In the fifth generation 1024 people learnt the art of quilling.
What is a geometric series?A geometric series is a series for which the ratio of each two consecutive terms is a constant and called the common ratio.Nth term of the Geometric series is given as [tex]t_{n} = ar^{n-1}[/tex] where a is the first term of the series and r is the common ratio.How to find how many people will know the art of quilling?In the first generation , 4 people learnt the art of quilling.In second generation (4 x 4) = 16 people learnt the art of quilling.In the third generation (16 x 4) = 64 people learnt the art of quilling.In the fourth generation (64 x 4) = 256 people learnt the art of quilling.In the fifth generation ( 256 x 4) = 1025 people learnt the art of quilling.In the fifth generation 1024 people learnt the art of quilling.
The series is going as a geometric pattern.In total 5 generations total (16+ 64 + 256 + 1024) = 1364 people learnt the art of quilling.
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Using the exponential growth formula, it is determined that by the end of five generations, 4096 people will know the art of quilling, starting with one teacher teaching four students, and each subsequent student teaching four others.
Explanation:The question involves an exponential growth scenario where Amanda teaches the art of quilling to four students, and then these students each teach four others, and so on for five generations. To find out how many people will know the art of quilling by the fifth generation, we use the formula for exponential growth: Total = a(1 + r)^n, where a is the initial amount (number of people who know the art at the beginning), r is the rate of increase (each person teaches 4 others means the rate is 4), and n is the number of generations.
The initial teacher, Amanda, is not counted in the first generation of students she teaches, so we begin with 4 students as our initial amount (a=4). Thus, the calculation for five generations becomes: Total = 4(4)^5. The formula simplifies to 4 * 1024 = 4096 people. Therefore, by the end of five generations, 4096 people will know the art of quilling.
If f(12) = 100(0 .50)12, which expression gives f(x)? Explain.
A . f(x) = 12^x
B . f(x) = 100^x
C . f(x) = 100(x)^12
D . f(x) = 100(12)^x
Answer:
[tex]f(x)=100(0.50)^{x}[/tex] or [tex]f(x)=100(1/2)^{x}[/tex]
Step-by-step explanation:
we have
[tex]f(12)=100(0.50)^{12}[/tex]
we know that
f(12) is the value of the function for x=12
therefore
The function f(x) should be
[tex]f(x)=100(0.50)^{x}[/tex] or [tex]f(x)=100(1/2)^{x}[/tex]
Answer:
D . f(x) = 100(1/2)^x
Step-by-step explanation:
If f(12) = 100(0 .50)¹²
∴ f(x) = 100(1/2)ˣ
The graph of an equation representing a direct variation passes through the point (6, 10). Give another point with integral coordinates that is also on the graph of this equation.
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{6},\stackrel{y}{10})\qquad \textit{we know that } \begin{cases} x=6\\ y=10 \end{cases}\implies 10=k6\implies \cfrac{10}{6}=k\implies \cfrac{5}{3}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{5}{3}x}[/tex]
to get another point, we simply can pick a random independent variable, namely "x", say hmmmm x = 9, thus
[tex]\bf y=\cfrac{5}{3}(\stackrel{\stackrel{x}{\downarrow }}{9})\implies y=5\cdot \cfrac{9}{3}\implies y=10~\hspace{7em}\boxed{(9, 10)}[/tex]
To find another point with integral coordinates on the graph of the equation representing a direct variation, we can use the given point (6, 10) and the fact that the equation represents a direct variation. By finding the value of the constant of variation, we can substitute an integral x-value to find the corresponding y-value for another point on the graph.
Explanation:To find another point with integral coordinates on the graph of the equation representing a direct variation, we need to use the given point (6, 10) and the fact that the equation represents a direct variation. A direct variation equation has the form y = kx, where k is the constant of variation. In this case, we can use the given point to find the value of k. When x = 6 and y = 10 in the equation y = kx, we can substitute these values to solve for k: 10 = k * 6. Solving for k, we get k = 10/6 = 5/3.
