The remainder when the 100th term of the Fibonacci sequence is divided by 8 is 3.
Explanation:The Fibonacci sequence is a sequence where each term is the sum of the previous two terms. The sequence starts with 1, 1, and then continues with 2, 3, 5, and so on. To find the remainder when the 100th term of the sequence is divided by 8, we can calculate the terms of the sequence modulo 8 until we reach the 100th term.
First term: 1 mod 8 = 1Second term: 1 mod 8 = 1Third term: (1 + 1) mod 8 = 2Fourth term: (1 + 2) mod 8 = 3Fifth term: (2 + 3) mod 8 = 5Sixth term: (3 + 5) mod 8 = 0Seventh term: (5 + 0) mod 8 = 5Eighth term: (0 + 5) mod 8 = 5Ninth term: (5 + 5) mod 8 = 2Tenth term: (5 + 2) mod 8 = 7We can see from the pattern that the terms modulo 8 repeat every 6 terms. Therefore, to find the remainder when the 100th term is divided by 8, we can calculate the remainder when 100 is divided by 6. 100 mod 6 = 4. So, the remainder when the 100th term of the Fibonacci sequence is divided by 8 is the same as the remainder when the 4th term is divided by 8, which is 3.
what does a subtraction sign mean
Answer:
If you take a number and 'subtract" it with another number, it means that you take your second number and remove that amount from the first number
If this helped, say thanks on my profile ;)
Answer:
Definition of subtraction sign. : a mathematical symbol used to indicate that a particular quantity is to be subtracted from another to which it is joined by the symbol : a symbolic representation of the relation of subtrahend and minuend —symbol −
Step-by-step explanation:
What is the answer to this problem -34=m-16
Answer:
m = -18
Step-by-step explanation:
-34=m-16
+16. +16
-18 = m
Answer:
m = -18
Step-by-step explanation:
to evaluate for the correct answer of this problem , we would simply combine the like terms together.
solution
-34=m-16
-34 + 16 = m
-18= m
m = -18
1) Find f(0) when f(x) = x2 - 4x - 4.
A) 16
B) -8
C) -4
D) 4
Answer: -4
Step-by-step explanation:
If you replace x for 0 it will eliminate the variable. The only remaining term without a variable is -4
Find the equation of the line. Use exact numbers.
y = __x + __
Answer:
y = 3x+3
Step-by-step explanation:
We know the y intercept since it crosses the y axis at (0,3) and we know the x intercept since it crosses the x axis at (-1,0)
We can fidn the slope
m = (y2-y1)/(x2-x1) (0,3) (-1,0)
=(0-3)/(-1-0)
= -3/-1
=3
The equation for the line is in the form
y = mx +b where m is the slope and b is the y intercept
y = 3x+3
Choose 1 answer:
A. Vertical angles
B. Complementary angles
C.Supplementary angles
D. None of the above
Answer:
A
Step-by-step explanation:
vertical are always opposite each other
complementary are 180
supplementary are 90
can i please know the answer
Answer:
3840 cubic inches
Step-by-step explanation:
10*24 = 240 in
240*16 = 3840 cubic in
Have three witches each holding a broom and a spoon. Witches say witch plus witch plus witch =45. Three brooms say broom plus broom plus a broom =21 and three spoons say spoon plus spoon plus spoon = 12 then final question is a plain witch plus broom x spoon equal a ? What’s answer?
Answer:
Either 43 or 88
Step-by-step explanation:
45/3 = 15 (one witch)
21/3 = 7 (one broom)
12/3 = 4 (one spoon)
PEMDAS:
Equation: 15 + 7 x 4
if there are parenthesis and the equation looks like:
(15 + 7) x 4
the answer is 88.
if there is NOT parenthesis and the equation looks like:
15 + 7 x 4
the answer is 43.
Answer:
31
Step-by-step explanation:
witch with spoon and wand equals 15 each...wand = 7 spoon =3
Find the area of the parallelogram below.
Image result for area and perimeter of parallelograms
Answer:32 cm2
Step-by-step explanation:Use the formula A=BH, The 7 does not count because it isn't base or height. Use 4 times 8 which will make 32 cm2.
Area of the parallelogram is 32 cm²
Area of the parallelogram:Given that;
Base of parallelograms = 8 cm
Height of parallelograms = 4 cm
Find:
Area of the parallelogram
Computation:
Area of the parallelogram = l × b
Area of the parallelogram = 8 × 4
Area of the parallelogram = 32 cm²
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A bookshelf contains 9 mysteries, 7 biographies, and 4 science fiction books. A book is randomly selected, not replaced, then another is selected. Find the probability of selecting a biography then a mystery.
