Alex learned 80 new vocabulary words for his English exam. The following function gives the number of words he remembers after t days: W(t) = 80(1 - 0.1t)^3 What is the instantaneous rate of change of the number of words Alex remembers after 5 days? Choose 1 answer: A. 10 days B. 10 words per day C. -6 days D. -6 words per day

Answers

Answer 1

The instantaneous rate of change is -6 words per day,

the number of words Alex remembers after 5 days, option (D).

What is the instantaneous rate of change ?

An instantaneous rate is the rate at some instant in time. An instantaneous rate is a differential rate: -d[reactant]/dt or d[product]/dt. We determine an instantaneous rate at time t: by calculating the negative of the slope of the curve of concentration of a reactant versus time at time t.

Have given,

Alex learned 80 new vocabulary words

and after t days he learned,

W(t) = [tex]80 (1-0.1t)^{3}[/tex]

differentiate respect of t

W'(t) = [tex]80 \frac{d}{dt} (1-0.1t)^{3}[/tex]

W'(t) = [tex]80 * 3(1-0.1t)^{2} \frac{d}{dt}(1-0.1t)[/tex]

W'(t) = [tex]240(1-0.1*5)^{2} (0.1)[/tex]

W'(t) = 6

That's mean , the instantaneous rate of change is -6 words per day.

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Related Questions

What are m21 and m_2?

Answers

Answer:

<1  = 35degrees

<2  = 30degrees

Step-by-step explanation:

Using the theorem that the sum of external angle is equal to sum of interior angle

Considering the smaller triangle

Exterior angle = 115 degrees

Sum of interior = <1 + 80

Equating both

<1 + 80 = 115

<1 = 115 - 80

<1  = 35degrees

For the big rectangle

Exterior angle = 115 degrees

Sum of interior = <2 + 85

Equating both

<2 + 85 = 115

<2 = 115 - 85

<2 = 30degrees

A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT). Find the probability of getting exactly two heads.
The probability of getting two heads is
(Type an integer or a simplified fraction.)

Answers

Answer:

1/4

Step-by-step explanation:

Two Heads = HH,

From four options one of them is HH,

So likely the answer is 1/4,

Hope this helps!

Will it fit in a pot with a height of 20 cm and a bottom radius of 10 cm of 2.5 liters?
Can someone help me pls I need it fast

Answers

Answer:

Step-by-step explanation:

Volume of pot = πr²h

                       = 3.14 * 10 * 10 * 20

                       = 6280 cubic cm

1000 cubic cm = 1 litre

6280 cubic cm = 6.28 litre

∵ 2.5 litres will fit in the pot as the capacity of pot is 6.28 litre

In a park, the ratio of adults to children is 11 to 9. If there are 320 people in the park, how many children are there?

Answers

Answer:

144

Step-by-step explanation:

320 ÷ 20 = 16

adults : children

11 : 9

9×16 = 144

What is the cos(65)?

Answers

= 0.4226182617, or 0.423 if rounded to 3 d.p

Which of the following expressions had a constant of 6 and a coefficient of 2/3?

Answers

Answer:

The answer is d, 2/3y-6

Step-by-step explanation:


One of two complementary angles is 71 degrees. Let x = the measure of
the other complementary angle. Write and solve an equation to find the
measure of angle x.

Answers

Answer:

19 degrees

Step-by-step explanation:

Sum of 2 angles is complementary,

x + 71 = 90

x = 90 - 71

x = 19 degrees

please help me with this asap

Answers

Answer:

Upper left is 9, upper right is 9, lower left is 21

Step-by-step explanation:

They tell us there are 9 birds that are yes fly and yes fish, so that’s the upper right.

They tell us there are 18 yes fish total. Subtract the 9 from the upper right, and that leaves 9 for the upper left.

They tell us there are 39 birds total.

39 - 18 (all fish eaters) - 4 (no fly, no fish) = 17 that can fly but don’t eat fish.

Make sense? lmk if you have questions

Are 20,30, and 16 the sides of a right triangle? Please show workkk

Answers

Yes 20,30, and 16 is the sides of a right triangle

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Answers

1.5 / 1
A 1has to be the denominator so for example, 100 yards / 1 minute of jogging

Justin is making a poster for Bike Safety Week. The diameter of circle A is 16 in.

If the area of circle B is the area of circle A, what is the area of circle B? (Use 3.14 for .)

Answers

Step-by-step explanation:

Given Area of Circle B = Area of Circle A

Given r = 1/2d = 1/2(16) = 8 in

and Area of Circle =

[tex]\pi {r}^{2} \\ = (3.14) ({8}^{2} ) \\ = (3.14)(64) \\ = 200.96 {in}^{2} [/tex]

Can the sides of a triangle have lengths 8, 17, and 18?

Answers

Answer:

Step-by-step explanation:

Tak

find the missing side.

Answers

no sides are missing !

2, 1, 1/2, 1/4 which number should come next​

Answers

1/8 should come next

Cara is making 25 sundaes with mint, chocolate, and vanilla ice cream. 1/5 of the sundaes are mint ice cream and 1/2 of the remaining sundaes are chocolate. The rest will be vanilla. How many sundaes will be vanilla?

Answers

Answer:

5

Step-by-step explanation:

HOPE THIS HELPS YOU!

brainliest?

