8 is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003.
What are Integers in Math?
An integer is a number that includes negative and positive numbers, including zero. It does not include any decimal or fractional part. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043Let m be the number of main courses the restaurant serves, so 2m is the number of appetizers.
Then the number of dinner combinations is 2m * m * 3=6m².
Since the customer wants to eat a different dinner in all $365$ days of 2003, we must have
6m² ≥ 365
m² ≥ 60.83
Also, year 2003 is not a leap year, because 2003 divided by 4 does not equal an integer. The smallest integer value that satisfies this is E = 8.
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Find the quadratic function with vertex (1,-2.9) and no intercepts.
Please help me I really just don't understand how to get the answer y+2.9 = -12(x-1)^2 as I need to mathematically prove this equation works.
Answer:
[tex]y+2.9=-12(x-1)^2[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex.a is some constant.Given vertex: (1, -2.9)
Therefore:
h = 1k = -2.9Substitute the values of h and k into the formula:
[tex]\implies y=a(x-1)^2-2.9[/tex]
As the function has no x-intercepts, and the vertex is in Quadrant IV, the parabola will open downwards. Therefore, "a" will be negative. Without any further information, any number can be substituted for "a". Therefore, according to the given answer, let a = -12:
[tex]\implies y=-12(x-1)^2-2.9[/tex]
Note: If "a" was positive, the parabola would open upwards, which means there would be two x-intercepts (two points at which the curve intercepts the x-axis).
Finally, add 2.9 to both sides of the equation so that the equation is in the format of the given answer:
[tex]\implies y+2.9=-12(x-1)^2-2.9+2.9[/tex]
[tex]\implies y+2.9=-12(x-1)^2[/tex]
ten students are taking both algebra and drafting. there are $24$ students taking algebra. there are $11$ students who are taking drafting only. how many students are taking algebra or drafting but not both?
25 students are taking algebra and drafting but not both.
How to find how many students are taking algebra or drafting but not both?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values.
given that
10 students are taking both algebra and drafting.
24 students taking algebra.
11 students who are taking drafting only.
now, find how many students are taking algebra or drafting but not both?
from the question
10 students are taking both algebra and drafting.
24 students taking algebra.
so, subtract 10 in 24
24 - 10 = 14
so, 14 students are taking algebra only.
now, add the both students who are taking algebra and drafting.
11 + 14 = 25.
Hene, 25 students are taking algebra or drafting but not both.
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Evaluate (f+2)(g+8) , when f=4 and g=2.
Answer:
60
Explanation below
elowHope this helps :)
Step-by-step explanation:
1. Substitute the variables with the given numbers.
(4 + 2) (2 + 8)
2. Add the numbers to get the sum.
(6) (10)
3. Since they are in parenthesis multiply the two numbers.
(6) (10) = 60
What is the median of 35, 2, 7, 33, 25, 70, 75, 40, 42, 12,
15, 7, 44, 20, 25, 3, 65, 62
The sum of all proportions in a frequency distribution should be______.
Simplify the expression
Answer:
A
Step-by-step explanation:
Answer:
your answer will be A the first one
Step-by-step explanation:
What can you say about the 3s in 43,862 and 75,398?
Answer:
Step-by-step explanation:
43,862 - place value - 3,000
75,398 - place value - 300
they are also numbers
Hope it helps!!!
:)
3 is subtracted from three times a number
“a number” is x
Answer:
3x - 3
The answer above matches with the statement:
"Three is subtracted from three times a number."
Hope this helps :)
Use version 2 of the arc length formula to find the length of the curve defined by 16xy^2 - y^6 = 9 from (9/16,1) to (9/8,2)
The arc length of the curve is 1.3125
What do you understand by length of the curve?The length of an arc is the separation of two locations along a segment of a curve.
