The sum of the first ten terms of any Fibonacci-like sequence is 88.
How to find the sum of the first ten terms of any Fibonacci-like sequence?The Fibonacci numbers, sometimes known as Fn in mathematics, are a series. Each number in the Fibonacci sequence is composed of the sum of the two numbers before it. Typically, the sequence begins with 0 and 1.
means
0+1 = 1
1+1 = 2
1+2 = 3
2+3 = 5,like this.
The Fibonacci sequence includes the numbers 0, 1, 1, 2, 3, 5, 8, 13, 21 and so on.
Sum = 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 = 88 is what we get when we add up the numbers in the series.
The first ten Fibonacci numbers sum is 88.
Hence, The sum of the first ten terms of any Fibonacci-like sequence is 88.
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What is the probability of drawing a red marble?
Answer:
[tex] \sf \: \frac{1}{4} [/tex]
Step-by-step explanation:
since the total of red marbles is 5 and the total of all the colours of marble is 20
therefore we write it like this;
[tex] \sf \frac{Total \: of \: red \: marbles}{Total \: of \: all \: the \: marbles}[/tex]
[tex] \rightarrow \sf \: \frac{5}{20} = \frac{1}{4}[/tex]
ive put 3 more of the same question gain lots of points! Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
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Question Add −1.5+1.75 Plot the first addend and the sum on the number.
Answer:
Step-by-step explanation:
Review the graph. A student spends 16.5 hours studying and receives a mark of 61.4%. Which statement
describes this result?
A. The result is not an outlier and there is a gap in the data.
B. The result is not an outlier and there is no gap in the data.
C. The result is an outlier and there is a gap in the data.
D. The result is an outlier and there is no gap in the data.
Answer: D. The result is an outlier and there is no gap in the data.
The statement describes this result is; D. The result is an outlier and there is no gap in the data.
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set.
From the graph, at 16.5 hours, the exam score is approximately 90%. Thus, we can conclude that if a student spends 16.5 hours studying and receives a mark of 61.4%, then the result is an outlier and there is no gap in the data.
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Find the distance between the pair of points: (-9, -5) and (6, -5)
Answer:15
Step-by-step explanation: if your at -9,-5 you would be on the 3rd quadrant, and in order to get to 6,-5 (4th quadrant) you would just move to the right. you would only move right because the y-axis stays the same but the x-axis changes.
Answer: 15
Step-by-step explanation:
the equation to find the length of a line using the points given:
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
therefore you should understand which is y2, x2,y1 and x1
so you should always check which y value is bigger (the y value is the number in the right side of the point) so if the y value is bigger (y2) then eventually the value next to it which is x will always become x2 if the y value is big (y2)
so the other two values of the other point should become x1 and y1 since you already figured out the lager y value.
so now as for this question y2= -5, y1= -5, x2= 6 and x1= -9
now substitute these values to the equation I mentioned before ( you should make sure to remember the equation for sure as it is required when doing these types of questions)
[tex]\sqrt{[6-(-9)]^{2} +[-5-(-5)]^2} \\\sqrt{(6+9)^2 + (-5+5)^2[/tex]
[tex]\sqrt{15^2+0^2} \\\sqrt{225} \\15[/tex](therefore 15 is the answer you have been looking for!)
I hope you understood and don't forget the equation which is the main help!
E is the midpoint of DF, DE=6x+1 and EF = 7x-4. Find DE, EF, and DF
The value for the given line DF are-
DE = 31 units.EF = 31 units.DF = 62 unit.What is meant by the mid point of the line?A midpoint is a point in the middle of a line connecting two points. The 2 points of reference are the line's endpoints, and also the midpoint is located between the two.For the points on the coordinate axes, the midpoint formula is defined. Let the endpoints of the a line segment be (x)1, (y)1, and (x)2, (y)2. The midpoint is equal to one-half of the sum of the two points' x-coordinates and half of a sum of the two points' y-coordinates.For the given values in question,
DE = 6x + 1 and EF = 7x - 4.
As, E is the midpoint of DF.
Thus,
DE = EF
Pu the values.
6x + 1 = 7x - 4
On solving.
x = 5
Put the values in the lines.
DE = 6x + 1
DE = 6×5 + 1
DE = 31 units.
EF = 7x - 4
EF = 7×5 - 4
EF = 31 units.
