We will prove that if we remove the root of a k-th order binomial tree, it results in k binomial trees of smaller orders.
Base case: If k = 1, the binomial tree consists of a single node. Removing the root node leaves an empty tree, which can be considered as a collection of 0 binomial trees of smaller orders.
Induction hypothesis: Assume that the statement is true for a k-th order binomial tree.
Induction step: We need to prove that the statement is true for a (k+1)-th order binomial tree, which is formed by joining two k-th order binomial trees.
Remove the root node of the (k+1)-th order binomial tree. This results in two trees, each of which is a k-th order binomial tree.
By the induction hypothesis, removing the root node of each of the two k-th order binomial trees results in k binomial trees of smaller orders.
Thus, removing the root node of the (k+1)-th order binomial tree results in a total of 2k binomial trees of smaller orders, which completes the proof.
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*HELP ASAP*
Mr. Mackinson has to choose 2 students to lead the class field trip. If he draws from a list of 6 boys and 6 girls, what is the probabilty of 2 girls getting drawn?
Answer:
The probability of choosing 2 girls from a list of 6 girls and 6 boys can be calculated using combinations.
The number of combinations of choosing 2 girls out of 6 girls is given by the formula: C(6,2) = 6! / (6-2)!2! = 15.
So, the probability of choosing 2 girls is 15 / (C(12,2) = 66) = 15/66 = 5/22.
Therefore, the probability of Mr. Mackinson choosing 2 girls to lead the class field trip is 5/22 or approximately 0.227.
Please help! Thank you so much!
The non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.
The simplified expression that represents the total number of members after the third year is 4.5(53 + x).
How to explain the expressionLet's call the number of members from the other club "x".
After the first year, the total number of members is 20 + x, and it doubles to 2(20 + x) = 40 + 2x.
After the second year, half of the members from the other club leave, so there are 0.5x members left from the other club. And another 40 members join, so the total number of members is (40 + 2x - 0.5x) + 40 = 80 + 1.5x.
After the third year, the total number of members triples, so we have 3(80 + 1.5x) = 240 + 4.5x.
Therefore, the non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.
To simplify, we can factor out 4.5 from the expression to get 4.5(53 + x). So the simplified expression that represents the total number of members after the third year is 4.5(53 + x).
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If s² = 80 and n = 6, what is the sum of squares?
Answer:
s^2 + n^2 = 116
Step-by-step explanation:
s^2 + n^2 = ?
s^2 = 80
n = 6
n^2 = 36
s^2 +n^2 = 80 + 36
s^2 +n^2 = 116
An online retailer has found that the probability that a visitor to the website will make a purchase is 7/8. Of these purchases, 4 out of 5 are for more than one item. Based on the information, what is the probability that the next visitor to the website purchases more than one item?
Answer: 7/10
Step-by-step explanation:
multiply 4/5 by 7/8=28/40 or 7/10
help pls
Find the value of the following expression and round to the nearest integer:
Answer:
53
Σ900(1.04)n+1
n=1
Submit Answer
The expression is a summation formula, representing the sum of a series of values. To find the value of the expression, we need to evaluate the sum for each term.
The general formula for each term is:
900(1.04)^n
where n is the term number and 1.04 is the common ratio.
For the first term (n = 1), the formula is:
900(1.04)^1 = 900 * 1.04 = 937.6
For the second term (n = 2), the formula is:
900(1.04)^2 = 900 * 1.04^2 = 976.9792
And so on, for each term. We can continue evaluating the formula for each term until we reach the desired number of terms.
Let's evaluate the expression for n = 10 terms.
The sum of the first 10 terms is:
937.6 + 976.9792 + 1018.057312 + ... + 1412.14803883
The value of the expression is approximately 1412.15.
Rounding to the nearest integer, the answer is 1412.
On a blueprint of a house, the kitchen is 5 inches long. If the actual kitchen is 20 feet long, find the scale of the blueprint.
The scale of the blueprint is 1 in : 4 ft.
What is scale?A map scale is the relationship between a distance on a map and the corresponding distance on the earth.
Given that, on a blueprint of a house, the kitchen is 5 inches long, the actual kitchen is 20 feet long, we are asked to find the scale of the blueprint.
Since, the kitchen in the map is 5 in long whereas n earth it is 20 ft long.
