Answer:
-0.2 ppm/mi -0.025 ppm/miStep-by-step explanation:
Given C(x) = 0.1/x², you want the rate of change of C(x) for x=1 and x=2. (C is ppm; x is miles.)
DerivativeThe rate of change is given by the derivative of the function. The power rule applies.
\(C(x)=\dfrac{0.1}{x^2}=0.1x^{-2}\\\\\dfrac{dC}{dx}=0.1(-2)x^{-3}=-\dfrac{0.2}{x^3}\qquad d(x^n)=n\cdot x^{n-1}dx\)
(A) 1 MileFor x=1, the rate of change is ...
C'(1) = -0.2/1³ = -0.2 . . . . ppm/mi
(B) 2 MilesC'(2) = -0.2/2³ = -0.1(2/8) = -0.025 . . . . ppm/mi
__
Additional comment
Some graphing calculators work nicely with derivatives. The second attachment shows this. It doesn't "show work," but it gives you a way to check your result.
ANSWERS ASAP PLEASEEE
In how many ways can the letters of the word ‘CAR’ be reordered to produce distinct ‘words’?
Answer:2
Step-by-step explanation:
car, and arc, however ar is also a word, not distinctly though.
uy Islari
ce Area and Volume
1
Note: Figure is not drawn to scale
If h = 8 units and r = 5 units, then what is the approximate volume of the cone shown above?
Answer:
\(209.43 \: \: {units}^{3} \)
Step-by-step explanation:
\(v = \pi {r}^{2} \frac{h}{3} \\ = \pi \times {5}^{2} \times \frac{8}{3} \\ = 209.439\)
if y=3x - 5, find the value of y when x = -1yn
Answer:
\(y = 3x - 5 \\ x = - y \\ substitute \: - y \: in \: the \: place \: of \: x \\ y = - 3y - 5 \\ y + 3y = 5 \\ 4y = 5 \\ y = \frac{5}{4} \)
1/10 (x + 11) = -2 (8 - x)
Answer: (5/8)x
Step-by-step explanation:
8. Choose all decimals that are equivalent to (7 x 100) + (5 × 1) + (8 × 7) + X 10 (1 × 100). 75.081 705.810 705.801 75.810 705.81 705.081
Answer:
705.81 and 705.810
Step-by-step explanation:
700 + 5 + 0.8 + 0.01 = 705.81
Answers:
705.810
705.81
pls help with this..
Answer:
B
Step-by-step explanation:
given scale is 1 inch represents 7.5 feet
then we require to calculate how many 7.5 feet there are in each dimension.
to obtain this divide each dimension by 7.5, that is
13 ÷ 7.5 ≈ 1.73 ( to 2 decimal places )
26 ÷ 7.5 ≈ 3.47 ( to 2 decimal places )
then dimensions are approximately 1.73 inches by 3.47 inches
Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
System A
x+3y=9
-x-3y=9
System B
-x-3y=-3
x+3y=3
O The system has no solution.
O The system has a unique solution:
(x, y) = (
O The system has infinitely many solutions.
They must satisfy the following equation:
y = 0
O The system has no solution.
O The system has a unique solution:
(x, y) = (D)
O The system has infinitely many solutions.
They must satisfy the following equation:
y=0
The system A has no solution.
The system B has the solution y=( 3-x )/3
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
System A:
x+3y=9..........(1)
-x-3y=9 ..........(2)
(1) => x=9-3y........(3)
Substitute (3) into (2)
(2) = > - ( 9-3y ) - 3y = 9
-9 + 3y - 3y = 9
-9 =9
This is false.
So, the system has no solution.
System B:
-x-3y=-3..........(1)
x+3y=3..........(2)
(2) => x=3-3y........(3)
Substitute (3) into (1)
-(3-3y)-3y=-3
-3+3y-3y= -3
-3=-3
This is true,
So, the solution is:
x=3-3y
=> 3y= 3-x
=> y=( 3-x )/3
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Find two consecutive even integers whose sum is 90?
eight hundred twenty nine and six tenths as a decimal
If the light is coming from the same position, the length of a person's shadow is proportional to their height. Adam and Cara are standing side-by-side, facing their shadows. Adam is 159 centimeters tall and casts a shadow 105 centimeters in height. If Cara is 140 centimeters tall, how many centimeters will she need to walk forward for the tip of her shadow to be directly in line with Adam's?
16 multiplied by what gives you 1600?
Answer:
The answer is 100. One way to find it out is 1600/16, and then you get 100.
What is the least common multiple of 9 , 12, 15
Answer:
3
Step-by-step explanation:
9÷3 , 12÷3 , 15÷3
= 3
done
6 R
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-2
4 6
4 2
4
Help❗️❗️
Answer:
drop the 0 then add the 0 o. the top or I think
a circle has a diameter of 32 inches find the circumference of the circle to the nearest tenth. use 3.14 for pi
The circumference of the circle which has a diameter of 32 inches is 100.5 inches to the nearest tenth.
