The solution for the given differential equation is [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex].
We have given a differential equation:
[tex]\frac{d}{dx}(C_1e^{12x})[/tex]
since C1 is a constant,
=[tex]C_1\frac{d}{dx} (e^{12x})[/tex]
we know that [tex]\frac{d}{dx} (e^{ax}) = e^{ax}\frac{d}{dx} (ax)[/tex]
= [tex]C_1e^{12x}(12) = 12C_1e^{12x}[/tex]
Therefore, [tex]\frac{d}{dx}(C_1e^{12x}) = 12C_1e^{12x}[/tex]
Now, let y = [tex]C_1e^{12x}[/tex]
Therefore, [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex]
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The complete question is:
Fill in the blank. The symbol C represents a constant. [tex]\frac{d}{dx}C_1e^{12x}[/tex]= ____ Write this result as a linear first-order differential equation that is free of the symbol C1 and has the form dy/dx = f(x, y).
The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s) to f(x)=g(x)? Explain your answer(s).
a. The solutions to the system of equations f(x) = g(x) are given as follows: x = 0 and x = 1.
b. The explanation is that they have the same numeric value at these values of x.
How to interpret the solution of a system of equations?A system of equations is composed by multiple equations.
The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.
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what is the area of a triangular prism with dimensions of 13ft, 5 ft,12 ft, 6 ft
The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.
What is the surface area of a triangular prism?Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.
Then the surface area of the triangular prism will be
Surface area = 2 Area of triangle + 3 Area of rectangle
Surface area = (h x b) + (L₁ + L₂ + L₃) x W
The dimension of the triangle is 13 feet, 5 feet, and 12 feet. And the width of the rectangle is 6 feet.
The surface area of the triangular prism will be given as,
Surface area = 5 x 12 + (5 + 12 + 13) x 6
Surface area = 60 + 180
Surface area = 240 square feet
The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.
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AB + BC = AC by what property?
O Distributive Property
O Segment Addition Postulate
O Definition of ≅ Segments
O Transitive Property
It is very important to note that this property is only valid for addition and multiplication. If, AC = AB + BC, then AB + BC = AC by the commutative property.
What is called commutative property?
According to the commutative property, a mathematical principle, the product will not be affected by the order in which we multiply the integers. The commutative property of addition states that the sum is unaffected by the order of the addends.
Only addition and multiplication processes can use the commutative property. So, when adding or multiplying any two integers, we can swap the numbers around or modify their order. This is one of the fundamental characteristics of integers.
Adjective. involving, pertaining to, or involving commutation, exchange, substitution, or interchange. Mathematics. Commutative law for multiplication makes reference to the binary operation's property that one term working on another is equal to another term operating on the first, as in a + b = b a.
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56. Kotkit is the hottest new social media app. It is lowkey fire. It slays! There were no crumbs left. Users post their Tiktoks to Kotkit, but play them backwards. At the start of the year, there are 1500 users, but the number of users grows exponentially at a rate of 12% per day.
a. Write a function K(t) that expresses the number of users t days after the start of the year.
b. How many users are of the Kotkit after 30 days?
.c After how many days will the numbers of users reach one million users?
