The ratio of outputs for any two inputs that are one value apart 2 .
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b. where b is not zero. A ratio is an equation that equates two ratios. For example, if you have one boy and her three girls, the ratio can be written as: 1:3 (3 girls for 1 boy). A ratio is the comparison of the two numbers by division.
Taking the first two outputs, or the -1/8 and -1/4, we can divide not the second one by the first one to find the
ratio:
-1/4-1/8
When dividing fractions, we multiply by the reciprocal:
-1/4x-8/1
To multiply fractions, multiply straight across:
(-1x-8)/(4x1) 8/4=2
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The growth in the population of a certain rodent at a dump site fits the exponential function, A(t)=336e^(0.031t), where t is the number of years since 1963. Estimate the population in the year 2000.
The population in the year 2000 is 395.808
Exponential Function
Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent. An example of an exponential function is the growth of bacteria. Some bacteria double every hour
Where t is the number of months since the population was first recorded. And the population after 36 months so we need to replace t=36 months into the function
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
So then can conclude that after 38 months the population of mouse is between 1963 and 2000.
A(t)=336e^(0.031t)
The population can be represented with this formula:
A(38)=336e^(0.031*38)
Where t is the number of months since the population was first recorded. And the population after 38 months so we need to replace t=38 months into the function and we got:
A(38)=336e^(0.031*38)
A(38)=336e^(1.178)
=395.808
So then can conclude that after 38 months the population of mouse is between 1963 and 2000.
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melissa has $5000 and adds $20 each week to it. chris has $6820 and spends $50 from it each week. after how many weeks will both melissa and chris have the same amount
Answer:
It will take approximately 36.4 weeks for Melissa and Chris to have the same amount of money.
Step-by-step explanation:
To determine how many weeks it will take for Melissa and Chris to have the same amount of money, you can set up an equation based on the information given. Let W be the number of weeks it takes for Melissa and Chris to have the same amount of money.
Melissa's total amount of money after W weeks will be 5000 + 20W.
Chris's total amount of money after W weeks will be 6820 - 50W.
Therefore, you can set up the equation 5000 + 20W = 6820 - 50W and solve for W.
First, you can add 50W to both sides of the equation to get 50W + 5000 = 6820.
Next, you can subtract 5000 from both sides of the equation to get 50W = 1820.
Finally, you can divide both sides of the equation by 50 to get W = 36.4.
Find the value of √17+4√13-√17-4√13
Answer:0
Step-by-step explanation:
By adding like terms,
4√13 and -4√13 equal to 0, and √17 and -√17 equal 0
Anyone please help in this part!
Answer:
x= 40 degree
y = 80 degree
Step-by-step explanation:
where is z?
Prepared building plans for Spangler Construction Company. Sent Spangler an invoice for $900 requesting payment within 30 days. (The appropriate revenue account is entitled Drafting Fees Earned.)
The appropriate sales journal entry for the building plans prepared for Spangler Construction Company is as follows:
Sales Journal Entry:Debit Accounts Receivable (Spangler Construction Company) $900
Credit Drafting Fees Earned $900
(To record the revenue from drafting fees.)
What are sales journals?Sales or service journals are used to record sales or service revenue transactions.
When the services are performed on credit, the Accounts Receivable account is debited while the Service Revenue account is credited.
Transaction Analysis:Accounts Receivable (Spangler Construction Company) $900 Drafting Fees Earned $900
Thus, the above demonstrates the appropriate recording of the service revenue transaction in the sales/service revenue journal.
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Question Completion:Prepare the appropriate journal entry.
A construction worker earns and average biweekly net pay of $1,764. Which compound inequality correctly shows the amount of money, t, the worker can spend if the monthly budget for food is between 10% and 20% ?
The compound inequality of amount of money is 176.4 < f < 352.8
What is compound inequality?
A compound difference (or combined difference ) is 2 or a lot of inequalities joined along with or or and.
