a bag contains 16 coins each with a different date. the number of possible combinations of three coins from the bag is
The number of possible combinations of three coins from the bag of 16 coins with different dates can be calculated using the formula for combinations, which is nCr = n! / r!(n-r)!, where n is the total number of objects, r is the number of objects to be chosen, and ! denotes factorial (the product of all positive integers up to the given number).
In this case, we have n = 16 (the total number of coins in the bag) and r = 3 (the number of coins to be chosen for each combination). Using the formula for combinations, we can calculate the number of possible combinations as follows:
nCr = 16! / 3!(16-3)!
nCr = (16 x 15 x 14) / (3 x 2 x 1)
nCr = 560
Therefore, 560 possible combinations of three coins can be chosen from the bag of 16 coins with different dates. These combinations could represent different historical events, significant dates, or other symbolic meanings depending on the dates inscribed on the coins. The calculation of combinations is an important concept in combinatorics and probability theory, and it has many real-world applications in fields such as statistics, economics, and computer science.
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The lines y=(n-2)x-4 and y=3x+2 are perpendicular. Find the value of n.
Must include an explanation to get more points!
Answer:
n=5/3
Step-by-step explanation:
In order for the two lines to be perpendicular the slopes have to be flipped and so do the signs so the slope of the unknown value has to be -1/3
all you do is -1/3+2=5/3
5/3-2=-1/3 which make the two lines perpendicular
sorry if this doesnt make sense its hard to explain it virtually
find a function that models the area a of a circle in terms of its circumference c.
Answer:
A = C²/(4π)
Step-by-step explanation:
You want a formula for the area of a circle, given its circumference.
Circle relationsRelevant relations for a circle are ...
A = πr² . . . . . . . . A = area, r = radius
C = 2πr . . . . . . . . C = circumference
Area from circumferenceSolving the circumference equation for r, we find ...
r = C/(2π)
Substituting that into the area equation, we have ...
A = π(C/(2π))²
A = C²/(4π)
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The function that models the area A of a circle in terms of its circumference C is A = C²/(4π).
Explanation:The formula for the circumference of a circle is C = 2πr or C = πd, where r is the radius and d is the diameter. To find a function that models the area A of a circle in terms of its circumference C, we can rearrange the formula for the circumference to solve for the radius: r = C/(2π). Substituting this value of r into the formula for the area, we get A = π(C/(2π))² = C²/(4π).
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In a lab a 30% acid solution is being mixed with a 5% acid solution to create a 10% acid solution. What is the ratio of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution
Answer:
1:4
Step-by-step explanation:
Let it be:
30% solution = x5% solution = ythen
10% solution = x + y----------
Amount of acid:
0.3x + 0.05y = 0.1(x+y)0.3x + 0.05y = 0.1x + 0.1y0.2x = 0.05y20x = 5y4x = yx/y = 1/4So the ratio of 30% solution to the 5% solution is 1:4
Answer:
1 : 4
Step-by-step explanation:
For a problem of this nature, a simple diagram makes the solution trivially easy. In the attached, the constituent concentrations are listed on the left, the solution concentration is in the middle, and the numbers on the right are the differences along the diagonals. These are the ratios of the respective solutions on the left.
That is, the ratio of 30% solution to 5% solution is 5 : 20 or 1 : 4.
Answer ASAP!!! 100 pts and Brainliest for best answer. :) ANY nonsensical answers will be reported!!!
Figure 1: Here x = 17, y = 8
Figure 2: Here x = 8, y = 21
Figure 1:
8x - 31° = 6x + 3° , here these angle are alternate interior angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Therefore from the above equation, we can find the value of x
8x - 31° = 6x + 3°
2x= 34°
x = 17°
Now we know that 8x - 31° and 5y + 35° form a line whose sum is equal to 180°.
8x - 31° + 5y + 35° = 180°
Now put the value of x = 17°
136° - 31° + 5y + 35° = 180°
5y= 40°
y = 8°
Therefore x = 17° and y = 8°
Figure 2:
7x +12 = 12x - 28 , as they are alternate interior angles
From this equation, we can have a value of x.
5x = 40°
x = 8°
12x - 28° and 9y - 77° form a line whose sum is equal to 180°
12x - 28° + 9y - 77° = 180°
Now put the value of x = 8°, then we have
96 - 28 + 9y -77 = 180°
9y = 189°
y = 21°
So here x = 8° and y = 21°.