Given that,
Diameter of a circle = 32 inches
Radius = Half of the diameter
= 32/2
= 16 inches
The formula to find the circumference of the circle is,
Circumference = 2πr, where r is the radius of the circle.
Circumference = 2π × 16 = 32π inches
= 100.48 inches ≈ 100.5 inches
Hence the circumference of the circle is 100.48 inches.
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lamonte car used 5 gallons to travel 125 miles.how many gallons of gas would he need to travel 400 miles
Answer:
Step-by-step explanation:
1. Get mileage per gallon by dividing miles traveled by gallons used
\(\frac{125}{5} = 25 mpg\\\)
2. Divide miles you want to travel by the mileage per gallon you got on the first step
\(\frac{400}{25} = 16 gallons\)
Hunter surveys a random sample of 64 students at his community college and finds that
37.5% of the students saw a film at the local movie theater in the last 30 days. Find a 90% confidence interval for the proportion p of all students at the community college who saw a film at the movie theater in the last 30 days.
We can be 90% confident that the true proportion of all students who saw a film at the movie theater in the last 30 days is between 0.277 and 0.473.
What is proportion?
Proportion is a mathematical term that represents a relationship between two quantities or numbers. It refers to the comparison of one part of a whole to the whole itself.
To find a confidence interval for the proportion p of all students who saw a film at the movie theater, we can use the formula:
CI = p ± z * √(p(1-p)/n)
where p is the sample proportion, n is the sample size, z is the z-score corresponding to the desired level of confidence (90% in this case), and √(p(1-p)/n) is the standard error of the proportion.
First, we need to find the sample proportion p:
p = 37.5% = 0.375
Next, we need to find the z-score corresponding to a 90% confidence level. We can use a z-table or a calculator to find this value. The z-score for a 90% confidence level is 1.645.
Now we can plug in the values into the formula:
CI = 0.375 ± 1.645*√(0.375(1-0.375)/64)
Simplifying:
CI = 0.375 ± 0.098
Therefore, the 90% confidence interval for the proportion of all students who saw a film at the movie theater in the last 30 days is:
CI = (0.277, 0.473)
Hence, we can be 90% confident that the true proportion of all students who saw a film at the movie theater in the last 30 days is between 0.277 and 0.473.
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What is the length of segment XY?
The length of segment XY in this problem is given as follows:
XY = 5 cm.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.In this problem, we have that segment XY is adjacent to an angle of 45º, with the opposite side has a length of 5 cm, hence the tangent of the angle can be used, as follows:
tan(45º) = 5/XY
It is known that the tangent of 45 degrees is of 1, hence the length of the segment XY is calculated as follows:
1 = 5/XY
XY = 5 cm.
Meaning that the third option is the correct option.
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Answer:
5 cm
Step-by-step explanation:
Ian suffered a loss of 10% when his watch was sold at $90. How much should he have sold his watch if he wanted to make a gain of 20%?
Explanation:
This problem is a simple percent chage problem. The absoluge change in price was $12−$8=$4. Relative to the original price, it was 412, which is 0.3333 or 33.33%.
If the force acting on an object stays the same, then the acceleration of the object varies inversely as its mass. If an object with a mass of 27 kilograms accelerates at a rate of 2 meters per second per second by a force, find the rate of acceleration of an object with a mass of 3 kilograms that is pulled by the same force.
The rate of acceleration of an object with a mass of 3 kilograms that is pulled by the same force is given as follows:
18 m/s².
What is the relation between force, mass and acceleration?According to Newton's Second Law, the force is given by the multiplication of the mass and of the acceleration, as follows:
F = ma.
The force is obtained as follows, considering a mass of 27 kg and an acceleration of 2 m/s².
F = 27 x 2
F = 54N.
Then the acceleration of an object of 3 kilograms with the same force is given as follows:
3a = 54
a = 54/3
a = 18 m/s².
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How many 11-card hands are possible with a 20-card deck?
There is only 1 possible 11-card hand that can be formed from a 20-card deck.
To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.
The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.
The formula for combinations is:
nCk = n! / (k!(n-k)!)
Where "!" denotes the factorial of a number.
Substituting the values into the formula:
20C11 = 20! / (11!(20-11)!)
Simplifying further:
20C11 = 20! / (11! * 9!)
