The example of the function equation is f(x+3) = x² + 8x + 16 .
In the question ,
we have been asked to give an example of the function equation .
The Function Equation is defined as equations where the unknowns are functions, rather than a traditional variable.
For Example :
If f(x+3) = x² + 8x + 16 , then what is f(x)?
the above question is an example of function equation .
to find the solution ,
we let ,y = x + 3; then x = y - 3 .
Substituting the value of x in f(x+3) we get ,
f(y) = 2y² + 2y + 1 .
hence f(x) = 2x² + 2x + 1 that is = (x + 1)² .
Therefore , the example is f(x+3) = x² + 8x + 16 .
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An economics graduate student in the united states earns an $18,000 stipend per year. the u.s. sees significant inflation. how might the student react?
The reaction of the graduate student on inflation is that a cost-of-living increase to her stipend.
What is inflation?Inflation is the pace of expansion in costs over a given time-frame. Inflation is regularly a wide measure, like the general expansion in costs or the expansion in the typical cost for many everyday items in a country.
According to question:Inflation is term which states there is an expansion in the cost level for any labor and products.
In the unique situation, a set of experiences graduate living in the US got a payment of 18,000 dollar. However, there is a critical expansion that US economy endures. In this way the expense of products and the administrations accessible to individuals increments quickly. Individuals presently need to spend more on everything. Accordingly the alumni understudy requirements to request the typical cost for most everyday items to be remembered for the payment as need might arise to spend more on living.
Thus, graduate student argue on the a cost-of-living increase to her stipend.
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what is the best big-o function for the worst case scenario analysis of a linar search of a list of size n (counting the number of comparisons)?
Big O notation focuses on the worst-case scenario analysis, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.
Imagine that you're a teacher with a student named Ram. You want to find his records, so you use a simple search algorithm to go through your school district's database.
You know that a simple search takes O(n) times to run. This means in the worst case, you'll have to search through every single record to find Ram
After a simple search, you find that Ram records are the very first entry in the database. You don't have to look at every entry.
Did this algorithm take O(n) time Or did it take O(1) time because you found Ram records on the first try?
In this case, 0(1) is the best-case scenario – you were lucky that Ram records were at the top. But Big O notation focuses on the worst-case scenario, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.
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A 2-column table with 4 rows. Column 1 is labeled statement with entries cosine (2 x), = cosine (x + x), = cosine (x) cosine (x) minus sine (x) sine (x), = cosine squared (x) minus sine squared (x). Column 2 is labeled reason with entries given, 1, 2, 3. The table shows the derivation of cos(2x). Select the correct reason for each step. Reason 1 is. Reason 2 is. Reason 3 is.
Answer:
Step-by-step explanation:
c
Describe in detail how can you use problem-solving in personal, professional, or mathematical problems?.
In order to solve the challenges we encounter every day, Problem solving strategies are needed. To tackle a specific problem, we must first comprehend it, then create a plan for resolving it, and finally, put the plan into action.
The techniques that a person uses to solve difficulties are referred to as problem-solving strategies. A person may experience difficulties at their place of employment or home. A problem-resolution strategy must be in place in order to address such issues.One must first understand the issue. Then, potential solutions to the issue must be identified, and the best one among the available options must be picked. The chosen approach would subsequently be put into practice.Mathematical problem-solving techniques are also necessary. One must first comprehend the issue at hand before attempting to resolve it in order to tackle a particular mathematical problem.To sum up, everyone must use problem-solving techniques to overcome the obstacles we confront.
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Chase looks around at an assembly. He notices his younger sister to his right and his older brother 16 feet ahead of him. If Chase's brother and sister are 20 feet apart, how far apart
are Chase and his younger sister?
The 16 feet distance from Chase to his older brother and the 20 feet distance from his older brother to his younger sister, using Pythagorean, Theorem, indicates that the distance from Chase to his younger sister in the assembly is 12 feet
What is Pythagorean Theorem?Pythagorean Theorem states how the length of the sides of a right triangle are related, that is the square of the longest side of a right triangle is equivalent to the sum of the square of the other two sides.
The location of Chase, his younger sister, and his older brother forms a right triangle.
The distance from Chase to his older brother = A leg of the right triangle
The distance from Chase to his sister = A second leg of the right triangle
The distance from his older brother to his sister = The hypotenuse side of a right triangle
From the question, we get;
Distance between Chase and his older brother = 16 feet
Distance between Chase's older brother and his sister = 20 feet
According to Pythagorean Theorem, we get;
Distance between Chase and his younger sister = √(20² - 16²) = 12
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What is the angle of 1?
