To find how many ways you can buy 60 cookies using single cookies or packages of 10 or 30, you solve for non-negative integer solutions to the equation x + 10y + 30z = 60 and count the combinations.
Explanation:The question concerns the number of ways to purchase a specific quantity of an item when given different packaging options. Here, we want to find out how many ways you can buy 60 cookies when they are sold singly or in packages of 10 or 30.
To solve this, we can set up a mathematical equation where x, y, and z represent the number of single cookies, 10-cookie packages, and 30-cookie packages, respectively. The equation would be:
x + 10y + 30z = 60
We are looking for all non-negative integer solutions to this equation. By examining the possible combinations, we can systematically list out the ways to achieve the total of 60 cookies using these packaging options.
If we start by using no 30-cookie packages, we can have 0 to 6 packages of 10, with the remainder being single cookies.When using one 30-cookie package, we can have 0 to 3 packages of 10, with the remainder being single cookies.Lastly, if we use two 30-cookie packages, we don't need any 10-cookie packages, and we can just have 0 singles.By counting all the combinations, we can determine how many different ways there are to purchase exactly 60 cookies.
How many quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture?
To obtain a 50% mixture, 2.4 quarts of water must be added to 4 quarts of an 80% mixture.
To solve this problem, we'll use the concept of mixtures.
Let's denote:
x = the number of quarts of water to be added.
We have 4 quarts of an 80% mixture. This means that in these 4 quarts, 80% is the actual substance (let's call it A) and 20% is water.
So, the amount of substance A in the 4 quarts is [tex]\(0.80 \times 4 = 3.2\)[/tex]quarts, and the amount of water is [tex]\(0.20 \times 4 = 0.8\)[/tex] quarts.
When we add \(x\) quarts of water, the total amount of water becomes 0.8 + x, and the total volume of the mixture becomes 4 + x quarts.
For the mixture to be 50%, the amount of substance A in the mixture should be equal to the amount of water. So, we set up the equation:
[tex]\[3.2 = 0.5 \times (4 + x)\][/tex]
Solving for x:
[tex]\[3.2 = 2 + 0.5x\]\[0.5x = 3.2 - 2\]\[0.5x = 1.2\]\[x = \frac{1.2}{0.5}\]\[x = 2.4\][/tex]
So, 2.4 quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture.
what is 89972 rounded to 3 significant figures
The approximation of 89972 to three significant digits is 900
How to round the number?The number is given as:
89972
To round to three signficant digits, we simply count three digits from the left.
i.e. 899
Next, we start the approximation from the next digit
i.e. 7
Hence, the approximation of 89972 to three significant digits is 900
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After 6 months the simple interest earned annually on an investment of $3000 was $811. Find the interest rate to the nearest tenth of a percent.
what is 3.45 repeating as a mixed number
Answer:
3 9/20
Step-by-step explanation:
3.45 is 69/20
60 goes into 20 3 times
which leaves you with 3 9/20
Can you help me with theses problems plz.Also can you explain to me how to get it.Thank you
x+6 /3 = 2+x-2/5
x+6 is a fraction so it's the numerator and the 3 is underneath
same with the right side, x-2 is the numerator and 5 is denominator. help please, i know the answer but I don't know how to get it
Solve for c.
a(c−b)=d
A)c=d − ab/a
B)c=d − ab/b
C)c=ab − d/a
D)c=d + ab/a
Answer: the correct option is
(D) [tex]c=\dfrac{d+ab}{a}.[/tex]
Step-by-step explanation: We are given to solve the following equation for the value of c :
[tex]a(c-b)=d~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for c, we need to take c on one side and all other values on the other side of the equation.
The solution for c of equation (i) is as follows :
[tex]a(c-b)=d\\\\\Rightarrow ac-ab=d\\\\\Rightarrow ac=d+ab\\\\\Rightarrow c=\dfrac{d+ab}{a}.[/tex]
Thus, the required value of c is [tex]c=\dfrac{d+ab}{a}.[/tex]
Option (D) is CORRECT.
