Patti uses the associative and commutative properties to simplify the expression by first adding 70 and 30. Then, she combines the result with the other numbers step-by-step. This approach makes mental math easier and more efficient.
Patti is using mental math to evaluate the expression (70 + 12.8 + 30) + 6.1. She recognizes that the expression will be easier to simplify if she can combine 70 and 30 before she works with the other numbers. The properties of operations that allow Patti to take this approach are the associative property and the commutative property.
The commutative property of addition states that the order in which numbers are added does not affect the sum, meaning (a + b) + c = a + (b + c). The associative property of addition states that the way in which numbers are grouped when added does not affect the sum, meaning a + (b + c) = (a + b) + c.
Here’s a step-by-step breakdown:
Combine 70 and 30 first: (70 + 30) = 100.Re-write the expression: (100 + 12.8) + 6.1.Combine the next two numbers: 100 + 12.8 = 112.8.Add the final number: 112.8 + 6.1 = 118.9.Thus, using the commutative and associative properties makes it easier to simplify the expression and arrive at the correct answer of 118.9.
Which of the following is the most appropriate unit to describe the time you can drive a car based on the amount of gas?
A.minutes per gallon,because the independent quantity is the gallons
B.minutes per gallon,because the independent quantity is in the minutes
C.gallons per minute,because the independent quantity is the gallons
D.gallons per minute,because the independent quantity is the minutes
what is the slope and y intercept of the line 4x-2y=7
How to turn Standard Form ( -x + 2y = 10) to Point slope form?
How do i convert five and one sixth into a (terminating or repeating) decimal
3(p+q)=p solve for p and I need the answer asap
Select the graph that would represent the best presentation of the solution set for |x| < 5.
Answer:
It's the graph with -5 to 5.
Step-by-step explanation:
The best presentation of the solution set for |x| < 5 will be - 5 < x < 5.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x |
The inequality is given below.
|x| < 5
Then the solution set for |x| < 5 will be - 5 < x < 5.
The graph is given below.
More about the function link is given below.
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Bonnie has 16 coins worth $1.50. What are the two different combinations of coins she could have?
For a party, 20 sandwiches are being made. If each sandwich is cut into thirds, how many sandwich pieces are there?
How many gallons of a plant food that is 9% nitrogen must be combined with another plant food that is 25% nitrogen to make 10 gal of a plant food that is 19% nitrogen?
To determine the amounts of two plant foods with different nitrogen percentages to create a desired mixture, we set up and solve a system of equations based on the total volume and total nitrogen content.
Explanation:A mixture problem that involves combining two solutions with different percentages of nitrogen to achieve a solution with a desired percentage of nitrogen.
Let's denote the amount of the 9% nitrogen plant food as x gallons and the amount of the 25% nitrogen plant food as y gallons.
Given that we want to end up with 10 gallons of a 19% nitrogen mixture, we can form the following two equations based on the problem's requirements:
Equation 1: x + y = 10 (Total volume of the mixture)
Equation 2: 0.09x + 0.25y = 0.19 × 10 (Total amount of nitrogen in the mixture)
By solving this system simultaneously, we can find the values of x and y.
The second equation can also be written as 9x + 25y = 190 to work with whole numbers.
We can multiply the first equation by negative 9 and add it to the second equation to eliminate x and solve for y.
This will give us the amount of 25% nitrogen plant food needed, and by subtraction of y from 10, we can find the amount of 9% nitrogen plant food required.
Based on the results, we may need multiple gallons of the 9% nitrogen plant food and a specific number of gallons of the 25% nitrogen to achieve our desired 19% nitrogen plant food.
Final answer:
To find the number of gallons of a 9% nitrogen plant food to be combined with a 25% nitrogen plant food, we can set up an equation based on the principle of conservation of mass and solve for the variable representing the number of gallons of the 9% nitrogen plant food.
Explanation:
To find out how many gallons of a plant food that is 9% nitrogen must be combined with another plant food that is 25% nitrogen to make 10 gallons of a plant food that is 19% nitrogen, we can set up an equation based on the principle of conservation of mass.
Let x be the number of gallons of the 9% nitrogen plant food.
Then, (10 - x) would be the number of gallons of the 25% nitrogen plant food.
The equation can be set up as follows:
0.09x + 0.25(10 - x) = 0.19(10)
Solving the equation will give us the value of x, which represents the number of gallons of the 9% nitrogen plant food needed to be combined with the 25% nitrogen plant food.
Find the prime number of 465 822 600 743
Show or explain how to solve the equation for x: 7x = 3
simplify 6³. please help
help! 65-32/8 (/=divided by)
Final answer:
The calculation 65 - 32/8 follows the order of operations, starting with division and then subtraction. Dividing 32 by 8 gives 4, and subtracting this from 65 gives a final answer of 61.
