From the given information. Write the recursive and explicit functions for each geometric sequence. Please use these terms. recursive f(1) = first term, f(n) = pattern*f(n-1). what is the 1st term and pattern? explicit is y = pattern^x * 0 term. work backwards to find 0 term
Answers
We know that a geometric sequence is given by:
[tex]f(n)=f(1)r^{n-1}[/tex]where r is the common ratio of the sequence.
For this sequence we have that the common ratio is r=2, this comes from the fact that in the first day we have 6 dots, for the second day we have twelve and for the third day we have 24. We also notice that the first term is:
[tex]f(1)=8[/tex]Therefore the sequence is given by:
[tex]f(n)=8(2)^{n-1}[/tex]Now, to find the zeoth term we plug n=0 in the sequence above, therefore the zeroth term is:
[tex]\begin{gathered} f(0)=8(2)^{0-1} \\ f(0)=8(2)^{-1} \\ f(0)=4 \end{gathered}[/tex]Related Questions
The sum of three consecutive integers is −387. Find the three integers.
Answers
Answer:
-130, -129, -128
Step-by-step explanation:
consecutive integers are when one integer is greater than the previous one and so on... so assuming the smallest integer which we start with is "x", the next integer is "x+1", and the next integer is "x+1+1".
Adding all these together will give us the sum of three consecutive integers:
[tex]x+(x+1)+(x+1+1)[/tex]
Simplifying inside the parenthesis gives us
[tex]x+(x+1)+(x+2)[/tex]
Simplifying the entire expression gives us the following:
[tex]3x+3[/tex]
This is equal to -387 as stated in the problem, so let's set it equal to -387
[tex]3x+3=-387[/tex]
Subtract 3
[tex]3x=-390[/tex]
Divide by 3
[tex]x=-130[/tex]
Since the consecutive integers are just +1, then +2, we can define the three consecutive integers as
-130, -130 + 1, -130 + 2
which simplifies to
-130, -129, -128
I solved for Part A and the correct graph was answer A I just need Part B to be solved (at the bottom)
Answers
In Part (b) of this problem, we want to determine which function is the bes representation for the graph and table.
We are given:
To determine which function matches best, we can look at the parent function of a linear, logarithmic, and exponential function.
(see comparisons below):
Notice that our graph most closely resembles that of the exponential function. Therefore, the best model for the data would be an exponential function.
g(x)=2x-2f(x)=4x-1Find (g*f) (-9)
Answers
Given:
[tex]\begin{gathered} g(x)=2x-2 \\ f(x)=4x-1 \end{gathered}[/tex]The expression for g(f(x)) is,
[tex]\begin{gathered} g(f(x))=2(f(x))-2 \\ =2(4x-1)-2 \\ =8x-2-2 \\ =8x \end{gathered}[/tex]Substitute x=-9 in the above expression.
[tex]\begin{gathered} g(f(-9))=8\times-9 \\ =-72 \end{gathered}[/tex]Thus, the final value of the expression is -72.
Is 4b-2c leqslant 12 inequalities or not inequalities[tex] ax+by \leqslant c[/tex]
Answers
First, let's write the expression below:
[tex]4b-2c\leqslant12[/tex]Since the expression contains the symbol "<=" (that is, "lesser than or equal to") between two terms, the complete expression is an inequality.
In order to solve this inequality for a given variable, we need to rewrite the inequality such as one side of the inequality has only the wanted variable.
For example, solving the inequality for b, we have:
[tex]\begin{gathered} 4b-2c\leqslant12\\ \\ 4b\leq12+2c\\ \\ b\leq\frac{12+2c}{4}\\ \\ b\leq3+0.5c \end{gathered}[/tex]Given that the height of a trapezoid is 16 m and one base’s length is 25 m. Calculate the dimension of the other base of the trapezoid if its area is 352 m².
Answers
ANSWER:
19 m
STEP-BY-STEP EXPLANATION:
We have that the formula for the area of a trapezoid is the following:
[tex]A=\frac{B+b}{2}\cdot h[/tex]We substitute each value and calculate the length of the other base, like so:
[tex]\begin{gathered} 352=\frac{25+b}{2}\cdot16 \\ \\ 25+b=352\cdot\frac{2}{16}\frac{}{} \\ \\ b=44-25 \\ \\ b=19 \end{gathered}[/tex]The dimension of the other base of the trapezoid is 19 m
Find all the factors of 99.