DF = DE + EF
DF = 31+ 31
DF = 62 units.
Thus, the values for the line segment are obtained.
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Beth knows the perimeter, P, and width, w, of a
rectangular window in her living room. Which
formula can she use to find the length, 1, of the
window?
Beth knows the perimeter, P, and width, w, of a
rectangular window in her living room. Which
formula can she use to find the length, 1, of the
window?
First we know about How to Find the perimeter?
Rectangles have four sides, congruent opposite sides, and four right angles and we find the perimeter of a rectangle with the equation P=2l+2w. Explore this formula, rectangles, and examples of finding rectangle perimeters.
so ,
The formula for the perimeter of a rectangle is given below: Perimeter = length + length + width + width P = l + l + w + w Or, P = 2 ( l + w) Hence, the formula for the perimeter of a rectangle, P = 2 × (length + width) = 2 × (sum of adjacent sides) .
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Each of these sequence or series formulas involves four quantities that are represented by a variable. For each fomula, describe the four quantities.
d. S n = a₁ (1-rⁿ ) / 1-r
The formula for finding the sum of a geometric series is:
S n = a₁ (1-rⁿ )/(1-r)
The four quantities in the formula are S n, a₁, r, n
How to describe the four quantities?An infinite geometric series is the outcome of an unlimited geometric sequence. An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series.
The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.
The formula for finding the sum of a geometric series is:
S n = a₁ (1-rⁿ )/(1-r)
The four quantities in the formula are S n, a₁, r, n
The description is as follows:
n be the number of terms
a₁ be the first term
r be the common ratio
[tex]S_n[/tex] be the sum of a geometric series
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Enlarge the triangle by scale factor - with centre (-1,2).
YA
5
4
43WA
2
1
OT N 345
-5-4-3-2-1 1 2 3 4 5 x
-2
-3
-4
-5
Extend the triangle's size by -1/3 with the center point (-1,2).
The triangle's vertices of new location point are (-2,1),(0,1) and (-3,4).
The triangle's vertices' coordinates are not specified. Assume that the triangle's vertices are located at points A(2, 5), B(-4, 5) and C. (5, -4).
A point is transformed when it is moved from its original location to a new one. Reflection, rotation, translation, and dilation are examples of Dilation is the growth or contraction of an object's size. A point A(x, y) is displaced from a point (a, b) by a factor k as follows:
[tex]A^{'}= (k(x-a)+a,k(y-b)+b)[/tex]
Where, (a,b)=(-1,2) and k=[tex]\frac{-1}{3}[/tex].
The triangle's vertices are located at points A(2, 5), B(-4, 5), and C. (5, -4). The new address is:
[tex]A^{'}= (\frac{-1}{3} (2-(-1))-1,\frac{-1}{3}(5-2)+2)=(-2,1)\\B^{'}= (\frac{-1}{3} (-4-(-1))-1,\frac{-1}{3}(5-2)+2)=(0,1)\\C^{'}= (\frac{-1}{3} (5-(-1))-1,\frac{-1}{3}(-4-2)+2)=(-3,4).[/tex]
Therefore, The triangle's vertices of new location points are (-2,1),(0,1) and (-3,4).
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What is the slope of a line perpendicular to the line through the points (-1,6) and (3,-4) ?
A. m=-5/2
B. m=-1
C. m=-2/5
D. m=2/5
The slope of the line passing through two points (-1, 6) and (3, -4) is Option A ( m = [tex]\frac{-5}{2}[/tex] )
It is given that, the line is passing through two points (-1, 6) and (3, -4)
Slope is the measurement of the level of steepness of the line or it is a line's steepness determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The formula to find the slope of the line passing through two points is given by
m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
We need to find the slope of the line passing through both points
where y1 = 6, y2 = -4, x1 = -1, x2 = 3
Putting values in the formula to find the slope of the line
we get,
m = [tex]\frac{-4 - 6}{[3 -(-1)]}[/tex]
m = [tex]\frac{-10}{4}[/tex]
m = [tex]\frac{-5}{2}[/tex]
Hence The slope of the line passing through two points (-1, 6) and (3, -4) is m = [tex]\frac{-5}{2}[/tex]
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=
A
C
F
xº
E
G
80°
160°
D
B
The value of angle ∠AEF or ∠x is 80°.
