The least number of main courses that the restaurant should offer is 8.
What is linear inequality ?The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
Calculationslet m be the number of main courses restaurant serves
so, 2m is the number of appetizers
then the number of dinner combination is = 2m x m x 3 = 6m^2
since the customer wants to eat a different dinner in all 365 days of 2003,
we must have ,
[tex]6m^{2}[/tex] ≥ 365
[tex]m^{2}[/tex] ≥ 60.83.....
also the 2003 is not a leap year
because 2003 / 4 is not equal to an integer
the smallest integer value satisfies this is 8 .
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A box is used to hold bolts for an assembly line. When there are 40 bolts in the box, the total mass is 280 g. When there are 65 bolts in the box, the total mass is 405 g. Find the mass of the box and the mass of each bolt.
The box contains 40 bolts, each weighing 280 g. The package weighs 405 g when there are 65 bolts inside. The bolt's mass is thus 5g, while the box's mass is 80g.
What makes linear equations significant?In many practical applications in daily life, linear equations are a crucial tool in science.
They let scientists, among other things, make predictions, compute rates, and characterize connections between two variables in the physical world. In order to see trends, linear equations are often graphed.
What exactly is the idea behind solving equations?A condition on a variable is an equation when it ensures that two expressions in the variable have the same value.
The variable’s value for which the equation holds true is referred to as the equation’s solution.
Bolts are kept in a box for an assembly line. The package weighs 280 g when there are 40 bolts inside.
In the event that there are 65 bolts in the box, the total mass is 405 g. Find the mass of the bolt and box.Let ‘x’ be the mass of each bolt and ‘y’ be the mass of the box, then we have:
40x + y = 280(1)
65x + y = 405(2)
If we subtract these 2 equations that are for (2) – (1) we get:
25x = 125
X = 5
Using (1) we get
Y = 280-40x
Y = 280-40*5
Y = 80.
Hence the mass of the bolt is 5g and the mass of the box is 80g.
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Identify the mistake and explain why the graph of the aggregate expenditures line does not correctly illustrate the economy's equilibrium.
Given that the 45° line is appropriately positioned in the graph, we may conclude that the aggregate expenditure line does not accurately depict the economy's equilibrium. [See attached Image]
What is the explanation for the above answer?The economy reaches equilibrium when the 45° line intersects the Aggregate Expenditure line. It is worth noting that this occurs at a real domestic output of 280, rather than 340, as indicated by the dashed lines in the graph.
It is to be noted that Aggregate spending is a measure of national income in economics. The present value of all finished products and services in the economy is described as aggregate spending. Thus, aggregate spending is the total of all expenditures made in the economy by the factors over a certain time period.
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Martha paid $6.35 for five pounds of chicken last week .What is the chicken's price per pound.
Answer:
$1.27
Step-by-step explanation:
Question 2(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight.
eleven square root of two minus five square root of seven
eleven square root of four minus five square root of fourteen
six square root of five
six square root of nine
Answer:1. eleven square root of two minus five square root of seven.
Step-by-step explanation:
Given-nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight.
•we can write √8 as 2√2 as 8 =2*2*
•we can write √28 as 2√7 as 28=2*2*
•Now putting these in the given equation we get
•9√2-3√7+2√2-2√7
•11√2-5√7
You have 200 feet of fencing to enclose a rectangular plot that borders on a river (a long side borders the river). If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
The maximum Area that can be enclosed will be 5000 square feet.
In the given question, it is stated that 200 feet of fencing will be done to enclose a rectangular plot with borders on a river. It has a long side on the border of a river which does not needs fencing. We need to find out the Length and Width of the plot that will maximize the area and also find out the Maximum area that can be enclosed.
It is given that the total length of the fence is 200 feet.
Let the length of the plot be l
let the width of the plot be w
=> Total Perimeter will be = l + 2w because the longer side or 1 side of length does not need fencing. Putting the perimeter as 200 we get
=> l + 2w = 200 => Equation (1)
Now, we know the Area of the plot will be l*w,
By equation (1) we get l = 200 - 2w, Putting the values in the Area:
=> Area = (200-2w) * w
=> A = 200w - 2w²
For maximum Area, the derivative of A with respect to w will be 0
=> [tex]\frac{dA}{dW} = 200 - 4w[/tex]
=> [tex]0 = 200 - 4w[/tex]
=> w = 50
Putting w = 50 in Equation (1) we get
=> l = 100
We got our Length l = 100 feet, and Width w = 50 feet. Now we will Calculate the maximum Area to enclose.