A defined integral between the two points is used to calculate the area under a curve between two points. Integrate y = f(x) between a and b's limits to find the area under the curve y = f(x) between x = a & x = b. Integration within the defined bounds can be used to calculate this area.
the arc length formula
[tex]$$L=\int_C d s=\int_a^b \sqrt{1+\left(\frac{d x}{d y}\right)^2} d y$$[/tex]
now
[tex]$$\begin{aligned}16 x y^2-y^6 &=8 \\y^2\left(16 x-y^4\right) &=8 \\16 x-y^4 &=8 y^{-2} \\16 x &=8 y^{-2}+y^4 \\x &=\frac{1}{2} y^{-2}+\frac{1}{16} y^4\end{aligned}$$[/tex]
[tex]\frac{d x}{d y}=-y^{-3}+\frac{1}{4} y^3[/tex]
now differential line element is
[tex]$$\begin{aligned}d s &=\sqrt{1+\left(\frac{d x}{d y}\right)^2} d y \\&=\sqrt{1+\left(-y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\sqrt{1+y^{-6}-\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{y^{-6}+\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{\left(y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\left(y^{-3}+\frac{1}{4} y^3\right) d y\end{aligned}$$[/tex]
now arc length of the curve in the given interval
[tex]$$\begin{aligned}L &=\int_C d s \\&=\int_1^2\left(y^{-3}+\frac{1}{4} y^3\right) d y \\&=\left[-\frac{1}{2} y^{-2}+\frac{1}{16} y^4\right]_1^2 \\&=-\frac{1}{2}\left(\frac{1}{2^2}-\frac{1}{1^2}\right)+\frac{1}{16}\left(2^4-1^4\right) \\&=\frac{\mathbf{2 1}}{\mathbf{1 6}} \approx \mathbf{1 . 3 1 2 5}\end{aligned}$$[/tex]
this is the arc length of the curve
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the store has a speaker equipment listed for a price of $100 per set of speakers there is a sale, the current selling price is 89.99 how much money does the customer save ?
The amount of money saved by the customer is $10.01
If the selling price is greater than the cost price, then the difference between the selling price and cost price is called profit or the money saved.
If the selling price is less than the cost price, then the difference between the cost price and the selling price is called loss or the money loss.
Profit/ Loss= Cost Price(CP)- Selling Price(SP)
When CP> SP, then we can say there is a profit.
When CP<SP, then we can say there is a loss.
When CP=SP, then we can say neither there is a loss nor profit.
Given data, CP= $100
SP= $89.99
Profit/Loss= CP- SP
= $100- $89.99
= $10.01
As we can see our result is positive, so there is a profit.
Final answer: The amount of money saved by the customer is $10.01
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What is the equation of the slant asymptote of the rational function f(x) = 4x^2+6x-1 / x+2?
Answer:
Hello,
y=4x-2
Step-by-step explanation:
1: slope.
[tex]\displaystyle \lim_{n \to \infty} \dfrac{f(x)}{x}\\\\= \lim_{n \to \infty} \dfrac{4x^2+6x-1)}{x(x+2)}\\\\= \lim_{n \to \infty} \dfrac{4x^2}{x^2}\\\\=\boxed{4}\\[/tex]
2:
[tex]\displaystyle \lim_{n \to \infty} (f(x)-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1}{x+2}-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1-4x^2-8x}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x-2}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x}{x})\\\\=\boxed{-2}\\[/tex]
Slant asymptote is y=4x-2
What does the symbol bc represent
Answer:
ray BC
Step-by-step explanation:
The coordinates of the endpoints of
DE
are D(–13,–10) and E(3,14). Point F is on
DE
and divides it such that DF:EF is 5:3.
What are the coordinates of F?
Write your answers as integers or decimals.
Using proportions, the coordinates of F are given as follows: F(-3,5).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Point F divides the segment such that DF:EF is 5:3, hence the point F is 5/8 of the way, that is:
F - D = 5/8(E - D).
The x-coordinate of F is given by:
x + 13 = 5/8(3 + 13)
x + 13 = 10
x = -3.
The y-coordinate of F is given by:
y + 10 = 5/8(14 + 10)
y + 10 = 15
y = 5.
The coordinates of F are given as follows: F(-3,5).
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6. Select all the expressions that result in the same value as
40 + 120.
A. 4 (10
+30)
B. 2 (20 + 120)
C. 40 (1 + 3)
D. 40 (1 +30)
E. 10 (4+12)
Answer:
A, C, E
Step-by-step explanation:
40 + 120 = 160
Remember the correct order of operations, and do the operation inside parentheses first.
A. 4(10 + 30) = 4(40) = 160
B. 2(20 + 120) = 2(140) = 280
C. 40(1 + 3) = 40(4) = 160
D. 40(1 + 30) = 40(31) = 1240
E. 10(4 + 12) = 10(16) = 160
Answer: A, C, E
Based on the given information, choose the similarity statement that you would use to say ABC~DEF. If you could NOT conclude the triangles similar, then choose NOT.