What are angles?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. The term angle is derived from the Latin word angulus, which means "corner." The basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation.So,
∠CEB is 160° with EG being an angle bisector leaving ∠CEG = 80° and ∠BEG = 80°FEG is a straight line with ∠FEG being 180°.∠FED + ∠DEB + ∠BEG = ∠FEG80° + ∠DEB + 80° = 180°160° + ∠DEB = 180°∠DEB = 180° - 160°∠DEB = 20°Then,
∠AEC = 20° = ∠DEB (Inversely opposite angles)Now,
FEG is a straight line with ∠FEG being 180°.∠CEG + ∠AEC + ∠AEF = ∠FEG80° + 20° + ∠AEF = 180°100° + x = 180°x = 180° - 100°x = 80°∠AEF = 80°Therefore, the value of angle ∠AEF or ∠x is 80°.
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Points O, A, B lie on the same line. OA = 12 cm, OB = 9 cm. Find the distance between the midpoints of segments OA and OB if: Point O does not lie on the segment AB pls help ASAP with explnation
The distance between the midpoints of segments OA and OB is 1.5 cm.
Given that, points O, A, and B lie on the same line. OA = 12 cm, OB = 9 cm.
We need to find the distance between the midpoints of segments OA and OB.
What is the midpoint of the line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments. The midpoint of a line segment is the point on a segment that is at the same distance or halfway between the two ending points.
Let X be the midpoint of OA and Y be the midpoint of OB.
Now, the midpoint of OA is OX=AX=OA/2
=12/2=6 cm
Then, the midpoint of OB is OY=YB=OB/2
=9/2=4.5 cm
The distance = 6-4.5=1.5 cm
Therefore, the distance between the midpoints of segments OA and OB is 1.5 cm.
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PLEASE HELP LE WITH THIS ANSWET
Answer: 5
Step-by-step explanation:
GH=GD+DH
GD=DH ==> indicated by the ticks on the two line segments GH and DH.
GH=DH+DH
4x-4=8+8
4x-4=16
4x=20
x=5
Find the coordinates of the points of intersection of the graph of
y=2x+6 with the axes. Find the area of the right triangle
formed by this line and the coordinate axes.
The coordinate of intersection with the x-axis is: (-3, 0).
The coordinate of intersection with the y-axis is: (0, 6).
The area of the triangle is 9 unit²
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The linear equation is given as:
y = 2x+6
Intersection with the y-axis
Substitute, x = 0
⇒ y = 2x + 6
⇒ y = 2(0) + 6
⇒ y = 6
As a result,: y = 2x+6 intersects with the y-axis at (0, 6)
Intersection with the x-axis
Substitute, y = 0
⇒ y = 2x + 6
⇒ 0 = 2x + 6
⇒ 2x = - 6
⇒ x = - 3
As a result,: y = 2x + 6 intersects with the x-axis at: (-3, 0)
The area of the right-angled triangle
The area is calculated as:
Area of triangle = 1/2×Base×Height
Area of triangle = 1/2×3×6
Area of triangle = 9 unit²
The coordinate of intersection with the x-axis is: (-3, 0).
The coordinate of intersection with the y-axis is: (0, 6).
The area of the triangle is 9 unit²
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Aleena thinks of a number that has 2 decimal places.
Her number is 2.8 when rounded to 1 decimal place.
What is the smallest number that Aleena could be thinking of?
Answer:
The smallest number that Aleena could be thinking of is 2.75.
HELPPP mathhhhhhh 20 pointsss
7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B).
b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.
What is Equation?Two expressions with equal sign in between is called as equation.
4. 7^4.3^-6.y
In the given expression, 7 has 4 exponent and 3 has -6 exponent.
This can be written as 7.7.7.7.y/3.3.3.3.3.3.
5. b^10/b^4 is b^10-4=b^6.
6. (p^2+p-8)-(-4p^2-p+3)
=p^2+p-8+4p^2+p-3
=5p^2+2p-5.
Therefore 7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B), b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.
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In the figure below, =m∠JKM 98°, =m∠LKM 70°, and KN bisects ∠LKM. Find m∠JKN.
In the given question angle ∠JKN is 63°.
What are angles?An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angulus," which means "corner." The two rays are referred to as the sides of an angle, and the common endpoint is referred to as the vertex.So,
Since KN bisects ∠LKM which is 70°.
