the monthly cost of driving a car depends on the number of miles driven. lynn found that in may it cost her $434 to drive 460 mi and in june it cost her $546 to drive 740 mi. (a) express the monthly cost c as a function of the distance driven d, assuming that a linear relationship gives a suitable model.
Answers
C (d) = 0.57731d + 168.74374 is a linear relationship gives a suitable model.
What is point- slope in graph ?The general form of a linear equation is y-y1=m (x-x1). It draws attention to the line's slope and one of the tips (that is not the y-intercept).
To graph the point-slope form (y - y1 = m(x - x1), first plot the point (x1,y1). Then, using the slope (m), determine a second point on the line. Plot that spot. Finally, draw a straight line connecting the two places.
CalculationSince we will be using a linear model, we want, first, to find the slope of the line.
Clearly, if the line goes through the points (460, 434) and (740, 546), then the slope of
the line is
(546 - 434 ) / ( 740 - 546 ) = 112/194 = 0.57731
Now we use the point-slope formula with the point (460, 434):
C - 434 = 0.57731( d - 460) = 0.57731d - 265.5626
hence ,
C (d) = 0.57731d + 168.74374
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Related Questions
1. find all closed intervals of length 1 in which the function has a unique zero.
Answers
All closed intervals of length 1 in which a function has a unique zero, we need to find all pairs of zeros that are exactly 1 unit apart and consider the intervals between them as described above.
To find all closed intervals of length 1 in which a function has a unique zero, we need to look for intervals where the function changes sign exactly once. This is because if a function has a unique zero, it must change sign from positive to negative or negative to positive at that point.
Let's call the function f(x). To find these intervals, we can use the Intermediate Value Theorem. This theorem states that if a function is continuous on a closed interval [a, b] and takes on values f(a) and f(b) at the endpoints, then it must also take on every value between f(a) and f(b) somewhere on the interval.
So, to apply this theorem, we need to find values of x such that f(x) = 0. Then, we can look at the intervals between these values and see if f(x) changes sign exactly once on any of them.
Let's say we find two zeros of the function at x = a and x = b, where a < b. Then, we can consider the intervals [a, a+1] and [b-1, b] (assuming these intervals have length 1). If f(x) is positive on the interval [a, a+1] and negative on the interval [b-1, b], or vice versa, then f(x) must change sign exactly once on each of these intervals and therefore has a unique zero in each interval.
In general, to find all closed intervals of length 1 in which a function has a unique zero, we need to find all pairs of zeros that are exactly 1 unit apart and consider the intervals between them as described above.
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i neeeedd helpp asap
Answers
Answer:
oh it c .
Step-by-step explanation:
1) To the nearest tenth of a foot, what is the distance from the wall to
the base of the ladder?
A) 1.9 feet
B)2.1 feet
C)4.5 feet
D)10.7 feet
Answers
the answer might be C=4.5 feet
Five friends share the cost of a dinner equally.
a. Let x represent the total cost of the dinner. Write an expression for the cost per person.
Expression:
Answers
Answer:
x/5
Step-by-step explanation:
x is the money so if you divide it equaly you would divide it by the five freinds.
Evaluate the determinant of each matrix. [2 3 0 1 2 5 7 0 1]
Answers
The determinant of the given matrix is 99. To evaluate the determinant of a matrix, we can use the determinant formula for a 3x3 matrix. Let's calculate the determinant of the given matrix:
[2 3 0]
[1 2 5]
[7 0 1]
In this case, the elements of the matrix are:
a = 2, b = 3, c = 0
d = 1, e = 2, f = 5
g = 7, h = 0, i = 1
Substituting these values into the determinant formula, we have:
det = (2*2*1 + 3*5*7 + 0*1*0) - (0*2*7 + 1*5*2 + 1*0*3)
= (4 + 105 + 0) - (0 + 10 + 0)
= 109 - 10
= 99
Therefore, the determinant of the given matrix is 99.
The determinant is a measure of the matrix's properties and can be used for various purposes, such as solving systems of linear equations, determining invertibility, and calculating eigenvalues. In this case, the determinant of 99 indicates that the given matrix is non-singular and has a non-zero volume in three-dimensional space.
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juanyra,hannah,and bella went out for pizza.juanyra ate 1/3 of the pizza,hannah ate 2/6 of the pizza,and bella ate 1/4 of the pizza.how much did they eat toghether.
Answers
Answer:
1 - (1/4 + 2/3)
1 - (3/12 + 8/12)
1 - 11/12
1/12 left
Please help!!!!!