Answer: Acute
Step-by-step explanation:
I don't know
water is leaking out of an inverted conical tank at a rate of 13100.013100.0 cm3/mincm3/min at the same time that water is being pumped into the tank at a constant rate. the tank has height 15.0 m15.0 m and the the diameter at the top is 3.0 m3.0 m. if the water level is rising at a rate of 20.0 cm/min20.0 cm/min when the height of the water is 3.0 m3.0 m, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
The rate at which water is being pumped into the tank in cubic centimeters per minute is 289.252.7 [tex]cm^{3}/min[/tex]
what is volume?the volume that a substance or thing takes up or the space it takes up inside a container, especially when it is large.
given
For the given cone the ratio of radius to height is [tex]\frac{1}{3}[/tex]
so [tex]r= \frac{1}{3}h[/tex]
V=[tex]\pi \frac{r^{2}h}{3}[/tex] becomes V= [tex]\frac{\pi h^{3} }{27}[/tex][tex]\frac{800000}{9}cm^{3}/min[/tex]
[tex]\frac{dV}{dh}=\frac{\pi h^{2} }{9}[/tex]
We are interested in how Volume has changed over time and see that
[tex]\frac{dV}{dt}=\frac{dV}{dh} * \frac{dh}{dt}[/tex]
Using the result we already determined for [tex]\frac{dV}{dh}[/tex] in addition to the given figure of 20 cm/min (at a height of 200 cm )
we get,
[tex]\frac{dV}{dt } = \frac{\pi (200 cm)^{2}*20 cm }{9 min}[/tex]
= [tex]\frac{800000}{9}cm^{3}/min[/tex]
or roughly, 279,252.7 [tex]cm^{3}/min[/tex]
This is the inflow rate necessary to cause an increase in height while ignoring the rate of leakage.
The sum of these two has to represent the actual inflow rate:
279,252.7 [tex]cm^{3}/min[/tex] + 10000 [tex]cm^{3}/min[/tex]
289.252.7 [tex]cm^{3}/min[/tex]
hence the rate at which water is being pumped into the tank in cubic centimeters per minute is 289.252.7 [tex]cm^{3}/min[/tex]
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I need this done by tonight!!! this is the last question please help!!
The equation of best fit is y = (-22/5)x + 10.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The following coordinates are given:
Pick two coordinates.
(0, 10) and (25, -100)
The equation of best fit.
y = mx + c
Now,
m = (-100 - 10) / (25 - 0)
m = -110 / 25
m = -22/5
Now,
(0, 10) = (x, y)
10 = (-22/5) x 0 + c
c = 10
Now,
y = mx + c
y = (-22/5)x + 10
Thus,
Using the coordinates the equation of best fit is y = (-22/5)x + 10.
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m is a two-digit integer. the two-digit integer n is obtained by reversing the digits of m. the difference between m and n is one eleventh (1/11) of the sum of m and n. find the value of m n.
The values will be of two digit either 92 or 29, 74 or 47 etc.
Let M = AB(A..B = 0…9) and N = BA. where A and B are numbers from 0 to 9.
The subtraction rule requires the last digit of the difference to be the Difference of A-B. To explain further, for example 44, take the last digit 4. This can be expressed as the difference of 5-1, 8-4, 4-0. (meaning 1st digit is A and 2nd digit is B) = 88 - 44 = 44, similarly 99-55 = 44, 44-0 = 44. So we can represent 44 according to the rules above.
For numbers greater than 100, the last digit can be represented as the sum of the numbers 0 through 9 and the numbers greater than 5. To explain this, let's analyze 121. The last digit is 1.
digit can be represented as the sum of the numbers 0 through 9 and the numbers greater than 5. To explain this, let's analyze 121.
The last digit is 1. Since the number is greater than 100, it must be expressed as the sum of single digit numbers that sum to 11,
so 9+2.8+3.7. + 4.6+5, then applying any of these gives 92+29 = 121, 83+38 = 121, 74+47+121, 65+56=121. So 121 is removed.
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Please help me out pretty please
Answer:
postivie first
equal to 0 next
postivie next
negative
If the purchase price for a house is $218,500, what is the monthly payment if you put 3. 5% down for a 30 year loan with a fixed rate of 6. 5%?.
Assuming you are asking for the monthly principal and interest payment for the loan, it would be:
$1,021.76.
