match the following. 1. an angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon center of a regular polygon 2. the common center of its inscribed and circumscribed circles apothem of a regular polygon 3. the distance from the center of the polygon to a vertex radius of a regular polygon 4. the perpendicular distance from the center of the polygon to a side central angle of a regular polygon
Answers
Match the following with the given options:
1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygon2. The common center of its inscribed and circumscribed circles - Center of a regular polygon3. The distance from the center of the polygon to a vertex - Radius of a regular polygon4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonA polygon is a two-dimensional object that has three or more straight sides and angles. A regular polygon is a polygon with equal sides and equal angles.
A regular polygon is a shape that has all its sides the same length and all of its angles the same degree. Below are the matched answers for the given options.1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygonThe central angle of a regular polygon is defined as the angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon.
The angle measures (360 / n) degrees, where n is the number of sides of the polygon.2. The common center of its inscribed and circumscribed circles - Center of a regular polygonThe center of a regular polygon is the point at which its axes of symmetry intersect. The center is also the common center of the circumscribed and inscribed circles.3. The distance from the center of the polygon to a vertex - Radius of a regular polygonThe radius of a regular polygon is defined as the distance from the center of the polygon to any vertex. It is also the distance from the center of the polygon to the midpoint of a side
.4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonThe apothem of a regular polygon is defined as the perpendicular distance from the center of the polygon to a side. It is also the radius of the inscribed circle.
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Related Questions
Multiply: (x + 3)(x – 4) What is the middle term in the simplified product?
Answers
Answer:
-x
Step-by-step explanation:
(x + 3)(x – 4) = x^2 - 4x + 3x - 12 = x^2 - x - 12
The middle term is -x.
Answer:
-x
Step-by-step explanation:
(x+3)(x-4)
x(x) +x(-4) +3(x) +3(-4)
x^2 + -4x +3x -12
x^2 -x-12
Hope fully this is what a middle term means :)
Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height, but each side of its base is 6 units long.
Answers
Answer:
The volume of pyramid B is 81 cubic units
Step-by-step explanation:
Given
Pyramid A
\(s = 4\) -- base sides
\(V = 36\) -- Volume
Pyramid B
\(s = 6\) --- base sides
Required
Determine the volume of pyramid B [Missing from the question]
From the question, we understand that both pyramids are equilateral triangular pyramids.
The volume is calculated as:
\(V = \frac{1}{3} * B * h\)
Where B represents the area of the base equilateral triangle, and it is calculated as:
\(B = \frac{1}{2} * s^2 * sin(60)\)
Where s represents the side lengths
First, we calculate the height of pyramid A
For Pyramid A, the base area is:
\(B = \frac{1}{2} * s^2 * sin(60)\)
\(B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}\)
\(B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}\)
\(B = 4\sqrt 3\)
The height is calculated from:
\(V = \frac{1}{3} * B * h\)
This gives:
\(36 = \frac{1}{3} * 4\sqrt 3 * h\)
Make h the subject
\(h = \frac{3 * 36}{4\sqrt 3}\)
\(h = \frac{3 * 9}{\sqrt 3}\)
\(h = \frac{27}{\sqrt 3}\)
To calculate the volume of pyramid B, we make use of:
\(V = \frac{1}{3} * B * h\)
Since the heights of both pyramids are the same, we can make use of:
\(h = \frac{27}{\sqrt 3}\)
The base area B, is then calculated as:
\(B = \frac{1}{2} * s^2 * sin(60)\)
Where
\(s = 6\)
So:
\(B = \frac{1}{2} * 6^2 * sin(60)\)
\(B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}\)
\(B = 9\sqrt 3\)
So:
\(V = \frac{1}{3} * B * h\)
Where
\(B = 9\sqrt 3\) and \(h = \frac{27}{\sqrt 3}\)
\(V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}\)
\(V = \frac{1}{3} * 9 * 27\)
\(V = 81\)
Answer:
81
Step-by-step explanation:
the region r in the first quadrant is enclosed by the lines x=0 and y=5 and the graph of y=x^2+1
Answers
Therefore, the area of the region r is 8 square units.
