Estimate the sum by rounding each number
to the nearest hundredth: 0.052 +0.028
A 0.06
B 0.08
0.09
D 0.07

Answer:

In 59 days, the number of bacteria reaches 1000.

Step-by-step explanation:

 Given the data in the question;

by placing 100 spores of the bacteria at the start of the project,

p(0) = 100

dP over dt equals the product of 0.05 times P and the quantity 1 minus P over 2000

dp/dt = 0.05p( 1 - p/200 )

2000dp / p( 2000 - p ) = 0.05dt

[1 / p + 1 / 200-p ]dp = 0.05 dt

Now, we integrate

∫[1 / p + 1 / 200-p ]dp = ∫ 0.05 dt

ln p - ln [2000 - p ]  = 0.05 + c'

ln[ p / 2000 - p ] = 0.05 + c'

p / 2000 - p  = [tex]e^{0.05t + c'[/tex]

p / 2000 - p  = k[tex]e^{0.05t[/tex]

Now, since p(0) = 100, we substitute

100 / (2000 - 100)  = k[tex]e^{0.05(0)[/tex]

100 / 1900  = k × [tex]e^{0[/tex]

100 / 1900  = k × 1

k = 1 / 19

Therefore,

p / 2000 - p  = k[tex]e^{0.05t[/tex]

p / 2000 - p  = (1/19)[tex]e^{0.05t[/tex]

when p( t ) = 1000, then t will be;

1000 / (2000 - 1000)  = (1/19)[tex]e^{0.05t[/tex]

1000 / 1000  = (1/19)[tex]e^{0.05t[/tex]

1  = (1/19 ) × [tex]e^{0.05t[/tex]

1/(1/19 )  = [tex]e^{0.05t[/tex]

(1 × 19)/1 = [tex]e^{0.05t[/tex]

[tex]e^{0.05t[/tex] = 19

0.05t = ln( 19 )

0.05t = 2.9444

t = 2.9444 / 0.05

t = 58.888 ≈ 59 days

Therefore, In 59 days, the number of bacteria reaches 1000.

Answer:

-1/2

Step-by-step explanation:

Answer:

A: Southeast

B: Northwest

C: Southwest

D: Northeast

Step-by-step explanation:

Answer:

B: Northwest

C: Southwest

   D: Northeast                     A: Southeast

Answer:

V = 502.4 cm³

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume of a Cylinder Formula: V = πr²h

Step-by-step explanation:

Step 1: Define

r = 4 cm

h = 10 cm

Step 2: Find Volume

Answer:

85%

Step-by-step explanation:

The students who read less than six magazines would be placed in the intervals: 0-1, 2-3, and 4-5 on the graph. Adding up the total amount in those intervals gives us:

2 + 15 = 17

So, using the answer from b, we can say that 17/20 kids read magazines. Now, we need to convert it into a percent by multiplying by 100:

17/20 *100

17 * 5

85%

Answer:

24π cm³

Step-by-step explanation:

Given the following data;

Radius, r = 3 cm

Height = 8 cm

To find the volume of a cone;

[tex] V = \frac{1}{3} \pi r^{2}h[/tex]

Where;

V is the volume of the cone.

r is the radius of the base of the cone.

h is the height of the cone.

Substituting into the equation, we have;

[tex] Volume = \frac{1}{3} * \pi * 3^{2}*8 [/tex]

[tex] Volume = \frac{1}{3} * \pi *9 *8 [/tex]

[tex] Volume = \pi * 3 *8 [/tex]

Volume of cone = 24π cm³

.460Answer:

Step-by-step explanation:

Answer:

It is better to have a variety of plants because if the species of plants die out, the whole ecosystem becomes extinct.

Step-by-step explanation:

Answer:

Option 2: 1 + 1/2 + 1/4 + 1/8+...

Step-by-step explanation:

When a geometric series converges, it has a common ratio that is in between -1 and 1. We can start by finding the common ratios of all the options and then see which one converges.

In the first option, each term is 3 times the term before it, meaning it has a ratio of 3. 3 does not fit in the range we defined, so this series does not converge.

In the second option, each term is half the term before it. This means the common ratio is 1/2. 1/2 is in the range, so this series converges.

In the third option, we can see that the common ratio is -4 since it is the number being brought to a power. -4 does not fit in the range we defined, so this series does not converge.

In the fourth option, we can see the common ratio is 2 since it is the number you multiply by tone more time to get the next term. 2 does not fit in the range we defined, so this series does not converge.

From this, we can see the second option(1 + 1/2 + 1/4 + 1/8+...) is the solution.

The geometric series [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] converges by the rule of convergence. Thus, the option [tex]2[/tex]  from the given options is correct.

     When a geometric series converges, it has a common ratio that is in between [tex]-1[/tex] and [tex]1[/tex].

The convergence of the geometric series depends on the common ratio [tex]r[/tex]. When [tex]r[/tex]>1, then the series diverges.When [tex]r[/tex]<1, then the series converges, and when [tex]r[/tex] = 1, then the series oscillates.

The common ratio [tex]r[/tex] of the series  [tex]\dfrac{1}{81} +\dfrac{1}{27} +\dfrac{1}{9} +\dfrac{1}{3}[/tex]  is greater than [tex]1.[/tex] So, the series diverges.

For the series, [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] , the common ratio  [tex]r[/tex] is  [tex]\dfrac{1}{2}[/tex], which is less than [tex]1[/tex] . So, the series converges.

