According to the question, the Fibonacci series is a series of sequence of numbers. It follows one standard property which states that every third term in the series is the addition of first term and second term.
Now, the first ten terms of the Fibonacci sequence is as follows:
Fibonacci Series = [tex]{1,1,2,3,5,8,13,21,34,55}[/tex]
The sum of the first ten number of the Fibonacci series is as follows:
Sum = [tex]1+1+2+3+5+8+13+21+34+55 = 143[/tex]
As per question, divide the calculated sum by eleven. Therefore, it can be written as:
Required Division = [tex]\frac{143}{11} = 13[/tex]
Hence, the solution for the given series is [tex]13[/tex].
What is a Fibonacci series?
Fibonacci series is an infinite series of sequences of numbers. The important property of this series is, every third term is the addition of the first and second term. In this, the first term either starts with zero or one.
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Simplify. Assume a is greater than or equal to zero.
Answer:
3a² √2a
(o´▽`o)ﾉ xx
find two consecutives positive integers such that the square of the smaller integer, added to 3 times the larger integer is 24
Answer:
4 and 5
Step-by-step explanation:
Give Brainliest if I helped!
On his quiz, Jim answered 1
10
of the questions incorrectly.
What percent is equal to?
10
Answer:
90%
Step-by-step explanation:
Abdoulaye is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up 1 gallon of gas. How much gas would be in the tank after driving for 3 hours? How much gas would be left after tt hours?
The amount of gas he would have in the tank after 3 hours is 8 gallons.
The gas left after tt hours is 11 - tt.
How much gas would be left in the tank?In order to determine the amount of gas that would be left in the tank, the amount of gas used would have to be subtracted from the initial amount of gas in the car.
Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.
Amount of gas left = initial amount of gas - (gas used per hour x number of hours travelled)
11 - tt
11 - 3 = 8 gallons
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The hobbits Frodo, Sam, Pippin and Merry have breakfast at different times. Each one takes a quarter of the porridge in the pan, thinking that the other three have not yet eaten. What fraction of the porridge is left after all four hobbits had their breakfast?
Step-by-step explanation:
Let us start with Frodo's breakfast. He starts eating a quarter of the porridge. Let us say the porridge is 100 spoons, to make dividing easier. After Frodo we have [tex]\frac{3}{4}[/tex] left of the original bowl; we are left with 75 spoons.
100 - [tex]\frac{1}{4}[/tex] = 100 - 25 = 75
Next, comes Sam's breakfast. He eats 75 - [tex]\frac{1}{4}[/tex] = 75 - 18.75 = 56.25 spoons left.
Next, we have Pippin's breakfast. He eats 56.25 - [tex]\frac{1}{4}[/tex] = 42.1875 spoons.
Lastly, we have Merry's breakfast. He eats 42.1875 - [tex]\frac{1}{4}[/tex] = 31.640625 spoons.
Now, we know we have 31.640625 spoons left. However, we need to know what fraction this is out of the original porridge bowl. So, we do:
31.640625 * 100 = 3164.0625 * 1 = 3164.0625
3164.0625% of the bowl remaining!
What a yummy breakfast!
Points A and B have coordinates A(-4,2) and B(3,-6). Find the coordinates of point P, the weighted average of points A and B, in which point A has a weight of 4 and point B has a weight of 3.
A (-7/2, -5)
B (-1,-10/7)
C (-1/2, -2)
D (0,-20/7
The coordinates of the point P is P(x, y) = (- 1, - 10 / 7). (Correct choice: B)
How to determine the coordinates of a resulting point by weighted averages approach
In this problem we find the coordinates of two points on Cartesian plane, of which we must determine the location of a third point by using a formula based on a weight average-like formula:
P(x, y) = (4 / 7) · A(x, y) + (3 / 7) · B(x, y)
P(x, y) = (4 / 7) · (- 4, 2) + (3 / 7) · (3, - 6)
P(x, y) = (- 16 / 7, 8 / 7) + (9 / 7, - 18 / 7)
P(x, y) = (- 7 / 7, - 10 / 7)
P(x, y) = (- 1, - 10 / 7)
The coordinates of the point P is P(x, y) = (- 1, - 10 / 7).
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Is 3 + (-4) the same as -4 + 3? Explain
Answer:
Yes, 3 + (-4) is the same as -4 + 3.
Step-by-step explanation:
When doing addition problems such as this, the order of the numbers does not matter, even when negative numbers are included.
For example, 1 + 2 or 2 + 1 would equal 3.
