Use the line of best fit to predict the total amount of money earned in tips after working 12 hours. (8,80)(2,20)
Answers
Answer:
The line of best fit will look like this (see attatchement):
The total amount of money earned in tips after working 12 hours is $120.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given coordinate points are (8, 80) and (2, 20).
Here, slope (m) = (20-80)/(2-8)
= 10
Substitute m=10 and (x, y)=(8, 80) in y=mx+c, we get
80=10×8+c
c=0
So, the equation of a line is y=10x
Here, x=12
Then, y=120
Therefore, the total amount of money earned in tips after working 12 hours is $120.
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Related Questions
A spherical balloon is being inflated with helium at a rate of 20π cm3/min. How fast is the balloon's radius changing when the radius is 1 cm?
Answers
Answer:
5 cm/min
Step-by-step explanation:
A spherical balloon is being inflated with helium at a rate of 20π cm³/min.
The volume of a sphere is given by :
\(V=\dfrac{4}{3}\pi r^3\) ...(1)
Differentiate equation (1) wrt t as follows :
\(\dfrac{dV}{dt}=3\times \dfrac{4}{3}\pi r^2\times \dfrac{dr}{dt}\\\\\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}\ ....(1)\)
Put dV/dt = 20π cm³/min and r = 1 cm, we can fin dr/dt
\(\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}\\\\20\pi =4\pi (1)\times \dfrac{dr}{dt}\\\\\dfrac{dr}{dt}=5\ cm/min\)
So, the radius of changing at the rate of 5 cm/min.
Using implicit differentiation, it is found that the radius is changing at a rate of 5 cm/min.
The volume of a sphere of radius r is given by:
\(V = \frac{4\pi r^3}{3}\)
Applying implicit differentiation, the rate of change is of:
\(\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}\)
A spherical balloon is being inflated with helium at a rate of 20π cm3/min, hence \(\frac{dV}{dt} = 20\pi\)The radius is of 1 cm, hence \(r = 1\).Then:
\(\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}\)
\(20\pi = 4\pi (1)^2\frac{dr}{dt}\)
\(\frac{dr}{dt} = \frac{20}{4}\)
\(\frac{dr}{dt} = 5\)
The radius is changing at a rate of 5 cm/min.
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NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
Simplify: [3(2a)^3/2]^2
A: 34^4√2a^9
B: 72a^3
C: 216a^3
D: 24a^3
Answers
==================================================
Explanation:
We have something of the form [M*N]^2 where M = 3 and N = (2a)^(3/2)
Squaring the M leads to M^2 = 3^2 = 9
Squaring the N leads to N^2 = (2a)^3 = 8a^3
Notice how the fractional exponent goes away. The denominator '2' cancels with the '2' from the squaring operation
In other words, the rule is \(\left(x^{1/2}\right)^2 = x\) where x is nonnegative.
A more general form of the rule is \(\left(x^{p/2}\right)^2 = x^p\)
-------------
After squaring M and N, we then get to
[MN]^2 = M^2*N^2 = 9*8a^3 = 72a^3
So that shows why choice B is the answer.
5x - 8 = 11 - 7x + 12x
Answers
The given linear equation, 5x - 8 = 11 - 7x + 12x , has no solution
Solving linear equations
From the question, we are to solve the given linear equation.
From the given information,
The given linear equation is
5x - 8 = 11 - 7x + 12x
To solve the linear equation, we would determine the value of the unknown variable.
In the given equation, the unknown variable is x. Thus, we would solve for x.
Solving for x
5x - 8 = 11 - 7x + 12x
Simplify
5x - 8 = 11 + 5x
Add 8 to both sides of the equation
5x - 8 + 8 = 11 + 8 + 5x
5x = 19 + 5x
Subtract 5x from both sides
5x - 5x = 19 + 5x - 5x
0 = 19
Hence, no solution
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Solve the equation for the indicated variable. C=680x/h^2 for x
Answers
Answer:
C h^2 / 680 = x
Step-by-step explanation:
C=680x/h^2
Multiply each side by h^2
C h^2=680x/h^2 * h^2
C h^2=680x
Divide each side by 680
C h^2 / 680=680x/680
C h^2 / 680 = x
That gives you Ch^2= 680x
Second step: divide both sides by 680
That gives you (ch^2)/680=x
Simplify: x= (ch^2)/680
That is the simplest form
y - 4x = -2
2y - 8x = -4
Answers
Answer:
Using substitution method
First make y in equation 1 the subject of formula
Y=4x-2
Sub in equation 2
2(4x-2)-8x=4
8x-4-8=4
8x=4+12
8x=16
X=2
Sub in any of equation to get y
Step-by-step explanation:
Y =4(2)-2=6
Answer:
(x, -2+4x)
Step-by-step explanation:
See The image below:)
Finance Math homework
How much should you deposit at the end of each month into an investment account that pays 7% compounded monthly to have $4 million when you retire in 42 years? How much of the $4 million
comes from interest?