Now that we know the value of k, we can find another point with integral coordinates. Let's try x = 3. Using the equation y = kx, we can substitute x = 3 and k = 5/3 to find y: y = (5/3) * 3 = 5.
So, another point with integral coordinates on the graph of the equation representing a direct variation is (3, 5).
Which of the following is the graph of f(x) = x2 − 4x − 5?
A. graph of a quadratic function with a minimum at 2, negative 9 and x intercepts at negative 1 and 5
B. graph of a quadratic function with a minimum at 3, negative 4 and x intercepts at 1 and 5
C. graph of a quadratic function with a minimum at 2.5, negative 2.4 and x intercepts at 1 and 4
D. graph of a quadratic function with a minimum at negative 1.5, negative 6.2 and x intercepts at 1 and negative 4
The answer is A because completing the square gives a minimum of 2,-9 and factorising gives roots of 5 and -1 :)
Answer:
Minimum at (2,-9) and intercepts are (-1,5)
Step-by-step explanation:
f(x) = [tex]x^2 -4x-5[/tex]
completing square method adding and subtracting the square of half of coefficient of 4 ,we get
f(x) = [tex]x^2 -4x+4 -4 -5[/tex]
f(x) =[tex](x-2)^2 -9[/tex]
on comparing it with standard vertex form [tex](x-h)^{2} +k[/tex]
where k is suppose to be the minimum value
on comparing it we get k = -9
which is minimum value of f(x)
at x =2
and if we find the zeros of
[tex]x^2 -4x-5[/tex] ,we get
[tex]x^2 -5x+x -5[/tex]
[tex]x^2 -4x-5[/tex]
x(x-5)+1(x-5)
(x+1)(x-5)
on setting it equals zero ,we get
x+1 =0 and x=5
x =-1 and x=5
therefore option A is answer
Minimum at (2,-9) and intercepts are (-1,5)
Simplify -3 over 5 divided by 7 over 6.
A = -7 over 10
B = -18 over 35
C = 18 over 35
D = 7 over 10
Answer:
Simplify:
-3/5 ÷ 7/6
Step-by-step explanation:
1. To solve you have to switch the ÷ to x, but once you do that 7/6 would be switched too:
-3/5 x 6/7
2. Simplify,
-18/35
So, the answer to this is B.
Hope this Helped!!!!!
~Shane
Solve -9.4 > 1.7x + 4.2. I need this ASAP
Hello.
We are solving -9.4 > 1.7x + 4.2.
First we need to swap sides:
[tex]1.7x + 4.2 = -9.4[/tex]
Now we need to subtract 4.2 from both sides.
1.7x + 4.2 = -9.4
-4.2 . -4.2
Now let's combine -4.2 + 4.2 which is 0.
We get 1.7x < -9.4 - 4.2
Now let's divide both sides by 1.7
1.7x | -13.6
1.7 1.7
x < -13.6
1.7
So we just divided to get x < -8.
Answer:
[tex]\boxed{\bold{x<-8}}[/tex]
Step By Step Explanation:
Switch Sides[tex]\bold{1.7x+4.2<-9.4}[/tex]
Multiply Both Sides by 10[tex]\bold{1.7x\cdot \:10+4.2\cdot \:10<-9.4\cdot \:10}[/tex]
Refine[tex]\bold{17x+42<-94}[/tex]
Subtract 42 From Both Sides[tex]\bold{17x+42-42<-94-42}[/tex]
Simplify[tex]\bold{17x<-136}[/tex]
Divide Both Sides By 17[tex]\bold{\frac{17x}{17}<\frac{-136}{17}}[/tex]
Simplify[tex]\bold{x<-8}[/tex]
What is the product? (7x2y3)(3x5y8)
i don't know if this is the correct answer 3360y^2
Answer:
Product [tex](21) ( x^{7})(y^{11})[/tex].
Step-by-step explanation:
Given : [tex](7x^{2} y^{3})(3x^{5} y^{8})[/tex].
To find : product .
Solution : We have given that
[tex](7x^{2} y^{3})(3x^{5} y^{8})[/tex].
