========================================================
Work Shown:
The notation f(-1) = 30 tells us that (x,y) = (-1,30) is a point on the exponential curve.
Plug in x = -1 and y = 30 and solve for 'a'
y = a*b^x
30 = a*b^(-1)
30 = a*(1/b^1)
30 = a/b
a = 30b
--------------------------------------------------
Now plug that into the equation to get
y = a*b^x
y = 30b*b^x
y = 30b^1*b^x
y = 30b^(1+x)
Afterward, plug in x = 4 and y = 85 to solve for b.
85 = 30b^(1+4)
85 = 30b^5
b^5 = 85/30
b = (85/30)^(1/5)
b = 1.23157122757057
We can then determine the value of 'a'
a = 30b
a = 30*1.23157122757057
a = 36.947136827117
--------------------------------------------------
To summarize,
a = 36.947136827117b = 1.23157122757057both of which are approximate.
Since we want f(3) to the nearest hundredth, we don't really need to go too overboard with precision. Let's round 'a' and b to 4 decimal places.
We then get
a = 36.9471b = 1.2316This means
y = a*b^x
turns into
y = 36.9471*(1.2316)^x
As a check, plug in x = -1 to get y = 29.999269; we'll have rounding error since we rounded those 'a' and b values earlier. But when rounding 29.999269 to the nearest hundredth, we get y = 30.
Also, plug x = 4 into the equation to get y = 85.00785875 which rounds to 85.
--------------------------------------------------
The last step is to plug x = 3 into the equation
y = 36.9471*(1.2316)^x
y = 36.9471*(1.2316)^3
y = 69.0222951885528
y = 69.02 which is the final answer
--------------------------------------------------
If you were to use those more accurate values of 'a' and b, then x = 3 would lead to y = 69.0175266335801; that rounds to 69.02 when rounding to the nearest hundredth (aka 2 decimal places). So this shows we can stick with the less accurate 'a' and b values while still getting the correct final answer.
GeoGebra and Desmos are great tools to help quickly verify the answer.
Answer:
f(3) = 69.02 (nearest hundredth)
Step-by-step explanation:
Exponential FunctionAn exponential function is used to calculate the exponential growth or decay of a given set of data. In an exponential function, the variable is the exponent.
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Given:
f(-1) = 30f(4) = 85Substitute these values into the general form of an exponential function to create two equations in terms of a and b:
[tex]\begin{aligned}\implies f(-1)&=30\\ab^{-1}&=30\end{aligned}[/tex]
[tex]\begin{aligned}\implies f(4)&=85\\ab^{4}&=85\end{aligned}[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\begin{aligned}\implies \dfrac{ab^4}{ab^{-1}}&=\dfrac{85}{30}\\\\\dfrac{b^4}{b^{-1}}&=\dfrac{85}{30}\\\\\end{aligned}[/tex]
Solve for b:
[tex]\begin{aligned}\implies \dfrac{b^4}{b^{-1}}&=\dfrac{85}{30}\\\\b^{4-(-1)}&=\dfrac{17}{6}\\\\b^{5}&=\dfrac{17}{6}\\\\b&=\sqrt[5]{\dfrac{17}{6}}\end{aligned}[/tex]
Substitute the found value of b into ab⁴ = 85:
[tex]\implies a\left(\sqrt[5]{\dfrac{17}{6}}\right)^4=85[/tex]
Solve for a:
[tex]\implies a=\dfrac{85}{\left(\sqrt[5]{\dfrac{17}{6}}\right)^4}[/tex]
[tex]\implies a=\dfrac{85}{\sqrt[5]{\dfrac{17^4}{6^4}}}[/tex]
[tex]\implies a=\dfrac{85}{\sqrt[5]{\dfrac{83521}{1296}}}[/tex]
Substitute the found values of a and b into the exponential function formula to create an exponential equation for the given parameters:
[tex]f(x)=\left(\dfrac{85}{\sqrt[5]{\dfrac{83521}{1296}}}\right)\cdot \left(\sqrt[5]{\dfrac{17}{6}}\right)^x[/tex]
To find the value of f(3), substitute x = 3 into the equation:
[tex]\begin{aligned}\implies f(3)&=\left(\dfrac{85}{\sqrt[5]{\dfrac{83521}{1296}}}\right)\cdot \left(\sqrt[5]{\dfrac{17}{6}}\right)^3\\\\&=69.0175266...\\\\&=69.02\; \;\sf (nearest\;hundredth)\end{aligned}[/tex]
Therefore, the value of f(3) to the nearest hundredth is 69.02.
