The piecewise function that describes what the instructor charges is; f(x) = 500x , 0 < x ≤ 10
400x , 10 < x < 25
350x , x ≥ 25
How to create piecewise functions?
Let x represent the number of participants and let y represent the charge per participant.
Now, y depends on x, and as such we can say that;
f(x) = y
For, 0 < x ≤ 10, the total charges is 500x,
f(x) = 500x , 0 < x ≤ 10
For 10 < x < 25, total charge is 400x,
f(x) = 400x , 10 < x < 25
For x ≥ 25, the total charge is 350
f(x) = 350x x ≥ 25
Therefore, we can say that;
f(x) = 500x , 0 < x ≤ 10
400x , 10 < x < 25
350x , x ≥ 25
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Write the piecewise function that describes what the instructor charges.
i need help because i dont gettt itttt
Answer:
[tex]\boxed{3} \;v^2 + \boxed{4}\;v + \boxed{5}[/tex]
Step-by-step explanation:
Original expression: 3 + v + 4v² + 2 - v² +3v
Combining like terms in a equation means grouping them together to get a single instance of that term instead of multiple
For example in this expression we can see there is a +4v² and a -v². Group these together and simplify algebraically to get a single v² expression. Do the same with the others.
3 + v + 4v² + 2 - v² +3v
Group the v² terms together to get 4v² - v² = 4v² - 1v² = 3v² (v² == 1v²)
(since the variables are same we can simply add the coefficients
Now group the v terms and simplify
3 + v + 4v² + 2 - v² + 3v
v + 3v = 4v
Finally group the constants
3 + v + 4v² + 2 - v² +3v
3 + 2 = 5
So the final expression is
3v² + 4v + 5
The numbers are what you put in the boxes for each
Usually this process is done in a few steps
3 + v + 4v² + 2 - v² +3v
= (4v² - v²) + (v + 3v) + (3 +2)
= 3v² + 4v + 5
The kinetic energy k of an object varies jointly with its mass m and its velocity v. The formula to kinetic energy is K = 1/2mv^2. Rearrange the formula to write the mass m in terms of K and v, where v is not equal to 0.
(I will rate brainliest if only right)
The mass m in terms of K and v is expressed as m= 2K/v^2
Subject of formulaThe subject of formula is a way of representing a variable in terms of other variables.
Given the equation below;
K = 1/2mv^2
Make m the subject of the formula
2K = mv^2
Divide both sides by v^22K/v^2 = mv^2/v^2
2K/v^2 = m
Swap
m= 2K/v^2
Hence the mass m in terms of K and v is expressed as m= 2K/v^2
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What is
3² + √25 [2²(2² - 3)(5² - 4²) - 201]
If Kevin has a total of 81 hours of service, how many weeks has he volunteered?
If Kevin has a total of 81 hours of service, then he volunteered for 0.48 weeks.
As per the question statement, Kevin served as a volunteer for 81 hours.
We are required to find out the number of weeks, he volunteered his service.
To solve this question, we just need to know that a week consists of how many hours ?
We can proceed with the facts that a week consists of 7 days and each day consists of 24 hours. Therefore, a week consists of [tex](24*7)=168[/tex] hours, of which, Kevin volunteered for 81 hours.
Therefore, as per the unitary method, we get that,
168 hours make 1 week, then
1 hour makes [tex](\frac{1}{168})[/tex] weeks, and
81 hours make [tex](\frac{81}{168})=0.48[/tex] weeks approximately.
Unitary Method: This is a technique for solving a problem where first, we find the value of a single unit, and then find the necessary value by multiplying the single-unit value.To learn more about Unitary Method, click on the link below.
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Is the equation always, sometimes, or never true?
Answer:
never
Step-by-step explanation:
-1=0 is not possible
an amusement park charges 18 dollars for 4 rides. how much will 7 rides cost
Martin wants to clean his swimming pool.
He hired a cleaning machine to do this job.
The cost of hiring the cleaning machine was
£35.54 for the first day,
then £18.25 for each extra day.
Estimate how much it would cost to rent the machine for 4 days.
