11. A pizza parlor has four types of crust, 12 different toppings, and three different cheese blends to choose from. In how many ways could you order a three-topping pizza (one type of crust, three different toppings, and one cheese blend)
Answers
Answer: 1320
Step-by-step explanation:
Given: In pizza parlor, Number of types of crust = 4
Number of types of different toppings = 12
Number of types of cheese blends = 3
Now, the number of ways to choose a pizza with one type of crust, three different toppings, and one cheese blend
= \(^{4}C_1\times\ ^{12}C_3\times\ ^3C_1\)
= \(4\times \ \dfrac{12!}{3!(12-3)!}\times 3\ \ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!},\ ^nC_1=n]\)
= \(12\times\dfrac{12\times11\times10\times9!}{2\times6\times9!}\)
= \(12\times11\times10= 1320\)
Hence, the required number of ways = 1320
Using the Fundamental Counting Theorem, it is found that you could order a three-topping pizza in 144 ways.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:
\(N = n_1 \times n_2 \times \cdots \times n_n\)
In this problem, we have that a pizza parlor has four types of crust, 12 different toppings, and three different cheese blends to choose from, hence:
\(n_1 = 4, n_2 = 12, n_3 = 3\)
Then:
\(N = 4 \times 12 \times 3 = 144\)
You could order a three-topping pizza in 144 ways.
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Related Questions
Please answer these questions in the image ( click image to see fully )
Answers
9) x= -7
10) x= 10
11) x= 5
12) x= 6
13) x= 4
14) x= -9
15) x= 3
16) x= 9
sorry it took so long! hope this helps!! :)
Mabel spends 4 hours to edit a 3 minute long video. She edits at a constant rate. How long does Mabel spend to edit a 15 minute long video
Answers
The number of hours spent by Mabel to edit the 15 minute long video according to the task content is; 20 hours.
What is the time taken by Mabel to edit the hour?According to the task content, it can be inferred that for a 3 minute video, Mabel spends 4 hours.
On this note, it follows from proportion that the time taken by Mabel to edit the 15 minute video would be; 4hours × 5 = 20 hours.
Hence, the time taken to edit the 15minute long video is; 20 hours.
hi
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Write a sine function with an amplitude of 5, a period of
Pi/8,and a midline at y = 7.
f(x) = 4sin(8x) + 5
f(x) = 5sin(16)+7
f(x) = 5sin(16x) + 4
f(x) = 4sin(8x) + 7
Answers
Answer:
\(\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}\)
Step-by-step explanation:
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function\(\boxed{f(x) = A \sin (B(x + C)) + D}\)
where:
A is the amplitude (height from the midline to the peak).2π/B is the period (horizontal distance between consecutive peaks).C is the phase shift (horizontal shift - positive is to the left).D is the vertical shift (y = D is the midline).Given values:
Amplitude, A = 5Period, 2π/B = π/8Phase shift, C = 0Vertical shift, D = 7Calculate the value of B:
\(\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16\)
Substitute the values of A, B C and D into the standard formula:
\(f(x) = 5 \sin (16(x + 0)) + 7\)
\(f(x) = 5 \sin (16x) + 7\)
Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:
\(\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}\)
Let the demand function for a product be given by the function
D
(
q
)
=
−
1.85
q
+
240
, where
q
is the quantity of items in demand and
D
(
q
)
is the price per item, in dollars, that can be charged when
q
units are sold. Suppose fixed costs of production for this item are
$
3
,
000
and variable costs are
$
4
per item produced. If
100
items are produced and sold, find the following:
A) The total revenue from selling
100
items (to the nearest penny).
Answer: $
B) The total costs to produce
100
items (to the nearest penny).
Answer: $
C) The total profits to produce
100
items (to the nearest penny. Profits may or may not be negative.).
Answer: $
Answers
The inverse demand function of the given demand function is p = 50 - q/2.
A graph that depicts the relationship between a product's price and demand is called a demand curve. On a demand graph, the horizontal axis represents the amount desired, while the vertical axis represents the product's price.
The price is a function of the quantity required when there is an inverse demand curve. The inverse of a demand curve indicates that variations in the amount required cause changes in price levels. The formula for calculating the demand curve for a product yields the graph of an inverse demand curve.
Given demand function: q = 100 - 2p.
To find the inverse demand function, we find the inverse of the equation, by isolating p, to get:
q = 100 - 2p,
or, 2p = 100 - q,
or, p = 100/2 - q/2,
or, p = 50 - q/2.
Thus, the inverse demand function of the given demand function is p = 50 - q/2.
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A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.
(a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.
(b) The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.