Main Body:
Given,
A construction worker earns an average bi-weekly net pay of $1,764.00.
and, the worker can spend if the monthly budget for food is between 10% and 20%.
To find the which compound inequality correctly shows the amount of money?
Now, According to the question:
Total earning is $1,764.00
Amount can be spent on food is :
0.1× 1764.00 < f < 0.2 ×1764.00
176.4 < f < 352.8
Hence, The compound inequality of amount of money is 176.4 < f < 352.8
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Change the circle equation into standard form then answer the following questions:
Coordinates of the center?
Coordinates of the vertices?
How long is the radius?
Domain?
Range?
X²+ Y²-6X-2Y+6=0
The circle equation in standard form is (X - 3)² + (Y - 1)² = 2²
How to change the circle equation into standard form?
We must transform the current polynomial to circle standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We will do so by completing the square, which produces a perfect square trinomial that can be factored into a square binomial in the form of the circle standard form.
According to the given question:
Equation of circle in polynomial form is X²+ Y²- 6X - 2Y + 6 = 0
Converting to standard form using completing the square method
X²+ Y²- 6X - 2Y + 6 = 0
(X² - 6X) + (Y² - 2Y) = -6
(X² - 6X + 9) + (Y² - 2Y + 1) = -6 + 9 + 1
(X - 3)² + (Y - 1)² = 4
(X - 3)² + (Y - 1)² = 2²
The circle is now in standard form.
Coordinates of the center (h,k) = (3, 1)
Coordinates of the vertices = (3, 1), (3, -6), (2, -4), (8, -1)
Domain = [2, 8]
Range = [-6, 1]
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Amy decided to live at home while going to college how much would she save each month?
The difference between living with family and on campus is 27299 and she will be able to save an average of $4549.9 every month.
How Much Will Amy Save?To determine how much she will save, we have to find the total cost of living with parents or relative and the cost of living on/off campus and then divide it by the total number of months which is six and the find their difference.
The total cost of living with parents or relative for 6 months is = 900 + 4158 + 2259 + 675 + 11205 + 19197 + 36587 + 44579 = 119560
The cost of living on or off campus for 6 months = 900 + 12798 + 2259 + 468 + 11205 + 27630 + 36587 + 55012 = 146859
The average cost of living with relative or family for 6 months = 119560 / 6 = 19926.6
The average cost of living on or off campus for 6 months = 146859 / 6 = 24476.5
The difference is = 24476.5 - 19926.6 = 4549.9
Amy will save approximately $4549.9 monthly
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solving temperature math problems; temperature word problems with solutions; time and temperature math problems; if the temperature is 3 degrees and falls by 12 degrees what is the new temperature; the temperature at noon is 12; the temperature at 6pm was 31 1 2 f; what was the difference in temperature at 10 00 am and 12 00 noon
On solving the provided question we got to know that - Thus, the temperature will be 14°C below zero at midnight.
What is equation?Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.
The answer to the query is provided as,
Temperature at the start, or at midday, is 10°C.
Temperature change at a rate of 2°C per hour
Then,
[tex]Temperature at 1 PM = 10 + (-2) = 10 - 2 = 8[/tex] °C
[tex]Temperature at 2 PM = 8 + (-2) = 8 -2 = 6\\[/tex]°C
[tex]Temperature at 3 PM = 6 + (-2) = 6 - 2 = 4\\[/tex]°C
[tex]Temperature at 4 PM = 4 + (-2) = 4 - 2 = 2\\[/tex]°C
[tex]Temperature at 5 PM = 2 + (-2) = 2 - 2 = 0\\[/tex]°C
[tex]Temperature at 6 PM = 0 + (-2) = 0 -2 = -2\\[/tex]°C
[tex]Temperature at 7 PM = -2 + (-2) = -2 -2 = -4\\[/tex]°C
[tex]Temperature at 8 PM = -4 + (-2) = -4 – 2 = -6\\[/tex]°C
[tex]Temperature at 9 PM = -6 + (-2) = -6 – 2 = -8[/tex]°C
At nine o'clock at night, it will be eight degrees below zero.