For Saturday matinees, a movie theater charges $5 for adult tickets and $3 for children's tickets. If the movie theater sold a total of 166 matinee tickets and made
$718 in revenue on Saturday afternoon, how many adult matinee tickets were sold?
Answer:
Let's use A to represent the number of adult tickets sold and C to represent the number of children's tickets sold.
We know that A + C = 166, since the total number of tickets sold is 166.
We also know that the revenue earned from adult tickets is $5A and the revenue earned from children's tickets is $3C. Since the total revenue earned is $718, we can write:
5A + 3C = 718
Now we have two equations with two variables:
A + C = 166
5A + 3C = 718
We can solve for A in the first equation to get:
A = 166 - C
Then we can substitute this expression for A into the second equation:
5(166 - C) + 3C = 718
Simplifying and solving for C, we get:
830 - 2C = 718
2C = 112
C = 56
So 56 children's tickets were sold. We can substitute this value back into the first equation to solve for A:
A + 56 = 166
A = 110
Therefore, 110 adult tickets were sold.
Answer:
Step-by-step explanation:
Let's use the following variables:
a = number of adult tickets sold
c = number of children tickets sold
We know that:
a + c = 166 (total number of tickets sold)
5a + 3c = 718 (total revenue)
We can solve this system of equations by substitution or elimination. Here, we'll use elimination:
Multiply the first equation by 3: 3a + 3c = 498
Subtract the second equation from the first: 2a = 220
Solve for a: a = 110
So 110 adult tickets were sold. We can find the number of children's tickets by substituting a = 110 into either of the original equations:
c = 166 - a = 166 - 110 = 56
Therefore, 110 adult tickets and 56 children's tickets were sold.
The average cost to build a 4 , 000 sq ft fast-food restaurant in Miami is about $ 952 , 000 . Find the average cost per square foot to build a fast-food restaurant.
Average cost per square foot to build a fast-food restaurant is $238 .
What is division?The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers.
Given,
Area of the restaurant = 4000 sqft
Total average cost to build the restaurant
= $952000
Average cost of per sqft
= 952000/4000
= $238
Hence, $238 is the average cost per square foot to build a fast-food restaurant.
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Now that you have the height of the cone, how can you solve for the slant heights
Height = 21 mm
Volume = 8792 mm
Radius 20mm
The slant height [tex]l = 29 \: mm[/tex].
What is a Cone?A cone is a three-dimensional geometric shape with a smooth transition from a flat, usually circular base to the apex or vertex, which forms an axis to the base's center.
As per the given data:
Height = 21 mm
Volume = 8792 mm
Radius = 20 mm
For slant height of the one ([tex]l[/tex]):
[tex]l = \sqrt{r^2 + h^2}[/tex] {using Pythagoras theorem}
[tex]l = \sqrt{(20)^2 + (21)^2}[/tex]
[tex]l = \sqrt{(20)^2 + (21)^2}[/tex]
[tex]l = \sqrt{400 + 441}[/tex]
[tex]l = 29 \: mm[/tex]
Hence, the slant height [tex]l = 29 \: mm[/tex].
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Make and label the dimensions of four prisms, each with a volume of 1 dm3 (a cubic decimeter)
- Make one a rectangular prism that is not a cube.
- Make one a tall triangular prism.
- Make one a trapezoidal prism.
- Make one an octagonal prism.
Explain your thinking for each prism.
Prove that each prism has a volume of 1 dm3
The calculation of volume for the different kind of prisms are:
Rectangular Prism- 1 dm³
Tall triangular prism- 1 dm³
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
Rectangular prism: A rectangular prism that is not a cube can have dimensions of 0.5 dm x 0.5 dm x 4 dm.