Which rational number equals 0.1 repeating?
Answer:
0.1111.... = [tex]\frac{1}{9}[/tex].
Step-by-step explanation:
Given : 0.1 repeating
To find : Which rational number equals 0.1111......
Solution : We have given 0. 11111.........
We can see there is only one number is repeating , we will multiply it by 10
Let x = 0.1111.......
Multiply both sides by 10
10x = 10 * 0.1111.......
10x = 1.1111.......
We can write it in terms of x
10x = 1. 000 + 0.11111....
10 x = 1 + x
On subtracting both sides by x
10 x -x = 1
9 x = 1
On dividing both sides by 9
x = [tex]\frac{1}{9}[/tex].
0.1111.... = [tex]\frac{1}{9}[/tex].
Therefore, 0.1111.... = [tex]\frac{1}{9}[/tex].
The rational number that equals 0.1 repeating is 1/9.
The rational number that equals 0.1 repeating can be represented as follows:
Let x = 0.1 repeating
To convert the repeating decimal to a fraction, we can use the following method:
Let's multiply both sides of the equation by 10 to shift the decimal point one place to the right:
10x = 1.1 repeating
Now, subtract the original equation from this new equation to eliminate the repeating part:
10x - x = 1.1 repeating - 0.1 repeating
9x = 1
Divide both sides of the equation by 9 to solve for x:
x = 1/9
Therefore, the rational number that equals 0.1 repeating is 1/9.
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Which values for x and y make the statement (x - 5)(y + 6) = 0 true?
A. x = -5, y = 6
B. x = 5, y = -6
C. x = -5, y = -6
D. x = 5, y = 6
its b sis.
:') your welcome
can someone please explain what I did wrong and, how I can fix this problem. can I get the explanation as soon as possible please. ❤️
Which expression is equivalent to −10+(−40)+(−90) ?
a −(10−40)+(−90)
b −10−(40−90)
c 10+40+90
d −10+(−90)+(−40)
The required expression is equivalent to −10+(−40)+(−90) is −10+(−90)+(−40). Option D is correct.
Given that,
An equivalent expression to −10+(−40)+(−90) is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
= −10+(−40)+(−90)
= -10 -40 - 90
= -140
a
= −(10−40)+(−90)
= +30 - 90
= -60
b
= −10−(40−90)
=-10+50
= 40
c
= 10+40+90
= + 140
d
=−10+(−90)+(−40)
= -10 - 90 -40
=-140
Thus, the required expression is equivalent to −10+(−40)+(−90) is −10+(−90)+(−40). Option D is correct.
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A high school had 740 students at the start of the year, but then some students left the school. After that, the school had 726 students. If s = the number of students who left the school, which mathematical sentence expresses the information above? A. 740 - s = 726 B. s - 740 > 726 C. s - 740 = 726 D. 740 - s > 726
Answer:
A. 740 - s = 726
Step-by-step explanation:
The equation states: the original number of students, subtracting the number of students that left, represents the number of students now.
Correct option is (A) 740 - s = 726
Given that a high school had 740 students at the start of the year.
However some students left the school. After that, the school had 726 students.
Let 's' be the the number of students who left the school
Thus as 's' students left the school, there will be deduction of 's' students from the school
Now this deduction 's' would be from the 740 students which were present in the school and the resultant students after deduction is given to be '726'
Thus we can form the mathematical expression as follows,
[tex]740 - s = 726[/tex]
Thus '740 - s = 726' is the requires expression
How can you find the sum [8 +(−4)] + (−8 + 4) using mental math?
Identify an ordered pair of the equation 2x = 6y – 24.
In a class, 21 students have black hair, 11 students have blonde hair, 9 students have brown hair and 4 students have red hair. Determine the sector angles needed to construct a circle graph. Determine a name for the circle graph.
