Aadya is building towers by stacking identically shaped cubes of different colors on top of each other. She has $1$ red cube, $2$ yellow cubes, $3$ green cubes, and $4$ blue cubes. How many different $10$-cube-high towers can Aadya build using these $10$ cubes so that neither of the bottom two cubes of the tower are green?
Answers
Using the Fundamental Counting Theorem, it is found that Aadya can build 1,693,440 cube towers.
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:
\(N = n_1 \times n_2 \times \cdots \times n_n\)
Considering that she has 10 cubes, and the bottom and top cubes cannot be green, the parameters are given by:
\(n_1 = 7, n_10 = 6, n_2 = 8, n_3 = 7, \cdots n_9 = 1\)
Hence the number of cubes is given by:
N = 7 x 6 x 8! = 1,693,440.
Aadya can build 1,693,440 cube towers.
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Related Questions
PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS RIGHT (NO LINKS)
Identify the surface area of the composite figure to the nearest tenth.
Answers
Answer:
D.
Step-by-step explanation:
6a² = surface area for cube
6(5)² = 150
2\(\pi\)(r)(h)+2\(\pi\)r² = surface area cylinder
2\(\pi\)(2)(3)+2\(\pi\)(4) = 20pi
150 + 20pi = 212.8318531
The probability that it is Monday and that a student is absent is 3/100. Because there are 5 school days in a week, the probability that a randomly selected day of the school week is Monday is 1/5.
What is the probability that a student is absent given that today is Monday?
Enter your answer as a fraction in simplest form, formatted like this: 3/14
Answers
The probability that the student is absent is 3/20
What is Probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The probability that the student will be absent and it will be on Monday is 3 /100.
The probability that it will be Monday is 1/5
Therefore the probability that the student will be absent any day is 3/100÷1/5 = 3/20
Since it is certain that it is Monday , the probability that it is Monday is 1.
Therefore, the probability that the student is absent on that Monday is 1 × 3/20 = 3/20
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Find a value of z0 such that for the standard normal random variable z it is true that P(-z0 ≤ z ≤ z0) = 0.98.
Answers
P(-2.33 ≤ z ≤ 2.33) = 0.98 for a standard normal random variable Z.
We are aware that the area under the curve between - and - is equal to 1 for a standard normal random variable Z.
The task of finding a number for z0 such that P(-z0 z z0) = 0.98 is given to us.
We can divide the area of 0.98 evenly between the two tails of the distribution since the normal distribution is symmetric around the mean.
(1 - 0.98 / 2) = 0.01 would be the area in each tail.
We can determine the z-score that corresponds to the area of 0.01 by using a calculator or a conventional normal distribution table. An area of 0.01 equates to a z-score of roughly -2.33.
Thus, z0 would have the value:
z0 = -(-2.33) = 2.33
Hence, for a typical normal random variable Z, P(-2.33 z z 2.33) = 0.98.
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Which line has a constant of proportionality between y and x of 4/3
Answers
Answer:
Line A: constant of proportionality is 4/3
Step-by-step explanation:
The equation in question is y = (4/3)x, where (4/3) is the constant of proportionality as well s the slope of the line. The only line here that has a slope greater than 1 is the blue line (A).
2
Let g(x) = x + 4x-7.
What is g(x) in graphing form?
(x + 2) - 7 = 4
O g(x) = (x + 2)²-7
Onone of the answer choices
x² + 4x-7=0
O g(x) = (x + 2)² - 11
Answers
The graphing form of the function g(x) is: C) none of the answer choices.
The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.
Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:
a = 1 (coefficient of x^2)
b = 4 (coefficient of x)
c = -7 (constant term)
Therefore, the graphing form of the function g(x) is:
C) none of the answer choices
None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.
In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.
The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C
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Which answer is an equation in point-slope form for the given point and slope?
point: (-4, 1); slope: 7
Oy+1=7 (x-4)
Oy+1=7 (x+4)
Oy-1=7 (x+4)
Oy-1=7(x-4)
Answers
Answer: C y-1=7 (x+4)
Step-by-step explanation:
Point slope formula
y - y₁ = m ( x - x₁ ) Where m= slope and (x₁ , y₁) is your point
Given:
point: (-4, 1); slope: 7
plug in to formula
y - 1 = 7 (x+4)
Consider the lines that contain the segments in the figure and the planes that contain the faces of the figure. All angles are right angles. Which plane(s) contain point B and appear to be parallel to plane CDH?
Answers
The plane containing point B and parallel to the plane CDH is plane ABF.