Then,
the temperature at 12 AM, or midnight
Temperature change over 12 hours = -2°C divided by 12 equals - 24°C
Therefore, the temperature at midnight will be 10 + (-24)
= - 14°C
Thus, the temperature will be 14°C below zero at midnight.
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image Complete the table for the function y = + 7. Question 19 options: A) –9, –8, –6, –5 B) –5, –6, –8, –9 C) 5, 6, 8, 9 D) 9, 8, 6, 5
The values are 5, 6, 8, 9 for the given function y=∛x+7.
So, option D is correct.
What is a function?In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y.
The earliest known concept of a function was created by two Persian mathematicians, Al-Biruni and Sharaf al-Din al-Tusi. [4] At first, functions were envisioned as the perfect representation of the relationship between two variables. In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output. Each function has a codomain or range.
Given,
y=∛x+7
Let x=-8,
y=∛8+7
y=-2+7
y=5
x=-1, y=∛(-1)+7
y=-1+7
y=6
x=1, y=∛1+7
y=1+7
y=8
x=8, y=∛8+7
y=2+7
y=9
Therefore, the values are 5, 6, 8, 9
So, option D is correct
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The complete question is:
"Complete the table for the function y = ∛x+7
OA) -5, -6, -8, -9
OB) -9, -8, -6, -5
Oc9,8. 6. 5
OD) 5,6, 8, 9".
assume that for each n, fn is an integrable function on [a, b]. further, assume that the sequence (fn) converges uniformly to f on [a, b]. prove that f is integrable on [a, b].
fn is an integrable function on [a, b]. further, assume that the sequence (fn) converges uniformly to f on [a, b]. f is integrable on integral [a, b].
Let ε > 0. Since (fn) converges uniformly to f on [a, b], there exists an N such that |fn(x) - f(x)| < ε for all x ∈ [a, b] and all n ≥ N.
Since fn is integrable on [a, b], it follows that
∫a b|fn(x)|dx < ∞ for all n ≥ N.
We have
∫a b|f(x)|dx ≤ ∫a b|fn(x)|dx + ∫a b|fn(x) - f(x)|dx
Since |fn(x) - f(x)| < ε, it follows that
∫a b|f(x)|dx ≤ ∫a b|fn(x)|dx + ε(b - a)
Since the right hand side is finite, it follows that ∫a b|f(x)|dx is finite. Hence, f is integrable on integral [a, b].
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12-5e^(-x) ) list all critical numbers of . if there are no critical numbers, enter 'none'. critical numbers
There are no crictical numbers of the given function 12-5e^(-x).
Let's Consider
[tex]f(x) = 12 - 5*e^-x[/tex].
What is critical number of a function.
If a number causes the derivative of an expression to equal 0, it is critical.
As a result, we must set the derivative of the expression to 0.
Local Maxima and Local Minima points are also consider as critical number of a function.
f`(x) = 0 or f`(x) =1/0 by solving both equation we can find all the critical points of a function f(x).
Derivative of given funciton f(x) is f`(x).
f`(x) = [tex]0 - 5*(e^-x)*(-1).[/tex]
f`(x) = [tex]5*(e^-x)[/tex].
f`(x) = 0
[tex]5*e^-x[/tex] = 0
[tex]e^-x[/tex] = 0
[tex]e^-x[/tex] never going to zero because e^-x is an exponential decreasing function.
So there are no crictical numbers of the given function f(x).
So We enter none in this question.
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The Fitzhugh-Nagumo model for the electrical impulse in a neuron states that, in the absence of relaxation effects, the electrical potential in a neuron v(t) obeys the differential equation dv dt = −v[v2 − (1 + a)v + a] where a is a positive constant such that 0 < a < 1. (a) For what values of v is v unchanging (that is, dv/dt = 0)? (Enter your answers as a comma-separated list.) v = (b) For what values of v is v increasing? (Enter your answer using interval notation.) (c) For what values of v is v decreasing? (Enter your answer using interval notation.)