Find the surface Area.
Answers
Answer:
5
Step-by-step explanation:
Answer:
140
Step-by-step explanation:
7x5x4
kevin is building a dog house. for the trim around the roof, he bought 4 pieces of wood for a total of $6.52 how much was each piece of trim
Answers
The cost of each piece of trim is $1.63
To find the cost of one piece of trim, we can use the unitary method, which involves dividing the total cost by the number of pieces. In this case, we can use the following formula
Cost of one piece of trim = Total cost / Number of pieces
We know that Kevin bought 4 pieces of trim for a total of $6.52, so we can substitute these values into the formula
Cost of one piece of trim = $6.52 / 4
Simplifying this expression, we get
Cost of one piece of trim = $ 1.63
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to determine whether a metal lathe that produces machine bearings is properly adjusted, a random sample of 36 bearings is collected and the diameter of each is measured. if the standard deviation of the diameters of the bearings measured over a long period of time is 0.001 inch, what is the approximate probability that the mean diameter of the sample of 36 bearings will fall between (mu- 0.0001) and (mu 0.0001) inch where mu is the population mean diameter of the bearings?
Answers
For a sample of 36 bearings is collected with measured diameter, the approximate probability that sample mean of bearings will fall between \((\mu - 0.0001)\) and \((\mu + 0.0001)\) inch is equals to 0.4514.
We have a metal lathe that produces machine bearings is properly adjusted.
Sample size for diameter , n = 36
Standard deviations, s = 0.001
We have to determine probability that the mean diameter of the sample of 36 bearings will fall between \((\mu - 0.0001)\) and \((\mu + 0.0001)\) inch. Let X be a random variable for mean diameter of sample. There is normal distribution of X random variable, \(X \: \tilde \: N( \mu, \frac{\sigma²}{n})\).
Now, probability that sample mean of diameter will fall between \((\mu - 0.0001)\) and \((\mu + 0.0001)\)
\(= P( \mu - 0.0001 < \bar x < \mu - 0.0001) \\ \)
\(= P( \frac{\mu - 0.0001 - \mu }{\frac{\sigma} {\sqrt{n}}}< \frac{\bar x - \mu}{\frac{\sigma} {\sqrt{n}}}<\frac{ \mu + 0.0001 - \mu } { \frac{\sigma} {\sqrt{n}}}) \\ \)
\(= P( \frac{- 0.0001 }{\frac{0.001} {\sqrt{36}}}< z <\frac{ 0.0001} { \frac{0.001} {\sqrt{36}}})\)
\(= P( \frac{- 0.0006}{0.001} < z <\frac{ 0.0006}{0.001})\)
= P( -0.6 < z < 0.6)
= P(z< 0.6) - P( z < - 0.6)
Using the p-value calculator or normal table or Excel command, the values of are calculated.
= 0.4514
Hence, required value is 0.4514.
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-90 divided by -31 help
Answers
Answer:
2.903225
Step-by-step explanation:
if you divide 2negativezs, you get a positive. -90/-31 =2.903225
Stefan sells Jin a bicycle for $139 and a helmet for $17 The total cost for Jin is %130 of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answers
Answer: Spent $120 originally, profited by $36
Step-by-step explanation:
The total cost Stefan earned from selling the helmet and the bicycle is $139 + $17 = $156.
130% can be rewritten as \(\frac{130}{100}\) which is simplified to 1.3.
Set up and this equation to find 130% of this price.
\(1.3x = 156\\x = 120\)
Stefan spent $120 on these items.
Subtract this value from the selling price and solve.
\(156-120 = 36\)
Stefan made $36 from selling the helmet and bicycle.
an average of 20 cars per hour arrive at the drive-in window of a fast food restaurant, where the interarrival times are exponentially distributed. assume the service time for each car is exponentially distributed with a mean of 2 minutes. due to concerns about safety, the restaurant management is considering implementation of a rule to limit the queue length to three cars. (that is, if three cars are in the waiting line for service, another car cannot enter the waiting line until the queue length is 2 or fewer.) if such a rule is instituted, what is the (long-run) percentage of time that cars will be unable to enter the queue?
Answers
To find the percentage of time that cars will be unable to enter the queue, we need to use the M/M/1 queueing model with finite queue length. The M/M/1 model assumes that the arrival and service times are both exponentially distributed, which is the case in this problem. The finite queue length means that there is a limit to the number of cars that can be in the waiting line.
