Answer:
The teacher establishes 7 work stations in each of the classrooms.
Step-by-step explanation:
Each work station has 1/16 pounds of clay.
There are two classrooms with the same number of workstations.
The total amount of clay is 7/8
Then, we look for a number of work stations per classroom x, which multiplied by the number of classrooms (2) and multiplied by the amount of clay per work station (1/16) is equal 7/8.
Then we propose the following equation
[tex]\frac{1}{16}(2x) =\frac{7}{8}\\\\ \frac{2}{16}x = \frac{7}{8}\\\\ x = \frac{16 * 7}{8 * 2}\\\\ x = 7[/tex]
The teacher establishes 7 work stations in each of the classrooms.
Workstations the teacher set up in each of the classrooms is is mathematically given as
x=7
Workstations the teacher set upQuestion Parameters:
An art teacher has a total of 7/8 pound of clay.
The teacher puts 1/16 pound of clay at each workstation.
The teacher sets up an equal number of workstations in each of 2 classrooms
Generally the equation for the workstations is mathematically given as
1/16(x)=7/8
x=16*7/(8*2)
x=7
Therefore,workstations the teacher set up in each of the classrooms is
x=7
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8a - 3(2a + 5) = 13.
a = 14
distribute parenthesis on left side and simplify
8a - 6a - 15 = 13
2a - 15 = 13 ( add 15 to both sides )
2a = 28 ( divide both sides by 2 )
a = [tex]\frac{28}{2}[/tex] = 14
paper clips costs $7.20 what is the unit price of the paper clips
Taylor is comparing the prices of two mattress cleaning companies. Company A charges $30 per mattress and an additional $15 as service charges. Company B charges $28 per mattress and an additional $21 as service charges.
Part A: write equations to represent company A’s and Company B’s total mattress cleaning charges for a certain number of mattresses. Define the variable used in the equations.
Part B: which company would charge less for cleaning 6 mattresses? Justify your answer.
Part C: How much money is saved by using the services of Company B instead of Company A to clean 3 mattresses?
part A:
company a
30m+15
m= matress
company b
28m+21
m=matresses sold
part B:
company a
30(6)+15
195$
company b
28(6)+21
189$
company B charges less
part C:
company a
30(3)+15
105$
company b
28(3)+21
105$
there is no change at all so you do not save anything.
Equations represent Company A and B's charges. Company B charges less to clean 6 mattresses. No savings are made cleaning 3 mattresses with Company B compared to Company A.
Part A: Let x represent the number of mattresses. The total charges for Company A can be represented by the equation: y = 30x + 15, where y is the total cost. The total charges for Company B can be represented by the equation: y = 28x + 21, where y is the total cost.
Part B: To determine which company would charge less for cleaning 6 mattresses, we substitute x = 6 in both equations:
Company A: y = 30(6) + 15 = 180 + 15 = $195
Company B: y = 28(6) + 21 = 168 + 21 = $189
Therefore, Company B charges less for cleaning 6 mattresses.
Part C: To find out how much money is saved by using Company B instead of Company A to clean 3 mattresses, we substitute x = 3 in both equations:
Company A: y = 30(3) + 15 = 90 + 15 = $105
Company B: y = 28(3) + 21 = 84 + 21 = $105
The charges are the same for 3 mattresses, so there is no money saved by using Company B instead of Company A.
Is it true that to finding the LCM you have to divide the product but he GCF? If not give in example why not, and if it’s true, why does it work?
To find the LCM, you CAN divide the product of the two numbers by the GCF.
This is not a very well-known fact, but it is useful at times, especially when we are asked to calculate both the LCM and GCF.
For example, the GCF of 18 and 48 is 6, by inspection or by factors.
Therefore the LCM of 18 and 48 is 18*48/6=864/6=144.
It works because by definition the GCF is the products of all common factors between the two given numbers. Dividing the product by the GCF will therefore remove the duplication of the common factors, leaving a number which contains the factors of each of the two numbers, thus a lowest common multiple.
