Drag each number to the correct location on the statements. Not all numbers will be used. Consider the sequence below. --3, -12, -48, -192, ... Complete the recursively-defined function to describe this sequence. f(1) =...... f(n) = f(n-1) × .....for n = 2, 3, 4... 3, 2, 3, 4, 12, -4
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following sequence:
[tex]-3,-12,-48,-192...[/tex]f(1), is the first term of the sequence, therefore, it would be:
[tex]f(1)=-3[/tex]Now, we calculate the common ratio, just like this:
[tex]\begin{gathered} r=\frac{-192}{-48}=4 \\ \\ r=\frac{-48}{-12}=4 \\ \\ r=\frac{-12}{-3}=4 \end{gathered}[/tex]So the sequence would be:
[tex]f(n)=f(n-1)\cdot4[/tex]
Related Questions
Translate and solve: The difference of a and 7 is 11
Answers
Answer:
(B)a=18
Explanation:
The difference of a and 7 translated as an expression is:
[tex]a-7[/tex]Thus, the equation is:
[tex]a-7=11[/tex]To solve for a, add 7 to both sides of the equation:
[tex]\begin{gathered} a-7+7=11+7 \\ a=18 \end{gathered}[/tex]The correct choice is B.
A granite pyramid is 50 feet high and has a square base 30 feet on a side. If granite weighs 180 pounds per cubic foot, what is the weigh in tons of the pyramid?
Answers
The weight of the granite pyramid in tons is 1350 tons.
How to find the weight of the pyramid granite in tons?A pyramid is a three-dimensional shape.
The granite pyramid is 50 feet high and has a square base of 30 feet on a side.
Granit weighs 180 pounds per cubic foot.
Therefore, the weight in tons of the pyramid can be calculated as follows;
Hence,
volume of the granite pyramid = 1 / 3 b² h
Therefore,
volume of the granite pyramid = 1 / 3 × 30² × 50
volume of the granite pyramid = 45000 / 3
volume of the granite pyramid = 15000 ft³
Hence,
1 ft³ = 180 pounds
15000 ft³ = ?
weight = 2700000 pounds
1 pounds = 0.0005 tons
2700000 pounds = ?
Therefore,
weight of the pyramid granite in tons = 1350 tons
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In the right trapezoid ABCD, BC is parallel to AD, and AD is contained in the line whose equation is y=−12x+10 y = − 1 2 x + 10 . What is the slope of the line containing BC? Explain how you got your answer
Answers
how to find the width to a pyramid with the volume height and length
Answers
The volume of a pyramid is given by the formula
[tex]V_{\text{pyramid}}=\frac{1}{3}\times base\text{ area}\times height[/tex]Write out the given dimensions
[tex]\begin{gathered} \text{Volume}=80\operatorname{cm}^3 \\ \text{Height}=10\operatorname{cm} \\ \text{length}=6\operatorname{cm} \\ \text{width}=\text{unknown} \end{gathered}[/tex]Since the base of the pyramid is a rectangle, the base area is
[tex]A_{\text{rectangle}}=\text{width }\times length[/tex]Substituting the given dimensions to get the value of the width\
[tex]\begin{gathered} V_{\text{pyramid}}=\frac{1}{3}\times width\times length\times height \\ 80=\frac{1}{3}\times width\times6\operatorname{cm}\times10\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} 80\operatorname{cm}=20\times width \\ \text{width}=\frac{80}{20} \\ \text{width}=4\operatorname{cm} \end{gathered}[/tex]Hence, the width of the pyramid is 4cm
Factor out the greatest negative common factor for the expression.- 8mºn - 40m?n4Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.OA. - 8mºns - 40mºn4-(Factor completely.)OB. There is no common factor other than 1.
Answers
Solution
- The question tells us to factor out the greatest negative common factor of the expression below:
[tex]-8m^3n^5-40m^3n^4[/tex]- The greatest negative common factor is the negative monomial with the largest magnitude, which divides evenly into each term of the given expression.