What is defined as the parallel plane?Parallel planes are spatial planes that never intersect. The length about any line segment perpendicular both to planes connecting two parallel planes is indeed the distance between them. There are an infinite number of perpendicular line segments between two parallel planes. Two of the perpendicular segments the above are line segments AB and CD. Any line segment that is perpendicular to both planes also has the shortest distance between them.As, from the diagram we can see that there are two plane passing from point B; plane ABF and ABC.
But plane ABC is intersecting the given plane CDH, while plane ABF is not.
Thus, plane ABF is parallel to the plane CDH.
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Boris started to run on a treadmill after setting its timer for 92 minutes. The display says that he has finished 73% of his run. How many minutes have gone by?
Round your answer to the nearest tenth.
Answers
Answer:
67 minutes
Step-by-step explanation:
pleaseeeeeeeeeeeeeeeeeeeeee help me i'm begging you so the questions is what is the multiplicative of 5 and 10-5k
Answers
Answer:
1/5 and -k/5+2
Step-by-step explanation:
inverse of 5= 1/5
swap the variables: y=10−5k becomes k=10−5y
Now, solve the equation k=10−5y
for y
y=−k/5+2
What is the area of the figure?
Answers
Answer:
Area = 28 cm^2
Step-by-step explanation:
Triangle Area = 1/2 * 5 * 4 = 10 cm^2
Big Rectangle = 4 * 3 = 12 cm^2
Small Rectangle = 4 * 1.5 = 6 cm^2
Total Area = 10 + 12 + 6 = 28 cm^2
Answer:
Step-by-step explanation:
Discussion
Area of the Triangle
3 4 5 is the first triangle most people encounter when they begin their study of the Pythagorean Theorem. You can show this to be true by trying it.
c = 5
b = 3
a = 4
c^2 = a^2 + b^2 Equation Substitute values
c^2 = 3^2 + 4^2 Expand
c^2 = 9 + 16 Combine
c^2 = 25 Take the square root of both sides.
√c^2 = √25
c = 5 Which is exactly what you are given.
A right triangle has the property of Area = 1/2 * a * b using the values given above.
Find the area of the triangle
Area = 1/2 a * b
Area = 1/2 3 * 4
Area = 6
Find the area of the rectangle
L = 3 + 1.5 =4.5 Just add the two parts of the vertical line together.
w = 8 - 4 = 4
Area of the rectangle = L * w Substitute values
Area of the rectangle = 4.5 * 4
Area of the rectangle = 18 Add
Total area 24
Answer
24 cm^2
Nina by 20 yards of ribbon to make a gift decorations the first step in making the decorations was to cut 10% of the revenue from 20 yards which step would result in the same outcome as cutting of 10% of the ribbion
Answers
We need to identify the step that is equivalent to cutting 10% of the ribbon.
In order to do so, notice that 10% means 10 out of 100 of something:
\(10\%=\frac{10}{100}\)Then, simplifying the above fraction, we can divide both the numerator and the denominator by 10 to obtain:
\(\frac{10\div10}{100\div10}=\frac{1}{10}\)Thus, 10% of 20 is given by:
\(10\%\text{ of }20=\frac{1}{10}\text{ of }20=\frac{1}{10}\times20=\frac{20}{10}=2\)Therefore, the equivalent step would be:
\(\text{ Cut off }\frac{1}{10}\text{ of the 20 yards of ribbon.}\)Can anyone help me with this please?
Answers
Answer: 6(x+7)° = 24(x-8)°
Step-by-step explanation:
We know that both angles are equal as they are alternate exterior angles.
6(x+7)=24(x-8)
6x+42=24x-192
6x -6x +42 +192 =24x -6x -192 +192
234 = 18x
18x/18 = 234/18
x = 13
And then for question B and C, you need to calculate the expression with x being equal to 13.
Finley and Cooper are wanting to go to SkyZone. Finley pays $53.75 for 5 hours. How much will Cooper pay for 3 hours?
Answers
Answer:
10.75 x 3 = $32.25
Step-by-step explanation:
first, we need to figure out how much the cost is for one hour:
53.75/5 = 10.75
therefore, the cost at skyzone for 1 hour is $10.75 , BUT, we still need to figure out the time for 3 hours.
so, 10.75 x 3 = $32.25
Answer: 32.25
Step-by-step explanation:
ASAP NOW! PLSS! I WILL MARK 5 STARS! PLSSS! thank you!! At noon, the temperatures in Portland, Maine and Phoenix, Arizona had opposite values. The temperature in Portland was lower than in Phoenix. What was the temperature in each city? Explain your reasoning.
Answers
Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.
What are opposite values?Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.
