For the quadratic function f(x) = 3x² - 8x + 2, the x-intercepts are x1 = (4 + √10) / 3 and x2 = (4 - √10) / 3.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The given quadratic function is - f(x) = 3x² - 8x + 2.
The quadratic function is in the standard form ax² + bx + c = 0.
Here, a = 3, b = -8 and c = 2.
The x-intercepts can be found using the formula -
x1 = (-b + √Δ) / (2a)
x2 = (- b - √Δ) / (2a)
Here, Δ = b² - 4ac.
Substitute the values in the above equation -
Δ = b² - 4ac
Δ = (-8)² - 4(3)(2)
Δ = 64 - 24
Δ = 40
Now, substitute the value of Δ in the x-intercepts formula -
x1 = [-(-8) + √40) / [2(3)] x2 = [-(-8) - √40) / [2(3)]
Open the brackets and use arithmetic operation of multiplication -
x1 = (8 + √40) / 6 x2 = (8 - √40) / 6
Take out the common value -
x1 = (8 + 4√10) / 6 x2 = (8 - 4√10) / 6
Use arithmetic operation of division -
x1 = (4 + √10) / 3 x2 = (4 - √10) / 3
Therefore, the x-intercepts are x1 = (4 + √10) / 3 and x2 = (4 - √10) / 3.
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Solve by graphing
4x - 4y = 22
y = -5.5
The system of equations has a unique solution. The solution is (0,-5.5).
What is the system of equations?
A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables.
The system of equations is
4x - 4y = 22 ....(i)
y = -5.5 ...(ii)
Putting x = 0 in 4x - 4y = 22:
4 × 0 - 4y = 22
- 4y = 22
y = -5.5
Putting x = 1 in 4x - 4y = 22:
4 × 1 - 4y = 22
- 4y = 18
y = -4.5
The points on equation (i) are (0,-5.5) and (1, -4.5).
The points on the line y = -5.5 are (-3,-5.5), (2,-5.5).
Plot the points and join them.
The intersection point is the solution of the system of equations.
The solution is x = 0 and y = -5.5
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Water flows at a speed of 20 cm/s along a rectangular channel into a lake. The width of the channel is 15 cm, the depth of the water is 2.5 cm. Calculate the amount of water that flows from the channel into the lake in 1 hour. Give your answer in litres.
Answer is 2.7 million liters/hour
What is speed?
Speed tells us how fast something or someone is travelling.
The flow rate of water can be calculated as the cross-sectional area of the channel multiplied by the speed of the water.
The cross-sectional area of the channel can be calculated as width x depth = 15 cm x 2.5 cm = 37.5 cm^2
The flow rate of water can be calculated as 37.5 cm^2 x 20 cm/s = 750 cm^3/s
To convert this to liters, we need to multiply by 1000 to convert cubic centimeters to cubic centimeters:
750 cm^3/s x (1000 cm^3/L) = 750 L/s
Finally, to find the amount of water that flows into the lake in 1 hour, we need to multiply the flow rate by the number of seconds in an hour:
750 L/s x (3600 s/hr) = 2700000 L/hr = 2.7 million liters/hour.
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PLEASE HELP ME WITH THESE QUESTIONS IM SO DESPERATE
WILL GIVE BRAINLIEST
Answer:
11.55m², 181.12mm²,11ft,
Step-by-step explanation:
Simplify the expression.
and multiply A=1/2bh
In 2015, the per capita consumption of bottled water in the United States was reported to be 36.2 gallons. Assume that the per capita consumption of bottled water in the U.S. is approximately normally-distributed with a standard deviation of 10 gallons.
Find the Z-score of someone who consumed 26.2 gallons of water. Using the Empirical Rule, what is the approximate probability that someone in the United States consumed less than 26.2 gallons of water, what is the approximate probability that someone in the United States consumed between 26.2 and 36.2 gallons of water, and what is the approximate probability that someone in the United States consumed between 26.2 and 46.2 gallons of water?
