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cluponka [151]
3 years ago
6

A bacterium in a petri dish multiplies by a factor of 31 every day. On day O,

Mathematics
1 answer:
Kamila [148]3 years ago
8 0

Answer:

Step-by-step explanation:

Given that,

The bacterial increase a factor of 31 every day ,

Day 0 = 1 bacterium = 31^0

Day 1 = 31 bacterial  = 31¹

Day 2 = 31× 31 bacterial = 31²

Day 3 = 31 × 31 × 31 bacterial = 31³

And so on,

Then, nth day will have

Day n = 31ⁿ bacterial

So, when will the bacterial be 1,000,000,000

Then,

31ⁿ = 1,000,000,000

Take the Natural logarithmic to base 31 of both sides

Log_31 (31)ⁿ = Log_31 (1,000,000,000)

n•Log_31 (31) = Log_31 (1,000,000,000)

Then, log_a (a) = 1

n = Log_31 (1,000,000,000)

Check attachment for better view

Then,

The correct answer is A

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How many people swimming during this time
ludmilkaskok [199]

Answer:

954 people swimming

Step-by-step explanation:

Definition

A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

Example

Stem "1" Leaf "5" means 15

Total are:

9 +

11 +

23 + 29 +

47 +

55 + 57 + 57 + 59 +

65 + 65 + 66 + 66 + 67 + 68 + 69

70 + 71

= 954

8 0
3 years ago
A grocery store offers a 15% discount on your entire purchase when you spend more than $60. You have $85 to spend on groceries a
Serga [27]

0.85(a + 60) ≤ 85

0.85a + 51 ≤ 85

-51 on both sides

0.85a ≤ 34

/0.85 on both sides

a ≤ 40

Answer:

a ≤ 40

5 0
2 years ago
X - 3y +3=0
Arte-miy333 [17]

Answer:

We know that for a line:

y = a*x + b

where a is the slope and b is the y-intercept.

Any line with a slope equal to -(1/a) will be perpendicular to the one above.

So here we start with the line:

3x + 4y + 5 = 0

let's rewrite this as:

4y = -3x - 5

y = -(3/4)*x - (5/4)

So a line perpendicular to this one, has a slope equal to:

- (-4/3) = (4/3)

So the perpendicular line will be something like:

y = (4/3)*x + c

We know that this line passes through the point (a, 3)

this means that, when x = a, y must be equal to 3.

Replacing these in the above line equation, we get:

3 = (4/3)*a + c

c = 3 - (4/3)*a

Then the equation for our line is:

y = (4/3)*x + 3 - (4/3)*a

We can rewrite this as:

y = (4/3)*(x -a) + 3

now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.

We can find this by solving:

(4/3)*(x -a) + 3 =  y = -(3/4)*x - (5/4)

(4/3)*(x -a) + 3  = -(3/4)*x - (5/4)

(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)

(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4

(7/12)*x = -(4/13)*a - 17/4

x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7

And the y-value is given by inputin this in any of the two lines, for example with the first one we get:

y =  -(3/4)*(- (48/91)*a - 51/7) - (5/4)

  = (36/91)*a + (153/28) - 5/4

Then the intersection point is:

( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4)

And we want that the distance between this point, and our original point (3, a) to be equal to 4.

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)^2 + (b - d)^2)

So here, the distance between (a, 3) and ( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4) is 4

4 = √( (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a + (153/28) - 5/4 )^2)

If we square both sides, we get:

4^2 = 16 =  (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a - (153/28) + 5/4 )^2)

Now we need to solve this for a.

16 = (a*(1 + 48/91)  + 51/7)^2 + ( -(36/91)*a  + 3 - 5/4 + (153/28) )^2

16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a  - (43/28) )^2

16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 +  a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2

16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) +  (51/7)^2 + (43/28)^2

At this point we can see that this is really messy, so let's start solving these fractions.

16 = (2.49)*a^2 + a*(23.47) + 55.44

0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16

0 = (2.49)*a^2 + a*(23.47) + 39.44

Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:

a = \frac{-23.47  \pm  \sqrt{23.47^2 - 4*2.49*39.4}  }{2*2.49} \\\\a =  \frac{-23.47  \pm  12.57 }{4.98}

Then the two possible values of a are:

a = (-23.47 + 12.57)/4.98  = -2.19

a = (-23.47 - 12.57)/4.98 = -7.23

4 0
3 years ago
Joni has two U.S coins in her pocket. One of the coins is not a dime. If the total value of coins in her pocket is 11 cents, wha
Snezhnost [94]
There is one dime and i penny

because it says one coin is not a dime 
that does dot mean the other coin is not a dime
6 0
3 years ago
The function f(x) varies directly with x and f(x)=160 when x=40.
DaniilM [7]
160÷40 is 4 so i think the function f multiplies x by 4.
when x is 8, 8×4=32 so the answer shld be 32
4 0
3 years ago
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