The number of handshakes altogether exists 45.
What is meant by combinations?In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset's components can be arranged in any sequence when used together. The components of the subset are arranged in a particular order in a permutation.
A combination in mathematics is a choice of elements from a set with distinct members, where the order of the choices is irrelevant.
Combinations are a mathematical method for calculating the number of alternative arrangements in a collection of objects where the order of the selection is irrelevant. You are free to choose any combination of the things.
Given:
Number of people in the conference = 10
Each person shakes hands with others.
The total number of handshakes [tex]$={ }^n \mathrm{C}_2$[/tex]
Total number of handshakes [tex]$={ }^{10} C_2=(10 \times 9) / 2=45$[/tex] handshakes.
The complete question is:
At the end of a meeting all the ten people present shake hands with each other once. The number of handshakes altogether is
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construct the general solution of involving complex eigenfunctions and then obtain the general real solution. describe the shapes of typical trajectories.
The ODE's general solution has real solution and complex eigen functions. Typical trajectories are sinusoidal curves.
The general solution of the ODE involves complex eigenfunctions, which are solutions of the form e^(ikx), where k is a real number and i is the imaginary unit. By combining these complex eigenfunctions with real coefficients, a general real solution can be obtained. Typically, these solutions will take the form of sinusoidal curves, with the amplitude and period determined by the coefficients of the eigenfunctions. The coefficients can be determined using initial conditions, allowing for more specific trajectories to be determined. For example, if the initial condition is known, then the coefficients of the eigenfunctions can be determined using Fourier analysis, allowing for the trajectory of the system to be determined.
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the graphs below show changes in a population over time. the dashed line represents the carrying capacity of the species. which of the following graphs best shows the population size of a k-selected species over time in a stable environment?
The graph in the upper left corner best shows the population size of a K-selected species over time in a stable environment.
This graph shows the population of the species increasing at a slow rate until it reaches the carrying capacity of the species (the dashed line). After reaching the carrying capacity, the population of the species remains relatively stable, fluctuating slightly around the carrying capacity. This is evidence of a K-selected species, which tend to have a higher carrying capacity and longer life spans, and the population size remains relatively stable over time in a stable environment. Mathematically, this can be expressed as y = K = C, where y is the population size, K is the carrying capacity, and C is the constant value of the carrying capacity.
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Class members that should be public are:I. ConstructorsII. Instance VariablesIII. Accessors/ MutatorsIV. Methods the class uses for itself, but the user does not needV. Methods the user needs to manipulate the objects of the classa. I, II, IVb. I, II, IIIc. I, III, Vd. I, II, III, V
Constructors, instance variables, accessors/mutators, and methods the user needs to manipulate the number of objects of the class should all be public.
Public members of a class are those that are visible and accessible to users of the class. These include constructors, instance variables, accessors/mutators, and methods that the user needs to manipulate the objects of the class. These members should be designed and implemented carefully, since they form the interface between the class and its users. Properly designed public members can ensure that the class is easy to use and understand. Making the wrong members public can lead to confusion, bugs, and difficult-to-maintain code.
Constructors, instance variables, accessors/mutators, and methods the user needs to manipulate the number of objects of the class should all be public.
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Calculate and record the net income or net loss. Label the amount in the Account Title column. Total the Income Statement and Balance Sheet columns.
Net income is the amount of accounting profit a business has left over after covering all of its expenses. Sales revenue is multiplied by COGS, SG&A, depreciation and amortisation, interest expenditure, taxes, and any other expenses to arrive at net income.
What is meant by net income?Net income is the amount that may still be left over from your paycheck after taxes and other withholdings. Net income for a company is the money that is still available after covering all operational costs, administrative expenses, cost of products sold, taxes, insurance, and other business charges. The COGS of a company in the manufacturing sector, for instance, would probably be listed, whereas the COGS of a company in the service sector might be listed under operational expenses. Net Income = Total Revenue – Total Expenses is the general formula for calculating net income. Employees' gross pay is their salary before any payroll deductions such as taxes, benefits, and other expenses are made.To learn more about net income, refer to:
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please help due TONIGHT!! GRADED /35
The amount in the bank after 2.5 years will be $241.875.
