The longest worm is blank times as long as the shortest worm

Hi there!

For the graph on the left, we know that the area A is equal to:
[tex]A = \int\limits^a_0 {e^x} \, dx[/tex]

Area 'B' is 9 times this area, so:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx[/tex]

We can evaluate the integral:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx \\\\B = 9 \cdot e^x \left \| a}} \atop {0}} \right. \\\\B = 9 (e^a - 1)[/tex]

We also know that:
[tex]B = \int\limits^b_0 {e^x} \, dx[/tex]

Evaluate:

[tex]B = e^x \left \| b}} \atop {0}} \right. = e^b - 1[/tex]

Set the two equations for 'B' equal:
[tex]e^b - 1 = 9(e^a - 1)\\\\e^b - 1 = 9e^a - 9 \\\\e^b = 9e^a - 8[/tex]

Take the natural log of both sides:
[tex]ln(e^b) = ln(9e^a - 8)\\\\\boxed{b = ln(9e^a - 8)}[/tex]

Answer:

2,4 possibly

Step-by-step explanation:

if its V (intersection) W

then its 2,4

if it has something to do with patterns then i dont know

Answer:

f(x) = 2x3 + 4

Stretch vertically be a factor of 2:

f(x) = 2*2x3 + 4 = 4x3 + 4

Shift 5 units to the left:

f(x) = 4(x+5)3 + 4

Answer:

64=4^3

Step-by-step explanation:

4x4x4=64. 4x4x4=4^3 as there are three 4s. Hope it helps!

Answer:

Use the given functions to set up and simplify f(x+2).

5x2+18x+19 This is the Answer if using The Function Operation.

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10x−2 This is the Answer if you want to find the Derivative

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I don't know if my answer is right if it's wrong I am sorry.

Anyways have an amazing day!

Answer:

Well, i would just say you just had to do your best in everything that you do. No pressure , no stress don't overwork yourself and simply take action. Then you will have a chance to get what you want because you tried your best to get to it. Although sometimes we don't get what we want, atleast we'll be closer. As they say, 'Aim for the sun to reach the moon"

Step-by-step explanation:

You're welcome

Answer:

65.2 cm

Step-by-step explanation:

P = a + b + c + d

P = 16.7 cm + 12.9 cm + 16.7 cm + 18.9 cm

P = 65.2 cm

The perimeter of the trapezoid is 65.2 cm.

Answer:

To find the perimeter of this trapezoid, simply add all four sides (since there are only four sides to a trapezoid):-

16.7 + 12.9 + 16.7 + 18.9

= 65.2 centimetres is the perimeter.

You can picture it like this;

Answer:

1360 seats sold

Step-by-step explanation:

total seats = 1600

total seats sold = 85% of 1600

= 85/100 × 1600

= 85 × 16

= 1,360 seats sold

Answer:

Graphs pairs of numerical data, with one variable on each axis, to look for a relationship between them

Step-by-step explanation:

The scatter diagram graphs pairs of numerical data, with one variable on each axis, to look for a relationship between them. If the variables are correlated, the points will fall along a line or curve. The better the correlation, the tighter the points will hug the line.

Answer:

a=5 b=7 c=9

hope I helped :)

Answer:

9(n+2) = 4

Step-by-step explanation:

9(n+2) = 4

to solve for 'n' first distribute the 9 to get:

9n + 18 = 4

subtract 18 from each side to get:

9n = -14

n = -14/9

Answer:

Choice C.

An isosceles triangle always has two sides of the same length.

in 20 days 4 half life will be completed

so n = 4

formula :-

[tex] \frac{ A\degree}{ {2}^{n} } = \frac{9056}{ {2}^{4} } = \frac{9056}{16} = 566grams[/tex]

The radioactive kind of promethium will have 566 grams left after 20 days.

Half-life is the time required for a quantity to reduce to half of its initial value.

Given, A radioactive kind of promethium with 9,056 grams and a half-life is 5 days.

∴ In the next 5 days, it'll have (9056/2) = 4528 grams.

Next 5 days it'll have (4528/2) = 2269 grams.

As it has a half-life in 5 days and 20 is multiple (4×5).

After 20 days the radioactive material will have (9056/2⁴) grams.

= 566 grams left.

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Answer:

720

Step-by-step explanation:

n*180

n

the answer is 720

Answer:

20 lb of 31 cent candy, 30 lb of 46 cent candy

Step-by-step explanation:

sorry don't have one

here is a smiley face for you

:D

The amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, we can assume the separate weights of each type of candies to be represented by variables.

Let we have:

x pounds of first type of candy is mixed with y pounds of second candy.