In order to have $4 million in 42 years, you should deposit $ each month.
(Round up to the nearest dollar.)
Answers
a) you should deposit $ 580169.5 into an investment account that pays 7% compounded monthly to have $4 million
b) interest amount = $3419830.5
Using the formula below;
P= A(r/n) / (1+r/n)^nt - 1 --------(1).
From given data:
A(annuity)= $3,000,000
t= 42 years,
n= 12,
r = 7%
= 7/100
= 0.07
Substitute these values in above formula,
P= [4,000,000 * (0.07/12)]/ (1+0.07/12)^12×42 -1
= 23333.33/(1.006)^503
= 23333.33/ 20.27
= 1151.13
My monthly payment will be $1151.13
Now we find the Principle payment
Principle = n × t × monthly payment
= 12× 42 × 1151.13
= $ 580169.5
(b).
We know that Interest = Annuity - principle
$(4,000,000 - 580169.5
= $3419830.5
Therefore, a) you should deposit $ 580169.5 into an investment account that pays 7% compounded monthly to have $4 million
b) interest amount = $3419830.5
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Help
Please ..................
Answers
8(-11) + 2.
-86
Answer:
-86
Step-by-step explanation:
Substitute -11 for x in the equation:
8(-11)+2
=-88+2
=-86
PLS HELP WILL GIVE BRAINLIEST IVE BEEN ASKING FOREVER :(((((
Answers
Answer:
__C) 0.36
Step-by-step explanation:
4÷11= 0.36363636363636
so it's 0.36 with a line over it indicating a repeating decimal
B. The perimeter of this rectangle is 20 centimeters. What is the value of X
Answers
Statement Problem: Find the value of x in the diagram below, given the perimeter of a rectangle as 20centimeters.
Solution:
The perimeter of a rectangle is;
\(P=2(l+w)\)Where the length and width of the given rectangle is;
\(\begin{gathered} l=(x+3)cm \\ w=(x+1)cm \end{gathered}\)Thus, the value of x is;
\(\begin{gathered} 2(l+w)=20 \\ 2(x+3+x+1)=20 \\ \text{Divide both sides by 2},\text{ we have;} \\ \frac{2\mleft(x+3+x+1\mright)}{2}=\frac{20}{2} \\ x+3+x+1=10 \\ \text{Collect like terms, we have;} \\ 2x+4=10 \\ \end{gathered}\)Then, we subtract 4 from both sides of the equation, we have;
\(\begin{gathered} 2x+4-4=10-4 \\ 2x=6 \\ \text{Divide both sides by 2, we have;} \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}\)The value of x is 3
Each volleyball set costs $63.74.
Which equation represents the cost, c, of n sets?
Answers
The equation that represents the cost, c, of n sets is c = 63.74n
Which equation represents the cost, c, of n sets?from the question, we have the following parameters that can be used in our computation:
Each volleyball set costs $63.74.
Let the total number of sets be n
So we have
Cost of n = 63.74 * n
This gives
c = 63.74n
Hence, the equation is c = 63.74n
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10 points I need help ASAP please
Answers
Step-by-step explanation:
All you need to do to answer this is multiply 9/10 and 4/9
9/10 * 4/9 = 2/5
Checking the answer:
plug in play
2/5 / 4/9 = 9/10
In short, your answer is 2/5
Hope this helps <3
Please nswer this question.
Answers
Answer:
4.75 megabytes per second
Step-by-step explanation:
500-25 = 475
475 / 100 = 4.75
Question 7 )
Lucy, Milan, and Tony have a total of $85 in their wallets. Tony has 3 times what Milan has. Milan has $10 less than Lucy. How much do they
have in their wallets?
Answers
Answer:
Tony has 45 dollars
Milan has 15 dollars
Lucy has 25 dollars
Explanation:
Let x represent the amount of money Milan has in his wallet.
TONY: 3x
MILAN: x
LUCY: x+10
Lucy, Milan, and Tony have a total of $85 in their wallets. Hence, the following equation.