The values of v for the electric impulse model in the Fitzhugh-Nagumo model are 0, 1, and a.
What is electric impulse?The strength of the field is shown by the distance between the lines; the closer they are to one another, the stronger the field.
In this scenario, the field weakens as we travel away from the charge because the distance between the lines widens (it actually obeys an inverse square law,
The electric field, which is pointed away from the core charge, is indicated by the direction of the lines.
This is due to the fact that a positive test charge would be repelled away from the electric field if it were placed there because the direction of the electric field corresponds to the direction of the force that a positive test charge would experience when immersed in the electric field.
Hence, The values of v for the electric impulse model in the Fitzhugh-Nagumo model are 0, 1, and a.
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Need help on theses PLEAZE
The congruency of the right triangles by the Hypotenuse-Leg Congruency Theorem can be made true by the following sides.
1. [tex]\overline{RP}[/tex] ≅ [tex]\overline{MF}[/tex] and [tex]\overline{DP}[/tex] ≅ [tex]\overline{QF}[/tex]
2. [tex]\overline{CI}[/tex] ≅ [tex]\overline{CE}{}[/tex] and [tex]\overline{AI}[/tex] ≅ [tex]\overline{GE}[/tex]
3. [tex]\overline{TR}[/tex] ≅ [tex]\overline{RT}[/tex] and ;[tex]\overline{TQ}[/tex] ≅ [tex]\overline{RS}[/tex]
4. [tex]\overline{DG}[/tex] ≅ [tex]\overline{KN}[/tex] and [tex]\overline{AD}[/tex] ≅ [tex]\overline{HK}[/tex]
What are congruent triangles?Two right triangles are congruent if the hypotenuse side and one leg of one triangle is congruent to the hypotenuse side and one leg of the other triangle.
The hypotenuse leg congruency theorem states that two right triangles are congruent if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle
The hypotenuse side of ΔDPR = [tex]\overline{RP}[/tex]
The hypotenuse side of ΔQMF = [tex]\overline{MF}[/tex]
The corresponding legs of both triangles are;
[tex]\overline{DP}[/tex] corresponds to [tex]\overline{QF}[/tex]
[tex]\overline{DR}[/tex] corresponds to [tex]\overline{MQ}[/tex]
Therefore, ΔDPR is congruent to ΔQFM if [tex]\overline{RP}[/tex] ≅ [tex]\overline{MF}[/tex]
And the leg [tex]\overline{DP}[/tex] ≅ [tex]\overline{QF}[/tex] or [tex]\overline{DR}[/tex] ≅ [tex]\overline{MQ}[/tex]
2. The sides that makes the congruency statement, ΔACI ≅ ΔGCE are found as follows;
The hypotenuse side of ΔACI = [tex]\overline{CI}[/tex]
The hypotenuse side of triangle ΔGCE = [tex]\overline{CE}{}[/tex]
Therefore,
ΔACI ≅ ΔGCE ican be proved when [tex]\overline{CI}[/tex] is congruent to [tex]\overline{CE}{}[/tex], and
[tex]\overline{AI}[/tex] is congruent to [tex]\overline{GE}[/tex] or [tex]\overline{AC}[/tex] is congruent to [tex]\overline{CG}[/tex]
3. In the figure the specified information are;
[tex]\overline{TR}[/tex] is congruent to [tex]\overline{RT}[/tex] by reflexive property
The triangles are congruent if either;[tex]\overline{TQ}[/tex] iis congruent to [tex]\overline{RS}[/tex] or;[tex]\overline{TS}[/tex] iis congruent to [tex]\overline{RQ}[/tex]
4. The appropriate sides that can be used to prove that ΔADG ≅ ΔHKN are the hypotenuse side of both triangles;[tex]\overline{DG}[/tex] and [tex]\overline{KN}[/tex]
and either the legs; [tex]\overline{AD}[/tex] and [tex]\overline{HK}[/tex] or [tex]\overline{AG}[/tex] and [tex]\overline{HN}[/tex]
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,
The equation s equals two fifths times f represents the proportional relationship between the amount of sugar (s) and flour (f) in a recipe. Which table represents the equation of the proportional relationship?