Answers
Answer:
Step-by-step explanation:
From the information given:
mean life span of a brand of automobile = 35,000
standard deviation of a brand of automobile = 2250 miles.
the z-score that corresponds to each life span are as follows.
the standard z- score formula is:
\(z = \dfrac{x - \mu}{\sigma}\)
For x = 34000
\(z = \dfrac{34000 - 35000}{2250}\)
\(z = \dfrac{-1000}{2250}\)
z = −0.4444
For x = 37000
\(z = \dfrac{37000 - 35000}{2250}\)
\(z = \dfrac{2000}{2250}\)
z = 0.8889
For x = 3000
\(z = \dfrac{30000 - 35000}{2250}\)
\(z = \dfrac{-5000}{2250}\)
z = -2.222
From the above z- score that corresponds to their life span; it is glaring that the tire with the life span 30,000 miles has an unusually short life span.
For x = 30,500
\(z = \dfrac{30500 - 35000}{2250}\)
\(z = \dfrac{-4500}{2250}\)
z = -2
P(z) = P(-2)
Using excel function (=NORMDIST -2)
P(z) = 0.022750132
P(z) = 2.28th percentile
For x = 37250
\(z = \dfrac{37250 - 35000}{2250}\)
\(z = \dfrac{2250}{2250}\)
z = 1
Using excel function (=NORMDIST 1)
P(z) = 0.841344746
P(z) = 84.14th percentile
For x = 35000
\(z = \dfrac{35000- 35000}{2250}\)
\(z = \dfrac{0}{2250}\)
z = 0
Using excel function (=NORMDIST 0)
P(z) = 0.5
P(z) = 50th percentile
a. The z score of each life span should be -0.4444, 0.889, and 2.2222.
b. The percentile of each life span should be 0.0228, 0.8413 and 0.5000.
Given that,
mean life span of 35,000 miles, with a standard deviation of 2250 miles.The calculation is as follows:(a)
The z score should be
\(Z1 = \frac{34000-35000}{2250} = -0.4444\\\\Z2 = \frac{37000-35000}{2250} = 0.8889\\\\Z3 = \frac{30000-35000}{2250} = -2.2222\\\\\)
The tire with life span of 30000 miles would be considered unusual
(b)
The percentile should be
\(Z1 = \frac{30500-35000}{2250} = -2\)
p(Z1 < -2) = NORMSDIST(-2) = 0.0228
\(Z2 = \frac{37250-35000}{2250} = 1\)
p(Z2 < 1) = NORMSDIST(1) = 0.8413
\(Z3 = \frac{35000-35000}{2250} = 0\)
p(Z3 < 0) = NORMSDIST(0) = 0.5000
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1 Which triangle appears to be an obtuse
triangle?
C
B
D
Answers
Answer:D you can tell it’s much wider and it’s not at a 90 degree or less
Step-by-step explanation:
PLZZ ANSWER THE QUESTION
Answers
Answer:
option A
I hope it helps
julia needs to make 500 hamburgers for the a school function... hamburger patties are sold in packets of 12
how many packets of patties should she buy ?
Answers
Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:
12x = 500
x = 500/12
x = 41.67
x≅ 42
Julia needs to buy 42 packets
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Write 0.6 as a percentage.
Answers
Answer:
60%
Step-by-step explanation:
all you need to do is multiply this by 100 (move two decimal places to the right).
0.6--> 60
60 percent
Answer: 60%
Explanation: .6 x 100 = 60
hey peeps help with this
Answers
You and your friend's choice to take a bus back home, each 2 miles you have to pay 60 cents, write this in an Equation
Answers
Answer:
Step-by-step explanation:
Let x be the number of miles you and your friend travel.We know that the cost of the bus ride is 60 cents per mile, so the total cost of the trip is 60 * x.This can be written as an equation as follows:Cost = 60 * xOr, more simply:Cost = 60xThis equation represents the relationship between the number of miles you and your friend travel and the cost of the trip. As the number of miles increases, the cost of the trip also increases at a rate of 60 cents per mile.
When you add a positive number and a negative number, how can you tell whether the sum will be positive or negative?
Answers
Answer:
Rule: The sum of any integer and its opposite is equal to zero. Summary: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.
Step-by-step explanation:
Need help on this one. Sort of confused.
Answers
Answer:
I'm just as confused as you lol
-32>-5+9x soLve for x
Answers
Answer:
-3>x
Step-by-step explanation:
Rearrange the equation
1. Move - 5 onto the other side with - 32.
2. - 32 + 5 > 9x now because 5 was moved to the other side so the sign has changed.
3. - 27>9x, move 9 to the other side
4. - 27/9>X DIVIDE 27 by 9
5. - 3>X
Answer:
-4 ≥ x or 3>x
Step-by-step explanation:
UT is the midsection of triangle QRP. If UT= x+9 and QP=4x-27, what is the length of QP?