3x+x+x+10=85
5x+10=85
5x=75
x=75/5
x=15
Tony has 45 dollars (3*15=45)
Milan has 15 dollars (x=15)
Lucy has 25 dollars (10+15=25)
Tony = $ 45
Milan = $15
Lucy = $25
Suppose you have a $15 coupon that can be used on any purchase over $100 at your favorite clothing store. The discounted price of a sports jacket is $203. What is the retail price of the jacket?
a.
$235.70
b.
$303.00
c.
$188.00
d.
$218.00
Answers
You deposit $3000 in an account that pays 3.5% annual interest compounded continuously. What is the balance after 3 years?
Answers
Answer:
Step-by-step explanation:
3000*e^(.035*3)= 3332.131831
Write the coordinates for
each given point on the
coordinate plane below.
1. Point A
2. Point B
3. Point C
4. Point D
Answers
Answer:
Point A (-3,3)
Point B about (3,-2.75)
Point C (-4,-4)
Point D (1,0)
Step-by-step explanation:
What is the range of the function y=3√√x+8 1x
Answers
Answer:
The range of the function is: -∞≤y≤∞.
Consider the provided function.
The range of the function is the set of all values which a function can produce or the set of y values which a function can produce after substitute the possible values of x.
The range of a cubic root function is all real numbers.
Now consider the provided function.
The above function can be written as:
Taking cube on both sides.
The graph of the function is shown in figure 1:
For any value of x we can find different value of y.
Here, the cube root function can process negative values. Since, the function can produce any values, the range of the given function is -∞≤y≤∞ .
Therefore, the range of the function is: -∞≤y≤∞ (A).
The original Cars movie made 450 million dollars at the box office. Cars three made 297 million dollars at the box office. What was the percent of change?
Answers
Answer:
34% decrease
Step-by-step explanation:
(V1-V2)/V1x100
450-297=153
153/450=0.34
0.34 x 100=34
34% decrease
xyz company's cost function for four months is c=500000+5q
find the break even dollar volume of sales if the selling price is 6 unit
Answers
The break even of a company is when cost equals selling function. The break even of xyz company is 500000 units.
Given that:
\(c=500000+5q\) --- cost function
\(s = 6q\) --- selling function
The break even is when the functions are equal
i.e.
\(s = q\)
So, we have:
\(6q=500000+5q\)
Collect like terms
\(6q - 5q=500000\)
\(q=500000\)
The break even is at 500000 units
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A pizzeria will bake and deliver a round pizza with a 12-inch diameter. Find the exact area of the top of the pizza and an approximation. Use 3.14 as an approximation
Answers
A = 78.54
A = 3.14r^2
Based on the pattern, what are the next two terms of the sequence?
Answers
Answer:
33 , 39
Step-by-step explanation:
given
9 , 15 , 21 , 27
there is a common difference between consecutive terms, that is
15 - 9 = 21 - 15 = 27 - 21 = 6
to obtain terms in the sequence add 6 to the preceding term
27 + 6 = 33
33 + 6 = 39
the next two terms are 33 and 39
15-9=6
21-15=6
27-21=6
That means we are adding 6 at every step. Therefore the next two elements must be
27+6=33 and 33+6=39
Paul drove during a snowstorm for 40 miles. When it stopped snowing, he increased his
speed by 30 miles per hour and drove for an additional 132 miles. If Paul drove for a total
of 4 hours, which equation can be used to find his average rate of speed (x) in miles per
hour during the snowstorm?
Answers
During the snowstorm, Paul drove for a certain amount of time, let's call it t.
Then, his distance traveled during the snowstorm would be:
distance1 = rate1 x t
After the snow stopped, Paul increased his speed by 30 mph and drove for 4 - t hours (since he drove for a total of 4 hours and spent t hours driving in the snowstorm).
Then, his distance traveled after the snowstorm would be:
distance2 = rate2 x (4 - t)
We know that in total, Paul traveled 40 + 132 = 172 miles. So, we can set up an equation:
distance1 + distance2 = total distance
rate1 x t + rate2 x (4 - t) = 172
Now, we can solve for Paul's average rate of speed (x) during the snowstorm:
rate1 = x
rate2 = x + 30
x(t) + (x + 30)(4 - t) = 172
Simplifying:
xt + 120 - xt + 30t = 172
Combining like terms:
30t + 120 = 172
Subtracting 120 from both sides:
30t = 52
Dividing by 30:
t = 1.73 hours
Now we can substitute t back into one of the equations we derived earlier:
distance1 = x(1.73)
distance2 = (x + 30)(2.27)
We know that distance1 + distance2 = 172:
x(1.73) + (x + 30)(2.27) = 172
Expanding:
1.73x + 2.27x + 68.1 = 172
Combining like terms:
4x = 103.9
Dividing by 4:
x = 25.98 mph
Therefore, Paul's average rate of speed during the snowstorm was approximately 26 mph.
find three consecutive even integers such that the sum of the smaller and three times the larger Is 84
Answers
Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.
