects between 325 and 375 people. Estimate the number of patties needed for this year? ----- I'm really not sure on this one but I got 81 lbs but it does seem right!???
3. To make maple syrup, Kyle must boil 40 gallons of maple tree sap to produce one gallon of syrup. Ken sells his maple syrup in containers that hold one quart. At that rate, how many gallons of maple tree sap must be boiled to make one quart of syrup?----I got 160 gallons
4. Kyle collects sap in a cylindrical bucket having a diameter of 10 inches. If the bucket is filled with maple sap to a depth of 5 inches, how many gallons of sap does it contain? Give your answer to the nearest tenth of a gallon. USE ! GALLON = 231 CUBIC INCHES AND USE 3.14 FOR PIE------I got 1.7
6.9
Let's go through each question and check your answers.
1. The question asks for the number of times more scent receptors a bloodhound has compared to a human. To find the answer, we can divide the number of scent receptors in a bloodhound's nose by the number of scent receptors in a human's nose:
Bloodhound's scent receptors: 4.0 x 10^9
Human's scent receptors: 1.2 x 10^7
Dividing the two numbers: (4.0 x 10^9) / (1.2 x 10^7) = 333333.333...
To round to the nearest whole number, we get 333333. Therefore, your answer of 333 is correct.
2. To estimate the number of patties needed for this year, we can find the average number of people expected and then proportionally scale the number of patties.
Last year:
People served: 250 - 300
Patties cooked: 65 pounds
This year:
People expected: 325 - 375
To find the average number of people, we can add the lower and upper bounds and divide by 2:
(325 + 375) / 2 = 700 / 2 = 350
Now, we can set up a proportion:
(65 pounds) / (average number of people last year) = (number of patties needed for this year) / (350 people)
Solving for the number of patties needed for this year:
(65 pounds) / (average number of people last year) = (number of patties needed for this year) / (350 people)
65 / 275 = (number of patties needed for this year) / 350
Cross-multiplying:
275 * (number of patties needed for this year) = 65 * 350
(number of patties needed for this year) = (65 * 350) / 275
(number of patties needed for this year) = 82.727...
Rounding to the nearest whole number, we get 83. Therefore, your answer of 81 lbs is incorrect.
3. To find the number of gallons of maple tree sap needed to make one quart of syrup, we can set up a proportion using the given conversion rate:
40 gallons sap / 1 gallon syrup = x gallons sap / 1 quart syrup
To find x, we can cross-multiply and solve:
(40 gallons sap) * (1 quart syrup) = (1 gallon syrup) * (x gallons sap)
x = (40 * 1) / (1 * 1)
x = 40 gallons
Therefore, your answer of 160 gallons is incorrect.
4. To find the number of gallons of sap in the cylindrical bucket, we need to calculate the volume of the bucket and then convert it to gallons.
The formula for the volume of a cylinder is: V = πr^2h
Given:
Diameter = 10 inches, so radius (r) = 10/2 = 5 inches
Depth = 5 inches
Plugging in the values into the formula:
V = 3.14 * (5 inches)^2 * 5 inches
V = 3.14 * 25 sq. inches * 5 inches
V = 3.14 * 125 cubic inches
V ≈ 392.5 cubic inches
Now, to convert cubic inches to gallons:
1 gallon = 231 cubic inches
Dividing the volume by the conversion factor:
392.5 cubic inches / 231 cubic inches/gallon ≈ 1.7 gallons
Therefore, your answer of 1.7 gallons is correct.