This gives a volume of:
0.5 dm x 0.5 dm x 4 dm = 1 dm³
The rectangular prism has six faces, all of which are rectangles.
Tall triangular prism: A tall triangular prism can have a triangular base with sides of length 1 dm, 1 dm, and 2/√3 dm, and a height of 2√3/3 dm. This gives a volume of:
(1 dm x 1 dm x 2/√3 dm) x (2√3/3 dm) = 1 dm³
The tall triangular prism has five faces, one of which is a parallelogram and the other four are triangles.
To prove that each of these prisms has a volume of 1 dm³, we can use the formula for the volume of a prism, which is:
Volume = Base Area x Height
For each of the prisms above, we have calculated the base area and height such that their product equals 1 dm³.
Therefore, each prism has a volume of 1 dm³.
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QUESTION 3 Read the extract below and answer the questions that follow. Cape Town- a thirteen-year-old-boy was arrested and released on warning after he was caught on video assaulting an assistant teacher on the body and on head using his closed fists. Published: Dec 7, 2021 By: Siphokazi Vuso The grade 12 pupil from Harmony Primary in Steenberg can be seen on the video assaulting an assistant teacher after she had confiscated a ball from another pupil. Spokesperson Captain Frederick Van Wyk said witnesses tried to keep the learner away from the teacher when he broke loose and assaulted her. He said the boy was arrested on December 3 and was released in the care of his parents on a warning to appear in the Wynberg Magistrate's Court on Wednesday. [Adapted from: https://www.iol.co.za Accessed on 02 January 2023] /15/ 3.1 Define the term 'conflict resolution' and explain how the above situation is an example of bad conflict resolution. (1+2)(3) 3.2 Suggest TWO strategies that learners and teachers could put in place to decrease the culture of violent within their schools.
These two situations are examples of poor conflict resolution because they do not offer a space for dialogue between the individuals involved, but rather there is only judgment by law without any mediation.
What is conflict resolution?Conflict resolution is a term that refers to the ability of individuals to resolve conflicts or differences with others in a peaceful manner agreed upon by all parties involved. In this case, these two examples are not examples of good conflict resolution because there is no space for dialogue between students and teachers, but rather there is only aggression and prosecution before the entities in charge of justice in each country.
Due to the above, we believe that some strategies to end the culture of violence in schools is to spread messages of dialogue and conflict resolution in a peaceful manner. Also, offer workshops for parents so that from home conflict resolution is reinforced through dialogue.
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A corn plant will be killed by the aphids if the total number of aphids on the plant exceeds 2,000. If there are 50 corn plants in this field, will there be enough aphids after 3 weeks to completely destroy the plants?
There won't be enough aphids to completely harm the maize plants because 10,000 is less than 2,000 50 (the maximum number of aphids that can be on all the plants without killing them).
Application of linear equationTo determine if there are enough aphids to kill the corn plants, we need to know the total number of aphids on each plant after 3 weeks. Let's assume that on average, each plant has 200 aphids after 3 weeks.
Then, the total number of aphids in the field would be:
50 plants × 200 aphids/plant = 10,000 aphids
Since 10,000 is less than 2,000 × 50 (the maximum number of aphids that can be on all the plants without killing them), there will not be enough aphids to completely destroy the corn plants.
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Which number completes the table for y=x²?
x y
00
4 16
-3
6
-6
-9
9
Answer: -3,9
Step-by-step explanation: plug in -3 for x which gives u 9
y = 2x - 4
Write the equation of the graph in slope-intercept form
y=-2x - 4
Supersonic
y =
- 4
y =
12/200
-x-4
Answer:
The correct equation is y = -2x - 4.
Can someone help me please i really need help with this.
use the Remainder Theorem and synthetic division please
The solution for the function at the different values of x are,
f(-10) = 20001
f(2) = 49
f(3) = 214
What is a function?In mathematics, functions are often represented by equations or formulas, and take one or more input values to produce an output value. They can be used to model a wide variety of phenomena, from physical systems to economic behavior to social dynamics.
