A student has a $50 bill, a $10 bill, a $5 bill, and a $1 bill.
a. If the student must select at least one bill, and the student may select up to all of the bills how many different sub somebody could the student make?
Answers
The student can select 1 bill or more than one bill. The student could make 15 different sum of money.
What is permutation?
An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.
Given that a student has a $50 bill, a $10 bill, a $5 bill, and a $1 bill.
He must select at least one bill.
To find the number of ways where the order does not matter is nCr.
The number of bills is 4.
Case 1:
Assume that he select 1 bill.
The number of ways to select one bill is ₄C₁ = 4!/1!(4-1)! = 4
Case 2:
Assume that he select 2 bill.
The number of ways to select two bill is ₄C₂ = 4!/2!(4-2)! =6
Case 3:
Assume that he select 3 bill.
The number of ways to select two bill is ₄C₃ = 4!/3!(4-3)! =4
Case 4:
Assume that he select 4 bill.
The number of ways to select two bill is ₄C₄ = 4!/4!(4-4)! =1
The total number of ways is 4 + 6 + 4 + 1 = 15
To learn more about combination, click on below link:
https://brainly.com/question/28788209
#SPJ1
Related Questions
4x - 8y + 2z = 10
-3x + y – 2z = 6
2x – 4y + z = 8
Answers
Answer:
100900000099899887765544422
i’ll give brainliest!! please help and answer correctly! plsss answer quick
Answers
Answer:
A
Step-by-step explanation:
if q is the point x, 4 3 − x , find the slope of the secant line pq (correct to six decimal places) for the following values of x.
Answers
You can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:
For x = 2:
slope = -1 / (3 - 2(2))
slope = -1 / (3 - 4)
slope = -1 / (-1)
slope = 1
To find the slope of the secant line PQ, we need two points on the line: P(x, 4) and Q(3 - x, 3).
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the coordinates of P are (x, 4) and the coordinates of Q are (3 - x, 3). Plugging these values into the slope formula, we have:
slope = (3 - 4) / (3 - x - x)
slope = -1 / (3 - 2x)
To find the slope of the secant line for different values of x, we substitute those values into the expression for the slope.
For example, if x = 1, the slope of the secant line PQ is:
slope = -1 / (3 - 2(1))
slope = -1 / (3 - 2)
slope = -1 / 1
slope = -1
Similarly, you can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:
For x = 2:
slope = -1 / (3 - 2(2))
slope = -1 / (3 - 4)
slope = -1 / (-1)
slope = 1
And so on, you can calculate the slope of the secant line for different values of x.
Learn more about expression from
brainly.com/question/1859113
#SPJ11
How many groups of 4 are in 4/5
Answers
Answer:
4
kind of confusing question
what is the variable and inequality to this question
Answers
An object's velocity can be described by its acceleration and direction.
true or false
Answers
because acceleration and direction are different units. an objects velocity can be described by its direction but not by its acceleration.
Answer: False
Step-by-step explanation:
hope it helped xx
A person with five children earns₦613200 per month. Calculare the tax allowances
Answers
The total tax allowances are ₦1,300,000
Let us consider the tax allowances and rates established by the Federal Inland Revenue Service (FIRS) as
the basic tax allowance = ₦300,000
additional allowance for each dependent child = ₦200,000
tax rates range from 7.5% to 24% for different incomes.
To calculate their tax liability, we would need to apply the relevant tax rates to their taxable income like their income minus their tax allowances.
Let us Assume this person lives in Nigeria, we can calculate their tax allowances as follows:
Basic tax allowance = ₦300,000
Allowance for 5 children = 5 x ₦200,000 = ₦1,000,000
Total tax allowances = ₦300,000 + ₦1,000,000 = ₦1,300,000
To learn more about tax liability:
https://brainly.com/question/16950901
#SPJ4
RIGHT ANSWER GETS 15 POINTS
In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x.