Answer:
[tex]\textsf{a)} \quad K(t)=1500(1.12)^t[/tex]
b) 44940
c) 57.4 days
Step-by-step explanation:
Exponential Growth Function
[tex]f(t)=a(1+r)^t[/tex]
where:
a is the initial value (y-intercept)r is the growth rate (in decimal form)t is the timeGiven values:
a = 1500r = 12% per day = 0.12t = time in daysPart aTo create a function K(t) that expresses the number of users t days after the start of the year, substitute the given values into the exponential growth formula:
[tex]\implies K(t)=1500(1+0.12)^t[/tex]
[tex]\implies K(t)=1500(1.12)^t[/tex]
Part bTo calculate how many users there are after 30 days, substitute t = 30 into the function K(t) from part a:
[tex]\implies K(30)=1500(1.12)^{30}[/tex]
[tex]\implies K(30)=44939.8831...[/tex]
[tex]\implies K(30)=44940\; \rm users[/tex]
Part cTo calculate after how many days it takes to reach one million users, substitute K(t) = 1,000,000 into the function and solve for t:
[tex]\implies 1000000=1500(1.12)^t[/tex]
[tex]\implies \dfrac{2000}{3}=1.12^t[/tex]
[tex]\implies \ln \left(\dfrac{2000}{3}\right)=\ln 1.12^t[/tex]
[tex]\implies \ln \left(\dfrac{2000}{3}\right)=t \ln 1.12[/tex]
[tex]\implies t=\dfrac{\ln \left(\frac{2000}{3}\right)}{\ln 1.12}[/tex]
[tex]\implies t=57.3755016...[/tex]
[tex]\implies t=57.4\; \rm days[/tex]
A wage earner receives a gross pay of $983.15 for 52.5 hours of work. What is his hourly rate of pay if a regular workweek is 44 hours and overtime is paid at timeand-a-half the regular rate of pay?
Answer:
$17.32
Step-by-step explanation:
44 hours
52.5 - 44 = 8.5 hours over time for 1.5x regular pay
assume regular pay is x
so 44x + 8.5 * 1.5x =983.15
44x + 12.75x = 983.15
56.75x=983.15
x=17.324
check to see if it's correct
44*17.324 + 12.75*17.324 = 983.14
the output column, s, was created from the student id 21444368 using the algorithm: if id digit n (left-to-right) is an even integer, place a 0 in s, row n (top-down) if id digit n (left-to-right) is an odd integer, place a 1 in s, row n (top-down) create a similar table, but with s reflecting the result of the algorithm applied to your student id (do this on scratch paper). on the quiz essay: record your student id, id
My student ID is 21444367.
The algorithm states that if the digit in the student ID (from left to right) is an even number, then a 0 is placed in the s column in the corresponding row (from top to bottom). If the digit in the student ID (from left to right) is an odd number, then a 1 is placed in the s column in the corresponding row (from top to bottom). Thus, the result of the algorithm applied to my student ID is s = 01101000.
This can be calculated by multiplying the even digits of the student ID by 0 and the odd digits of the student ID by 1 and then adding them together.
For my student ID, 21444367, the calculation would be:
0 * 2 + 1 * 1 + 0 * 4 + 1 * 4 + 0 * 4 + 1 * 3 + 0 * 6 + 1 * 7 = 01101000.
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in a certain large population of adults, the distribution of iq scores is strongly left-skewed with a mean of 122 and a standard deviation of 5. suppose 200 adults are randomly selected from this population for a market research study. for srss of size 200, the distribution of sample mean iq score is
If in a certain large population of adults. the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.
Given data:
Mean = 122
Standard deviation = 5
Sample size = 200
Now let find the the standard deviation of the sampling distribution of the mean sample using this formula
Distribution of sample mean = Standard deviation/√Sample size
Let plug in the formula
Distribution of sample mean = 5 /√ 200
Distribution of sample mean = 5/14.14
Distribution of sample mean = 0.35
Therefore the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.
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On January 1, 2017, the capital balances in Hollings worth Company are Lois Holly $26,000 and Jim Worth $24,000. In 2017 the partnership reports net income of $30,000. The income ratio provides for salary allowances of $12,000 for Holly and $10,000 to Worth and the remainder to be shared equally. Neither partner had any drawings in 2017, Instructions
(1) Prepare a schedule showing the distribution of net income in 2017.
Answer:
see below
Step-by-step explanation:
1-1-2017
H 26K
W 24K
Net income 30K
H salary 12K
W salary 10K
remain: 8K shared EQUALLY so each gets 4K extra
Distribution:
30K - H gets12+4 =16K, and W gets 10+4 = 14K
now view the partitioned circle as a protractor, and think of using it to measure angles that are drawn on a page. give examples and make (rough) math drawings to show how this protractor could measure the following kinds of angles. in each case, determine the size of the angle in degrees and explain your answer.