Answers
The factors of 99 are: 1, 3, 9, 11, 33 and 99.
Find the probability of obtaining exactly seven tails when flipping seven coins. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
Answer:
Concept:
If you flip a coin once, there are
[tex]\text{2 possiblities}[/tex]Using the binomial probability formula below, we will have
[tex]P(x)=^nC_rp^xq^{x-r}[/tex]Where
[tex]\begin{gathered} p=probability\text{ of success} \\ q=probability\text{ of failure} \end{gathered}[/tex][tex]\begin{gathered} p=\frac{1}{2} \\ q=\frac{1}{2} \\ n=7 \\ x=7 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} P(x)=^nC_rp^xq^{x-r} \\ P(x=7)=^7C_7(\frac{1}{2})^7(\frac{1}{2})^{7-7} \\ P(x=7)=(\frac{1}{2})^7 \\ P(x=7)=\frac{1}{128} \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow\frac{1}{128}[/tex]Given the median QR and trapezoid MNOP, what is the value of X?M3.8033Rکد 73PA. 6B. 19(C. 2D, 5E 7F. Cannot be determined
Answers
SOLUTION
Consider the diagram below
Applying the rule in the diagram above, we have
[tex]|QR|=\frac{1}{2}(|ON|+|PM|)[/tex]Recall from the questions
[tex]\begin{gathered} |QR|=33 \\ |ON|=3x-8 \\ |PM|=7x+4 \end{gathered}[/tex]Then we substitute the parameters above into the expression above
[tex]\begin{gathered} 33=\frac{1}{2}(3x-8+7x+4) \\ \text{ Multiply both sides by 2} \\ 66=3x-8+7x+4 \\ \text{rerrange the terms and simplify } \\ 66=10x-4 \\ \text{collect like terms } \\ 66+4=10x \end{gathered}[/tex]simplify further
[tex]\begin{gathered} 70=10x \\ \text{divide both sides by 10} \\ x=\frac{70}{10} \\ \text{then} \\ x=7 \end{gathered}[/tex]Therefore the value of x is 7
Therefore the right option is E
Is the prime factor of 121 11x11?
Answers
The prime factor of 121 is simply 11.
11x11 =121, since you can't take 11 two times.
If f(2)= Vwhat is the rule of the inverse?
Answers
To find the inverse do these steps
1- Put f(x) = y
2- Switch x and y
3- solve to find the new y
Let us do that
[tex]y=\sqrt[]{\frac{x+4}{3}}[/tex]Switch x and y
[tex]x=\sqrt[]{\frac{y+4}{3}}[/tex]Now square the two sides to cancel the root
[tex]x^2=\frac{y+4}{3}[/tex]Multiply both sides by 3 to cancel the denominator
[tex]3x^2=y+4[/tex]Subtract 4 from both sides
[tex]3x^2-4=y[/tex]The rule is the answer D
What was the initial population at time t=0?Find the size of the bacterial population after 4 hours.
Answers
Answer;
[tex]\begin{gathered} a)\text{ 195 bacteria} \\ b)\text{ 3,291,055,916 bacteria} \end{gathered}[/tex]Explanation;
a) We want to get the initial population of the bacteria
We start by writing a formula that links the initial bacteria population to a later bacteria population after time t
[tex]A(t)=I(1+r)^t[/tex]where A(t) is the bacteria population at time t
I is the initial bacteria population
r is the rate of increase in population
t is time
Now, let us find r
At t = 10; we know that A(t) = 2I
Thus, we have it that;
[tex]\begin{gathered} 2I=I(1+r)^{10} \\ (1+r)^{10}\text{ = 2} \\ 1+r\text{ = 1.0718} \\ r\text{ = 1.0718-1} \\ r\text{ = 0.0718} \end{gathered}[/tex]Now, let us find I, since we have r. But we have to make use of t= 80 and A(t) = 50,000
Thus, we have;
[tex]\begin{gathered} 50,000=I(1+0.0718)^{80} \\ I\text{ = }\frac{50,000}{(1+0.0718)^{80}} \\ I\text{ = 195} \end{gathered}[/tex]The initial population is 195 bacteria
b) For after 4 hours, we have to convert to minutes
We know that there are 60 minutes in an hour
So, in 4 hours, we have 4 * 60 = 240 minutes
Now, we proceed to use the formula above with I = 195 and t = 240
We have that as;
[tex]\begin{gathered} A(240)=195(1+0.0718)^{240} \\ A(240)\text{ = 3,291,055,916 bacteria} \end{gathered}[/tex]Which equation is equivalent to StartRoot x EndRoot + 11 = 15?
