Final answer:
Using the formula for combinations with repetition, with 15 different toppings and no limit on the number of toppings per pizza, we find that there can be 32,768 different possible pizzas.
Explanation:
The question you're asking relates to combinations with repetition, a topic in combinatorics, a branch of mathematics. Given 15 different pizza toppings and the possibility of choosing any number of these toppings for a single pizza (including the possibility of a pizza with no toppings at all), we're essentially looking at how many different pizzas can be created.
To calculate the total number of different pizzas that can be ordered, we use the formula for combinations with repetition, which is (n+r-1)C(r), where 'n' is the number of toppings to choose from (15 in this case), 'r' is the number of toppings chosen, and 'C' represents the combination function. Since there's no limit to the number of toppings, 'r' can vary from 0 (a pizza with no toppings) to 15 (a pizza with all the toppings). However, because the question allows any number of toppings and we consider repetitions, the calculation simplifies to 2ⁿ, where n is the number of toppings.
Therefore, calculating this gives us 2¹⁵, which equals 32,768 different possible pizzas. This includes every combination from no toppings at all to a pizza with all 15 toppings.
What is the logarithmic function modeled by the following table
x
8
16
32
f(x)
3
4
5
A. F(x)= log_x2
B. F(x)= log_2 x
C. F(x)= 2 log_10 x
D. F(x)= x log_10 2
Log_2 8 = 3 (because 2^3 = 8), log_2 16 = 4 and log_2 32 = 5.
What are Logarithms?A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.
For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8. In the same way, 2 = log10 100 since 102 = 100. The latter type of logarithms, those with base 10, are known as common or Briggsian logarithms and are denoted by the letter log n.
Logarithms, which were developed in the 17th century to expedite calculations, significantly decreased the amount of time needed to multiply integers with numerous digits.
Therefore, Log_2 8 = 3 (because 2^3 = 8), log_2 16 = 4 and log_2 32 = 5.
To learn more about Logarithms, refer to the link:
https://brainly.com/question/30085872
#SPJ5
Evaluate: 3 x 5 3x5 when x=2 x=2 . Select one: a. 486 b. 96 c. 30 d. 7,776
how can exponential and logarithmic functions be created to use in real world situations?
what is (13x+9k)+(17x+6k) simplified
The expression (13x+9k)+(17x+6k) simplifies to 30x + 15k. This is done by adding the coefficients of the like terms which in this case are 13x with 17x, and 9k with 6k.
Explanation:The expression (13x+9k)+(17x+6k) is a mathematical expression in algebra with two variables, x and k. The goal here is to simplify the expression by combining like terms. In mathematics, 'like terms' refer to the terms that have the same variables and powers. The coefficients of the like terms can be different.
Now to simplify this expression, we add the coefficients of the like terms. The like terms here are 13x and 17x, and also 9k and 6k.
Add 13x and 17x, you get 30x. And when you add 9k and 6k, you get 15k.
So, the simplified version of the given expression (13x+9k)+(17x+6k) is 30x + 15k.
Learn more about Simplifying Expressions here:https://brainly.com/question/29003427
#SPJ12
a culture started with 5000 bacteria. after 2 hours, it grew to 6500 bacteria. Predict how many bacteria will be present after 18 hrs
A liquid substance was left at the scene of the crime. Krisann uses a beaker that measures to the nearest tenth of a liter and finds that it is 4.9 liters. If there are five or more liters of the substance, it needs to be sent to the lab for testing. If it is less than five liters, the test can be done immediately. Does Krisann need to send the substance to the lab? Why or why not?
If the volume of the substance of 4.9 liters is from x rounded to the nearest tenth of a liter, that means 4.85 <= x < 4.95 then this does NOT leads to x > 5. Therefore the substance does not need to be sent to the lab.
Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 5, 7. Q is at 9, 7. R is at 9, 12. S is at 5, 12 . Rectangle JKLM with vertices J 4, 5. K is at 6, 5. L is at 6, 10. M is at 4, 10. Which statement is correct?
Vera and her roommates ate 1 1/3 pints of ice cream on Friday night and 1 1/6 pints of ice cream on Saturday night. How many pints did they eat in all
1 1/3 + 1 1/6
add the 1 +1 = 2
add 1/3 + 1/6 ( find common denominator, which in this case is 6)
so 1/3 becomes 2/6
2/6 + 1/6 = 3/6 which reduces to 1/2
they ate 2 1/2 pints total
The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + xz2 + yz – 24.