=> Area = l*w
=> A = 100*50
=> A = 5000
Hence, the Maximum area to enclose will be 5000 square feet.
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Is the following a function??
The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. Alternatively, we may say that the graph of f is the graph of the equation y.
Explain about the function?A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Up until function composition, that is essentially all there is to "operations on functions." Don't be alarmed by the topic's notation; it simply means what it says: add, subtract, multiply, or divide; then, when necessary, simplify and evaluate.
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If log (m + n) = log m+log n, show that m =n/n-1
log (m + n) = log m+ log n and proved it m =n/n-1
Given;
If log (m + n) = log m+ log n
To show that the m =n/n-1
Now, According to the question:
We know that,
Log (m + n) = log m + log n
Log (m + n ) = log (mn). [log a + log b = log ab ]
Cancelling the log on both sides.
then,
m + n = mn
=> n = mn - m
=> n = m (n - 1)
=> m = n / n - 1
Hence Proved
log (m + n) = log m+ log n and proved it m =n/n-1
What is Logarithm?
A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2.
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Which graph represents the solution to the inequality 2(b + 2) > 24?
Answer:
number line with open point at 10 with arrow pointing left
Step-by-step explanation:
Answer:a
Step-by-step explanation:
Which statement best defines an angle?
A.
two lines that share a common line segment called the vertex
B.
two rays that share a common endpoint called the vertex
C.
two line segments that intersect at a point called the vertex
D.
two lines that intersect at a point called the vertex
The correct statement for the best definition of an angle is,
''two rays that share a common endpoint called the vertex''.
Option B is true.
What is mean by angle?
A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Given that;
Define an angle with the help of definition.
Now,
Since, We know that;
A figure which is formed by two rays that shares a common endpoint vertex is called an angle.
Thus, the best definition of an angle is,
''two rays that share a common endpoint called the vertex''.
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Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5
The equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe is D. y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe.
The equation will be:
y = 5.5 + x
where y = total wheat
The option that correctly reflects this is D.
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Answer:
The answer is D
Step-by-step explanation:
HELP MEEEE PLEASEEEE
A pound of peppers costs $0.62. The total cost varies directly with the pounds of peppers purchased. Write an equation that relates the total cost, c, and the number of pounds of peppers purchased, p.
If a pound of peppers costs $0.62, then multiply the cost by how many pounds you're getting.
At school, the maximum number of students that can be in a classroom is 27. If there are 18 students signed up for the art class, how many more students can join the class?
I am trying to get the inequality as a problem
Step-by-step explanation:
x is the number of students than can still join.
x <= 27 - 18
so,
x <= 9
max. 9 more students can join.
suppose the reading rate of 6th grade students is uniformly distributed (this phrase tells you to use the uniform distribution!) between 100 and 180 words per minute. calculate probability that a selected student has a reading rate less than 115 words per minute.
Answer:
0.84 or 0.48 I cant remember
Step-by-step explanation:
my picture of good luck
Which table does not represent a proportional relationship?
Answer:
Table 3
Step-by-step explanation:
The ratio of x and y is not constant.
A laptop is selling at Digital Direct. The store has an anniversary sale, and everything is 25% off. We have to pay 13% HST on all items purchased from the store. What is the original price of the laptop if you have to pay a total of $677.15 at the cash register?
The original price of the laptop is $479.40.
Given:
Discount on the laptop = 25%
HST paid on the laptop = 13%
Total price of the laptop = $677.15
Let the original price of the laptop be $x.
Price of the laptop after 25% off = x + 25% of x
= $ (125x/100)
Total Price of the laptop after paying 13% HST
= (125x/100) + 13% of (125x/100)
= (125x/100) + (65x/400)
= $ (565x/400)
Now, it is given that the total price paid is $677.15 at the cash register.
565x/400 = 677.15
x = (677.15 × 400)/565
x = $479.40
Therefore, the original price of the laptop is $479.40.