The calculation for the monthly mortgage payment is as follows:
P = (r * (1 + r)^n) / [(1 + r)^n - 1] * A
P = Monthly Payment
r = Monthly Interest Rate (6.5%/12 = 0.00542)
n = Number of Months (30 x 12 = 360)
A = Loan Amount (218,500 - (218,500 x 0.035 = 7,645) = 210,855)
Therefore, the monthly payment would be:
P = (0.00542 * (1 + 0.00542)^360) / [(1 + 0.00542)^360 - 1] * 210,855
P = $1,021.76
Where can I find compound interest?When calculating compound interest, the starting principle amount is multiplied by one along with the annual interest rate raised to the number of compound periods minus one. The resulting value is then reduced by the full initial loan amount. Investopedia, 2019. Katie Kerpel, "Copyright."
How is compound interest demonstrated?For instance, after a year, if you deposited $1,000 in an account with 1% yearly interest, you would have received $10 in interest. Compound interest allows you to earn 1% on $1,010 in Year Two (principal plus interest), which translates to $10.10 in interest payments for the year.
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Phil is going rollerblading. The cost to rent rollerblades for x hours at Roller Central is f(x) = 5x + 10. The cost to rent rollerblades at Skate World is f(x) = 6x + 5. If Phill skates for 4 hours, which location is the best to go to? What is the difference in price?
Answer:
Skate World is better because it is $1 less than Roller Central.
Step-by-step explanation:
f(4) = 5(4) + 10
f(4) = 20 + 10
f(4) = 30
f(4) = 6(4) + 5
f(4) = 24 + 5
f(4) = 29
Roller Central is $30 and Skate World is $29.
As monte carlo simulation is essentially statistical sampling, the larger the number of trials used, the more precise is the result.
a. True
b. False
True, Monte Carlo simulation is used for statistical sampling where larger number of trials are used for the precise result.
Step by Step Explanation:
Monte Carlo simulation is a mathematical technique or statistical sampling which is used to predict all possible outcomes of any uncertain event.The larger the number of trials more is the accuracy as it is based on the past data to predict the future outcomes.example : For the prediction of first month sale of any new launch product you can revise more number of old data.It help to calculate probability more accurately.Therefore, it is true to have more number of trials in Monte Carlo simulation statistical sampling for precise result.
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is 7.33 a terminating or repeating decimal?
Answer: 7.33 is a terminating decimal. 7.333333... or 7 1/3 is a repeating decimal.
Step-by-step explanation:
Evaluate 12.5s + 11.9t when s = 3 and t = 4
Answer: 85.1
Step-by-step explanation:
Why is there an equation of a line?
Equations' true strength is in their ability to explain numerous aspects of the world in a highly accurate manner.
The set of points that make up a line in a coordinate system are represented algebraically by a line's equation.
An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.
We may determine whether a given point lies on a line using the equation of any line. The line's equation is a linear equation of degree one. The slope of the line and a point on the line can be used to create the equation of a line.
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How many times does 13 go into 54?
times, with a remainder of ?
The number 13 is 3 times the number 54 with the remainder of 15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the number 54 is divided by 13 with some remainder. The division will be done as below,
13 ) 54 ( 3
-39
___________
15
Hence, the division with the remainder can be written in mixed form as 3¹⁵/₁₃.
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CAN SOMEONE PLEASE HELP ME FASTT!!
Answer:
Its C
Step-by-step explanation:
if a1 = 2 and an = -5an-1 +3 then what's the value of a5
HELP PLEASE
Answer:
10
Step-by-step explanation:
a1=2
a=2
an=-5an-1+3
plug in
(2)5=10
f(x)=2x^2+7x-4. solve using quadratic fomula
The given function is solved to obtain x = -4, 0.5.
What is the quadratic formula?Quadratic formula is used to find the roots of a quadratic function f(x) = ax² + bx + c as x = (-b ± √(b² - 4ac))/2a.
The expression b² - 4ac is called the determinant D.
When D = 0, roots are real and equal.
For D > 0, roots are real and unequal and for D < 0, roots are complex conjugates.
The given quadratic function is f(x) = 2x² + 7x - 4.
It can be solved by using quadratic formula as follows,
2x² + 7x - 4 = 0
x = (-7 ±√(-7²- 4 × 2 × -4))/(2 × 2)
= (-7 ± 9)/(2 × 2)
= -4, 0.5
Hence, the value of x found by using quadratic formula are -4 and 0.5 respectively.