- Let us factorize the expression to derive this greatest negative common factor below:
[tex]\begin{gathered} -8m^3n^5-40m^3n^4 \\ -8,m^3,\text{ and }n^4\text{ are all co}mmon\text{ in the expression above.} \\ \text{Thus, we have:} \\ \\ -8m^3n^4(n-5) \end{gathered}[/tex]Final Answer
The answer is
[tex]-8m^3n^4(n-5)[/tex]Hello! I think the answer is 398. Would you mind guiding me?
Answers
Given -
Total Personal Videos Players = 400
Video Players with no defects = 398
Number of Video Players sent = 2000
To Find -
The number of Video Players with no defects =?
Step-by-Step Explanation -
Total Personal Videos Players = 400
Video Players with no defects = 398
So,
Two video players in every 400 are defected
So,
2000 = 5 × 400
So,
Total number of Video Players with defects = 5 × 2 = 10
Hence,
The number of Video Players with no defects = 2000 - 10 = 1990
Final Answer -
The number of Video Players with no defects = 1990
If the point (-6, 4) is dilated by a scale factor of 1/2, the resulting point is (-3,2).TrueFalse
Answers
(-6,4)
Multiply each coordinate by 1/2
( -6 * 1/2 , 4 * 1/2) = (-3,2)
True
This is a non graded practice that I am doing. I don’t under these questions 5-11
Answers
7. The intersection of two intersecting lines is a point.
In the given image, we see that lines NQ and ML intersect at point P.
Therefore, the intersection of NQ and ML is P.
Solve the system of two linear inequalities graphically.Sy < -2x + 3y > 6x – 9Step 1 of 3: Graph the solution set of the first linear inequality.
Answers
The red graph represents y < -2x + 3
The blue graph represents y > 6x - 9
The solutions of the system of inequalities lie on the red-blue shaded
The part which has two colors
Since the first inequality is y < -2x + 3, the shaded is under the line
Since the second inequality is y > 6x - 9, the shaded is over the line
The common shaded of the two colors represents the area of the solutions of the 2 inequalities
The type of boundary lines is dashed
The points on the boundary lines are
For the red line (0, 3) and (4, 0)
For the blue line (0, -9) and (1, -3)
There is a common point on the two lines (1.5, 0)
multiply mentally to find the product
Answers
8 * 404 = 8(----- + 4)
At first, we will split 404 into two numbers one of them is 4
To find the other number subtract 4 from 404
404 - 4 = 400
8 * 404 = 8(400 + 4)
Now we will multiply 8 by 40 and 8 by 4
8(400 + 4) = 8 * 400 + 8 * 4
It is easy to find the product of 8 and 4
8 * 4 = 32
8 * 400 = 3200
Let us add them
3200 + 32 = 3232
The answer is 3232
Which of the following represents the translation of R (-3, 4), along the vector <7, -6> <-1, 3>.
Answers
Solution
Step 1:
The translation is a term used in geometry to describe a function that moves an object a certain distance.
Step 2:
Pre-mage R = (-3,4)
Step 3:
When moved along (7, -6) the new coordinates become:
R' = (-3+7 , 4 - 6 ) = (4 , -2)
R' = ( 4 , -2 )
Step 4:
When moved along (-1, 3) the new coordinates become:
R'' = ( 4-1 , -2+3 ) = ( 3 , 1 )
R'' = (3 , 1)
Final answer
[tex]R(-3\text{ , 4\rparen }\rightarrow\text{ R'\lparen4 , -2\rparen }\rightarrow\text{ R''\lparen3 , 1\rparen}[/tex]Solve each equation for the given variable.-2x + 5y = 12 for ySolve each equation for y. Then find the value of y for each value if x.y + 2x = 5; x = -1, 0, 3
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
-2x + 5y = 12
y = ?
Step 02:
We must apply algebraic rules to find the solution.
-2x + 5y = 12
5y = 12 + 2x
y = 12 / 5 + 2x / 5
[tex]y\text{ =}\frac{12}{5}\text{ + }\frac{2x}{5}[/tex]The answer is:
y = 12 / 5 + 2x / 5
Please it’s due todayAre there any limitations on the inputs of the equation?Does the graph have any symmetry?If so, where? When will the graph point upward? When will it point downward?