Write and solve an equation to determine the measure of angle x. (5 points)
Your answer:
Answers
Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.
What is the vertical angles theorem?In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;
60° + 70° + y = 180°
130° + y = 180°
y = 180° - 130°
y = 50°
Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.
Read more on vertical angles theorem here: brainly.com/question/17876852
#SPJ1
please help. Which scale factors produce an expansion under a dilation of the original image?
Select each correct answer.
0.3
0.75
2
3
Answers
Answer:
It's 2 and 3
Step-by-step explanation:
Hope this helps
How can I rotate a coordinate system onto another coordinate
system using matricies?
thanks
Answers
To rotate a coordinate system onto another coordinate system using matrices, you can follow these steps:
1. Determine the angle of rotation: First, determine the angle by which you want to rotate the coordinate system. This angle will be used to create a rotation matrix.
2. Create a rotation matrix: The rotation matrix is a 2x2 or 3x3 matrix that represents the transformation of points in the original coordinate system to points in the rotated coordinate system. The elements of the rotation matrix can be determined based on the angle of rotation.
For a 2D rotation, the rotation matrix is:
\(\[ \begin{matrix} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{matrix} \]\)
For a 3D rotation around the x-axis, y-axis, and z-axis, the rotation matrices are:
\(Rx = \left[\begin{array}{ccc}1&0&0\\0&cos\theta&-sin\theta\\0&sin\theta&cos\theta\end{array}\right]\)
\(Ry = \left[\begin{array}{ccc}cos\theta&0&sin\theta\\0&1&0\\-sin\theta&0&cos\theta\end{array}\right]\)
\(Rz = \left[\begin{array}{ccc}cos\theta&-sin\theta&0\\sin\theta&cos\theta&0\\0&0&1\end{array}\right]\)
Note that θ represents the angle of rotation.
3. Apply the rotation matrix: To rotate a point or a set of points, multiply the coordinates of each point by the rotation matrix. This will yield the coordinates of the points in the rotated coordinate system.
For example, if you have a 2D point P(x, y), and you want to rotate it by angle θ, the rotated point P' can be obtained by multiplying the column vector [x, y] by the rotation matrix:
[ x' ] = [ cosθ -sinθ ] [ x ]
[ y' ] = [ sinθ cosθ ] * [ y ]
Similarly, for 3D rotations, you would multiply the column vector [x, y, z] by the appropriate rotation matrix.
Rotating a coordinate system onto another coordinate system using matrices involves the use of rotation matrices. These matrices define how points in the original coordinate system are transformed to points in the rotated coordinate system.
The rotation matrices are constructed based on the desired angle of rotation. The elements of the matrix are determined using trigonometric functions such as cosine and sine. The size of the rotation matrix depends on the dimensionality of the coordinate system (2D or 3D).
To apply the rotation, the coordinates of each point in the original coordinate system are multiplied by the rotation matrix. This matrix multiplication yields the coordinates of the points in the rotated coordinate system.
By performing this transformation, you can effectively rotate the entire coordinate system, including all points and vectors within it, onto the desired orientation defined by the angle of rotation.
Matrix transformations provide a mathematical and systematic approach to rotating coordinate systems, allowing for precise control over the rotation angle and consistent results across different coordinate systems. They are widely used in computer graphics, robotics, and various scientific and engineering fields.
To know more about matrices, refer here:
https://brainly.com/question/30646566#
#SPJ11
simplify the following numerical expression as much as possible. write your answer in exponential form. let a and b be positive integers. 23a x 23b
Answers
The simplified expression in exponential form would be 23^(a + b).
To simplify the numerical expression 23a x 23b, we can combine the like terms.
Step 1: Simplify 23a and 23b individually.
The expression 23a means multiplying 23 by a, and 23b means multiplying 23 by b. We cannot simplify them further because we do not have specific values for a and b.
Step 2: Combine the simplified terms.
