To adhere to the fire code and server capacity, the restaurant should ideally buy 18 four-seat tables and 4 two-seat tables. This results in a total of 22 tables and maximizes seating capacity at 72.
Explanation:This problem can be solved using a system of linear equations. Let's denote the number of two-seat tables as T and the number of four-seat tables as F.
From the information given, we can establish two equations:
The total number of tables must not exceed 22, so T + F ≤ 22The total number of seats cannot exceed 72, so 2T + 4F ≤ 72To figure out how many of each type of table they should purchase, we need to solve this system of equations.
The goal is to maximize the number of customers (seats) while not exceeding the limits on tables and seats. So, a possible solution to maximize seating would be to have 18 four-seat tables (F = 18) and 4 two-seat tables (T = 4). This gives a total of 22 tables and 72 seats.
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What is 1/4 of 268 ?
To find 1/4 of 268, you divide 268 by 4. The result of this operation is 67.
Explanation:Calculating 1/4 of a number involves a simple mathematical operation known as division. In this case, we want to find out what is 1/4 of 268. To do this, you simply divide 268 by 4.
The calculation is as follows:
Divide the number 268 by 4.268 ÷ 4 equals 67.This means that 1/4 of 268 is 67.
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Which statement is true?
What is the step by step process of solving for the GCF from a list of terms.
Ex. (see picture)
There are two aircraft carriers, A and B, and the carrier A is longer in length the carrier B. The total length of these two carriers is 4178 feet, while the difference of their lengths is only 14 feet.
Answer:
Length of carrier A = 2096 feet Length of carrier B=2082 feet.Step-by-step explanation:
Given , two air craft carriers are A and B . The carrier A is longer than the carrier B in length.
Total length of two carriers =4178 feet
Difference of two carriers = 14 feet
Let
Length of carrier A =x feet
And
Legth of carrier B =y feet
According to question
The I equation is
x+y=4178
The II equation is
x-y= 14
Substitution method: In this method step I : we find value of x or y from the equation I
Step II: put the value of x or y in II equation then we get the value of another varaiable x or y
Step : Again put the obatined value of variable x or y from step II in equation I then we get value of other variable x or y .
By using substitution method ,
we find value of x from equation I
x= 4178-y
Now, put the value of x in equation II then we get
4178-y-y=14
4178-2y=14
4178-14=2y
4164=2y
[tex]y=\frac{4164}{2}[/tex]
y= 2082
Again , put the value of y in equation I
2082 +x=4178
x= 4178-2082
x=2096
Hence, the length of carrier A = 2096 feet
The length of carrier B= 2082 feet
Final answer:
To solve the problem, we set up two equations based on the given total length and the length difference of the two aircraft carriers. By solving these equations, we find that carrier A is 2096 feet long and carrier B is 2082 feet long.
Explanation:
The student's question involves solving a system of linear equations to find the lengths of two aircraft carriers, A and B. Given that the total length is 4178 feet and the length difference is 14 feet, we can set up the following equations:
Equation 1: A + B = 4178
Equation 2: A - B = 14
To solve for A and B, we can add the two equations together to eliminate B.
This gives us 2A = 4192, hence A = 2096 feet.
Substituting A back into one of the equations, we find B = 2082 feet.
Therefore, carrier A is 2096 feet long and carrier B is 2082 feet long.
how to solve this linear equation step by step please
What is the equation of the line that passes through (4,3) and (2,2)
Answer:
The equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].
Step-by-step explanation:
Given information: The line passes through the point (4,3) and (2,2).
If a line passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through the point (4,3) and (2,2), so the equation of line is
[tex]y-3=\frac{2-3}{2-4}(x-4)[/tex]
[tex]y-3=\frac{-1}{-2}(x-4)[/tex]
[tex]y-3=\frac{1}{2}(x-4)[/tex]
Using distributive property, we get
[tex]y-3=\frac{1}{2}(x)+\frac{1}{2}(-4)[/tex]
[tex]y-3=\frac{1}{2}(x)-2[/tex]
Add 3 on both sides.
[tex]y=\frac{1}{2}(x)-2+3[/tex]
[tex]y=\frac{1}{2}(x)+1[/tex]
Therefore the equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].
A rubber ball has a radius of about 2.86 in. Can the ball be packaged in a box shaped like a cube with a volume of 125 in3?
volume of the ball = 4/3 * PI *r^3 =
4/3 * 3.14 * 2.86^3 = 97.99 cubic inches
this is less than the volume of the box, so yes it will fit
Determine whether each of the functions log(n + 1) and log(n2 + 1) is o(log n)
Both functions log(n + 1) and log(n^2 + 1) are not o(log n). For large values of n, log(n + 1) is approximately equal to log n, and log(n^2 + 1) behaves like 2*log n, none of which grows strictly slower than log n.
To determine whether the functions log(n + 1) and log(n2 + 1) are o(log n), we'll use the definition of little-o notation. A function f(n) is said to be o(g(n)) if for any positive constant c > 0, there exists a threshold n0 such that for all n > n0, f(n) < c * g(n). In other words, f(n) grows slower than any constant multiple of g(n) as n approaches infinity.
Analysis for log(n + 1)
When n is very large, the +1 becomes negligible, and log(n + 1) behaves similarly to log n. Therefore,
log(n + 1) ≈ log n when n is large.
This implies that log(n + 1) is not o(log n) because it does not grow strictly slower than any multiple of log n.
Analysis for log(n2 + 1)
Using logarithm properties:
log(n2 + 1) < log(n2 + n2) = log(2n2) = log 2 + 2*log n.