The instrument used here is a protractor.
ProtractorAn instrument used to measure angles in degrees is a protractor. When measuring angles using a protractor, it's crucial to check that the vertex of the angle is in the protractor's centre and that the angle's base is lined up with the protractor's baseline.
Acute Angle: - An angle that is less than 90 degrees is considered to be acute. For instance, if the angle is 30 degrees, we would line up the vertex of the angle with the protractor's centre and one of its sides with the baseline. The measurement would be read off the protractor scale, which in this instance would be 30 degrees.
Right Angle: - A right angle is a triangle with a 90 degree angle on each side. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a right angle. The measurement would be read off the protractor scale, which in this instance would be 90 degrees.
Obtuse Angle: - An angle that is more acute than 90 degrees is referred to as an obtuse angle. When using a protractor to measure an obtuse angle, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline. The measurement would then be taken from the protractor scale and would be more than 90 degrees in this instance.
Straight Angle: - A straight angle is one that is 180 degrees in length. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a straight angle. The measurement would then be taken from the protractor scale, which would be 180 degrees in this instance.
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what is the answer???
Answer: Semi-Conservative, and old.
Step-by-step explanation:
identify the sampling method that was used. three representatives from each employee type (faculty, staff, administrators) are chosen for a salary committee.
The sampling method that was used. three representatives from each employee type (faculty, staff, administrators) are chosen for a salary committee. This uses stratified sampling.
ABOUT STRATIFIED SAMPLEIn a stratified sample, researchers divide a population into homogeneous subpopulations called strata (the plural of stratum) based on specific characteristics (e.g., race, gender identity, location, etc.). Every member of the population studied should be in exactly one stratum.
Each stratum is then sampled using another probability sampling method, such as cluster sampling or simple random sampling, allowing researchers to estimate statistical measures for each sub-population.
Researchers rely on stratified sampling when a population’s characteristics are diverse and they want to ensure that every characteristic is properly represented in the sample. This helps with the generalizability and validity of the study, as well as avoiding research biases like under coverage bias.
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Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the index of summation. 1+4+9+16+25 +36 Express the sum in sigma notation. Σ" k 1
∑[tex](k^2)[/tex] for k = 1 to 6 is the sum in sigma notation for this series of terms.
The series is 1 + 4 + 9 + 16 + 25 + 36. The lower limit of summation is 1, which means, the sum starts at the initial term in the series.
The index of summation is k, which implies, the ongoing term in the series is represented by the variable k.
In the expression [tex]k^2[/tex] which implies that we are adding up the square of the index of summation.
So, the sigma notation for this series of terms is ∑[tex](k^2)[/tex] for k = 1 to 6, which means, we are adding up the squares of the numbers from 1 to 6 (1, 4, 9, 16, 25, and 36)
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if you are standing 45 feet away from a school and the angle of elevation is 66 degrees how tall is the building?
Answer:
50 m
Step-by-step explanation:
The angle of elevation of the top of the building from the foot of the tower is 30 and the angle of the top of the tower from the foot of the building is 60. the tower is 50 m high
how to simplify 32/5
Answer: 6 2/5
Step-by-step explanation:
32 divided by 5 equals 6 with a remainder of 2.
Circle E has a radius of 5.1 meters. FG is a chord and is a perpendicular bisector of FG. If FG = 6.3 meters, calculate the distance of IH.
The distance of IH is 1.089 meters.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Given that,
Radius = 5.1 meters
EF = EI = 5.1
FG = 6.3 meters
HE is a perpendicular bisector of FG.
FH = HG = 6.3 / 2 = 3.15
Also, FH is the projection of EF in the vertical axis.
FH = EF sin (θ), where θ is the angle FEH.
3.15 = 5.1 sin (θ)
sin (θ) = 0.6176
θ = sin⁻¹ (0.6176)
θ = 38.14°
IH = EI - EH
We have, EH is the projection of EF into the horizontal axis.