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1. A solar lease customer built up an excess of 17,500 kilowatt hours (kwh) during the summer using his solar panels. When he turned his electric heat on, the excess began to be used up at a rate of 75 kilowatt hours per day.
(a)lf E represents the excess left and d represents the number of days since the heat has been turned on, write an equation for E in terms of d.
(b)How much of the excess will be left after two months (use a month length
of 30 days)?
Using the concept of exponential function, the exponential decay after
2 months is 13000kwh
Exponential FunctionAn exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
In this problem, we can model an exponential function to represent the problem.
E = a(1 - r)⁻^d
a = Initial valueE = final valuer = rate d = timea)
This function is an exponential decay function which when we substitute the values, we can easily express E in terms of d.
E = 17500(1 - 75)⁻^d
b) The excess energy left after 2 months ?
Using proportions;
75 kwh/ d = 1 day
x kw/h = 60 days
x = 60 * 75
x = 4500
The amount left will be 17500 - 4500 = 13000 kwh
We will have 13000kwh after 60 days
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movie ticket sales. according to box office mojo, the film black panther achieved the top opening weekend gross domestic box office ticket sales in 2018 with $202,033,951. the ticket sales revenue in dollars for a sample of 30 theaters is provided in the file black panther. a. what is the 95% confidence interval estimate for the mean ticket sales revenue per theater? interpret this result. b. using the movie ticket price of $9.11 per ticket, what is the estimate of the mean number of customers per theater? c. the movie was shown in 4020 theaters during its opening weekend. estimate the total number of customers who saw black panther and the total box office ticket sales for the weekend.
a) The 95% confidence interval estimate for the mean ticket sales revenue per theater is $21613 to $24857.
b) The estimated of the mean number of customers per theater is 2536 customers.
c) The total number of customers who saw black panther are 10194720 and the total box office ticket sales for the weekend is 92862000.
What is meant by margin error?A number derived from a random sample that provides an estimation of the probable magnitude of the sampling error in a population parameter estimate.
a) The goal of this section is to calculate and understand the 95% confidence interval estimate for the mean ticket sales revenue per theater.
The following is a definition of the confidence interval formula:
[tex]\bar{x}[/tex]±margin of error
The margin of error is the value obtained as a 95% confidence interval.
The sample mean is so calculated to be $23100.
Additionally, a margin of error of 1486.864 is determined.
When these values are used in the formula above, we get
[tex]\bar{x}[/tex]±margin of error
=23100±1486.864
=23100-1486.864 to 23100+1486.864
=21613.136 to 24586.864
=21613 to 24857
The 95% confidence interval estimate for the mean ticket sales revenue per theater is $21613 to $24857.
b) Mean number of customers per theater=23100/9.11
=2573.675
=2536 customers per theater.
The estimated of the mean number of customers per theater is 2536 customers.
c) Total number of customers=2536(4020)
=10194720
The total number of customers who saw black panther are 10194720
Total box office sales in weekend=4020(23100)
=92862000
The total box office ticket sales for the weekend is 92862000
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jarod paid $18.50 for 5 tickets to the game at the same rate how much would 3 tickets cost?
Answer:
$11.10
Step-by-step explanation:
divide 18.50 by 5 to find out how a single ticket costs. 18.50/5=3.70then multiply 3.70 by 3 to find the cost of three tickets. 3.70×3=11.10this means that three tickets costs $11.10Answer:
Step-by-step explanation:
18.50 x 3
Let S be the part of the plane 2x+4y+z=2 which lies inthe first octant, oriented upward. Find the flux of the vectorfield
F=1i+1j+2k across the surface S
The flux of the vector-field F = 1i + 1j + 2k across the surface S is 2. We find out the flux of the vector-field using Green's Theorem.
Define Green's Theorem.Flux form of Green's Theorem for the given vector-field
φ = ∫ F.n ds
= ∫∫ F. divG.dA
Here G is equivalent to the part of the plane = 2x+4y+z = 2.
and given F = 1i + 1j + 2k
divG = div(2x+4y+z = 2) = 2i + 4j + k
Flux = ∫(1i + 1j + 2k) (2i + 4j + k) dA
φ = ∫ (2 + 4 + 2)dA
= 8∫dA
A = 1/2 XY (on the given x-y plane)
2x+4y =2
at x = 0, y = 1/2
y = 0, x = 1
1/2 (1*1/2) = 1/4
Therefore flux = 8*1/4 = 2
φ = 2.
