In 3–5 sentences, describe the similarities and differences between scientific laws and scientific theories.(4 points)
Scientific laws are concise and mathematical descriptions of observable phenomena that have been proven true through repeated experimental evidence. They describe what happens or how things work. On the other hand, scientific theories are comprehensive explanations that integrate multiple observations and phenomena. They provide a framework for understanding the laws and principles of nature, and are often subject to revisions and improvements as new evidence emerges. Both laws and theories are based on empirical evidence and are fundamental to the scientific understanding of the natural world, but theories are broader and more complex than laws.
Ninety students auditioned for the school play. One-third of those who auditioned were cast, 6 in major roles. What fraction of those who were cast got major roles? Write your answer as a decimal.
To find the fraction of those who were cast got major roles, we need to divide the number of students who got major roles by the total number of students who were cast.
Since 1/3 of the 90 students who auditioned were cast, there were 90 * (1/3) = 30 students who were cast.
Out of these 30 students, 6 got major roles.
So, the fraction of those who were cast got major roles is 6/30, which simplifies to 1/5.
As a decimal, 1/5 is equal to 0.2.
At Point Pleasant Park, the Advanced Trail is 3.6 times as long as the Medium Trail, and the Medium Trail is 1.2 times as long as the Beginner's Trail. How many times as long as the Beginner’s Trail is the Advanced Trail? Write your answer as a decimal
To find out how many times as long the Advanced Trail is compared to the Beginner's Trail, we need to multiply the different lengths together.
The Medium Trail is 1.2 times as long as the Beginner's Trail.
The Advanced Trail is 3.6 times as long as the Medium Trail, which is equivalent to 3.6 * 1.2 = 4.32 times as long as the Beginner's Trail.
Therefore, the Advanced Trail is 4.32 times as long as the Beginner's Trail.
As a decimal, this is written as 4.32.
There are 78
cups of sugar in a canister in the kitchen. Ms. Johnson used 12
of the sugar when she was preparing dessert for her daughter's birthday cake. How much sugar did she use?
Ms. Johnson used 12 cups of sugar when she was preparing dessert for her daughter's birthday cake.
There are 7\8
cups of sugar in a canister in the kitchen. Ms. Johnson used 1\2
of the sugar when she was preparing dessert for her daughter's birthday cake. How much sugar did she use?
To find out how much sugar Ms. Johnson used for the dessert, we need to calculate 1/2 of 7/8 cups.
To do this, we multiply the fractions:
(1/2) * (7/8) = 7/16
Therefore, Ms. Johnson used 7/16 cups of sugar for the dessert.
How much did Mr. Romanov pay for 9.3 gallons of gas at $3.30 a gallon?
To find out how much Mr. Romanov paid for 9.3 gallons of gas at $3.30 a gallon, we need to multiply the number of gallons by the cost per gallon.
9.3 gallons * $3.30/gallon = $30.69
Therefore, Mr. Romanov paid $30.69 for 9.3 gallons of gas.
One-third of the campers at Rosewood Performing Arts Camp play an instrument. Two-fifths of those campers play the guitar. What fraction of the campers at Rosewood Performing Arts Camp play the guitar?
To find out the fraction of campers at Rosewood Performing Arts Camp that play the guitar, we need to multiply the fractions that represent the proportion of campers who play an instrument (1/3) and the proportion of campers who play the guitar among those who play an instrument (2/5).
(1/3) * (2/5) = 2/15
Therefore, 2/15 of the campers at Rosewood Performing Arts Camp play the guitar.
Which model best represents the expression 2(-4)?
The model that best represents the expression 2(-4) is a number line.
On the number line, you would start at zero and move to the left by 4 units. Then, you would multiply this position by 2.
So, the final position on the number line would be -4 units, and since you multiplied it by 2, the value represented by the expression 2(-4) is -8.
In September, a sporting goods store offers a kayak for $378. Over the next four months, the store reduced the price of the kayak $15 each month. What is the price of the kayak at the end of four months?