Sugar Flour
1 two fifths
2 four fifths
Sugar Flour
four fifths 1
two fifths 2
Sugar Flour
1 four fifths
2 two fifths
Sugar Flour
two fifths 1
four fifths 2
The table which represents the equation of the proportional relationship as described is;
Sugar Flour
two fifths 1
four fifths 2
Which table represents the equation of the proportional relationship?It follows from the task content that the table which represents the proportional relationship is to be identified among the given answer choices.
Since the given relationship is defined by the equation;
s = (2/5) f.
Hence, when f = 1; s = (2/5) • 1; s = 2/5.
Also, when f = 2; s = (2/5) • 2 = 4 / 5.
Therefore, the table which represents the equation of the proportional relationship is;
Sugar Flour
two fifths 1
four fifths 2
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What is 1/2 equivalent to as a fraction?; Why are 1/2 and 2/4 called equivalent fractions?; What is 1/3 equivalent to as a fraction?; How do I find the equivalent fraction?
The equivalent fraction of 1/2 is 2/4 and equivalent fraction of 1/3 is 2/6.
Given that,
Why are the fractions 1/2 and 2/4 referred to as identical, and what fractional value does 1/2 equal? What is 1/3's equivalent in fractions
The fractions 2/4, 3/6, 4/8, etc. are identical to 1/2. Reduced fractions of equivalent fractions have the same value. Simply multiplying or dividing both the numerator and the denominator by the same number produces equivalent fractions.
By multiplying the numerator and denominator of each fraction by the same number, we can determine the equivalent fraction for each fraction. For instance, we must multiply 2/3 by 3/3 after determining the third equivalent fraction of 23. Consequently, 2/3 (3/3) = 6/9 is the fraction that equals 2/3.
As a result, the equivalent fractions of 1/2 and 1/3 are 2/4 and 2/6, respectively.
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Which matrix will be used as the inverted coefficient matrix when solving the following system? 3x1+ X2 = 4 5x1+2x2 =7 2 -1 -5 3 -2 5 -3 5 2
the inverted coefficient matrix is
[tex]\left[\begin{array}{ccc}2&-1&-5\\3&-2&5\\-3&5&2\end{array}\right][/tex]
1. The inverted coefficient matrix is found by taking the inverse of the coefficient matrix.
3x1 + x2 = 4
5x1 + 2x2 = 7
3. Therefore, the inverted coefficient matrix is
2 -1 -5
3 -2 5
-3 5 2
It is used to represent and manipulate complex data, such as linear equations, vectors, and polynomials. A matrix can also be used to represent a system of linear equations or to graph a function. Matrices are key elements in linear algebra, a branch of mathematics that studies vector spaces, linear transformations, and systems of linear equations.
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The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that The probability of being awarded the first job (event A) is 0.75; . The probability of being awarded the second job (event B) is 0.5; and The probability of being awarded both jobs (event (A and B)) is 0.375.
If the owner's beliefs are correct, Event A and Event B are not mutually exclusive and are independent and must be true for event A and event B.
Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative. In the sections that follow, let's go into greater detail on the fundamentals of probability.
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when you graduated from high school you had a choice between coming to jmu and working at walmart where you would earn $37,870 per year. suppose tuition at jmu is $20,000 per year, textbook expenses are $2,699 per year, and room and board expenses are $15,000 per year. assume that when you graduate you will get a job that pays you $75,000 per year.
Therefore , the best choice is you to join jmu and after that you will able to earn the same amount you spend on the graduation in 2 year.