The weight of the mixture = x + y = 50 pounds

The cost of the mixture = 40 cents per pound  = [tex]40 \times 50 = 2000[/tex] cents

Cost of the mixture = cost of x pounds of first candy+ cost of y pounds of second candy = [tex]31x + 46y[/tex]
Thus, we get [tex]31x + 46y =2000[/tex]

Therefore, we got a system of two linear equations as:

[tex]x +y = 50\\31x + 46y =2000[/tex]

From first equation, we get:

[tex]x = 50 -y[/tex]

Substituting this value in second equation, we get:

[tex]31(50-y) + 46y =2000\\1550 + 15y = 2000\\15y = 450\\\\y = 450/15 = 30[/tex]

Putting this value of y in equation for x, we get:

[tex]x = 50-y = 50-30 = 20[/tex]

Thus, the amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

Learn more about solving system of linear equations here:

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Answer:

2,3,4

Step-by-step explanation:

Given data:

2,0,2,4,4,4,3,2,3,4,1,3,3,2

Solution:

Mode = Most often number

There are

4 = two's

1 = zero's

4 = four's

4 = Three's

1 = ones's

Hence the mode is:

2,3,4

~lenvy~

[tex]P= \dfrac FA \implies F = PA[/tex]

Answer:

£78

Step-by-step explanation:

65 divided by 5= £13

13+65=£78

Answer:

£78

Step-by-step explanation:

Let the total value be T.

contact +2348021312463, he can help you

after approximately 137 minutes, there will be 10 bacteria remaining.

To find the time at which there will be 10 bacteria remaining, we can use the half-life model for exponential decay, which is given by:

N(t) = N₀ * [tex](1/2)^{(t / t_{half})[/tex]

where:

N(t) = the number of bacteria at time t

N₀ = the initial number of bacteria

t = time (in minutes)

t_half = the half-life of the bacteria

We are given that the initial number of bacteria (N₀) is 500 and after 17 minutes there are 150 bacteria (N(17) = 150).

Let's use this information to find the value of k (the decay constant):

150 = 500 * [tex](1/2)^{(17 / t_{half})[/tex]

Divide both sides by 500:

[tex](1/2)^{(17 / t_{half})[/tex] = 150 / 500

[tex](1/2)^{(17 / t_{half})[/tex] = 0.3

Now, we can write the equation as an exponent:

17 / t_half = log base (1/2) of 0.3

Using logarithms:

t_half = 17 / log base (1/2) of 0.3

Now, calculate t_half:

t_half = 17 / log base 2 of 0.3 ≈ 38.555

Now, we can find the time at which there will be 10 bacteria remaining (N(t) = 10):

10 = 500 * [tex](1/2)^{(t / 38.555)[/tex]

Divide both sides by 500:

[tex](1/2)^{(t / 38.555)[/tex] = 10 / 500

[tex](1/2)^{(t / 38.555)[/tex] = 0.02

Write the equation as an exponent:

t / 38.555 = log base (1/2) of 0.02

Using logarithms:

t = 38.555 * log base 2 of 0.02 ≈ 137.08

Rounding to the nearest whole number:

t ≈ 137

So, after approximately 137 minutes, there will be 10 bacteria remaining.

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Answer:

19000

Step-by-step explanation:

1 hour = 50 miles

2 hour = 100 miles

50×380 = 19000

Answer:

used formula to find Area of parallelogram

area of parallelogram =b× h

Step-by-step explanation:

solution :

given ,

h = 7cm

b = 9 cm

we know ,

Area of parallelogram = b× h

=63cm²

Answer:

-1/2

Step-by-step explanation:

2/5 * - 3/7 - 1/14 - 3/7 * 3/5

= - 6/35 - 1/14 - 9/35

= - (6*2)/(35*2) - (1*5)/(15*5) - (9*2)/(35*2)

= - 12/70 - 5/70 - 18/70

= (-12 - 5 - 18)/70

=- 35/70

= - 1/2

Hello!

Please remember that

Example:

4T+5H

In this example, the coefficient of T is 4, and the coefficient of H is 5.

So let's identify the coefficient of x.

It seems like x doesn't have a coefficient, but it does.

It's equal to 1.

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

:-)

Answer:

16 children

Step-by-step explanation:

divide 12 by .75 you get 16

hope that helps

Answer:

125x 12 and divide the answer

Step-by-step explanation:

Answer:

125x 12 and divide the answer

Step-by-step explanation:

There are several ways to reduce how much does it cost to run an air conditioner. The two main ones are:Buying an air conditioner with a high energy efficiency rating (EER, SEER, CEERratings are valid specifications).Reducing the number of hours per day that you use a given air conditioner.Note: It’s recommended to estimate how much electricity does an air conditioner use before buying a specific unit.On average, running an air conditioner costs between $0.06 and $0.88 per hour. Let’s calculate how much does air conditioning cost per month (running 8h per day):

Answer:

First convert two feet into yards, knowing that:

1 foot = 0.333... yards

So,

2 feet in yards would mean double of 0.333... because one single foot is 0.333... yards.

2(0.333...)

= 0.666..., which we can round to 0.67.

So our new ratio will be 32 bulbs per 0.67 yards.

Now we convert this ratio into a unit rate,

Order your units;

Bulbs         32           47.76

______   ______ = ______, which rounds to about 48.

Yards        0.67             1

So the unit rate is 48 bulbs per yard.

Answer:

y=90(0.5)^x

The y-intercept is (0,90), so when x=0, y should be 90.

By replacing x=0 in all equations you get;

1)

y=90(2)^0 =90 accepted

2)

y=2(90)^0 =2 rejected

3)

y=0.5(90)^0 =0.5 rejected

4)

y=90(0.5)^0 =90 accepted

Since this is an exponential decrease,

y=90(2)^x is rejected.

Answer:

Step-by-step explanation:

Answer: 120cm

Step-by-step explanation:

Multiply length x width x height

10 x 6 x 2 is equal to 120, so the volume is 120cm or centimetres.

Answer:

10cmx6cmx2cm

6x2=12

12×10=120cm