Use the paragraph to answer the question.
Mr. Washington spent the whole summer running a student car wash to raise money for the big garden project. He wants to create a farm-to-table type of program that allows for the school to grow its own fruits and vegetables. Mr. Washington made a pledge to the community last year that, as the new principal, he would do everything in his power to improve the nutritional value of school lunches.
Which answer is explicit evidence from the text about Mr. Washington?
(1 point)
Responses
Mr. Washington is part of the garden project.
Mr. Washington is part of the garden project.
Mr. Washington wants students to wash cars.
Mr. Washington wants students to wash cars.
Mr. Washington made a pledge to the community.
Mr. Washington made a pledge to the community.
Mr. Washington likes fruits and vegetables.
Mr. Washington made a pledge to the community.
Use the paragraph to answer the question.
Dana complained to the produce manager that none of the avocados were ripe. The manager told her that an avocado will ripen quickly if placed in a paper bag with a banana. He also explained that the ripening process can be slowed down by placing the fruit in a refrigerator's crisper drawer. Dana thanked him for the information, and he gave her a coupon for two free avocados.
Which of the following does the text say explicitly about the produce manager?
(1 point)
Responses
He knows a lot about avocados.
He knows a lot about avocados.
He thanked Dana.
He thanked Dana.
He likes to help customers.
He likes to help customers.
He gave Dana a coupon.
He gave Dana a coupon.
Which of the following describes an inference?(1 point)
Responses
a definition of an important term in a text
a definition of an important term in a text
a guess made about what a text is saying
a guess made about what a text is saying
evidence from the text that supports a conclusion
evidence from the text that supports a conclusion
information directly provided in a text
a guess made about what a text is saying
Use this paragraph to answer the question.
Seaweed is used in most ice creams as a thickening agent. The food additive, carrageenan, is made from edible seaweeds and is often listed on the labels of ice cream and other products. There is some controversy over its use in foods that are labeled as "all-natural" or "healthy." The issue over carrageenan is that some studies have suggested it might cause inflammation in the intestines, while others have indicated that it might even contribute to the production of cancer cells. However, many scientists have found these studies to be flawed and declared the food additive as safe to eat.
What does the text explicitly state about carrageenan?
(1 point)
Responses
People like the taste of it in ice cream.
People like the taste of it in ice cream.
Carrageenan is made from edible seaweed.
Carrageenan is made from edible seaweed.
Carrageenan is studied by scientists.
Carrageenan is studied by scientists.
People are concerned over its safety.
People are concerned over its safety.
Which statement is true about the relationships between the number sets?(1 point)
Responses
Some irrational numbers are also integers.
Some irrational numbers are also integers.
All rational numbers are also integers.
All rational numbers are also integers.
Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
Not all natural numbers are real numbers.
Whole numbers include all natural numbers and 0.
Which of the following is true about −9?(1 point)
Responses
It is both an integer and a whole number.
It is both an integer and a whole number.
It is a whole number but not an integer.
It is a whole number but not an integer.
It is an integer but not a whole number.
It is an integer but not a whole number.
It is an integer but not a rational number.
It is both an integer and a whole number.
A sign in a gas station advertises gas at the rate of $3.39910 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?(1 point)
$__
The price per gallon is $3.39910.
Which set of numbers is always rational?(1 point)
Responses
positive numbers
positive numbers
fractions
fractions
decimals
decimals
integers
fractions
The height of an equilateral triangle equals 3√2 times the side length. Using 74 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)
The height of an equilateral triangle equals 3√2 times the side length. Given that the square root of 3 is approximately 74, we can calculate the approximate height as follows:
Height = 3√2 * side length
Height = 3 * 74 * 2 * 8
Height = 3 * 148 * 8
Height = 3 * 1184
Height = 3552
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 3552 meters.
The diagonal of a square equals 2–√ times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side?(1 point)
The diagonal of a square equals 2–√ times the side length. Given that the square root of 2 is approximately 1.4, we can calculate the approximate length from one corner to an opposite corner of a square park that is 700 feet on a side as follows:
Length of diagonal = 2–√ * side length
Length of diagonal = 2 * 1.4 * 700
Length of diagonal = 2.8 * 700
Length of diagonal = 1960
Therefore, the approximate length from one corner to an opposite corner of a square park that is 700 feet on a side is 1960 feet.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between __
and __
.