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The local seven-digit telephone numbers in city a have 291 as the first three digits. how many different telephone numbers are possible in city a?
The total number of different telephone numbers are possible in city is 6561.
What is permutation?A term permutation relates to a mathematical process that determines the number of possible arrangements of a given set.
Simply put, a permutation is a term that refers to the number of different ways something can be ordered as well as arranged. The sequence of the arrangement is important in permutations.Now, according to the question;
Because the first three digits are fixed, we must select the next four digits.
A total number of available telephone numbers is increased by selecting one of nine numbers for the fourth digit;
nine numbers for the fifth digit;
nine numbers for the sixth digit;
and nine numbers for the seventh digit.
Thus,
= 9×9×9×9
= 6561
Therefore, the total number of ways in which telephone numbers are possible in city are 6561.
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.
Describe how to find the product of the two terms 3x²y^5 and 4x³y^7
Answer:
see explanation
Step-by-step explanation:
using the property of exponents
• \(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)
given
3x²\(y^{5}\) × 4x³\(y^{7}\) ( separate like parts in the product )
= 3 × 4 × x² × x³ × \(y^{5}\) × \(y^{7}\)
= 12 × \(x^{(2+3)}\) × \(y^{(5+7)}\)
= 12\(x^{5}\)\(y^{12}\)
I NEED HELP ITS URGENT!!! I WILL MARK BRAINLIST!! LOOK AT THE IMAGE ABOVE AND DO BOTH PROBLEMS BY SHOWING THE ENTIRE WORK!!
Do NOT answer if you DONT know. This could lead to serious consequences. Ex: “idk” could lead to the monitor marking you to loose points.
PLEASE HELP
Answer:
okay well all i can explain is the image on the far left, the answer would be x=112 and then for the one on the far right (im not sure ) i think its 17
explanation: so a straight line had 180 degress and the outside angle is 126 meaning that if you do 180-126 you can find the amount of the inside angle on the bottom right. When you do this you get 54 degress. Then remember that a triangle has a total of 180 degrees all added up so the final angle inside the triagle is 80 minus the sum of the other two angles. 58+54=112 and 180-112=68. remember that 68 is the angle on the INSIDE and x is clearly on the outside meaning that you would need to do 180-68. your final answer would be 112. (and im really sorry i couldn't answer the other ones they're too blurry :(
Write the slope intercept form of the equation of each line given the slope and y intercept
Answer:
11) y= -1x-2
12) y= 3/2x+3
13) y= 3x-2
14) y= 3/4x+1
15) y= 1/2x+1
16) y= -2/5x+0
17) y=7x+2
18) y= 4/3x-4
Step-by-step explanation:
y=mx+b
m is slope and b is y intercept
sara chose a date from the calendar. what is the probability that the date she chose is a prime number, given that the date is after the 7th of the month?
The probability that the date sara chose is a prime number is 0.2.
Given that, sara chose a date from the calendar.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Here, total number of outcomes = 30
Number of favourable outcomes = 6
Now, probability = 6/30
= 1/5
= 0.2
Therefore, the probability that the date sara chose is a prime number is 0.2.
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what is -7/9 as a repeating decimal.
Answer:
Step-by-step explanation:
The repeating decimal of -⁷/9 is -0.7777777777777.......................
How do you write the equation in slope intercept form given (2,2) and (0,-2)?
Answer:
y = 2x - 2
Step-by-step explanation:
The slope-intercept form of the equation of a line is
y = mx + b
where m is the slope, and b is the y-intercept.
y = mx + b
First we find the slope, m.
slope = (difference in y)/(difference in x)
It does not make a difference which point is first and which point is second in finding the differences, but you must do the x- and y-differences in the same order.
slope = (-2 - 2)/(0 - 2) = -4/(-2) = 2
The slope is 2, so m = 2, and now we have:
y = 2x + b
We need to find the value of b, the y-intercept.
We use one of the given points. Let's use (2, 2). We plug in 2 for x and 2 for y and solve for b.