The required probabilities = 0.16
The required probabilities = 0.68
What is z-score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a particular data collection.
As given that,
μ = 36.2
σ = 10
As per empirical Rule:
μ± σ = 36.2 ±10 = 26.2, 46.2 = 68%
μ± 2σ = 36.2 ±20 = 16.2, 56.2 = 95%
μ ± 3σ = 36.2 ±30 = 6.2, 66.2 = 99.7%
less than 26.2:
13.5% + 2.35% + 0.15% = 0.16
between 26.2 and 36.2:
68% = 0.68
The required probabilities = 0.16
The required probabilities = 0.68
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You roll a 6-sided die two times. What is the probability of rolling a number less than 4 and then rolling a number greater than 3? Write your answer as a percentage%.
Answer:
Step-by-step explanation:
3/6
Use the distributive property to write an expression that is equivalent to 5(- 2x - 3)
Answer: -10x - 15
Step-by-step explanation:
The distributive property is used when you multiply a number over an addition or subtraction problem.
5 x (-2x - 3)
Step 1
Take 5 and multiply it by -2x
5 x -2x = -10x
Step 2
Take 5 and multiply it by - 3
5 x - 3 = -15
Step 3
Put the entire problem together.
5 x (-2x - 3) = -10x - 15
Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (a) Length of time to complete an exam (b) Time of fi rst class (c) Major field of study (d) Course evaluation scale: poor, acceptable, good (e) Score on last exam (based on 100 possible points) (f) Age of student
The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.
(a) Length of time to complete an exam - Ratio: This is measured on a scale of time, and can be expressed as a ratio (i.e. the amount of time spent on the exam divided by the total time allotted for the exam).
(b) Time of first class - Interval: The time of the first class is measured on a scale of minutes, hours, and days, and can be expressed as an interval (i.e. the amount of time between two classes).
(c) Major field of study - Nominal: This is a categorical measurement and can be expressed as a nominal variable (i.e. the student's major field of study is either engineering, business, etc).
(d) Course evaluation scale: poor, acceptable, good - Ordinal: This is a scale of quality and can be expressed as an ordinal variable (i.e. the quality of the course can be rated as poor, acceptable, or good).
(e) Score on last exam (based on 100 possible points) - Ratio: This is measured on a scale of points, and can be expressed as a ratio (i.e. the student's score on the exam divided by the total number of points possible).
(f) Age of student - Ratio: This is measured on a scale of years, and can be expressed as a ratio (i.e. the student's age divided by the total number of years they have been alive).
The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.
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greatest common factor for 90 and 80
Answer:
10
Step-by-step explanation:
The GCF of 80 and 90 is 10.
. use implicit function theorem to verify whether the relation x y 2 cos(x − y) = c defines an implicit solution of the differential equation
Yes, the relation x y 2 cos(x − y) = c defines an implicit solution of the differential equation.
To verify this we can use Implicit Function Theorem. According to the theorem, if a relation f(x,y) = c is given, then if the partial derivative of f(x,y) concerning y is nonzero at the point (x0,y0), there is a unique function y = g(x) such that f(x,g(x)) = c.
In this case, the partial derivative of f(x,y) concerning y is -2 sin(x-y). At the point (x0,y0), this derivative is nonzero, so there exists a unique function y = g(x) such that f(x,g(x)) = c. This implies that the given relation does indeed define an implicit solution of the differential equation.
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Research On effects of poor scale Interpration in maths
The effects of poor scale interpretation in maths are discussed below.
What are the effects of poor scale Interpretation in maths?Poor scale interpretation in mathematics can have significant effects on various areas of life and work that require the use of mathematical concepts and skills. Some of the consequences of poor scale interpretation are:
1. Inaccurate Results: Poor interpretation of scales on graphs, charts, and other mathematical representations can lead to incorrect conclusions and decisions based on the resulting data.