Now, let's calculate the factorial values:
20! = 20 * 19 * 18 * ... * 2 * 1
11! = 11 * 10 * 9 * ... * 2 * 1
9! = 9 * 8 * 7 * ... * 2 * 1
By canceling out common terms in the numerator and denominator, we get:
20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)
Performing the multiplication:
20C11 = 39,916,800 / 39,916,800
Finally, the result simplifies to:
20C11 = 1
Consequently, with a 20-card deck, there is only one potential 11-card hand.
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HELP PLEASE....I REALLY DONT KNOW WHAT THIS WANTS FROM ME
Step-by-step explanation:
Area of the circle=
\( \frac{\pi {d}^{2} }{4} \)
3.14•(17)²/4
=226.865in²
Area of the rectangle=length•width
=(8•15)in²
=120in²
Area of the shaded portion=Area of the circle-Area of a rectangle
=(226.865-120)in²
=106.865in²
=106.87in² to the nearest hundredth
Jennifer is a runner and ran a 10k last weekend. The function t=7k represents the relationship between kilometers, k, and the total running time, t. What is a reasonable range for this situation?
Answer:
We know that Jennifer ran 10k last weekend.
Now, we have the function:
t = f(k) = 7*k
(notice that this is a linear function)
First, let's define what is the range.
The range is the possible values that the outcome, t, can take.
To see the range, we first must see the domain (the possible values of of the input)
In this case, we know that the minimum value of k is 0 (the time to run 0 kilometers)
t(0) = 7*0 = 0
Here we found the minimum of the range.
Now, the maximum value in the domain is 10 (because she ran 10km, we can not have a value of k larger than 10)
The time is:
t(10) = 7*10 = 70
This will be the maximum of the range.
Then the range can be written as:
R = [0, 70]
ACD is a triangle and B is a point on AC. AB = 8cm and BC is 6cm. Angle BCD = 48° and angle BDC = 50°. (a) Find the length of BD. (b) Find the length of AD. (c) Find the area of triangle ABD. (This is all one question)
Answer:
5.8206 cm10.528 cm23.056 cm^2Step-by-step explanation:
(a) The Law of Sines can be used to find BD.
BD/sin(48°) = BD/sin(50°)
BD = (6 cm)(sin(48°)/sin(60°)) ≈ 5.82064 cm
__
(b) We can use the Law of Cosines to find AD.
AD^2 = AB^2 +BD^2 -2·AB·BD·cos(98°) . . . . . angle ABD = 48°+50°
AD^2 ≈ 110.841
AD ≈ √110.841 ≈ 10.5281 . . . cm
__
(c) The area of ∆ABD can be found using the formula ...
A = ab·sin(θ)/2 . . . . . where a=AB, b=BD, θ = 98°
A = (8 cm)(5.82064 cm)sin(98°)/2 ≈ 23.0560 cm^2
_____
Angle ABD is the external angle of ∆BCD that is the sum of the remote interior angles BCD and BDC. Hence ∠ABD = 48° +50° = 98°.
ill mark brainlist plss he,p
Answer:
blue and red
Step-by-step explanation:
hope it helped
Ms. Thomspon needs 15/2 yards of red fabric and 7 1/2 yards of silver fabric. which comparison is true.
Step-by-step explanation:
To compare the two amounts of fabric, we need to express them with a common denominator:
15/2 = 30/4
7 1/2 = 15/2
Now we can compare the two amounts:
30/4 > 15/2
This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.
Therefore, Ms. Thompson needs more red fabric than silver fabric.
The pay collected for working per hour is known as your hourly wage. It varies directly linearly with the hours that you work.
A. If you earn $100 when you work for 8 hours, what is your hourly wage?
B. Use your answer for (A) to write a direct linear variation equation.
C. If you work for 5 hours, how much will you earn?
show your work
Answer:
hola
Step-by-step explanation:
es buena la app.verdad gracias
complete the partial two-way frequency table below that shows the extracurricular activities of high school students. Based on the data in the table, how many students do not play an instrument
According to the information, the missing number from the box is number 40.
How to find the missing number in the box?To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.
According to the above we can infer that the missing number is 40.
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-8x+y=6
-8x+3y=-14
How would you solve this using the elimination method? Thanks!
Answer:
x = -1,375
y = -5
Step-by-step explanation:
{-8x + y = 6, / : (-1)
{-8x + 3y = -14;
Multiply the first equation by -1, so that we could eliminate 8x:
+ {8x - y = -6,
{-8x + 3y = -14;
----------------------
4y = - 20 / : 4
y = -5
Now, make x the subject from the first equation (you can do it from the 2nd one instead):
8x = -6 + y / : 8
x = -0,75 + 0,125y
x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375
Keith is a gardener and he can plant 40 bushes in 8 hours. How many bushes can he plant in 2 hours?
Answer:
Keith can plant 10 bushes in 2 hours
Step-by-step explanation:
40 divided by 8 is 5 and 5 times 2 is 10.