2 = 2(2) + b
2 = 4 + b
-2 = b
b = -2
Now that we know the y-intercept is -2, we substitute b with -2.
y = 2x + b
y = 2x - 2
Answer: y = 2x - 2
(3.6 X 102)(1.9 x 10-4)
Multiply write the answer in scientific notation
Question 2
(4.7. x 10)(2.0 x 10
Answer:
1.)5508 2.)5600 x^2
Step-by-step explanation:
I don't remember how to solve this
Answer:
me too i fogort eventhough i did something just like it
Suppose that X is normally distributed with a mean of 20 and a standard deviation of 18. What is P(X 2 62.48)? a) 0.991 b) 0,012 c) 0.491 d) 0.009 e) 0.014 f) None of the above
The value of P(X 2 62.48) is (d) 0.009.
How we get the value of P(X 2 62.48)?To solve this problem, we need to standardize the random variable X by subtracting the mean and dividing by the standard deviation to obtain a standard normal variable Z.
Calculate Z-score
\(Z = (62.48 - 20) / 18 = 2.9167\)Look up the probability in the standard normal table or use a calculator to find the area under the standard normal curve to the right of Z.
Using a standard normal table, we can find that the area to the right of 2.9167 is approximately 0.002.
The probability of X being greater than 62.48 is equivalent to the probability of Z being greater than 2.9167, which is the standardized version of X.
We use a standard normal table or calculator to find the area under the standard normal curve to the right of Z. The answer is the probability that Z is greater than 2.9167.
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Find the volume of the rectangular prism with dimensions 11in×9in×3in. a)23in^3. b)297in^3. c)318in^3. d)159in^3.
The answer is (B) 297 in^3. To find the volume of a rectangular prism, we need to multiply its length, width, and height.
Using the dimensions given in the problem, we have:
Volume = Length x Width x Height
= 11 in x 9 in x 3 in
= 297 in^3
Therefore, the answer is (B) 297 in^3.
To understand this concept better, we can visualize a rectangular prism as a solid shape with six rectangular faces. The length, width, and height correspond to the dimensions of the three pairs of opposite faces.
To find the volume of the prism, we can imagine filling it with small cubes of unit volume. The number of cubes required to fill the prism gives us its volume.
In this case, we need 11 rows of cubes, each containing 9 cubes, and each row having a height of 3 cubes. Therefore, the total number of cubes required is 11 x 9 x 3 = 297. Hence, the volume of the rectangular prism is 297 cubic inches.
Overall, understanding the concept of volume and how to calculate it is crucial in various fields such as engineering, physics, and architecture.
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please answer quick!! thank you
Answer:
Question 2 :
\(\boxed{-35}\)
Question 3:
\(\boxed{7}\)
Question 4:
\(\boxed{-5}\)
Question 5:
\(\boxed{-5}\)
Step-by-step explanation:
The easiest points to take on the line are those where x =0, y = 35 (0,35) and x = 7, y =0 (7,0)
Question 2.
We can see that between these two points, the y value decreases linearly from 35 to 0. So the rise between (0, 35) and (7,0) = \(0 -35 = -35\)
Question 3
\(\textrm{Between (0, 35) and (7,0) the x value increases from 0 to 7 so the run is 7}\)
Question 4
\(\dfrac{rise}{run}= \dfrac{-35}{7}= -5}\)
Question 5
Slope is the same as rise over run
We can also write this as
\(\dfrac{0-35}{7-0} = \dfrac{-35}{7} = -5\)
Though not asked for, the equation of the line is
\(y = -5x + 35\)
What is the solution to this equation?
-6x + 3 = 21
Answer:
x=(-3)
Step-by-step explanation:
-6x(-3) is 18
18+3=21
Answer: -3
Step-by-step explanation:
Move all terms that don't contain
x to the right side and solve.
x = −3
PLS GIVE ME BRAINLIEST, IT WILL MEAN A LOT TO ME
chose the correct correspondence
The angle R corresponds to the angle E.
This comes from the fact that they are alternate interior angles.