What is the measure of angle x?
m∠x = __ °
in the given figure ABIICD . prove that angle BPO + angle POQ + angle DOQ = 4 right angles. 360 degrees
how to find the volume of the cone?
you have 2 quaters and 5 dimes in your pocket write the ratio of quaters to the total number of coins
the angle of elevation from a ship to the top of a 35 m lighthouse on the shore measure 28 degrees. How far is the ship from shore
Garth estimated the height of the door to his classroom in meters.what is a reasonable estimate
What's 3/4 times 168
Beatrice has 15 glasses and 20 mugs. She would like to set them out in identical groups, with none left over. In preparation for a dinner party. What is the greatest number of groups Beatrice can set out?
What does volume measure?
Volume is a measurement that quantifies the amount of three-dimensional space occupied by an object, substance, or region.
What is a volume?Volume is a fundamental physical quantity that describes the extent or size of an object in the context of its three dimensions: length, width, and height.
Volume is commonly expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or cubic feet (ft³), depending on the system of measurement used. It can apply to various entities, including solid objects, liquids, gases, or even abstract concepts like the volume of data.
For solid objects, the volume represents the total amount of space enclosed within its boundaries. It is typically determined by measuring or calculating the product of the object's length, width, and height or through more complex mathematical formulas for irregular shapes.
In the case of liquids or gases, the volume refers to the amount of space occupied by the substance within a container. It can be measured directly using tools such as graduated cylinders or indirectly through displacement methods.
Understanding volume is essential in fields like physics, engineering, architecture, chemistry, and many others where knowledge of spatial quantities is required for designing, analyzing, or describing various objects or systems.
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what is the what is the unit rate of $32.05 / 15 gallons
To find the unit rate of $32.05 for 15 gallons, divide the total cost by the number of gallons, resulting in $2.14 per gallon. This unit rate helps to compare the cost per gallon with other price points.
Explanation:The unit rate is a way to compare a quantity to one unit of another quantity. For the case of $32.05 per 15 gallons, we can calculate the unit rate by dividing the total cost by the number of gallons to find the cost per one gallon.
Step-by-step Calculation
Divide $32.05 by 15 gallons to find the unit rate in dollars per gallon.$32.05 ÷ 15 gallons = $2.14 per gallon.This means the unit rate, or the cost for one gallon of gasoline, is $2.14 per gallon.
Comparing this with other unit prices provided: $2.20 per gallon, $2.00 per gallon, $1.80 per gallon, $1.60 per gallon, $1.40 per gallon, $1.20 per gallon, and $1.00 per gallon, we can observe how this unit rate fits within the broader range of prices and quantities.
Can you ever use a calculator to determine if a number is irrational or rational?
What is the value of s?
0.7(3s+4)−1.1s=7.9
Enter the answer as a decimal in the box.
The value of s from the equation 0.7(3s+4)−1.1s = 7.9 is 5.1.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have,
Equation:0.7(3s+4)−1.1s=7.9
Now, solving equation for s we get
2.1 s + 2.8 - 1.1 s = 7.9
1 s = 7.9- 2.8
s = 5.1
Thus, the value of s is 5.1
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The sales tax rates from 4 different countries are shown in the table. Convert each sales tax rate to a decimal. Then sort the countries from least to greatest tax rates.
Hamilton: 9/160
Oakland: 5.75%
Green: 5 7/8%
Campbell: 11/200
One of the events at the circus starred Gabriella the Human Cannonball. On Saturday she performed in four shows. Shot from a cannon, her distances measured 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters. What was the total distance Gabriella flew that day?
Final answer:
To calculate the total distance Gabriella flew in four shows at the circus, add up the distances she covered in each performance.
Explanation:
The total distance Gabriella flew on Saturday can be calculated by adding up the distances she covered in each show:
Distance 1: 8.05 meters
Distance 2: 17.71 meters
Distance 3: 14.38 meters
Distance 4: 19.35 meters
By adding these distances together, you can find the total distance Gabriella flew that day i.e. 8.05+17.71+14.38+19.35 = 59.49 m
Jessica had $150 in her savings account on the first Sunday of November. Beginning this that week, she say $35 each week. Write a recursive rule that describes how much money Jessica Addie her savings account at the end of n weeks.