To find the whole number and rational number that 40−−√ is between, we need to determine the integers on both sides of it. We'll start by approximating the square root of 40:
√40 ≈ 6.32
The whole number less than 40−−√ is 6, and the whole number greater than it is 7. Now, we need to find the rational numbers to the nearest half:
To the nearest half, 6 is 6.0 and 7 is 7.0.
Therefore, 40−−√ is between 6.0 and 7.0.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 7.5 and 8
between 7.5 and 8
between 7 and 7.5
between 7 and 7.5
between 8 and 8.5
between 8 and 8.5
between 8.5 and 9
To find the whole number and rational number that 58−−√ is between, we need to determine the integers on both sides of it. We'll start by approximating the square root of 58:
√58 ≈ 7.61
The whole number less than 58−−√ is 7, and the whole number greater than it is 8. Now, we need to find the rational numbers to the nearest half:
To the nearest half, 7 is 7.0 and 8 is 8.0.
Therefore, 58−−√ is between 7.0 and 8.0.
thats not an option
I apologize for the oversight. Given the options provided, the correct answer is:
between 7.5 and 8
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.
To compare 81−−√ and 8–√8 using rational approximations, we can simplify the expressions:
81−−√ ≈ 9
8–√8 ≈ 7.83
Since 9 is greater than 7.83, the correct inequality statement is:
81−−√ > 8–√8
Write 6,739 in expanded form.(1 point)
Responses
(9×1,000)+(3×100)+(7×10)+(6×1)
left parenthesis 9 times 1,000 right parenthesis plus left parenthesis 3 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis
(6×1,000)+(7×100)+(3×10)+(9×1)
left parenthesis 6 times 1,000 right parenthesis plus left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 9 times 1 right parenthesis
(6×1,000)+(7×100)+(3×10)+(0×1)
left parenthesis 6 times 1,000 right parenthesis plus left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 0 times 1 right parenthesis
(7×100)+(3×10)+(9×1)
(6×1,000)+(7×100)+(3×10)+(9×1)
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 811 as a repeating decimal, we need to divide 811 by the desired denominator. In this case, let's use 9 as the denominator to create the repeating decimal:
811 ÷ 9 = 90 remainder 1
Now, we can express the remainder (1) as a fraction with the same denominator:
1 ÷ 9 = 0.111...
The repeating decimal representation of 811 is 90.111... with a bar over the 1 indicating the repeating cycle of digits.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the method of fraction conversion.
Let's assume the repeating decimal as the variable:
x = 0.727272...
Multiply both sides of the equation by 100 (to shift two decimal places):
100x = 72.727272...
Subtracting the original equation from the new equation eliminates the repeating part:
100x - x = 72.727272... - 0.727272...
Simplifying the equation on both sides:
99x = 72
Dividing both sides of the equation by 99:
x = 72/99
The fraction 72/99 can be further simplified by finding the greatest common divisor (GCD) of both the numerator and denominator, which is 9:
72 ÷ 9 = 8
99 ÷ 9 = 11
So, the simplest form of the rational number equivalent to the repeating decimal 0.72¯¯¯¯¯ is 8/11.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
513
5 Start Fraction 1 over 3 end fraction
525
5 Start Fraction 2 over 5 end fraction
26−−√
start root 26 end root
517
5 Start Fraction 1 over 3 end fraction
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.(1 point)
To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we need to find a rational number that fits these criteria.
We can approximate the square roots as follows:
7–√ ≈ 2.65
8–√ ≈ 2.83
To find a rational number between these two values with a denominator of 7, we can consider the fractions that fall between 2.65 and 2.83 when converted to fractions with a denominator of 7.
One such rational number is 2¾, which is equivalent to 2.75. Converting 2.75 to an improper fraction:
2¾ = 11/4
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 11/4.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.(4 points)
Rational numbers and whole numbers are related, but they are not the same.
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. This includes numbers like 1/2, -3/4, and 5/1. Rational numbers can be positive, negative, or zero.
On the other hand, whole numbers are a subset of rational numbers that include only positive integers (including zero). This means that whole numbers do not include fractions or decimals. Examples of whole numbers are 0, 1, 2, 3, and so on.
While all whole numbers are rational numbers (since they can be expressed as a fraction with a denominator of 1), not all rational numbers are whole numbers. Rational numbers can include fractions and decimals that are not whole numbers, such as 3/2 or 1.5.
To summarize:
- All whole numbers are rational numbers.
- Not all rational numbers are whole numbers.
Examples:
1. Whole number: 5 is a whole number. It is also a rational number since it can be expressed as 5/1.
2. Rational number: 1/3 is a rational number, but it is not a whole number because it is a fraction.