3 + (-4) = -1
-4 + 3 = -1
Hope this helped you! Let me know if you need more clarification. :)
Use the Hypotenuse Theorem
Answer:
Image result for Use the Hypotenuse Theorem
The Pythagoras theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle. Or, the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse.
Step-by-step explanation:
grapn
given conditions.
The graph of f passes through (-9,8) and is perpendicular to the line whose equation is x = 4.
Answer:
y = 8
Step-by-step explanation:
x = 4 is the equation of a vertical line parallel to the y- axis.
A perpendicular line will be a horizontal line with equation
y = c ( where c is the value of the y- coordinates the line passes through )
the line passes through (- 9, 8 ) with y- coordinate 8 , then
y = 8 ← equation of perpendicular line
Is 22/25 a terminating or repeating decimal
of the line given the following information. Write the
The slope is 5, and the line passes through the point (9, -9).
Answer:
y = 5x - 54
Step-by-step explanation:
that is the solution above
Find the sum of each series. Σ⁵ n=1 (3 n+1)
The sum of the given series is 50
The summation notation or sigma notation is used to simplify the writing of long summation into a single formula.
The given series in sum notation is:
[tex]\sum\limits^5_{n=1} {(3n+1)}[/tex]
Substitute n = 1 ...5 into the nth term formula inside the sum notation:
a(1) = 3 . (1) + 1 = 4
a(2) = 3. (2) +1 = 7
a(3) = 3. (3) +1 = 10
a(4) = 3. (4) +1 = 13
a(5) = 3. (5) +1 = 16
Hence, the series:
4 + 7 + 10 + 13 + 16
We can evaluate the sum directly by adding all the terms:
S(5) = 4 + 7 + 10 + 13 + 16 = 50
Or we can also use the sum formula of an arithmetic series:
S(n) = n/2 [a(1) + a(n)]
For n = 5
S(5) = 5/2 (4 + 16)
S(5) = 5/2 . 20 = 50
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help...................................................
5 is the correct scale factor
This is because there are 5 little segments that go from C to the larger point in the top right corner. We need 5 pieces of segment CB to get segment CB' where B' is that top right corner point.
Put another way: If the distance from C to B is 1 unit, then the distance from C to B' is 5 units. This shows the distance has multiplied by 5, and that's the scale factor.
What is the answer okkkkkkkkkkk
Step-by-step explanation:
well,
23 < 12 + 0.04×x
11 < 0.04×x
11/0.04 < x
275 < x
x > 275 or x >= 276
so, for more than 275 monthly calls (that means 276 or higher) plan 1 is more economical.
at 275 calls is is plain even between both plans.
for fewer calls than 275 plan 2 is more economical.
I will Mark Brainlist Please Help Its A Math Problem !!! Approximate the unknown angle A, in the diagram to the nearest degree. ?
Thank you for the help !!! have good day :)
Two spherical pieces of cookie dough have radii of 3 centimeters and 5 centimeters, respectively. The pieces are combined to form one large spherical piece of dough. What is the approximate radius of the new sphere of dough? Round to the nearest tenth.
The radius of the new sphere of dough is 5.3368
In the given statement is :
Two spherical pieces of cookie dough have radii of 3 centimeters and 5 centimeters, respectively. The pieces are combined to form one large spherical piece of dough.
To find the approximate radius of the new sphere of dough
V 1 = 4/2 · 3³ π = 108/3 π
V 2 = 4/3 · 5³ π = 500/3 π
The new sphere: V = V 1 + V 2 = 608/3 π
4/3 r³ π = 608/3 π / : π/3
4 r³ = 608
r³ = 608 : 4 = 152
r = ∛152
r = 5.3368 cm
Hence, The radius of the new sphere of dough is 5.3368
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each linear graph to its slope
Use the spinner to find following probability. The spinner is spun again if it stops on a line.
P (pointer landing on green)
The probability of the spinner's point landing on green is 22.23%.
What exactly is a pie chart?A pie is a kind of chart that displays data in the form of a circular graph.
We understand that the total value of the pie is always 100%. It is also understood that a circle does have a circumference of 360°. As an outcome, the total of all data points equals 360°. There appear to be mainly two pie chart formulas based on these:
To determine a percentage of a data set, we use the following format: 100 (Frequency ÷ Total Frequency) × 100To convert the information to degrees, we use the given equations: (Informed Data ÷ Total value of Data) × 360°When a circle is completely rotated, it forms a 360-degree angle in the center.
At the center of the circle, a complete rotation yields 360 degrees.