What is simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. Mathematically -
[tex]$A = P (1 + rt)[/tex]
{A} = final amount
{P} = initial principal balance
{r} = annual interest rate
{t} = time (in years)
Given is the amount deposited by Velvet in a bank for 2.5 years at a rate of 3%.
The amount in the bank after 2.5 years will be -
A = 225(1 + 0.03 x 2.5)
A = 225(1 + 0.075)
A = 225 x 1.075
A = 241.875
Therefore, the amount in the bank after 2.5 years will be $241.875.
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type the correct answer in the box. use numerals instead of words. what is the solution to this equation 7-3sqrt2-x?
The solution to this equation is 7-∛2-x is x=127
Rearrange the radical on the left side of the equation:[tex]\sqrt[3]{2-x}=12-7[/tex]
Calculate the sum or difference:[tex]\sqrt[3]{2-x}=5\\[/tex]
Divide both sides of the equation by the coefficient of the variable:[tex]\sqrt[3]{2-x} =-5[/tex]
Power on both sides:[tex](\sqrt[3]{2-x})^3=(-5)^3[/tex]
Remove the parentheses:[tex](\sqrt[3]{2-x} )^3=(-5)^3[/tex]
Simplify the radical expression: 2-x=(-5)³
Rearrange unknown terms to the left side of the equation: -x=-5³-2
Divide both sides of the equation by the coefficient of the variable:x=5³+2
Calculate the power:x=125+2
Calculate the sum or difference:x=127
When x=127
LHS= 7-∛2-127=12
RHS=12
LHS=RHS
x=127 is valid
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Use inductive reasoning to predict the most probable next number in the list.
4, 7, 1, 4, -2, 1, -5, -2, -8, ?
The next number in the list would be -11.
What is Inductive reasoning?
Inductive reasoning is a form of reasoning that derives a general principle from a set of observations. It entails drawing broad conclusions from specific observations. Deductive reasoning differs from inductive reasoning.
Based on the pattern in the list, the next number in the sequence using inductive reasoning would likely be -11.
The pattern appears to be that each number is the previous number minus 3.
Hence, By using inductive reasoning the next number in the list would be -11.
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Use the x-cube tool to graph the x-cube function
The graph of the y = x³ function is given by the image given at the end of the answer.
How to graph the function?The function for this problem is defined as follows:
y = x³.
The domain and the range of the function are given as follows:
Domain: all real values, as the function has no restrictions regarding the input.Output: all real values.Some points on the graph of the function are given as follows:
(-3, -27), as when x = 3, y = (-3)³ = -27.(-2,-8).(-1,-1).(0,0).(1,1).(2,8).(3,27).More can be learned about functions at https://brainly.com/question/24808124
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Can Someone help Me, what is the correct box i have to pick?
After two hours, Cesar and Camden are both 48 kilometers from their homes as per the coordinates.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
given, Cesar and Camden are brothers and live in the same house. Cesar is 80 kilometers away from home and bikes toward home at a rate of 16 kilometers per hour. Camden is 20 kilometers away from home and keeps walking away from home at a rate of 14 kilometers per hour.
Linear Equation for Cesar:
y = 80- 16x
Linear equation for Camden:
Y = 14x + 20
The coordinates (2, 48) is showing the position of both brothers after 2 hours.
(2, 48) this graph represents that both brothers will be met at 48 kilometers if they are walking the same road.
therefore, As per the given coordinates Cesar and Camden are both 48 kilometers away from home after 2 hours.
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If a persons eye level is 8 m above sea level and she can see de kilometers to the horizon the D equals 3.6 radical H suppose the person can see 13.5 km to the horizon what is the height of her eye level above the sea
The height of her eye level above the sea is 45.6 km
How to determine the height?Height talks about how high the persons eye is above te sea level.
The equation so formed is
3.6√h = 13.5 Kilometers
Making √h the subject of the relation we have
√h = 3.75 Kilometers
Making h the subject by squaring both sides of the equation we have
h = √3.75 Kilometers above sea level
h = 1.9 Kilometers above sea level rounded
Taking these various steps, the height of the eye is 1.9 kilometers above sea level.