What is equation ?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
Here,
Given:
You would earn $37,870 per year at walmart
Tuition at jmu is $20,000 per year, textbook expenses are $2,699 per year, and room and board expenses are $15,000 per year.
and you will get a $75,000 per year after graduation.
So the total expense is = 20,000 + 15000 + 2699 =37,699
Therefore , the total expense at jmu = $37,699
and total 4 year graduation course fees = 37,699 * 4=1,50,796
Thus, total fees you have to pay = $1,50,796
and after this you will get a job of $75,000 per year.
you will able to earn the same amount you spend on the graduation in 2 year.
Therefore , the best choice is you to join jmu and after that you will able to earn the same amount you spend on the graduation in 2 year.
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The universities budget covers cost for nine months what is Amy’s monthly budget for textbooks in course supplies? What is her monthly budget for rent on utilities and food? What is your monthly budget for a personal and miscellaneous cost? what is her total monthly budget?
1. Using division operations, Amy's monthly budget for textbooks and course supplies is $100.
2. Amy's monthly budget for rent, utilities, and food is $1,422.
3. Amy's monthly budget for personal and miscellaneous costs is $251.
4. Amy's total monthly budget is $1,825
How is the monthly budget determined?The total monthly budget is the total budget divided by the period (nine months).
We can use division operations to determine the individual monthly budgets for each expense class.
Living On/Off-Campus:Textbooks and Course Supplies = $900 $100
Rent, Utilities, and Food = $12,798 $1,422
Personal & Miscellaneous Expense = $2,259 $251
Transportation = $468 $52
Total non-tuition expenses = $16,425 $1,825 ($16,425/9)
The number of months = 9 months
Monthly expenses = $1,825
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if a polygon layer and a line layer are intersected, the geometry of the output feature class may be chosen as a. Poinnts b. Lines c. Polygons
if a polygon layer and a line layer are intersected, the geometry of the output feature class may be chosen as either a polygon or a line.
If the line layer is used to clip the polygon layer, the output feature class will be a polygon feature class that contains the part of the polygon layer that intersects with the line layer. The output will be a polygon feature class that contains the same attributes as the input polygon layer, plus a new attribute field indicating the line layer's object ID (OID) that was used to clip the feature. If the line layer is used to split the polygon layer, the output feature class will be a line feature class that contains the line features that were used to split the input polygon layer. The output will be a line feature class that contains the same attributes as the input line layer, plus a new attribute field indicating the polygon layer's OID that was used to split the features.
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use the given function value, and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions.
sin 30'=1/2 tan 30'=v3/3
a. csc 30'
b. cot 60'
c. cos 30'
d. cot 30'
The value for given trigonometric functions are csc 30° = 2, cot 60° = √3/3, cos 30 ° = √3/2, and cot 30° = √3.
A branch of mathematics called trigonometry examines correlations between side lengths and angles of the triangle. Trigonometric Identities are equality conditions that apply to all values of the variables in the equation and which require trigonometry functions.
Given, sin 30° = 1/2 and tan 30° = √3/3.
The formula for csc or cosec x = 1/sinx.
Then,
[tex]\begin{aligned}\csc 30^{\circ} &=\frac{1}{\frac{1}{2}}\\&=2\end{aligned}[/tex]
The formula for cot θ = tan(90°- θ)
Then,
[tex]\begin{aligned}\cot 60^{\circ} & = \tan(90^{\circ}-60^{\circ}) \\&= \tan 30^{\circ}\\&=\frac{\sqrt{3}}{3}\end{aligned}[/tex]
The formula for cos θ = sin θ/tan θ.
Then,
[tex]\begin{aligned}\cos 30^{\circ} &= \frac{\sin 30^{\circ}}{\tan 30^{\circ}}\\&= \frac{\frac{1}{2}}{\frac{\sqrt{3}}{3}}\\&=\frac{3}{2\sqrt3}\times \frac{\sqrt3}{\sqrt3}\\&=\frac{\sqrt3}{2} \end{aligned}[/tex]
The formula for cot θ = 1/tan θ.