Note that this method is not the only way to find LCM's.
algebra solving equations with the variable on each side
[tex]\frac{2}{3} n[/tex] [tex]+ 8[/tex][tex]=\frac{1}{2} n[/tex] [tex]+2[/tex]
Firstly, we have to SUBTRACT by [tex]\frac{1}{2}n[/tex] on each of your SIDES [tex]\frac{2}{3}n[/tex] [tex]+ 8[/tex] [tex]-[/tex][tex]\frac{1}{2}n[/tex] [tex]=[/tex][tex]\frac{1}{2} n[/tex][tex]+2[/tex][tex]-[/tex][tex]\frac{1}{2} n[/tex]We get the result of ↓[tex]\frac{1}{6}n[/tex] [tex]+ 8[/tex] [tex]= 2[/tex]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Secondly we have to SUBTRACT by [tex]8[/tex] on each of your SIDES [tex]\frac{1}{6} n+[/tex] [tex]8-8[/tex] [tex]= 2[/tex] [tex]-8[/tex][tex]2 -[/tex] [tex]8[/tex] [tex]= -[/tex][tex]6[/tex]We get the result of ↓[tex]\frac{1}{6} n[/tex] [tex]=-[/tex][tex]6[/tex]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Thirdly, we have to MULTIPLY by [tex]6[/tex] on each of your SIDES [tex]6[/tex][tex](\frac{1}{6}n)[/tex] [tex]=[/tex] [tex]6(-6)[/tex] [tex]6(-6)[/tex] [tex]-36[/tex]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ANSWER: [tex]n[/tex] [tex]=[/tex] [tex]-36[/tex]____________________________________________Good luck on your assignment and enjoy your day! `````````````````````````````````````````````````````````````````````````````````````````````````````~[tex]LoveYourselfFirst:)[/tex]please solve
|q-8|=14
Is 6 a factor, multiple of 24 and is 36and 48 a factor or multiple of 24
Answer:
6 is a factor and 36 is neither and 48 is a multiple
Step-by-step explanation:
need help with this math problem
Which expression can be used to find 20 percent of 92?
Answer:
18.4 but io do not know what expression can be used to find out your questions
Step-by-step explanation:
Answer:
A. 1/5 × 92 is the Expression that can be used in order to find 20% of 92.
Simplify the expression.
(6g)^3
Well, the exponent is distributed to the 6 and g.
g cannot be changed and therefore remains as [tex]g^3[/tex]
[tex]6^3[/tex] can be simplified even further and into the number 216
Therefore, your answer should be:
[tex]216g^3[/tex]
When the highest exponent of any variable is three, then the the expression is termed as cubic expression.
Thus,the given expression is a cubic expression and the answer to the given expression is [tex]216g^3[/tex].
Given expression has two components, a whole number and a variable.
Variables cannot be solved with powers and remain same. Whole number needs to be multiplied by the times its power is.Calculations:
Solving the expression [tex][6\rm g]^3[/tex] :
[tex](6\times\ 6 \times6) g^3 = 216g^3[/tex]
Thus, the final value of the expression is [tex]216g^3[/tex].
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Mrs. Sheppard cuts 1/2 of a piece of construction paper. She uses 1/6 of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower?
she uses 1/12 of the paper
She uses ¹/₁₂ of the sheet of paper to make the flower
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem!
Let :
Total Area of Paper = X
Given:
Mrs. Sheppard cuts 1/2 of a piece of construction paper
[tex]\texttt{Cutting Piece Area of Paper} = \frac{1}{2} \times \texttt{Total Area of Paper}[/tex]
[tex]\texttt{Cutting Piece Area of Paper} = \frac{1}{2} \times X[/tex]
[tex]\texttt{Cutting Piece Area of Paper} = \boxed {\frac{1}{2} X}[/tex]
She uses 1/6 of the piece to make a flower
[tex]\texttt{Area of Paper for Making Flower} = \frac{1}{6} \times \texttt{Cutting Piece Area of Paper}[/tex]
[tex]\texttt{Area of Paper for Making Flower} = \frac{1}{6} \times \frac{1}{2} X[/tex]
[tex]\texttt{Area of Paper for Making Flower} = \frac{1 \times 1}{2 \times 6}X[/tex]
[tex]\texttt{Area of Paper for Making Flower} = \boxed {\frac{1}{12}X}[/tex]
Learn morePerimeter of Rectangle : https://brainly.com/question/12826246Elimination Method : https://brainly.com/question/11233927Sum of The Ages : https://brainly.com/question/11240586Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
a woman has $28,000. part is invested for one year in a certificate of deposit paying 7% interest, and the remaining amount in cash management fund paying 9%. after 1 year, the total interest on the two investments is $2,200. how much is invested at each rate
Answer:
Amount invested at 7% = 16000
Amount invested at 9% = 12000
Step-by-step explanation:
Let x be the amount invested at 7% and y be the amount invested at 9%.
