on a 10 question quiz you correctly answer four one point questions and five two point questions. you earn 87.5% of the possible points on the quiz.
a. how many possible points is the quiz worth
b. how many questions did you miss
c. how many points was each missed question worth
a. To find the total possible points on the quiz, we can calculate the points earned for each question type separately and then add them together.
For the four one-point questions, you earn 4 points (4 correct answers * 1 point per question).
For the five two-point questions, you earn 10 points (5 correct answers * 2 points per question).
Adding these together, you earned a total of 14 points (4 + 10).
To find the total possible points, we can use the equation:
Total possible points = Points earned / Percentage earned
In this case, the percentage earned is 87.5%, which can be written as a decimal as 0.875.
Total possible points = 14 / 0.875
Total possible points = 16
Therefore, the quiz is worth 16 possible points.
b. To find the number of questions missed, we can subtract the number of questions answered correctly from the total number of questions.
Total number of questions = 4 (one-point questions) + 5 (two-point questions)
Total number of questions = 9
Number of questions missed = Total number of questions - Number of questions answered correctly
Number of questions missed = 9 - (4 + 5)
Number of questions missed = 9 - 9
Number of questions missed = 0
Therefore, you did not miss any questions.
c. Since you did not miss any questions, each missed question did not have any point value.
To answer these questions, we can use the information provided:
a. To find the total possible points on the quiz, we need to calculate the total points earned. We know that you earned 87.5% of the possible points, so we can use this percentage to determine the total possible points. Let's denote the total possible points as "P."
Total points earned = (Total possible points) * (Percentage earned)
Since you earned 87.5% of the possible points:
(Total possible points) * (87.5%) = (4 * 1) + (5 * 2)
Coverting the percentage to decimal form: (Total possible points) * (0.875) = 4 + 10
0.875P = 14
P = 14 / 0.875
P = 16
Therefore, the quiz is worth a total of 16 points.
b. To calculate the number of questions you missed, we can subtract the number of questions you answered correctly from the total number of questions on the quiz. In this case, you answered four one-point questions correctly and five two-point questions correctly:
Number of questions answered correctly = (Number of one-point questions answered correctly) + (Number of two-point questions answered correctly)
Number of questions answered correctly = 4 + 5
Number of questions answered correctly = 9
Number of questions missed = Total number of questions - Number of questions answered correctly
Number of questions missed = 10 - 9
Number of questions missed = 1
Therefore, you missed one question.
c. To determine how many points each missed question was worth, we need to divide the points earned by the number of questions answered correctly. Since you earned 87.5% of the possible points:
Points earned = (Number of one-point questions answered correctly) + (Number of two-point questions answered correctly)
Points earned = (4 * 1) + (5 * 2)
Points earned = 4 + 10
Points earned = 14
Points earned per question = Points earned / Number of questions answered correctly
Points earned per question = 14 / 9
Therefore, each missed question was worth approximately 1.56 points.
a. To find the total possible points on the quiz, we can use the given percentage of earned points. Since you earned 87.5% of the possible points, we can set up the following equation:
(4 * 1) + (5 * 2) = (87.5/100) * x
Simplifying, we have:
4 + 10 = (87.5/100) * x
14 = (87.5/100) * x
To solve for x, we can divide both sides of the equation by 87.5/100:
x = 14 / (87.5/100)
x = 14 * (100/87.5)
x ≈ 16
Therefore, the quiz is worth approximately 16 possible points.
b. To find the number of questions you missed, we can subtract the number of questions you answered correctly from the total number of questions:
Total number of questions - Number of questions answered correctly = Number of questions missed
10 - (4 + 5) = Number of questions missed
10 - 9 = Number of questions missed
Number of questions missed = 1
So, you missed one question.
c. To find out how many points each missed question was worth, we first need to calculate the total points earned. We know that you correctly answered four one-point questions and five two-point questions, so the total points earned is:
(4 * 1) + (5 * 2) = 4 + 10 = 14 points
Since the quiz is worth 16 possible points (as calculated in part a), we can find the points per missed question by subtracting the points earned from the total possible points:
Total possible points - Total points earned = Points per missed question
16 - 14 = Points per missed question
Points per missed question = 2
Therefore, each missed question was worth 2 points.