To start, let's graph the two lines and the equation y=x^2+1 in the first quadrant:
As we can see from the graph, the region r is a triangle with a curved bottom. To find the area of this region, we can use integration.
First, we need to find the x-coordinates of the points where the line y=5 intersects with the curve y=x^2+1. To do this, we set the two equations equal to each other:
5 = x^2 + 1
Subtracting 1 from both sides gives us:
4 = x^2
Taking the square root of both sides, we get:
x = ±2
Since we are only interested in the positive x-value (since we are in the first quadrant), we have:
x = 2
Next, we need to set up our integral to find the area of the region r. Since the region is bounded by the lines x=0 and y=5, and the curve y = x^2+1, we can integrate with respect to y, using the limits of integration y=1 and y=5 (since the curve starts at y=1 when x=0).
The area of the region r can be found using the following integral:
A = ∫[1,5] [√y - 1] dy
Integrating, we get:
A = [2/3 y^(3/2) - y] [1,5]
A = [2/3 (5)^(3/2) - 5] - [2/3 (1)^(3/2) - 1]
A = 25/3 - 1/3
A = 8
Therefore, the area of the region r is 8 square units.
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(8 – 3r) 6
Need help simplify this expression
Answers
A twelve pack of Orange Crush is priced at $3.00. What is the unit rate or the price per soda?
Answers
Divide price by quantity:
3.00 / 12 = $0.25 per can.
Maximize Z = 23x1 + 73x2 subject to x1 ≤ 40 x2 ≤ 25 x1 + 4x2 ≤ 120. What is the optimal value of Z?
Answers
The optimal value of Z is 3000.
Find out the optimal value of Z?To find the optimal value of Z, we need to solve the given linear programming problem. The problem can be formulated as follows:
Maximize Z = 23x1 + 73x2
subject to:
x1 ≤ 40
x2 ≤ 25
x1 + 4x2 ≤ 120
To solve this problem, we can use the graphical method. Let's plot the feasible region and find the corner points to evaluate the objective function.
First, let's graph the inequalities on a coordinate plane:
x1 ≤ 40:
Draw a vertical line at x1 = 40.
x2 ≤ 25:
Draw a horizontal line at x2 = 25.
x1 + 4x2 ≤ 120:
Rearranging the equation, we have x2 ≤ (120 - x1)/4.
Plot the line with x2 = (120 - x1)/4.
The feasible region is the shaded area where all the inequalities are satisfied.
yaml
Copy code
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| x2 ≤ (120 - x1)/4
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| x1 ≤ 40
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| x2 ≤ 25
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Next, we need to find the corner points of the feasible region, as these are the only points where the objective function can attain its maximum value.
From the graph, we can identify the corner points as (0, 0), (0, 25), (40, 0), and the intersection of x1 = 40 and x2 = (120 - x1)/4, which is (40, 20).
We can now evaluate the objective function Z = 23x1 + 73x2 at each of these corner points:
(0, 0): Z = 23(0) + 73(0) = 0
(0, 25): Z = 23(0) + 73(25) = 1825
(40, 0): Z = 23(40) + 73(0) = 920
(40, 20): Z = 23(40) + 73(20) = 3000
Comparing the values, we find that the maximum value of Z is 3000, which occurs at the point (40, 20).
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The ____ statement is useful when you need to test a single variable against a series of exact integer, character, or string values.
Answers
The "switch" statement is useful when you need to test a single variable against a series of exact integer, character, or string values.
The switch statement is a control structure found in many programming languages, including C++, Java, and JavaScript. It allows you to evaluate a variable or expression and compare it against multiple cases.
Each case represents a specific value that the variable or expression is tested against. When a match is found, the corresponding block of code associated with that case is executed.
The switch statement is particularly useful when you have a variable that can take on different values and you want to perform different actions based on those values. Instead of writing multiple if-else statements, the switch statement provides a more concise and efficient way to handle such scenarios.
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what is the electron domain charge cloud geometry of brf5
Answers
The electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.
To determine the electron domain charge cloud geometry of \(BrF_5\), we need to examine the number of electron domains around the central atom (Br).
\(BrF_5\) consists of one central bromine atom (Br) surrounded by five fluorine atoms (F). Each bond and lone pair of electrons represents an electron domain.
