Mathematics College

Question 5
5 pts
Let f(x)
40e^.06t. What is the average rate of change of f over the
interval [0,3]? Give your answer as a decimal with one place of
accuracy to the right of the decimal point.

Answers

Answer 1

Answer:

[tex]R= 2.6[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 40e^{.06t[/tex]

[tex][a,b] = [0,3][/tex]

Required

Determine the average rate of change (R)

This is calculated as follows:

[tex]R = \frac{f(b) - f(a)}{b - a}[/tex]

Where

[tex]a = 0[/tex] and [tex]b = 3[/tex]

Substitute 0 for a and 3 for b

[tex]R = \frac{f(3) - f(0)}{3 - 0}[/tex]

[tex]R = \frac{f(3) - f(0)}{3}[/tex]

[tex]R = \frac{1}{3}[f(3) - f(0)][/tex]

Calculate f(3)

[tex]f(x) = 40e^{.06t[/tex]

[tex]f(3) = 40e^{.06*3}[/tex]

[tex]f(3) = 40e^{0.18}[/tex]

[tex]f(3) = 40 * 1.197[/tex]

[tex]f(3) = 47.88[/tex]

Calculate f(0)

[tex]f(x) = 40e^{.06t[/tex]

[tex]f(0) = 40e^{.06*0}[/tex]

[tex]f(0) = 40e^{0}[/tex]

[tex]f(0) = 40*1[/tex]

[tex]f(0) = 40[/tex]

So, the expression:

[tex]R = \frac{1}{3}[f(3) - f(0)][/tex]

[tex]R= \frac{1}{3}[47.88 - 40][/tex]

[tex]R= \frac{1}{3}[7.88][/tex]

[tex]R= 2.62666666667[/tex]

[tex]R= 2.6[/tex]

Hence, the average rate of change is approximately 2.6

Related Questions

Martina spent $24 on fruit at the grocery store. She spent a total of $80 at the store. What percentage of the total did she spend on fruit?

Answers

Answer: 30%

Step-by-step explanation:

She spent $24 dollars out of the total money she had which was $80. The 24 represents the portion of the money that was spent on fruits. So therefore to find the percentage for put the portion used ($24) divided by the the total ($80) multiplied by a hundred to get the 30%.

i need help with this asap! i will give brainliest!!

Answers

Answer:

97

Step-by-step explanation:

Angle on a straight line = 180

106 + ∠st = 180

∠st = 180 - 106 = 74

x = ∠st + 23

= 74 + 23

= 97

Answer:

51 degrees

Step-by-step explanation:

This is a scalene triangle. Which means it sums up to 180 degrees. Therefore, you have to add up all the degrees to 180. 106+23 is 129, and 180 - 129 is 51.

if Scott types 210 words in 5 minutes how many words can he type in a minute​

Answers

Answer:

42

Step-by-step explanation:

210 divided by 5 is 42

A reading teacher brought sets of different numbers of books for her class. She paid the same price for each book

Complete the table to show the number of books she bought or the price she paid
(Put your answers in the Order of a,b,c)

Answers

Answer:

A) $15

B) 8

C) $25

Step-by-step explanation:

this is due in a few hours can yall help me

Answers

Answer:

18%, 34%, 9/25, 0.25

Step-by-step explanation:

36% = 18%

17/50 = 34%

0.18 = 9/25

1/4 = 0.25

help me pleaseeeeeeeee

Answers

C. None of the x-values repeat.

Answer:

C is because it doesn't have any repeating x-values or y-values

Step-by-step explanation:

A chemist has 100 ml of 25% acid solution. how much of the solution does she need to drain and replace with 70% acid solution to obtain 100 ml of 60% acid solution?

Answers

Answer:

The proportion of acid at 70% that the chemist must use will be 77.8%, while the remaining 22.2% will be acid at 25%.

Step-by-step explanation:

Since the chemist has 100 ml of solution with 25% acid, and wants to obtain a solution of 60% acid by mixing the first with another 70% acid solution, to determine how much of each solution the chemical should use necessary to perform the following calculation:

70 x 1 + 25 x 0 = 70

70 x 0.9 + 25 x 0.1 = 65.5

70 x 0.8 + 25 x 0.2 = 61

70 x 0.7 + 25 x 0.3 = 56.5

Therefore, the proportion to be used is between 70% and 80% of acid at 70%, and 20% to 30% of acid at 25%.

70 x 0.75 + 25 x 0.25 = 58.75

70 x 0.76 + 25 x 0.24 = 59.2

70 x 0.77 + 25 x 0.23 = 59.65

70 x 0.78 + 25 x 0.22 = 60.1

Thus, the proportion should be between 77 and 78% of acid at 70% and 22 and 23% of acid at 25%.

70 x 0.778 + 25 x 0.222 = 60.01

Thus, finally, the proportion of acid at 70% that the chemist must use will be 77.8%, while the remaining 22.2% will be acid at 25%.

solve cos^30- sin^30​

Answers

Answer:

hi

Step-by-step explanation:

hdisbkaab

bhai kyun dimag kharab kr raha hai chup chap apni mam se puch

which of these is not a linear graph.​

Answers

Answer:

D

Step-by-step explanation:

It isn't linear

Answer:

D)

Step-by-step explanation:

Linear graphs are straight they can be positive or negative but they do not have bending points in them.

I added a picture to help you

A store sells shirts at a price of 2 for $5.00. At this price, how much do 7 shirts cost?

Answers

Answer:

$17.50

Step-by-step explanation:

2 goes into 7 3 times, and 5 times 3 is $15.00, so theres one shirt left. If 2 shirts cost $5, one will cost $2.50. So, 15+2.50= $17.50

5/2 equals 2.50 so 2.50x7 equals 17.50

Fine the values of x and y. Please explain .

Answers

.hhdjekekeke kekelekwkwkwkww

Q#2 Pleaseeee answer my guy it’s literally the biggest grade I got and I’m tiredddd

Answers

Answer:

Add 3 to both sides.

2x=9+3

simplify 9+3 to 12

2x=12

Divide both sides by 12

x= 12

     2

simplify

x=12

I need help with this I’ll mark you

Answers

Answer:

The answer is C

Which translation moves point Z so that the whole image is only in quadrant 1 and 2
Captionless Image

Answers

Answer:

I can’t see the picture!

Step-by-step explanation:

Rick’s scores in his last 15 rounds of golf are 72, 80, 75, 84, 78, 72, 75, 68, 81, 74, 79, 70, 77, 83, and 72. If he scores an 80 on each of the next three rounds, which measure of center would increase more, the mean or median?

Answers

Answer:

The median increased more

Step-by-step explanation:

Given that:

Scores on last 15 :

72, 80, 75, 84, 78, 72, 75, 68, 81, 74, 79, 70, 77, 83, 72

Obtaining the range, mean, median and mode from the data above :

Rearranged data:

68, 70, 72, 72, 72, 74, 75, 75, 77, 78, 79, 80, 81, 83, 84

Range = 84 - 64 = 16

Mode = 72 - frequency of 3)

Mean = ΣX / n where n = sample size

Mean = 1140 / 15 = 76

Median = 0.5(n+1)th term = 0.5(16)th term =

8th term = 75

A score of 80 on each of next 3 rounds :

72, 80, 75, 84, 78, 72, 75, 68, 81, 74, 79, 70, 77, 83, 72, 80, 80, 80

Rearranged data:

68, 70, 72, 72, 72, 74, 75, 75, 77, 78, 79, 80, 80, 80, 80, 81, 83, 84

Range = 84 - 68 = 16

Mean = ΣX / n where n = sample size

Mean = 1380 / 18 = 76.67

Median =0.5(n+1)th term = 0.5(19)th term =

9.5 = (9th term +. 10th term) / 2 = (77 +78) / 2 = 77.5

WILL GIVE BRAIANLEST PLZZZZ HELP MEEE 50 POINTS
Elevator 1 in an office building moved from ground position to a final position of +12 feet. Elevator 2 in the same building moved from ground to a final position of −15 feet. Which statement best describes the final positions of these two elevators? (5 points)

Question 4 options:

1)

Elevator 1 is 12 feet above ground level, and Elevator 2 is 15 feet below the position of Elevator 1.

2)

Elevator 1 is 12 feet below ground level, and Elevator 2 is 15 feet above the position of Elevator 1.

3)

Elevator 1 is 12 feet above ground level, and Elevator 2 is 15 feet below ground level.

4)

Elevator 1 is 12 feet below ground level, and Elevator 2 is 15 feet above ground level.

Answers

Answer: The answer would be option 3

Step-by-step explanation:

What is 2,356 divided by 27​

Answers

Answer:336.57

Step-by-step explanation:

Answer:

87.259.

Step-by-step explanation:

HELP ASAP what's the reason for statement 3, WILL GIVE BRAINLIEST​

Answers

Answer:

From prove

Step-by-step explanation:

from prove

Explanation

Two angles are called complementary when their measures add to 90 degrees

Helpppppppppppppppppp

Answers

Answer:

ik that problem gimmie a sec

Step-by-step explanation:

Step-by-step explanation:

since 1 and 2 are same the lines which create 1(g and p) and 2(h and r)

the lines g h and p r shoul be parallel. we also know that g h is parallel which proves that p and r should be parallel as well

Help me please, thank you :)​

Answers

Answer:

300 children

Step-by-step explanation:

half hour: 25 children

1 hour: 25×2= 50 children

6 hours: 50×6= 300 children

hope it helps ☺️!

300 kids in 6 hours

Element X is a radioactive isotope such that every 40 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 110 grams, how much of the element would remain after 29 years, to the nearest whole number?

Answers

Answer:67 or 66.549674907

Step-by-step explanation:

Man women baby

20 POINTS!!!!please help due in 20 mins

Answers

Answer:

rate of change is -1/3 (table) and 4 (graph)

Function 2 has the greater rate of change because the graph is steeper, and |4| is bigger than |-1/3|

Step-by-step explanation:

Answer:

(a) Function 1 : -2 Function 2 : 3.

(b) Function 2

Step-by-step explanation:

For function #1, you can calculate the rate of change (another word for slope) by counting the change between each y value. So, when x is 2, y is -3. When x is 3, y is -5. The rate of change is -2!

Show your work by marking an arrow for each y and writing -2.

Function #2, you need to find the slope (rate of change) by drawing a rise/run line when the equation line hits a point on the graph. One point is (-1,1) another point is (0,4). The slope/rate of change is 3.

If m is a multiple of 20 then m is also a multiple of 10 true or false​

Answers

True .... I think?? Cuz if m=40 (cuz 40 is a multiple of 20) and 40 is also a multiple of 10

ldentify the location of the values used to create a box
plot.

A=
B=
C=
D=
E=

Answers

A minimum
B Q1 ( first quartile )
C Median
D Q3 ( third quartile)
E maximum

I hoped that helped.

Answer:

A minimum

B Q1 ( first quartile )

C Median

D Q3 ( third quartile)

E maximum

Step-by-step explanation:

HOPED THIS HELPED YOU OUT! AND TO EVERYONE THAT NEEDS THE HELP WITH THIS QUESTION

have a GOD-LIKE day

John travels 54 miles each day of his 5 day journey to Disney land. What is the distance from John’s house to Disney land? PLZZ

Answers

The distance is 270 miles
Answer: 270 miles so yes

PLEASE HELP. WILL MARK BRAINLIEST. !!50 points!!

Triangle A"B"C" is formed using the translation (x +0, y+ 2) and the dilation by a scale factor of 2 from the origin. Which equation explains the relationship between line
AC and line A"C"?

A. Line AC
——————- = 2
A"C"

B. Line A" C" 1
————— = —
AC 2

C. Line A"C"
Line AC = —————-
2



D. Line AC
Line A"C" = —————
2

Answers

Answer: i dont understand the question can you please elaborate

Step-by-step explanation:

I can see the problem sir

What is the equation of the line that passes through the point (2,0) and has a slope of 5/2

Answers

Answer :

y = 5/2x - 5

Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5/2 , thus
y = 5/2x + c ← is the partial equation
To find c substitute (2, 0) into the partial equation
0 = 5 + c ⇒ c = 0 - 5
y = 5/2x - 5 ← equation of line

which equation is equivalent to y= Ax + By = C

Answers

Answer:

slope intercept form

Step-by-step explanation:

that's what ax + by = c is

xoxo, your highness...


Identify each pair of angles as corresponding, alternate interior, or alternate exterior.

9)
A alternate exterior
B corresponding
C alternate interior

10)
A) Corresponding
B) Alternate exterior
C) Alternate interior

Answers

Answer:

9)  Corresponding

(The agles correcpond off of reflection)

10)  Alternate interior

(The interior brings the negative side and flips it to the possative on the x axis)

Step-by-step explanation:

Hopefully this helped, if not HMU and I will try my best to get you a better answer!

Have a wonderful day! :)

Find the maximum value of the function
f(x) = –22 – 15.9x – 57 to the nearest hundredth.

Answers

8 fishi i ndrysheses se nje numrime 7
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