What is the value of x?
What is the value of y?
Answer:
[tex]\text{The value of x and y is } x=5, y=29[/tex]
Step-by-step explanation:
Given the product of two expressions
[tex]4z^2+7z-8\text{ and }-z+3\text{ is }-4z^3+xz^2+yz-24[/tex]
we have to find the value of x and y
First we find the product of
[tex]4z^2+7z-8\text{ and }-z+3[/tex]
[tex](4z^2+7z-8)(-z+3)[/tex]
Opening the brackets
[tex]4z^2(-z+3)+7z(-z+3)-8(-z+3)[/tex]
Using distributive property, a.(b+c)=a.b+a.c
[tex](-4z^3+12z^2)+(-7z^2+21z)+(8z-24)[/tex]
Combining like terms
[tex]-4z^3+(12z^2-7z^2)+(21z+8z)-24[/tex]
[tex]-4z^3+5z^2+29z-24[/tex]
which is required product.
[tex]\text{Now compare above product with given product }-4z^3+xz^2+yz-24[/tex]
[tex]x=5, y=29[/tex]
-13x=90-2y
-6x=48-2y
The solution to the system of equations is x = 6 and y = 84.
Explanation:The given equations are:
-13x = 90 - 2y
-6x = 48 - 2y
To find the values of x and y, we can solve the system of equations. We can start by multiplying the second equation by -2 to eliminate the y variable. This gives us:
12x = -96 + 4y
Now we have two equations:
-13x = 90 - 2y
12x = -96 + 4y
We can add the two equations together:
-13x + 12x = 90 - 2y + (-96 + 4y)
-x = -6
Then, we can divide both sides of the equation by -1 to solve for x:
x = 6
Substituting the value of x back into one of the original equations, we can solve for y. Let's use the first equation:
-13(6) = 90 - 2y
-78 = 90 - 2y
-2y = -168
y = 84
Therefore, the solution to the system of equations is x = 6 and y = 84.
Find the factorization of the polynomial below.
2x²+7x+6
A. (2x+2)(x+4)
B. (2x+2)(x+3)
C. (2x+3)(x+1)
D. (2x+3)(2x+2)
Answer:
(2x+3)(x+2)
Step-by-step explanation:
i hope this helps
Factoring help. Need step by step guidance ....
35n ^ 2 + 22n + 3
The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r. The equation solved for P is P = . What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years? $60 $80 $90 $100
we know that
The simple interest formula is equal to
[tex]I=Prt[/tex]
where
I represents simple interest
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=5\ years\\ P=?\\ I=\$40\\r=0.10[/tex]
[tex]I=Prt[/tex]
Solve for P
[tex]P=I/(rt)[/tex]
substitute the values
[tex]P=40/(0.10*5)=\$80[/tex]
therefore
the answer is
[tex]\$80[/tex]
If BE−→ B E → bisects ∠ABD and m∠ABE = 62°, find m∠ABD
Based on the definition of an angle bisector, m∠ABD = 124°.
What is Angle Bisector?An angle bisector is a line segment that divides an angle into two smaller angles that are congruent.
BE is an angle bisector, therefore:
m∠ABD = 2(m∠ABE)
m∠ABD = 2(62)
m∠ABD = 124°
Learn more about angle bisector on:
https://brainly.com/question/24334771
#SPJ5
Evaluate the function rule for the given value. Y=6*4 for x=-3
How many roots do the following equations have?
-12x2 - 25x + 5 + x3 = 0
A. 4
B. 5
C. 3
D. 2
An open box is formed by cutting squares with side lengths of 3 inches from each corner of a square piece of paper. what is a side length of the original paper if the box has a volume of 675 cubic inches?
What are the vertex, focus, and directrix of the parabola with the equation x^2+8x+4y+4=0
Answer:
Vertex=(-4,3)
Focus=(-4, 2)
Directrix: y=4
Step-by-step explanation:
Given the equation
[tex]x^2+8x+4y+4=0[/tex]
we have to find the vertex, focus, and directrix of parabola.
