Which is greater? 12%, 8/25, 0.07, 4/25, 0..33
Let's convert each value to decimal form for easier comparison:
12% --> convert percent to decimal by dividing by 100 = 0.12
8/25 --> divide the numerator by the denominator = 8 ÷ 25 = 0.32
0.07 --> already in decimal form
4/25 --> divide the numerator by the denominator = 4 ÷ 25 = 0.16
0.33 --> already in decimal form
Now that we have all the numbers in decimal form, let's list them to easily compare:
- 0.12 (12%)
- 0.32 (8/25)
- 0.07 (0.07)
- 0.16 (4/25)
- 0.33 (0.33, assuming you meant 0.33 instead of 0..33)
From the list above, the greatest value is 0.33.
can you order them from greatest to least please
Certainly! Here is the list from greatest to least based on the decimal values:
1. 0.33 (assuming it represents 33% or 0.33 in decimal form)
2. 0.32 (8/25)
3. 0.16 (4/25)
4. 0.12 (12%)
5. 0.07 (0.07)
Which number would be closer to -77 in a number line?
-76.3, -76 3/5, -76.25, or -76 1/10
To determine which number is closer to -77 on a number line, you need to look at their values in decimal form and compare their distance from -77.
Here are the given numbers converted to decimal form:
- -76.3 is already in decimal form.
- -76 3/5: To convert 3/5 to decimal, divide 3 by 5, which results in 0.60, so the number is -76.60.
- -76.25 is already in decimal form.
- -76 1/10: To convert 1/10 to decimal, divide 1 by 10, which results in 0.10, so the number is -76.10.
Now, let's calculate their distance from -77:
- Distance for -76.3 = |-77 - (-76.3)| = |-0.7| = 0.7
- Distance for -76.60 = |-77 - (-76.60)| = |-0.40| = 0.40
- Distance for -76.25 = |-77 - (-76.25)| = |-0.75| = 0.75
- Distance for -76.10 = |-77 - (-76.10)| = |-0.90| = 0.90
The distances from the smallest to the largest are:
-76.60 (-76 3/5) < -76.3 < -76.25 < -76.10 (-76 1/10)
So, the number that is closest to -77 is -76.60, which is the decimal equivalent of -76 3/5.
A candy jar contains several small pieces of candy:
- 5 miniature peanut butter cups
- 7 dark chocolate candy bars
- 8 gummy worms
Roger randomly selected one piece of candy from the jar.
What is the probability in decimal form that the candy Roger selected was NOT a gummy worm?
To calculate the probability that the candy Roger selected was not a gummy worm, first determine the total number of pieces of candy in the jar and then subtract the number of gummy worms to find the number of favorable outcomes.
The total number of candies in the jar is the sum of all the candies:
5 (peanut butter cups) + 7 (dark chocolate bars) + 8 (gummy worms) = 20 pieces of candy
The number of gummy worms is 8, so the number of pieces of candy that are not gummy worms is:
20 (total pieces of candy) - 8 (gummy worms) = 12 pieces of candy
The probability that the piece of candy Roger selected was not a gummy worm can be calculated as the number of favorable outcomes (not being a gummy worm) divided by the total number of outcomes (total pieces of candy):
Probability = Number of favorable outcomes / Total number of outcomes
Probability (not a gummy worm) = 12 / 20
Probability (not a gummy worm) = 0.6
So, the probability that the candy Roger selected was not a gummy worm is 0.6 in decimal form.
you sure?
Apologies for the confusion in my previous response. Let us re-evaluate:
To calculate the probability that the candy Roger selected was not a gummy worm, we first determine the total number of candies:
- 5 miniature peanut butter cups
- 7 dark chocolate candy bars
- 8 gummy worms
Total candies = 5 + 7 + 8 = 20 candies
Out of these, 8 are gummy worms, which means:
Number of candies that are not gummy worms = Total candies - gummy worms
Number of candies that are not gummy worms = 20 - 8 = 12 candies
Now, we calculate the probability:
Probability (not a gummy worm) = Number of non-gummy worm candies / Total number of candies
Probability (not a gummy worm) = 12 / 20
Probability (not a gummy worm) = 0.6
So, the probability that the candy Roger selected was not a gummy worm is indeed 0.6 in decimal form. I confirm my previous statement was accurate.
Stacy and Clinton are setting up the community center for a freshman orientation. They set up 8 rectangular tables with 6 chairs each and 5 round tables with 4 chairs each. The chairs are randomly numbered starting with 1 and the freshman will be randomly assigned a seat number.
What is the probability that the first freshman to arrive will be seated at a round table?
To solve this problem, we need to calculate the total number of chairs and identify how many chairs are at round tables.