Read the case study below and answer ALL the questions that follow. The topic of a research proposal submitted by a Bachelor of Business Administration Honours student at a prestigious Business School in South Africa is: An investigation into the determinants of the sustainability of small and medium-sized enterprises in Soweto The student has proposed a quantitative approach to achieve the three research objectives below: * To determine the sustainability of Small and medium-sized enterprises (SMEs) in Soweto; * To determine the factors (determinants) of SME sustainability in Soweto, and * To make practical recommendations to owner-managers of SMEs in Soweto on how to enhance the sustainability of their businesses Answer ALL the questions in this section. QUESTION 1 (20 Marks) On the basis of the student's research topic and research objectives specified above, answer the following questions: 1.1 With reference to the 5W criteria (What? Who? Why? Where? When?), critically analyse the topic (10 marks) of the research proposal. 1.2 State the aim of the proposed study. (2 marks) 1.3 (3 marks) Formulate three (3) research questions for the proposed study (Hint: the research questions should be based on the student's research objectives ). 1.4 For the proposed study, choose an appropriate research design and motivate your choice. (5 marks) QUESTION 2 (20 Marks) Based on the design you have chosen above in question 1.4 above, discuss the methodology you would follow with regard to the following:
The research proposal focuses on investigating the determinants of the sustainability of small and medium-sized enterprises (SMEs) in Soweto. The research objectives are to determine the sustainability of SMEs, identify the factors that contribute to their sustainability, and provide practical recommendations to enhance their sustainability.
1.1 The research proposal addresses the "what" by examining the determinants of SME sustainability in Soweto. It focuses on "who" by targeting owner-managers of SMEs in Soweto. The "why" is to understand the factors that influence SME sustainability. The "where" is in Soweto, South Africa, and the "when" refers to the time period during which the research will be conducted.
1.2 The aim of the proposed study is to explore and analyze the determinants of sustainability for small and medium-sized enterprises in Soweto, with the ultimate goal of providing practical recommendations to enhance their sustainability.
1.3 Three research questions for the proposed study could be:
What are the key indicators of sustainability for SMEs in Soweto?
What factors contribute to the sustainability of SMEs in Soweto?
How can owner-managers of SMEs in Soweto improve the sustainability of their businesses?
1.4 An appropriate research design for the proposed study could be a mixed-methods approach. This design would involve both quantitative and qualitative data collection and analysis methods. Quantitative data could be collected through surveys or questionnaires to measure indicators of sustainability and assess the relationship between various factors. Qualitative data could be collected through interviews or focus groups to gain a deeper understanding of the experiences and perspectives of owner-managers. The mixed-methods approach would provide a comprehensive and holistic understanding of the determinants of SME sustainability in Soweto and enable practical recommendations to be formulated based on both quantitative and qualitative insights.
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What is the slope of this line!
Answer:
-1/3
Step-by-step explanation:
Slope is rise over run which is -1 over 3
Answer:
-1/3
Step-by-step explanation:
So do rise over run. It goes down 1 and right 3, so the slope os -1/3.
You can also do the change in y over the change in x and use two coordinates.
Consider the function y = x - 3x + 7. Using the values x = -4 and Ax= -0.9, calculate Ay-dy. Round your answer to three decimal places if necessary Answer How to enter your answer fopens in new window
The value of Ay-dy for the given function and values is approximately 2.7.
To calculate Ay-dy for the function y = x - 3x + 7, with x = -4 and Δx = -0.9, follow these steps:
1. Determine the original function value: y = (-4) - 3(-4) + 7
2. Calculate the new x value: x_new = -4 + (-0.9) = -4.9
3. Find the new function value: y_new = (-4.9) - 3(-4.9) + 7
4. Calculate Δy: Δy = y_new - y
5. Calculate Ay-dy: Ay-dy = Δy - Δx
Now, let's compute the values:
1. y = (-4) - 3(-4) + 7 = -4 + 12 + 7 = 15
2. x_new = -4 - 0.9 = -4.9
3. y_new = (-4.9) - 3(-4.9) + 7 ≈ -4.9 + 14.7 + 7 ≈ 16.8
4. Δy = y_new - y ≈ 16.8 - 15 ≈ 1.8
5. Ay-dy = Δy - Δx ≈ 1.8 - (-0.9) ≈ 2.7
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3x ≤21
XS
x≤ your answer goes here
Alice was provided with the following trinomial 3x2+7x-12x-34-2x2+10
The trinomial 3x²+7x-12x-34-2x²+10 simplifies to x² - 5x - 24, which factors into (x + 3) (x - 8).
Alice was provided with the trinomial 3x²+7x-12x-34-2x²+10. To simplify the trinomial, Alice will need to group the like terms and combine them. Here's how to do it:
3x² - 2x² = x²7x - 12x = -5xNow, the trinomial becomes:x² - 5x - 24To factorize the trinomial, Alice can use different methods such as factoring by grouping, completing the square, quadratic formula, or graphing.
Here's how to factorize the trinomial by grouping:x² - 5x - 24 = (x + 3) (x - 8)Therefore, Alice can check her answer by expanding the factored expression.
