Find the next two numbers in the sequence 1, 5, 17, 53, 161, _____, _____
The required missing term of the given sequence is given as 485 and 1457.
What is a sequence?The sequence is a pattern of placing the values in a specified manner.
here,
5 = 1 + 4
Since, [tex]b_0 = 4[/tex] and [tex]a_0 = 1[/tex]
17 = 5 + 12
So, the general term is given as
[tex]a_n = a_{n-1} + b_{n}[/tex]
Where, [tex]b_n = 3b_{n-1}[/tex]
For 6 th term
6 the term = 161 + 3(108)
6 the term = 485
For the 7th term
7th term = 485 + 3(324)
7th term = 1457
Thus, the required missing term of the given sequence is given as 485 and 1457.
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If a and b are positive numbers, find the maximum value of f(x) = xa(7 â x)b on the interval 0 ⤠x ⤠7.
Final Answer:
The maximum value of f(x) = xa(7 - x)b on the interval 0 ≤ x ≤ 7 occurs when x = 7/2 for a > 0 and b > 0.
Explanation:
To find the maximum value of f(x) on the interval 0 ≤ x ≤ 7, we'll use calculus. First, take the derivative of f(x) with respect to x.
f'(x) = a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a
Setting f'(x) = 0 to find critical points:
a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a = 0
Solving for x gives x = 7/2. To determine if this point is a maximum, minimum, or inflection point, we'll use the second derivative test.
f''(x) = a * (7 - x)^(b-1) * x^(a-2) * ((a - 1) * x - 7) - b * a * (7 - x)^(b-2) * x^(a-1) * ((b - 1) * x - 7)
When x = 7/2, f''(7/2) > 0, indicating a concave-up shape and confirming it as a local minimum. Therefore, the maximum value of f(x) occurs at the endpoints of the interval, x = 0 and x = 7, or potentially at x = 7/2 if it surpasses these values.
For a > 0 and b > 0, plugging in x = 7/2 into f(x) = xa(7 - x)b yields the maximum value of the function within the given interval.
Understanding the critical points through derivatives helps identify where the maximum or minimum points occur in the function. In this case, x = 7/2 stands as the point of maximum value within the interval 0 ≤ x ≤ 7 when a and b are both positive.
Take a look at the figure. What is the value of y?
A. y = 32 B. y = 64 C. y = 14 D. y = 16
1/2 divided by 5=1 over blank I need to know the blank number
Simplify 12 to the sixteenth power over 12 to the fourth power
Any number that is divisible by 2 is also divisible by 8. Find a counter example to show that the conjecture is false. 24 28 16 32
Mario bought $5 worth of stamps at the post office. He bought ten more 6-cent stamps than 10-cent stamps. The number of 8-cent stamps was three times the number of 10-cent stamps. He also bought two 20-cent stamps. How many of each kind of stamp did he purchase?
Help me Solve this and explain to me the steps thank you
The larger of two supplementary angles measures 20° less than four times the measures of the smaller angle .find the degree measure of each angle
We want to create a system of equations that allows us to find the values of two supplementary angles.
We will find that the larger angle measures 140° and the smaller one measures 40°.
------------------------
Two angles A and B are supplementary if their measures add up to 180°, so we have:
A + B = 180°.
Let's assume that B is the larger one, we also do know that:
"The larger is 20° less than 4 times the smaller"
Then we can write:
B = 4*A - 20°.
Then our system of equations is:
A + B = 180°.
B = 4*A - 20°.
To solve it we need to isolate one variable in one of the equations and replace it on the other equation. Here we can see that B is already isolated on the second equation, so we can replace it in the first one to get:
A + B = 180°.
A + (4*A - 20°) = 180°
Now we can solve this for A:
A + (4*A - 20°) = 180°
5*A - 20° = 180°
5*A = 180° + 20° = 200°
A = 200°/5 = 40°
Now that we know the value of A we can get the value of B:
B = 4*A - 20° = 4*40° - 20° = 140°
Then the larger angle measures 140° and the smaller measures 40°
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Check my answers please -
The yearly attendance at a local move theatre is 42,000 and grows continuously at a rate of 5.9% each year. what is the approximate attendance at the movie theater in seven years?
A. 43,467
B. 59, 346
C. 63, 476
D. 62, 737 **
The number of customers that visit a local small business is 29,600 and has been continuously declining at a rate of 2.9% each year. what is the approximate number of customers that visit the buisness in 10 years?
A. 22,149 **
B. 21,874
C. 39,558
D. 22,054
I can tell you for sure that the answer to the first one is
C) 63,475
and the second is
A) 22,149
The attendance at the movie theater in seven years will be 63,476. Then option C is correct. And the number of customers that visit the business in 10 years will be 22,149. Then option A is correct.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The yearly participation at a neighborhood movie theater is 42,000 and develops ceaselessly at a pace of 5.9% every year. Then the attendance at the movie theater in seven years will be given as,
[tex]\rm y = 42,000 \times (e)^{0.059\times 7}\\\\y = 42,000 \times (e)^{0.413}[/tex]
Simplify the equation further, then we have
y = 42,000 × 1.5113
y = 63,476
The quantity of clients that visit a neighborhood private venture is 29,600 and has been persistently declining at a pace of 2.9% every year.