EH = EF cos (θ)
Substituting,
IH = 5.1 - EF cos (θ)
IH = 5.1 - 5.1 cos (38.14)
IH = 5.1 ( 1 - cos (38.14))
IH = 1.089 meters
Hence the length of the line segment IH is 1.089 meters.
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The following data represent glucose blood levels (mg/100 ml) after a 12-hour fast for a random sample of 70 women (Reference: American Journal of Clinical Nutrition, Vol. 19, pp. 345-351).
45 66 83 71 76 64 59 59 76 82
80 81 85 77 82 90 87 72 79 69
83 71 87 69 81 76 96 83 67 94
101 94 89 94 73 99 93 85 83 80
78 80 85 83 84 74 81 70 65 89
70 80 84 77 65 46 80 70 75 45
101 71 109 73 73 80 72 81 63 74
For this problem, use six classes.
(a). Find the class width
(b). Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 4 decimal places.
(c). Draw a histogram.
(d). Draw a relative-frequency histogram.
(e). Categorize the basic distribution shape.
(f). Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)
The graph can be used to determine the median, quartiles, and other statistical measures.
(a). Class width = (maximum value - minimum value)/ number of classes = (109 - 45)/6 = 9
(b).
Class Limits Class Boundaries Midpoints Frequencies Relative Frequencies Cumulative Frequencies
45 - 54 44.5 - 54.5 49.5 2 0.0741 2
55 - 64 54.5 - 64.5 59.5 7 0.2593 9
65 - 74 64.5 - 74.5 69.5 17 0.6207 26
75 - 84 74.5 - 84.5 79.5 20 0.7407 46
85 - 94 84.5 - 94.5 89.5 14 0.5185 60
95 - 104 94.5 - 104.5 99.5 7 0.2593 67
(c). Histogram
(d). Relative-Frequency Histogram
(e). The basic distribution shape is right-skewed.
(f). Ogive
The ogive graph is a cumulative frequency plot that shows the number of data values that lie at or below each given value on the x-axis. It is constructed by plotting the cumulative frequencies of each data value on the y-axis against the corresponding data values on the x-axis. The points are then connected using closed line segments to form the ogive graph. The graph can be used to determine the median, quartiles, and other statistical measures.
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How is the work energy theorem represented as an equation? (1 point)
a. ΔW = E
b.W = ΔΕ
c.W = E
d. ΔW = ΔΕ
The work energy theorem represented as an equation is ΔW = ΔΕ is appropriate option.
Option D is correct.
The work-energy theorem is what?A fundamental physics principle known as the work-energy theorem asserts that the amount of work done to an object is proportional to the change in its kinetic energy. To put it another way, the kinetic energy of an object is proportional to the net work done to it.
The work-energy theorem can be expressed as an equation because the change in an object's kinetic energy (W) is equal to the change in its work (W). It states that a change in an object's kinetic energy equals the net work done on it. The conservation of energy is a fundamental physics principle that states that energy cannot be created or destroyed; rather, it can only be transferred or converted from one form to another.
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A student looks out of a second story school window and sees the top of the school flagpole at an angle of evelation of 22 degrees. The student is currently 18 feet above the ground. The building is 50 ft from the base of the flagpole. a. Draw a diagram of the above scenario. b. Find the height of the flagpole
The flagpole is visible to the student from 18 feet away and at a 22-degree inclination to the ground. The flagpole is 40.3 feet tall and 50 feet away from the structure.
At an elevation of 22 degrees, the student is looking out of a second-story school window. The building is 50 feet from the flagpole's base, and the window is 18 feet above the ground. We may compute the angle of the triangle formed by the window, the ground, and the top of the flagpole using the tangent ratio to determine its height. The opposing side (the flagpole) divided by the neighboring side equals the tangent of 22 degrees (the window to the ground). Consequently, the flagpole is 40.3 feet tall (50 divided by 1.224). This indicates that the student is 18 feet above the ground and is looking down at the flagpole.