2. Miscommunication: Poor scale interpretation can result in misinterpretation of information and lead to miscommunication between individuals and groups.
3. Ineffective Problem Solving: Poor scale interpretation can hinder the ability to solve mathematical problems effectively, resulting in incorrect solutions and wasted time and resources.
4. Limited Career Opportunities: Poor scale interpretation skills can limit career opportunities in fields that require mathematical proficiency, such as engineering, finance, and technology.
5. Low Confidence and Motivation: Poor scale interpretation skills can lead to frustration and low confidence in mathematics, causing students and individuals to lose interest in the subject.
To avoid the negative effects of poor scale interpretation, it is important to receive proper mathematical education and training, and to continually practice and improve one's mathematical skills. Additionally, seeking help and guidance from teachers and mentors can be beneficial in improving one's scale interpretation skills.
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Arnold is drawing another part of his blueprint. He draws a line that is 1/8 an inch and then draws another line next to it that is 14 of an inch. How long is this line Arnold has drawn?Arnold is drawing another part of his blueprint. He draws a line that is 1/8 an inch and then draws another line next to it that is 1/4 of an inch. How long is this line Arnold has drawn?
The length of the new line is twice the length of the old line and total length is given by the equation L = (3/8 ) of an inch
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the length of the old line be A
Now , the value of A = 1/8 of an inch
Let the length of the new line be B
Now , the value of B = 1/4 of an inch
So , the equation will be
The number of times the new line is greater than old line is given by
B / A = x
Substituting the values in the equation , we get
x = ( 1/4 ) / ( 1/8 )
x = 8/4
x = 2 times
So , the total length of the line = A + B
Substituting the values in the equation , we get
The total length of the line L = ( 1/4 ) + ( 1/8 )
The total length of the line L = 3/8 of an inch
Hence , the equation is L = (3/8 ) of an inch
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Solve for xxx. Enter the solutions from least to greatest.Round to two decimal places. (x + 7)^2 - 11 = 0
The value of x in the equation (x + 7)² - 11 = 0 are x = -7 + √11 and x = -7 - √11
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
The variable to be solved is x . Variables are numbers represented by letters in an equation.]
Therefore,
(x + 7)² - 11 = 0
(x + 7)(x + 7) - 11 = 0
x² + 7x + 7x + 49 - 11 = 0
x² + 14x + 38 = 0
Therefore, let's factorise the quadratic equation as follows:
x² + 14x + 38 = 0
Using the quadratic formula,
[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] or [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
Hence,
a = 1
b = 14
c = 38
Therefore,
x = -7 + √11 and x = -7 - √11
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Suppose that y(t) solves the ordinary differential equation
dy/dt = (4-3Y)/(5+2Y) Y(0)=0 Find d2y/dt2 (0)
To find the second derivative of y(t) at t = 0, we can use the chain rule. We can write the given equation as dy/dt = f(y), where f(y) = (4-3y)/(5+2y).
Then the second derivative of y at t = 0 can be calculated as: d2y/dt2 (0) = f'(y) * dy/dt (0) = f'(0)f(0) = [-3/(5+20)](4-30)/(5+2*0) = -3/5.
A differential equation is an equation that relates one or more unknown functions and their derivatives. It is mainly used in the fields of biology, physics, engineering, economics, and other sciences.
A differential equation states how a rate of change (a "differential") in one variable is related to other variables. For example, the Single Spring simulation involves a differential equation that describes the displacement of a spring in response to a force.
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15 POINTS! WILL MARK BRAINLIEST
If f(x) and g(x) are inverse functions, use the information shown to find g(x)
f(2x - 10) = x + 1
f(-10) = 1
f(-12) = 0
f(2x - 12) = x
Answer Choices:
g(x) = -12
g(x) = 2x - 10
g(x) = -10
g(x) = 2x - 12
The function g(x) is defined as follows:
g(x) = 2x - 12.
