Ms. Francis is planning a birthday party for her daughter. There will be 22 children at the party, and in order to seat them all she needs to rent square card tables. Only 1 child can sit at each side of a card table.
Ms. Francis wants to arrange the tables in a rectangular shape so they look like one large table. The room is large enough that
the rectangle can be made with more than one row of tables.
Part A: How many different arrangements can Ms. Francis make to seat all 22 children?
Part B: What is the smallest number of tables that Ms. Francis needs to rent?
DIRECTIONS: To solve the problem, apply the steps of the Mathematical Problem-Solving Routine.
Understand
1. Try to visualize the situation. Consider drawing a diagram
2. State the problem in your own words.
3. What is the important information in the problem?
Plan
4. What strategy will you use to solve the problem? Why?
Predict an answer.
Answers to both the subparts are:
(A) Ms. Francis would have to rent 6 tables in order for everyone to have their own side.(B) She could have all of the children sitting at their tables, each with their own side, but the sixth table would only have two other children.What are mathematical operations?An operation is a function in mathematics that takes zero or more input values (also known as "operands" or "arguments") and produces a well-defined output value. The arity of the operation is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied. A constant is an operation of arity zero, also known as a nullary operation. The mixed product is an example of a 3rd order operation, also known as a ternary operation.So, there will be 22 children at the party and each table will have 1 child sitting on each side.
This means that at 1 table there will be sitting 4 children.(A) Ms Francis would have to rent 6 tables in order for everyone to have their own side.
Then,
4 × 6 = 24
(B) She could have all of the children sitting at their tables, each with their own side, but the sixth table would only have two other children.
Therefore, the answers to both the subparts are:
(A) Ms. Francis would have to rent 6 tables in order for everyone to have their own side.(B) She could have all of the children sitting at their tables, each with their own side, but the sixth table would only have two other children.Know more about mathematical operations here:
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A rose bush grows at a rate of 1.5 inches per week about how tall will the rose bush be after 40 weeks will it be reasonable why and why not explain pls ASAP
The rose bush will be 60 inches tall after 40 weeks
Calculating heightFrom the question, we are to calculate how tall the rose bush would have grown in 40 weeks
From the given information,
"A rose bush grows at a rate of 1.5 inches per week"
To calculate how tall the rose bush would have grown in 40 weeks, we will multiply the rate at which the bush grows by 40
That is,
1.5 × 40
= 60 inches
Hence, the rose bush will be 60 inches tall after 40 weeks
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-2x-y+10-x+7y-5 simplified please show steps
Answer:
-3x+6y+5
Step-by-step explanation:
The equation- -2x-y+10-x+7y-5
Next, combine all the x, y, and real numbers.
X's: (-2x)+(-x)= -3x
Y's: (-y)+(7y)=6y
Real Numbers: (10)+(-5)=5
insert back into an equation
-3x+6y+5
:-) hope this helps
- 8x9
8x (3+6)
(8 x) + (8 x.
8x9=
Answer:
72
Step-by-step explanation:
Assume that each circle shown below represents one unit. Express the shaded amount as a single fraction and as a mixed number.
Answer: One fraction: 5/4. Mixed Number:
Step-by-step explanation: One fraction: you need to count the number of green squares on the top, and on the bottom you need to count how many are you each square.
The area of a triangular pendant on a necklace is 3/4 square inch. The height of the
triangle is 1 1/4 inches. What is the length of the base of the triangle?
The length of the base of the triangle is 1 1/5 inches
What are areas?The area of a shape is the amount of space on the shape
How to determine the length of the base of the triangle?The given parameters are
Area = 3/4 square inches
Height = 1 1/4 inches
The length of the base of the triangle is calculated as
Base = 2 * Area/Height
Substitute the known values in the above equation
This gives
Base = 2 * (3/4)/(1 1/4)
Evaluate
Base = 1 1/5
Hence, the length of the base of the triangle is 1 1/5 inches
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Solve for x
5x³-15x²-90x=0
Answer:x=0,6,−3
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero
Rewrite without parentheses and simplify.