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Correct question:
If a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d = 3.6√h . Suppose the person can see 13..5 kilometers to the horizon
write the simplest polynomial function with the given zeros (use the math equation editor) and write out your answer in box below.
simplest polynomial function with zeroes -2 and 3 is expanded form is f(x) = [tex]x^2 - x - 6[/tex].
To write a polynomial function with given zeros, we can use the factorization method. The zeros of a polynomial function are the solutions of the equation f(x) = 0. So, if we know the zeros of a polynomial function, we can use them to write the function in factored form.
For example, if the zeros of the polynomial function are -2 and 3, we can write the function as:
f(x) = (x + 2)(x - 3)
This function can be expanded into:
f(x) = [tex]x^2 - x - 6[/tex]
It's important to notice that the degree of the polynomial function is determined by the highest exponent of the variable in the equation, in this case 2.
It's also important to notice that the zeroes of the function are -2 and 3, as when you substitute them in the equation, the result is zero.
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The complete question is:
What is the simplest polynomial function with zeroes -2 and 3? Write the equation in the expanded form.
A certain forest covers an area of 3400 km2. Suppose that each year this area decreases by 5.5% . What will the area be after 7 years? Use the calculator provided and round your answer to the nearest square kilometer.
The area that the forest would occupy after 7 years is 2288 km²
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Let y represent area of the forest after x years.
y = abˣ
a is the initial value and b is the multiplication factor.
A certain forest covers an area of 3400 km², hence a = 3400 km². The area decreases by 5.5%, hence b = 100% - 5.5% = 94.5%. Hence:
y = 3400(0.945)ˣ
After 7 years:
y = 3400(0.945)⁷ = 2288 km²
The area of the forest after 7 years is 2288 km²
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Consider an election with 521 votes
a) If there are 5 candidates, what is the smallest number of first-place votes a candidate could win with under the Plurality method?
The smallest number of first-place votes a candidate could win with under the Plurality method is 105.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, an election with 521 votes.
considering an election with 521 votes and 5 candidates up for the election
Dividing the votes amongst 5 candidates
= 521/5 = 104.2
So, the least number of first-place votes needed by a candidate using the plurality method would be = 105 votes
104.2+ 104.2 + 104.2 + 104.2 + 104.2 = 521 (Dividing the votes equally)
104+104+104+104+104= 520
Thus, the remaining vote = 521 - 520 = 1
Least first-place vote = 104+1= 105 votes
Therefore, the smallest number of first-place votes a candidate could win with under the Plurality method is 105.
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There are twenty-four 4 digit whole numbers that use each ofth four digits, 2, 4, 5, and 7 exactly once. Listed in numbericalorder from smallest to largest, the number in the 17th position inthe list is;
a. 4527 b. 5724 c. 5742 d. 7245 e. 7524
A straight concrete sidewalk is to be 3 feet wide, 60 feetlong and 3 inches thick. How many cubic yards of concretemust a contractor order for the sidewalk if concrete must beordered in a whole number of cublic yards?
a. 2 b. 5 c. 12 d.20 e. more than 20
The number in the 17th position in the list is 7425
We start by eliminating some of the options. The smallest possibility for the larger number is if the larger number were twice the smaller number. [tex]$2457\times2=4914$[/tex], since [tex]$2457$[/tex] the least value in the group. In order for the largest possibility to be less than or equal to 7542, the largest number in the set, when multiplied by 2, it must be twice as large as the largest number in the set.This happens to be [tex]$2754\times2=5508$[/tex]. As a result, the number would need to be even and between 4914 and 5508. 5472 and 5274 are the only even numbers in the set and in this range. Both of these numbers are not twice a number in the set, according to a cursory check. The number cannot be four times or higher than any other number in the set because [tex]$2457\times4=9828$[/tex], well past the range of the set. Therefore, the number must be triple another number in the set. The least possibility is [tex]$2457\times3=7371$[/tex]and the greatest is [tex]$2475\times3=7425$[/tex], since any higher number in the set multiplied by 3 would be out of the range of the set. Reviewing, we find that the upper bound does in fact work, so the multiple is [tex]$2475\times3=7425[/tex].
