Help with Math Question 1

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:

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:

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

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Answer:

Ask you teachers if they can give you extra assignments for extra credit! Sometimes they will!

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?

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:

53 1/3 cups

Step-by-step explanation:

if there are 80 glasses and each glass has 2/3 of juice in it, there will be 53 1/3 cups in total because 80 x 2/3 = 53 1/3

Answer:

Use geogebra it is a helpful website that helps you plot points, and find where things go. The second one is c. y=25x.

Step-by-step explanation:

Answer: The width of the rectangle is 10.2 inches, the perimeter is 71.4 inches,  the area is 260.1 inches.

Step-by-step explanation:

25.5/5=5.1

5.1*2=10.2

The width is 10.2 inches

25.5*2+10.2*2=71.4

The perimeter is 71.4 inches

20.5*10.2=260.1

The area is 260.1

1) The width of the rectangle is 10.2 in.

2) The perimeter of the rectangle is 71.4 in.

3) The area of the rectangle is 260.1 sq.in.

[tex]P=2\times(l+w)[/tex]

where, 'l' is the length of the rectangle

'w' is the width of the rectangle

[tex]A=l\times w[/tex]

For given example,

The sides of a rectangle are in the ratio 2:5

The longer side of the rectangle is 25.5 in.

This means the length of the rectangle is [tex]l=25.5~in.[/tex]

Let 'x' represents the width of the rectangle.

⇒ [tex]\frac{2}{5} =\frac{x}{25.5}[/tex]

⇒ 2 × 25.5 = 5 × 'x'

⇒ 51 = 5x

⇒ x = 51/5

⇒ x = 10.2 in.

This means the width of the rectangle is 10.2 in.

⇒ [tex]l=25.5~in,~w=10.2~in.[/tex]

Using the formula of perimeter of the rectangle,

⇒ P = 2 × (25.5 + 10.2)

⇒ P = 2 × 35.7

⇒ P = 71.4 in.

Using the formula of area of the rectangle,

⇒ A = 10.2 × 25.5

⇒ A = 260.1 sq. in.

Therefore, the width of the rectangle is 10.2 in.

The perimeter of the rectangle is 71.4 in.

The area of the rectangle is 260.1 sq.in.

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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:

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

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:

Surface area of figure = 200.52 meter²

Step-by-step explanation:

Given:

Side of square cut = 12 meter

Diameter of semi circle = 12 meter

Find:

Surface area of figure

Computation:

Diameter of semi circle = 12 meter

Radius of semi circle = Diameter of semi circle / 2

Radius of semi circle = 12 / 2

Radius of semi circle = 6 meter

Surface area of figure = Surface area of square + Surface of cylinder

Surface area of figure = [Side x Side] + πr²/2

Surface area of figure = [12 x 12] + (3.14)(6)²/2

Surface area of figure = [144] + (3.14)(36)/2

Surface area of figure = 144 + 56.52

Surface area of figure = 200.52 meter²

Answer:

[tex]x = 4.8[/tex]

Step-by-step explanation:

[tex] \frac{3}{4} = \frac{3.6}{x} [/tex]

[tex]3x = 14.4[/tex]

[tex]x = 4.8[/tex]

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,

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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Let x be the amount invested at 10%;

SO we have;

.10x=amount invested at 10%

(4000-x).12=amount invested at 12%

So our equation would be;

.10x+(4000-x).12=460

Distribute the 12%;

.10x+480-.12x=460

Put like terms together so you can see them better;

.10x-.12x+480=460

-.02x+480=460;

subtract 480 from both sides;

-.02x=-20

Multiply each side by -.02;

x=1000

Now that we know what was invested at 10% we can subtract that from $4000 to get what was invested at 12%;

$4000-$1000=$3000

Hope you understand

=)

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:

lateral area = 308 ft

surface area = 616 ft

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: A

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:

45/22

Step-by-step explanation:

Answer:

50?

Step-by-step explanation:

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

Answer:

the buttons are alredy on the calculator.

Step-by-step explanation:

Answer:

6/5

Step-by-step explanation:

For this you need to clear the formula for the area which is bxh/2=A, now you need to clear the base and the formula would be b=Ax2/h, and would be (9/20)x2/ 3/4 equal to 18/20 / 3/4 and gives the result of 72/60,now you need to simplify and the simplest form is 6/5

The base of the triangle with area of 9 / 20 centimetres squared and height of 3 / 4 centimetres is 6 / 5 centimetres.

area of a triangle = 1 / 2 bh

where

Therefore,

area = 9 / 20 cm²

height = h = 3 / 4 cm

b = ?

Hence.

area of the triangle = 1 / 2 bh

9 / 20 = 1 / 2 × 3 / 4 × b

9 / 20 = 3 / 8 b

cross multiply

9 × 8 = 20 × 3b

72 = 60b

b = 72 / 60

b = 12 / 10 = 6 / 5

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