First, we calculate the total number of chairs at rectangular tables:
8 rectangular tables × 6 chairs each = 48 chairs
Next, we calculate the total number of chairs at round tables:
5 round tables × 4 chairs each = 20 chairs
Now, we can find the total number of chairs overall:
Total chairs = chairs at rectangular tables + chairs at round tables
Total chairs = 48 + 20 = 68 chairs
To find the probability that the first freshman to arrive will be seated at a round table, we divide the number of chairs at round tables by the total number of chairs:
Probability (first freshman at a round table) = Number of chairs at round tables / Total number of chairs
Probability (first freshman at a round table) = 20 / 68
The probability requires simplification to get the final answer:
Probability (first freshman at a round table) = 20 / 68
The numerator 20 and denominator 68 can both be divided by 4 to simplify the fraction:
Probability (first freshman at a round table) = (20 ÷ 4) / (68 ÷ 4)
Probability (first freshman at a round table) = 5 / 17
This fraction cannot be simplified further, so the probability that the first freshman to arrive will be seated at a round table is 5/17, which is approximately 0.2941 when converted to decimal form.
0.2941 as a decimal
Certainly, 5/17 when expressed as a decimal is approximately 0.2941. This is a rounded value, as the division of 5 by 17 produces a repeating decimal. To be more precise, the number is actually 0.2941176470588235..., with "2941176470588235" being the repeating unit. However, for most practical purposes, 0.2941 provides a sufficient level of precision.
A bag contains the following prize tickets:
• 6 tickets labeled “8-ounce bottle of SLIME”
• 2 tickets labeled “4 RINGTONES”
• 8 tickets labeled “32-ounce SLUSHIE”
• 4 tickets labeled “16-ounce ICE CREAM SUNDAE”.
Each of the 190 7th grade students who passed the Math benchmark test will draw a prize ticket from the bag. The prize will be recorded for that student, then the ticket will be returned to the bag.
What is a reasonable prediction for the number of times a slushie or an ice cream sundae prize ticket will be drawn?
Responses
A 7676
B 38
C 104
D 114
To predict the number of times a Slushie or an Ice Cream Sundae prize ticket will be drawn, we need to determine the probabilities for those prizes and then multiply by the total number of students.
Calculating the total number of tickets:
6 (SLIME) + 2 (RINGTONES) + 8 (SLUSHIE) + 4 (ICE CREAM SUNDAE) = 20 tickets
Now, find the total probability for drawing a SLUSHIE or an ICE CREAM SUNDAE ticket:
Probability of drawing a SLUSHIE ticket = Number of SLUSHIE tickets / Total number of tickets
Probability of drawing a SLUSHIE ticket = 8 / 20
Probability of drawing a SLUSHIE ticket = 0.4
Probability of drawing an ICE CREAM SUNDAE ticket = Number of ICE CREAM SUNDAE tickets / Total number of tickets
Probability of drawing an ICE CREAM SUNDAE ticket = 4 / 20
Probability of drawing an ICE CREAM SUNDAE ticket = 0.2
Combined probability for drawing either a SLUSHIE or an ICE CREAM SUNDAE ticket:
Combined probability = 0.4 (SLUSHIE) + 0.2 (ICE CREAM SUNDAE)
Combined probability = 0.6
Now multiply the combined probability by the total number of students to predict how many times these tickets will be drawn:
Number of predictions = Combined probability × Number of 7th grade students
Number of predictions = 0.6 × 190
Number of predictions = 114
The reasonable prediction is that a Slushie or an Ice Cream Sundae prize ticket will be drawn approximately 114 times out of the 190 draws. Therefore, the correct answer is D: 114.
The College of Veterinary Medicine at Texas A&M University conducted a study of the rattlesnake vaccine for dogs. The researchers determined that:
•12 out of 15 cases of dogs that received the vaccine prior to the rattlesnake bite survived, and
•8 out of 18 cases of dogs who did not receive the vaccine prior to the rattlesnake bite survived.
If there were 900 dogs in the study that received the vaccine and were then bitten by a rattlesnake, how many of this group did NOT survive the rattlesnake bite?
Responses
A 720
B 400
C 180
D 500
To determine how many dogs did not survive the rattlesnake bite after receiving the vaccine, we first need to find the survival rate of vaccinated dogs from the data provided:
Survival rate for vaccinated dogs = Number of surviving vaccinated dogs / Total cases of vaccinated dogs
Survival rate for vaccinated dogs = 12 / 15
Now we apply this survival rate to the 900 dogs in the study that received the vaccine:
Number of surviving vaccinated dogs (in the large study) = Survival rate for vaccinated dogs × Total vaccinated dogs in the study
Number of surviving vaccinated dogs (in the large study) = (12 / 15) × 900
Calculate this:
Number of surviving vaccinated dogs (in the large study) = (0.8) × 900
Number of surviving vaccinated dogs (in the large study) = 720
Now, to find how many did not survive, we subtract the number of survivors from the total number of vaccinated dogs that were bitten:
Number of non-surviving vaccinated dogs (in the large study) = Total vaccinated dogs in the study - Number of surviving vaccinated dogs (in the large study)
Number of non-surviving vaccinated dogs (in the large study) = 900 - 720
Number of non-surviving vaccinated dogs (in the large study) = 180
The number of dogs that did not survive after receiving the vaccine and being bitten by a rattlesnake is 180. The correct answer is C: 180.