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distinguishing between linear growth and exponential growth identify the type of function graphed to the right. linear exponential other graph
To distinguish between linear growth and exponential growth, you need to look at the equation of the function and the shape of the graph.
Linear functions have a constant rate of change, meaning that the slope of the line is always the same. The equation for a linear function is y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear function is a straight line.
Exponential functions, on the other hand, have a variable rate of change, meaning that the slope of the line changes as the x-value increases. The equation for an exponential function is y = ab^x, where a and b are constants. The graph of an exponential function is a curve that increases or decreases rapidly.
If the graph is a straight line it is linear, if it is curved and increases or decreases rapidly then it is exponential, otherwise, it would be considered as other.
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You are given the 2012 value of a product and the rate at which the value is expected to change during the next 5 years. Use this information equation that gives the dollar value V of the product in terms of the year. (Let t-12 represent 2012.) 2012 Value $159Rate $4.50 (increase per year) _____, 12 ≤ t ≤ 17
The linear equation is [tex]$V=21.45+5.15 t$[/tex].
What is the Slope-Intercept Form of a Linear Equation?When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation. A line's equation can be written in the slope-intercept form such that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are instantly visible. A common name for this form is the y = mx + b form.We are given the dollar value [tex]$\$ 72.95$[/tex] of a product in 2010 and it is changed [tex]$\$ 5.15$[/tex] increase per year.
We are asked to write a linear equation that gives the dollar value V of the product in terms of the year t.
The general linear equation for this case would be,
[tex]$$V=C+5.15 t$$[/tex]
Since the dollar value increases by [tex]$\$ 5.15$[/tex]per year, the slope is[tex]$5.15$[/tex]. And, C is the V-intercept (the value of V when t=0 ).
Let us first determine the value of $C$ by substituting the given dollar value $ 72.95 in 2010 . This gives us:
[tex]V & =C+5.15 t \\[/tex]
[tex]72.95 & =C+5.15(10) \\[/tex]
[tex]72.95 & =C+51.5 \\[/tex]
[tex]72.95-51.5 & =C+51.5-51.5 \\[/tex]
[tex]21.45 & =C[/tex]
[Given that[tex]$\mathrm{t}=10$[/tex] at 2010
[Subtract 51.5 to both sides]
Thus, the value of C=21.45.
Let us substitute the value of C in the Eqn(1):
[tex]$$V=21.45+5.15 t$$[/tex]
Therefore, the linear equation is [tex]$V=21.45+5.15 t$[/tex].
The complete question is,
You are given the dollar value of a product in 2010 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t=10 represent 2010 .)
[tex]$\frac{2010 \text { Value }}{\$ 72.95}$[/tex]
Rate
[tex]$\$ 5.15$[/tex] increase per year
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please help me, im nose sure how to do this work
The measure of angle C is 149°.
What is Angle?In mathematics, an angle is a figure made up of two rays that share a terminal and are referred to as the sides of the angle and the vertices of the angle, respectively.
Angles, which are frequently expressed in terms of degrees or radians, are used to quantify the size of turns.
The law of cosines, the law of sines, and the Pythagorean theorem are only a few examples of mathematical equations that use angles, which are a key component of geometry.
When understanding shapes, angles are equally crucial.
The angles within a triangle, a quadrilateral, and a polygon can provide information on the number of sides a shape has in addition to whether or not it is regular.
Angles are also used to calculate the arcs and circles of an object.
From the given figure,
It is a pentagon, sum of sides of a pentagon is 540°
It is clear that,
90 + 90 + 90 + 6x + 1 + (8x - 11) = 540°
⇒ 260 + 14x = 540°
⇒ 14x = 540 - 260
⇒ 14x = 280
⇒ x = 20
∠ C = 8 × 20 - 11 = 160 - 11 = 149°
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Find the volume and the total area of the largest cube of the wood that can be from a log of circular section whose radius is 16.8in.
The volume and the total area of the largest cube of the wood that can be from a log of circular section whose radius is 16.8in is: 7.76 ft³, 23.52 ft².