In \(BrF_5\), there are five bonding pairs (Br-F) and no lone pairs around the central bromine atom. Therefore, the total number of electron domains is five.
Based on this information, the electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.
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James has 1/2 pound of candy that he is sharing with 6 friends how much will each friend get
Answers
The amount of candy that each of his 6 friends will get is 1/14 of a pound.
It is given in the question that James has 6 friends with those he has to share 1/2 pound of the candy.
We have to find the amount of candy each of his 6 friends gets.
We know that,
Total number of people among those the candy will be shared = James + 6 friends = 7 people
Total amount of candy with James = 1/2 pound
We know that,
Amount of candy each person gets = Total amount of candy/No. of people.
Hence,
Total amount of candy each person gets = (1/2) /7 =(1/2)*(1/7) = 1/14 of a pound.
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Solve the math problem
Answers
Answer:
a. independent is the value of the car when she bought the dependent variable is the how much the value goes down each year
b. 3.233.33
c. (25,000 - 15,300) ÷ 3 = x
Step-by-step explanation:
A) the value goes down each year because of the "aging of the car"
B) 25,000 - 15,300 = 9,700
The value went down 9,700 in 3 years
9,700 / 3 = 3233.33333
round it to 3,233.33
The value went down abt 3,233.33 a year
C) (25,000 - 15,300) ÷ 3 = x
25,000 = is the value of the car when she bought it
15,300 = is the value of the car when she is selling it
3 = the years
hope this helps <33
Answer:
bro this will take some time
Step-by-step explanation:
What is NOT a transformation of y=-8|x-4|-16 from the parent function f(x)=|x|.
Answers
The transformation, y = -8 | x -4 | -16 from the parent function f(x) = |x| are the following:
the constant -16, means that it is down by 16 units.
the negative in the coefficient 8 means it is reflected over x-axis.
the coefficient 8 also means that is steeper by a factor of 8
and the binomial |x - 4| means that it is shifted right by 4 units.
Therefore, what is NOT a transformation among the choices is Left 4.
( cosec20 + cot40 = cote - cosects
Answers
Hi there!
~
cosec 20 -cot 40= 1/sin 20 - cos 40/sin 40
= (sin 40 -cos 40 sin20)/(sin 40 sin 20)
= 1/sin 40 ( 2 cos 20 - cos 40)
=1/sin20 ( 2 cos(60-40)-cos 40)
=1/sin40( 2 cos 60 cos 40 - 2 sin 60 -sin 40-cos 40)
Put the value of cos 60
= 1/sin 40 ( 2 sin 60 sin 40)
=root(3)
Hope this helped you!
Let X be the number of students who show up for a professor's office hour on a particular day. Suppose that the pmf of X is p(0) = .20, p(1) = .25, p(2) = .30, p(3) = .15, and p(4) = .10. a. Draw the corresponding probability histogram. b. What is the probability that at least two students show up? More than two students show up? c. What is the probability that between one and three students, inclusive, show up?
d. What is the probability that the professor shows up?
Answers
a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.
b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25
c) The probability that between one and three students show up = 0.7
d) The probability that the professor shows up = 0.20
First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.
x p(x)
0 0.20
1 0.25
2 0.30
3 0.15
4 0.10
The probability histogram of this data is shown below.
The probability that at least two students show up would be,
P(x ≥ 2) = p(2) + p(3) + p(4)
P(x ≥ 2) = 0.30 + 0.15 + 0.10
P(x ≥ 2) = 0.55
Now the probbability that more than two students show up:
P(x > 2) = p(3) + p(4)
P(x > 2) = 0.15 + 0.10
P(x > 2) = 0.25
The probability that between one and three students show up would be:
P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)
P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15
P(1 ≤ x ≤ 3) = 0.7
And the probability that the professor shows up would be: p = 0.20
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use Gaussian elimination to determine the solution set to the given system.
9.