(u+6)²
Ú
Answer:
u² + 36 + 12uStep-by-step explanation:
(u + 6)² =
u² + 36 + 12u
Answer:
[tex]u^2+12u+36[/tex]
Step-by-step explanation:
[tex]\begin{aligned}& \textsf{Given}: & & (u+6)^2 \\\\& \textsf{Expand the square}: & & (u+6)(u+6)\\\\& \textsf{Distribute}: & & u(u+6)+6(u+6)\\\\& \textsf{Distribute}: & & u^2+6u+6u+36\\\\& \textsf{Combine like terms}: \quad & &u^2+12u+36\end{aligned}[/tex]
(6(2 + 4) - 1)/(2 * 3 + 1)
Evaluate each expression using the order of operations
Answer:
11/7 is the answer
to your question
1.
Tank A has a length, in feet, represented by 25x + 12 and a width, in feet, represented by 7x + 18. Write and simplify an expression used to determine the total amount of rubber stripping, in feet, needed for both rectangular tanks.
The value of the total amount of rubber stripping, in feet, needed for the rectangular tanks is 64x + 70.
How to calculate the perimeter?It should be noted that the perimeter of a rectangle is given as:
= 2(Length + Width)
= 2(25x + 12) + 2(7x + 18)
= 50x + 24 + 14x + 46
= 64x + 70
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How many zeros will be in the product of 7 times 5,000? Without calculating the answer, explain how to use place value strategies to find the number of zeros in the product
The number of zeros in the product of 7 and 5,000 is 3.
The place value is defined as the value of each digit in a given number.
Here, we are given that 7 is multiplied by 5000
We can see that in 5000, the hundreds, tens and units digits are all zero.
Also, we know that 0 multiplied by any number gives us a zero only.
Thus, when we multiply 5000 and 7, each digit of 5000 will be multiplied by 7.
We can thus see that there will definitely be at least 3 zeroes in their product.
when we 7 is multiplied by 5, the unit digit will not be 0 as 7 is an odd number.
Thus, there are 3 zeroes in the product of 7 and 5000.
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g less than the quotient of 7 and 8
Answer:
"g - (7 • 8)" is correct. :)
Top and bottom needed
The length of the arcs are as follows
L = 1.94 pi cmL = 0.55 pi cmL = 2.50 pi cmL = 5.0 pi cmL = 4.44 pi cmL = 5.0 pi cmL = 4.88 pi cmGiven data
<BAC = 90 degrees
<BEA = 70 degrees
<DEA = 180 degrees
BE = radius = 5 cm
How to determine length of arcstop
Length of arc = ( ∅ / 360 ) * 2 * pi * r
1. length of arc AB
L = ( ∅ / 360 ) * 2 * pi * r
L = ( 70 / 360 ) * 2 * pi * 5
L = 1.94 pi cm
2. length of arc CD
L = ( ∅ / 360 ) * 2 * pi * r
∅ = 180 - 90 - 70 = 20
L = ( 20 / 360 ) * 2 * pi * 5
L = 0.55 pi cm
3. length of arc CB
L = ( ∅ / 360 ) * 2 * pi * r
L = ( 90 / 360 ) * 2 * pi * 5
L = 2.50 pi cm
4. length of arc CAD
∅ = 90 + 70 + 20 = 180
L = ( ∅ / 360 ) * 2 * pi * r
L = ( 180 / 360 ) * 2 * pi * 5
L = 5.0 pi cm
5. length of arc BCA
∅ = 90 + 70 =
L = ( ∅ / 360 ) * 2 * pi * r
L = ( 160 / 360 ) * 2 * pi * 5
L = 4.44 pi cm
6. length of arc DA
∅ = 180
L = ( ∅ / 360 ) * 2 * pi * r
L = ( 180 / 360 ) * 2 * pi * 5
L = 5.0 pi cm
Bottom
7. length of arc from off to volume 7
∅ = 110
r = 8
L = ( ∅ / 360 ) * 2 * pi * r
L = ( 110 / 360 ) * 2 * pi * 8
L = 4.88 pi cm
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Which of the following pairs consists of equivalent fractions?
Answer:
I think it's the last answer
cost to rent a pavilion is $50 plus $15 for each hour of use.
e a rule for the cost of renting a park pavilion. Write ordered
= to represent the cost of renting a pavilion for 3, 4, 5, and 6 hours.