B = E
B = E is solely not possible to prove that triangle △ABC≅△DEF with any congruency condition so the correct option is (D) NOT.
What do we mean by the congruency of triangles?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.The triangle congruence criteria are as follows:
SSS (Side-Side-Side)SAS (Side-Angle-Side)ASA (Angle-Side-Angle)AAS (Angle-Angle-Side)RHS (Hypotenuse-Leg, right angle)For the given figure it is said that B=E and it is solely not possible to prove that △ABC≅△DEF with any congruency condition.
Therefore, B = E is solely not possible to prove that triangle △ABC≅△DEF with any congruency condition so the correct option is (D) NOT.
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The correct question is given below:
Based on the given information, choose the similarity statement that you would use to say ABC~DEF. If you could NOT conclude the triangles similarly, then choose NOT.
B = E
Options:
(A) AA
(B) SAS
(C) SSS
(D) NOT
Round 45.8 to the nearest whole number
Answer: 46
Step-by-step explanation: 8 is closer to 10, so 45.8 would round to 46
Charlie drove for 5 hours to get from his house to grandma’s house. He averaged 47 miles per hour on the trip. Write
and solve an expression that represents the approximate distance from Charlie’s house to grandma’s house.
Answer:
Answer:
420 miles
Step-by-step explanation:
Distance traveled per hour = 55 miles
Distance traveled in 6 hours = 55 * 6 = 330 miles
Distance of the trip = 330 + 90 = 420 miles
Step-by-step explanation:
helpp me teacher said this is a quadratic formula 3x2+x+1
Answer: 0.434
Step-by-step explanation:
Answer:
3 (x + 16) 2 + 11 12
Step-by-step explanation:
brainliest please
A 4-pound box of blackberries costs $16.64. What is the price per ounce?
Cost of 4 pound box of blackberries = $16.64
Cost of 1 pound box of blackberry = [tex]\bf\frac{\cancel{16.64}}{\cancel{4}}4.16[/tex]
Hence, the cost of 1 pound of blackberry is $4.16.
The perimeter of a geometric figure is the distance around the outside of the figure. The perimeter of a rectangle is 44 feet. The length of the rectangle is 6 feet more than the width. What is the measure of the width?
Write the equation for find the perimeter of the rectangle. (Use the variable w)
How fast is the second car traveling>
The width of the rectangle is 8 feet.
What is the Area of Rectangle?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area.
Perimeter = 44
Length = width + 6
perimeter formula of rectangle = 2(L +W)
44 = 2(W+6 +W)
22 = 2W +6
11 = W + 3
W = 8
therefore , the width of the rectangle is 8 feet
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What is the standard notation for the following expression?
4.62 × 10⁻³
Answer:
Step-by-step explanation:
Calculate 10 to the power of −3 and get 1 over 1000
4.62(1/1000)
the answer is 231 over 50000 or 0.00462
Solve negative four and one third ÷ two and one fifth.
Answer: -2/15 according to the calculator.
Answer:
-1.9681
the 81 is repeating
Step-by-step explanation:
3
5
Dan reads chapters in
56
hours.
What is the unit rate in chapters per hour?
Write your answer in simplest form.
Answer:
How many chapters does Dan read in 56 hours?
Step-by-step explanation:
Number 8 only is algebra
which function below has the largest slope? f(x) x f(x) −3 −10 −1 −7 1 −4 g(x) equals one half x plus 3 h(x) lance gains 1 level each time he plays his favorite video game. he started at level 10. (2 points) f(x) g(x) h(x) the functions all have the same slope
According to the question, the points are [tex](-3,-10)[/tex] and [tex](-1,-7)[/tex] for the function [tex]f(x).[/tex]
The calculated slope for these values are as follows:
[tex]m = \frac{(y(2)-y(1))}{(x(2)-x(1))} = \frac{(-7-(-10))}{(-1-(-3))} = \frac{3}{2} = 1.5[/tex]
The slope for the function [tex]f(x)[/tex] is: [tex]m=1.5[/tex]
Now, the function [tex]g(x)=\frac{1}{2} x+3[/tex]
Using the standard formula that is [tex]y = mx+c[/tex] to calculate the slope for the function [tex]g(x).[/tex]
Slope(m) for [tex]g(x) = \frac{1}{2} = 0.5[/tex]
As per the question, lance gains [tex]1[/tex] level each time he plays the video game.