Combine like terms
[tex](7 * 3) ( x^{2}*x^{5})(y^{3}*y^{8})[/tex].
By the exponential rule : if the base of two exponent is same then power must be added . [tex]x^{a} *x^{b} = x^{a+b}[/tex].
Then
[tex](21) ( x^{2+5})(y^{3+8})[/tex].
[tex](21) ( x^{7})(y^{11})[/tex].
Therefore, Product [tex](21) ( x^{7})(y^{11})[/tex].
Write the ratio 14:56
In its simplest form
Answer:
14/14 = 1 and 56/14 = 4
Thus, 14:56 ratio simplified is 1:4
hope this helps:)sorry if it doesnt
brainliest plz
Is 976-522 more or less than 400? Explain how you can tell without finding the exact difference
[tex]\bold{Hey\ there!} \\ \bold{976-522=454}\\ \boxed{\boxed{\bold{Thus, 400\ is\ \underline{LESS\ THAN}\ 976-522}}} \\ \bold{Just\ solve\ your\ particular\ equation} \\ \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
How did the absent minded professor burn his ear?
He was ironing when the phone rang.
The absent-minded professor burned his ear due to the lens effect caused by sunlight reflecting off a concave mirror. The mirror focused the sunlight onto his ear, causing it to burn.
Explanation:The absent-minded professor burned his ear due to the lens effect caused by sunlight reflecting off a concave mirror. When the professor held the mirror close to his ear and exposed it to sunlight, the mirror focused the sunlight onto his ear, causing it to burn.
The concave mirror has a curve that causes the light rays to converge at a specific point called the focal point. This concentrated light energy resulted in the burning sensation on the professor's ear.
This phenomenon is similar to using a magnifying glass to focus sunlight onto an object and create heat. The concave mirror acted as a magnifying glass, amplifying the intensity of the sunlight and leading to the ear burn.
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harold deposits $30 a week into a savings account. hid balance in his savings account grows by a constant rate. true or false
Examine the two-step equation. − 7 4 + x 4 = 2 Which property of operations allows you to add the same constant term to both sides?
Answer:
The addition property of equality tells us that adding the same number to each side of an equation gives us an equivalent equation
Step-by-step explanation:
if a−b=c,then a−b+b=c+b,or a=c+b
Answer:
addition property of equality
Step-by-step explanation:
Write an expression that, when simplified is equivalent to 15x +7
Answer:
2(7.5x+3.5)
Step-by-step explanation:
I can't remember what these equations are actually called, however in order to solve this you simply multiply 7.5 by 2, and then 3.5 by 2.
Which of the following could be the equation for a parabola that opens to the left with vertex (-17,2)?
Answer:
C
Step-by-step explanation:
Just plugging in the given x or y values, you can rule out both A and B, only C and D work out logically.
-17=-3(2-2)²-17
-17=0-17
-17=-17✓
2=3(x+17)1+2
2=0+2
2=2✓
With parabolas, if you're talking in terms of y=x², it will be vertical. If talking in terms of x=y², it will be horizontal. As we're looking for something horizontal (open to the left), we need a x=y² formula. Of C and D, only C is an x=y² formula, and thus the answer.
Which statement BEST describes how the graph of g(x)=-3x^2 compares to the graph of f(x)=x^2?
Reminder:(Number 12 for the picture has the answers for the question)
Answers are attached in the 2 pics below. Please check!
Min's hose can pump 21 gallons of water every hour. How many gallons of water will he fill up if he runs the hose for 2/3 of an hour?
Answer:
14
Step-by-step explanation:
21 divided by 3 =7 7 per 1/3
7x2=14
Final answer:
Min will fill up 14 gallons of water if he runs his hose, which pumps 21 gallons per hour, for 2/3 of an hour.
Explanation:
If Min's hose can pump 21 gallons of water every hour, and he runs the hose for 2/3 of an hour, you would calculate the total gallons of water filled by multiplying the rate (21 gallons/hour) by the time (2/3 hour).