2x1−x2−4x3=5
3x1+2x2−5x3=8,
5x1+6x2−6x3=20,
x1+x2−3x3=−3
11.
x1+2x2−x3+x4=1
2x1−3x2+x3−x4=2,
x1−5x2+2x3−2x4=1,
4x1+x2−x3+x4=3
Answers
9. The system of equations has a solution set by using Gaussian elimination.\(x_1 = 10, x_2 = -1, x_3 = 4\). 11. The system of equations has no solution because: 0 ≠ -1
To determine the solution set of the given system using Gaussian elimination, we need to perform row operations to transform the augmented matrix into row echelon form or reduced row echelon form.
Let's consider each system separately:
\(2x_1 - x_2 - 4x_3 = 5\\3x_1 + 2x_2 - 5x_3 = 8\\5x_1 + 6x_2 - 6x_3 = 20\\x_1 + x_2 - 3x_3 = -3\)
Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)\begin{bmatrix}
2 &-1 & -4& 0 & |&5 \\
3 &2 & -5& 0 & |&8 \\
5&6 &-6 & 0 & |& 20\\
1& 1 &-3 & 0 & |&-3\\
\end{bmatrix}
R1 / 2 → R1 (divide the 1 row by 2)
\(\begin{bmatrix}1 &-0.5 & -2& 0 & |&2.5 \\3 &2 & -5& 0 & |&8 \\ 5&6 &-6 & 0 & |& 20\\ 1& 1 &-3 & 0 & |&-3\\\end{bmatrix}\)
R2 - 3 R1 → R2 (multiply 1 row by 3 and subtract it from 2 row); R3 - 5 R1 → R3 (multiply 1 row by 5 and subtract it from 3 row); R4 - 1 R1 → R4 (multiply 1 row by 1 and subtract it from 4 row)
\(\begin{bmatrix}1 &-0.5 & -2& 0 & |&2.5 \\0 &3.5 & 1& 0 & |&0.5\\ 0&8.5 &4 & 0 & |& 7.5\\ 0& 1.5 &-1 & 0 & |&-5.5\\\end{bmatrix}\)
R2 / 3.5 → R2 (divide the 2 row by 3.5)
\(\begin{bmatrix}1 &-0.5 & -2& 0 & |&2.5 \\0 &1 & 1& 2/7 & |&1/7\\ 0&8.5 &4 & 0 & |& 7.5\\ 0& 1.5 &-1 & 0 & |&-5.5\\\end{bmatrix}\)
R1 + 0.5 R2 → R1 (multiply 2 row by 0.5 and add it to 1 row); R3 - 8.5 R2 → R3 (multiply 2 row by 8.5 and subtract it from 3 row); R4 - 1.5 R2 → R4 (multiply 2 row by 1.5 and subtract it from 4 row)
\(\begin{bmatrix}1 &0 & -13/7& 0 & |&18/7 \\0 &0& 1& 2/7 & |&1/7\\ 0&0 &11/7 & 0 &|& 44/7\\ 0& 0 &-10/7 & 0 & |&-40/7\\\end{bmatrix}\)
R3/ 11 / 7 → R3 (divide the 3 row by 11/7 )
\(\begin{bmatrix}1 &0 & -13/7& 0 & |&18/7 \\0 &1& 2/7 &0 &|&1/7\\ 0&0 &1& 0 & |& 4\\ 0& 0 &-10/7 & 0 & |&-40/7\\\end{bmatrix}\)
R1+13/7R3→R1(Multiply 3 row by 13/7 and add it to 1 row) R2-2/7R3--> R2(Multiply 3 row and subtract it from 2 row. R4 +10/7R3→R4(multiply 3 row by10/7 and add it to 4 row.
\(\begin{bmatrix}1 &0 & 0& 0 & |&10 \\0 &1& 0 &0 &|&-1\\ 0&0 &1& 0 & |& 4\\ 0& 0 &0 & 0 & |&0\\\end{bmatrix}\)
Therefore, the system of equations has a solution set by using Gaussian elimination.