Answers
Answer:
Step-by-step explanation:
4x - 27 = 2(x + 9)
2x = 27 + 18
x = 45 ÷ 2 = 22.5
QP = 4(22.5) - 27 = 63 units
Andrea saves 65 each day.if this is 25% of hair daily allowance, how much is her daily allowance
Answers
25/100 = x/65
100x = 1625
x = $16.25
$16.25 is her daily allowance
When Alexander moved into a new house, he planted two trees in his backyard. At
the time of planting, Tree A was 36 inches tall and Tree B was 21 inches tall. Each
year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per
year. Let A represent the height of Tree At years after being planted and let B
represent the height of Tree Bt years after being planted. Write an equation for each
situation, in terms of t, and determine which tree is taller after 3 years.
Answers
Answer:
The equations for each situation are
A = 36 + 6t
B = 21 + 9t
After 3 years, Tree A is taller.
Step-by-step explanation:
From the question,
Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and
Tree A grew by 6 inches per year and Tree B grew by 9 inches per year after planting.
For Tree A,
Given a period of t years after planting, the height would have increased by 6t
∴ A = 36 + 6t
For Tree B,
Given a period of t years after planting, the height would have increased by 9t
∴ B = 21 + 9t
To determine, which tree is taller after 3 years,
t = 3
For Tree A
A = 36 + 6t
A = 36 + 6(3)
A = 36 + 18
A = 54 inches
For Tree B
B = 21 + 9t
B = 21 + 9(3)
B = 21 + 27
B = 48 inches
Hence, After 3 years, Tree A is taller.
Select the correct answer. Maria donates a fixed amount, a, to a charity each month. If she donates $300 in 12 months, what is the equation for a? A. a + 300 = 12 B. a × 300 = 12 C. a × 12 = 300 D. a + 12 = 300 E. a + 32 = 100
Answers
Answer: C
she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.
Question 15 of 60
Choose the symbol that correctly compares the fractions below.
8 8
-?-
10 10
OA. None of these are correct.
OB. <
C. >
OD. =
SUBMIT
Answers
Answer:
D
Step-by-step explanation:
What is the length of the hypotenuse of the right triangle shown below? Type your answer as an integer. A right triangle has two sides of length 3 and 4.
Answers
Answer:
5
Step-by-step explanation:
This is the Pythagorean theorem:
\(a^{2} +b^{2} =c^{2}\)
The hypotenuse is c so we need to make c the subject:
\(c = \sqrt{a^{2}+b^{2} }\)
To do this I simply square rooted both sides.
Now we substitute values given to get the answer of the hypotenuse:
\(c = \sqrt{3^{2} + 4^{2} }\)
\(c = \sqrt{9+16}\)
\(c = \sqrt{25}\)
c=5
The lengths 3,4,5 of a triangle are known as a Pythagorean triple.
A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c².
Complete this sequence -5,-12,-19,-26,[??],[??]
Answers
Answer:
-33, -40
Step-by-step explanation:
If you figure out the patern here, the patern is (-7).
So I did (-26-7) which got me -33, and then did, (-33-7) which got me -40.
Hopefully this helps :)
A technical machinist is asked to build a cubical steel tank that will hold 220 L of water.Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest 0.001 m.
Answers
As per given by the question,
The given value is 220 L, i.e volume.
Now,
There is need to calculatea cube volume.
So,
Cube volume is calculated by multiplying the lenght cube .
That means,
\((\text{length)}^3\)Then,
The volume of the tank is 220 L.
So,
From the formula of volume,
\(V=R^3\)Then,
\(\begin{gathered} V=R^3 \\ 220=R^3 \\ R=\sqrt[3]{\frac{220}{1000}} \end{gathered}\)Then, according to properties;
\(\begin{gathered} 1L=\frac{1}{1000}m^3,\text{ so} \\ 220L=\frac{220}{1000} \end{gathered}\)Then,
\(\begin{gathered} R=\sqrt[3]{\frac{220}{1000}} \\ R=6.0368 \end{gathered}\)Now,
For the nearest 0.001,
\(\begin{gathered} R=\frac{6.0368}{10}m \\ R=0.6038 \end{gathered}\)Hence, the smallest possible inside length is 0.604.
Match the definition.
A relationship between two similar things written as a to b,
a : b, or
An equation stating that two ratios are equal.
A multiple of the length of the sides from one figure to the
transformed figure.
:: Scale Factor
Answers
Answer:
you should have studied instead of going to a wed site
Step-by-step explanation:
many people can give u a wrong answer
Eliana loves music, especially 80's punk rock. Eliana looked at the number of songs in her itunes account and she has 6 less than 4 times her best friend. Eliana's classmate David has 3 more than double her best friend. When talking to her Social Studies teacher, Eliana found out social study teacher has 7 more than two times the number of songs in his library than Eliana. Define a variable, then write and solve an equation. If the total number of songs is 382, how many songs does Eliana, her best friend, David and her social study teacher have?