To calculate the price of the kayak at the end of four months, we need to subtract $15 from the original price of $378 for each of the four months.
$378 - $15 - $15 - $15 - $15 = $318
Therefore, the price of the kayak at the end of four months is $318.
A diver descends at a rate of 8 m/min. Which expression CANNOT be used to find her depth after 5 minutes?
The expression that cannot be used to find the diver's depth after 5 minutes is:
8 m/min * 5 minutes = 40 meters
The reason this expression cannot be used is that it directly multiplies the rate of descent (8 m/min) by the time (5 minutes) to calculate the total depth. However, this assumes a constant descent rate throughout the entire duration, which may not be the case. The actual depth may vary depending on any changes in the descent rate. Therefore, this expression assumes a constant descent rate and may not accurately represent the diver's depth after 5 minutes.
A diver searches for a sunken treasure that is 97.2 feet below the surface. What is the diver’s elevation when he is 23
of the way down?
To find the diver's elevation when he is 23% of the way down, we need to calculate how much of the total depth he has descended.
23% of 97.2 feet can be found by multiplying 0.23 by 97.2:
0.23 * 97.2 = 22.356
Therefore, when the diver is 23% of the way down, his elevation is 97.2 - 22.356 = 74.844 feet.
A diver searches for a sunken treasure that is 97.2 feet below the surface. What is the diver’s elevation when he is 2\3
of the way down?
To find the diver's elevation when he is 2/3 of the way down, we need to calculate how much of the total depth he has descended.
2/3 of 97.2 feet can be found by multiplying 2/3 by 97.2:
(2/3) * 97.2 = 64.8
Therefore, when the diver is 2/3 of the way down, his elevation is 97.2 - 64.8 = 32.4 feet.
A basketball player is 6 2\3
feet tall. His infant son is 1\4
as tall. How tall is his son?
To find out how tall the basketball player's son is, we need to multiply the height of the basketball player by 1/4.
6 2/3 feet can be converted to an improper fraction as (6 * 3 + 2) / 3 = 20/3 feet.
So, the height of the son is (20/3) * (1/4) = 20/12 = 5/3 feet.
Therefore, the son is 5/3 feet tall.
Sara discarded 1\10
of the 200 apples she picked as defective. The rest were sold as fresh fruit. How many apples picked were sold as fresh fruit?
To find out how many apples Sara sold as fresh fruit, we need to subtract the number of apples she discarded from the total number of apples she picked.
Sara discarded 1/10 of the 200 apples, which is (1/10) * 200 = 20 apples.
Therefore, the number of apples picked that were sold as fresh fruit is 200 - 20 = 180 apples.
How-to books make up 0.3 of the books in the school library. Of these how-to books, 0.2 deal with carpentry and 0.4 deal with electronics.
0.3×0.4=0.12
Interpret what the answer 0.12 represents in this equation above.
(1 point)
Responses
The portion of how-to books that are either carpentry or electronics
The portion of how-to books that are either carpentry or electronics
The portion of books in the library that are how-to books
The portion of books in the library that are how-to books
The portion of books in the library that are how-to books on electronics
The portion of books in the library that are how-to books on electronics
The portion of books in the library that are how-to books on carpentry
The answer 0.12 in the equation represents the portion of books in the library that are how-to books on electronics.
A basketball player is 6 2\3
feet tall. His infant son is 1\4
as tall. How tall is his son?(1 point)
Responses
2 1\6
ft
2 and 1 sixth ft
1 2\3
ft
1 and 2 thirds ft
2 2\3
ft
2 and 2 thirds ft
1 1\2
ft
The correct response is 1 2/3 ft or 1 and 2 thirds ft.
A diver descends at a rate of 8 m/min. Which expression CANNOT be used to find her depth after 5 minutes?(1 point)
Responses
−8+(−8)+(−8)+(−8)+(−8)
negative 8 plus negative 8 plus negative 8 plus negative 8 plus negative 8
−8(5)
negative 8 times 5
−8−8−8−8−8
negative 8 minus 8 minus 8 minus 8 minus 8
−8\5