Answer:
63/380
Step-by-step explanation:
Initially,
# of Mysteries, M = 9
# of Biographies, B = 7
# of Sci. Fiction, S = 4
Total number of books = 9 + 7 + 4 = 20 books
P (first book selected is biography) = 7/20
After selecting 1 biography book,
# of Mysteries, M = 9
# of Biographies, B = 7 - 1 = 6
# of Sci. Fiction, S = 4
Total number of books remaining = 9 + 6 + 4 = 19 books
P (second book selected is a mystery) = 9/19
Hence (P first book is biography and 2nd book is mystery)
= (7/20 )(9/19)
= 63/380
The probability of selecting a biography then a mystery is 0.14.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, a bookshelf contains 9 mysteries, 7 biographies, and 4 science fiction books.
Total number of outcomes = 9+7+4
= 20
The probability of selecting a biography = 7/20
The probability of selecting a mystery = 9/20
Probability of an event = 7/20 × 9/20
= 56/400
= 0.14
Therefore, the probability of selecting a biography then a mystery is 0.14.
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find the area of the shaded region
Answer:
[tex]x^{2} \\[/tex]+3x
Step-by-step explanation:
2x(2x+1)
x(x+1)
2[tex]x^{2}[/tex]+2x-[tex]x^{2}[/tex]+x
=[tex]x^{2}[/tex]+3x
If a pool table measures 4 ft by 8 ft , what is the diagonal length from the bottom right pocket to the nearest tenth?
Answer:
8.9 ft
Step-by-step explanation:
Use Pythagorean theorem,
a² + b² = c²
√(a² + b²) = c
The diagonal is the hypotenuse of the rectangular pool table.
So,
√(4² + 8²) = c
√(16 + 64) = c
√(80) = c
8.944... = c
Nearest tenth:
8.9
The dimensions of a garden are shown.
Write an expression to find the perimeter.
Answer:
P=3x-14
Step-by-step explanation:
P=2(x+1/2 x-7)
=2x+x-14
or P=3x-14
The perimeter of the garden will be;
⇒ 3x - 7/2
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The garden is shown in figure.
Width of garden = 1/2x - 7
Length of garden = x
Now,
Since, Width of garden = 1/2x - 7
Length of garden = x
Hence, The perimeter of garden = 2 (Length + Width)
⇒ The perimeter of garden = 2 (x + 1/2x - 7)
⇒ The perimeter of garden = 2 (3/2x - 7)
⇒ The perimeter of garden = 3x - 7/2
Thus, The perimeter of the garden will be;
⇒ 3x - 7/2
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Can someone help me with this question?
Answer:
C). 30 I just learned about this!
Step-by-step explanation:
If the smaller diamond is 12 and the bigger one is 36 then its times 3 and whatver you do to the top you do to the bottom so it would be 10 times 3 which would equal 30! (:
Answer:
C - 30
Step-by-step explanation:
Since one side of the smaller diamond is 12 and the side on the bigger diamond is 36 it is 3 times the perimeter on each side so since the side on the small diamond is 10 then you would times it by three to get the perimeter of the side on the bigger diamond , which is 30 .
Solve the equation using the quadratic formula.
-x^2+27 = 6x
x=-3, X=9
X=-3X=3
x=-9,f=3
x=-9, x=3
The value of x is -9 and 3.Option D.
Step-by-step explanation:
Given,
[tex]-x^{2} +27 = 6x[/tex]
To find the value of x.
We will apply middle term factor formula.
The given equation can be written as,
[tex]x^{2} +6x-27 = 0[/tex]
or, [tex]x^{2}[/tex]+(9-3)x-27 = 0
or, x²+9x-3x-27= 0
or, x(x+9)-3(x+9)=0
or, (x+9)(x-3) = 0
So, x = -9 and x = 3
Hence,
The correct option is Option D.
Which points are on the graph of g(x)=(1/5)^x ? Select each correct answer. (3, 1/125) (−2, 1/25) (1, 0) (−1, 5)
Answer:
(3,1/125) and (-1,5)
Step-by-step explanation:
plug in the first coordinate (x-coordinate) in each pair for x in the original equation and the second coordinate (y-coordinate) for g(x)
Consider triangle ABC and triangle ACD in the diagram below. Which of the following complete the proof above?
Options
- AB =AD
- AC=AC
- AC=BD
- BC=DC
Given:
AC is perpendicular bisector of BD
AB ≅ AD
To prove:
ΔABC ≅ ΔACD
Solution:
In triangle ABC and triangle ACD,
Step 1: Given
AC is perpendicular bisector of BD and
AB ≅ AD (Side)
Step 2: By perpendicular bisector definition,
BC ≅ CD (Side)
Step 3: By reflexive property,
AC ≅ AC (Side)
Step 4: By SSS congruence criterion,
ΔABC ≅ ΔACD
Hence proved.