1/5=20%

25. 100%
X. 20%
X=25•20/100
X=500/100
X=5.
5 are mint ice cream

25-5=20
1/2 of 20 is 10
10 are chocolate

25-(5+10)=25-15=10
10 are vanilla

Which is the graph of g(x)? ​

Answers

Answer: A because its always A

Step-by-step explanation:

What’s the answer to this

Answers

Answer:

D: 39.71 pi m cubed

Step-by-step explanation:

To find the volume of a cylinder, you must use the equation V=pi times the radius squared times the height.

For this problem, the radius is 1.9 and the height is 11, and this gives you 124.75 which divided by pi, is rounded to 39.71

A cube has a surface area of 54cm2. What is the volume of the cube?

Answers

Answer:

27 cm³

Step-by-step explanation:

A = 6 a²

V = a³

V=6A3/2

36=6·543/2

36≈27cm³

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Answers

Answer:C

Step-by-step explanation:

Answer: bro i cant see it can you make it lighter

Step-by-step explanation:

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-Solving Equations with variables on both sides

Answers

Answer:

1) x = -1

2) x = 11

3) x = -3

4) x = -14

5) x = -7

6) x = 5

7) x = 12

8) x = -4

Step-by-step explanation:

use the photomath app

1. Use the formula V = Bh to find the volume of a gift box that is 3.5 inches
high, 7 inches long, and 6 inches wide.

Answers

Answer:

147

Step-by-step explanation:

Length x Width = base

Base x Height = Volume

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Answers

Answer:

3/2

Step-by-step explanation:

MNOP to ABCD: The answer has to be greater than one because ABCD increases in size from MNOP.

To get the scale factor you have to compare the sides.

Line AD = 6 in.

Line MP = 4 in.

6/4 = 3/2

3.
1- =
How do you subtract 1 - 1/2?

Answers

Answer:

You can just type it in the calculator. 1/2=0.5 so 1 - .05= 0.5 . Lmk if there is more to the question!

Step-by-step explanation:

I NEED THE ANSWER(ASAP)

The list below shows the allowance earned by eight of the students in Ms. Tomas's class. What is the mean allowance earned in Ms. Tomas's class?

$7, $12, $8.50, $ 10, $7, $8, $10.50, $11​

Answers

Answer:

9.25

Step-by-step explanation:

For the mean, you have to add all and divide it by the numbers.

7 + 12 + 8.50 + 10 + 7 + 8 + 10.50 + 11 = 74

74 divided by 8 = 9.25

What is the slope of the line below?

Answers

up two over one so the slope is 2
The slope is 2 :) dndjes
Dmfirkdnd

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Answers

I think its 10



Correct me if im wrong

But all u have to do is multiply 2.5 x 4=10

A book costs $1.49 and is sold in a retail store for $8.99. What is the percentage in mark up? mmnle 10 percent would be 10% You can find the percent​

Answers

Answer:

The percentage in mark up is 503.56%.

Step-by-step explanation:

The percentage in markup is the change(retail - cost) divided by the initial cost, and multiplied by 100%.

In this question:

Cost: 1.49

Change: 8.99 - 1.49 = 7.5

Percentage change:

(7.5*100%)/1.49 = 503.56%.

The percentage in mark up is 503.56%.

The national mean annual salary for a school administrator is $90,000 a year (The Cincinnati Enquirer, April 7, 2012). A school official took a sample of 25 school administrators in the state of Ohio to learn about salaries in that state and to see if they differed from the national average. Click on the datafile logo to reference the data.
A. Formulate hypotheses that can be used to determine whether the population mean annual administrator salaries in Ohio differ from the national mean of $90,000.
B. The sample data for 25 Ohio administrators is contained below. What is the p-value for your hypothesis test in part A?
C. At alpha = 0.05, can your null hypothesis be rejected? What is your conclusion?
D. Repeat the preceding hypothesis test using the critical value approach?
Salary Data
77600
76000
90700
97200
90700
101800
78700
81300
84200
97600
77500
75700
89400
84300
78700
84600
87700
103400
83800
101300
94700
69200
95400
61500
68800

Answers

The answer is C okay

Mark rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 5

Answers

Answer:

1/3

Step-by-step explanation:

p=1/6+1/6

=2/6

=1/3

One positive number is 9 more than twice another. If their product is 95, find the numbers.

Answers

Answer:

The numbers are 19 and 5

Step-by-step explanation:

Given

Let the numbers be [tex]x\ and\ y.[/tex]

So:

[tex]x = 9 + 2y[/tex] --- First statement

[tex]x*y = 95[/tex] --- second statement

Required

Find x and y

Substitute [tex]x = 9 + 2y[/tex] in [tex]x*y = 95[/tex]

[tex](9 + 2y) * y = 95[/tex]

[tex]9y + 2y^2 = 95[/tex]

Rewrite as:

[tex]2y^2 + 9y - 95 = 0[/tex]

Expand

[tex]2y^2 -10y +19y- 95 = 0[/tex]

Factorize

[tex]2y(y -5) +19(y- 5) = 0[/tex]

[tex](2y +19)(y- 5) = 0[/tex]

Solve for y

[tex]2y + 19 =0[/tex] or [tex]y - 5 = 0[/tex]

[tex]2y = -19[/tex] or [tex]y = 5[/tex]

[tex]y = -\frac{19}{2}[/tex] or [tex]y=5[/tex]

Since the numbers are positive, we take only:

[tex]y=5[/tex]

Substitute [tex]y=5[/tex] in [tex]x = 9 + 2y[/tex]

[tex]x = 9 + 2 * 5[/tex]

[tex]x = 9 + 10[/tex]

[tex]x = 19[/tex]

The numbers are 19 and 5

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