How to obtain the inverse function?The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:
The fact that the variables are exchanged means that the functions are symmetric over the line y = x.
As the lines are symmetric over the line y = x, these following statements regarding the composition of a function with it's inverse is given as follows:
f(g(x)) = x.g(f(x)) = x.We have that f(2x - 12) = x, hence the function g(x) is defined as follows:
g(x) = 2x - 12.
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a sample of n = 9 scores has a variance of s2 = 18. if the scores were a population, what value would be obtained for the population variance?
Value 02 = 16 represents the population variance.
What is meant by value?The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. Value is concerned with how much something is worth, whether in monetary terms or in terms of significance. It can mean "identify how much something is worth" like a reward valued at $200 or it can indicate "hold something in high esteem" like "I value our friendship."The occurrence of two complete sets of tens gives the number 24 its place value of two.To learn more about value, refer to:
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Sahara's dog has a mass of 25 kilograms. What is the mass of the dog in grams?
Answer:
25,000g
Step-by-step explanation:
multiply the mass value by 1000
25 x 1000 = 25,000g
two telephone calls come into a switchboard at random times in a fixed one-hour period. assume that the calls are made independently of one another. (a) what is the probability that the calls are made in the first quarter hour? 1/16 correct: your answer is correct. (b) what is the probability that the calls are made within six minutes of each other? (round your answer to four decimal places.)
The probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16
Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1
What is Probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
A statistical function known as a probability distribution explains all the potential values and probabilities for a random variable within a certain range.
The uniform probability distribution is a distribution composed by two bounds, given by a and b, in which each possible outcome within these two bounds is equally as likely.
The probability that a call is made in the first quarter is 15/60
Now the probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16
Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1
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Simplify 3/7 =7^1/3.
The cube root of a cube of the number is the same number for any number. Thus, option A is the answer.
In the given question,
[tex]\sqrt[3]{7} = 7^{1/3} \\[/tex]
We have to prove L.H.S = R.H.S
Let's take R.H.S
= [tex]7^{1/3}\\[/tex]
Taking a cube for this,
[tex]= (7^{1/3} )^{3}[/tex]
We can separate this into three terms.
[tex]= 7^{1/3} . 7^{1/3} . 7^{1/3}[/tex]
We know that [tex]x^{n}. x^{m} = x^{n+m}[/tex]
Then,
[tex]= 7^{1/3 + 1/3 +1/3} \\= 7^{3/3}\\ = 7[/tex]
From L.H.S
We have to take cube root,
[tex](\sqrt[3]{7})^{3} \\= 7[/tex]
Hence, L.H.S = R.H.S, and it is verified.
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Help me because why is math so hard now
Answer:
Step-by-step explanation:
The answer will be the third one because 2/3 * (3/10 X 1) is the same as 2/3 already being multiplied to 3/10.
If you use a calculator and put 2/3 * (3/10 X 1), you will get 0.2 and if you put (2/3 * 3/10) x 1 you will also 0.2.
So (2/3 * 3/10) x 1 is equal to 2/3 * (3/10 X 1)
anderson and addison leave from the same restaurant and the same time, traveling in opposite directions. if anderson travels 15 mph and addison travels 6 mph, how long until they are 126 miles apart?
After 6 hours, Anderson and Addison will be 126 miles apart.
Let's call the time they have been traveling "t" (in hours).
Anderson will have traveled 15t miles and Addison will have traveled 6t miles. The total distance between them is 15t + 6t = 21t miles.
We know that they need to be 126 miles apart, so we can set up the equation:
21t = 126
Now we can solve for t:
t = 126 / 21
t = 6
So after 6 hours, they both will be 126 miles apart.
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PROOF Complete the proof.
Given BC AD, BCLDC, ADL DC
Prove ABCD is a rectangle.