x1 = 10
x2 = -1
x3 = 4
11. x1 + 2x2 - x3 + x4 = 1
2x1 - 3x2 + x3 - x4 = 2
x1 - 5x2 + 2x3 - 2x4 = 1
4x1 + x2 - x3 + x4 = 3
\(\begin{bmatrix}1 &2 & -1& 1 & 1|&1 \\2 &-3& 1 &-1 &|&2\\ 1&-5 &2& 2 & |& 1\\ 4& 1 &-1 & 1& |&3\\\end{bmatrix}\)
R2 - 2 R1 → R2 (multiply 1 row by 2 and subtract it from 2 row); R3 - 1 R1 → R3 (multiply 1 row by 1 and subtract it from 3 row); R4 - 4 R1 → R4 (multiply 1 row by 4 and subtract it from 4 row)
\(\begin{bmatrix}1 &2 & -1& 1 & 1|&1 \\0 &-7& 3 &-3 &|&0\\ 0&-7 &3& 1 & |& 0\\ 0& -7 &3 & -3& |&-1\\\end{bmatrix}\)
R2 / -7 → R2 (divide the 2 row by -7)
\(\begin{bmatrix}1 &2 & -1& 1 & |&1 \\0 &1& -3/7 &3/7 &|&0\\ 0&-7 &3& 1 & |& 0\\ 0& -7 &3 & -3& |&-1\\\end{bmatrix}\)
R1 - 2 R2 → R1 (multiply 2 row by 2 and subtract it from 1 row); R3 + 7 R2 → R3 (multiply 2 row by 7 and add it to 3 row); R4 + 7 R2 → R4 (multiply 2 row by 7 and add it to 4 row)
\(\begin{bmatrix}1 &0 & -1/7& 1/7 & |&1 \\0 &1& -3/7 &3/7 &|&0\\ 0&0 &0& 4 & |& 0\\ 0& 0 &0 & 0& |&-1\\\end{bmatrix}\)
R3 / 4 → R3 (divide the 3 row by 4)
\(\begin{bmatrix}1 &0 & -1/7& 1/7 & |&1 \\0 &1& -3/7 &3/7 &|&0\\ 0&0 &0& 1 & |& 0\\ 0& 0 &0 & 0& |&-1\\\end{bmatrix}\)
The system of equations has no solution because: 0 ≠ -1
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In lines 63-64, "psychological reality" describes which
quality?
(A) The versatility of a performer
(B) The physical gestures of a character
(C) The essence of an identity
(D) The accuracy of an audience’s expectations
(E) The logical consistency of certain actions
Answers
In lines 63-64, "psychological reality" describes the essence of an identity (option C).
What is a comprehension passage?In a comprehension passage, some questions are given that follow the passage. The questions are to be answered by using the data given in the passage, even if it differs from real-life facts.
Now, given:
"I needed evidence of the limitations of basing a character on a series of metaphors from an actors real life. I wanted to develop an alternative to the self-based technique, a technique that would begin with the other and come to the self, a technique that would empower the other to find the actor rather than the other way around."With the help of these lines, the author wants to state that individual must realize his or her psychology truth.Hence, in the given lines, "psychological reality" describes the essence of an identity (option C).
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Select the correct answer.
Which equation represents the line that is perpendicular to y = 1/5 and passes through (-4,-3)?
A.X=-4
B.X=-3
C. y=-5
D. y=-3
Answers
Step-by-step explanation:
The answer is b for sure.
11. Find the value of x. x=______
Answers
Answer: x = 3.5
Step-by-Step Solution:
Let us first label the figure.
Let the Triangle be ABC with a line DE || BC.
Now, in ∆ABC,
DE || BC (given)
=> AD/DB = AE/EC (by B.P.T)
Substituting the given values,
AD/DB = AE/EC
2/4 = x/7
1/2 = x/7
2x = 7
x = 7/2
=> x = 3.5
Therefore, x = 3.5
What is the value of x in the equation -2/3x9=-3
Answers
Answer:
your equation is false
Please help ASAP!
George believes the Art Club students at his school have an unfair advantage in being assigned to the art class they request. He asked 500 students at his school the following questions: "Are you in the Art Club?" and "Did you get the art class you requested?" The results are shown in the table below:
Art Club Not in Art Club Total
Received art class requested 100 265 365
Did not get art class requested 65 70 135
Total 165 335 500
Help George determine if all students at his school have an equal opportunity to get into the art class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
Answers
165 total students in art club. 100 of those got the requested class.
100/165 = 0.6061
335 total students not in art club. 265 got the requested class.