Then,
[tex]\begin{aligned}\cot 30^{\circ}&=\frac{1}{\tan30^{\circ}}\\&=\frac{1}{\frac{\sqrt3}{3}}\\&=\frac{3}{\sqrt3}\times\frac{\sqrt3}{\sqrt3}\\&=\sqrt{3}\end{aligned}[/tex]
Therefore, the answers are 2, √3/3, √3/2, and √3.
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onsider the line =+7x5y−4. Find the equation of the line that is parallel to this line and passes through the point −−4, 5. Find the equation of the line that is perpendicular to this line and passes through the point −−4, 5.
The equation of the line perpendicular to 7x+5y = 4 is y = 5/7(x) -15/7. The equation of the line parallel to 7x+5y = 4 is y = -7/5(x) -53/5
How to find the equation of the lines parallel and perpendicular to 7x+5y = 4?Given that: the line is perpendicular/parallel to the line 7x+5y = 4 and it passes through (−4,-5)
The slope-intercept form of a straight line is:
y = mx + c
where m is the slope and c is the y-intercept
For perpendicular case:
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ x m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the given line be m₁ and the slope of the unknown line be m₂
Line1(given):
7x+5y = 4 => y = (-7/5)x + 4/5
Thus, m₁ = -7/5
m₁ x m₂ = -1
-7/5 x m₂ = -1
m₂= 5/7
Line 2(unknown) with the point (−4,-5):
y = mx + c
-5 = 5/7 (-4) + c
-5 = -20/7 + c
c = -15/7
Thus, the equation of the line is y = 5/7(x) -15/7
For parallel case:
When the two lines are parallel, they have equal slope i.e. m₁ = m₂
Line1(given):
7x+5y = 4 => y = (-7/5)x + 4/5
Thus, m₁ = -7/5
m₂= -7/5
Line 2(unknown) with the point (−4,-5):
y = mx + c
-5 = -7/5(-4) + c
-5 = 28/5 + c
c = -53/5
Thus, equation of the line is y = -7/5(x) -53/5
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find the value of for 19 degrees of freedom and an area of 0.010 in the right tail of the chi-square distribution curve. enter the exact answer from the chi-square distribution table.
The right tail of the chi-square distribution curve's value for 19 degrees of freedom and an area of 0.010 is 3.162.
To find the value of chi-square for 19 degrees of freedom and an area of 0.010 in the right tail of the chi-square distribution curve, we need to consult a chi-square distribution table. The table will list the chi-square values corresponding to different degrees of freedom and areas of the right tail of the distribution. In this case, the table should list the chi-square value corresponding to 19 degrees of freedom and an area of 0.010 in the right tail of the distribution. The value of this chi-square is 3.162, which is the exact answer from the chi-square distribution table.
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Joe Jan wants to receive $22,000 each year for the next 22 years. Assume a 6% interest rate compounded annually. How much must Joe invest today? (Round your answer to the nearest cent.)
9482.7 must Joe invest today to receive $22,000 each year for the next 22 years.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Joe Jan wants to receive $22,000 each year for the next 22 years.
6% interest rate compounded annually.
Convert 6% to decimal value
6/100=0.06
A=P(1+rt)
22000=P(1+0.06(22))
22000=P(1+1.32)
22000=P(2.32)
Divide both sides by 2.32
P=9482.7
Hence, 9482.7 must Joe invest today to receive $22,000 each year for the next 22 years.
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a triangle is to have sides of lengths a and b. find the angle between these sides that maximizes the area of the triangle
The angle between the two sides of lengths a and b that maximizes the area of the triangle is θ = π/2.
What is the formula for finding the area of a triangle?The area of a triangle whose sides of lengths a and b with an angle θ between them is
A = 1/2ab sinθ
Calculation:The given triangle has two sides of lengths a and b.