Help plssss
Answer:
90.29
Step-by-step explanation:
I did math
The graph of y=
-2x²5x+2 is drawn below
Draw a suitable line to solve -2x² - 5x + 2 = -5
Answer:
x = 1 and x = -3.5
Step-by-step explanation:
y = -2x² -5x + 2
-2x² -5x + 2 = -5
which means y = -5
Draw the line on y = -5 like the green line in the attached file
and see where this line intersects with the graph
the values are:
x = 1 and x = -3.5
Answer:
Draw a line at y = -5.
x ≈ -3.5
x ≈ 1
Step-by-step explanation:
Given equation:
[tex]y = -2x^2 - 5x + 2[/tex]
This is the equation of the graphed parabola.
To solve the equation [tex]-2x^2 - 5x + 2 = -5[/tex] draw a line at y = -5 and find the points of intersection of the two graphed equations.
From inspection of the graph, the x-values of the points of intersection are:
x ≈ -3.5x ≈ 1Solving algebraically
Add 5 to both sides of the equation:
[tex]\implies -2x^2-5x+2+5=-5+5[/tex]
[tex]\implies -2x^2-5x+7=0[/tex]
Factor out -1 from the left side:
[tex]\implies -1(2x^2+5x-7)=0[/tex]
Divide both sides by -1:
[tex]\implies 2x^2+5x-7=0[/tex]
Find two numbers that multiply to -14 and sum to 5: 7 and -2
Rewrite b as the sum of these two numbers:
[tex]\implies 2x^2+7x-2x-7=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(2x+7)-1(2x+7)=0[/tex]
Factor out the common term (2x + 7):
[tex]\implies (x-1)(2x+7)=0[/tex]
Apply the zero-product property:
[tex](x-1)=0 \implies x=1[/tex]
[tex](2x+7)=0 \implies x=-\dfrac{7}{2}=-3.5[/tex]
Evaluate the expression when b = -2 and x = 4.
b-3x
Answer:
- 14
Step-by-step explanation:
You can substitute the given values into the expression.
b - 3x
= -2 - 3(4)
= -2 - 12
= - 14
Hope this helped! ^^
Answer:
give the other person the brainliest the answer is -14
Step-by-step explanation:
Find the value of x such that the data set has the given mean.
100, 122, 107, 115, 107, x; mean 108
X=
(Type an integer or a decimal.)
Sh
The value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.
According to the given question.
We have a data set 100, 122, 105, 115, 107, x .
Also, the mean of the data set is 108.
As we know that, mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Therefore, the mean of the data set 100, 122, 105, 115, 107, x is given by
Mean = [100 + 122 + 107 + 115+ 107 + x]/6
⇒ 108 × 6 = (551 + x)
⇒ 648 = 551 + x
⇒ x = 648 - 551
⇒ x = 97
Hence,the value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.
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(Type exponential notation with positive exponents.)
The correct answer to the exponential expression which is as given in the task content is; 8³.
Based on the given task content, Gina's error from her workings is dividing the bases of the exponent.
Exponential notationThe bases of exponential expression, if same, should be taken as one.If the bases of exponential notation are entirely different, then it should be simplified.In indices, Division between two different expressions simply means Subtraction of powers.Multiplication means addition of powersGina's working:
8^12 / 8^9
= 0^12 / 0^9
The Correct workings:
8^12 / 8^9
= 8^(12-9)
= 8³
So therefore, the correct answer to the exponential expression which is given in the above expression is 8³.
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B ABCD is a parallelogram and angle A< 90°. The height through the vertex D intersects the diagonal AC at point M. The height through vertex B intersects the diagonal AC at point N. Prove that MBND is a parallelogram.
MBND is a parallelogram as BN=MD and BN║MD.
A parallelogram is a quadrilateral whose both pair of opposite side are equal and parallel. Few examples of parallelograms are square, Rhombus and rectangle.
Given ABCD is a parallelogram and ∠A=90°
Now we have to prove that MBND is a parallelogram
Given BN⊥AC and DM⊥AC
Since BN and DM are both perpendicular to the same straight line AC then we cam say that BN║DM.
Again we know from the properties of parallelogram that the diagonal divides a parallelogram into two equal triangles.
Therefore the diagonal AC divides the parallelogram into two equal triangles ΔABC and ΔADC.
Now we know that the area of a triangle is given by [tex]\frac{1}{2}[/tex] ×base ×height .
Area of ΔABC =Area of ΔADC
Since BN⊥AC and DM⊥AC
∴[tex]\frac{1}{2}[/tex]×BN×AC=[tex]\frac{1}{2}[/tex]×DM×AC
This above equation can be simplified as
BN=MD
Hence BMND is a parallelogram as we know from the properties of parallelogram that when a pair of opposite sides are equal and parallel in a quadrilateral it is a parallelogram.