Since the total amount invested is $28000, therefore, we can set up the first equation as:
[tex]x+y=28000[/tex]
Secondly, we are give that sum of two investments is $2200. Therefore, we can write the second equation as:
[tex]0.07x+0.09y=2200[/tex]
Now we need to solve these two equations to get the values of x and y.
First of all, we multiply the second equation with 100 in order to get rid of decimal values.
[tex](0.07x+0.09y)*100=2200*100\\7x+9y=220000[/tex]
Let us use substitution method here. First of all we will solve for y from first equation and plug that into second equation.
[tex]y=28000-x[/tex]
[tex]7x+9(28000-x)=220000\\7x+252000-9x=220000\\-2x=-32000\\x=16000[/tex]
Therefore, amount invested at 7% is $16000 and amount invested at 9% is 28000-16000=$12000.
Seven less than one-fourth of a number is -1 (Write this as an equation) HELP FAST!!!!!
1/4n - 7 = -1
Hope this helps and was fast enough!
The phrase 'Seven less than one-fourth of a number is -1' translates into the mathematical equation: 1/4x - 7 = -1.
Explanation:The subject of your question is Mathematics, and based on the content, it seems like it's geared toward a Middle School level. 'Seven less than one-fourth of a number is -1' can be translated into the equation: 1/4 x - 7 = -1, where 'x' represents the number in question.
To achieve this, the phrase 'one-fourth of a number' translates into 1/4x in mathematics and 'seven less' means you subtract seven from that quantity (hence, -7). Hence, the equation becomes '1/4x - 7'. This equals -1, according to your statement, so the final equation is 1/4x - 7 = -1.
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A 35-inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
Answer:
Step-by-step explanation:
Kylie opened a bank account. She deposited $76.50 into her account every month for 10 months. She used $30.50 every month to pay for singing lessons. After 10 months, she used 1/4 of the total money left in her account to go to a talent camp. What is the total amount of money Kylie spent to go to the talent camp
Answer:
The answer is 115
I need help D: (The question is on the image!)
I am sprry bit I am not sure if I got it right but 560 centimeters if you group the sum of each side and multiply it like 2(2+12)*2(4+6), maybe I switched the multiplications around
Remark
You have to make an assumption here. I know of no other way to do the problem than by making the assumption that 10 * 14 figure is a rectangle. If that is not true, the problem is not solvable.
Step One
Find the length of the shaded area.
The length will be the length of the hypotenuse of a right triangle formed by the two smaller sides = the hypotenuse.
a = 4
b = 12
c = ????
Length
L = square root (a^2 + b^2)
L = √(4^2 + 12^2)
L = √(16 + 144)
L = √160 = √(4*4 * 10)
L = 4√(10)
Width
The width is done the same way.
a = 6
b = 2
w = c = ??
w = √(6^2 + 2^2)
w = √(36 + 4)
w = √40
w = √(2 * 2 * 10)
w = 2 √ 10
Area
Area = L * W
Area = 4√10 * 2√10
Area = 8 * 10
Area = 80
One hot summer day in Austin, Texas the temperature rose 32 degrees over the course of 4 hours. What would be the average increase in temperature per hour.
8 degrees per hour because 32/4 is 8. Hope that helped!
Alba ran 21 miles in three hours what was her average speed
Divide the total amount traveled with the time it took.