Answer:
the cost of renting the pavilion for 8 hours = $130
Step-by-step explanation:
$50 plus $10 per hour
so 8 hour = 10 * 8 = $80
$50 + $80 = $130
The annual tuition at a specific college was $20,500 in 2000, and $45,4120
in 2018. Let x be the year since 2000, and y be the tuition. Write an
equation that can be used to find the tuition y for x years after 2000. Use
your equation to estimate the tuition at this college in 2020.
y = 20500 + 24090(x - 1) can be used to find the tuition y for x years after 2000. The tuition at this college in 2020 was $5,02,300.
We assume that the rate of increase in the cost of tuition fee per year is linear and hence the tuition fees of subsequent years will be in an Arithmetic Progression. The formula for determining the nth term of an arithmetic sequence which is expressed as-
Tn = a + (n - 1)d
Where
a = first term of the sequence.
d = common difference.
n = number of terms in the sequence.
According to the question,
a = $20500 (amount in 2000)
From 2000 to 2018, the number of terms is 19, hence,
n = 19
Thus, T19 = 454120
Therefore,
4,54,120 = 20500 + (19 - 1)d
454120 - 20500 = 18d
18d = 433620
d = 433620/18
d = 24,090
Therefore, the equation that can be used to find the tuition y for x years after 2000, is as follows-
y = 20500 + 24090(x - 1)
Now, the number of terms between 2000 and 2020 is 21, hence
x = 21
y = 20500 + 24090(21 - 1)
y = 20500 + 481800
y = $502300
Therefore, the tuition at this college in 2020 was $5,02,300.
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Is 87 3 times as many as 29?
Answer:
Yes
Step-by-step explanation:
29 times 3 is 87
Hope It Helps
Sorry If I'm Wrong
Is 1 an unequal number
Answer:
Step-by-step explanation:
i 1=i i+i = 1 paulit ulit lg pag dalawa ung term i po sagot jan
find the circomference of the circle.
Answer:
d=23in
circumference= πd
= 23×3.14
=72.22 probably
A box turtle Marcos found is 0.115 of a meter long. What is this length in expanded form?
If a box turtle Marcos found is 0.115m long, then the length in expanded form is (0.1 + 0.01 + 0.005).
As per the question statement, a box turtle Marcos found is 0.115m long.
We are required to find out the expanded form of the length.
To solve this question, we need to know the procedure to convert a decimal into a fraction:
First, we will have to eliminate the decimal point and then, consider the digits in the same order as a complete number which will be our numerator. Secondly, we will use (10ⁿ) as our denominator where "n" is the number of digits on the right side of the decimal point in the original decimal number. Thus, 0.115 can be written as [tex]\frac{115}{1000}[/tex], since there are three digits after decimal point.
Now [tex]\frac{115}{1000}[/tex] can be written in the following manner as shown below.
[tex]\frac{115}{1000}=\frac{100+10+5}{1000}\\ or, \frac{115}{1000}=\frac{100}{1000}+\frac{10}{1000}+\frac{5}{1000}\\ or, \frac{115}{1000}=\frac{1}{10}+\frac{1}{100}+\frac{5}{1000}\\ or, \frac{115}{1000}=0.1+0.01+0.005[/tex]
Therefore, 0.115 can be written as (0.1 + 0.01 + 0.005) in its expanded form.
Expanded Form (of a number or decimal): This is a format of writing a number as a summation of its individual digits multiplied by their place values.
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Find the distance between the points J(-8, 0) and K(1, 4). Answer in simplest exact form.
What’s the exact distance?
Answer:
distance = [tex]\bf \sqrt{97}[/tex] units
Step-by-step explanation:
To find the distance between two points given their coordinates, we can use the following formula:
[tex]\boxed{\mathrm{distance} = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}}[/tex],
where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are coordinates of the two points.
The two points we are given are:
• J(-8, 0)
• K(1, 4).
Using these coordinates and the formula above, we can calculate the distance between the points:
distance = [tex]\sqrt{(-8 - 1)^2 + (0 - 4)^2}[/tex]
= [tex]\sqrt{(-9)^2 + (-4)^2}[/tex]
= [tex]\sqrt{81 + 16}[/tex]
= [tex]\bf \sqrt{97}[/tex]
Therefore, the distance between J and K is [tex]\bf \sqrt{97}[/tex] units.