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Complete the statement below. Then use a number line to find the sum 5 + (-2). 5 + (-2) is ___ units from 5, in the ___ direction.
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $61. A season ski pass costs $350. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
7 days would the skier have to go skiing in order to make the season pass less expensive than the daily passes.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. Every mathematical equation begins with L.H.S = R.H.S.
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.
Let s be the cost of skiing per day.
So, the season pass plus ski rentals equates to daily skiing plus ski rentals
450 + 20s = 64s + 20s
450 = 64s
7.03 ≈ s
Hence, 7 days would the skier have to go skiing in order to make the season pass less expensive than the daily passes.
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Is y=x(1-x)-(1-x^2) a linear, quadratic, or absolute value
The y=x(1-x)-(1-x²) is a linear value that is not absolute.
Simplifying,
y=x(1-x)-(1-x²)
y=x-x²-1+x²
y=x-1
Thus, it is a linear equation with a negative value therefore it is not an absolute value.
Ax+By=C is the general form of a two-variable linear equation. When the equation is written in this manner, it is quite simple to obtain both segments (x and y).
Any polynomial that can be rewritten in the canonical form is a quadratic equation. where x represents an unknown quantity and a, b, and c represent known quantities, with a = 0. This indicates that f(x) = 0 is the root of function f(x) = ax2 + bx + c, which is the answer to the quadratic equation ax2 + bx + c = 0.
The absolute value of a real figure x, denoted by |x|, is the non-negative real value of x, regardless of its sign.
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Rollaround skate rink charges $5 admission and $3 per hour for a skate rental. Spinaround skate rink charges $8 admission and $1.50 per hour for a skate rental. Write an equation to determine at what point the cost of both roller skating rinks is the same.
Answer:
2 hours
Step-by-step explanation:
Let x be the time, in hours, for which the cost of Rollaround and Spinaround are the same.
Rollaround Cost (Cr): Cr = $5 + $3x
Spinaround Cost (Cs): Cs = $8 + $1.50x
We want to find the value of x that makes Cr = Cs
Cr = Cs
$5 + $3x = $8 + $1.50x
$1.50x = $3
x = 2 hours
====
CHECK:
Cr = $5+$3(2) = $11
Cs = $8+$1.50(2) = $11
At 2 hours, both cost the same.
An 8 1/2 sheet of paper is being cut into 1 9/16 inch strips to make a paper chain. How many strips can be made from one sheet of paper?
Answer:27/5
Step-by-step explanation: divid 8 1/2 by 1 9/16 and get 5.4 then you put that in fraction form and if I’m correct you get 27/5
Nolan drank 2/3 of a glass of water in the morning and 1/2 of a glass in the afternoon. How much water did Nolan drink in all?\
Answer: 7/6
Step-by-step explanation:
4/6 + 3/6
4+3+6
=7/6
p(x) = -3x - 1
graph the linear function
Answer:
Step-by-step explanation:
1) First find the y-intercept point
You can find it easily by finding the number without the variable. In this case, it is -1. With this draw a point on the y-axis line down to -1.
2) Find the slope.
Next, you can find a point by substituting a number for x. So in this example, I will be subbing x for 1.
y = -3(1) - 1
y= -3 - 1
y= -4
So there will be a point at (1,-4).
3) Graphing.
After you find that you can easily draw a straight line through both points.
Evaluate. Write your answer as a fraction in simplest form. 4/3 to the power of 3
Answer:
[tex]2 \frac{10}{27}[/tex]
Step-by-step explanation:
4/3 to the power of 3 = to 4/3 x 4/3 x 4/3
which in the end equals to 64/27
there's no common factor between them to simplify, but we can turn them into a mixed number, which is 2 10/27 by dividing 64 and 27
Question 22 (3 points)
Given that you are starting with:
4 + 2x = 10 - 4x
What are the equivalent equations in order to solve.
>
6x = 6
Xx = 1
4 +6x = 10
Answer:
Step-by-step explanation:
4+2x=10-4x
4+6x=10
6x=6
x=1
:]
A sailboat costs $26,232. You pay 10% down and amortize the rest with equal monthly payments over a 8-year period. If you must pay 7.5% compounded monthly.what is your monthly payment? How much interest will you pay?Monthly payments: $(Round to two decimal places.)Interest: $(Round to two decimal places.)