To find out how much water Min fills up:
Multiply the amount of water his hose pumps per hour by the fraction of the hour he runs it.21 gallons/hour × 2/3 hour = 14 gallons.Therefore, Min will fill up 14 gallons of water if he runs the hose for 2/3 of an hour.
Evaluate the exponential function f(x)=8^x+1 Which value completes the table?
A.0
B.3
C.9
D.25
The value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
Exponential function is the function in which the function growth or decay with the power of the independent variable.
The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
[tex]y=a^x[/tex]
Here, [tex]x[/tex] is the variable in the power of a number.
Given information-
The given exponential function in the problem is,
[tex]f(x)=8^x+1[/tex]
The value of function at the value of variable x as 1/3 has to be find to complete the table. Put 1/3 in the above equation on the place of x as,
[tex]f(x)=8^{\frac{1}{3}}+1[/tex]
The number 8 can be written as the [tex]2^3[/tex]. Thus,
[tex]f(x)=(2^3)^{\frac{1}{3}}+1\\f(x)=(2)^{\dfrac{3\times1}{3}}+1\\f(x)=(2)^1+1\\f(x)=2+1\\f(x)=3[/tex]
Thus the value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.
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What is the answer to 8x^3+125 by factoring the perfect cube?
Answer:
[tex]\large\boxed{8x^3+125=(2x+5)(4x^2-10x+25)}[/tex]
Step-by-step explanation:
[tex]8x^3+125=2^3x^3+5^3=(2x)^3+5^3\\\\\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+5)((2x)^2-(2x)(5)+5^2)\\\\=(2x+5)(4x^2-10x+25)[/tex]
What is the value of x?
Answer options: 15, 35, 25, 30
➷ Angles subtended by the same arc are equal
Therefore, x = 30 degrees.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
The answer is 30 Degrees
..............................................
What is 10 minutes before 9
➷ To figure this out, you need to understand that there are 60 minutes in an hour
Subtract 10 from this value:
60 - 50
As it isn't 60 minutes, it wouldn't be 9 anymore
9-1 = 8
The correct answer would be: 8:50
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➶ Good Luck (:
➶ Have A Great Day ^-^
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an online retailer sells cans of tennis balls look at the first rule to find the unit rate then use the unit rate to complete the table to show the cost of ordering 100 and 250 cans.
please help as soon as possible.
To find the unit rate, divide total cost by number of cans bought.
$30 / 12 cans = $2.50 per can.
Now multiply the unit cost by the number of cans you want to buy:
2.50 x 100 = $250.00
2.50 x 250 = $625
Which of the following equations will make a V-shaped graph?
y = |x|
y = 2x
x 2 + 5 = y
y = 1/3x
Y=|x|. An absolute value has a V shape.
Final answer:
The equation that will make a V-shaped graph is y = |x|, as it plots the absolute value of x, creating a V shape by reflecting points on the positive side of the y-axis for both positive and negative values of x.
Explanation:
The student asked which of the following equations will make a V-shaped graph. The answer is y = |x|. This is because the absolute value function produces a graph that is V-shaped, reflecting the positive distance from zero for both positive and negative values of x. The other options presented, such as y = 2x, would produce a straight line; x² + 5 = y (correctly read as y = x² + 5) would produce a parabola; and y = 1/3x would also result in a straight line, just with a different slope. Only the graph of y = |x| has the distinct V shape as it plots the absolute value of x, meaning it reflects the points on the positive side of the y-axis for both positive and negative values of x.
help and show work for #7
Answer:
If you give the diameter and the radius, as well as the circumference, I will be of more help :)
Step-by-step explanation:
I hope this helps, if it doesn't then just message me and ill be more than happy to help :)
in a bag if marbles there are 7 blue, 6 red, pick one marble out. without replacing the first marble pick another marble out. how many ways can u pick two red marbles?
Answer:
1
Step-by-step explanation:
If you only take out 2 marbles, you have to take out red marbles both times to have 2 red marbles. There is no other option.
Start with the standard formula for the area of a triangle, and rewrite it to solve for the base, b.