Therefore, the ratio =
5 in / 20 ft = 1 in / 4 ft
Hence, the scale of the blueprint is 1 in : 4 ft.
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What is the value of b?
Answer:
b-value is the middle number hope that helps
Step-by-step explanation:
The b-value is the middle number, the number next to the x. The other letters, a and c, are also numbers like b. Each of these can be any number. In combination, they tell you what the quadratic function will look like when graphed
Use the associative property to simplify the expression.
43 +30+70
OA. 43+30+70 = 73 +70 = 143
OB. 43+ (30+70) = 43+ 100 = 143
OC. 43+ 10(3 + 7) = 43 + 10(10) = 143
OD. 43 +70+ 30 = 113 +30 = 143
SUBMIT
Answer:jjj
Step-by-step explanation:because
pls help asap geometry
Answer:
the answer is x=23.84 which is A
Step-by-step explanation:
using SOH CAH TOA
tan0 =opp/adj
where 0=40,opposite =20,adjacent =x
tan 40=20/x
0.8391=20/x
0.8391x=2
divide both sides by 0.8391
x=23.84
A bakery sold 73 bagels in the first hour of business if the bakery had 246 bagels to start with how many bagels were left after the first hour?
Step-by-step explanation:
173 bagels left after the first hour.
Please help me by determining the value of the missing angle using the inverse trig function.
On solving the provided question, we cans ay that in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here, in this triangle by Pythagorean theorem
[tex]A^2 = B^2 + C^2[/tex]
AC = [tex]\sqrt{14^2 - 9^2}[/tex]
AC = [tex]\sqrt{196 - 81}[/tex]
AC = [tex]\sqrt{115}[/tex]
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Suppose the graph of rectangle ABCD shows the plans for a safety fence that Kenny is setting up around a construction area. Each unit on the graph represents 25 feet. After studying the plans, Kenny decides to build a fence that encloses a larger area. If Kenny dilates rectangle ABCD by a scale factor of 2.5, and fencing costs $5.25 per foot, how much will he spend on fencing?
The cost of spending the fencing around will be $1312.5.
What is a perimeter?The perimeter of any two-dimensional figure is defined as the sum of all the sides of the figure. For a rectangle, the perimeter will be the sum of all the sides of the rectangle.
Given that the graph of rectangle ABCD depicts Kenny's intentions for erecting a safety fence to surround a construction site. The units on the graph each correspond to 25 ft.
Kenny decides to construct a fence that encloses a wider region after carefully reviewing the drawings. Given that fencing costs $5.25 per foot and Kenny enlarges rectangle ABCD by a scale factor of 2.5
Perimeter = 4 x side x scale factor
Perimeter = 4 x 25 x 2.5
Perimeter = 250 feet.
The cost of fencing will be,
Cost = 250 x $5.25
Cost = $1312.5
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In a group of 70 college students, 24 own only a laptop, 20 own only a desktop, 16 own both a
laptop and a desktop, and 10 own neither a laptop nor a desktop. What is the probability of
randomly selecting a student who owns at least one laptop or one desktop?
Answer:
85.71% chance of randomly selecting a student who owns at least one laptop or one desktop
Step-by-step explanation:
Out of a total of 70 students, only 10 own neither a laptop nor a desktop. This means that the probability of selecting a student with at least one of the two is [tex]\frac{60}{70}[/tex] or [tex]\frac{6}{7}[/tex].
If we convert this fraction into a percentage and round to the nearest hundredth, it equals:
85.71%
on the z table with a 90% confidence interval, what is 1.645 called? group of answer choices critical value confidence interval margin of error point estimate
On the z-table with a 90% confidence interval, the value 1.645 is called the critical value. The critical value is used to determine the boundary values for the confidence interval. Correct option is A.
In a confidence interval, we use sample data to estimate the true population parameter with a certain degree of certainty or confidence. The critical value is determined based on the desired confidence level and the degrees of freedom (sample size - 1) of the distribution.
For example, if we want a 90% confidence interval, we use the z-table to find the critical value that corresponds to a probability of 0.05 in the tail of the distribution. The critical value represents the number of standard errors that correspond to the probability in the tail of the distribution.
Once we have determined the critical value, we can use it to find the margin of error for the confidence interval, which represents the range of values within which the true population parameter is likely to lie. The margin of error is calculated by multiplying the critical value by the standard error of the sample statistic.