A
B
D
C
In algebra, a number exists even equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.
What is meant by Reflexive Property?In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.
2. AD = BC due to the congruence of a rectangle's opposite sides.
3. Due to the reflexive property of congruence, DC=DC, each segment is identical to itself.
4. ADC and BCD are right angles since any rectangle's internal angles are right angles (Definition of rectangle).
5. Since they form right angles and all right angles are congruent, ADC=BCD.
6. ADC and BCD are congruent because they have two congruent sides (AD with BC and DC with DC) and a congruent angle between them: Side Angle Postulate Side Congruence Postulate (SAS Congruence Postulate).
7. AC must match BD because Congruent Parts in Congruent Triangles must match (CPCTC).
Statement Reason
1. Rectangle ABCD Given
2. AD=BC Opposite sides of a rectangle are congruent
3. DC=DC Reflexive Property of Congruence
4. <ADC and <BCD are Definition of rectangle
right angles
5. <ADC=<BCD All right angles are congruent
6. ∆ADC=∆BCD SAS Congruence Postulate
7. AC=BD CPCTC
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Please help !,,,!,!,,!,,,meeee long division step by step
A charitable organization in Oxford i hoting a black tie benefit for charity and the organization member hope to bring in at leat $1,200 tandard ticket are available for 21 each wherea vip ticket are offered for 43 a piece
To reach the goal of $1,200, the organization needs to sell at least 28 standard tickets (1,200 / 42 = 28.57) or 28 VIP tickets (1,200 / 43 = 27.91). They can also combine the sales of standard and VIP tickets to reach the goal.
The charitable organization is hosting a black-tie benefit event and aims to raise at least $1,200 through ticket sales.
The standard tickets are priced at $21 each, while the VIP tickets are priced at $43 each.
To reach the goal of $1,200, the organization needs to sell a minimum of 28 standard tickets ($1,200 / $21 = 57.14).
However, if they only sell VIP tickets, they will need to sell at least 28 VIP tickets ($1,200 / $43 = 27.91).
Finally, they can also achieve their goal by selling a combination of standard and VIP tickets.
For example, they can sell 20 standard tickets and 8 VIP tickets, which would result in a total of 20 * $21 + 8 * $43 = $840 + $344 = $1,184, reaching their goal of $1,200.
In conclusion, the charitable organization has multiple options to reach their goal of $1,200 through ticket sales for their black-tie benefit event.
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An iterative formula is shown below.
Xn+1 = 3/4xn-1
Work out the values of x2, x3 and x4, starting
with x1 = 2.
Give your answers to 2 d.p.
The value for the following order of the given iterative formula of xₙ + 1 = 3/4 xₙ₋₁ are:
x₂ = 0.5x₃ = - 0.63x₄ = - 1.47Iterative formula is used to process a repeating procedure to produce a series of results
We have an iterative formula of:
xₙ + 1 = 3/4 xₙ₋₁
We know that:
x₁ = 2
Hence:
x₂ + 1 = 3/4 x₁
x₂ + 1 = 3/4 (2)
x₂ + 1 = 3/2
x₂ = 1/2 = 0.5
x₃ + 1 = 3/4 x₂
x₃ + 1 = 3/4 (1/2)
x₃ + 1 = 3/8
x₃ = -5/8 = - 0.63
x₄ + 1 = 3/4 x₃
x₄ + 1 = 3/4 (-5/8)
x₄ + 1 = -15/32
x₄ = - 47/32 = -1.47
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Find the indicated measure.
Using the inscribed angle theorem:
7. m<A = 79°
8. m<B = 90°
9. m(BC) = 152°
What is the Inscribed Angle Theorem?The Inscribed Angle Theorem states that if two chords of a circle intersect, the measure of the inscribed angle formed by the two chords is equal to half the measure of the central angle that subtends the same arc as the inscribed angle.