The total percentage of all colors is 100%.
Divide a value of green by 3.6 since 360 degrees / 100% = 3.6.
The total percentage of green displayed by the spinner's pointer is 80%.
P (probability of the cursor landing on green) = 80/3.6
Probability P (cursor landing on green) = 22.222... = 22.23 (approx.)
As a result, the probability which the pointer will land on the green is 22.23%.
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Triangle ABC has vertices A(–1, 0), B(4, 0), and C(2, 6). If ΔABC is translated using the function rule (x, y) → (x – 6, y – 5) and then rotated 180° clockwise, what would be the coordinates of the vertices of ΔA’’B’’C’’?
a. A’’(–5, 7), B’’(–5, 2), C’’(1, 4)
b. A’’(7, 5), B’’(2, 5), C’’(4, –1)
c. A’’(7, 5), B’’(2, 5), C’’(4, 1)
d. A’’(–7, –5), B’’(–2, –5), C’’(–4, 1)
Answer:
b. A''(7, 5), B''(2, 5), C''(4, –1)
Step-by-step explanation:
Given vertices of ΔABC:
A = (-1, 0)B = (4, 0)C = (2, 6)Translation mapping rule:
(x, y) → (x – 6, y – 5)
Therefore:
A' = (-1 - 6, 0 - 5) = (-7, -5)B' = (4 - 6, 0 - 5) = (-2, -5)C' = (2 - 6, 6 - 5) = (-4, 1)Rotation of 180° clockwise rule:
(x, y) → (-x, -y)
Therefore:
A'' = (-7, -5) = (7, 5)B'' = (-2, -5) = (2, 5)C'' = (-4, 1) = (4, -1)Learn more about transformations here:
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Find the value of x2 values that separate the middle 80 % from the rest of the distribution for 20 degrees of freedom.
The value of x² values that separate the middle 80 % from the rest of the distribution is
With alpha and degrees of freedom χ²= 12.443
And with alpha and degrees of freedom χ²= 28.412
Chi - Square Distribution:
The chi square distribution is the continuous distribution, where the degree of freedom is the sample size minus 1, and it is the parameter of the chi-square probability distribution.
Given,
Here we need to find the value of x² values that separate the middle 80 % from the rest of the distribution for 20 degrees of freedom.
Based on the given details,
Degrees of freedom = 20
Middle separate value = 80%
Which is equal to 0.8 in decimal point.
The significance level
=> ∝ = 1 - 0.8
=> ∝ = 0.2
But we need the area of the middle so we divide this significance level with 2
so that we get exactly the middle area .
Dividing
=> 0.2/2= 0.1
So we will have two values for chi square
One with
=> 0.8 + 0.1 = 0.9 alpha
and
one with
=> 0.1 alpha .
This is because the chi square is right tailed.
Now based on the chi square distribution table,
So with alpha 0.9 and 20 degrees of freedom χ²= 12.443
And with alpha 0.1 and 20 degrees of freedom χ²= 28.412
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if there are 72 residents on 12 floors in a hotel, then there are 18 residents on _____ floors of the hotel
A 20
B 18
C 9
D 3
Answer: D. 3
Step-by-step explanation:
Let's make a proportion:
72 residents - 12 floors
18 residents - х floors
Hence,
[tex]\displaystyle\\x=\frac{18*12}{72} \\\\x=\frac{18*4*3}{18*4} \\\\x=3\ floors[/tex]
Classify the function
-10
-5
10
5
-5
-10
5
10
the function is (5)(-10)
What is the critical value of the test statistic to test the mean child mortality rate for countries in africa is more than the mean child mortality rate for countries in south asia?
The critical value is [tex]5[/tex] for the statistical test to test the mean child mortality rate for countries in Africa and the mean child mortality rate for countries in South Asia.
The child mortality rate or under age as five mortality rate tells that the child is dying during birth timing or exactly at the age of five. Globally million kids are dying at the age of five due to diseases like pneumonia or diarrhea or malaria etc. It is a big concern as well as a matter of responsibility for the child's survival at the age of five.
Many places in the world suffer from these problems and countries with low income ranges have a burden of child mortality. This problem is unevenly distributed throughout the world. Child survival is a constrained resource nowadays. The maximum child death is in sub Saharan Africa due to severe acute malnutrition.