Which two expressions are equivalent to 7(t + 5)?
Responses
A (5 + t) • 7(5 + t ) • 7
B 7 • 5 + 7 • t7 • 5 + 7 • t
C 5(t + 7)5( t + 7)
D 7 • 5 • t7 • 5 • t
E 7 • 5 + t
To find out which expressions are equivalent to 7(t + 5), we need to use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac.
Applying this to 7(t + 5):
7(t + 5) = 7*t + 7*5
7(t + 5) = 7t + 35
Now let's go through the answer choices to identify the equivalent expressions:
A) (5 + t) • 7(5 + t) • 7
This choice seems to be a repetition or typo and does not equal 7t + 35.
B) 7 • 5 + 7 • t
This choice simplifies to 35 + 7t, which is equivalent to 7t + 35 when rearranged according to the commutative property of addition. This is equivalent to 7(t + 5).
C) 5(t + 7)
This simplifies to 5t + 35, which isn't equivalent to 7t + 35 due to the different coefficient before t.
D) 7 • 5 • t
This choice is not equivalent since it's essentially 35t, which does not match 7t + 35.
E) 7 • 5 + t
This simplifies to 35 + t, which isn't equivalent to 7t + 35 because the coefficient of t is 1 instead of 7.
Based on this analysis, the only expression equivalent to 7(t + 5) is:
B) 7 • 5 + 7 • t
So the correct answer for the expression equivalent to 7(t + 5) is B.
Which expression is equivalent to (12 + 5) – (14 ÷ 7)² ?
Responses
A 2 × (9 × 5 + 3²) + 42 × (9 × 5 + 3²) + 4
B 7 + 10 × 5 + 107 + 10 × 5 + 10
C 5 + 15 ÷ (3 + 2)²5 + 15 ÷ (3 + 2)²
D 5 • 6 + 1 – (10 + 8)
To find the expression equivalent to (12 + 5) – (14 ÷ 7)², we must first evaluate each part of the expression within the parentheses, and then apply the arithmetic operations.
(12 + 5) – (14 ÷ 7)²
Calculate what's within the parentheses:
12 + 5 = 17
14 ÷ 7 = 2
Now square the result of (14 ÷ 7):
(2)² = 2 * 2 = 4
Now substitute these results back into the original expression:
(12 + 5) – (14 ÷ 7)² = 17 – 4 = 13
We're looking for the final result of 13. Let's evaluate each of the provided options:
A) 2 × (9 × 5 + 3²) + 4
This expression is not equivalent to 13.
B) 7 + 10 × 5 + 10
This expression is not equivalent to 13.
C) 5 + 15 ÷ (3 + 2)²
This expression is not equivalent to 13.
D) 5 • 6 + 1 – (10 + 8)
This simplifies to 5*6 + 1 - 18, which is 30 + 1 - 18 = 31 - 18 = 13
Thus, the expression from the choices provided that is equivalent to (12 + 5) – (14 ÷ 7)² is:
D) 5 • 6 + 1 – (10 + 8)
What is the prime factorization of 48?
Responses
A 6 • 86 • 8
B 24 • 32 4 • 3
C 23 • 62 3 • 6
D 22 • 12
The prime factorization of a number is expressing it as a product of its prime factors. Let's find the prime factorization of 48:
48 can be divided by 2, which is the smallest prime number, to begin the factorization:
48 ÷ 2 = 24
Now, continue dividing by 2 until you can no longer divide by 2:
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
Since 3 is a prime number, the factorization stops here. Now, let's collect all the factors:
48 = 2 × 2 × 2 × 2 × 3
We can express this with exponents:
48 = 2^4 × 3^1
The prime factorization of 48 is therefore 2^4 × 3. None of the provided responses (A, B, C, or D) correctly express this prime factorization. If we are restricted to the responses given, none matches the prime factorization of 48 accurately:
A) 6 × 8 is not a prime factorization.
B) 24 × 3 does not represent the prime factorization; it breaks down further.
C) 2^3 × 6 is incorrect as 6 is not a prime number.
D) 2^2 × 12 also does not represent the prime factorization as 12 is not a prime number.
We would need an option that says 2^4 × 3 to represent the correct prime factorization of 48. Assuming there was a typographical error in the options provided, the closest one in form would be option B, if it were meant to represent the exponents of the prime factors (though it is still incorrectly written).
Suzanne correctly answered 32 of the 40 questions on her math test.
What decimal is equivalent to the fraction of questions Suzanne answered correctly?
To determine the decimal equivalent to the fraction of questions Suzanne answered correctly, you simply divide the number of questions she answered correctly by the total number of questions on the test.
Suzanne correctly answered 32 out of 40 questions.
So we divide 32 by 40:
32 ÷ 40 = 0.8
Therefore, the decimal equivalent to the fraction of questions Suzanne answered correctly is 0.8.