9 of 20 9 of 20 Items
Bar graph of average movie lengths based on type of movie. The horizontal axis is kind of movie: drama, comedy, romance, and animated. The vertical axis is average length in minutes numbered from 0 to 140 in increments of 5 with a break between 0 and 75. The bar for drama is shaded up to 135, the bar for comedies is shaded up to 90, the bar for romance is shaded up to 120, and the bar for animated is shaded up to 75.
Circle graph of number of books read by students over the summer with 5 sections, showing that 18% of students read only 1 book, 24% read 2 books, 42% read 3 books, 12% read 4 books, and 4% read 5 or more books
Question
Jacob has a mean score of 78 after his first four math tests. He wants to make a B, or an average of 80, in math. What does he need to score on the fifth test to have a mean score of 80?
(1 point)
Responses
82
82
88
88
94
94
108
108
Skip to navigation
A box and whisker plot is shown. A number line graph with a green rectangle extending from 5 to 9.5 above the line. There is a green dot at each end of the rectangle. There is a vertical line inside the rectangle at 8 with a red dot on it. There are black dots to the right and left of the green rectangle at 4 and 10. These black dots are connected to the green dots at their end of the green rectangle with black line segments.
Line graph of tuition rates for a period of time. The horizontal axis is years: 1996, 1997, 1998, and 1999. The vertical axis is tuition, in dollars, numbered from 0 to 10,500 in increments of 500 with a break between 0 and 8,500. The points on the line are 1996 comma $8,500, 1997 comma $9,000, 1998 comma $10,000, 1999 comma $10,500.
A box and whisker plot is shown. A number line graph with a green rectangle extending from 5 to 9.5 above the line. There is a green dot at each end of the rectangle. There is a vertical line inside the rectangle at 8 with a red dot on it. There are black dots to the right and left of the green rectangle at 4 and 10. These black dots are connected to the green dots at their end of the green rectangle with black line segments.
A box and whisker plot is shown. A number line graph with a rectangle extending from 46 to 63 above the line. There is a vertical line inside the rectangle at 58. There are lines extending out from the left and right of the rectangle. The left line extends to 46, and the right extends to 66.
Based on the information provided, we can see that Jacob has a mean score of 78 after his first four math tests. He wants to have a mean score of 80, or a B average, in math. To determine what score he needs on the fifth test, we can use the formula for finding the mean:
Mean = (sum of all scores)/(number of scores)
We can rearrange this formula to solve for the sum of all scores:
Sum of all scores = Mean * number of scores
In this case, Jacob wants to have a mean score of 80 and has already taken 4 tests. So, the sum of all his scores so far is:
Sum of all scores = 80 * 4 = 320
Since we know the sum of his scores so far, we can find the score Jacob needs on the fifth test by rearranging the formula for finding the mean:
Score on fifth test = (Sum of all scores + score on fifth test)/(number of scores + 1)
Plugging in the values we know:
320 + score on fifth test = 80 * 5
320 + score on fifth test = 400
Subtracting 320 from both sides:
score on fifth test = 400 - 320 = 80
Therefore, Jacob needs to score 80 on the fifth test to have a mean score of 80.
I apologize, but I am unable to generate the visuals you described. However, I can still help answer your question.
To find what Jacob needs to score on the fifth test to have a mean score of 80, we can set up an equation using the mean formula.
Mean = (sum of all scores) / (number of scores)
Since Jacob has already taken four tests with a mean score of 78, we can write the equation as:
80 = (sum of first four scores + score on fifth test) / 5
Solving for the sum of the first four scores:
(sum of first four scores) = 78 * 4
Now we substitute the known values back into the equation:
80 = (78 * 4 + score on fifth test) / 5
Multiplying both sides of the equation by 5:
5 * 80 = 78 * 4 + score on fifth test
400 = 312 + score on fifth test
Subtracting 312 from both sides of the equation:
400 - 312 = 312 - 312 + score on fifth test
88 = score on fifth test
Therefore, Jacob needs to score 88 on the fifth test to have a mean score of 80.