Answers
We have the following:
1.
There is no limitation on the input values, the domain is all real numbers.
2.
Yes, it has an axis of symmetry at the point (0,0)
3.
The graph point upward in the interval:
[tex](0,\infty)[/tex]The graph point downward in the interval:
[tex](-\infty,0)[/tex]An initial amount of $3500 is invested in an account at an interest rate of 6% per year, compounded continuously. Assuming that no withdrawals aremade, find the amount in the account after two years.Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
For this problem we use the continuously compounded interest formula:
[tex]M=M_0e^{rt}[/tex]where M_0 is the initial amount, r is the interest rate per year and t is the number of years.
Substituting M_0=$3500, r=0.06, and t=2 we get:
[tex]\begin{gathered} M=3500e^{0.06\cdot2}=3500e^{0.12} \\ M=3946.24 \end{gathered}[/tex]The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 30.8 miles per gallon, with a standard deviation of 4.1 miles per gallon. Assume that a Normal model applies. Find the probability that a randomly selected automobile will average: 1. Less than 28 miles per gallon. Chapter 6 Assignment 2. More than 26 miles per gallon.
I need much help with this normal distribution question.
Answers
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean.
What is meant by normal distribution?The probability density function for a continuous random variable in a system defines the Normal Distribution.
A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean. This shows that data close to the mean occur more frequently than data far from the mean. On a graph, the normal distribution is represented by a "bell curve."
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Ethan's income is 4500 per month a list of some of his expenses appear below what percent of Ethan's expenses is food?
Answers
Ethan's earns 4500$ per month*
the amount spent on the food is 600 $
so percentage will be'
[tex]=\frac{4500}{600}=\frac{1500}{200}=7.5\text{ \%}[/tex]so the answer is the percentage amount spent on food is, 7.5 %
Find the perimeter of the isosceles triangle in simplest form. x2 + 20 units 2x units
Answers
The perimeter of an isosceles triangle is given by:
[tex]P\text{ = 2a + b}[/tex]From the question, b = 2x; a = x^2 + 20
[tex]P\text{ = 2a }+b=2(x^2+20)+2x=2x^2+40\text{ + 2x}[/tex][tex]P=2x^2\text{ + 2x + 40}[/tex]The amount of freight transported by rail in the u.s was about 580 billion ton-miles in 1960 and has been increasing at a rate of 2.32% per year since then.a. write a function representing the amount of freight, in billions of ton-miles, transported annually. ( 1960 = year 0 )b. graph the functionc. in what year would you predict that the number of ton-miles would have exceeded or would exceed 1 trillion (1,000 billion)?
Answers
The amount of freight transported by rail was 580 billion ton-miles in 1960.
The amount increased at a rate of 2.32% per year.
a. The growth in freight transport with respect to the passing years can be expressed as exponential growth. The general form of this equation is
[tex]y=a(1+r)^x[/tex]Where
y represents the final number after "x" periods of time
a represents the initial number at x=0
r represents the growth rate, expressed as a decimal value
x represents the number of time intervals that have passed
For this example, the initial amount is a=580 billion
The growth rate is r=2.32/100=0.0232
You can determine the equation as follows:
[tex]y=580(1+0.0232)^x[/tex]b. This function is of exponential increase, its domain is all real numbers and its range is all positive real numbers, you can symbolize it as y > 0, it's increasing, and it has a horizontal asymptote as x approaches -∞
To graph it, you have to determine at least two points of the graph, I will determine 3
For x=-100
[tex]\begin{gathered} y=580(1+0.0232)^{-100} \\ y=58.53 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} y=580(1+0.0232)^0 \\ y=580 \end{gathered}[/tex]For x=10
[tex]\begin{gathered} y=580(1+0.0232)^{10} \\ y=729.51 \end{gathered}[/tex]The points are
(-100,58.53)
(0,580)
(10,729.51)
Plot the points and then draw an increasing line from -∞ to +∞
c. To determine the time when the freight transported will exceed 1000 billion tom-miles, you can use the graph, just determine the value of x, for which y=1000
This value is approximate x=23.57
This means that counting from 1960 will take 23 and a half years to reach over a trillion ton-miles transported.