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Complete question is:
On the z table with a 90% confidence interval, what is 1.645 called? group of answer choices
a. critical value
b. confidence interval
c. margin of error point
d. estimate
Find the nth term of this quadratic sequence
2, 8, 18, 32, 50, ...
The nth term of the given quadratic sequence is expressed as; aₙ = 2n²
How to find the nth term of a quadratic sequence?To find the nth term, we have to find the relation between the given terms.
Here we see that;
1st term = 2 = 2 × 1 × 1 = 2 × 1²
2nd term = 8 = 2 × 2 × 2 = 2 × 2²
3rd term = 18 = 2 × 3 × 3 = 2 × 3²
4th term = 32 = 2 × 4 × 4 = 2 × 4²
5th term = 2 × 5² = 2 × 50 = 100
Thus, we clearly see a pattern that can represent the nth term as;
aₙ = 2 × n²
aₙ = 2n²
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A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 18 centimeters. The height of the figure is 12 centimeters. The portion from the vertex to the perpendicular height is 4 centimeters. The portion from a point to a vertical line created by two vertices is 3 centimeters.
Which of the following represents the total area of the figure?
222cm
240cm
258cm
294cm
Answer:
258cm
it is the vertex's hieght as well as the length of the sides to multiply together and also divide since there is 5 sides
need help explain and answer
The length of points IJ given the total length of HJ and length HI is 8
What is the length of points IJ?The line HJ is measured as 20
If HI = 12
Then, subtract to find IJ
IJ = HJ - HI
= 20 - 12
IJ = 8
Therefore, length of points IJ is 8
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Identify the point from the equation: y + 3 = 2(x - 4)
Answer:
y-2x=11
Step-by-step explanation:
y+3=2(x-4)
y+3=2x-8
y-2x=-3-8
y-2x=-11
PLEASE HELP ME ASAP
The equation of the graph is y = (5x + 10)/(x²-1).
The correct option is c.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
The graph of the equation is given in the image.
From the graph:
When x = 0, then y = -10.
And when y = 0, then x = -2.
y = (5x + 10)/(x²-1)
Substituting the values,
we get,
when x = 0, then y = -10.
And when y = 0, then x = -2.
From the given choices:
The equation,
y = (5x + 10)/(x²-1) satisfies the points.
Hence, the equation is y = (5x + 10)/(x²-1).
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Solve for x: xm=-3x+y
Answer:
x = y/(m + 3)
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ xm = -3x + y
Then the value of x will be,
→ xm = -3x + y
→ xm + 3x = y
→ x(m) + x(3) = y
→ x(m + 3) = y
→ x = y/(m + 3)
Hence, value of x is y/(m + 3).
1. If LM = 6, what is the perimeter of APKQ?
X-6
P
3
X
M
5
Answer:
24.67
Step-by-step explanation:
6 x 3 = 18
18 plus 6 = 24
X-M=0.60
P-3=7
24.67
1. Completeby Filling >, < 0r= 9 10 19 20
The expression when completed is 0.9 [<] 0.95
How to complete the blankFrom the question, we have the following parameters that can be used in our computation:
9 10 19 20
Rewrite the expression properly
So, we have the following representation
9/10 [ ] 19/20
Next, we evaluate the expressions
This gives
0.9 [ ] 0.95
0.9 is less than 0.95
So, we have
0.9 [<] 0.95
The above represents the complete statement
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Dilate a square with vertices $\left(0,\ 0\right)$ , $\left(0,\ 4\right)$ , $\left(4,\ 4\right)$ , and $\left(4,\ 0\right)$ using the scale factor $k=0.5$ . What is the value of the ratio (new to original) of the perimeters? the areas?
just in case anyone was wondering
The value of the ratio (new to original) of the perimeters as required in the task content is; 0.5.
The value of the ratio (new to original) of the perimeters as required in the task content is; 0.25.
What is the constant of proportionality of the perimeter and area of the square?Recall, a dilation of a point, (x, y) using a scale factor of k is; (kx, ky).
Also; for shapes A and B;
Perimeter (A) / Perimeter (B) = k.
Also, Area (A) / Area (B) = k².
On this note, since the dilation factor of the pre-image is 0.5, it follows that the ratio of the perimeters of the new to original is; 0.5.
Also, the ratio of the area of the new to original is; 0.5² = 0.25.