Therefore, [tex]slope = \frac{1}{1} =1[/tex]
Hence, the slope for the function [tex]h(x)[/tex] is [tex]1[/tex].
Therefore, the function [tex]f(x)[/tex] has the largest slope and it is [tex]1.5.[/tex]
What is the equation of the line?
To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.
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What is 96,902,123 in expanded form
Answer: 90,000,000 + 6,000,000 + 900,000 + 2,000 + 100 + 20 + 3
Step-by-step explanation: you add each one and get 96,902,123
Convert five hours into minutes
Answer:
300 minutes
Step-by-step explanation:
1 hour = 60 Minutes
60x5=300
Oliver and his friends like to collect and trade cards from a certain combat card game. Oliver used his allowance to purchase 5 booster packs and 4 premade decks, which included a total of 178 cards. For his birthday, he received 4 booster packs and 7 premade decks, which included a total of 264 cards. How many cards come in every booster pack and every premade deck?
Solving system of equations in two variable gives that the number of cards in every booster pack are 10 and number of cards in every premade deck are 32
What is system of equations in two variables and how to find its solution by substitution?
Let x and y be two variables and
a₁x+b₁y =c₁
a₂x+b₂y =c₂
Where a₁, a₂, b₁, b₂, c₁, c₂ are constants then we can solve these simultaneous equations by substitution take value of x from equation (1) and then put it in (2) to get an equation for y only and then solve for y. put value of y in equation (1) to get value of x.
Let the number of cards in every booster pack are x and the number of cards in every premade deck be y
Number of cards in 5 booster packs will be 5x and Number of cards in 4 premade deck will be 4y
As Oliver purchases 5 booster packs and 4 premade decks, which included a total of 178 cards.
Thus we get 5x + 4y = 178 .....(1)
Number of cards in 4 booster packs will be 4x and Number of cards in 7 premade deck will be 7y
As Oliver received 4 booster packs and 7 premade decks, which included a total of 178 cards.
Thus we get 4x +7y = 264 ...(2)
System of equations to be solved is
5x + 4y = 178 .....(1)
4x +7y = 264 ...(2)
From (1) , we get x = [tex]\frac{178-4y}{5}[/tex]
Put this value in (2)
[tex]4(\frac{178-4y}{5}) +7y= 264\\\frac{712}{5} -\frac{16y}{5} +7y = 264\\\frac{712}{5}-264=\frac{16y}{5} -7y\\ y= 32\\x= \frac{178-4(32)}{5 }\\ x=50/5\\x=10[/tex]
Therefore x=10 and y= 32
The number of cards in every booster pack are 10 and number of cards in every premade deck are 32
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in jeff’s sample, the number of siblings each person has is as follows: one, two, three, four, and ten. what is the median number of siblings in his sample?
If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3
Given,
The number of siblings each person has = 1,2,3,4 and 10
Arrange them in ascending order =1,2,3,4 and 10
We know the median is the middle term of the ordered pair
The number of terms n= 5
Middle term is = [tex]\frac{n+1}{2}[/tex]
=[tex]\frac{5+1}{2}[/tex]
=3
The 3rd term is 3.
The median = 3
Hence, If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3
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q equals 4 l plus 2 k with l on the horizontal axis and k on the vertical axis, draw an isoquant. the slope of this isoquant equals
The slope of this isoquant equals -2.
What is an isoquant?A contour line formed across a set of locations where the same quantity of output is produced while changing the quantities of two or more inputs is called an isoquant (derived from quantity and the Greek word iso, meaning equal). A factor of production, like as labor, money, land, or organization, is typically represented by the x and y axes on an isoquant. Another name for an isoquant is a "Iso-Product Curve" or a "Equal Product Curve."
The isoquant mapping deals with the cost-minimization, profit, and output maximization problems of producers, whereas an indifference curve mapping helps consumers address the utility-maximizing problem. Indifference curves and isoquants diverge much more.
Calculations:
q=4L+2K
So, MPL=dq/dL =4
MPK=dq/dK =2
So,Slope=-MPL/MPK
=-4/2=-2
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