A can of soup is composed of 40% solids and 60% water. If a can of soup is mixed with two cans of water, what percentage of the mixture is water?
Assuming that a can of soup which has 60% water is mixed with two cans of water, the percentage mixture that is water is 87%.
What percentage is water?Assuming the total quantity of a can is 100 ml, the quantity of water in the can of soup would be:
= 60% x 100
= 60 ml
If two more cans of water are added, the total amount of water is:
= 60 + 100 + 100
= 260 ml
The percentage of water is:
= 260 / (100 + 100 + 100)
= 87%
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The post office will only accept packages for which the length plus the "girth" (distance around) is no more than 108 inches. Thus, we must have L+2(x+y)<=108.
What is the greatest acceptable length for a package that has a square base measuring 9 inches by 9 inches?
answer
6 in. wide, 8 in. deep and 5 feet long.
In a video game, players start with a score of 100 points.
They earn 8 points for each gold coin and 25 points for
each gem they find. Mario finds 3 gold coins and 2 gems.
Write and evaluate an algebraic expression to find Marios
score. Use c for the number of gold coins found and g for
the number of gems found. Show your work.
SOLUTION
Mario's score in the video game is 174.
What is Mario's score?
Mario's score is a function of the number of points started with, the point per coin, the point per gem , number of gem and coins found. The mathematical operations that would be used are addition and multiplication.
Addition is the process of determining the sum of two or more numbers. Multiplication is the process of determining the product of two or more numbers.
Mario's score = beginning point + (number of gold coins x score per gold coin) + (number of gems x score per gem)
Mario's score = 100 + 3c + 2g
Mario's score = 100 + (3 x 8) + (2 x 25)
Mario's score = 100 + 24 + 50 = 174
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Describe the transformation from the graph off to the graph of g. PLEASE HELP!
Answer: x=-3
Step-by-step explanation: Linear function of -3. This is because you subtract by 3 from f to g each time.
18
26
52
44
Mandy is working at the zoo. She must record the ages of the tortoises There are 9 tortoises.
Their ages are 29, 2, 12, 26, 18, 34, 54, 44, and 18.
What is the mean age of the tortoises? You may use a calculator. Round to the nearest whole
number.
3) Read the following and answer the question
Answer:
26 is the approximate mean
Nina wants to download games for her video game console. Older games cost 150 points and new releases cost 600 points. Nina has 6000 points to use. The equation 150a+600b=6000, where a is the number of older games and b is the number of new releases, models the situation. How many older games can she download if she downloads one new game? four new games?
Considering the definition of an equation and the way to solve it, Nina can download 36 older games and 24 older games if she downloads one and four new games respectively.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseIn this case, Nina wants to download games for her video game console. Older games cost 150 points and new releases cost 600 points. Nina has 6000 points to use.
The equation 150a+600b=6000, where a is the number of older games and b is the number of new releases models the situation.
If Nina downloads one new game, that means that the value of the variable "b" is 1. Substituting in the equation that models the previously mentioned situation, and solving, you obtain:
150a+600×1=6000
150a + 600=6000
150a= 6000 - 600
150a= 5400
a= 5400÷150
a= 36
If Nina downloads four new game, that means that the value of the variable "b" is 4. Substituting in the equation that models the previously mentioned situation, and solving, you obtain:
150a+600×4=6000
150a + 2400=6000
150a= 6000 - 2400
150a= 3600
a= 3600÷150
a= 24
Finally, Nina can download 36 older games and 24 older games if she downloads one and four new games respectively.
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As Lucia fills her fish tank, she notices that it fills 8 cubic centimeters of water in 4 minutes.
How many cubic centimeters of water does it fill in 1 minute?
Distribute 10(3x+8x^2)
Answer:
Evaluate
30x + 160xn
Step-by-step explanation:
Answer:
Solution :
30x + 80x^2
Step-by-step explanation:
1) Distribute the outer term into the first by multiplying the numerical values and then the terms
2) Repeat for the second one.
If you multiply two decimals that ares less then 1 can you predict whether the product will be less than or greater than either of the factors Explain.