265/335 = 0.7910
the probability was higher for kids not in art club, so all students had an equal opportunity.
(6x2 + 7x + 1) + (x2 + 5x + 6)
Answers
Step-by-step explanation:
combine the like terms
(6x^2 + x^2) + (7x + 5x) + (1 + 6)
7x^2 + 12x + 7
Anyone help ASAP plss!!!
Answers
Question 1-
A scatter plot is shown on the coordinate plane.
Which two points would a line of fit go through to best fit the data?
A. (1,9) and (9,5)
B. (1,9) and (5,7)
C. (2,7) and (4,3)
D. (2,7) and (6,5)
Question 2-
Laila participated in a dance-a-thon charity event to raise money for the Animals are Loved Shelter. The graph shows the relationship between the number of hours Laila danced, x, and the money she raised, y.
Determine the slope and explain its meaning in terms of the real-world scenario.
A. The slope is 1/4, which means that the amount of the student raised increases by $0.75 each hour.
B. The slope is 4, which means that the amount the student raised increases by $4 each hour.
C. The slope is 12, which means that the student will finish raising money after 12 hours.
D. The slope is 20, which means that the student started with $20.
Answers
Question 1-
To determine which two points would a line of fit go through to best fit the data on the scatter plot, we need to visually analyze the pattern of the data points and choose two points that the line would pass through to represent the overall trend.
Without the actual scatter plot provided, I am unable to directly analyze it. However, based on the given answer choices:
A. (1,9) and (9,5)
B. (1,9) and (5,7)
C. (2,7) and (4,3)
D. (2,7) and (6,5)
Since I don't have the scatter plot, I cannot accurately determine which points would best fit the data. I would recommend carefully reviewing the scatter plot and selecting the two points that seem to represent the general trend or pattern of the data. The two points that form a line that closely follows the general direction of the data points would be the best choices.
Question 2-
To determine the slope of the relationship between the number of hours Laila danced, x, and the money she raised, y, we need to examine the graph and calculate the slope using the formula:
Slope = (change in y) / (change in x)
However, since the graph is not provided, it is not possible to directly calculate the slope. However, we can still evaluate the given answer choices based on their explanations:
A. The slope is 1/4, which means that the amount the student raised increases by $0.75 each hour.
B. The slope is 4, which means that the amount the student raised increases by $4 each hour.
C. The slope is 12, which means that the student will finish raising money after 12 hours.
D. The slope is 20, which means that the student started with $20.
From the explanations provided, it seems that option B would be the most reasonable choice. A slope of 4 would indicate that for each additional hour Laila danced, she raised $4. However, without the actual graph, it is challenging to confirm the accuracy of the answer choice or its real-world interpretation.
H(n)=-91\cdot\left(-\dfrac{1}{7}\right)^{\large{\,n-1}}h(n)=−91⋅(− 7 1 ) n−1 h, left parenthesis, n, right parenthesis, equals, minus, 91, dot, left parenthesis, minus, start fraction, 1, divided by, 7, end fraction, right parenthesis, start superscript, n, minus, 1, end superscript Complete the recursive formula of h(n)h(n)h, left parenthesis, n, right parenthesis.
Answers
Given:
\(h(n)=-91\cdot\left(-\dfrac{1}{7}\right)^{\large{\,n-1}}\)
To find:
The recursive formula.
Solution:
We have,
\(h(n)=-91\cdot\left(-\dfrac{1}{7}\right)^{\large{\,n-1}}\)
It is in the form of explicate formula of a GP, .i.e., \(a_n=ar^{n-1}\).
Here, \(a=-91\) and \(r=-\dfrac{1}{7}\).
The recursive formula of a GP is
\(a_n=a_{n-1}\times r\)
Using this the recursive formula for given problem is
\(h(n)=h(n-1)\times (-\dfrac{1}{7})\)
Therefore, the required recursive formula is \(h(n)=h(n-1)\times (-\dfrac{1}{7})\).
