The weight of a red blood cell is about 4.5 × 10*11 grams. A blood sample has 1.6 × 10 red blood cells. What is the total weight, in grams, of red blood cells in the sample the answer with the correct scientific notation.
- A. 2.9 × 10^18
- B. 7.2 × 10^(-4)
- C. 7.2 × 10^(-77)
- D. 6.1 × 10^(-4)
Correct Answer & Rationale
Correct Answer: B
To find the total weight of the red blood cells, multiply the weight of one red blood cell (4.5 × 10^-11 grams) by the total number of cells (1.6 × 10^6). This calculation yields 7.2 × 10^-5 grams, which can be expressed in scientific notation as 7.2 × 10^(-4) grams. Option A (2.9 × 10^18) is incorrect because it suggests an unrealistically high total weight, indicating a misunderstanding of scientific notation. Options C (7.2 × 10^(-77)) and D (6.1 × 10^(-4)) also fail to represent the correct multiplication, with C being far too small and D lacking accuracy in the calculated value.
To find the total weight of the red blood cells, multiply the weight of one red blood cell (4.5 × 10^-11 grams) by the total number of cells (1.6 × 10^6). This calculation yields 7.2 × 10^-5 grams, which can be expressed in scientific notation as 7.2 × 10^(-4) grams. Option A (2.9 × 10^18) is incorrect because it suggests an unrealistically high total weight, indicating a misunderstanding of scientific notation. Options C (7.2 × 10^(-77)) and D (6.1 × 10^(-4)) also fail to represent the correct multiplication, with C being far too small and D lacking accuracy in the calculated value.
Other Related Questions
The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The owner has decided to take out a loan to purchase updated equipment. A bank has agreed to loan the owner $2,000 for the purchase of the equipment at a simple interest rate of 4.69% payable annually.
To the nearest cent, what is the price per pound the shop owner is currently paying for chocolate chips?
- A. $0.10
- B. $4.38
- C. $0.23
- D. $4.28
Correct Answer & Rationale
Correct Answer: D
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
Daniel is planning to buy his first house. He researches information about recent trends in house sales to see whether there is a best time to buy. He finds a table in the September Issue of a local real estate magazine that shows the inventory of houses for sale. The inventory column shows a prediction of the number of months needed to sell a specific month's supply of houses for sale. The table also shows the median sales price for houses each month.
Daniel wonders whether housing prices are more likely to increase or decrease in any special month. If he randomly selects a month other than January from the table, what is the price as a fraction, that the median sales price in that month was an increase over the previous month?
Correct Answer & Rationale
Correct Answer: 4\7
To determine the fraction of months where the median sales price increased over the previous month, one must analyze the data presented in the table. The correct answer, 4/7, indicates that out of the seven months considered (excluding January), there were four months where prices rose compared to the month prior. Other options, such as 3/7 or 5/7, misrepresent the data by either underestimating or overestimating the actual increases. A fraction of 3/7 would imply that only three months saw an increase, which contradicts the evidence. Similarly, 5/7 would suggest an unrealistic majority of months experienced price hikes, not aligning with the data. Thus, 4/7 accurately reflects the observed trends in the provided data.
To determine the fraction of months where the median sales price increased over the previous month, one must analyze the data presented in the table. The correct answer, 4/7, indicates that out of the seven months considered (excluding January), there were four months where prices rose compared to the month prior. Other options, such as 3/7 or 5/7, misrepresent the data by either underestimating or overestimating the actual increases. A fraction of 3/7 would imply that only three months saw an increase, which contradicts the evidence. Similarly, 5/7 would suggest an unrealistic majority of months experienced price hikes, not aligning with the data. Thus, 4/7 accurately reflects the observed trends in the provided data.
The equation d/f = g represents gallons of gasoline used, g, in terms of distance traveled in miles, d, and fuel efficiency, / miles per gallon of gasoline. Which combination of distance traveled and fuel efficiency uses 3 gallons of gasoline?
- A. 7 miles and 21 miles per gallon
- B. 57 miles and 19 miles per gallon
- C. 23 miles and 20 miles per gallon
- D. 32 miles and 35 miles per gallon
Correct Answer & Rationale
Correct Answer: B
To determine which combination uses 3 gallons of gasoline, we can rearrange the equation d/f = g to find d = g * f. For g = 3 gallons, we calculate d for each option. A: 7 miles and 21 mpg results in d = 3 * 21 = 63 miles, which is incorrect. B: 57 miles and 19 mpg gives d = 3 * 19 = 57 miles, matching the distance traveled. C: 23 miles and 20 mpg leads to d = 3 * 20 = 60 miles, which is incorrect. D: 32 miles and 35 mpg results in d = 3 * 35 = 105 miles, which is also incorrect. Only option B correctly satisfies the equation for 3 gallons of gasoline used.
To determine which combination uses 3 gallons of gasoline, we can rearrange the equation d/f = g to find d = g * f. For g = 3 gallons, we calculate d for each option. A: 7 miles and 21 mpg results in d = 3 * 21 = 63 miles, which is incorrect. B: 57 miles and 19 mpg gives d = 3 * 19 = 57 miles, matching the distance traveled. C: 23 miles and 20 mpg leads to d = 3 * 20 = 60 miles, which is incorrect. D: 32 miles and 35 mpg results in d = 3 * 35 = 105 miles, which is also incorrect. Only option B correctly satisfies the equation for 3 gallons of gasoline used.
Which graph represents the solution of x + 5 ≤ 3?
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A.
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B.
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C.
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D.
Correct Answer & Rationale
Correct Answer: A
To solve the inequality x + 5 ≤ 3, we first isolate x by subtracting 5 from both sides, giving us x ≤ -2. Option A correctly represents this solution with a closed circle at -2, indicating that -2 is included in the solution set, and a shaded line extending to the left, showing all values less than -2. Options B, C, and D either depict open circles, which imply that the endpoint is not included, or incorrectly shade in the wrong direction or range, failing to accurately represent the solution x ≤ -2.
To solve the inequality x + 5 ≤ 3, we first isolate x by subtracting 5 from both sides, giving us x ≤ -2. Option A correctly represents this solution with a closed circle at -2, indicating that -2 is included in the solution set, and a shaded line extending to the left, showing all values less than -2. Options B, C, and D either depict open circles, which imply that the endpoint is not included, or incorrectly shade in the wrong direction or range, failing to accurately represent the solution x ≤ -2.