In general, the temperature equation for Portland, Maine is stated mathematically as
PoT=-PhT
As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,
PoT=-PhT
PhT =+PoT
Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.
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Which symbol correctly relates 23 ? 16 check all that apply
Answers
Answer:
C and E
Step-by-step explanation:
23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.
Kylie makes $8.50 an hour at a local restaurant. Her paycheck shows she worked 20.88 hours last week. how much money did Kylie make?
Answers
If Kylie's hourly wage at a nearby restaurant is $8.50. She worked 20.88 hours last week, according to her paycheck. Kylie's salary is $177.48.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Kylie makes $8.50 an hour at a local restaurant. Her paycheck shows she worked 20.88 hours last week.
We have to find the money did Kylie make,
We can utilize multiplication for a number of common tasks, such as figuring out how much it will cost to buy several identical things, calculating sales tax, and figuring out area and other geometric measurements.
Suppose the money did Kylie make is x,
x = 8.50 × 20.88
x=$ 177.48
Thus, if Kylie's hourly wage at a nearby restaurant is $8.50. She worked 20.88 hours last week, according to her paycheck. Kylie's salary is $177.48.
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Ms. Jackson emptied 16 boxes of crayons into a classroom crayon bucket in each box 2/9 The crayons were green how many crayon boxes could she filled with all the green crayons?
Answers
Answer:
2 boxes
Step-by-step explanation:
do 16 times 2 you get 32 so there are 32 green crayons 32/9 9 times 3 is 36 which is over 32 so you cant fill 3 boxes 9 times 2 equals 27 so the answer would be she can fill 2 boxes
What’s the value of x solve the equation
-3x+4=2x-6
Answers
Answer: x=2
Step-by-step explanation:
−3x+4=2x−6
Subtract 2x from both sides.
−3x+4−2x=−6
Combine −3x and −2x to get −5x.
−5x+4=−6
Subtract 4 from both sides.
−5x=−6−4
Subtract 4 from −6 to get −10.
−5x=−10
Divide both sides by −5.x=−5−10
Divide −10 by −5 to get 2
x=2
A cycle wheel does 2169 full turns in 9 minutes. Work out the number of full turns per minute
Answers
Answer:
241 per min
Step-by-step explanation:
just take 2169/9 and get 241 per min
Answer:
241 turns in 1 minute.
Step-by-step explanation:
to find the answer 241 you need to divide 2169 by 9 which will get you 241 turns
So the wheel does 241 turns a minute.
HOPE IT HELPS YOU PLEASE MARK AS BRAINLIESTA pizza chain plans to locate a new pizza franchise on the CCSU campus if the results of a survey show that more than 10% of CCSU students would eat there at least once a week. Suppose the company is about to carry out a hypothesis test. 7.
a. State the hypotheses.
b. Clearly state, in terms of this particular problem, what a Type I error would mean.
c. Describe possible consequences of a Type I error in this situation.
d. Clearly state, in terms of this particular problem, what a Type II error would mean.
e. Describe possible consequences of a Type II error in this situation.
Answers
Answer:
a) Null and alternative hypothesis:
\(H_0: \pi=0.1\\\\H_a:\pi>0.1\)
b) A Type I error is made when a true null hypothesis is rejected. In this case, it would mean a conclusion that the proportion is significantly bigger than 10%, when in fact it is not.
c) The consequences would be that they would be more optimistic than they should about the result of the investment, expecting a proportion of students that is bigger than the true population proportion.
d) A Type II error is made when a false null hypothesis is failed to be rejected. This would mean that, although the proportion is significantly bigger than 10%, there is no enough evidence and it is concluded erroneously that the proportion is not significantly bigger than 10%
e) The consequences would be that the investment may not be made, even when the results would have been more positive than expected from the conclusion of the hypothesis test.
Step-by-step explanation:
a) The hypothesis should be carried to test if the proportion of students that would eat there at least once a week is significantly higher than 10%.
Then, the alternative or spectulative hypothesis will state this claim: that the population proportion is significantly bigger than 10%.
On the contrary, the null hypothesis will state that this proportion is not significantly higher than 10%.
This can be written as:
\(H_0: \pi=0.1\\\\H_a:\pi>0.1\)
What are the solutions to the quadratic equation 4x2 = 64?
x = −16 and x = 16
x = −8 and x = 8
x = −4 and x = 4
x = −2 and x = 2
Answers
Answer:
x = −4 and x = 4
Step-by-step explanation:
if you do divide its all the opposite 8÷64=8 4×2=8 8×32=4 or 8÷-2=-4
There were 5 players in a game. -2 players scored 40 points each -2 players scored 50 points each -1 player scored 90 points What was the mean number of points scored by the 5 players in the game? A. 36 B. 50 C. 54 D. 60.