21/3 = 7/1
Alba's average speed is 7 miles per hour
hope this helps
7 miles per hour. 21/3
Find the product of 20 x 9 x 5. Tell which property you use?
The answer to 20 x 9 x 5 is 900. You use multiplication property.
Hope this helps! :)
What is the sum of 4 8/10 and 1 1/2
What is the value for y?
Enter your answer in the box.
y =
The given triangle has two sides marked equal and hence is an isosceles triangle.In isosceles triangle base angles are equal <A=<B=50.
Sum of angles in any triangle is 180 degrees.
<A+<B+<C=180°
50+50+5y+10=180
Adding like terms :
110+5y=180
Subtracting 110 on both sides:
5y=70
Dividing both sides by 5:
y=14.
The isosceles triangle, with base angles both at 50 degrees, is solved for the variable y, resulting in y = 14. This value, when substituted, gives angle C as 65 degrees.
The triangle in question is an isosceles triangle, meaning that two of its sides are of equal length. Consequently, the base angles, denoted as angle A and angle B, are also equal, and both are given as 50 degrees. In any triangle, the sum of its angles equals 180 degrees, so for this isosceles triangle:
[tex]\[ \angle A + \angle B + \angle C = 180^\circ \][/tex]
Substituting the known values:
50 + 50 + 5y + 10 = 180
Combining like terms:
110 + 5y = 180
To isolate the variable term, subtract 110 from both sides:
5y = 70
Now, divide both sides by 5 to find the value of y:
y = 14
In conclusion, the value of y is determined to be 14. This signifies that in the given isosceles triangle, angle C is represented as 5y + 10, which becomes 65 degrees. Therefore, the solution provides a comprehensive understanding of the triangle's angle distribution.
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jess buys 5/8 pound turkey and 7/16 pound of cheese. how much turkey and cheese does jess buy?
Jess buys a total of 17/16 pounds, which is equivalent to 1 1/8 pounds, of turkey and cheese combined.
Jess buys 5/8 pound of turkey and 7/16 pound of cheese. To find out how much turkey and cheese Jess buys in total, we need to add these two amounts together. Since both quantities are given in pounds, we can add them directly.
First, let's find a common denominator for the fractions 5/8 and 7/16. The common denominator is 16. Now we write 5/8 with the common denominator, which is the same as 10/16. With the fractions having the same denominator, we can add the numerators together:
(10/16) + (7/16) = (10+7)/16
17/16 pounds
So, Jess buys a total of 17/16 pounds of turkey and cheese. This is equivalent to 1 ⅛ pounds when expressed as a mixed number.
In 2005, 24.8% of all Americans
were under 18 years old. Rhonda
conducts a survey of the ages of
students in eleventh grade at her school.
On November 1, she finds the average
age is 200 months. She also finds that
two-thirds of the students are within
6 months of the average age. Write and
solve an equation to determine the age
limits for this group of students. How
many months will it be until the first of
these students turn 18?
Let's assume
x is the age of 11th grade student
we are given
Rhonda conducts a survey of the ages of students in eleventh grade at her school.
On November 1, she finds the average age is 200 months.
and
She also finds that two-thirds of the students are within 6 months of the average age.
so, we can set up equation as
[tex]|x-200|=3[/tex]
now, we can solve for x
[tex]x-200=3, x-200=-3[/tex]
[tex]x-200=3[/tex]
[tex]x-200+200=3+200[/tex]
[tex]x=203[/tex]
[tex]x-200=-3[/tex]
[tex]x-200+200=-3+200[/tex]
[tex]x=197[/tex]
So, the minimum age of 11th grade student is 197 months
So, the maximum age of 11th grade student is 203 months
now, we are given age is 18 years
we will change into months
[tex]18 years=12*18 months[/tex]
[tex]18 years=216 months[/tex]
So, first of these students turn 18 is
[tex]=216 -203[/tex]
[tex]=13[/tex] months...........Answer
name all the number sets the number 0 belongs to
The number zero (0) belongs to the following sets:
Integers - which are all whole numbers. Zero (0) is a whole number and thus an integer.Real numbers - which are all rational and irrational numbers. Zero (0) is a rational number and thus a real number.Divide x^3 -3x^2 by x-2
. Step 1 - Fill in the missing number:
To divide x^3 - 3x^2 by x - 2, use long division. The quotient is x^2 - x - 4.