Consider θ is the angle between the a and b sides. Then the area of the triangle is
A = 1/2ab sinθ
For maximizing the area of the triangle, derivating the area we have and equate to zero i.e.,
dA/dθ = 0
⇒ dA/dθ = 1/2 ab cosθ = 0
⇒ cosθ = 0
∴ θ = π/2
And the condition for the maximum area is d²A/dθ² < 0.
I.e., d²A/dθ² = -1/2ab sinθ
⇒ d²A/dθ² = -1/2ab sin(π/2) = -1/2ab < 0
So, the maximum area is
Δ(max) = 1/2 ab sin(π/2) = 1/2ab
Thus, the angle between the two sides of lengths a and b of a triangle is π/2 when its area is maximum.
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20,245,70 Find the LCM of the following whole numbers.
Answer: 980
Step-by-step explanation: 20 = 2 x 2 x 5
245 = 5 x 7 x 7
70 = 2 x 5 x 7
= 2 x 2 x 5 x 7 x 7
= 980.
Greatest common divisor: 5
Given the vector u equal to 7 (cos 330°, sin 330°) and vector v equal to
4 (cos 90°, sin 90°), find the sum u + v and write your answer in magnitude and
direction form with the magnitude rounded to the nearest tenth and the direction
rounded to the nearest degree, 0° ≤0 < 360°.
The magnitude of u + v is 6.08 and the direction of the vector u + v is 4.7°.
What is rounded to the nearest tenth?
To write a decimal number up to one decimal place, round it to the nearest tenth. This is done in a way that leaves one digit after the decimal point after rounding.
Given that vector u is 7 (cos 330°, sin 330°)
Vector v equal to is 4 (cos 90°, sin 90°)
Calculating the value of cos 330° and sin 330°:
cos 330°
= cos (3×90° + 60°)
= sin 60°
= √3/2
sin 330°
= sin (3×90° + 60°)
= -cos 60°
= -1/2
The vector u can be written as 7 (cos 330°, sin 330°) = 7(√3/2, -1/2) =(7√3/2, -7/2) = 7√3/2 i - 7/2j
The vector v can be written as 4 (cos 90°, sin 90°) = 4(0,1) = (0,4) = 0i + 4j
Add vector u and v:
u + v
= 7√3/2 i - 7/2j + 0i + 4j
= 7√3/2 i + 1/2 j
= 6.06 i + 0.5 j
The magnitude of the vector u+v is √( 6.06² + .5²) = 6.08
The angle is
tan θ = y/x
tan θ =0.5/6.06
θ = 4.7°
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4. What function represents how much more water can be added to the bucket before it
overflows? Explain how you solved this problem.
The function that represents how much more water can be added to the bucket before it overflows is given as follows:
c(x) = 6x³ + 3x² - 2x - 2.
How to define the function?The function to calculate the space remaining in the pool is given by the subtraction of the capacity function by the function representing the current amount of water in the pool.
The functions in this problem are defined as follows:
f(x) = 8x³ + 4x² - 6x + 5.g(x) = 2x³ + x² - 4x + 7.Then the capacity function is obtained as follows:
c(x) = f(x) - g(x)
c(x) = 8x³ + 4x² - 6x + 5 - (2x³ + x² - 4x + 7)
Then the distributive property is applied to the negative sign as follows:
c(x) = 8x³ + 4x² - 6x + 5 - 2x³ - x² + 4x - 7.
Finally, the like terms are combined, that is, the terms that have the same variable and exponent, as follows:
c(x) = 6x³ + 3x² - 2x - 2.
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the difference of set1 and set2 is a set that contains only the elements that appear in set1 but do not appear in set2. True/False
The difference operation in set removes every common element between the set and give the remaining element of first set. The answer is True.
What is a set?In mathematics, a set is a logically arranged group of items that can be represented in either set builder or roster form.
What is Set Difference?The set that contains the items of S that are not elements of T is the difference between the two sets, denoted by the symbol S-T.
set1={1,2,3,4,5}
set2={4,5,6,7}
Set Difference= set1-set2 = {1,2,3}
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