The parameters for this model are:
λ = 20 cars per hour = 0.333 cars per minute (arrival rate)
μ = 1 car per 2 minutes = 0.5 cars per minute (service rate)
K = 3 (maximum queue length)
The probability that the queue is full and a car cannot enter is given by the formula:
P(K) = (1 - ρ) * (ρ^(K+1)) / (1 - ρ^(K+1))
where ρ = λ / μ is the traffic intensity.
Plugging in the values for λ, μ, and K, we get:
ρ = 0.333 / 0.5 = 0.666
P(3) = (1 - 0.666) * (0.666^(3+1)) / (1 - 0.666^(3+1))
P(3) = 0.334 * 0.197 / (1 - 0.197)
P(3) = 0.0658
Therefore, the percentage of time that cars will be unable to enter the queue is 6.58%.
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yo guys can u help me on this and show ur work...?
Answers
Answer:
12750
how to find the area -
Multiply length by width, and double it. That gives you the total area of the top and bottom surfaces, so you multiply them all together, then when you get the answer multiply it by 2, then that will be your answer!
The following table presents the heights (in inches) of a sample of college basketball players.Height: 68-71, 72-75, 76-79, 80-83, 84-87Freq: 3,5,2,2,2
Answers
The approximate variance that needs to be evaluated for the given set of heights is 18 , since 18 is close to 19 with a difference one 1 , then the correct answer is Option C.
Now, the formula for variance is
Var (X) = E [ (X – μ)² ]
Here
Var (X) = variance,
E = expected value,
X = random variable
μ = mean
Then, we need to evaluate the mean of heights and then further find the sum of squares of deviations from mean for each height value.
And divide this sum by n-1
here
n = sample size
Mean height = (2 x 69.5 + 2 x 73.5 + 4 x 77.5 + 2 x 81.5 + 3 x 85.5)/13 = 79
The addition of squares of deviations from mean is
(68-79)² + (68-79)² + (72-79)² + (72-79)² + (76-79)² + (76-79)² + (76-79)² + (76-79)² + (80-79)² + (80-79)² + (84-79)² + (84-79)² + (84-79)²
= 220
Hence,
variance = sum of squares of deviations from mean / n-1
= 220/12
= 18.33
≈ 18
The approximate variance that needs to be evaluated for the given set of heights is 18 , since 18 is close to 19 with a difference one 1 , then the correct answer is Option C.
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The complete question
The following table presents the heights (in inches) of a sample of college basketball players. Height Freq 68-71 2 72-75 2 76-79 4 80-83 2 84-87 3 Considering the data to be a population, approximate the variance of the heights
a) 5.6
b) 5.4
c) 19.2
d) 31.6
min ti x₁ = x₂-u x₂ = u -144²1 (x₁, x₂) arbitrary starting point. Let (0,0) be the Check whether situation (x₁, x₂)→ (0,0) shortest time is met. the beginning of the the coordinate. generality condition of the
Answers
It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).
Here, we have,
given that,
min t_i
x₁ = x₂-u
x₂ = u
-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.
and origin (0,0) be the begging of the coordinate.
also given that, (x₁, x₂)→ (0,0)
so, min t_i at origin (0,0) = t
Therefore, the generality condition of the situation does not met.
so, we get,
The given system can be represented by the following equations:
x₁' = x₂ - u
x₂' = u
To analyze the behavior of the system, we can examine the dynamics of each variable separately.
For x₁:
x₁' = x₂ - u
The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.
For x₂:
x₂' = u
The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.
Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).
By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).
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help what is 36,000÷10 with a power of 3
Answers
Answer:
36
Step-by-step explanation:
Graph the following features Y-intercept=-1 slope=7/4
Answers
Step-by-step explanation:
the graph is in photo
________________
The graph of the line with slope 7/4 and y - intercept - 1 is show in figure.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that the slope = 7 / 4
And, y - intercept = - 1
Now,
The equation of line with slope 7 / 4 and y - intercept - 1 is;
⇒ y = mx + b
⇒ y = 7 / 4 x + (-1)
⇒ y = 7/4 x - 1
So, We can graph the equation y = 7/4x - 1 as shown in figure.
The graph of the line with slope 7/4 and y - intercept - 1 is show in figure.
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PLEaseeeEEE help will give brainliest and 20 points!
Given the following polynomial describe the end behavior:
f(x) = 6x^5 + 5x^4 + x-10
Answers
Answer:
Falls to the left and rises to the right
Hope this helps!