Then, ∠NKM will automatically be 35°.Now, we know that: (refer to the diagram below)
∠JKN = ∠JKM - ∠NKM∠JKN = 98° - 35°∠JKN = 63°Therefore, in the given question angle ∠JKN is 63°.
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The previous question you found the slope for the points (1,0) and (3,8), now find the b and write the equation in slope intercept form.
y =
Question Blank 1 of 2
type your answer...
x +
Question Blank 2 of 2
type your answer...
Answer:
Step-by-step explanation:
y = mx + b is the equationof the line where m is the slope and b is the y intercept
slope between t points = (8 - 0)/ (3 -1 )
= 8/2
= 4
y = 4x + b
substitute (1,0) in the equation to get b
0 = 4(1) + b
b = -4
equation will be y = 4x -4
Xio is rolling marbles down a ramp. Every second that passes, she
measures how far the marbles travel. She records the information in the table
shown below.
eau marit
Second
1st
2nd 3rd 4th
Distance (cm) 20 60 100 140
Make a conjecture about how far the marble will roll in the fifth second
The marble will roll 180cm distance in fifth second.
Distance travelled by an object in rectilinear motion is always in arithmetic Progression. Arithmetic Progression is collection of number in increasing or decreasing order with a common difference.
The marble rolls 20cm, 60cm, 100cm, 140cm in 1st, 2nd, 3rd, 4rth second respectively
As the ball travels in rectilinear motion on floor, so the distance covered by it in successive seconds will be in Arithmetic Progression
so, 5th term of the AP 20,60,100,140..... will be the distance travelled by it 5th second
Since A=20 and common difference(d)=40
then, 5th term= A + (5-1)d
or, 20+ (4×40) = 180cm
Final answer, the marble will roll 180cm in 5th second.
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Given: BD ⊥ BC ; ∠ABD ≅ ∠DBE
Prove: ∠ABD and ∠EBC are complementary
Statement in step 8 is the proof that <ABD and <EBC are complementary angles.
What are a complementary angles?An angle in mathematics refers to an arc that joins two points. For angles to be formed there should be two points, the starting point and the ending point. In some cases the starting point coincides with the ending point, in this case the angle formed is 360 degrees which is equivalent to a circle. We can hence say that angle in a circle is 360 degrees
When angles are formed by two points in the same straight line or say two colinear points the angle formed here is 180 degree. Hence we say angles in a straight line is 180 degrees. In a case where a line intersects the straight line, the intersecting line bisects the the angle in a straight line. The sum of the two angles formed is 180 degrees. Such angles are said to be supplementary angles.
Assuming the bisector of the straight line in a perpendicular bisector, here the angle 180 is divided into two equal parts then each angle is 90 degrees.
When angle 90 degrees is bisected two different angles are formed. The sum of these two angles are known as complementary angles.
Hence angle <ABD and <EBC are complementary angles formed from bisecting angle <DBC which is 90 degrees or a right angle triangle
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2|4w-1|=3|4w+2| Solve for W, but it’s absolute value so 2 and 3 cannot be distributed
Answer:
w = -2, (-1/5)
Step-by-step explanation:
2|4w - 1| = 3|4w + 2|
8w - 2 = 12w + 6
-12w -12w
-------------------------
-4w - 2 = 6
+2 +2
---------------------
-4w = 8
÷-4 ÷-4
w = -2
2|4(-2) - 1| = 3|4(-2) + 2|
2|-8 - 1| = 3|-8 + 2|
2|-9| = 3|-6|
18 = 18
----------------------------------------------------------------------------------------------------------
2|4w - 1| = -(3|4w + 2|)
2|4w - 1| = -3|4w + 2|
8w - 2 = -12w - 6
+12w +12w
-------------------------
20w - 2 = -6
+2 +2
20w = -4
÷20 ÷20
------------------
w =(-1/5)
2|4(-1/5) - 1| = 3|4(-1/5) + 2|
2|(-4/5) - 1| = 3|(-4/5) + 2|
2|(-9/5)| = 3|(6/5)|
3.6 = 3.6
I hope this helps!
b. What are the heights of the 6 th and 10 th bounces?
PQ is a building of height 70 m. The angle of depression of a car R from the top is 40 degrees. The distance between R nd Q is?