Add the number of years to the initial year to determine the date:
[tex]1960+23=1983[/tex]By 1983 the number of ton-miles transported will exceed the trillion.
(a) How high is the javelin when it was thrown? How do you know?(b) How far from the thrower does the javelin strike the ground?
Answers
The height of the javelin is given by
[tex]h(x)=-\frac{1}{20}x^2+8x+6[/tex]Here, x is the horizontal distance from the point at which the javelin is thrown.
a)
When the javelin is thrown, the horizontal distance from the point at which the javelin is thrown is zero. So, put x = 0 to find the height of the javelin when thrown. So, the distance:
[tex]\begin{gathered} h(0)=-\frac{1}{20}(0)^2+8(0)+6 \\ =0+0+6 \\ =6 \end{gathered}[/tex]Thus, the height of the javelin when it was thrown is 6 ft.
b)
When the javelin strikes the ground the value of h(x) is zero.
Find the value of x when h(x) is zero.
[tex]\begin{gathered} h(x)=0 \\ -\frac{1}{20}x^2+8x+6=0 \\ -x^2+160x+120=0 \\ x^2-160x-120=0 \end{gathered}[/tex]Now, the roots of the equation are x = 160.74 and x = -0.74.
The distance cannot be negative. So, the javelin is 160.74 ft far from the thrower when it strikes the ground.
find the slop of the line passing through the points (1,-1) and (-1,1)
Answers
Answer:
I think its done this way. But I don't know if the answer is correct.
find the perimeter of a garden that measures 6 feet by 3/4 foot?
Answers
The perimeter of a garden that measures 6 feet by 3/4 foot is 13.50 feet.
What is the perimeter?The perimeter of a rectangle is calculated thus:
Perimeter = 2(Length + Width)
From the information, we want to find the perimeter of a garden that measures 6 feet by 3/4 foot.
This will be illustrated thus:
Perimeter = 2(Length + Width)
Perimeter = 2(6 + 3/4)
Perimeter = 2(6 + 0.75)
Perimeter = 2(6.75)
Perimeter = 13.50
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open up or down, vertex:(0,-4), passes through: (-3,5)
Answers
open up or down, vertex:(0,-4), passes through: (-3,5)
In this problem we have a vertical parabola open upward
the equation in vertex form is equal to
y=a(x-h)^2+k
where (h,k) is the vertex
we have
(h,k)=(0,-4)
substitute
y=a(x)^2-4
Find the value of a
with the point (-3,5)
substitute in the equation
5=a(-3)^2-4
5=9a-4
9a=5+4
9a=9
a=1
therefore
the equation is
y=x^2-4
answer is
f(x)=x^2-4Adam is working in a lab testing bacteria populations. After starting out with a population of 390 bacteria, he observes the change in population and notices that the population quadruples every 20 minutes.Step 2 of 2 : Find the population after 1 hour. Round to the nearest bacterium.
Answers
The given information is:
The starting population of bacteria is 390.
The population quadruples every 20 minutes.
To find the equation of the population in terms of minutes, we can apply the following formula:
[tex]P(t)=P_0\cdot4^{(\frac{t}{20})}[/tex]Where P0 is the starting population, the number 4 is because the population quadruples every 20 minutes (the 20 in the power is given by this), it is equal to 4 times the initial number, and t is the time in minutes.
If we replace the known values, we obtain:
[tex]P(t)=390\cdot4^{(\frac{t}{20})}[/tex]To find the population after 1 hour, we need to convert 1 hour to minutes, and it is equal to 60 minutes, then we need to replace t=60 in the formula and solve:
[tex]\begin{gathered} P(60)=390\cdot4^{(\frac{60}{20})} \\ P(60)=390\cdot4^3 \\ P(60)=390\cdot64 \\ P(60)=24960\text{ bacterias} \end{gathered}[/tex]Thus, after 1 hour there are 24960 bacterias.
Determine whether each linear function is a direct a variation. If so, state the constant of variation. If not, explain why notI need help for number 6
Answers
In direct variation function, variables x and y are related by the next formula:
y = kx
where k is the constant of variation.