For the series, [tex]\sum 7(-4)^n[/tex] , here the common ratio is [tex]-4[/tex]  which does not lie in the range of convergence. Thus the given series is not convergent.

For the series,[tex]\sum \dfrac{1}{5}(2)^{n-1}[/tex] the common ratio is 2.  So, the series is not convergent.

The geometric series is [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex].

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Answer:1320

Step-by-step explanation:Only one person can win first, second and third place. The total number of placers is 12 times 11 times 10.

Answer:

Usig their skills by:

Step-by-step explanation:

Using their strengh, force, move your feet, and arms with strong force to push you ahead faster and faster, if u are really tired I would keep going,

Answer:

A circle.

Step-by-step explanation:

Ok, any plane has a vector normal to it.

Then the plane that cuts the sphere, has a normal vector.

If we draw that normal vector such that it passes through the center of the circle, we can think of this as the "axis" of a cylinder.

Such that when we step on any point of that vector, all the points of the spere that can be reached with a perpendicular line to the vector (like the radius in polar coordinates) are at the same distance of the vector.

Then we can conclude that when we cut a sphere with a plane, the cross-section will be always a circle.

Then the shape that is a representation of the cross-section is a circle.

Answer:

61 units

Step-by-step explanation:

Answer:

y=-x+8

Step-by-step explanation:

Slope = (y₂-y₁)/(x₂-x₁) = (1-8)/(7-0) = -7/7 = -1

Y-intercept = (0,8)

Therefore, the equation of the trend line is y=-x+8

Answer:

lateral area = 308 ft

surface area = 616 ft

Answer:

I think it's A but I'm not sure

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

Answer:

72 miles

Step-by-step explanation:

To solve this problem, you can use the pythagorean theorem, which is a^2 + b^2 = c^2. We already have b equal to 54 miles, and since c is the hypotenuse, it equals 90 miles. We can substitute the values into the formula to get:

a^2 + 54^2 = 90^2

a^2 + 2916 = 8100

a^2 = 5184

a = 72 miles

7.3 is the range

Step-by-step explanation:

The range of a set of data is the difference between the largest and smallest values.

The value of the range of the data is,

⇒ 7.3

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

The data set is,

⇒ 4.8, 5.5, 4.2, 8.9, 3.4, 7.5, 1.6, 3.8

Since, We know that;

Difference between the highest and smallest value of the data set is called range.

Hence, We get;

The value of the range of the data is,

⇒ 8.9 - 1.6

⇒ 7.3

Thus, The value of the range of the data is,

⇒ 7.3

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Answer:

d) $7.82

Step-by-step explanation:

just multiply the 2 numbers

Answer:

50?

Step-by-step explanation:

im not sure please think about it, but I think it might be 50

Answer:

d

Step-by-step explanation:

The freight charge on a shipment of 1200 kg is $84.00. So, the rate per 100 kg would be $7.00. option D is correct.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

It is given that the freight charge on a shipment of 1200 kg is $84.00. we need to find the rate per 100 kg.

So, by the unitary method,

The freight charge on a shipment of 1200 kg = $84.00.

The freight charge on a shipment of 1 kg = 84/ 1200

The freight charge on a shipment of 100 kg = 84/ 1200

                                                                           = 84 x 100/ 1200

                                                                            = $7.00

Learn more about the unitary method;

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You want math problems???

Answer:

Hᴇʏᴀᴀᴀ!! ᴍʏ ɴᴀᴍᴇ ɪꜱ ᴘɪɴᴋʏ ᴀɴᴅ ɪ ᴀᴍ ʜᴇʀᴇ ᴛᴏ ᴀɴꜱᴡᴇʀ ʏᴏᴜʀ Qᴜᴇꜱᴛɪᴏɴ!!ʕ ꈍᴥꈍʔ☆

Step-by-step explanation:

ɪ ᴅᴏɴ'ᴛ ʀᴇᴀʟʟʏ ʟɪᴋᴇ ᴍᴀᴛʜ ʙᴜᴛ ɪꜰ ɪ ʜᴀᴅ ᴛᴏ ᴄʜᴏᴏꜱᴇ ᴀ ꜰᴀᴠᴏʀɪᴛᴇ ɪᴛ ᴡᴏᴜʟᴅ ʙᴇ ᴀʟɢᴇʙʀᴀ!!  (◕ᴗ◕✿)

  ʜᴀᴠᴇ ᴀɴ ᴀᴍᴀᴢɪɴɢ ɴɪɢʜᴛ ᴏʀ ᴅᴀʏ!

      *:･ﾟ✧*:･ﾟꜰʀᴏᴍ ʏᴏᴜʀ ᴏɴᴇ ᴀɴᴅ ᴏɴʟʏ ᴘɪɴᴋʏ  ʕ ﾟ ● ﾟʔ✧✧･ﾟ: *✧･ﾟ:* *:･ﾟ✧*:･ﾟ

Answer:

45/22

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

multiply the length value by 5.5

Answer:

Step-by-step explanation:

(x-1)²+(y-2)² =4 compare the given equation with the general one

(x-h)² +(y-k)² =r², where (h, k) are coordinates of the center and r is radius

so center is at ( 1, 2) and radius is 2

Answer:

Im pretty sure the answer is C

Step-by-step explanation:

Because neither cm lengths are more than a 90 degree angle, but im not 100% sure so can you provide a picture of the problem or is that how it actually showed?