A sandwich shop offers ham, turkey, tuna, chicken salad, and roast beef. It has Swiss, American, and provolone cheese. You can order a sandwich on white, wheat, or rye bread. If a person orders a sandwich and chooses a meat, cheese, and bread at random, how many sandwich choices are there?
Answers
5 different meats
3 different cheeses
3 different breads
5x3x3 = 15*3 = 45
there are 45 choices
Final answer:
The sandwich shop offers a total of 45 different sandwich combinations based on the given options of meats, cheeses, and breads. Each sandwich consists of one type of each category.
Explanation:
The question asked is related to the concept of combinations in mathematics. It gives a variety of choices for making a sandwich - 5 types of meats, 3 types of cheeses, and 3 types of breads. Assuming that each sandwich will have one meat, one cheese, and one type of bread, we can calculate the total combinations by multiplying the number of options in each category together. Combinations are used when the order of selection does not matter.
So, the total number of sandwich combinations would be 5 (meats) * 3 (cheeses) * 3 (breads) = 45 different sandwich choices.
Learn more about Sandwich Combinations here:
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Related Questions
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The number b less the quotient of a number k and 5
Find the vertex, focus, and directrix. y = 1/24(x+1)² - 3.
A Bus can travel 18 3/8 km in an hour. how far can it travel in 3/8 hours
Answers
weekly pay : 420 per week
social security tax rate : 7.65%
federal taxes : 22%
state taxes: 5.95%
All these tax rates are applied to the weekly earnings.
social security tax : 420 x 7.65% = 32.13
federal tax : 420 x 22% = 92.40
state tax : 420 x 5.95% = 24.99
420 - 32.13 - 92.40 - 24.99 = 270.48 take home pay.
Answers
Answer:
the completed factor is (2x + 2)(x + 3).
Step-by-step explanation:
To complete the given factor, we need to find two binomials that multiply together to give us the expression 2x^2 + 8x + 6.
First, let's look at the coefficient of x^2, which is 2. The only way to factor 2x^2 is as 2x * x.
Next, let's look at the constant term, which is 6. We need to find two numbers that multiply to give us 6 and also add up to the coefficient of x, which is 8. The numbers that satisfy this condition are 2 and 3.
Therefore, the factors of 2x^2 + 8x + 6 are:
(2x + 2)(x + 3)
You can verify this by multiplying the two binomials together using the distributive property.
So, the completed factor is (2x + 2)(x + 3).
Answers
-17 = 2x ;
x = - 17 / 2 = - 8.5 ;
2.12 = -7.5 False !
There is no solution !
(a) Find the cost of building 75 sewing machines.
(b) How many sewing machines should the company manufacture
to minimize the cost C?
Answers
OK. So the cost to manufacture any number 'm' machines is
C(m) = 20m^2 - 830m + 15,000 .
Whatever number of machines you're interested in, you write
that number in place of 'm', and this equation tells you the cost
for that many.
Examples:
-- The cost to manufacture zero sewing machines ... what the
company had to invest in equipment and building space before
they could even start manufacturing anything:
C(m) = 20m^2 - 830m + 15,000
C(0) = 20(0)² - 830(0) + 15,000 = 15,000 .
-- The cost to manufacture one sewing machine ... buy the
building, set up the manufacturing equipment, and turn out
the first one:
C(m) = 20m^2 - 830m + 15,000
C(1) = 20(1)² - 830(1) + 15,000 = 14,190 .
Now, part-a) wants to know the cost to build 75 sewing machines.
If you've been paying attention so far, you know you have to take
the same equation, and write '75' in place of 'm'.
C(m) = 20m^2 - 830m + 15,000
C(75) = 20(75)² - 830(75) + 15,000
= 20(5,625) - 830(75) + 15,000
= 112,500 - 62,250 + 15,000 = 65,250 .
===================
Now you need to find the number of sewing machines
that can be built for the lowest total cost.
I'm sure you noticed that the equation for the cost C(m) is a
quadratic equation. So if you drew it on a graph, it would be
a parabola. It would have a minimum value at some 'm', and
for greater 'm', it would start going up again.
(Why should your cost start increasing past some number of
sewing machines ? Well, maybe the manufacturing equipment
is starting to wear out, and needs repair more often. All of that
is actually built into the equation for C(m) . )
Now, I'm not sure what method you've learned for finding the
minimum value of a parabola (quadratic equation). Here are
the two ways I know:
Way #1). If you've had some pre-calculus, then you'll take the
derivative of the equation, set the derivative equal to zero, and
that leads you to the minimum:
The equation: C(m) = 20m^2 - 830m + 15,000
Its first derivative: C'(m) = 40m - 830
'C'; is minimum when C'=0 : 40m - 830 = 0
Add 830 to each side: 40m = 830
Divide each side by 40 : m = 20.75
The number of sewing machines manufactured for the
minimum total cost is 20 or 21 .
Way #2). Really the same as Way-#1 but it's not called 'derivative'.
I looked online for rules of parabolas, and found the one that
you may have learned to use:
For the quadratic expression Ax² + Bx + C ,
the axis (midline) of the parabola is at
x = - B / 2A .
That's exactly what we need.
Our equation is C(m) = 20m^2 - 830m + 15,000
so the axis of the parabola is at m = - (-830)/2(20)
= 830/40 = 20.75 .
Same as Way-1 .
so just input the value you put for m for all the other m's in the problem
ex. if you had f(x)=3x and you wanted to find f(4) then you replace and do f(3)=3(4)=12 so f(3)=12 and so on
A. cost of 75 sewing machines
75 is the number you replace m with
C(75)=20(75)^2-830(75)+15,000
simplify
20(5625)-62250+15000
112500-47250
65250
the cost for 75 sewing machines is $65,250
B. we notice that in the equation, that the only negative is -830m
so we want anumber that will be big enough to make -830m destroy as much of the other posities a possible
-830m+20m^2+15000
try to get a number that when multiplied by 830, is almost the same amount as or slightly smaller than 20m2+15000 so we do this
830m<20m^2+15000
subtract 830m from both sides
0<20m^2-830m+15000
factor using the quadratic equation which is
(-b+ the square root of (b^2-4ac))/(2a) or (-b- the square root of (b^2-4ac))/(2a)
in 0=ax^2+bx+c so subsitute 20 for a and -830 for b and 15000 for c
you will get a non-real result I give up on this meathod since it gives some non real numbers so just guess
after guessing and subsituting, I found that the optimal number was 21 sewing machines at a cost of 6420
−8xy2 + 4x4y2 + 3x3
x4y2 + 4x3y5 + 10x4
x6y2 + 4x3y8 + 10x7
Answers
Answer:
Option A is the correct option.
Step-by-step explanation:
Polynomials given in the question are
1)
2)
3)
4)
In a standard form of a polynomial term with the highest degree should be written first, then second highest degree term and similarly other terms should be written.
Here 1st polynomial is in the standard form only in which degree of terms are as followed.
1 term degree of term = (5 +2) = 7
2nd term degree of term = (3 +1) = 4
3rd term 10x² degree of term = 2
So the answer is option A.
-3x^5^2 + 4x^3y + 10x^2
As you can see, the terms are arranged based on the value of the exponents. From the largest exponent x^5 to the smallest exponent x^2.
Answers
Answer:
B ) Quadrant I andQuadrant III.