Jiani gets paid for a job every 9 weeks and Rosa gets paid for a job every 12 weeks. How many weeks will it take for them to get paid at the same time? Type your response into the box below.(1 point)
To find out when Jiani and Rosa will get paid at the same time, we need to find the smallest common multiple of 9 and 12.
The prime factorization of 9 can be written as 3 * 3.
The prime factorization of 12 can be written as 2 * 2 * 3.
To find the smallest common multiple, we take the highest power of each prime factor that appears in the factorization of either number. In this case, we have two 3's and two 2's.
Therefore, the smallest common multiple of 9 and 12 is 2 * 2 * 3 * 3 = 36.
So, it will take 36 weeks for Jiani and Rosa to get paid at the same time.
Add the following fractions. You must type your response as a simplified fraction. To type your fraction, click the box to the right of the equal sign and then select the fraction button where you see an x to the left of a fraction bar. Use your mouse or the up and down arrows on your keyboard to move between the numerator and denominator. The link below is a screen shot of the button you want to select. Fraction Bar.JPG (1 point) 215+13=
To add the fractions 2/15 and 1/3, we need to find a common denominator.
The least common multiple of 15 and 3 is 15, so we can convert both fractions to have a denominator of 15.
2/15 + 1/3 = (2/15) * (1/1) + (1/3) * (5/5)
= 2/15 + 5/15
Now that the fractions have the same denominator, we can add the numerators:
2/15 + 5/15 = (2 + 5)/15
= 7/15
Therefore, the sum of 2/15 and 1/3 is 7/15.
Spencer is solving 913−223 . What is the correct result?(1 point) Responses 729 7 and 2 ninths 12 12 623 6 and 2 thirds 423
To solve the subtraction problem 913 - 223, we subtract the corresponding place values:
9 - 2 = 7
1 - 2 = -1 (Since we cannot subtract 2 from 1, we need to borrow from the tens place.)
The borrowed 1 from the tens place becomes -10 in the ones place.
-10 + 3 = -7 (Adding -10 and 3 gives -7)
Combining the results, we have:
913 - 223 = 700 - 7 = 693
So, the correct result is 693.
Spencer is solving 9 1/3−2 2/3 . What is the correct result?(1 point) Responses 7 2/9 7 and 2 ninths 12 12 623 6 and 2 thirds 423
To solve the subtraction problem 9 1/3 - 2 2/3, we need to find a common denominator.
The denominators are already the same, so we can subtract the fractions directly:
1/3 - 2/3 = -1/3
Now we subtract the whole numbers:
9 - 2 = 7
Putting it all together, we have:
9 1/3 - 2 2/3 = 7 - 1/3
Since 7 can be written as 7/1, we can subtract the fractions:
7 - 1/3 = (7/1) - (1/3) = (21/3) - (1/3) = (21 - 1)/3 = 20/3
So, the correct result is 6 and 2/3, or in mixed fraction form, 6 2/3.
Add 357+712 . What is the sum?(1 point) Responses 10314 10 and 3 over 14 11314 11 and 3 over 14 1023 10 and 2 thirds 1157
To add 357 and 712, we need to add the corresponding place values:
357
+ 712
_____
1069
So, the correct sum is 1069.
Add 3 5/7+7 1/2 . What is the sum?(1 point) Responses 10 3/14 10 and 3 over 14 11 3/14 11 and 3 over 14 10 2/3 10 and 2 thirds 11 5/7
To add 3 5/7 and 7 1/2, we first need to find a common denominator. The least common multiple of 7 and 2 is 14.
Converting the fractions to have a denominator of 14:
3 5/7 = 3 * (7/7) + 5/7 = 21/7 + 5/7 = 26/7
7 1/2 = 7 * (2/2) + 1/2 = 14/2 + 1/2 = 15/2
Now, we can add the whole numbers and the fractions separately:
3 5/7 + 7 1/2 = 26/7 + 15/2
To add the fractions, we need to find a common denominator, which is 7 * 2 = 14.
26/7 + 15/2 = (26/7) * (2/2) + (15/2) * (7/7) = 52/14 + 105/14
Now, we can add the numerators:
52/14 + 105/14 = (52 + 105)/14 = 157/14
Now, we simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 7:
157/14 = (157/7) * (1/2) = 22 * (1/2) = 22/2 = 11
So, the correct sum is 11.
Question Subtract 9 7/10−6 1/4 . What is the difference?(1 point) Responses 3 9/20 3 and 9 over 20 2920 2 and 9 over 20 3 1/2 3 and 1 half 15 19/20 15 and 19 over 20
To subtract 9 7/10 from 6 1/4, we need to find a common denominator. The least common multiple of 10 and 4 is 20.
Converting the fractions to have a denominator of 20:
9 7/10 = 9 * (2/2) + 7/10 = 18/2 + 7/10 = 36/20 + 7/10 = 43/20
6 1/4 = 6 * (5/5) + 1/4 = 30/5 + 1/4 = 150/20 + 5/20 = 155/20
Now, we can subtract the whole numbers and the fractions separately:
9 7/10 - 6 1/4 = 43/20 - 155/20
To subtract the fractions, we can directly subtract the numerators:
43/20 - 155/20 = (43 - 155)/20 = -112/20
Now, we simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 8:
-112/20 = (-112/8) * (1/20) = -14 * (1/20) = -14/20
We can further simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 2:
-14/20 = (-14/2) * (1/10) = -7 * (1/10) = -7/10
So, the correct difference is -7/10.
Prairie Street is 378 miles long. Plains Avenue is 3510 miles long. Ellis rides his bike the length of both Prairie Street and Plains Avenue. How many total miles does he ride?(1 point) Responses 38 3 eighths 6712 6 and 7 over 12 638 6 and 3 eighths 738
To find the total distance Ellis rides, we need to add the lengths of Prairie Street and Plains Avenue.
Prairie Street: 378 miles
Plains Avenue: 3510 miles
Total distance = Prairie Street + Plains Avenue
Total distance = 378 + 3510
Total distance = 3888 miles
Therefore, Ellis rides a total of 3888 miles.
Prairie Street is 3 7/8 miles long. Plains Avenue is 3 5/10 miles long. Ellis rides his bike the length of both Prairie Street and Plains Avenue. How many total miles does he ride?(1 point) Responses 38 3 eighths 6 7/12 6 and 7 over 12 6 3/8 6 and 3 eighths 7 3/8
To find the total distance Ellis rides, we need to add the lengths of Prairie Street and Plains Avenue.
Prairie Street: 3 7/8 miles
Plains Avenue: 3 5/10 miles
First, we need to convert the mixed numbers to improper fractions:
3 7/8 = (3 * 8 + 7) / 8 = 31/8
3 5/10 = (3 * 10 + 5) / 10 = 35/10 = 7/2
Total distance = Prairie Street + Plains Avenue
Total distance = 31/8 + 7/2
To add the fractions, we need to find a common denominator, which is 8.
31/8 + 7/2 = (31/8) + (28/8) = 59/8
Therefore, Ellis rides a total of 59/8 miles.
LESSON 11 math 6 a
Add and Subtract Fractions Unit Test
ansers
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Marri bought 12 pound licorice, 13 pound of candy worms, and 25 pound of jawbreakers. how many more pounds of licorice than jawbreakers did she buy?(1 point) Responses 910 pound 9 tenths pound 25 pound 2 fifths pound 34 pound 3 fourths pound 110 pound
To find how many more pounds of licorice Marri bought than jawbreakers, we need to subtract the weight of the jawbreakers from the weight of the licorice.
Licorice: 12 pounds
Jawbreakers: 25 pounds
Licorice - Jawbreakers = 12 - 25 = -13
Since the result is negative, it means Marri bought 13 pounds less of licorice than jawbreakers, not more.
Therefore, Marri bought 13 pounds less of licorice than jawbreakers.
Marri bought 1/2 pound licorice, 1/3 pound of candy worms, and 2/5 pound of jawbreakers. how many more pounds of licorice than jawbreakers did she buy?(1 point) Responses 9/10 pound 9 tenths pound 25 pound 2 fifths pound 3/4 pound 3 fourths pound 1/10 pound
To find the difference in weight between the licorice and jawbreakers that Marri bought, we need to subtract the weight of the jawbreakers from the weight of the licorice.
Licorice: 1/2 pound
Jawbreakers: 2/5 pound
Licorice - Jawbreakers = 1/2 - 2/5
To subtract fractions, we need to find a common denominator, which is 10 in this case:
1/2 - 2/5 = 5/10 - 4/10 = 1/10
Therefore, Marri bought 1/10 pound more of licorice than jawbreakers.