How to find the volume and total area?Diameter of the log
d=2(16.8)
d=33.6in
Edge of cube
a²+a²=d²
2a²=33.6²
a²=564.48
a=23.76 in
Volume of the largest cube
V=a³
V=23.76³
V=13413.41 in³
V=13413.41 in³×(1 ft/12 in)³
V=7.76 ft³
Total area of the largest cube
A=6a²
A=6(23.76²)
A=3,387.23in²
A=3,387.23 in²×(1/ ft12 in)²
A=23.52 ft²
Therefore the Volume of the largest cube is 7.76 ft³ and the total area is 23.52 ft².
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College-Educated Workers. Based on data from the U.S. Census Bureau, a Pew Research study showed that the percentage of employed individuals ages 25-29 who are college educated is at an all-time high. The study showed that the percentage of employed individuals aged 25-29 with at least a bachelor's degree in 2016 was 40%. In the year 2000, this percentage was 32%, in 1985 it was 25%, and in 1964 it was only 16% (Pew Research website).
a. What is the population being studied in each of the four years in which Pew has data?
b. What question was posed to each respondent?
c. Do responses to the question provide categorical or quantitative data?
The population being studied in each of the four years is:
college educated individuals aged 25-29The question that was posed to each respondent is:
Have your earned a bachelor's degree (or higher)?What is meant by Population?The term "population" refers to all citizens who are present in a nation or who are temporarily absent from it, as well as all aliens who have made a nation their permanent home. The number of residents in a certain area is depicted by this indicator. The annual variations in population brought on by births, deaths, and net migration are measured as growth rates.
(a) Data and Calculations:
Percentage of employed individuals ages 25-29 with at least a bachelor's degree
in 2016 = 40%.
In the year 2000 = 32%,
in 1985 = 25%,
in 1964 = 16%.+
The percentage has continued to increase steadily.
(b) Numbers are not indicated by categorical data. They have a qualitative character. Instead, categories are used to organize the data. Data about ethnicity, sex, age group, and educational attainment are some examples of categorical data.
U.S. Census Bureau
a. The population being studied in each of the four years is:
O college educated individuals aged 25-29
b. The question that was posed to each respondent is:
O Have your earned a bachelor's degree (or higher)?
c. O categorical
The complete question is,
Based on data from the U.S. Census Bureau, a Pew Research study showed that the percentage of employed individuals ages 25-29 who are college educated is at an all-time high. The study showed that the percentage of employed individuals aged 25-29 with at least a bachelor's degree in 2016 was 40%. In the year 2000, this percentage was 32%, in 1985 it was 25%, and in 1964 it was only 16%.+
(a) What is the population being studied in each of the four years?
O college educated individuals
O college educated individuals aged 25-29
O individuals aged 25-29
O employed individuals aged 25-29
O employed individuals
(b) What question was posed to each respondent?
O Have your earned a bachelor's degree (or higher)?
O Are you enrolled in college?
O Are you between the ages of 25 and 29?
O In what year did you receive your bachelor's degree?
O Are you employed?
(c) Do responses to the question provide categorical or quantitative data?
O categorical
O quantitative
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Explain why 96:38 is NOT the same as 38:96.
The two ratios are inverse of each other that's why 96:38 is not the same as 38:96.
What are inverse ratios?When two quantities are inversely related, that is, when an increase in one quantity causes a decrease in the other and vice versa, they are said to be in inverse proportion. The product of the given two quantities is equal to a constant value in inverse proportion.
Given that the two ratios are 96:38 and 38:96. The value of the two ratios will not be the same because both the ratios are inverse of each other or are reciprocals of each other.
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Answer:
The two ratios are inverse of each other that's why 96:38 is not the same as 38:96.
Step-by-step explanation:
I took the quiz.
SEE IMAGE!!! PLS HELP ASAPPP
Find the quotient. If possible, rename the quotient as a mixed number. Select the answer that is in simplest form.
3 5
8 ÷ 4 = ?
A.
1 5
8
B.
29
32
C.