As n grows, the constant term (log 2) becomes insignificant, and the function approaches the behavior of 2*log n. However, since there is a multiple of log n (which is 2*log n), this still means that log(n2 + 1) is not o(log n) because it grows faster, not slower, than log n.
In the rhombus, m<1=8y-6. Find the value of y. Please help!!
Answer: 12
The value of y= 12.
Step-by-step explanation:
We know that the diagonal of rhombus are perpendicular bisector of each other.
i.e. the angle made at the intersection of diagonal is 90 degrees.
Thus , for the given figure m∠1 = 90°
Since it is given that m∠1 = 8y-6
Thus , 8y-6= 90
⇒8y=96 [Adding 6 both sides]
⇒ y = 12 [Dividing both sides by 8]
Hence, the value of y= 12.
A rectangular yard measuring 26ft by 40ft is bordered (and surrounded) by a fence. Inside, a walk that is 2ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
What's the correct answer for this?
From 1980 to 1990, the consumer price index (CPI) increased from 82.4 to 130.7. If a bottle of dish soap cost $0.74 in 1980 and the price of dish soap increased at the same rate as the CPI from 1980 to 1990, by approximately how much did the price of a bottle of dish soap increase from 1980 to 1990?
Using proportions, it is found that the price of a bottle of dish soap increased $0.43 from 1980 to 1990.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The percent increase, as a proportion, of the CPI is given by:
P = 130.7/82.4 = 1.5862.
Hence, for the price of the bottle:
Pb = $0.74 x 1.5862 = $1.17.
The difference is:
1.17 - 0.74 = $0.43.
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Answer: $0.43
Step-by-step explanation:
The cool dude above me already explained it
Manuel is choosing a 3 -letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?
The building of Jim's Hardware is assessed at $109,000. The tax rate is $86.95 per $1,000 of assessed valuation. The tax due is A. $8,695.45. B. $947.75. C. $9,477.55. D. $8,659.54. E. 94,698.23.
write 103,727,495 in word form and expanded
other form to write 600,000+80,000+10
You have taken over an abandoned drilling project. After drilling for 2 hours, the depth is 110 feet. After 5 hours, the depth has increased to 114.5 feet. Write an equation in the form y = mx + b to describe the relationship between x, the hours of drilling, and y, the depth of the well.
A class tossed coins and recorded 165 heads and 172 tails. What is the experimental probability of tails?
Answer:
Probability of tails = 0.51
Step-by-step explanation:
Probability is the ratio of number of favorable outcome to the total number of outcomes.
Total number of outcomes = Total number of heads + Total number of tails
= 165 + 172 = 337
Number of favorable outcome = Total number of tails = 172
[tex]\texttt{Probability}=\frac{172}{337}=0.51[/tex]
A and B are mutually exclusive events. P(A) = 1/3 and P(B) = 1/2. What is the P(A or B)?
a class voted for either kayaking, fishing, or hiking as their favorite summer activity. if hiking got 17% percent of the vote and fishing got 33%, what percentage of the class voted kayaking?
The percentage of the class that voted for kayaking is 50%.
Given data:
To find the percentage of the class that voted for kayaking, use the fact that the total percentage of votes adds up to 100%.
Hiking got 17% of the vote.
Fishing got 33% of the vote.
Let x be the percentage of the class that voted for kayaking.
Since the total percentage of votes is 100%:
17% + 33% + x = 100%
On solving for x:
x = 100% - (17% + 33%)
x = 100% - 50%
x = 50%
Hence, 50% of the class voted for kayaking.
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A set of equations is given below:
Equation A: y = x + 1
Equation B: y = 4x + 5
Which of the following steps can be used to find the solution to the set of equations?
x + 1 = 4x + 5
x = 4x + 5
x + 1 = 4x
x + 5 = 4x + 1
Answer:
x + 1 = 4x + 5
Step-by-step explanation:
To solve this set of equation you can just equalize them ot one another, as you can see they are already in Y form, which means that they have already been solved for Y, so that makes things easier for us, we just insert the second equation in the place of Y in the first one, and we can solve for "x".
Two linear equations are shown.
What is the solution to the system of equations?
Answer:
B.
Step-by-step explanation:
A parallelogram has an area of 48 m². If the base is 12 m long, what is the height?
What is the value of b2 - 4ac for the following equation? x(x + 8) = 9 28 64 100
Answer:
C) 100
Step-by-step explanation:
The given equation is x(x + 8) = 9
Distributing x insides, we get
x^2 + 8x = 9
Now set the equation equal to zero.
x^2 + 8x - 9 =0
Here a = 1, b = 8, and c = -9
b^2 - 4ac = (8)^2 - 4*1*-9
= 64 + 36
= 100
Therefore, b^2 - 4ac = 100.
Answer: C) 100
Hope this will helpful.
Thank you.
Answer:
C. 100
Step-by-step explanation:
Explain the place value relationship when the same two digits are next to each other in a multi-digit number.
Devaughn is 13 years older than Sydney. The sum of their ages is 77 . What is Sydney's age?
Malia is observing the velocity of a cyclist at different times. After two hours, the velocity of the cyclist is 15 km/h. After five hours, the velocity of the cyclist is 12 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 12 hours? (5 points)
53 ℃ below zero degrees
Express the ratio of A's to N's in the word SAVANNAH, in simplest form
A school graduation class wants to hire buses and vans for a trip to Jasper National Park. Each bus
holds 40 students and 3 teachers and cost $1200 to rent. Each van holds 8 students and 1 teacher
and costs $100 to rent. The school has at least 400 students wanting to go, but at most 36 teachers.
What is the minimum transportation cost?