When we multiply 23a by 23b, we multiply the coefficients (23 x 23) and the variables (a x b). Therefore, the simplified expression is:
(23 x 23) x (a x b)
Step 3: Calculate the coefficient and write the answer in exponential form.
The coefficient (23 x 23) is equal to 529. In exponential form, we can write it as 23^2. So the final simplified expression is:
23^2 x (a x b)
In summary, the simplified numerical expression 23a x 23b can be written as 23^2 x (a x b) in exponential form.
To know more about exponential form refer here:
https://brainly.com/question/29166310
#SPJ11
what is the area of a circle with a radius of 1 foot
1/4 pi ft square
1/2 pi ft square
pi ft square
2 pi ft square
Answers
A=pie x radius^2
1 times 1=1.
Pi times 1 equal 1
Pi ft square
7. A farmer plants 987 apple trees in
9 rows. Can each row have the same
number of trees? How do you know?
Answers
Answer:
No because you can split a tree
Step-by-step explanation:
let be the solution of the equation y''-5y' 6y=0 satisfying the conditions y(0)=1 and y'(0)=2 and . find ln(y(1))
Answers
The given differential equation y'' - 5y' + 6y = 0 can be factored as (D-2)(D-3)y = 0, where D denotes the derivative operator. Hence, the general solution is y = c1*e^(2x) + c2*e^(3x), where c1 and c2 are constants that depend on the initial conditions.
Using the given initial conditions, we can find c1 and c2 as follows:
y(0) = c1 + c2 = 1
y'(0) = 2c1 + 3c2 = 2
Solving this system of equations, we get c1 = -1 and c2 = 2. Therefore, the particular solution that satisfies the given initial conditions is:
y = -e^(2x) + 2*e^(3x)
To find ln(y(1)), we substitute x = 1 in the above expression:
y(1) = -e^2 + 2*e^3
Taking natural logarithm on both sides, we get:
ln(y(1)) = ln(-e^2 + 2*e^3)
Note that this is an exact value, which cannot be simplified further.
To find the solution of the given differential equation y'' - 5y' + 6y = 0 with initial conditions y(0) = 1 and y'(0) = 2, we will first find the complementary function and then apply the initial conditions to determine the constants.
The given equation is a second-order linear homogeneous differential equation with constant coefficients. We will start by finding the characteristic equation:
r^2 - 5r + 6 = 0
This can be factored as:
(r - 2)(r - 3) = 0
This gives us two roots, r1 = 2 and r2 = 3. Now, we can write the general solution for the differential equation as:
y(x) = C1 * e^(2x) + C2 * e^(3x)
Now, let's apply the initial conditions:
1. y(0) = 1:
C1 * e^(2*0) + C2 * e^(3*0) = 1
C1 + C2 = 1
2. y'(0) = 2:
The derivative of y(x) is:
y'(x) = 2C1 * e^(2x) + 3C2 * e^(3x)
y'(0) = 2C1 * e^(2*0) + 3C2 * e^(3*0) = 2
2C1 + 3C2 = 2
Solving this system of linear equations for C1 and C2, we get:
C1 = 1
C2 = 0
So, the particular solution is:
y(x) = e^(2x)
Now we need to find ln(y(1)):
ln(y(1)) = ln(e^(2*1)) = ln(e^2) = 2
So, ln(y(1)) = 2.
Learn more about differential equation here: brainly.com/question/14620493
#SPJ11
4. Show that f(x,y)=x^2y is homogeneous, and find its degree of homogeneity. 5. Which of the following functions f(x,y) are homothetic? Explain. (a) f(x,y)=(xy)^2+1 (b) f(x,y)=x^2+y^3 3
Answers
4. f(x,y) is homogeneous of degree 2.