Step 1- Write out the Present Value of Annuity formula:
[tex]PV=P\times\frac{1-(1+\frac{r}{n})^{-t\times n}}{\frac{r}{n}}[/tex]Where
[tex]\begin{gathered} PV=\text{ the present value} \\ P=\text{ the periodic payment} \\ n=\text{ the number of payments in a year} \\ r=\text{ annual interest rate} \end{gathered}[/tex]Step 2- Write out the given values and substitute them into the formula:
[tex]\begin{gathered} PV=\$26232(1-0.1)=\$26232\times0.9=\$23608.80 \\ n=12 \\ r=0.075 \end{gathered}[/tex]Substituting the values into the formula, we have:
[tex]23608.80=P\times\frac{1-(1+\frac{0.075}{12})^{-8\times12}}{\frac{0.075}{12}}[/tex]Therefore,
[tex]23608.80=72.0260P[/tex]Dividing both sides by 72.0260, we have:
[tex]P=\$327.78[/tex]Hence, the monthly payment is $327.78.
The total amount T paid is given by:
[tex]T=\$327.78\times8\times12=\$31466.88[/tex]Hence, the interest I is given by:
[tex]I=31466.88-23608.80=\$7858.08[/tex]Therefore, the monthly payment is $327.78 and the interest paid is $7858.08
Jill converted the equation of the line 15x-4y=-2 into slope-intercept form and found the slope and y-intercept of
the line as follows.
15x-4y=-2
15x-4y-15x--2-15x
-4y=-2-15x
-4y -2-15x
-4
22
-4
y-2--16x
y-1-15x
y=-15x+12/2
15
4
slope =
Answer: She got the sign of the slope wrong
Step-by-step explanation:
She did -4y -2 - 15x
-4 = -4
and turned that into ,
-2 - -15x
-4 (minus) -4
which is wrong, because she did the negative twice. Therefore, she mixed up the sign of the slope.
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72. At 6:00 a.m., the temperature was 7 degrees below zero Fahrenheit. At noon, the temperature was 10 degrees higher. At 6:00 p.m., the temperature was 5 degrees cooler than it was at noon. What was the
temperature at 6:00 p.m.?
E. -2°
F. -1°
G. 3°
H. 5°
Answer:
E. -2
Step-by-step explanation:
First, find the temperature at 6 am, which was -7 degrees Fahrenheit
Then, add the ten degrees from noon, making the temperature 3 degrees Fahrenheit
lastly, take away the 5 degrees that dropped making it -2 degrees Fahrenheit
Write the phrase "Four times the difference of six and y equals five less than y" as a variable expression:
Write the phrase "six more than nine times n is twenty" as an equation:
Answer: 4(6-y)
Step-by-step explanation: Since you are multiplying 4 by the difference of 6 and y, you put 6 and y in parenthesis with the 4 on the outside. Then 6-y goes inside the parenthesis.
Also the second one would be (6+9)n=20
How do the digestive and circulatory systems interact?
Answer:
(1) Digestive System gets nutrients (good) from food and hands it over to the blood and Circulatory System then carries those nutrients where they need to go. (2) Filters out waste from food and pushes it through intestines and out the body (and you know how and where it gets out).
Step-by-step explanation:
Digestive System gets nutrients (good) from food and hands it over to the blood and Circulatory System then carries those nutrients where they need to go. (2) Filters out waste from food and pushes it through intestines and out the body (and you know how and where it gets out).
Name one pair of parallel planes. All lines and planes that appear to be parallel are parallel.
The parallel plane is the plane that has the same in-between distance at all points on the plane so plane ABF is parallel with plane DCG so option (C) is correct.
What is the plane?The plane is a two dimension(2D) surface that has a surface area.
We can draw lines on a plane and two or more planes can intersect or parallel.
If two planes are parallel then the perpendicular distance between both planes must be the same.
The angle of inclination of two parallel planes with a single reference plane is also the same.
In the given cuboid the plane ABF is parallel with plane DCG.
So, ABF || DCG.
Hence "The parallel plane is the plane that has the same in-between distance at all points on the plane so plane ABF is parallel with plane DCG".
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