The given function is f(x) = 2x⁴ + x² - 10x + 1. The output of the function at the different values of x will be calculated as,
At x = -10,
f(x) = 2x⁴ + x² - 10x + 1
f(-10) = 2(-10)⁴ + (-10)² - 10(-10) + 1
f(-10) = 20001
At x = 2,
f(x) = 2x⁴ + x² - 10x + 1
f(2) = 2(2)⁴ + (2)² + 10(2) + 1
f(2) = 49
At x = 3,
f(x) = 2x⁴ + x² - 10x + 1
f(3) = 2(3)⁴ + (3)² + 10(2) + 1
f(3) = 214
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PLEASE HELP IM GOING TO FAIL
The correct statements regarding the translation are given as follows:
The measures of <ABC and <A'B'C' are equal.The orientation of <ABC and <A'B'C' are the same in the coordinate plane.What are the effects of each type of transformation?Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.A translation changes only the position of the figure, keeping angle measures and orientation correct, hence the second and the third options are correct.
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(x-1)(x+2)=x^2...-2
PLEASE HELP!!!!
Answer: (see attached file/screenshot)
Step-by-step explanation: You didn't specify the question so im guessing we solve with the quadratic formula
Electricity bills in a certain city have mean $ 106.27 . Assume the bills are normally distributed with standard deviation $ 17.15 . Find the value that separates the lower 40 % of the bills from the rest.
Write only a number as your answer. Round to two decimal places (for example: 42.81). Do not write any units.
Answer:
Step-by-step explanation:
To find the value that separates the lower 40% of the bills from the rest, we need to find the z-score corresponding to the 40th percentile of the standard normal distribution, and then use this z-score to find the corresponding value in the distribution of electricity bills.
Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 40th percentile is approximately -0.25.
To find the corresponding value in the distribution of electricity bills, we can use the formula:
z = (x - mu) / sigma
where z is the z-score, x is the corresponding value in the distribution, mu is the mean, and sigma is the standard deviation.
Rearranging this formula to solve for x, we get:
x = mu + z * sigma
Substituting the given values, we get:
x = 106.27 + (-0.25) * 17.15
x = 101.63
Therefore, the value that separates the lower 40% of the electricity bills from the rest is approximately $101.63.
Round 4,383,918 to the
nearest...
100:
Answer:4,383,900
Step-by-step explanation:
4,383,900
what is 92199+20923+29290+83292+2819+99279+38471+37814
Answer:404087
Step-by-step explanation:
use the calculator frfr
Answer:
404087
Step-by-step explanation:
What is the avantage of using exponential notion?
Answer:
Exponential notion makes a big number easier to write and read.
Step-by-step explanation:
can someone help me please
The two solutions to the linear equation is given by the ordered pairs (0, 6) and (-4, 5).
How to graph the solution to this linear equation?In order to to graph the solution to the given linear equation on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point that lie on it;
y = 0.25x + 6.00
Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that a possible solution for the linear equation is the ordered pairs (-4, 5) and (0, 6).
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Pedro tracks his steps when he runs. He sets a goal to run exactly 10,000 steps a day on his
running days.
Pedro estimates that there are approximately 2,000 steps in 1 mile. He uses this estimate to
make a plan.
He runs a total of 4 hours over 5 days.
He runs for an equal amount of time each day.
He runs at a rate of 6 miles per hour.
Pedro will not meet his daily running goal with this plan.
What is one change you can make to one value in Pedro's plan to ensure that Pedro meets his
daily running goal? Justify your response.
One change that Pedro can make to his plan to ensure that he meets his daily running goal is to increase the estimated number of steps per mile.
How would this help meet the running goal?If Pedro overestimates the number of steps in a mile, he will end up taking more steps than he initially planned for, which can help him reach his daily goal.
For example, if Pedro increases his estimate from 2,000 steps per mile to 2,500 steps per mile, he will need to run approximately 4 miles per day to reach his goal of 10,000 steps. This will make it more likely for him to reach his daily goal within the 4 hours of running over the 5 days.
Alternatively, Pedro can increase his running speed to cover more distance in a shorter period of time. For instance, if he increases his running speed from 6 miles per hour to 8 miles per hour, he will need to run for only about 2.5 hours per day to reach his goal of 10,000 steps.