Answer:
2A/h = b
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 bh
Multiply each side by 2
2A = 2*1/2 bh
2A = bh
Divide each side by h
2A/h = bh/h
2A/h = b
Answer:
b=2A/h
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 bh
Multiply each side by 2
2*1/2 bh = 2A
bh = 2A
Divide each side by h
bh/h = 2A/h
b = 2A/h
sharon is 3 years old less than twice her younger brother's age. Let (s) repressent sharons age and (b) repressent her brother's age. which equation could be used to show sharons age?
A: s = 3-2b
B: b = 2x-3
C: s = 2b-3
D: b = 3 -2x
E: s = 3b-2
If Sharon is 3 years younger, then it's s = 3-b. However, it's twice her brothers age, which makes the formula our final answer, A, or [tex]s = 3 - 2b[/tex]
The correct option is A
HELP PLX 46 POINTS!
The diameter of the semicircle with center O, shown below, is 4 units. What is the area of the shaded region?
Answer:
Area = 2
Step-by-step explanation:
Givens
The leg and the height of the right angle triangle are both radii of the semi circle.
The diameter of the semicircle is 4
Solution
radius = diameter /2
radius = 4/2
radius = 2
Area = 1/2 * b * h
b = 2
h = 2
Area = 1/2 * 2 * 2
Area = 2
Answer:
2 units²
Step-by-step explanation:
The diameter is 4 units.
The radius is 4/2 = 2 units.
The two legs of the triangle are a measure of 2 units or just the radius length.
Area of triangle = bh × 1/2
2 × 2 × 1/2
4/2 = 2
Emma has 5 3/8 punds of potato salad and 2 7/8 pounds of egg salad for a picnic. How many more pounds of potato salad than egg salad does Emma have? A - 3 pounds B- 2 3/4 pounds C - 2 1/2 pounds D - 2 1/4 pounds
Answer:
The correct answer option is C. [tex]2\frac{1}{2}[/tex] pounds
Step-by-step explanation:
We are given that Emma has [tex]5\frac{3}{8}[/tex] pounds of potato salad and [tex]5\frac{3}{8}[/tex] pounds of egg salad for a picnic.
We are to find out how much more pounds Emma has of potato salad than the egg salad.
To find this, we simple need to subtract the pounds of egg salad from the pounds of potato salad.
[tex]5\frac{3}{8} - 5\frac{3}{8}[/tex] [tex]=\frac{43}{8} -\frac{23}{8} =\frac{43-23}{8} = 2\frac{1}{2}[/tex] pounds
Help, please!
Show how the GCF of the numbers 10 and 15 can be used to reduce the fractions [tex]\frac{10}{15}[/tex]
Answer: [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The greatest GCF is 5 because 5 goes into 15, and 10. Therefor, the answer would be 2/3.
* Hopefully this helps:) Mark me the brainliest:)!!!
Answer:
⅔
Step-by-step explanation:
Find all the factors of 10 and 15.
Factors of 10: 1, 2, 5, 10
Factors of 15: 1, 2, 3, 5, 15
The highest factor that is in both 10 and 15 is 5.
To reduce the fraction 10/15, divide both the numerator and denominator
by 5.
10/15 = (10 ÷ 5)/(15 ÷ 5) = ⅔
Could someone help me plz???
The correct answer is B. approximately 250g
When making a telephone call using a calling card, a call lasting 5 minutes cost $0.95. A call lasting 13 minutes cost $1.75. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that models the cost of making a call lasting x minutes.
A. y = 10x - 981/20
B. y = -0.1x + 1.45
C. y = 0.1x + 0.45
The linear equation that models the cost of making a call lasting x minutes using a calling card is y = -0.1x + 1.45.
Explanation:To write a linear equation that models the cost of making a call lasting x minutes using a calling card, we can use the given information about two calls. If a 5-minute call costs $0.95 and a 13-minute call costs $1.75, we can set up two equations:
0.95 = 5m + b
1.75 = 13m + b
Solving these equations, we find that m = -0.1 and b = 1.45. Therefore, the linear equation that models the cost of making a call lasting x minutes is y = -0.1x + 1.45.