When she expands (x + 3) (x - 8), she should get the original trinomial:x² - 5x - 24 = x(x - 8) + 3(x - 8) = (x + 3) (x - 8).Alice can also use the quadratic formula to solve the trinomial.
Here's how:Given the trinomial ax² + bx + c, where a = 1, b = -5, and c = -24The quadratic formula is:x = [-b ± √(b² - 4ac)] / 2aSubstituting the values of a, b, and c:x = [5 ± √(5² - 4(1)(-24))] / 2x = [5 ± √(121)] / 2x = [5 ± 11] / 2x = 8 or x = -3
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Can someone help me out with this question fast!?!?!
Answer:
It is the 3rd one.C. -4<x<1
Is this right????????
Answer:
yep
Step-by-step explanation:
that's the tight answer!
Answer:
yes
Step-by-step explanation:
will the sampling distribution of x always be approximately normally distributed? Explain. Choose the correct answer below 0 ?. Yes, because the Central Limit Theorem states that the sampling distribution of x is always approximately normally distributed O B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough O C. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the population being sampled is normally distributed O D No, because the Central Limit Theorem states that the sampling d bution of x is approximately no aly distribui d only i the sa le sae is mere than 5% of the population.
B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.
The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution. However, this is only true if certain conditions are met, one of which is having a large enough sample size.
The CLT states that the sampling distribution of x will be approximately normally distributed if the sample size is large enough (usually greater than 30). If the sample size is small, the sampling distribution may not be normally distributed. In such cases, other statistical techniques like the t-distribution should be used.
Furthermore, the CLT assumes that the population being sampled is not necessarily normally distributed, but it does require that the population has a finite variance. This means that even if the population is not normally distributed, the sampling distribution of x will still be approximately normal if the sample size is large enough.
In conclusion, the answer is B, as the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.
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Find the best linear approximation, L(x), to f(x) = e' near x = 0. i.L(x) = x+1 ii. L(x) = x iii. LX) = c + 1
The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.
The given function is f(x) = e^x near x = 0.
To find the best linear approximation, L(x), we use the formula:
L(x) = f(a) + f'(a)(x-a),
where a is the point near which we are approximating.
Let a = 0, so that a is near the point x = 0.
f(a) = f(0) = e^0 = 1
f'(x) = d/dx (e^x) = e^x;
so f'(a) = f'(0) = e^0 = 1
Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1
Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.
For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.
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Let the graph of g be a vertical stretch by a factor of 2 and a
reflection in the x-axis, followed by a translation 3 units down of
the graph of f(x) = x². Write a rule for function g and identify the
vertex.
Vertex is slang for a corner or a place where two lines converge.The four corners of a square, for instance, are each referred to as a vertex.
Write a rule for function g and identify the vertex ?
The graph of g is a vertical stretch by a factor of 2 followed by a translation of 3 units down of the graph of f(x) = (x-1)²then the function g(x) = 2(x+4)²
f(x) =x²-2x+1 The graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of .f(x) =x²-2x+1
Rewrite the given function f(x).
f(x) = (x-1)²
Now, the graph is stretched vertically by a factor of 2.
= 2(-x-1)²
reflect the graph about the y-axis.
2(x+1)²
move to the left by 3 units.
= 2(x+3+1)²
=2(x+4)²
The function g(x) =2(x+4)²
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ind the average rate of change for the function over the given interval. y= e* between x = 0 and x = 3 The average rate of change of y between x= 0 and x = 3 is - (Round to four decimal places as needed.)
The average rate of change of function y over the given interval x = 0 and x = 3 is 6.3619. Here y = e×, where x is an exponential function and e is Euler's number.
What is exponential function and Euler's number?eˣ with an e basis, also referred to as Euler's number, x is an exponential function. f(x) = eˣ, where e is the Euler's number, is how it is expressed. Natural logarithms are built on Euler's number, a significant constant that can be used in a variety of situations. Euler's number, which starts with the letter e and is 2.71828..., is an irrational number where the sequence of digits never ends or repeats (similar to pi).
Average rate of change of function
f(x) = f(b) – f(a) / b – a
y = e×
f(a) = f(0) = e⁰ = 1
f(b) = f(3) = e³ = 20.0855
f(x) = 20.0855 – 1 / 3 – 0
f(x) = 6.3619
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