25
32
Answer: B
Step-by-step explanation:
[tex]3 \frac{5}{8} \div 4=\frac{29}{8} \div 4=\frac{29}{32}[/tex]
1. Determine whether the following numbers could be the sides of a right triangle. Show your work.
a.
17, 15, 8
b.
7, 25, 19
a. 17, 15, 8 this can be a right triangle, while b. 7 25 19 is not a right a triangle
How to know when triangles are formedThere are an endless number of triangles produced when no side is specified.
The three angles produce an unlimited number of distinct triangles if side lengths are not provided.
When the three sides are specified the sides will be such that addition of the two smaller sides will be greater than the third side
For a. 17, 15, 8
the two smaller sides are:15 and 8
15 + 8 > 17
this can be a triangle
For b. 7, 25, 19
the two smaller sides are:7 and 19
7 + 19 > 25
this can be a triangle
For a right triangle the Pythagoras rule should be observe: the squire of the smaller sides will be equal to the square of the longer side. let the longer side be x
x² = 15² + 8²
x² = 225 + 64
x² = 289
x = √289
x = 17
this is a right triangle
x² = 7² + 19²
x ² = 49 + 361
x² = 410
x = √410
x = 20.25
this is not a right triangle
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An employee is reimbursed at a rate of 29 cents per mile. Travels at a 25 miles 3 days a week
The total reimbursement for the employee will be $21.75.
How to calculate the word problem?It is important to note that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this situation, the employee is reimbursed at a rate of 29 cents per mile and he ravels at a 25 miles 3 days a week.
The total reimbursement will be:
= 0.29 × 25 × 3
= $21.75
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Complete question
An employee is reimbursed at a rate of 29 cents per mile. Travels at a 25 miles 3 days a week. Find the total reimbursement.
I just need to figure out how to write the equation
The rest I can do on my own
Katie is mixing a new blend of perfume. Her formula calls for 12% lavender solution. She has two bottles. One is 15% and the other is 6%. How many ounces of each does she need to make 18 ounces of 12%?
On solving the equation, it is seen that about 12 ounces of the 15% solution must be mixed with about 6 ounces of the 6% solution to get 18 ounces of the 12% perfume.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Let x = number of liters of the 15% solution
Let 18 − x = number of liters of the 6% solution
Solution Ounces Strength Amount of Perfume
15% x 15 15x
6% 18 - x 6 6(18 - x)
Mixture 18 12 (18)(12)
So, the equation will be -
(amount of perfume in 15% solution) + (amount of perfume in 6% solution) = (amount of perfume in mixture)
15x + 6(18 − x) = (18)(12)
Solve the equation using distributive property -
15x + 108 - 6x = 216
Combine the like terms -
15x - 6x = 216 - 108
Simplify the equation further -
9x = 108
x = 108/9
x = 12
Now, substituting the value of x in 18 − x = 18 - 12 = 6.
Therefore, the amount in ounces is obtained as 12 ounces and 6 ounces.
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PLEASE HELP ASAP (pic included)
Find the
equation
of this
line.
y = [? ]x + [ ]
Simplify your answer and enter as an integer.
Answer:
y=-3x+4
Step-by-step explanation:
If we use rise over run from one point to the next, you will see that you rise vertically 3 units, then run horizontally 1 unit.
Then Make the rise negative because this is a negative graph. So -3/1
Divide -3 by 1. -3/1=-3. mx=-3
Now we have to find the y-intercept. This is where the graph crosses/intersects the y-axis. As if you look at the y-axis, you will see that the graph intersects the y-axis at (0,4).
So your y-intercept is 4. b=4.
-Hope this helped
One federal tax schedule states that if you are single and your taxable income is between $37,450 and $90,750, then you owe $5156.25 plus 25%
of your taxable income over $37,450. Is the tax you owe a linear function of your taxable income if the taxable income is between $37,450 and $90,750?
If so, find a formula giving tax owed as a linear function of taxable income over $37,450.
The linear function for the amount of tax owed for a taxable income over $37,450 is given as follows:
y = 0.25x + 4191.5.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope.b is the intercept.If your taxable income is between $37,450 and $90,750, then you owe $5156.25 plus 25% of your taxable income over $37,450, hence the function is defined as follows:
y = 5156.25 + 0.25(x - 37450).
y = 5126.5 + 0.25x - 935
y = 0.25x + 4191.5.