[tex]x^2+8x+4y+4=0[/tex]
[tex]y=\frac{-x^2}{4}-2x-1[/tex]
[tex]h=\frac{-b}{2a}=\frac{2}{2(\frac{-1}{4})}=-4[/tex]
Now, k can be calculated by putting x=4 and y=k in given equation
[tex]k=-1-\frac{16}{4}-2(-4)=-1-4+8=3[/tex]
The vertex is (h,k) i.e (-4,3)
[tex]y=\frac{-x^2}{4}-2x-1[/tex]
[tex]y=\frac{1}{4}(-x^2-8x-4)[/tex]
[tex]=\frac{1}{4}(-x^2-8x-16+16-4)[/tex]
[tex]y=\frac{1}{4}(-(x+4)^4+12)[/tex]
[tex]y=\frac{-1}{4}(x+4)^2+3[/tex]
which is required vertex form [tex]4p(y-k)=(x-h)^2[/tex]
gives p=-1
Focus=(-4, 3+(-1))=(-4,2)
Now directrix can be calculated as
y=3-p=3-(-1)=4
The key idea of the transformation called a reflection is _____.
the object moves the plane a certain angle measure
the object moves in a straight line movement
the object and its image have opposite orientations
the rotating of a plane about a fixed point
Answer: The object and its image have opposite orientations
Step-by-step explanation:
A reflection is a type of rigid transformation in which the preimage is flipped across a line of reflection to produce the image, such that the figure and its image have opposite orientations.
Since, it preserves distance.
Therefore, the points of the image have the same distance from the line as the points of pre-image on the opposite side of the line.
Hence, the right option is "the object and its image have opposite orientations".
A game involves tossing a biased coin that has a 60% probability of landing on heads. If a player wins $50 when heads appears, what is the expected value of a player's winnings?
You unfold chicken wire to make a circular pen with a diameter of 2.9 meters. how many meters of chicken wire do you need?
circumference = PI x D
using 3.14 for PI
2.9 x 3.14 = 9.106 = 9.11 meters of chicken wire are needed.
what is the radius of a circle given by the equation x^2+(y-3)^2=21
Which statement is true about the discontinuation of the function F(x)? F(x)=x+1/6x^2-7x-3
Evaluate S5 for 600 + 300 + 150 + … and select the correct answer below
Answer:
Hence,
[tex]S_5=1162.5[/tex]
Step-by-step explanation:
We are asked to evaluate:
[tex]S_5[/tex]
We are given a geometric series.
( since each term of the series are in geometric progression as each term is half of the previous term of the series.
i.e. we have a common ratio of 1/2 )
Also, we know that sum of n terms in geometric progression is given by:
[tex]S_n=a(\dfrac{1-r^n}{1-r})[/tex]
where r is the common ratio.
a is the first term of the series.
Here we have:
[tex]a=600\ ,\ r=\dfrac{1}{2}[/tex]
Hence,
[tex]S_5=600(\dfrac{1-(\dfrac{1}{2})^5}{1-\dfrac{1}{2}})\\\\\\S_5=600(\dfrac{2^5-1}{2^4}})\\\\\\S_5=600(\dfrac{31}{16})\\\\\\S_5=1162.5[/tex]
The sum of the first five terms of the geometric progression 600 + 300 + 150 + … is 1162.5.
What is the ratio of geometric progression?A geometric progression is the series of numbers where the ratio of the two consecutive numbers is always the same.
As it is given to us the sequence 600, 300, 150 is a geometric progression. Therefore, the first term of the progression is 600, while the ratio between the two terms are,
[tex]r = \dfrac{300}{600} = \dfrac{1}{2}[/tex]
Now, we know that the sum of the geometric sequence of the first 5 terms can be written as where the value of the n is 5,
[tex]S=a\dfrac{(1-r^n)}{(1-r)}[/tex]
[tex]S=600\dfrac{(1-(\dfrac{1}{2})^n)}{(1-(\dfrac{1}{2}))}[/tex]
[tex]S = 1162.5[/tex]
Hence, the sum of the first five terms of the geometric progression 600 + 300 + 150 + … is 1162.5.
Learn more about Geometric Progression:
https://brainly.com/question/14320920
Find the length of the hypotenuse of a right triangle with legs of lengths 5 and 12. If necessary, round your answer to two decimal places
I need help please :( !!!
a bowl contains 80 M&M candies If 15 are orange what fraction of the candies is NOT orange. Answer reduced to lowest terms
What is the vertex of y=-6(2.5-x)(x-5.5)?
Use the change of base formula to evaluate log4 20.
solve the equation 2x^2-1x=5x
Please enter any square root values using "sqrt" or the decimal answer rounded to the nearest hundredth (i.e. / = sqrt(2) or 1.41).
Answer:
x=0, x=3
Step-by-step explanation: