Answer:
9 hours
Step-by-step explanation:
The total charge was $275 = $50 + ($25/hr)h
Simplifying: $225 = ($25/hr)h
$225
Then h = ---------------- = 9 hours
($25/hr)
Mr. D. spent 9 hours painting.
The function N(t) = 100e^−0.023t models the number of grams in a sample of cesium-137 that remain after t years. On which interval is the sample's average rate of decay the fastest?
Options:
A. [1,10] B. [10,20] C. [15,25] D. [1,30]
Answer:
A. [1,10]
Step-by-step explanation:
Given
[tex]N(t) = 100e^{-0.023t}[/tex]
Required
Interval with the fastest rate of decay
The rate of change over [a,b] is calculated as:
[tex]Rate = \frac{N(b) - N(a)}{b - a}[/tex]
So, we have:
A. [1,10]
[tex]Rate = \frac{N(10)-N(1)}{10 - 1}[/tex]
[tex]Rate = \frac{N(10)-N(1)}{9}[/tex]
Calculate N(10) and N(1)
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{79.45-97.73}{9} = \frac{-18.28}{9} = -2.03[/tex]
B. [10,20]
[tex]Rate = \frac{N(20)-N(10)}{20 - 10}[/tex]
[tex]Rate = \frac{N(20)-N(10)}{10}[/tex]
Calculate N(20) and N(10)
[tex]N(20) = 100e^{-0.023*20} = 100e^{-0.46} = 63.13[/tex]
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
So:
[tex]Rate = \frac{63.13 - 79.45}{10} = \frac{-16.32}{10} = -1.632[/tex]
C. [15,25]
[tex]Rate = \frac{N(25)-N(15)}{25 - 15}[/tex]
[tex]Rate = \frac{N(25)-N(15)}{20}[/tex]
Calculate N(25) and N(15)
[tex]N(25) = 100e^{-0.023*25} = 100e^{-0.575} = 56.27[/tex]
[tex]N(15) = 100e^{-0.023*15} = 100e^{-0.345} = 70.82[/tex]
So:
[tex]Rate = \frac{56.27 - 70.82}{10} = \frac{-14.55}{10} = -1.455[/tex]
D. [1,30]
[tex]Rate = \frac{N(30)-N(1)}{30 - 1}[/tex]
[tex]Rate = \frac{N(30)-N(1)}{29}[/tex]
Calculate N(30) and N(1)
[tex]N(30) = 100e^{-0.023*30} = 100e^{-0.69} = 50.16[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{50.16 - 97.73}{29} = \frac{-47.57}{29} = -1.64[/tex]
By comparing the values of the calculated rates,
-2.03 is the smallest, in other words; the fastest rate
Hence, the interval [1,10] has the fastest rate of decay
The required average rate of change is the fastest on [tex][1,10][/tex].
The average rate of change :The formula for the average rate of change on the interval [tex][a,b][/tex] is,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{b-a}[/tex]
Now, applying the given function into the above function is,
Now, [tex]a=1,b=10[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{10-1} =-2.03[/tex]
Now, [tex]a=10,b=20[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{20-10} =-1.6325[/tex]
Now, [tex]a=15,b=25[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{25-15} =-1.455[/tex]
Now, [tex]a=1,b=30[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{30-1} =-1.64[/tex]
So the average rate of change is fastest on [tex][1,10][/tex]
Learn more about the topic of the average rate of change:
https://brainly.com/question/20884505
Look at the graph shown below the blue line represents an _______ of the graph
Given:
The graph of a function and a blue line.
To find:
The correct name for the blue line.
Solution:
Domain: It is the set of inputs. These are the x-values for which the function is defined.
Range: It is the set of outputs. These are the y-values for the function.
Asymptote: The function approaches to a line as x approaches to -∞ or ∞ but not intersect the line, then the line is known as asymptote.
y-intercept: It is the intersection point of the function and the y-axis.
From the given graph it is clear that the function approaches to the blue line as x approaches to -∞ but not intersect the blue line.
So, the blue line is an asymptote of the function.
Look at the graph shown below the blue line represents an asymptote of the graph.
The equation of a circle is (x−2)2+(y−12)2=64 . What is the circle's center? Enter your answer by filling in the boxes.
Answer:
The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.
i also provided with a chart i dont know if it will help
sorry for the color yellow
Answer:
I believe it's the first option.
What is the value of x in this equation?
8x + 40 = 180
Answer:
17.5
Step-by-step explanation:
180 = 40+ 8x
140 = 8x
17.5 = x
Answer:
17.5 is the correct answer to the question
Step-by-step explanation:
8x+40=180
8x=180-40
8x=140
X=140/8
X=17.5
What is the measure of each angle if x = 13?
A. 42°, 38°
B. 527, 26°
C 429, 269
D. 527, 38°
The measures of two angles are 4x° and (2x + 12) °
Write an equation equivalent to 0.127
Answer:
127x10^-3
Step-by-step explanation:
0.127=
[tex]127 \times {10}^{ - 3} [/tex]
125
21
Find the value of the missing angle
Answer:
146°.................plz mark me brainliest
find x to the nearest 10th help pls
Answer:
5.9
Step-by-step explanation:
NEED HELP ASAP!!! Which of the following shows the prime factorization of 72 using exponential notation?
A) 8x9
B)2^2 x 3^2
C)2 x 6^2
D)2^3 x 3^2
Answer:
D)2^3 x 3^2
Step-by-step explanation:
2 x 2 x 2 = 8
3 x 3 = 9
8 x 9 = 72
Please help
solve the system of equations
Answer:
(x, y) = ( 5, 6)
(x, y) = ( - 1, 0)
Step-by-step explanation:
[tex] \begin{cases} y + x^2 - 5x = 6\\\\ y - x = 1\implies y = x + 1\end{cases} [/tex]
Plug [tex] y = x +1 [/tex] in the equation [tex] y + x^2 - 5x = 6[/tex] we find:
[tex] x + 1 + x^2 - 5x = 6[/tex]
[tex] x^2 - 4x - 5=0[/tex]
[tex] x^2 - 5x +x- 5=0[/tex]
[tex] x(x - 5) +1(x- 5)=0[/tex]
[tex] (x - 5) (x+1)=0[/tex]
[tex] (x - 5) =0, \: (x+1)=0[/tex]
[tex] x =5, \: x=-1[/tex]
[tex] When \:x =5 \implies y =5+1=6 [/tex]
(x, y) = ( 5, 6)
[tex] When \:x =-1 \implies y =-1+1=0 [/tex]
(x, y) = ( - 1, 0)
What is the cost of 1 pound of grapes?
A pair of jeans regularly sells for $24.00. They are on sale for 25% off. What is the sale price of the jeans.
Answer:
24 x 25/100 = 6
of means multiplication so you are multiplying the percent to the regular price. Always consider cent as a hundred and a percent out of 100 in fractions.
Answer:
18 dollars
Step-by-step explanation:
half of 24 is 12 and half of that is 6 so 24-6=18 :)
8/9÷3= 7/8 1/5 8/27 2/3
Solve ∣3x−2∣+4=0. Write your smaller answer first.
Answer:
wrong
Step-by-step explanation:
The density of an object is equal to the quotient of its mass, and volume. An object has a density of 10g per liter and a volume of 40 liters. What is its mass in grams.
Answer:
400 grams
Step-by-step explanation:
If the equation is density = mass / volume, fill it out to find mass
10 = x / 40
400 = x
x = 400 g
Convert the equation into Standard Form.
x^2 + y^2 + 10x - 12y+45 = 0
Answer:
(x−5)^2+(y+6)^2=9
Step-by-step explanation:
please answer will give brainlist and a thanks <3
Answer:
x=8
Step-by-step explanation:
Hope this helps and have a wonderful day!!!
Find the value of x.
9514 1404 393
Answer:
x = 20
Step-by-step explanation:
The external angle at V is half the difference of the subtended arcs:
(65° -25°)/2 = x° = 40°/2
x = 20
Al resolver la suma de ¾ + 5/4 obtenemos como resultado
Answer:
2
Step-by-step explanation:
3/4+5/4=8/4=2
Solve the system of equations. 2y-y=5 and 3x+2y=4
Answer:
Step-by-step explanation:
Answer:
y=5 x=-2
Step-by-step explanation:
mike is training to run a marathon. currently, he can run four miles in 44 minutes. if he maintains this running speed, how long will it take him to run 10 miles?
pls help:)!
mike is training to run a marathon. currently, he can run 4 miles in 44 minutes. if he maintains this running speed, how long will it take him to run 10 miles?
Answer:
110 minutes or 1 hour 50 minutes
Step-by-step explanation:
44 divided into 4 since we want to find out how much time it takes to run 1 mile, so 44 divided into 4 is 11
then simply multiply 11 with 10 and the answer is 110
: )
What is the point-slope form of a line with slope 2 that contains the point
(1,3)?
Answer:
(y-3) = 2(x-1)
Step-by-step explanation:
Point slope form is
(y-y1) = m(x-x1) where m is the slope and (x1,y1) is a point on the line
(y-3) = 2(x-1)
Is this correct???
I’m really worried this is a test worth 100 points?? Pls help if I made a mistake!!???
Answer:
There's supposed to be nothing in the 7 and 8 columns
Step-by-step explanation:
You were good, but there aren't any in the 7 or 8 columns, making 9 an outlier.
hope this helps:)
5x – 3y = 24
What is the Slope and Y Intercept?
Answer:
y=5/3x-8
Slope = 5/3
Y int = (0,-8) or y=-8
Step-by-step explanation:
Answer: 5/3x - 8
Step-by-step explanation:
-3y=24-5x
/3
5x/3 -8
5/3x - 8
What is the speed of a car that traveled a
total of 300 kilometers north in 2 hours?
Speed = Distance/Time
So, speed
= 300 km/2h
= 150km/h
= (150 × 1000m) / 3600s
= 150000m/3600s
= 41.66m/s [approximately]
Which set of ordered pairs is included in this relation?
A {(-5, 4), (-3, 2), (2, -1), (3, 0)}
B {(-4, 1), (-2, -5), (1, -2), (5, 2)}
C {(-3, -2), (0, 3), (1, -2), (4, 1)]
D {(-2,-5), (-1, 4), (2, -1), (3, 0)}
La montaña más alta del mundo es Everest cuya altura es de 8.848m y la altura de la segunda montaña más alta es de 2hm 3dam y 7m menos ¿Cuantos metros de altura tiene la segunda montaña más alta del mundo
Answer:
La segunda montaña más alta del mundo tiene 8611 metros.
Step-by-step explanation:
La montaña más alta del mundo es Everest cuya altura es de 8.848m.
La altura de la segunda montaña más alta es de 2hm 3dam y 7m menos. Para calcular la altura que tiene la segunda montaña más alta del mundo, debes realizar primero un cambio de unidades sabiendo que
1 hm= 100 m1 dam= 10 mEntonces podes aplicar las siguientes reglas de tres simple:
Si 1 hm equivale a 100 m, 2 hm equivale a ¿Cuántos metros?
[tex]metros=\frac{2 hm*100 m}{1 hm}[/tex]
metros= 200
Si 1 dam equivale a 10 m, 3 dam equivale a ¿Cuántos metros?
[tex]metros=\frac{3 dam*10 m}{1 dam}[/tex]
metros= 30
Entonces, la altura de la segunda montaña más alta es de 200 m+30 m+ 7 m menos que el Everest. Esto es, 237 metros menos que la montaña más alta del mundo. Entonces:
8848 metros - 237 metros= 8611 metros
La segunda montaña más alta del mundo tiene 8611 metros.
Paisley has $540 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
She buys a new bicycle for $446.60.
• She buys 3 bicycle reflectors for $4.09 each and a pair of bike gloves for $35.82.
• She plans to spend some or all of the money she has left to buy new biking outfits
for $72.82 each.
Which inequality can be used to determine x, the maximum number of outfits Paisley
can purchase while staying within her budget?
O 540 < 494.69% + 72.82
72.82x + 494.69 > 540
Submit Answer
72.82x + 494.69 < 540
540 > 494.69x + 72.82
The inequality that can be used to determine the maximum budget that can be spent on outfits is 72.82x + 494.69 < 540.
The first step is to determine the total cost of the items bought.
Cost of the bicycle = $446.60.
Cost of the 3 bicycle reflectors = $4.09 x 3 = $12.27
Cost of the bike gloves = $35.82
Total cost = $494.69
The amount left that can be spent on the new biking outfits = $540 - $494.69 = $45.31
The amount of money left is not sufficient to buy the new biking outfits.
To learn more about inequality, please check: https://brainly.com/question/5031619