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Paladinen [302]
3 years ago
9

PLEASE HELP ME!

Mathematics
1 answer:
sattari [20]3 years ago
3 0

You want to know how long it'll take for the bacteria to grow
to (800/500) = 1.6 times their initial population.

The number of double-times it'll take is 

                         [ log(1.6) / (log(2) ]  =  0.6781 .

The double-time for these particular critters is 12 hours,
so it'll take them

                             0.6781  x  12 hours  =  8.137 hours

                                                                =  8 hours  8.2 minutes .
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The solution for the system equations 8x-6y=-32 and -8x+5y=36
Ghella [55]

Answer:

x=47, y=68

Step-by-step explanation:

Add the two equations. Then we get

-y=-68

y=68

Substituting the value of y in the first equation,

8x-6(68)=-32

8x-408=-32

8x=376

x=47

6 0
3 years ago
Charlie is trying to cover the shape shown with paper. He will NOT be covering the top and the bottom. How much paper will he ne
DENIUS [597]

You need to determine how much paper you need to cover the lateral side of the cylinder shown in the picture. For this, you have to calculate the surface area of the cylinder, which you can do using the following formula:

A=2\pi rh

Where

A is the area

π is the number pi, for the calculations we usually use up to the first two decimal values of this number, 3.14

r is the radius

h is the height of the cylinder

The given cylinder has a height of h=15m and a diameter of d=6m

To calculate the lateral area you need to use the radius. The diameter is twice the radius, so to determine the radius of the cylinder you have to divide the diameter by 2

\begin{gathered} r=\frac{d}{2} \\ r=\frac{6}{2} \\ r=3 \end{gathered}

Now you can calculate the lateral area as follows:

\begin{gathered} A=2\pi rh \\ A=2\cdot3.14\cdot3\cdot15 \\ A=282.6m^2 \end{gathered}

Charlie will need 282.6 m² to cover the lateral side of the cylinder.

6 0
1 year ago
The minimum/maximum value of the function y = a(x − 2)(x − 1) occurs at x = d, what is the value of d?
daser333 [38]

Answer:

d=\frac{3}{2}=1.5

Step-by-step explanation:

We have the function:

y=a(x-2)(x-1)

And we want to find x=d for which the minimum/maximum value will occur.

Notice that our function is a quadratic in factored form.

Remember that the minimum/maximum value always occurs at the vertex point.

And remember that the x-coordinate of the vertex is the axis of symmetry.

Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.

Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.

Our factors are <em>(x-2) </em>and <em>(x-1)</em>.

Therefore, our roots/zeros are <em>x=1, 2</em>.

So, the average of them are:

d=\frac{1+2}{2}=3/2=1.5

Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.

Alternative Method:

Of course, we can also expand to confirm our answer. So:

y=a(x^2-2x-x+2)\\y=a(x^2-3x+2)\\y=ax^2-3ax+2a

The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.

And the formula for the vertex is:

x=-\frac{b}{2a}

So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:

x=-\frac{-3a}{2a}=\frac{3}{2}=1.5

Confirming our answer.

4 0
3 years ago
Renee has a triangular garden with an area of 24 square feet. Which drawing shows Renee's garden?
gulaghasi [49]

Answer:

The picture that represent her drawing is uploaded below. The height is 8 ft and the base is 6 ft.

Step-by-step explanation:

Renee garden is triangular in shape . The area of the triangular garden is given as 24 ft² . The area of a triangle can be represented below.

Area of a triangle = 1/2bh

where

b = base

h = height

The drawing that represent Renee drawing is given below. The height is 8 ft and the base is 6 ft .

Using the formula

Area of a triangle = 1/2bh

Area of a triangle = 1/2 × 6 × 8

Area of a triangle = 48/2

Area of a triangle = 24 ft²

6 0
3 years ago
Read 2 more answers
What is 5.092 rounded to the nearest hundredth?
goblinko [34]
5.09 because 2 is less then 5 so you round down
6 0
3 years ago
Read 2 more answers
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