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2.
a.
The tax rate at this restaurant is 9.5%.
Date: Sep 12th
Time: 6:04 PM
Server: # 27
Bread Stix
Ravioli Bites
Cheesecake
Subtotal
Sales Tax
Total
9.50
10.50
4.95
24.95
Date: Sep 12th
Time: 7:12 PM
Server: #27
Garden Salad
Broccoli Bites
Subtotal
Sales Tax
Total
1.61
Another person's subtotal is $24.95. How much will their sales tax be?
a) The sales tax of the person with a subtotal of $24.95 is of: $2.37.
b) The subtotal of a person with a sales tax of $1.61 is of: $16.95.
How to obtain the amounts?The amounts are obtained applying the proportion of 9.5%, which represents the sales tax of this restaurant.
The sales tax of the person with a subtotal of $24.95 is obtained with the multiplication of the subtotal by the sales tax of 9.5% = 0.095 as follows, hence:
Sales tax = 0.095 x 24.95 = $2.37.
The subtotal of a person with a sales tax of $1.61 is obtained considering that $1.61 represents 9.5% = 0.095 of the subtotal x, due to the tax rate, as follows:
0.095x = 1.61
x = 1.61/0.095
x = $16.95 -> which is the subtotal of the person.
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A right triangle is shown, where the horizontal leg has a measure of 42.7 centimeters(cm) and the hypotenuse has a measure of 52.5cm. Determine the length, in centimeters, of the vertical leg. Show your work for partial credit.
30.54cm is the length of the vertical leg.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In a right angled triangle the horizontal leg has a measure of 42.7 centimeters(cm).
The hypotenuse has a measure of 52.5cm.
We need to find the measure of the vertical leg.
We can find this by using pythagoras theorem.
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
52.5²=42.7²+x²
2756.25=1823.29+x²
Subtract 1823.29 on both sides
2756.25-1823.29=x²
932.96=x²
Taking square root on both sides
x=30.54
Hence, the length of the vertical leg is 30.54cm.
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please help with #2 and #3
Answer:*2 proof:intersect
*3 62 = wx__3x-14
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 18.8 in and a base with a diameter of 14.3 in. Round your answer to the nearest tenth of a cubic inch.
1006.46471 in³ is needed for the right circular cone's volume.
What is the right circular cone?The line connecting the vertex and the center of the circular base is the axis of a right circular cone.
In other words, the intersection of the cone's peak and the circular base's center point results in a right angle.
The appropriate circular cone volume formula is thus:
V=1/3hπr²
Diameter = 14.3 in
Radius = 14.3/2 = 7.15 in
Do the volume calculation now as follows:
V = 1/3hπr²
V = 1/3(18.8)π(7.15)²
V = 1006.46471 in³
Therefore, 1006.46471 in³ is needed for the right circular cone's volume.
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What is the solution to the compound inequality in interval notation?
4(x +1) > -4 or 2x - 4 < -10
Answer: [tex](-\infty, -3) \ \cup (-2, \infty)[/tex]
====================================================
Explanation:
Let's solve the first inequality.
4(x+1) > -4
4x+4 > -4
4x > -4-4
4x > -8
x > -8/4
x > -2
The inequality sign doesn't flip since we didn't divide both sides by a negative value.
Now let's solve the other inequality.
2x-4 < -10
2x < -10+4
2x < -6
x < -6/2
x < -3
-----------------------------------
To summarize:
solving 4(x+1) > -4 leads to x > -2solving 2x-4 < -10 leads to x < -3Draw out a number line. Place open holes at -3 and -2.
Shade to the right of -2 and to the left of -3 to indicate x > -2 and x < -3 respectively.
See the diagram below.
The interval in red is x < -3. This is the same as [tex]-\infty < \text{x} < -3[/tex] and that becomes the interval notation [tex](-\infty, -3)[/tex]
The interval in blue is x > -2. It is the same as [tex]-2 < \text{x} < \infty[/tex] which becomes the interval notation [tex](-2, \infty)[/tex]
Glue those interval notations together to end up with the final answer of [tex](-\infty, -3) \ \cup (-2, \infty)[/tex]
The "U" is the union symbol.
Marta makes 90\%90%90, percent of the free throws she attempts. She is going to shoot 333 free throws. Assume that the results of free throws are independent from each other. Let xxx represent the number of free throws she makes.
Answer: 299
Step-by-step explanation: 333 X .9 = 299.7; Can't make .7 of a free throw.