Given the height of building PQ and the angle of depression of a car R from the top of the building, the distance between R nd Q is approximately 58.7 meters.
What is the distance between R nd Q?Given the data in the question;
PQ is a building of height 70 mThe angle of depression of a car R from the top is 40 degrees Distance between R nd Q = ?This forms a right triangle as drawn in the image below and to determine the distance between R and Q,
We use one of the six function of angle used in trigonometry.
tanθ = Adjacent / Opposite
We plug in the values from the diagram and solve for RQ.
tanθ = Adjacent / Opposite
tan( 40° ) = RQ/70m
RQ = tan( 40° ) × 70m
RQ = 0.83909963 × 70m
RQ = 58.7m
Given the height of building PQ and the angle of depression of a car R from the top of the building, the distance between R nd Q is approximately 58.7 meters.
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The radius of the circle is 5 centimeters line segment ab is a diameter of the circle what is the value of x to the nearest tenth
The value of x to the nearest tenth is 8.9 cm.
How to find the diameter of a circle?The radius of the circle is 5 centimetres. Line segment ab is a diameter of the circle.
The diameter of the circle is twice the length of the radius.
Hence, the value of x can be found as follows:
AB = 10 cm
Using Pythagoras theorem,
c² = a² + b²
where
c is the hypotenusea and b are the other legs.Therefore,
10² - 4.5² = x²
100 - 20.25 = x²
x² = 79.75
x = √79.75
x = 8.93028554975
x = 8.9
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Find an equation of the line in the form y=f(x) that satisfies the given conditions. through (7, 1); slope 2
Answer:
y = 2x - 13.
Step-by-step explanation:
The point-slope form of a line is:
y - y1 = m(x - x1)
Substituting the given values:
y - 1 = 2(x - 7)
y = 2x - 14 + 1
y = 2x - 13.
Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
Eddie conducted a random survey of 50 students and fund that 14 nf them spend more than 2 hours each night doing homework. If there are 421 students at Eddie's school, predict how many of them spend more than 2 hours each night doing homework.
F. 118 H. 125
G. 124 J. 131
The prediction of the number of students who spend more than 2 hours each night doing homework are 118.
It is given in the question that in a random survey of 50 students and fund that 14 of them spend more than 2 hours each night doing homework.
There are 421 students in the school.
We have to predict the number of students who spend more than 2 hours each night doing homework.
Probability of number of students who spend more than 2 hours in doing homework = 14/50 = 7/25= 0.28
If there are 421 students, number of students who spend more than 2 hours in doing homework = 0.28*421 = 117.88 ≈ 118.
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Samantha owes her father 21.21. She just got paid 13 for babysitting. If she gives that money to her dad, how much will she still owe him? No dollar sign needed. Write your answer as a negative integer, rounded to the nearest h
Answer:
she'll still owe him 8.21
Step-by-step explanation:
i dont know what you mean by write it as a negative integer ?
Seeta did a puzzle in 3 minutes 45 seconds.
Ninal did the same puzzle in 7 minutes 28 seconds.
Seeta says,
'I did the puzzle in less than half the time Ninal did the puzzle.
(b) Is Seeta right?
You must show all your working.
Yes, Seeta is right a takes puzzle in 3 minutes 45 seconds time
3 x 60 = 180 + 45 = 225 seconds.
Seeta's time. 7 x 60 = 420 + 28 = 448 seconds. Nina's time.
if you times the 448 by 2 it =224.
Yes, Seeta is right.
Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the longer term.
Time is a quantity that is a part of several measurements that are used to compare the length of events or the gaps between them, to match how long they last, to order events, and to live how quickly things change in the real world or in our conscious experience. together with the three spatial dimensions, time is usually referred to as a fourth dimension.
Time has long been an important topic of study in philosophy, theology, and science, but scholars haven't been able to define it in a way that is applicable to all of these disciplines without becoming circular. Nevertheless, numerous industries and business domains.
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What is the mean of the temperatures shown
on the map below? Give your answer in °C.
-7
-1
-4
0
2
Temperatures given in °C
Answer:
the mean is -2 degrees celsius
Step-by-step explanation:
-7 + -1 + -4 + 0 + 2 = -10
-10 / 5 = -2
Please this is urgent I will give all of my points