More can be learned about linear functions at https://brainly.com/question/24808124
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A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25. How many of each type of frust was sold? please show the steps to solve THANK YOU!!!!
Answer:
5 oranges and 10 apples were sold
Step-by-step explanation:
Let x be the number of oranges sold and y be the number of apples sold
Since 15 fruits were sold in all we get the following equation
x + y = 15 ....................[1]
Each orange costs $1 so if x oranges were sold that would fetch x dollars in sales = x dollars in sales
Each apple costs $2 so if y apples were sold, that would result in 2y dollars in sales
Total sales in $ = x + 2y and we know this is $25 so we get the second equation as
x + 2y = 25 ..................[2]
Look at the two equations. The coefficient of the x term is the same. We can eliminate the x term by subtracting equation [1] from equation [2] as follows:
x + 2y = 25
-
x + y = 15
-----------------
y = 10
(2y - y = y and 25-15 = 10)
Now that we know y = 10, we can use equation [1] to find x
x + 10 = 15
which makes x = 5
ANSWER
5 oranges and 10 apples were sold
Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y) = C or y = F(x, C) where C is a needed constant.) 3x^2 − y^2 = C.
The orthogonal trajectories for the family of curves 3x^2 − y^2 = C are circles with the equation x^2 + y^2 = C/3.
To find this, we can take the derivative of the original equation 3x^2 − y^2 = C with respect to x, which will give us 6x. Then, we can take the negative reciprocal of this derivative, which is -1/6x. This is the slope of the orthogonal trajectories.
We then can use the point-slope form of a line to get y - y1 = -1/6x (x - x1). Since the slope of the orthogonal trajectories is always -1/6x, we can just set the equation y - y1 = -1/6x (x - x1) equal to 0 and solve for x to get x1 = -y1/6.
We can then plug this value back into the point-slope equation to get y - y1 = -1/6(-y1/6) (x - (-y1/6)), which simplifies to y - y1 = y1/6 + x. Now, if we let y1 = -C/3, then we get y - (-C/3) = C/6 + x, which can be rewritten as x^2 + y^2 = C/3.
Therefore, the orthogonal trajectories for the family of curves 3x^2 − y^2 = C are circles with the equation x^2 + y^2 = C/3.
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Can someone help me pleace
Answer:
A
Step-by-step explanation:
ABC is similar to DEF because similar triangles are triangles that have the same shape, but their sizes may vary.
THREE PARTS QUESTION PLEASE HELP EASYY
Philip pours wax into a cylindrical mold to make candles. The dimensions of a finished candle are shown in the diagram below.
PART
A candle shaped like a cylinder is shown. The height of the candle is labeled five and five tenths inches. A dashed line is drawn from the center of the circular base to the edge. The line is labeled three inches.
Question 1
Part A
How much wax does Philip use to make a candle rounded to the nearest cubic inch? Use 3.14 for π.
Enter the correct answer in the box.
Question 2
Part B
Philip spends $0.15 per cubic inch for the wax to make the candles. Approximately how much will it cost him to purchase enough wax to make 14 cylindrical candles?
A) $109.20 dollars
B) $218.40 dollars
C) $325.50 dollars
D) $598.50 dollars
Question 3
Part C
Philip wants to cover the lateral surface of one of the candles with glitter. How many square inches of the candle will he cover with glitter in terms of π?
Enter the correct answer in the box in terms of π.
Part A
Using the formula for the volume of a cylinder,
[tex]V=\pi r^2 h \approx (3.14)(3^2)(5.5)=\boxed{155.43}[/tex]
Part B
The total volume of 14 candles is [tex](155.43)(14)=2176.02[/tex] cubic inches.
So, the cost is [tex](2176.02)(0.15) \approx \boxed{\$325.50}[/tex]
Part C
Using the formula for the lateral surface area of a cylinder,
[tex]2\pi rh=2\pi(3)(5.5)=\boxed{33\pi}[/tex]