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14. The number of visitors to a system of county parks t years after 2010 can be modeled by A =20.6(1.03)', where A is the annual number of visitors in thousands. Find and interpret the constant
percent rate of change per unit interval in the context of the situation.
The constant percent rate of change per unit interval is approximately 0.0305 or 3.05%.
What is the exponential functions?
An exponential function is a mathematical function of the form:
[tex]f(x) = a^x[/tex]
The given formula for the number of visitors to the county parks system is:
[tex]A = 20.6(1.03)^t[/tex]
where t is the number of years after 2010 and A is the number of visitors in thousands.
To find the constant percent rate of change per unit interval, we can take the derivative of A with respect to t:
[tex]dA/dt = 20.6(1.03)^t * ln(1.03)[/tex]
The constant percent rate of change per unit interval is given by the expression:
r = (dA/dt) / A
Substituting the values of dA/dt and A, we get:
[tex]r = [20.6(1.03)^t * ln(1.03)] / [20.6(1.03)^t]\\r = ln(1.03)\\r = 0.0305[/tex]
Hence, the constant percent rate of change per unit interval is approximately 0.0305 or 3.05%.
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69 and 5.6 x 10^5 expressed in scientific notation
The product of 69 and 5.6 x 10⁵ expressed in scientific notation is 3.864 x 10⁷.
Describe Scientific Notation?Scientific notation, also known as standard form, is a way of writing very large or very small numbers in a concise and convenient way. It expresses a number as the product of a decimal number between 1 and 10 (known as the coefficient) and a power of 10.
The general form of a number written in scientific notation is:
a × 10^n
where a is the coefficient, and n is an integer exponent that indicates the number of places the decimal point must be moved to obtain the original number.
To multiply numbers in scientific notation, we multiply their coefficients and add their exponents.
69 x 5.6 x 10⁵ = (6.9 x 10¹) x (5.6 x 10⁵)
= (6.9 x 5.6) x 10¹⁺⁵
= 38.64 x 10⁶
= 3.864 x 10⁷ (in scientific notation)
Therefore, the product of 69 and 5.6 x 10⁵ expressed in scientific notation is 3.864 x 10⁷.
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The complete question is :
ixl prediction! URGENT, PLEASE.
The expected number of not blue is 54
How to evaluate the expected number of valueFrom the question, we have the following parameters that can be used in our computation:
Spinner
Using the above as a guide, we have the following probability
P(Not Blue) = Not Blue/Total
So, we have
P(Not Blue) = 6/9
When it is spun 81 times, the expected number of times is
Times = 6/9 * 81
Evaluate
Times = 54
Hence. the number of times is 54
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if x = 5 what is the value of 2x - 5
Answer:
answer is 5
Step-by-step explanation:
2x=5×2
so 2x=10
10-5=5
so 2x-5=5
Answer:
5
Step-by-step explanation:
2x - 5 first, substitute
2(5) - 5 then, multiply
10 - 5 = 5
Find perimeter please due in five minutes
Will give 30 pointsd
the perimeter of the shape is [tex]8 + 2\sqrt(2) units.[/tex]
AB = [tex]\sqrt ((4-2)^2 + (0-0)^2)[/tex] = [tex]\sqrt (4)[/tex] = 2
BC = [tex]\sqrt ((4-4)^2 + (3-0)^2) = 3[/tex]
CD =[tex]\sqrt ((3-4)^2 + (4-3)^2) = \sqrt (2)[/tex]
DE = [tex]\sqrt ((2-3)^2 + (3-4)^2) = \sqrt(2)[/tex]
EA =[tex]\sqrt ((2-2)^2 + (3-0)^2) = 3[/tex]
AB + BC + CD + DE + EA = [tex]2 + 3 + \sqrt(2) +\sqrt sqrt(2) + 3 = 8 + 2\sqrt(2)[/tex]
As a result, the shape has a perimeter of [tex]8 + 2 \sqrt(2)[/tex] units.
what is the perimeter?The whole distance around a shape is referred to as its perimeter. In essence, the length of any shape when it is expanded in a linear form equals its perimeter. A shape's perimeter in a two-dimensional plane is its complete circumference. Depending on their measurements, distinct shapes' perimeters may be equal in length. Units are used to measure perimeter (m, cm, in, feet, etc.)
