64grams of bismuth-214 must be prepared if the shipping time is 120minutes.
What is half cycle?
Time required for a quantity to reduce to half of its initial value is termed as half life. It can help us to know how quickly unstable atoms undergo radioactive decay. This is used generally to characterize any type of exponential decay. It occurs when unstable atomic particles lose energy. Twenty-nine elements are capable of this process.
Rutherford applied the principle of a radioactive element's half-life in the age determination of rocks by calculating the decay period of radium to lead-206.
Given half life of 20min of 1g of Bismuth-214
If the shipping time is 120minutes, then
10min/20min/half life
=6 half life
=1/2^6=1/64
Grams of bismuth-214 that can be prepared in 120 min,
=1gm*64
=64grams.
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If T1(x) and T2(x) are onto linear transformations from Rn to Rm, then so is w(x) = T1(x) + T2(x) True, by the definition of linear transformation. True, by the definition of linear transformation and the definition of onto. False. Consider T2(x) = T1(x), where T1 is onto. False. Consider T2(x) =-T1(x), where T1 is one-to-one False. Consider T2(x) =-T1(x), where T1 is onto
[tex]$W(\mathbf{x})$[/tex]is a linear transformation. it is not onto .The given statement is false.
The objective is to determine whether the following statement is true or false.
"If [tex]$$T_1(\mathbf{x})$ and $T_2(\mathbf{x})$[/tex] are onto linear transformations from [tex]$\mathbf{R}^n$[/tex] to [tex]$\mathbf{R}^m$[/tex] then [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex] is an onto linear transformation."
To check whether [tex]$W(\mathbf{x})$[/tex] is a linear transformation or not:
For a, b ∈ R and for x, y ∈ [tex]$\mathbf{R}^n$[/tex],
[tex]$$\begin{aligned}W(a \mathbf{x}+b \mathbf{y})= & T_1(a \mathbf{x}+b \mathbf{y})+T_2(a \mathbf{x}+b \mathbf{y}) \quad\left(\text { Since } W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})\right) \\= & {\left[a T_1(\mathbf{x})+b T_1(\mathbf{y})\right]+\left[a T_2(\mathbf{x})+b T_2(\mathbf{y})\right] } \\& \quad\left(\text { Since } T_1(\mathbf{x}) \text { and } T_2(\mathbf{x}) \text { are onto linear transformations }\right) \\\end[/tex]
[tex]= & a\left[T_1(\mathbf{x})+T_2(\mathbf{x})\right]+b\left[T_1(\mathbf{y})+T_2(\mathbf{y})\right] \\\\= & a W(\mathbf{x})+b W(\mathbf{y})\end{aligned}$$[/tex]
Therefore, [tex]$W(\mathbf{x})$[/tex] is a linear transformation.
To check whether [tex]$W(\mathbf{x})$[/tex] is onto:
Define the linear transformations:
[tex]$$T_1: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_1(\mathbf{x})=\mathbf{x}$[/tex]
[tex]$$T_2: \mathbf{R} \rightarrow \mathbf{R}$ such that $T_2(\mathbf{x})=-\mathbf{x}$[/tex]
Then, [tex]$T_2(\mathbf{x})=-\mathbf{x}=-T_1(\mathbf{x}) \Rightarrow T_2(\mathbf{x})=-T_1(\mathbf{x})$[/tex]
The range of both functions [tex]$T_1, T_2$ is $\mathbf{R}$[/tex] This is same as the co-domain of [tex]$T_1, T_2$[/tex]. So, they are onto functions.
If A and B are the two sets, if for every element of B, there is at least one or more element matching with set A, it is called the onto function.
Therefore, [tex]$T_1, T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex]are onto linear transformations.
And, [tex]$W=T_1+T_2: \mathbf{R} \rightarrow \mathbf{R}$[/tex] is a mapping.
Now, [tex]$W(\mathbf{x})=T_1(\mathbf{x})+T_2(\mathbf{x})$[/tex]
[tex]$$\begin{aligned}& =T_1(\mathbf{x})-T_1(\mathbf{x}) \\& =0\end{aligned}$$[/tex]
So, the range of [tex]$$W(\mathbf{x})$ is $\{0\} \neq \mathbf{R}($[/tex] co-domain of [tex]$W(\mathbf{x}))$[/tex]
Then, is [tex]$W(\mathbf{x})$[/tex] not onto.
So, the given statement is false.
Hence, the correct answer is 5th option
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Please help please! No fake answers pls
Answer:
[tex]x=60[/tex]
Step-by-step explanation:
[tex]3x=180\\x=\frac{180}{3} \\x=60[/tex]
Yaqub has a bag only containing green and yellow pins. 3 of the pins are green. 7 He picks out a green pin from his bag and gives it to his sister. of the remaining pins in his bag are green. How many of the remaining pins in his bag are green and how many are yellow?
Answer:
The answer is that there are 2 green pins and 5 yellow pins remaining in the bag.
Step-by-step explanation:
There are 3 green pins in the bag at the start and Yaqub gives one to his sister, so there are 3 - 1 = <<3-1=2>>2 green pins remaining in the bag. The rest of the pins in the bag must be yellow, so there are 2 green and 7 - 2 = <<7-2=5>>5 yellow pins remaining in the bag.
Answer:2 green 5 yellow
Step-by-step explanation:
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. n =12, x= 5, p=0.25?
x = random variable = number of successful trials = 4
n = number of trials = 6
P = likelihood of success = 0.55
Q = likelihood of failure = 0.45
nCx = number of combinations of n objects taken x at a time
.
Binomial Distribution
b(x; n, P) = nCx * P^x * Q^(n - x)
.
b(4; 6, 0.55) = 6C4 * (0.55)^4 * (0.45)^2 = (15)(0.09150625)(0.2025) = 0.2779502
dagogo uploads 333 videos on his channel every month. each video averages 151515 minutes in length and gets an average of 150{,}000150,000150, comma, 000 new views. the average ratio of likes-to-views of dagogo's videos is 1:51:51, colon, 5. dagogo wants to reach a total of 9{,}000{,}0009,000,0009, comma, 000, comma, 000 views on his channel. assuming these rates continue, how many likes does dagogo get, on average, for each minute of video he uploads?
In linear equation, For 20 Months Dagogo requires to upload videos to get 90,000,000 views on his channel.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Dagogo uploads 3 videos on his channel each month.
Each video gets an average of 1500000 views.
3 Video get Views = 3 * 1500000
= 4,500,000 Views
Views per month = 4,500,000 Views
Total Views = 90,000,000 views
Number of months = Total Views/Views per month
Number of months = 90,000,000/4,500,000
Number of months 20 Months
For 20 Months Dagogo requires to upload videos to get 90,000,000 views on his channel.
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The complete question is -
Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets an average of 150,000 new views. The average ratio of likes-to-views of Dagogo videos is 1:5. Dagogo wants to reach a total of 9,000,000 views on his channel. Assuming these rates continue, for how many months does Dagogo need to upload videos to get to 9,000,000 views on his channel?
Answer:
2000 likes per minute
Step-by-step explanation:
If each video averages 15 minutes and he gets an average of 150000 new views, we can divide.
150000/15=10000
If the ratio of likes to views is 1:5, we can assume 10000 is the "5" and divide it by 5.
10000/5=2000
2000:10000 = 1:5
2000 likes per minute
(KHAN)
8 17 26 Find the 41st term.
Answer:
368
Step-by-step explanation:
You want the 41st term of the arithmetic sequence that starts 8, 17, 26.
Arithmetic sequenceThe n-th term of an arithmetic sequence is given by ...
an = a1 +d(n -1)
for first term a1 and common difference d.
DifferenceThe difference between terms is ...
d = 17 -8 = 9
41st termThe first term is a1 = 8, so the 41st term is ...
a41 = a1 +d(41 -1) = 8 +9(41 -1) = 368
The 41st term of the sequence is 368.
<95141404393>
Find g(x), where g(x) is the reflection across the x-axis of f(x)=-9x+10.
Which ordered pair makes both inequalities true? y < –x + 1 and y > x?A.-3,5
B.-2,2
C.-1,-3
D.0,-1
The ordered pair -2,2 makes the inequalities y < –x + 1 and y > x true. Therefore, option B is true.
Inequality is the absence of an equality link between two expressions or values. An ordered pair is made up of the x and y coordinates, with two values stated in a certain order inside parenthesis.
Substitute the values from the given ordered pair one by one to check whether the given inequalities are true.
Substituting (-2,2) in y < –x + 1 and y > x,
For, y < –x + 1
2<2+1
2<3
For, y > x
2>-2
This ordered pair (-2,2) makes the given inequalities true.
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Hello. Could someone help me to solve this question? The answer is 86.61cm.
The perimeter of the whole diagram in cm is derived as 86.6158 cm using trigonometric ratios.
Trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the angle P for right-angled triangle formed by extending the line PQ to the base of the trapezium, so that we have opposite side of 7 cm (22 cm - 15 cm)
so; sinP = 7/25.3
P = sin^(-1)(7/25.3)
P = 16.06
The isosceles triangle PQR have the angle;
Q = 180 - 2(16.06) {sum of interior angles of Isosceles triangle with two equal base angles}
Q = 147.88°
Considering the smaller right-angled triangle formed by the height of the trapezium and one side of the Isosceles triangle, we have its angle;
Q = 180° - 147.88° {sum of angles on a straight line}
Q = 32.12
also;
sin32.12 = 7/hypotenuse (one of the equal sides of the Isosceles triangle)
hypotenuse = 7/sin32.12
hypotenuse = 13.1655
The length TS is equal to the adjacent side of the smaller triangle, so;
cos32.12 = TS/13.1655
TS = 13.1655 × cos32.12
TS = 1.51503
Therefore, the perimeter of the whole diagram is;
25.3 cm + 22 cm + 15 cm + 13.1655 cm + 11.1503 cm = 86.6158 cm.
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Leah want to buy a necklace for her mother’ birthday that cot $48. 50. She currently ha $14. 55. What percentage of the total doe Leah have?
Leah currently has 14.55 out of the total of 48.50, which is approximately 30% of the total amount.
To calculate the exact percentage, you would divide 14.55 by 48.50 and then multiply the result by 100. If you do this, you find that Leah has exactly 29.941%, which rounds up to 30%.
The remaining amount of money that Leah needs to buy the necklace is 33.95, which is approximately 70% of the total. To calculate the exact percentage, you would divide 33.95 by 48.50 and then multiply the result by 100. If you do this, you find that Leah needs exactly 69.907%, which rounds down to 69%.
Therefore, Leah currently has 30% of the total amount of money needed for the necklace, and she needs 69% of the total amount of money to buy the necklace for her mother's birthday.
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Jamie wrote out the following equence of number on a heet of paper. What number would be the next in the equence of number?
The number which would be the next in the sequence of number is sixty-four i.e., 64.
What is Geometric sequence?In mathematics, a geometric progression is a sequence of non-zero numbers where each term after the first multiplies the previous term by a fixed non-zero number called the common ratio. In other words, a geometric progression has consecutive terms with a common ratio. Example: a , a², a³, ..., where aₙ₊₁/aₙ= a
We have , Jamie noted the following sequence: 4, 8, 16, 32, . .. on a sheet of paper. After careful study of the sequence we have provided, is a geometric sequence and the ratio between consecutive terms in the geometric sequence is : (8/4), (16/8), ....
= 2, 2, .....
We have to locate the next number in sequence. To find the next term in a geometric sequence, simply multiply the last term given by the common ratio of the sequence. So, the next number in the sequence is 32 × 2 = 64. Hence, required number is 64.
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Complete question:
Jamie wrote out the following sequence of numbers: 2, 6, 14, 30,...on a sheet of paper. What number would be the next in the equence of number?
a _______ is a graph of each data value plotted as a point. stemplot dotplot Pareto chart frequency polygon
A dot plot is a graph of each data value plotted as a point.
In the given question, we have to fill in the blanks.
A _______ is a graph of each data value plotted as a point.
As we know that;
Data points are represented as dots on a graph with an x- and y-axis in a dot plot, sometimes referred to as a strip plot or dot chart, which is a straightforward type of data visualisation.
These kinds of graphs are employed to visually represent particular data trends or groupings. The distribution of a collection of data is shown by a dot plot, which is comparable to a histogram in that it shows the proportion of data points that fall into each category or value on the axis.
Hence, a dot plot is a graph of each data value plotted as a point.
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Please find the area and perimeter of the shapes!
I will give brainly to the best!
Answer:
0
Step-by-step explanation:
Don has a box of colored pencils. He uses 53 pencils And has 118 pencils left in the box.Write an equation to showing how many pencils are in the box before he starts drawing.
The correct equation is p - 53 = 118.
How did we figure this out?Dontavious has a box of colored pencils.Dontavious uses 53 pencils.Pencils still left in the box = 118.Let the total number of pencils in the box be p.So, the equation representing the situation given will be:
⇒ p - 53 = 118
Therefore, the correct equation is p - 53 = 118.
Simplify each algebraic expression. Drag the tiles to the correct boxes to complete the pairs.
Tiles
-5x - 2
Pairs
5x+2
5x-2
12z+872 - 10
z + 17-2 - 15
8- 12z 10+ 7x
-
9 - 올ㄹ - 글ㄹ - 7
-5x+2
PLEASE HELP ASAP
Answer:
.
Step-by-step explanation:
I need help with this image attached
Answer:
32
Step-by-step explanation:
y² + 7y-8
Please answer this and show work
The factorization of y²+7y-8 is (y+8)(y-1).
y²+7y-8
=y²+8y-y-8
=y(y+8)-1.(y+8)
=(y+8)(y-1)
The factors are (y+8), (y-1).
The method we are following here is factorize by grouping.
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The correct question is-
Factor y²+7y-8.
Complete the table below using the given function
Answer:
just write the value of y in the y table and replace x with the given value above : for example if x is -4
then,
y = 20*(-4)-5
Select each equation which is equivalent to 60% of 25. 0.6 • 25 = x x • 1.6 = 25 6/10=x/25 60/100=25/x x/25=60/100 6.0 • 25 = x
Answer:
the ture was
0.6 • 25 = x
6/10=x/25
x/25=60/100
the fault
6.0 • 25 = x
x • 1.6 = 25
60/100=25/x
Corey is making a wall-mounted bookshelf. it has 2 shelves, with a third piece of wood intersecting them. to support the shelves, corey orders some l-brackets to put between the shelves and the crosspiece. he measures angle 6. how many brackets should he order to have one for every angle that is congruent to angle 6? explain.
2; <3 is congruent to <6. Option B is correct.
What is Angle?Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Given that Corey is making a wall-mounted bookshelf.
It has 2 shelves, with a third piece of wood intersecting them. to support the shelves, corey orders some l-brackets to put between the shelves and the crosspiece.
To find a congruent angle you must find what can fit inside the giving number the best. If we compare all of the answer is wouldn't make sense, since 7 is greater than 6 it would be wrong. So, A is Incorrect.
C is about 3 and 7. C would fit but 7 wouldn't. So, C is incorrect.
D has both 2 and 3 but also have 4 and 7 which wouldn't match. So, D is incorrect.
Hence, option B is correct, 2; <3 is congruent to <6.
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One bouquet of flower ha 7 roe for every 2 tickeed. Another bouquet ha 3 tickeed for every 4 daiie. If both bouquet have 6 tickeed, which bouquet ha more flower? LOADING. Click the icon to view the table
If both bouquets have 6 tickseeds, the first bouquet ( roses + tickseeds) has more flowers.
The problem can be solved using ratio.
Bouquet 1 :
Every 2 tickseeds there are 7 roses
Hence, the ratio
Tickseed : rose = 2 : 7
If there are 6 tickseeds, then
2 : 7 = 6 : rose
rose = (6/2) x 7 = 21
Number of flowers = 6 tickseeds + 21 roses = 27 flowers
Bouquet 2 :
Every 3 tickseeds there are 4 daisies
Hence, the ratio
Tickseed : daisy = 3 : 4
If there are 6 tickseeds, then
3 : 4 = 6 : daisy
daisy = (6/3) x 4 = 8
Number of flowers = 6 tickseeds + 4 daisies = 10 flowers
Hence, if there are 6 tickseeds in each bouquet, the first bouquet contains more flowers.
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the degrees of freedom for a chi-square test of independence for the following data is 5. group of answer choices true false
The number of independent pieces of information used to calculate a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. I
What is the degree of freedom?Itbis determined by subtracting the number of restrictions from the sample size. Subtract the number of relations from the number of observations to determine degrees of freedom. You need to deduct one (1) from the total number of observations, n, in order to calculate the degrees of freedom for a sample mean or average.
The degrees of freedom for the chi-square are calculated as df = (r-1)(c-1) where
r = the number of rows
c = the number of columns.
If the observed chi-square test statistic is greater than the critical value, the null hypothesis can be rejected.
Note that an overview was given as the information you gave is incomplete.
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The table below represents the value, y, of an antique table x years after purchase.
The data was modeled with a linear best-fit function. What was the initial purchase price?
$5,625
$5,000
$625
$2,500
The initial purchase price of the best fit function is; $2500
How to interpret a linear best fit function?The equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
The formula to find the slope between two coordinates is;
m = (y₂ - y₁)/(x₂ - x₁)
If we take the coordinates (4, 5000) and (12, 10000), we have;
Slope = (10000 - 5000)/(12 - 4)
Slope = 625
Thus, the equation will be;
5000 = 625(4) + c
5000 - 2500 = c
c = $2500
y-intercept represents the intital price which is when x = 0 years.
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Haute cuisine is typically characterized by careful preparation and what kind of presentation?
Ο Α.
О в. cluttered
careless
C. detail-oriented
D.
casual
Answer:
C. detail-oriented
Step-by-step explanation:
Haute cuisine is typically characterized by careful preparation and detail-oriented presentation.
Given isosceles HIJ where HI ≈ IJ, m/H = (3x + 10)°, and m/I = (6x − 20)°, find the measures of angles H, I, and J.
The missing angles of the isosceles triangle are as follows:
m∠H = 55 degreesm∠I = 70 degreesm∠J = 55 degrees.How to find the angles of an isosceles triangle?An isosceles triangle is a triangle that has two sides equal to each other and two angles congruent to each other.
The base angles of an isosceles triangles are congruent and the two legs are also equal.
Therefore, ΔHIJ
where
HI ≅ IJ
m∠H = 3x + 10
m∠I = 6x - 20
Therefore,
m∠H ≅ m∠J
m∠H + m∠I+ m∠J = 180
3x + 10 + 6x - 20 + 3x + 10 = 180
12x = 180
x = 180 / 12
x = 15
Hence,
m∠H = 3(15) + 10 = 55 degrees
m∠I = 6(15) - 20 = 90 - 20 = 70 degrees
m∠J = 55 degrees.
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Expand the function.
f(x)=(3x+2)^4
The expanded equation of the function f(x) = (3x + 2)⁴ is f(x) = 81x + 216x³ + 216x² + 96x + 16
How to expand the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = (3x + 2)⁴
Using the pascal triangle at n = 4, we have the coefficients to be
Coefficient = 1 4 6 4 1
So, when the function f(x) = (3x + 2)⁴ is expanded, we have
f(x) = 1 * (3x)⁴ + 4 * (3x)³ * 2 + 6 * (3x)² * 2² + 4 * (3x) * 2³ + 1 * 2⁴
Evaluate
f(x) = 81x + 216x³ + 216x² + 96x + 16
Hence, the solution is f(x) = 81x + 216x³ + 216x² + 96x + 16
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Bottles of water come in three sizes.
Small bottle: A 200 ml bottle costs 25p;
Medium bottle: A 750 ml bottle costs 84p;
Large bottle: A 1 litre bottle costs £1.08.
Calculate the cost of 3 litres for each bottle.
Give your answer in pence to the nearest penny.
Write the bottle that is the better value in the comments.
Small:
Р
Medium:
P
Large:
Р
Answer:
Step-by-step explanation:
Please help me!