What is a word problem?A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"
What are conditions of the problem?In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.
Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:
x + (x+4) * 3 = 84
Expanding and solving for x:
x + 3x + 12 = 84
4x = 72
x = 18
So the three consecutive even integers are 18, 20, and 22.
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A car can go 420 miles on a tank of gas (15 gallons in a tank). How many kilometers can this car go on 6.5 gallons
Answers
Answer:
182 miles
Step-by-step explanation:
15 gallons ------------------------- 420 miles
1 gallons --------------------------- 420/15 miles
1 gallons --------------------------- 28 miles
6.5 gallons -------------------------- 6.5 × 28 miles
6.5 gallons -------------------------- 182 miles
The car can go 182 miles on 6.5 gallons.
It is given that the a car can go 420 miles on a tank of gas of 15 gallons in a tank.
It is required to find the how many kilometers can this car go on 6.5 gallons.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called denominator.
We have a car can go 420 miles on 15 gallons gas.
A car can go on 1 gallon = \(\frac{420}{15}\) = 28 miles ie.
A car can go on 1 gallon = 28 miles
On 6.5 gallons car can go = 6.5×28
= 182 miles
Thus, the car can go 182 miles on 6.5 gallons.
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a backpack that normally sells for $40 is on sale for $30. find the percentage of a change.
Answers
Answer:It would be 40•.25=10
Step-by-step explanation: which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off
I really need help
If AD = 12 and AC = 4y-36, find the value of y
Answers
Answer:
y=12
Step-by-step explanation:
in that case, then 12 = 4y -36
12 =4y -36
12+36=4y
48=4y
48/4=y
12=y
answer :y=12
Answer:
y = 15
Step-by-step explanation:
Consider that the attached screenshot is the figure given in the problem. Also consider that DC = 12, due to the fact that AD = 12, and there is a midpoint at point D.
AD + DC = AC
12 + 12 = 4y - 36
24 = 4y - 36
+ 36 + 36
60 = 4y
60/4 = 4y/4
y = 15
Does the table show direct variation? If so, state the constant of variation.
Answers
Okay, here we have this:
Considering the provided table, we are going to analize if the table shows direct variation, so we obtain the following:
To identify if there is direct variation then we will calculate the ratios between the points, and if they are all the same then the table does show direct variation, then we have:
y=kx
k=y/x
5/2=2.5
45/18=2.5
80/30=2.66
Since the ratios between the points are not the same, then it does not represent a direct variation.
BIG IDEAS MATH
K
Tell whether the information in the figure allows you to conclude that point P lies on the perpendicular bisector of
LM.
L
P
M
Yes
O No
N
Explain your reasoning.
Answers
Note that it is correct to state that LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK. See attached image.
What is a perpendicular bisector?A perpendicular bisector is a line that cuts another line segment across the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The phrase bisect implies dividing evenly or uniformly.
A simple technique to determine a perpendicular bisector is to measure the line segment you need to bisect. Then, divide the measured length by two to determine the midway. Draw a line at a 90-degree angle out from this middle.
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Full Question:
Tell whether the information in the diagram allows you to conclude that point P lies on the perpendicular bisector of LM. Explain your reasoning. See attached image.
A) No. You would need to know that LK ⊥ MK
B) No. You would need to know that KP ⊥ LM
C) Yes, t LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
D) Yes, NK ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
7c
2
−2c−15=
\,\,-c^2
−c
2
Answers
?........................................
Which of the following is equivalent to 7(2x+1)-2(6x+3)=15
2x+4=15
-2x+13=15
-2x+4=15
2x+1=15
Answers
Answer:
2x + 1 = 15
Step-by-step explanation:
Answer:
D or 2x+1
Step-by-step explanation:
first we have to distribute the 7 to the 2x+1
14x+7-2(6x+3)=15
now distribute the -2
14x+7-12x-6=15
combine like terms on the left side
2x+1=15
your answer would be D
hope this helps!