Explanation:To divide x^3 - 3x^2 by x - 2, we can use long division. Here are the steps:
Start by dividing the first term of the numerator, x^3, by the denominator, x. This gives us x^2.Multiply the entire denominator, x - 2, by the quotient we found in the previous step, x^2. This gives us x^2(x - 2) which simplifies to x^3 - 2x^2.Subtract this product from the numerator, x^3 - 3x^2 - (x^3 - 2x^2) = -x^2.Bring down the next term from the numerator, which is 0x.Divide this new term, -x^2, by the denominator, x, to get -x.Multiply the entire denominator, x - 2, by the quotient we found in the previous step, -x. This gives us -x(x - 2) which simplifies to -x^2 + 2x.Subtract this product from the previous result, -x^2 - (-x^2 + 2x) = -4x.Bring down the final term from the numerator, which is -6x^2.Divide this term, -4x, by the denominator, x, to get -4.Multiply the entire denominator, x - 2, by the quotient we found in the previous step, -4. This gives us -4(x - 2) which simplifies to -4x + 8.Subtract this product from the previous result, -4x - (-4x + 8) = -8.Therefore, the quotient of x^3 - 3x^2 divided by x - 2 is x^2 - x - 4.
The value of [tex]\( k \)[/tex] is 2.
Which gives a remainder of 0, indicating [tex]\( x - 2 \)[/tex] is a factor of the polynomial [tex]\( x^3 - 3x^2 - 10x + 24 \)[/tex]. The complete synthetic division process for [tex]\( k = 2 \)[/tex] would then be:
2 | 1 -3 -10 24
| 2 -2 -24
---------------------
1 -1 -12 0
The quotient of the division is [tex]\( x^2 - x - 12 \)[/tex] with a remainder of 0.
complete question given below:
Negative three times a number increased by seven less than -11
If there isn't any parenthesis it would be
-3n + 7 < 11
-3n < 4
n > 4 divided by 3
With parenthesis
-3(n+7) < 11
-3n - 21 < 11
-3n < 10
n > - 10 over 3
What is 2−b3=−52 thanks
Answer: 18
Step-by-step explanation:
which of these is not included in the set of rational numbers? all integers, all whole numbers, all repeating decimals, or all non-terminating decimals
Answer: non-terminating decimals
Integers and whole numbers can be converted to fraction form. Example, the whole number 3 can be written as 3/1 which is rational. A rational number is any fraction of whole numbers (eg: 7/19). The denominator can never be zero.
All repeating decimals can be converted into a fraction. A number like 0.8888 with the 8s repeating forever converts to the fraction 8/9, which is rational
Non-terminating decimals are decimals that go on forever. If there is no pattern to the decimal sequence, then the decimals don't repeat and the number cannot be converted to a rational number. Something like pi = 3.14159... has no pattern to the decimal sequence. Therefore, a number like pi is irrational, which literally means "not rational", so numbers like pi aren't rational and are not part of the set of rational numbers.
Non terminating and non repeating decimals cannot be written in fraction from . So they are not included in set of rational numbers.
Given :
Lets take set of rational numbers that can written as a fraction of two numbers.
All integers are positive and negative numbers.
Rational numbers includes integers
Whole numbers starts from 0,1,2..........
Whole numbers are included in rational numbers
Repeating decimals can be written in fraction form .
Non terminating and non repeating decimals cannot be written in fraction from . So they are not included in set of rational numbers.
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A plane intersects a prism parallel to the base of the prism. The cross section is a polygon with eight sides. The base of the prism has ----
sides.
Answer:
4
Step-by-step explanation:
Answer:
The answer is 8 sides.
Step-by-step explanation:
A plane intersects a prism parallel to the base of the prism. The cross section is a polygon with eight sides. The base of the prism has also 8 sides.
The cross-section of a plane parallel to the base is the same shape as the base. The cross section is also an eight sided polygon, so, the base of the prism has 8 sides.