Applying the inscribed angle theorem, we have:
7. m<A = 1/2(158)
m<A = 79°
8. m<B = 1/2(180)
m<B = 90°
9. m(BC) = 2(76)
m(BC) = 152°
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Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give a counterexample.
(a) lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4
(b) If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist.
(c) If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2.
(d) If lim t→0 h(t) does not exist, then h(0) cannot exist.
lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4, If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist, If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2, If lim t→0 h(t) does not exist, then h(0) cannot exist all these Limits statement are False
What do you mean by limits?A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.
lim x -> c f(x) = L
(a) False.
According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.
(b) False.
According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.
In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.
(c) False.
A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.
Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.
(d) False.
The absence of a limit does not imply the existence of the function's value at that time.
In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.
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All these given Limit statement are False.
(a) lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4
(b) If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist
(c) If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2
(d) If lim t→0 h(t) does not exist, then h(0) cannot exist.
What do you mean by limits?A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.
lim x -> c f(x) = L
(a) False.
According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.
(b) False.
According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.
In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.
(c) False.
A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.
Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.
(d) False.
The absence of a limit does not imply the existence of the function's value at that time.
In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.
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Which of the following statements is TRUE about the value of a college degree?
O A high school graduate can expect to earn about the same as a college graduate
• Every college graduate can expect to have a starting salary over $60,000 right after college
• A college graduate can expect to earn, on average, more than a high school graduate over a career
• A college graduate typically earns less than someone with a high school diploma for the first 10 years
Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.
what is proportionality ?Links are regarded to as appropriate when they typically have the same ratio. For instance, the trees in an estate and or the number of peaches in a harvest in apples depend on the average number of apples provided by each tree. A linear correlation between two numbers as well as variables is referred to as being proportional in mathematics. When the primary quantity doubles, the other amount also does so. Once one of the variables is reduced to 1/100th of its previous value, the other decreases as well. If two components are proportional, it suggests that if one rises, the other climbs as well, and their correlation is continuous at all values. The diameter and circumference of such a circle are used as an example.
given
The true statement is
starting salary = $60,000
average = $60,000 / 3
= $ 20,000
Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.
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72% it goes down by 20% what is the original price of the jacket
Answer:
4x/5
Step-by-step explanation:
the price of the jacket before goes down = x
20/100*x = x/5
the original price of the jacket= x-(x/5) = 4x/5
What is 65 Inches in Feet?
When 65 inches are converted to feet, the result is 5.41667 feet.
How do I convert an inch to a foot?To convert 65 inches to feet, divide 65 by 12.We can calculate 65 inches equals 5.41667 feet using a calculator or long division. As a result, 65 inches is equivalent to 5.41667 feet. It is important to note that inches and feet are both length units, so converting between the two involves moving the decimal point in the number two places to the left or right, depending on which unit you are converting to.Divide the number of inches by 12 to convert to feet, because a foot is 12 inches long. Similarly, multiply the number of feet by the number of inches.As a result, 65 inches equals 5.41667 feet, and you can convert inches to feet by dividing the number of inches by 12.To learn more about inches refer to :
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$122.62-$lal
5.) On February 3rd, Cardi B borrowed $17,500.00 at 6.5% exact interest to buy a new car. She had to pay back
a maturity value of $17,873.97 to pay off the loan. On what day did Cardi pay back the loan?
has a 10.3% ordinary
The day that Cardi B paid back the loan is given as follows:
June 3rd.
How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.The parameter values for this problem are given as follows:
A = 17873.97, P = 17500, r = 0.065.
Hence the time in years is obtained as follows:
17873.97 = 17500(1 + 0.065t)
1 + 0.065t = 17873.97/17500
1 + 0.065t = 1.02136971429
t = (1.02136971429 - 1)/0.065
t = 0.32876483523
A year is composed by 365 days, hence the time in days is given as follows:
0.32876483523 x 365 = 120 days.
120 days after February 3rd is June 3rd.
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