Answer:
BC=DC
Step-by-step explanation:
I did the test yourself and got it right :)
The center of a circle is (5,-3) and its radius is 4. Which point lies outside of the circle?
Answer:
-1
Step-by-step explanation:
The equation of a circle gives the positions of points inside or on its circumference. A point is outside the circle if the substitution in the equation results in a value greater than the square of the circle's radius.
Explanation:To understand this, we need first to understand the equation of a circle which is defined in the format (x-a)² + (y-b)² = r², where (a,b) is the center of the circle and r is the radius.
In this case, (a,b) = (5,-3) and r = 4. So, the equation of the circle becomes (x-5)² + (y+3)² = 16. Any point (X,Y) that satisfies this equation is inside or at the circumference of the circle. If the computation yields a result greater than 16, the point is outside the circle.
Let's take a point for example: (3,-1). Substituting the values gives (3-5)² + (-1+3)² = 4 + 4 = 8 which is less than 16, hence, lies inside the circle. But for a point like (10,0), it results in (10-5)² + (0+3)² = 25 + 9 = 34 which is greater than 16, so the point (10,0) is outside the circle.
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The Seattle Mariners baseball team wishes to determine the equilibrium price for seats for each of the next two seasons
Answer:
Price Qd1 Qd2 Qs
25 75000 60000 45000
30 60000 55000 45000
35 45000 50000 45000
40 30000 45000 45000
45 15000 40000 45000
[Find the attachment for the graph]
Final answer:
The equilibrium price for the Seattle Mariners baseball team's seats can be found using economic principles of supply and demand, taking into account factors that influence ticket demand, marginal revenue, and costs.
Explanation:
The question involves determining the equilibrium price for Seattle Mariners baseball team seats. This can be addressed using principles from Economics, specifically the supply and demand model. To determine the equilibrium price, one would need to establish the demand curve, which includes factors such as the population and income of the home city, the team's standing, and the number of superstars on the team. As economists such as Ferguson et al. suggest, the marginal cost for sports teams is often assumed to be zero due to the fixed costs of stadium operations. Therefore, the profit-maximizing quantity of seats sold is where marginal revenue is zero. This can be calculated and visualized with a graph showing both demand and marginal revenue curves. Additionally, adjustments such as the addition of new seats or external fees like licensing can affect the equilibrium dynamics, thus changing the equilibrium price and the total revenue.
What is the maximum recommended slope for straight-run stair?
A) 7-1/2" riser, 10" tread
B) 7' riser, 10" tread
C) 7-3/4" riser, 10-1/2" tread
D) 10" riser, 7-1/2" tread
What is the product? 4,3,-1,-1 x -3,1,-2,2
Answer:
B. [tex]\left[\begin{array}{ccc}-18&10\\5&-3\end{array}\right][/tex]
Step-by-step explanation:
The question is off edg. it is supposed to be [tex]\left[\begin{array}{ccc}4&3\\-1&-1\end{array}\right] * \left[\begin{array}{ccc}-3&1\\-2&2\end{array}\right][/tex] with multiple options. I just used the matrix calculator on edg.
is 8, 10, 12 a Pythagorean Triples ?
Answer:
No
Step-by-step explanation:
You use the formula a^2 + b^2= c^2. The biggest number is c.
So 8 ^2 + 10^2 has to equal 12^ 2
64 + 100= 144
164=144
That is not true.
Answer:
No, they are not
Step-by-step explanation:
If you simplify all 3 numbers, you get 4, 5, 6
If you graph the triangle on graph paper, it wouldn't work and there would be a gap.
3, 4, 5 triangles do work though!
8. sin 38 = x/16 what does x equal
2.375
Answer:
if the slash (/) is dividing then your answer would be
608
if the slash (/) means to multiply your answer would be
2.375
Step-by-step explanation:
if you were dividing then you have to do the opposite equation.In this case the opposite of dividing is multiply. Multiply the numbers you have then it will give your missing factor.
(Same goes with multiplying)
13. Jake earns 15% commission on the total amount he sells. If he sells $545 worth of items, how much commission
does Jake earn? A. $21.33 B. $36.33 C. $54.50 D. $81.75
Answer:
Option D - $81.75
Step-by-step explanation:
Given : Jake earns 15% commission on the total amount he sells. If he sells $545 worth of items.
To find : How much commission does Jake earn?