5. a) f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1
4. Show that f(x,y)=\(x^2\)y is homogeneous, and find its degree of homogeneity:
A function is said to be homogeneous of degree k, if it satisfies the condition:
f(tx,ty) = \(t^k\)f(x,y)
We have f(x,y) = \(x^2\)y. Let’s check if it satisfies the above condition:
f(tx,ty) = \((tx)^2(ty) = t^3x^2y = t^2(x^2y\)) = \(t^2\)f(x,y)
Hence f(x,y) is homogeneous of degree 2.
5. Which of the following functions f(x,y) are homothetic? Explain.
(a) f(x,y)=\((xy)^2\)+1
(b) f(x,y)=\(x^2+y^3\)
Let us first understand the meaning of homothetic transformation.
A homothetic transformation is a non-rigid transformation of the Euclidean plane that preserves the direction of the straight lines but not their length. It stretches or shrinks the plane by a constant factor called the dilation.
Let’s now find out whether the given functions are homothetic or not.
(a) f(x,y)=\((xy)^2\)+1
In order to check if f(x,y) is homothetic or not, we need to check if the function satisfies the following condition:
f(x,y) = g(h(x,y))
where g is a strictly monotonic function and h is a homogeneous function with degree 1
We have
f(x,y) = \((xy)^2\)+1
Let’s assume g(x) = x - 1, then g(x+1) = x
Similarly, let’s assume h(x,y) = (xy), then h(tx,ty) = \(t^2\)h(x,y)
Now, we have
g(h(x,y)) = h(x,y) - 1 = (xy) - 1
Thus f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1
(b) f(x,y)=\(x^2+y^3\)
We can’t write this function in the form f(x,y) = g(h(x,y)) where h(x,y) is a homogeneous function with degree 1. Hence this function is not homothetic.
To leran more about degree of homogeneity, refer:-
https://brainly.com/question/15395117
#SPJ11
Find the difference - 3.5 - 1.9
Answers
Answer:
1.6
Step-by-step explanation:
If g(x)= 2x +8x-1 what is g(-3)
A) -7
B) 11
C) 28
D)7
Answers
Step-by-step explanation:
Greetings !
Firstly, write down the given expression
\(g(x) = 2x + 8x - 1\)
simplify it to be more accurate where 2+8=10
\(g(x) = 10x - 1\)
plug in -3 in the value of x and simplify the expression
\(g( -3 ) = 10( - 3) - 1 \\ g( - 3) = - 30 - 1\)
Thus, subtract the numbers
\(g( - 3) = - 31\)
Hope it helps!
Plz help me!!! I'll give brainliest
Answers
Answer:
43.4
Step-by-step explanation:
im not sure, if im wrong sorry
White rice needs to cook for 20 minutes, while brown rice cooks for 25 minutes. What is the ratio of cooking times for white rice to brown rice?
Answers
Answer:
4:5
Step-by-step explanation:
20:25
Simplify, since both numbers are divisible by 5
4:5
Answer:
4:5
Step-by-step explanation:
20:25
Simplify the ratio.
Factors of 20 are 1, 2, 4, 5, 10, 20. Factors of 25 are 1, 5, 25
Both have factors of 5, so divide both sides with 5.
4:5
Jim and Carol recorded gas prices at five stations for their own towns in the table below. Gas Prices Name Station 1 Station 2 Station 3 Station 4 Station 5 Jim $3.45 $3.54 $3.71 $3.62 $3.49 Carol $3.89 $3.65 $3.39 $3.48 $3.49 Which person's town had the lower mean for gas prices and by about how much?
A Jim, by $0.02
B Carol, by $0.02
CJim, by $0.06
D. Carol, by $0.06
Answers
r= 2.2 in.
h = 4 in.
Answers
Answer:
85.7
Step-by-step explanation:
The surface area is 85.7 in.^2
Let me know if this helped
Rewrite the expression with a rational (fraction) exponent:
7Vz
PLEASE HELP ASAP
Answers
Answer:
z^1/7
Step-by-step explanation:
trust me
3^x = 1/9, the value of x
Answers
Answer: -2
Step-by-step explanation:
Find the MEAN, VARIANCE, STANDARD DEVIATION, and COEFFICIENT OF VARIATION for the following SAMPLE of the number of severe car accidents in 1-90 from 2015 to 2020. (YOU MUST SHOW YOUR WORK!!!)