From the question;
The lengths of all the sides must be added up in order to determine the shape's perimeter.
Let's begin by giving the shape's vertices the following labels:
A = (2, 0)
B = (4, 0)
C = (4, 3)
D = (3, 4)
E = (2, 3)
The lengths of each side can be determined using the distance formula:
AB = [tex]\sqrt ((4-2)^2 + (0-0)^2)[/tex] = [tex]\sqrt (4)[/tex] = 2
BC = [tex]\sqrt ((4-4)^2 + (3-0)^2) = 3[/tex]
CD =[tex]\sqrt ((3-4)^2 + (4-3)^2) = \sqrt (2)[/tex]
DE = [tex]\sqrt ((2-3)^2 + (3-4)^2) = \sqrt(2)[/tex]
EA =[tex]\sqrt ((2-2)^2 + (3-0)^2) = 3[/tex]
AB + BC + CD + DE + EA = [tex]2 + 3 + \sqrt(2) +\sqrt sqrt(2) + 3 = 8 + 2\sqrt(2)[/tex]
As a result, the shape has a perimeter of [tex]8 + 2 \sqrt(2)[/tex] units.
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Answer:the perimeter of the shape is
AB = = = 2
BC =
CD =
DE =
EA =
AB + BC + CD + DE + EA =
As a result, the shape has a perimeter of units.
what is the perimeter?
The whole distance around a shape is referred to as its perimeter. In essence, the length of any shape when it is expanded in a linear form equals its perimeter. A shape's perimeter in a two-dimensional plane is its complete circumference. Depending on their measurements, distinct shapes' perimeters may be equal in length. Units are used to measure perimeter (m, cm, in, feet, etc.)
From the question;
The lengths of all the sides must be added up in order to determine the shape's perimeter.
Let's begin by giving the shape's vertices the following labels:
A = (2, 0)
B = (4, 0)
C = (4, 3)
D = (3, 4)
E = (2, 3)
The lengths of each side can be determined using the distance formula:
AB = = = 2
BC =
CD =
DE =
EA =
AB + BC + CD + DE + EA =
As a result, the shape has a perimeter of units.
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Step-by-step explanation:
what are three ratios equal to 9.5/25?
Answer:
9.50 : 25
19 : 50
28.50 : 75
Step-b-step explanation:
If the graph function f (x)=e^x is shifted 6 units to the right what is the equation of the new graph
The equation of the new graph is:
f(x) = e^(x-6)
The graphs of the two functions f(x) = e^x and f(x) = e^(x-6) are shown below
Determining the equation of the new graphFrom the question, we are to determine the equation of the new graph.
If the graph of the function f(x) = e^x is shifted 6 units to the right, the equation of the new graph can be found by replacing x with (x - 6) in the original equation.
This is because a horizontal shift of a function f(x) to the right by c units can be achieved by replacing x with (x - c) in the equation of the function. So, for the given function, a shift to the right by 6 units would be achieved by replacing x with (x - 6) in the original equation f(x) = e^x.
Therefore, the equation of the new graph is:
f(x) = e^(x-6)
This can also be written as:
f(x) = e^x / e^6
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST!
The domain and the range of h(n) consist of all possible sets of whole numbers.
Other answers are listed below
The sequence of the figuresHow to determine the domain and the range of h(n)
From the question, we know that:
h(n) is the number of houses
n and h(n) can only take whole numbers as its values
So, we have
Thus, the domain and range consist of all possible sets of whole numbers.
How to determine h(5) and h(11)
From the figure, we can see that
The number of houses is the same as the figure number
This means that
h(5) = 5 and h(11) = 11
How to represent the explicit function of h(n)
By the computations above, we have the formula of h(n) to be:
h(n) = n
The values of s(4) and s(7)
Here, we have
s(n) is the number of segments
From the figure, we can see that
The number of segments is twice the the figure number
So, we have
s(4) = 8
s(7) = 14
The growth pattern of s(n)
Recall that:
The number of segments is twice the the figure number
This means that
The growth pattern of s(n) is linear, with a constant rate of change
The explicit function of s(n)
Above, we have
The number of segments is twice the the figure number
Mathematically, this can be expressed as
s(n) = 2n
The table of the infinite sequenceHow to complete the table for f(5) and f(7)
From the table, we can see that
The division of a term by 2 gives the next term
So, we have
f(5) = 2/2 = 1
f(7) = 1/2/2 = 1/4
How to determine the domain of f(n)
The possible values of n are real numbers
Thus, the domain consist of all possible sets of real numbers.