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If a person with an hourly pay of $9.50 per hour gets a 20$ raise, what is the new hourly pay?
Percent formula, show your work
======================================================
Work Shown:
20% of $9.50 = 0.20*9.50 = 1.90
You earn an extra $1.90 on top of the $9.50 already there. So the new wage is 9.50 + 1.90 = 11.40 dollars per hour
-----------
Shortcut:
1.20*9.50 = 11.40
Think of 1.20 as 100% + 20% = 1 + 0.20 = 1.20, and this represents an increase of 20%
Can you determine any purpose why these concepts are present in the pictures?
The purpose why these concepts are present in the pictures is to develop imagination power among students.
As you imagine more, your mind becomes stronger and you have greater mental control. Innovation requires a strong imagination. If you succeed in what you set out to do, the same individuals who now accuse you of daydreaming will begin to aspire to be like you. Keep your aspirations high and your imagination expanding.
Imagination is a potent brain stimulant because it forces you to think differently than most people do. Your imagination can help you come up with scenarios that most effectively handle difficulties, even though your brain might classify them as being unexpected.
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Consider the composite function g (f (x)) = x startroot 6 endroot. if f(x) = 3x2, what is g(x)?
Consider the composite function g (f (x)) = x startroot 6 endroot. if f(x) = 3x2, g (x) = StartRoot 2 x EndRoot.
What is squareroot?
In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3. The Babylonians had efficient techniques for calculating square roots as early as the second millennium bc.Example of a square root-
The radical symbol for the number's root is shown here. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of 3 is 9, the square root of 9 is 9, and 32 also equals 9.Learn more about square root
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Please help me solve this please
Answer:
Step-by-step explanation:
what is the question>
There are a total of 463,100 books in a library. What is the value of the exponet when this number is written in scientific notation?
Answer: 4.631*10^5
Step-by-step explanation:
463,100=
400,000+63,100=
4*100,000+(63,100/100,000)*100,000=
4*10^5+(631/1000)*10^5=
4*10^5+0.631*10^5=
(4+0.631)*10^5=4.631*10^5
Can someone give me the answer of D??
Answer:
Corrected - didn't see the 10 to the negative 2 in the denominator at first - sorry)
8000
Step-by-step explanation:
Simplify
5.12 x 10 ^6/ 1.6 X 10 ^5 X (.4 X 10^-2)
Do the math
3.2 x 10/.04 x 1- ^-2)
Simplify
8 X 10^3
Simplify
8000
find x: -3 = 4x - 12x^2 + 7x^3
Answer:
x = 0.3384663
Step-by-step explanation:
Leila says that 75% of a number will always be greater than 50% of any other number. complete one inequality to support leila's claim and one to show that she is incorrect. clear check support 75% of > 50% of refute 75% of < 50% of
The inequality for Leila claim is (0.75 × x) > (0.50 × y) and the support claim is x = 100 and y = 10 and that refutes the claim is x = 1 and y = 200
Inequality:
Inequality are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given,
Leila says that 75% of a number will always be greater than 50% of any other number.
Here we need to find the inequality and we also need to find one that supports Leila's claim and one to show that she is incorrect.
Let x and y be two numbers.
Leila says that 75% of a number will always be greater than 50% of any other number.
This means that the inequality is,
=> (0.75 × x) > (0.50 × y)
We know that,
75% of x = 0.75 × x
and
50% of y = 0.50 × y
So,
Numbers that support Leila's claim.
Let x = 100 and b = 10
=> 0.75 × x
=> 0.75 × 100 = 75
and
=> 0.50 × 10 = 5
As we know that, based in on the inequality,
=> 75 > 5
Hence, x = 100 and y = 10 support Leila's claim.
Similarly,
Numbers that refutes her claim.
Let x = 1 and y = 200
=> 0.75 × x
=> 0.75 × 1 = 0.75
and
=> 0.50 × 200 = 100
As we know that,
=> 0.75 < 100
Hence, x = 1 and y = 200 refutes Leila's claim.