256, 189, 172, 220, 320, 192
Answers
The Mean, Variance, Standard Deviation, and Coefficient of Variation for the given sample of the number of severe car accidents in 1-90 from 2015 to 2020 are:
Mean = 224.833
Variance = 1956.0667
Standard Deviation (SD) = 108.319
Coefficient of Variation (CV) = 48.163%
From the question above, Given data is: 256, 189, 172, 220, 320, 192
Mean, variance, standard deviation and coefficient of variation for the given sample of the number of severe car accidents in 1-90 from 2015 to 2020 are given below:
The mean of data is equal to the sum of all data points divided by the total number of data points.
N = 6
Sum of data = 256 + 189 + 172 + 220 + 320 + 192 = 1349 ∴ Mean = 1349 / 6= 224.833
Calculation of Variance: The variance of data is the average of the squared differences from the mean.
Variance is calculated by dividing the sum of squared deviations by N-1, where N is the number of data points and then find the average.
Calculation of standard deviation: The standard deviation of data is the square root of the variance.SD = √11736.4 = 108.319
Coefficient of variation (CV): The coefficient of variation (CV) is a normalized measure of the dispersion of the data points. It is the ratio of the standard deviation to the mean.
CV is used to analyze and compare data of different sizes.
So, CV = (SD / Mean) × 100%CV = (108.319 / 224.833) × 100%= 48.163%∴
Learn more about standard deviation at
https://brainly.com/question/1505056
#SPJ11
a transition matrix is called doubly stochastic if both rows and columns sum to 1. show that all finite-dimensional doubly stochastic matrices have a uniform stationary distribution.
Answers
Transition matrix is called a doubly stochastic matrix (if sum of each rows and columns is 1 ).
We can see that the distribution of doubly stochastic matrix for all finite dimensional has Uniform stationary distribution.
Doubly Stochastic Matrix
A transition random matrix P is defined as a dual random matrix if the sum of the rows and columns is one.
Therefore, for each column j of the doubly random matrix, let ∑ ipᵢⱼ = 1. Suppose the distribution π on S also has π₁ = π if the Markov chain starts with the initial distribution π₀ = π. That is, if the distribution at time 0 is π, the distribution of π remains 1, and this π is said to be stationary.
Example: A uniform distribution [[π(i) = 1/N for all i]] is stationary if the N × N stochastic transition matrix P is symmetric. More generally, the uniform distribution is stationary if the matrix P is doubly stochastic, i.e. the columns of P sum to 1 (we already know that the rows of P sum to all 1). are available). It is easy to see that when πn approaches a limiting distribution as n → ∞, this limiting distribution must be stationary. To see this, assuming lim n→∞ πn = π' , and n → ∞ in the equation πₙ₊₁ = πₙP, we get π = π'P. This shows that π' is stationary. So , the arguments given pass clearly and simply when the state space is finite.Hence, the required results is achieved .
For more information on the double random matrix, visit :
https://brainly.com/question/29025233
#SPJ4
47 divided by 25, work it out step by step
Answers
Answer:
1.88
Step-by-step explanation:
47/25
= 1.88
For the given linear function, find the average rate of change on the following intervals. g(x) = 3 + 18x- (a) Between x = -1 and x = 1 (b) Between x = 1 and x = 2 (c) Between x = a and x = a + h
Answers
The average rate of change for the given linear function is 18 on both intervals (a) and (b). For interval (c), the average rate of change will depend on the specific values chosen for a and h.
To find the average rate of change of the given linear function g(x) = 3 + 18x on different intervals, we calculate the difference in the function values divided by the difference in x-values for each interval.
(a) Between x = -1 and x = 1:
The average rate of change is determined by evaluating g(1) and g(-1) and finding the difference in the function values divided by the difference in x-values.