The observation of the function
Above, we have
The division of a term by 2 gives the next term
This represents the observation
The doubling sequence g(n)How to determine the value of g(4)
From the question, we have
First term, a = 9Common ratio, r = 2This means that
g(n) = 2(9)^n-1
So, we have
g(4) = 2(9)^3
g(4) = 1458
How to complete the statements
The function is a doubling function
So, we have
g(n) = g(n - 1) * 2, g(n) = g(n - 2) * 4 and g(n) = g(n - 3) * 8
How to determine the value of g(24)/g(21)
Recall that
g(n) = 2(9)^n-1
So, we have
g(24) = 2(9)^23
g(21) = 2(9)^20
When the equations are divided, we have
g(24)/g(21) = 2(9)^23/2(9)^20
Evaluate
g(24)/g(21) = 729
Hence, the value is 729
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28x to the power of 2 plus 20
Answer:
good morning!
Step-by-step explanation:
the answer to your question is 4(7x^2+5)
hope you have a great day!
Xinput
3
Rute:
Youtput)
59
X(input)
Rule:
2
4
7
The input rule to find the output is 19.67 multiplied by the input value.
What is division?One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.
Given:
An input value is 3, and the corresponding output value is 59.
The unit rate is 59 divided by 3.
We get,
59/3 = 19.67
The input rule to find the output is 19.67 multiplied by the input value.
Now, the required table is,
Input Output
2 39.33
4 78.67
7 137.67
Therefore, the required table is given above.
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solve for x.Leave your answer in simpliest form please
Answer:
492
Step-by-step explanation:
The GCF is found through p.i.g method.
6-2=3
Ben is using a map. Let x represent a distance in centimeters on the map. To find an actual distance y in kilometers, Beth uses the equation y=8x
The table that can be constructed with the following equation has vales x: 0, 1, 2, 3 and y = 0, 8, 16, 24.
A linear equation is what?When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0.
The slope of the linear relationship is eight. The solution is below, along with a picture of the line.
Substitute different values of x to obtain value of y:
The table is given below:-
x I y
-------
0 I 0
1 I 8
2 I 16
3 I 24
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The complete question is:
1. An advertising agency finds that of its 200 clients, 150 use television (T), 80 use magazines (M), and 50 use both. a. clients. Use these data to complete a Venn diagram displaying the use of mass media for these 200 b. Use your Venn diagram to determine the following probabilities: i. P(T) ii. P(T^M) iii. P(TUM) P(T|M)
By using Venn diagram the following probabilities are 0.75,0.25,0.9 and 0.625.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that;
Number of clients= 200
Number of television= 150
Magazines=80
Both magazine and television=50
Now,
To complete the diagram, we can fill in the following values:
The size of T is 150.
The size of M is 80.
The size of TM (the overlap between T and M) is 50.
The size of C (the total number of clients who use either T or M) is 150 + 80 - 50 = 180.
The size of U (the number of clients who use neither T nor M) is 200 - 180 = 20.
Now we can use the Venn diagram to answer the following probabilities:
i. P(T) is the probability that a randomly selected client uses television. This is the size of T divided by the total number of clients, which is 150/200 = 0.75.
ii. P(T ∩ M) is the probability that a randomly selected client uses both television and magazines. This is the size of TM divided by the total number of clients, which is 50/200 = 0.25.
iii. P(T ∪ M) is the probability that a randomly selected client uses either television or magazines (or both). This is the size of C divided by the total number of clients, which is 180/200 = 0.9.
iv. P(T|M) is the probability that a randomly selected client uses television given that they use magazines. This is the size of TM divided by the size of M, which is 50/80 = 0.625.
Therefore, by probability the answer will be 0.75,0.25,0.9 and 0.625.
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