Answers
Answer:
x+121=225
Step-by-step explanation:
√x+11=15
to find the equivalent let's square both sides
(√x)²+11²=15²
x+121=225
This answer is the only one that matches the question
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i need help please,solve and explain it's 4th grade math.. thank you.
Answers
What you can say about 12th, 18th and the 21st child, depends if these numbers are multiples of 4 (every 4th child is wearing spectacles), 3 (every 3rd child is a girl) and 2 (every 2nd child is wearing a white shirt).
If a numer is multiple of another one, then the quotient between them is an integer number.
for 12th:
12/4 = 3
12/3 = 4
12/2 = 6
12 is multiple of 3, 4 and 6.
Then, 12th child is wearing spectacles, a white shirt and is a girl.
for 18th:
18/4 = 4.5
18/3 = 6
18/2 = 9
18 is multiple of 3 and 2.
Then, 18th child is a girl and is weraing a white shirt
for 21th:
21/4 = 5.25
21/3 = 7
21/2 = 11.5
21 is multiple of 3.
THen, 21st child is a girl.
Describe the complement of the given event. 73% of nineteen year old males are at least 166 pounds
Answers
Solution
- The event is "73% of nineteen year old males are at least 166 pounds"
- The complement of this event is the set of all 19 year old males not in the event described above.
- These set of 19 year olds, must represent the remaining 27% of the population.
- Also, they would weigh less than 166 pounds.
- Thus, the complement of the event is:
"27% of nineteen year old males weigh less than 166 pounds"
Hi, the area of a circle is 100 sq. mm. The radius is 5.64 mm. What is the circumference?
Answers
11.28π mm
1) Since the area is 100 mm² we can plug into the Circumference formula to find out the perimeter of that circle
2)
[tex]\begin{gathered} C=2\pi\cdot r \\ C=2\cdot\pi\cdot(5.64)^{} \\ C=11.28\pi \end{gathered}[/tex]3) Hence, the circumference of that circle is 11.28π mm
If the carrier transmits 12 kW, what is the modulated power if modulation index is (1/√2) ?
Answers
The modulated power is 15 kW.
The modulated power is given by the formula P_T= P_C (1+ (m_a^2)/2) and is connected to the total power of the carrier signal and the modulation index.
To obtain the modulated power, substitute the values in the given equation and simplify.
Given,
Power of carrier signal (P_C) = 12 kW
= 12000 W
Modulation index ( m_a) = 1/√2
Consequently, when we change the variables in the equation, we get
P_T= P_C (1+ (m_a^2)/2)
=12000 (1+ (1/√2)^2/2)
= 12000 (1+ 1/4)
= 12000 * 5/4
= 3000*5
= 15000 W
= 15 kW
Hence, modulated power is 15 kW.
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q(v)= int 0 ^ v^ prime sqrt 4+w^ 5 dw ther; q^ prime (v)=
Answers
ANSWER
[tex]q^{\prime}(v)=\sqrt{4+(v^7)^5}[/tex]EXPLANATION
We want to find the derivative of the given function:
[tex]q(v)=\int_0^{v7}\sqrt{4+w^5}dw[/tex]When the lower limit of an integral is a constant and the upper limit of the integral is a variable, the derivative of this is the function inside the integral in terms of the upper limit of the integral.
In other words, the derivative of the given integral function is:
[tex]q^{\prime}(v)=\sqrt{4+(v^7)^5}[/tex]That is the answer.