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k) pq (r² + 1) - r (p² + q²)
Answer:
pqr²−p²r−q²r+pq
Step-by-step explanation:
Let's simplify step-by-step.
pq(r²+1)−r(p²+q²)
Distribute:
=(pq)(r²)+(pq)(1)+−p²r+−q²r
=pqr²+pq+−p²r+−q²r
=pqr²−p²r−q²r+pq
Solve for t.
|-3t - 1| - 3 = 3
Answer:
32028464937583748374
An observation deck extends 454 feet out above a valley. The deck sits 404 feet above the valley floor. If an object is dropped from the observation deck, its height h in feet, after t seconds, is given by
h=-16² +404. How long will it take for the object to be 4 feet above the valley floor?
Answer:4.12
Step-by-step explanation:
11 Write as a power of 5
125²
below is a list of volume of lava rates from four volcanoes. Which of the following is true of the rates at which lava flows? Choose all that apply.
PLEASE HELP, URGENT, POINTS GIVEN
A sheet of paper contains a list of 5 double-digit prime numbers.
Their mean is 31, while their median and mode is 29.
The largest number is 41.
Show how you can discover the 5 prime numbers written on the sheet.
Answer:
19, 29, 29, 37, 41
Step-by-step explanation:
1. What we know: x y 29 z 41
(x+y+29+z+41)/5 =31
x y and z each >9 and prime
Possibile numbers: 11, 13, 17, 19, 23, 29, 31, 37, 41
2. (x+y+29+z+41)/5 =31
x+y+29+z+41 = (31×5)
x+y+z = (31×5) -29 -41
x+y+z = 85
z>=29
x<=29
y<=29
x and y can be 11, 13, 17, 19, 23, 29
z could be 29, 31, 37, 41
At least one if them must equal 29 because it's the mode.
So two of them must equal 56
11+29=40 so both numbers cannot be less than or equal to 40
This means y is 29 because x + z has to equal 56 and that wouldn't be possible if x equals 29.
Now we know x+z=56
Possible numbers: 19+37
I found these by doing 56- each possible number for x and seeing if that equaled a possible number for z. For example 56-11=45 but z cannot be 45 therefore x cannot be 11 and so on.
Then you just plug in the numbers!
19, 29, 29, 37, 41
This was so much fun to solve! I hope this is helpful, let me know if you have any questions! You got this :)
If a lawnmower has a cost price of $2500 and was sold for $2895 what is the percentage profit
The profit percentage for the lawn owner is 15.8%
Profit Percentage:
Profit means, if the selling price of a product is more than its cost price, there is a profit earned in the transaction.
So, it can be calculated as,
Profit = Selling Price - Cost Price
The formulas for profit percentage is,
Profit percentage(P%) = (Profit /Cost Price) × 100
Given,
Here we need to find the profit percentage, If a lawnmower has a cost price of $2500 and was sold for $2895.
Based on the question,
We know that,
Cost Price = $2500
Selling Price = $2895
So, the profit is,
profit = $2895 - $2500
profit = $395
Now, the profit percentage is calculated by apply the values on the formula,
profit percentage (P%) = (395/2500) x 100
Therefore,
P% = 395/25
P% = 15.8%
Therefore, the profit percentage for the lawn owner is 15.8%.
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What did lambert call the difference between the angle-sum of a triangle and 180 degrees?
Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
Who is Lambert?Johann Heinrich Lambert (26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made significant contributions to mathematics, physics (particularly optics), philosophy, astronomy, and map projections. Lambert pioneered the use of hyperbolic functions in trigonometry. He also proposed theories about non-Euclidean space. Lambert is credited with being the first to demonstrate that is irrational by employing a generalized continued fraction for the function tan x. Euler believed the conjecture but was unable to prove it was irrational, and it is speculated that Aryabhata believed it as well in 500 CE. Lambert also developed theorems about conic sections that simplified the calculation of comet orbits.Lambert refers to the defect as the difference between the angle-sum of a triangle and 180 degrees.Therefore, Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
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Geometry -Triangle
Screenie attached
Answer:102
Step-by-step explanation:
The interior angles of a triangle have to measure 180 degrees, which is an isosceles triangle, and 39+39=78.
180-78=102.Therefore the answer is 102
Can someone help me with these so I can finish my math ??
1. -23 + 14 + (-33)
2. -7 + (-19) + 32
3. 102 + (-345) + 234
4. -78 + (-56) + 679
5. 178 + (-129) + 96
6. -312 + (-154) + 283
7. -14 + (-32)
8. -50 + 35
9. -81 + (-11)
10. 121 + (-232)
Answer:
Step-by-step explanation:
1. -42
2. 6
3. -9
4. 545
5. 145
6. -183
7. -46
8. -15
9. -92
10. -111