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Use the following frequency distribution of the weights in lb of 100 college students. Get the mean, the variance and the standard deviation. What is the range of weights from one standard deviation, below the mean to the mean?
Interval Frequency (f)
130 – 139
140 – 149
150 – 159
160 – 169
170 – 179
180 – 189
4
15
28
33
14
6
Total f=100
The required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.
Statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
From the table,
Mean = ∑fx / ∑f
Mean = 16010 / 100
Mean = 160.10
Standard deviation,
σ = √∑fd²/∑f
σ = √14265/100
σ = 11.94
The required range of weights from one standard deviation, below the mean is given as
= 160.10 - 11.94 ≤ mean
Thus, the required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.
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PLEASE HURRY
Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Commence at the beginning. The x-coordinate is Negative 3 and 12 units, thus move 3 and 12 units to the right. The difference between 3 and 4 is negative three-half.
What is the coordinate point?A point's exact location on a two-dimensional plane is determined by a pair of numbers called its coordinates. The x and y axes, which are two axes that are at right angles to one another, are known as the coordinate plane's axes. How far along each axis a specific point is located is indicated by its coordinates.
Ordered pairs are a way of describing locations on the coordinate plane. A point's location is revealed by an ordered pair by linking the point's positions along the x-axis (the ordered pair's first value) and the y-axis (the second value of the ordered pair).
To locate points, one uses the numbers on a coordinate grid. Using an ordered pair of numbers, each point may be located.
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An anesthetic is given at the dosage of 15 mg per 10 lb body weight. It is packaged in vials at a concentration of 100 mg per mL.
How many mL should be given to a patient who weighs 58 kg?
0.1920 mL of the anesthetic should be given to the patient.
Calculation of Dosage
First, we need to convert the patient's weight from kilograms to pounds:
58 kg x 2.20462 lb/kg = 128.01 lbs
Next, we can calculate the total amount of anesthetic to be given to the patient:
15 mg/10 lbs x 128.01 lbs = 19.20 mg
Finally, we can divide the total amount of anesthetic by the concentration of the anesthetic in each mL:
19.20 mg / 100 mg/mL = 0.1920 mL
So, 0.1920 mL of the anesthetic should be given to the patient.
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An exit poll shows how certain parties voted on Proposition #1. Explain how the given graph is deceptive.
Complete the statements based on the pie chart.
Pie charts are used to compare
, not
. This misleads the viewer to think
half the people in all three parties voted Yes on Issue #1, when
half of Republicans and Independents actually voted Yes on Issue #1.
1) ✔ parts of a whole
2)✔ the difference between groups
3)✔ less than
4)✔ more than
Pie charts are used to compare parts of a whole, not the difference between groups. This misleads the viewer to think more than half the people in all three parties voted Yes on Issue #1, when less than half of Republicans and Independents actually voted Yes on Issue #1.
What is a pie chart?This is a type of graph that resembles a pie because it is a circle that shows the proportion of different groups.
How to interpret the pie chart?Pie charts are used to determine percentages out of 100%, however, you cannot use them to compare groups.Due to this, you should be careful when interpreting the information. For example, in this case, you might think more than half the people in all three parties voted Yes but this might not be true.Note: Here is the missing information
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57. The population of Asheville, NC can be modeled by P(t) = 90000 · e^(0.027t) as a function of years since the start of 2020.
a. State the growth rate. Round to three places
b. How many residents does the model predict will live in Asheville, NC in 2030.
Answer:
a) Growth rate of 2.737% (3 d.p.) per year
b) 117,897
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$f(t)=ae^{rt}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $r$ is the continuous growth/decay rate.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}[/tex]
If a > 0 and r > 0, the function is an exponential growth function.
If a > 0 and r < 0, the function is an exponential decay function.
Given exponential function:
[tex]P(t) = 90000\cdot e^{0.027t}[/tex]
As r > 0 the function is an exponential growth function.