In the diagram below of triangle DEF, G is a midpoint of DE and H is a midpoint of EF. IfGH = 50 -- 87, and DF = 9x + 0, what is the measure of GH? E H D F
Answers
GH = 18
Explanations:From the diagram:
DF = 9x + 0
GH = 50 - 8x
Since G is a midpoint of DE and H is a midpoint of EF, using the midpoint theorem:
DF = 2GH
9x + 0 = 2 (50 - 8x)
9x = 100 - 16x
9x + 16x = 100
25x = 100
x = 100/25
x = 4
Substituting the value of x into GH = 50 - 8x
GH = 50 - 8(4)
GH = 50 - 32
GH = 18
Louis borrowed $500 from his bank. His bank will charge Louis 8% simple interest per year to loan him the money. If he paid back the total amount he owed the bank, including interest, in 6 months, how much should he have paid?
Answers
The amount that he owed the bank and paid is $520.
What will the interest be?The simple interest is calculated as:
= Principal × Rate × Time / 100
Principal = $500
Rate = 8%
Time = 6 months = 6/12 = 0.5 years
The interest will be:
= PRT / 100
= (500 × 8 × 0.5)/100
= 2000/100
= $20
The amount paid back will be:
= Principal + Interest
= $500 + $20
= $520
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f(x) varies inversely with x and f(x)=−10 when x = 20. What is the inverse variation equation? Responses f(x)=−2x f ( x ) = − 2 x f(x)=−5x f ( x ) = − 5 x f(x)=−200x f ( x ) = − 200 x f(x)=−0.5x f ( x ) = − 0.5 x
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The equation representing the constant of proportionality is k = xf(x) and the constant of proportionality k = -200
What is proportionality?In mathematics, proportionality indicates that two quantities or variables are related in a linear manner. If one quantity doubles in size, so do the other; if one of the variables diminishes to 1/10 of its former value, so does the other.
Likewise, if the variables are inversely proportional to one another, as one quantity increases, the other quantity decreases by the same proportion or quantity.
We can proceed to substitute the values into the equation above.
k = xf(x)
k = 20 * (-10)
k = -200
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Hello I need help with the following question. 8. Use the given graph of the function f to find the domain and range(−6,6)8 The domain of f is(Type a compound inequality.)The range of f is(Type a compound inequality.)
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We are to use the given graph in the question to find the domain and range
From the graph,
The lowest value of x plotted is x = -14
The highest value of x plotted is x = 12
The loowest value of y is y= -4
The highest value of y is y = 6
Hence, the domain is
[tex]-14\leq x\leq12[/tex]While the range is
[tex]-4\leq y\leq6[/tex]Determine whether the lines are parallel, intersect, or coincideY = 4x - 53x + 4y = 7
Answers
Answer:
Explanation:
Given:
y=4x-5
3x+4y=7
We can check if the lines are parallel, intersect, or coincide by graphing. To graph, we plug in any values for x to determine the y values.
The graph of the lines is shown below:
So based on the graph, the lines intersect at a point.
Therefore, the lines intersect.
which is an incorrect rounding for 53.864a) 50b) 54c) 53.9d) 53.87
Answers
The incorrect rounding is 53.87
Explanations:The given number is 53.864
If the number is approximated to 2 decimal places
53.864 = 53.86
If the number is approximated to 1 decimal place
53.864 = 53.9
If the number is approximated to the nearest unit
53.864 = 54
If the number is approximated to the nearest tens:
53.864 = 50
Note: 53.864 cannot be approximated to 53.87 because the third decimal place (4) is not up to 5
Fill in the blank. In the triangle below, Z = 52° 35
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Solution
Since the diagram given is a Triangle, therefore, the sum of it's interior angles is 180 degrees
However, the Triangle is a right angle Triangle since on of its angles is 90 degrees.