Average rate of change = (g(1) - g(-1)) / (1 - (-1))
(b) Between x = 1 and x = 2:
Similarly, we evaluate g(2) and g(1) and find the difference in the function values divided by the difference in x-values.
Average rate of change = (g(2) - g(1)) / (2 - 1)
(c) Between x = a and x = a + h:
Here, we substitute x = a + h and x = a into the function g(x) and find the difference in the function values divided by the difference in x-values.
Average rate of change = (g(a + h) - g(a)) / (a + h - a)
To calculate the average rate of change on each interval for the given linear expression g(x) = 3 + 18x, we substitute the x-values into the function and compute the differences in the function values divided by the differences in the x-values.
(a) Between x = -1 and x = 1:
g(1) = 3 + 18(1) = 21
g(-1) = 3 + 18(-1) = -15
Average rate of change = (g(1) - g(-1)) / (1 - (-1)) = (21 - (-15)) / (1 + 1) = 36 / 2 = 18
(b) Between x = 1 and x = 2:
g(2) = 3 + 18(2) = 39
g(1) = 3 + 18(1) = 21
Average rate of change = (g(2) - g(1)) / (2 - 1) = (39 - 21) / (2 - 1) = 18 / 1 = 18
(c) Between x = a and x = a + h:
To calculate the average rate of change between these two points, we need the values of a and h.
Without specific values for a and h, we cannot provide a numerical answer.
The average rate of change will depend on the specific values chosen for a and h.
In summary, the average rate of change for the given linear function is 18 on both intervals (a) and (b). For interval (c), the average rate of change will depend on the specific values chosen for a and h.
Learn more about Expression here:
https://brainly.com/question/11701178
#SPJ11
Graph (3,-3),(-2,0),(-2,4)and(5,4)and connect the points.
Answers
Answer:
look at the pic below and just connect the points
Step-by-step explanation:
McDonalds released a quote saying, "15% of all its customers prefer chicken nuggets compared to the other food we serve." To see if this quote was accurate you went out and got a simple random sample of 250 people that eat at Mcds, 50 of which said they prefer chicken nuggets compared to the other food Mcd's sells. Test to see if more than 15% of Mcds customers prefer their chicken nuggets. What is the value of the p-value? a. 0.0587 b. 0.9766 c. 0.0268 d. 0.0134
Answers
To test if more than 15% of McDonald's customers prefer chicken nuggets, conduct a one-sample proportion test. With 50 out of 250 preferring chicken nuggets, the p-value is 0.0268 (c).
To test if more than 15% of McDonald's customers prefer chicken nuggets, we can conduct a one-sample proportion test. The null hypothesis (H0) is that the true proportion is 15% or less, while the alternative hypothesis (H1) is that the true proportion is greater than 15%.
In our sample of 250 customers, 50 preferred chicken nuggets. We calculate the sample proportion as 50/250 = 0.2 (20%). We can then use the binomial distribution to determine the probability of observing a proportion as extreme as 0.2 or higher, assuming H0 is true.
Using statistical software or a calculator, we find that the p-value is 0.0268. This p-value represents the probability of observing a sample proportion of 0.2 or higher if the true proportion is 15% or less. Since the p-value is less than the conventional significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that more than 15% of McDonald's customers prefer chicken nuggets. Therefore, the answer is c. 0.0268.
To learn more about probability click here
brainly.com/question/32117953
#SPJ11
find the unknown sizes of an angles of the following polygons.
Answers
Answer:
A is an irregular pentagon - total angle is 540. So x is 100
(540 - 440=100)
B. 3a + 345 = 540
- 345 both sides
3a=195
÷3
a = 65
2a = 130 (65x2)
C. X = 120 (angles on straight lines adds to 180)
3y + 300 = 540
- 300
3y = 240
÷3
Y= 80
x 2
2Y = 160
Hope this helps!