Isolating k for the above formula, we get:
k = y/x
Computing y divided by x with the values of the table:
[tex]\frac{5}{10}\ne\frac{6}{11}\ne\frac{7}{12}\ne\frac{8}{13}[/tex]Given that all the quotients are different, then the linear function is not a direct variation
Based on the degree of the polynomial f(x) given below, what is the maximum number of turning points the graph of f(x)
can have?
f(x) = -3+x²-3x - 3x³ + 2x² + 4x4
Answers
The maximum number of turning points based on the degree of the polynomial is 2.
What is the turning point?A polynomial function is a function that can be expressed in the form of a polynomial. The definition can be derived from the definition of a polynomial equation. A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree.A turning point is a point in the graph where the graph changes from increasing to decreasing or decreasing to increasing.Turning point = n-1, where n is the degree of the polynomial.
The highest order of the polynomial is 3.n = 3Turning point = 3 - 1 = 2Therefore, the maximum number of turning points based on the degree of the polynomial is 2.
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The vertices of a rectangle are located at A(4, -1), B(-4, -1), C(-4, 6), and D(4, 6). What is the distance between the side AB and BC respectively?
Answers
The coordinates of the vertices of a rectangle are:
[tex]\begin{gathered} A\left(4,-1\right) \\ B\left(-4,-1\right) \\ C\left(-4,6\right) \\ D\left(4,6\right) \end{gathered}[/tex]Plotting these points:
is there one solution to the following system of equations by elimination 3x + 2y equals 3 3x + 2y equals 19
Answers
3x+2y= 3 (a)
3x+2y= 19 (b)
Subtract (b) to (a) ; elimination method.
3x+ 2y = 3
-
3x+2y= 19
_________
0 = 19
Since both variables were eliminated, the system has no solutions.
option c.
To beA train started from City A to City B at 13:30. The train travelledat an average speed of 180 miles per hour. If the distancebetween City A and City B is 756 miles, at what time did thetrain arrive at City B? Give your answer in a 24-hour clockformat, such as 19:00. DEnter the answer
Answers
Remember that
the speed is equal to divide the distance by the time
speed=d/t
solve for t
t=d/speed
we have
d=756 miles
speed=180 miles per hour
substitute
t=756/180
t=4.2 hours
4.2 hours=4 hours +0.20 hours
Convert 0.20 hours to minutes
Multiply by 60
0.20 h=0.20*60=12 minutes
so
4.2 hours=4 h 12 min
therefore
A train started from City A to City B at 13:30.
13:30+ 4h 12 min=17:42 hrs
figure0123456vehicles4122028364452linear ?pattern ?constant?
Answers
Problem
Solution
For this case we need to verify if the pattern is linear so we cna check this doing the following operations:
(12-4)/(1-0) =8
(20-12)/(2-1) =8
(28-20)/(3-2) =8
(36-28)/(4-3) =8
(44-36)/(5-4) =8
(52-44)/(6-5) =8
And as we can see we have the same constant so we can conclude that we have a linear pattern with a constant value of k=8
That means for every increase in the figure the vehicles increase by 8
We can also find the formula for the linear pattern and we have:
4 =8 (0)+b
And solving for b we got
b= 4
And the equation y=mx+b is:
y= 8x +4
Write an expression in terms of Pi that represents the area of the shaded part of N.
Answers
The area of the shaded part is:
[tex]=(PN)^2\lbrack\pi-\frac{1}{2}(75-\sin 75)\rbrack[/tex]Explanation:The area of the shaded part is the subtraction of the area of the unshaded part from the area of the whole circle.
Area of the ushaded part is:
[tex]\frac{1}{2}\times(PN)^2\times(75-\sin 75)[/tex]Area of the circle is:
[tex](PN)^2\pi[/tex]Area of the shaded part is:
[tex]\begin{gathered} (PN)^2\pi-\frac{1}{2}(PN)^2(75-\sin 75) \\ \\ =(PN)^2\lbrack\pi-\frac{1}{2}(75-\sin 75)\rbrack \end{gathered}[/tex]