Solution :
Using the commission formula,
[tex]\text{Commission}=\text{Sales}\times \text{Percentage}[/tex]
[tex]\text{Commission}=\$545\times 15\%[/tex]
[tex]\text{Commission}=545\times \frac{15}{100}[/tex]
[tex]\text{Commission}=81.75[/tex]
Therefore, commission does Jake earn is $81.75.
So, option D is correct.
A hot air balloon descended 2,250 feet in 15 minutes. Find the change in altitude per minute (show the process).
Answer:
150 ft/min
Step-by-step explanation:
The change in altitude per minute will have the units of ft/min.
We see that we are given the number of feet: 2250 ft, as well as the number of minutes: 15 min.
So, to get ft/min, we can divide 2250 ft (the distance) by 15 min (time) to get the rate: 2250/15 = 150 ft/min
Thus, the change in altitude per minute is 150 ft/min.
Hope this helps!
Answer:
-15 per minute
Step-by-step explanation:
2250/15 = 150
Since it's descending, height is decreasing.
Hence rate of change of height is -15 per minute
3% percent of the students at Lincoln High School are in orchestra, 5%
are in band and 1% are in both. If a student is selected at random, what is
the probability that the student is in orchestra OR band?
Answer:
The probability of a student to be in the orchestra or the band is 0.07 or 7%.
Step-by-step explanation:
The probability of a student to be in the orchestra or the band is given by the following formula:
p(orchestra or band) = p(orchestra) + p(band) - p(orchestra and band)
p(orchestra or band) = 0.03 + 0.05 - 0.01
p(orchestra or band) = 0.08 - 0.01
p(orchestra or band) = 0.07
The probability of a student to be in the orchestra or the band is 0.07 or 7%.
Final answer:
The probability that a student is in orchestra or band is 7%.
Explanation:
To calculate the probability that a student at Lincoln High School is in either orchestra or band, we will use the formula for the probability of the union of two events, P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where P(A) is the probability of being in orchestra, P(B) is the probability of being in band, and P(A ∩ B) is the probability of being in both orchestra and band.
In this case, we have been given that 3% of students are in orchestra, 5% are in band, and 1% are in both.
Therefore, we have:
P(orchestra) = 0.03 (3%)P(band) = 0.05 (5%)P(both orchestra and band) = 0.01 (1%)Applying the formula:
P(orchestra OR band) = P(orchestra) + P(band) - P(both orchestra and band) = 0.03 + 0.05 - 0.01 = 0.07
Therefore, the probability that a student is in either the orchestra or the band is 7%.
The table shows the height of a tree for various years after it was planted. Using the line of best fit, how tall would the tree be 30 years after it was planted?
A) 22 Feet
B) 36 Feet
C) 37 Feet
D) 23 Feet
Samuel needs 2 boards to make a shelf. One board is 84 centimeters long
and the other is 45 centimeters long.
What is the total length of the shelf?
centimeters
What would your answer be in millimeters?
millimeters
Answer:
The length of the shelf is 129 cm or 1290 mm.
Step-by-step explanation:
Since Samuel will use the two boards to make the shelf, then the total length of the shelf is the sum of the lengths of each board. So in order to solve this problem we must do as shown bellow:
length shelf = length board1 + length board2
length shelf = 84 + 45 = 129 cm
In order to convert this to milimeters we must multiply the answer above by 10. So we have:
length shelf = 129*10 = 1290 mm
The length of the shelf is 129 cm or 1290 mm.
Answer: 129 cm = 1290 mm
Step-by-step explanation:
Hi, to answer this question we simply have to add the length of both boards.
Mathematically speaking:
Total length = 84 cm + 45 cm = 129 centimiters
Since:
1 cm = 10mm
To convert 129 cm to mm we have to multiply it by 10.
129 cm x 10 mm/cm =1290 mm
Feel free to ask for more if needed or if you did not understand something.
Mrs. Vamer deposited q dollars in a bank account that has been earning annual interest The total value of the
account is based on the function f(x) = 1.025%, where x represents the number of years the money has been in the account If no deposits or withdrawals are made after the initial deposit, which equation represents the total value of
the account 5 years from now?
Answer:
the answer is b
Step-by-step explanation:
nun
Arrange these numbers from least to greatest: -2.5, 2/5, 5/2, -5.2
Answer:
-5.2, -2.5, 2/5, 5/2
Step-by-step explanation:
Arrange it
b and a win some money and share it in a ratio of 3:4 person b gets 39 how much does person a get?
Answer:52
Step-by-step explanation:
To find this
Total ratio=3+4
=7
Find the amount share
7/4×39
=91
So, to get a share's
3/7×91
=52