Find the value of k and yz if y is between x and z. x y = 3 k − 2 , y z = 7 k 4 , x z = 4 k 38
Answers
Considering that y is between x and z, we have that:
The value of k is of k = 6.The length of yz is 46 units.How to find the value of k and of yz?We consider that y is between x and z, hence the length of the segment is given by:
xz = xy + yz
The separate lengths are given as follows:
xz = 4k + 38.xy = 3k - 2.yz = 7k + 4.Hence:
4k + 38 = 3k - 2 + 7k + 4.
4k + 38 = 10k + 2
6k = 36
k = 6.
Hence the length of yz is given by:
yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.
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does friction increase speed ?
Answers
Answer:
That force is proportional to the velocity with which it is moving. This yes, the drag force or viscous force will increase as the velocity increases and this is generally associated with the object moving in fluids like water or air(freely falling).
Answer:
no
Step-by-step explanation:
Think of an object moving over ice or something flying through space. There's little or no friction and the object continues at its speed. But when you are flying down the road on a bicycle and you put your feet flat on the ground to slow down...the friction of the sole of your shoe drags across the road and slows you down. Friction decreases speed.
A number, added to its three quarters, is equal to its double decreased by 6. What is the number
Answers
Answer:
9
Step-by-step explanation:
i hope this is helpful........
a) Which of the lines A, B or C shows the best estimate for the
tangent to the curve at x = 4?
b) Use your answer to part a) to estimate the gradient of the curve
at = 4.
Answers
The gradient of the curve at x = 4 is:-3 / 0 = undefined (since division by 0 is undefined).Hence, the estimated gradient of the curve at x = 4 is undefined.
a) The line that shows the best estimate for the tangent to the curve at x = 4 is line A.
Line A shows the best estimate for the tangent to the curve at x = 4 because it passes through the point (4, 7) on the curve and is the closest to the curve at that point compared to lines B and C.
b) The gradient of the curve at x = 4 can be estimated using line A.
The gradient of the curve at x = 4 is equal to the gradient of line A at x = 4, which can be calculated using the formula: gradient = change in y / change in x At x = 4, the point on line A is (4, 10) and the point on line A closest to the curve is (4, 7).
Therefore, the change in y is -3 (7 - 10) and the change in x is 0 (since both points have an x-coordinate of 4).
Therefore, the gradient of the curve at x = 4 is:-3 / 0 = undefined (since division by 0 is undefined).Hence, the estimated gradient of the curve at x = 4 is undefined.
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it is known that about 90% of the population are right-handed, 9% are left-handed, and 1% are mixed-handed (also known as cross-dominance). for the following pr
Answers
Given that 90% of the population is right-handed, 9% is left-handed, and 1% is mixed-handed, we can determine the probability of different hand preferences for a randomly selected individual.
Let's denote the probabilities as follows: P(R) for right-handed, P(L) for left-handed, and P(M) for mixed-handed.
From the information given, we know that P(R) = 0.90, P(L) = 0.09, and P(M) = 0.01.
To find the probability of a randomly selected individual being left-handed or mixed-handed, we can simply add the corresponding probabilities:
P(L or M) = P(L) + P(M) = 0.09 + 0.01 = 0.10
Therefore, the probability of a randomly selected individual being left-handed or mixed-handed is 0.10, or 10%.
P(R) = 1 - P(L or M) = 1 - 0.10 = 0.90
Hence, the probability of a randomly selected individual being right-handed is 0.90, or 90%.
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Write the function in slope-intercept form
4y=-8x-10
WILL MARK BRAINLIEST
Answers
Answer:
Y=2x- 5
-----
2
Step-by-step explanation:
there are 97 men and 3 women in an organization. a simple random sample of 5 people is taken to form a committee. what is the probability that the committee includes all 3 women?
Answers
The probability that the committee includes all 3 women is 0.00018
In this question, we have been given there are 97 men and 3 women in an organization.
A simple random sample of 5 people is taken to form a committee.
We need to find the probability that the committee includes all 3 women.
Total number of people in the organization: 97 + 3 = 100
Usinng combination formula the possible number of 5 people committee:
100C5
= 100! / 5!(100 - 5)!
= 75287520
The number of outcomes for the committee includes all 3 women would be:
5C3 = (97C2)*3
= 13968
So, the probability that the committee includes all 3 women would be,
P = 13968 / 75287520
P = 0.00018
Therefore, the required probability is 0.00018
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