Answers
Answer:
C
Step-by-step explanation:
Equation
Mean = Total / 5
Total
Total = 2 * 40 + 2 * 50 + 90
Total = 80 + 100 + 90
Total = 270
Answer
Mean = Total / 5
Mean = 270 / 5
Mean = 54
create a histogram using the values from the list given using r studio or excel. upload the histogram
2, 2, 3, 11, 11, 11, 12, 14, 14, 14, 15, 15, 15, 15, 16, 16, 17, 18, 18, 19, 19, 19, 20
Answers
You can create a histogram by creating around 4 classes and then representing the frequency of the data within these classes (see the attachment).
What is a histogram?This is a type of graph that visually represents the frequency of data. Due to this, histograms use columns and classes. The classes group data according to specific ranges.
How to create a histogram?Create the classes and frequency of the data. Here is the way you can do it:
Class - Frequency
2-7 = 3
7-12= 3
12-17= 10
17-22= 7
You can see the graph below
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58 - 5X = 30X - 75 need help please
Answers
Answer:
3.8
Step-by-step explanation:
\(58-5x=30x-75\)
Let's add 5x to both sides of the equation...
\(58=35x-75\)
Then, let's add 75 to both sides of the equation...
\(133=35x\)
Divide by the coefficient of x, (35)...
\(x=3.8\)
Given A(-9, -12), B(-2, 2), C(x, 6).and D(-5, -2), find the value ofx so that AB || CD
Answers
1) Given these line segments, let's find the slope of them. Let's begin with AB
\(m=\frac{2-(-12)}{-2-(-9)}=\frac{14}{-2+9}=\frac{14}{7}=2\)2) Parallel lines have the same slope, so let's set this slope formula so that we can get the slope m=2. Bearing in mind CD:
\(\begin{gathered} 2=\frac{-2-6}{-5-x} \\ 2=\frac{-8}{-5-x} \\ 2(-5-x)=-8 \\ -10-2x=-8 \\ -2x=-8+10 \\ -2x=2 \\ x=-1 \end{gathered}\)Thus, x=-1
which is a line of symmetry?
Answers
(4x^2-2x-4)(2x+4) what is
the product of the polynomials below?
Answers
Answer:
8x³ + 12x² - 16x - 16
General Formulas and Concepts:
Order of Operations: BPEMDASDistributive PropertyStep-by-step explanation:
Step 1: Define expression
(4x² - 2x - 4)(2x + 4)
Step 2: Simplify
Expand: 8x³ - 4x² - 8x + 16x² - 8x - 16Combine like terms (x²): 8x³ + 12x² - 8x - 8x - 16Combine like terms (x): 8x³ + 12x² - 16x - 16Mr. Harris ran 2 miles in 14.5 minutes. Ms. Mullen ran 2.5 miles in 16 minutes. Ms. Hubbard ran 3.5 miles in 24 minutes.
A. Ms. Mullen was the fastest.
B. Ms. Hubbard was the fastest.
C. Mr. Harris was the fastest.
Answers
Answer:
A. Ms harris was the fastest considering she finished 2.5 miles under 14.5 minutes
Step-by-step explanation:
Find the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0)
Answers
The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.
To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.
The slope of a line can be found using the formula:
slope = (change in y) / (change in x)
For the line containing (1,2) and (5,3), the slope is:
slope1 = (3 - 2) / (5 - 1) = 1 / 4
To find the slope of the line containing (x,4) and (3,0), we use the same formula:
slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
So, we can set up the equation:
-1 / (1/4) = -4 / (3 - x)
Simplifying this equation:
-4 = -4 / (3 - x)
To remove the fraction, we can multiply both sides by (3 - x):
-4(3 - x) = -4
Expanding and simplifying:
-12 + 4x = -4
Adding 12 to both sides:
4x = 8
Dividing both sides by 4:
x = 2
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Please help me it due today at 11:59pm please help me will mark the brainiest please
Answers
Answer:
y = 69
Step-by-step explanation:
start with the distributive property:
5/9 * y and 5/9 * 3
and now you have: 5/9y + 15/9 = 40
and we have to isolate y so subtract 15/9 from both sides:
5/9y + 15/9 = 40
- 15/9 -15/9
and now you have 5/9y = 345/9
and now divide both sides by 5/9 so: 5/9y divided by 5/9 = y
and 345/9 divided by 5/9 = 345/5 and lets simplify....
y= 69
hope this helps luv