The sum of its Interior angles is given by;
[tex]\begin{gathered} z+52+90=180 \\ \\ \Rightarrow z+142=180 \end{gathered}[/tex]subtracting 142 from both sides,
[tex]\begin{gathered} \Rightarrow z+142-142=180-142=38 \\ \\ \Rightarrow z=38^0 \end{gathered}[/tex]Therefore, z = 38
1 punto Two distinct coplanar lines that do not intersect are known as lines * A. parallel B. perpendicular C. skew D. Tangent
Answers
Coplanar lines are lines that lies in the same plane.
By definition, two distince lines that lies in the same plane and that do not intersect are said to be parallel
Hence the correct choice is A
y=-5x+6y=-3x-2x=y= and the grap
Answers
y = -5x + 6 .................1
y = -3x - 2......................1
first equate the two equations to find x and y
-5x + 6 = -3x - 2
-5x +3x = -2 - 6
-2x = -8
x = -8/-2
x = 4
Next substitute x in equation 1
y = 5(4) + 6
y = 20 + 6
y = 26
Graphically,
y = -5x + 6
for x = 0
y = -5 x 0 + 6
y = 6
for y = 0
0 = -5x + 6
5x = 6
x = 6/5
x = 1.2
fiirst plot the coordinate (0,6) and (1.2,0) on the graph for the first equation to get the first straight line.
y = -3x - 2
x = 0
y = -3 x 0 - 2
y = -2
y = 0
0 = -3x - 2
3x = -2
x = -2/3
x = -0.67
plot the coordinate on the graph
solution for this question is (4,26)
If a projectile is fired straight upward from the ground with an initial speed of 224 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2.+224t Find the maximum height of the projectile.
Answers
The height reached by the projectile is 784 feet.
What is the maximum height of the projectile?
The projectile experiments an uniformly accelerated motion due to gravity, whose height is represented by the quadratic equation:
h(t) = - 16 · t² + 224 · t
Where t is the time, in seconds.
In this problem we need to find the maximum height reached by the projectile, which can be found by finding the vertex form of the quadratic equation:
h(t) = - 16 · (t² - 14 · t)
h(t) - 16 · 49 = - 16 · (t² - 14 · t + 49)
h(t) - 784 = - 16 · (t - 7)²
The maximum height of the projectile is 784 feet.
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The function c = 100+.30m represents the cost c (in dollars) of renting a car afterdriving m miles.How many miles would a customer have to drive for the cost to be $149.50?
Answers
149.5 = 100 + .30m
149.5 - 100 = .30m
49.5 = .30m
Divide both sides by 0.30
m = 49.5/0.3
m =165
Option D
Cleo can paint a room in 8 hours, while Phil can paint the same room in 6 hours. If they paint theroom together, how long will it take them to paint the room?How many hours and how many minutes?
Answers
According to the given data we have the following:
Cleo can paint a room in 8 hours, so this is=1/8x
Phil can paint the same room in 6 hours=1/6x
In order to calculate how long it take them to paint the room we would solve the following equation:
(1/6)(x)+(1/8)(x)=1
To solve this equation we would first multiply both sides by 24
Hence:
24*(1/6)(x)+24*(1/8)(x)=24
4x+3x=24
7x=24
x=24/7
x= 3 3/7 hours
Therefore It will take them 3 and 3/7 hours to pain the room.
In minutes it will take to them 205 minutes.
Determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. Express numbers as integers orsimplified fractions.u^2+20u+n
Answers
SOLUTION
The expression is given as
[tex]u^2+20u+n[/tex]The value of n makes the expression a perfect square trinomial.
To find the value of n, we have
Identify the coefficient of u and divide by 2
[tex]\begin{gathered} \text{the coefficient of u=20} \\ \text{divide by 2=}\frac{\text{20}}{2}=10 \end{gathered}[/tex]Then square the result, we have
[tex]\begin{gathered} 10^2=100 \\ \text{hence } \\ n=100 \end{gathered}[/tex]Then the complete trinomial of the polynomial becomes
[tex]u^2+20u+100[/tex]To factor as a square of a binomial we use the perfect square trinomial above
[tex]\begin{gathered} u^2+20u+100 \\ u^2+20u+10^2 \\ \text{Then} \\ (u+10)^2 \end{gathered}[/tex]Therefore
The vaue of n = 100
The factor as the square of a binomial is (u+ 10)²