Then the number of customers that visit the business in 10 years will be given as,
[tex]\rm y = 29,600\times (e)^{-0.029\times 10}\\\\y = 29,600 \times (e)^{-0.29}\\[/tex]
Simplify the equation further, then we have
y = 29,600 × 0.748
y = 22,149
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Determine whether the given value is a statistic or a parameter. upper a sample of students is selected and it is found that 25 % own a computer.a sample of students is selected and it is found that 25% own a computer.
A bag contains 44 red balls and 55 blue balls. 22 balls are selected at random. find the probability of selecting 22 red balls.
The probability of selecting 22 red balls is [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
A bag contains 44 red balls and 55 blue balls
The total number of balls=44+55=99
22 balls are selected at random from bag.
We need to find the probability of selecting 22 red balls.
The probability of selecting 22 red balls from 44 balls
[tex]^{44} C_{22}[/tex]
2,104,098,963,720
and [tex]^{99} C_{22}[/tex] is 5.7190121704386E+21
So probability of selecting 22 red balls is
[tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
Hence, the probability of selecting 22 red balls is [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
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What is the definition to an equation?
Karen Johnson rode her 27” bicycle to the store and back. The store is 1 mile from Johnson’s Home. Approximately how many rotations did Johnson’s bicycle wheels make in going to the store and back
You have the answer?
how do u do that 2*2/2*2
Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____?
Solve.
2x + 6 - 7x = 21
Two airplanes left the same airport and arrived at the same destination at the same time. The first airplane left at 8:00 a.m. and traveled at an average rate of 496 miles per hour. The second airplane left at 8:30 a.m. and traveled at an average rate of 558 miles per hour. Let x represent the number of hours that the first plane traveled. How many hours did it take the first plane to travel to the destination? Enter an equation that can be used to solve this problem
Answer:
4.5 hours
[tex]496 x= 558 x-279[/tex]
Step-by-step explanation:
We are given that two airplanes left the same airport and arrives at the same destination at the same time.
We have to find the number of hours taken by first plane to travel to the destination and find the equation that can be used to solve this problem
We are given that the first airplane left at 8:00 a.m
Let y be the distance traveled by the first airplane
The average rate of first airplane =496 miles per hour
The average rate of second airplane =558 miles per hour
Let x represents the number of hours that the first airplane traveled.
The number of hours that the second plane traveled =x-0.5
Because the second airplane take half an hour less than the first airplane
We know that [tex] distance=speed\times time [/tex]
[tex]d=496 x[/tex]
[tex]d=558(x-0.5)[/tex]
[tex]496 x= 558 x-279[/tex]
[tex]279=558 x-496 x[/tex]
[tex]279=62 x[/tex]
[tex]x=\frac{279}{62}[/tex]
x=4.5 hours
Hence, the first airplane takes 4.5 hours to travel to the destination.
N an algebra classroom, a teacher has created an estimation game using a jar of pennies. six students remain in the contest. each student makes one guess and their guesses are as follows: 62, 52, 59, 42, 49, 65. one guess is 12 away from the exact number of pennies in the jar while the other guesses are 1, 4, 6, 9, and 11 pennies away. determine exactly how many pennies are in the guessing jar.
How many ways can you split 12 people into 3 groups?
Algebra help please.
Find the value of 21 + 4(3^2 - 5).
25
37
100
the answer would be 37
What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y= x/3−1 ?
The drama club at smith valley middle school is selling cookie dough in order to raise money for costumes. if each tub cookie dough costs $4.75, how many tubs must members sell to make $570.00?
Sam deposited $350 into a savings account that paid 5% in simple interest. When he withdrew his money 8 months later, how much interest did he receive?
POINTS POINTS POINTS POINTS POINTS! harder question!
45(34- 2)
Answer:
answer is 1440,ok
Step-by-step explanation:
Greatest common factor
I need a little help please Brainliest
For the first image, the median range would be 88. In order to find the median, you'll place all your numbers in numerical order (smallest to largest). If there are an odd amount of numbers, find the one directly in the middle. If there is an even amount, you'll take the two most central ones and find the mean, that will tell you the median. Therefore, B (88) would be the answer to your first one.
The second one would be C (20.4). It's asking for the mean. In order to find the mean of a set of numbers, you'll simply add up all of the numbers and divide by how many numbers are in your number set. That gives you the mean.
a) Simplify the expression and explain each step. (2 points)
4(3x + 2) – 2
b) Factor the expression completely. (1 point)
20b – 16
Answer:
a) [tex]4\left(3x+2\right)-2=12x+6[/tex]
b) [tex]20b-16= 4\left(5b-4\right)[/tex]
Step-by-step explanation:
a) To simplify the expression you must:
Expand [tex]4(3x + 2)[/tex]:
Apply the distributive law: [tex]\:a\left(b+c\right)=ab+ac[/tex]
[tex]a=4,\:b=3x,\:c=2\\\\4\left(3x+2\right)=4\cdot \:3x+4\cdot \:2[/tex]
Simplify [tex]4\cdot \:3x+4\cdot \:2= 12x+8[/tex]
[tex]12x+8-2[/tex]
Subtract the numbers: [tex]4\left(3x+2\right)-2=12x+6[/tex]
b) To factor the expression [tex]20b - 16[/tex] you must:
Rewrite 16 as [tex]4\cdot 4[/tex] and 20 as [tex]4\cdot 5[/tex]
[tex]20b-16=4\cdot \:5b-4\cdot \:4[/tex]
Factor out common term 4
[tex]20b-16= 4\left(5b-4\right)[/tex]
Write an inequality that represents the verbal expression. All real numbers greater than or equal to 74