The annual growth rate is:
[tex]\begin{aligned}\textsf{Annual growth rate}& = e^{0.027}-1\\&=1.02736780...-1\\&=0.0273678027...\\&=2.73678027...\%\\&=2.737\%\; \sf (3\;d.p.)\end{aligned}[/tex]
To calculate how many residents the model predicts will live in Asheville, NC in 2030, substitute t = 10 into the given function:
[tex]\begin{aligned}\implies P(10) &= 90000\cdot e^{0.027 \cdot 10}\\&= 90000\cdot e^{0.27}\\ &= 90000\cdot 1.30996445...\\&=117896.800...\\&=117897\; \sf (nearest\;whole\;number)\\\end{aligned}[/tex]
Therefore, the model predicts that there will be a population of approximately 117,897 living in Asheville, NC in 2030.
Caitlin currently owes $13,000 to a friend who is charging him interest of 2.90% p.m. He is required to settle the loan with two equal payments, one today and the other in six months. Calculate the size of the payments using six months as the focal date.
The size of the payments that need to be made today and in six months are both $ 6, 961.69.
How to find the payment ?To find the payment that Caitlin needs to make today and in six months, assume this amount of x.
The payment in 6 months would be:
= (13, 000 - x) ( 1 + 2.4 / 100)⁶
The payment today would be x.
Equate them to find the payment:
x = (13, 000 - x) ( 1 + 2.4 / 100)⁶
x = 14, 988 - 1.1529x
x = 14, 987.979 / 2.1529
= $ 6, 961.69
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Solve
X/2 -3 = 5
A- x=4
B- x=16
C- x=13
Answer:
x=16
Step-by-step explanation:
x/2=5+3
x/2=8
x=8×2
x=16
the heptagon ($7$-sided polygon) and hexagon are drawn in plane so that they intersect at a finite number of points. let $n$ be the maximum possible number of points where two polygons can intersect. which one is correct?
The maximum possible number of points where two polygons can intersect is [tex]$n = 4$[/tex]. This is achieved when the two polygons are tangent to each other at four points.
Maximum Intersection Point CountThere are different ways to approach the problem of determining the maximum possible number of points where two polygons can intersect, but one possible method is to use geometric principles and constructive examples. Here is one possible way to do it:
Start with a heptagon and a hexagon that are both regular (i.e., all sides and angles are equal).Place the heptagon in the plane so that one of its vertices coincides with the center of the hexagon.Draw an equilateral triangle with sides of the same length as the heptagon's sides, and one of its vertices at the center of the hexagon.Connect the center of the hexagon to each vertex of the triangle, forming six congruent isosceles triangles.Draw a line segment from the center of the hexagon to the middle point of each side of the heptagon. This divides the heptagon into 14 congruent isosceles triangles.Now, it is clear that the heptagon and hexagon intersect at 4 points.This is a constructive example for showing that the maximum possible number of intersection points between heptagon and hexagon is 4.
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Karen wants to buy new shoes. There is a promotion for 3
pairs of sneakers for $450.75, how much would one pair of
sneakers cost?
This is hard to do I need help
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what is the constant of proportionality for the relationship shown in this table?
The required constant of proportionality for the relationship is 1/2.
What is Constant of proportionality?As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant. In other words, the cost is directly related to the number of gallons pumped.
According to question:Let the relation between x and y is
y = kx
Where k is proportionality constant.
Using the given values of x ad y
1 = k(2)
k = 1/2
So, the constant of proportionality for the relationship is 1/2.
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Suppose H(x)=7 root x-3 . Find two functions f and g such that (fog)(x)=H(x) .
The two functions such that composition (fog) (x) = H(x) are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
We have a function H(x) = 7 [tex]\sqrt{x-3}[/tex]
We have to find two functions f and g such that (fog) (x) = H(x).
Let f(x) = 7x
g(x) = [tex]\sqrt{x-3}[/tex]
The composition of these functions is,
(fog)(x) = f (g(x))
= 7 . g(x)
= 7 [tex]\sqrt{x-3}[/tex]
= H(x)
Hence the functions are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].
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