Explanation:
To solve the equation 65 - 32/8, you need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Firstly, you handle the division. You divide 32 by 8 to get 4.
Then, you subtract the result from 65. So, 65 minus 4 equals 61.
The answer to the calculation 65-32/8 (/=divided by) is 61.
I need to look for an answer for 3,547x523 please I need to know the answer please I would be really happy if you give me an answer for this problem
Which equation shoes how the properties of numbers extend to negative whole numbers by commutative property of addition A) -2+4=4+(-2) B)-2(4)=4(-2). C) (-2+4)+3=-2+(4+3. D)-2(4+3)=(2×4)+(-2×3)
A
20-minute
TV program consists of
two commercials, each
1
3
4
minutes
long, and three
equal‐length
entertainment segments. How long is each entertainment segment? Enter your answer as a mixed fraction.
Using the number 691,794 make two three digit numbers that are very close to each other
What is the rational number equivalent to 1.28 repeating A. 1 6 over 97 B.1 28 over 99 C. 1 8 over 33 D. 1 5 over 16
Answer: 1 28/99
Step-by-step explanation:
kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister?
A model to help you start your equation as: Kim’s age + Sister’s age = 36
(a) Write an equation that represents the situation. Explain any variable used.
(b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence
Solve for t. −3t≥39
A local grocery store sells oranges $1.15 per pound, tax included. A shopper buys 1.3 pounds of oranges from the store. Rounded to the nearest cent, how much does the shopper pay for the oranges?
the price for one pound is $1.15
to find the total cost you need to multiply the cost of one pound by the total weight of how much was bought
they bought 1.3 pounds, so multiply 1.3 by 1.15 for the total cost
1.15 * 1.3 = 1.495 which rounds up to $1.50
the shopper paid $1.50
Solve for q. 16−3q=10 Enter your answer in the box.
What are some numbers that have an absolute value greater than 2 1/2
The numbers that have an absolute value greater than 5/2 are 4 and 5.
In general, ImI > 5/2. Where m is any number.
What is an absolute value?The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.
Given:
The absolute value is [tex]2\frac{1}{2}[/tex].
[tex]2\frac{1}{2}[/tex] = 5/2
And we have to find the numbers that have the greater absolute value than 5/2.
5/2 = 2.5.
Any number that is greater than 2.5 is the required number.
Let 4 and 5 re the numbers.
Then, 4 > 5/2 and 5 > 5/2.
Therefore, 4 and 5 are the numbers.
To learn more about the absolute value;
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A team won 6 games and lost 8 games. What was the team's win-loss ratio?
a store is selling sculptures. The first week, it prices 6 sculptures at 80$ each. After each week, if a sculpture is not sold, it will be priced to sell for .85 times the previous weeks price. The store needs to sell the 6 sculptures for a total of at least $270 to make a profit. What is the last week in which all 6 sculptures could be sold so that the store makes a profit?
Answer:
they can stay for 4 weeks
Step-by-step explanation:
I WILL GIVE BRAINLIEST TO WHOEVER IS CORRECT.
Samuel has a coupon for 25% off the regular price of one item at the toy store. He buys a dirt bike that has a regular price of $419.99. The Kentucky tax rate is 6%, what is the price of the dirt bike after the coupon is used. Show your work!
The price of the dirt bike after the coupon is used and after applying the Kentucky sales tax is $333.89. The discount amount is $105, and the sales tax amount is $18.90.
Explanation:To find the price of the dirt bike after the coupon is used, we first need to calculate the amount of the discount. The regular price of the dirt bike is $419.99, and the coupon gives a 25% discount. To find the discount amount, we multiply the regular price by 0.25: $419.99 x 0.25 = $105. Next, subtract the discount from the regular price: $419.99 - $105 = $314.99.
Next, we need to calculate the sales tax. The regular price after the discount is $314.99. The Kentucky tax rate is 6%, which we convert to a decimal by dividing by 100: 6 ÷ 100 = 0.06. To find the amount of sales tax, multiply the regular price after the discount by the sales tax rate: $314.99 x 0.06 = $18.90.
Finally, to find the price of the dirt bike after the coupon and sales tax, add the regular price after the discount and the sales tax: $314.99 + $18.90 = $333.89. Therefore, the price of the dirt bike after the coupon is used and after applying the Kentucky sales tax is $333.89.
Sharon buys 14 folders for 0.75 each.How many change will she receive if she pays with 15
5 + 4 * 2 + 6 – 2 * 2 - 1
Add two different sets of parentheses to make the number 19
I already know (5 + 4) * 2 + 6 – 2 * 2 - 1
but I need one more
THANK YOU SO MUCH
9) Given an 8 foot length of tree trunk with a radius of 3 feet, what is the volume of the tree trunk section? (to the nearest whole ft3)