Which of the following shows the correct first step to solve x^2-18x=-45
A x^2 - 18x + 18= -45 + 18
B. x^2 - 18x + 9 = -45 + 18
C. x^2 -18x + 81 = -45
D. X^2 -18 + 81 = -45 + 81
Answers
Answer:
D, X^2 -18 + 81 = -45 + 81
Step-by-step explanation:
it is complating squer method that used for solving x in a quadratic equetion . in this step you will add
(y/2)^2 if y is the cofitient of x .
solve x , y , and z. Please help
Answers
Answer:
z and x equal 143
y equals 37
Step-by-step explanation:
37-180=143
On the highway, a car can travel 21 miles per gallon of gas. If the car travels for 4 hours on the highway at a rate of 65 miles per hour, how many gallons of gas should the car use, to the nearest tenth of a gallon?
Answers
Answer:
5.36
Step-by-step explanation:
If the car travels for 4 hours on the highway at a rate of 65 miles per hour,12.4 gallons of gas should the car used, to the nearest tenth of a gallon.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that a car can go 21 miles per gallon of gas on a highway and that the car can travel for 4 hours at a speed of 65 miles per hour.
As a result, the distance traveled by car,
Distance = speed × time
Distance = 65 miles / hr × 4 hr
Distance = 260 miles
The number of gallons of gas the car should consume is determined by dividing the entire distance driven by the per gallon of gas as follows:
= 260 miles / 21 miles per gallon
= 12.38 gallon
The value nearest tenth of a gallon is,
=12.4 gallons
Thus, if the car travels for 4 hours on the highway at a rate of 65 miles per hour,12.4 gallons of gas should the car used, to the nearest tenth of a gallon.
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A parallelogram is transformed according to the rule (x, y) → (x, y). Which is another way to state the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360°
Answers
Answer:
d) 360
Step-by-step explanation:
Answer: D. R0, 360°
Step-by-step explanation: RIGHT ON EDGE 2023
Steve connected a wire extension that is 3/8 foot long to another wire that is 1/2 foot long. How long is the wire with the extension?
Answers
Answer:
7/8 feet
Step-by-step explanation:
In order to add two frctions you need to make their denominator the same,
3/8 can be kept as it is and we can multiply the top and bottom of 1/2 by 4 in order to ger 4/8. Now it is easier to add together,
3/8 + 4/8= 7/8
What is the value of x?
O 1
O 5
O 25
0 37
Answers
Answer:
37
Step-by-step explanation:
when you plug in 37 for X which is 96 degrees. which is technically an obtuse angle
Answer:
It’s 25
Step-by-step explanation:
You look good today
Which expreion have a quotient of 6? Select all that apply. 0. 48 ÷ 0. 8
4. 8 ÷ 8
0. 48 ÷ 0. 08
4. 8 ÷ 0. 8
4. 8/0. 8
Answers
Expreion have a quotient of 6 is 0. 48 ÷ 0. 08.
What is quotient?
In mathematics, the quotient is the result of performing division operations on two integers. It is essentially the outcome of the division procedure. In arithmetic division, the terms divisor, dividend, quotient, and remainder are employed in four different ways.Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
0. 48 ÷ 0. 8
=0.06
The solution for Long Division of \($\frac{4.8}{8}$\) is 0.6
The solution for Long Division of \($\frac{0.48}{0.08}$\) is 6.
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find in centimeters the circumference of a circle with a diameter of 0.15 m give and exact answer in terms of pi
Answers
Answer:
15πcm
Step-by-step explanation:
2πr = circumference
radius = 0.075m = 7.5cm
Circumference = 7.5X2π
15π cm
Which of the following represents the quadratic function f (x) = 5(x − 2)2 − 7 in standard form?
Answers
Answer:
f(x) = 10x - 27. I can't find the answer anywhere
Step-by-step explanation:
The tax rate is 6.8% what is the tax on $9.95
Answers
Answer:
$10.60
Step-by-step explanation:
6.8% = .068
.068 x 9.95
0.64675
since this is money
$.65
$9.95 + $.65
$10.60
Plot the graph y=3x from x=-1 from x=2
Answers
Answer:
(-1,-3) and (2,6)
Step-by-step explanation:
Plug x (x value) into equation (outputs y value)
(x value, y value) which gives coordinates
calculate the coefficient of variation for a sample of cereal boxes with a mean weight of 340 grams and a standard deviation of 5.2 grams.? 0.15% A
1.53% B
15.29% C
0.65% D
Answers
The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.
In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.
CV = (Standard Deviation / Mean) * 100
CV = (5.2 / 340) * 100
CV ≈ 1.53%
Therefore, the correct answer is option B: 1.53%.
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