Answers
Answer
Step by step explantion:
bsf= 26
Eliana:98
SS teacher=203
David=55
Step-by-step explanation:
m= music
bsf: m
eliana:4m-6
David:2m+3
SS teacher: 2(4m-6)+7
m+4m-6+2m+3+8m-12+7
382=15m-7
7+ +7
389=15m
/15m /15m
m=26
multiply 26 to each one of them
Convert 35°F to degrees Celsius.If necessary, round your answer to the nearest tenth of a degree.Here are the formulas.C= (F-32)9F=-C+3235 °F =0 °c°CХ5?.
Answers
Given
\(\begin{gathered} C=\frac{5}{9}(F-32) \\ F=\frac{9}{5}C+32 \end{gathered}\)To convert 35 degree F to degree Celsius.
Now,
It is given that,
\(C=\frac{5}{9}(F-32)\)Substitute F=35 degrees in the above equation.
That implies,
\(\begin{gathered} C=\frac{5}{9}(35-32) \\ C=\frac{5}{9}\times3 \\ C=\frac{5}{3} \\ C=1.6666\degree \\ C=1.7\degree \end{gathered}\)Hence, the answer is 1.7 degrees.
The diagram shows the ratio of trees Maeve plants to the trees she harvests.
Thank u
Answers
Answer:
Wednesday is 45 to 18.
Thursday is 55 to 22
Step-by-step explanation:
Wednesday: The original ratio was 5 to 2 And the info tells us that the new ratio is ? to 18. To find the first part we have to find how we got from 2 to 18. 2 * 9 = 18. So to find out the first part you do 5 * 9 = 45. We multiply 5 because Thats the original 1st part. We multiply 9 because that's how we got to 18 in the 2nd part. So the answer is 45 for Wednesday.
Thursday: The original ratio was 5 to 2 And the info tells us that the new ratio is 55 to ?. To find the first part we have to find how we got from 5 to 55. 5 * 11 = 55. So to find out the 2nd part you do 2 * 11 = 55. We multiply 2 because That's the original 2nd part. We multiply 11 because that's how we got to 55 in the 1st part. So the answer is 22 for Thursday.
Answer:
The answer is 45 to 18 and 55 to 22 hope this helps
Step-by-step explanation:
If a hamburger shop sold a combined total of 423 hamburgers and cheeseburgers but the number of cheeseburgers sold was two
times the number of hamburgers sold. How many hamburgers were sold
Answers
Answer:
141
Step-by-step explanation:
First, we choose two variables to represent the two unknown numbers, the number of hamburgers and the number of cheeseburgers.
Let x = number of hamburgers.
Let y = number of cheeseburgers.
Now we use the given information to write two equations using the variables we defined above.
"If a hamburger shop sold a combined total of 423 hamburgers and cheeseburgers"
x + y = 423
"the number of cheeseburgers sold was two
times the number of hamburgers sold"
y = 2x
We have a system of two equations.
x + y = 423
y = 2x
Since the second equation is already solved for y, we can easily use the substitution method. We substitute what y equals to (2x) for y in the first equation.
x + y = 423
x + 2x = 423
3x = 423
x = 141
Since we let x = number of hamburgers, we have the answer.
Answer: 141
use the binomial expansion
(a+b)⁴ = a⁴+4a³b+6a²b²+4ab³+b⁴ to expand and simplify (x-3)⁴
Answers
Answer:
\(x^4-12x^3+54x^2-108x+81\)
Step-by-step explanation:
We have been given the following binomial expansion for (a + b)⁴:
\(\boxed{(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4}\)
To use this to expand and simplify (x - 3)⁴, first identity the values of a and b:
a = xb = -3Substitute the values of a and b into the expansion, and simplify:
\(\begin{aligned}(x-3)^4&=x^4+4x^3(-3)+6x^2(-3)^2+4x(-3)^3+(-3)^4\\\\&=x^4+4x^3(-3)+6x^2(9)+4x(-27)+81\\\\&=x^4-12x^3+54x^2-108x+81\end{aligned}\)
Pls help a girl out :/ and show work pls
Answers
Answer:
it is B
Step-by-step explanation:
A survey of 800 school employees yielded the following information: 430 were instructors, 589 were full-time faculty, and 340 of the instructors were full-time faculty. How many school employees were full-time faculty but were not instructors
Answers
Answer:
249Step-by-step explanation:
let n(U) be the total number of school employees = 800
Let n(I) be amount of instructors = 430
Let (F) be full-time faculty = 589
Let n(InF) be the instructors who were full-time faculty = 340
The number of employees who were full-time faculty but were not instructors is expressed as:
n(FnI') = n(F) - n(InF)
n(FnI') = 589 - 340
n(FnI') = 249
Hence the number of school employees who were full-time faculty but were not instructors are 249