I need to deliver it tomorrow.
i'm kind of sure it's -4.7
equation of a circle whose center at P (3,-7) and tangent to 2x+3y-4=0
Answer:
[tex](x-3)^2+(y+7)^2=\dfrac{361}{13}[/tex]
Step-by-step explanation:
The tangent of a circle is always perpendicular to the radius.
Therefore, the center is on a line that is perpendicular to the tangent.
Rearrange the equation of the tangent to make y the subject:
[tex]\begin{aligned}2x+3y-4&=0\\3y&=-2x+4\\y&=-\dfrac{2}{3}x+\dfrac{4}{3}\end{aligned}[/tex]
Therefore, the slope of the tangent line is -²/₃.
If two lines are perpendicular to each other, their slopes are negative reciprocals. Therefore, the slope of the perpendicular line is ³/₂.
To write the equation of the line perpendicular to the tangent, substitute the found slope and the center point into the point-slope formula:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\implies y-(-7)&=\dfrac{3}{2}(x-3)\\y+7&=\dfrac{3}{2}x-\dfrac{9}{2}\\y&=\dfrac{3}{2}x-\dfrac{23}{2}\end{aligned}[/tex]
The point on the circle is the point of intersection of the tangent line and the perpendicular line.
To find the point of intersection, substitute the equation for the perpendicular line into the equation for the tangent line:
[tex]\implies \dfrac{3}{2}x-\dfrac{23}{2}=-\dfrac{2}{3}x+\dfrac{4}{3}[/tex]
[tex]\implies \dfrac{13}{6}x=\dfrac{77}{6}[/tex]
[tex]\implies x=\dfrac{77}{13}[/tex]
Substitute the found value of x into one of the linear equations and solve for y:
[tex]\implies y=-\dfrac{2}{3}\left( \dfrac{77}{13} \right)+\dfrac{4}{3}[/tex]
[tex]\implies y=-\dfrac{34}{13}[/tex]
Therefore, the point of intersection and hence the point on the circle is:
[tex]\left( \dfrac{77}{13}, -\dfrac{34}{13}\right)[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
To find r², substitute the given center of the circle (3, -7) and the found point into the equation of the circle:
[tex]\implies \left(\dfrac{77}{13} -3 \right)^2+ \left(-\dfrac{34}{13}+7\right)^2=r^2[/tex]
[tex]\implies \left(\dfrac{38}{13} \right)^2+ \left(\dfrac{57}{13}\right)^2=r^2[/tex]
[tex]\implies \dfrac{1444}{169} + \dfrac{3249}{169}=r^2[/tex]
[tex]\implies \dfrac{4693}{169}=r^2[/tex]
[tex]\implies \dfrac{361}{13}=r^2[/tex]
Therefore, the equation of the circle whose center is P(3, -7) and tangent to 2x+3y-4=0 is:
[tex]\boxed{(x-3)^2+(y+7)^2=\dfrac{361}{13}}[/tex]
if the pile contains only 25 quarters and only 40 dimes but at least 50 of each other kind of coin, how many collections of 50 coins can be chosen? collections
if the pile contains only 25 quarters and only 40 dimes but at least 50 of each other kind of coin, then 20,281 collections of 50 coins can be chosen.
what are quarters?
A quarter fraction is the division of one whole into four equal parts, where one represents the referred-to part and four represents the number of parts into which the whole has been divided. It is written as 14 in numerical form.Given that:
25 quarters and only 40 dimes
No. of. Ways with at least 26 quarters and 41 dimes.
26 + 41 = 67 coins, but we have only 50 coins.
There are 0 ways to select at least 26 quarters and 41 dimes.
[tex]A_{1}[/tex] = at least 26 quarters
[tex]A_{2}[/tex] = at least 41 dimes
Using inclusion / exclusion rule for the two sets:
N([tex]A_{1} U A_{2}[/tex]) = N ( [tex]A_{1}[/tex]) + N ( [tex]A_{2}[/tex])- N ([tex]A_{1}[/tex] ∩ [tex]A_{2[/tex])
= 2925 + 220 - 0
= 3145
Therefore, no . of . ways with at most 25 quarters and at most 40 dimes are
= 23426 - 3145
= 20,281 ways
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