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What equation in the point slope form matches the graph line shown
A• y+6= 4/5 (x+3)
B•y-2=-3/4(x-6)
C•y-6=4/5(x-3)
B•y-5=-2/3(x+9)
to get the equation of any straight line, we simply need two points off of it, let's use the ones in the picture below.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-3)}}} \implies \cfrac{-2 +6}{2 +3} \implies \cfrac{ 4 }{ 5 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{\cfrac{4}{5}}(x-\stackrel{x_1}{(-3)}) \implies y +6= \cfrac{4}{5} (x +3)[/tex]
Please help me find the answer to this question.
The lengths 12, 16, 10, 5, and 2 of the sides, AP, DQ, CS, PQ, and QR respectively, using the triangle proportionality theorem, gives the area of trapezoid BRSC as 40 square units.
What is the triangle proportionality theorem?The triangle proportionality theorem states that a line parallel to a side of a triangle and also intersects the other two sides, it divides the two sides proportionally.
Based on the theorem, where the other two sides are perpendicular, the parallel side divides the two sides equally.
The given parameters are;
The figure represented by ABCD = A parallelogram
The lengths of the sides of the figure are;
AP = 12
DQ = 16
CS = 10
PQ = 5
QR = 2
Required: The area of figure BRSC
Solution;
Given that ABCD is a parallelogram, we have;
AD = BC (definition of a parallelogram)
Using the triangle proportionality theorem, we have;
PQ = RS = 5 (segments bounded by equidistant parallel lines)
DQ - CS = AP - BR = 16 - 10 = 6 (Parallel vertical lines intersected by parallel lines at different heights)
AP - BR = 6
BR = 12 - 6 = 6
The area, A, of trapezoid BRSC is therefore;
A = RS × (BR + CS)/2
Which gives;
A = 5 × (6 + 10)/2 = 40
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What is the distance between points J and K?
Please, show your work.
Answer:
the answer would be 12 units.
Step-by-step explanation:
now you may count the number line and find that you find 6 units, BUT you need to check the values. You can simply do an equation 4 - - 8 = 12 or you can do 6 *2 which is 12.
Write and solve the inequality that represents negative one fifth is greater than or equal to the product of negative two thirds and a number.
The solution of the given inequality is given as [tex]x\geq \frac{3}{10}[/tex]
What is an inequality?
Inequality is a declaration of an order connection between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).
According to the question, the inequality may be written and solved as follows:
[tex]-\frac{1}{5}\geq -\frac{2}{3} x[/tex]
[tex]or, \frac{1}{5}\leq \frac{2}{3} x[/tex]
[tex]or,\frac{1}{5}* \frac{3}{2} \leq x[/tex]
[tex]or, x\geq \frac{3}{10}[/tex]
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Please help me solve the true or false math problem included in the picture!
Answer:
c=0/0
Step-by-step explanation:
Let's solve for c.
x−c
c−x
=−1
Step 1: Multiply both sides by c-x.
−c+x=−c+x
Step 2: Add c to both sides.
−c+x+c=−c+x+c
x=x
Step 3: Add -x to both sides.
x+−x=x+−x
0=0
Step 4: Divide both sides by 0.
0
0
=0/0
c= 0/0
Answer:
Step-by-step explanation:
False for all value of x, because "x" should not be equal "c"
Write an equation in slope-intercept form for the line described.
passes through (-12,3), perpendicular to y=-2/3x-11
The equation in slope-intercept form for the line that passes through (-12,3), perpendicular to y = -(2/3)x-11 is y = (3/2)x + 21.
The slope intercept form of a line is:-
y = mx + b
Where:-
m represents the slope of a line
b represents the y-intercept of a line
x and y represent the ordered pairs (x,y) throughout a line
We are given the line y = - (2/3)x-11 is perpendicular to the line whose equation we have to find.
Hence,
slope of the line*(-2/3) = -1
slope of the line, m = 3/2
Also, (-12,3) passes through the line,
Hence,
3 = (3/2)*(-12) + b
3 = -18 + b
b = 21
Hence, the equation of the line in slope intercept form is y = (3/2)x + 21.
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A coin is tossed and a die is rolled. What is the probability that the coin lands heads up and the number rolled is a 6 ?
The probability that the coin lands heads up and the number rolled is a 6 is 1/12.
Given that a die is rolled and a coin is tossed.
We have to find the probability that the coin lands heads up and the number rolled is a 6.
Probability of getting heads in tossing a coin = 1/2
Probability of getting 6 in rolling a die = 1/6
The event of tossing a coin and rolling die are independent.
Hence,
Probability that the coin lands heads up and the number rolled is a 6 =
Probability of getting heads in tossing a coin * Probability of getting 6 in rolling a die = (1/2)*(1/6) = 1/12.
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