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what is the approximate volume of the sphere ? use 3.14 to approximate pi and round to the hundredth is necessary. (3 in)
The required, approximate volume of the sphere is 113.04 cubic inches.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.
If the radius of the sphere is 3 inches, we can substitute this value into the formula and use 3.14 to approximate π,
V = (4/3) x 3.14 x 3³
V = (4/3) x 3.14 x 27
V = 113.04 cubic inches
Therefore, the approximate volume of the sphere is 113.04 cubic inches.
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The measures of the exterior angles of a heptagon are x, 4x, 5x, 6x, 7,x 8x, and 9x. Find the measure of the smallest exterior angle.
Answer:
9°
Step-by-step explanation:
x + 4x + 5x + 6x + 7x + 8x + 9x = 360
40x = 360
x = 9
The smallest angle measures x, and x = 9, so its measure is 9°.
Answer: 9°
please help asap thankyouu
Answer:
2.57 square meters
Step-by-step explanation:
r = Radius of circle
Area of shaded region = Area of semi-circle:
[tex]= \frac{1}{2}(\pi r^{2})[/tex]
= [tex]\frac{\pi}{2} r^{2}[/tex]
= [tex]\frac{\pi }{2} (1.28m)^{2}[/tex]
= 2.57 [tex]m^{2}[/tex] (Rounded to 2 decimal places)
Brandon has a cup of quarters and dimes with a total value of $ 9. 6. The number of quarters is 348 less than 8 times the number of dimes. How many quarters and how many dimes does Brandon have?
To represent Brandon's total collection of quarters and dimes, let's use variables.
Let:
q be the number of quarters
d be the number of dimes
The following equations can be used to represent the given information:
The quarters and dimes are worth a total of $9.6:
0.25q + 0.10d = 9.6
The quantity of quarters is 348 less than 8 times that of dimes.
q = 8d - 348
To get a solution for one of the variables, we can use substitution. We may solve for d by substituting the expression for q from equation 2 into equation 1:
0.25q + 0.10d = 9.6
0.25(8d - 348) + 0.10d = 9.6 (substitute q = 8d - 348)
2d - 87 + 0.10d = 9.6
2.10d = 96.6
d = 46
Now that we know d = 46, we can use equation 2 to solve for q:
q = 8d - 348
q = 8(46) - 348
q = 16
Therefore, There are 46 dimes and 16 quarters in Brandon.
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D=S×T
150×2 1/2
please help
The cost of fuel per litre is calculated using the following formula. (1 + 100) X + X 160 C = cost of oil per barrel. F = rate of fuel duty tax in %. P = percentage profit the petrol station wants to make. Fuel duty is 50%, and oil costs £128 per barrel. A petrol station wants to make 100% profit. Work out the cost of fuel per litre at this petrol station.
If a petrol station wants to make 100% profit. the cost of fuel per litre at this petrol station is 1.4 pence.
How to find the cost?Given, the formula to calculate the cost of fuel per litre:
(1 + 100) X + X 160 C = cost of oil per barrel.
Where :
X = cost of oil per litre
C= rate of fuel duty tax in %.
We know that fuel duty is 50% and oil costs £128 per barrel, so we can substitute these values into the equation:
(1 + 100) X + X 160 * 0.5 = 128
Expanding the equation:
100 X + 80 X = 128
180 X = 128
Dividing both sides by 180:
X = 128/180 = 7/10 = 0.7
So, the cost of oil per litre is 0.7 pence.
The petrol station wants to make 100% profit, so we add the profit to the cost of oil per litre:
0.7 + 0.7 * (100/100) = 1.4 pence
Therefore, the cost of fuel per litre at this petrol station is 1.4 pence.
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f the following, which is the smallest sample size that will result in a margin of error of no more than 5 percentage points? responses 73 73 97 97 271 271 385 385 1,537 1,537 skip to navigation
The smallest sample size that will result in a margin of error of no more than 5% for a 95% confidence interval is given as follows:
385.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is modeled as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
We have no estimate, hence we consider that:
[tex]\pi = 0.5[/tex]
The minimum sample size is obtained as n when M = 0.05, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96 \times 0.5[/tex]
[tex]\sqrt{n} = 1.96 \times 10[/tex] (0.5/0.05 = 10).
[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]
n = 384.16
Hence rounded to 385, as a sample size of 384 would have a margin of error slightly above 0.05.
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