A bag contains 6 red marbles, 4 black marbles, and 5 blue

A bacteria culture contains 1500 bacteria initially and doubles every hour. (a) Find a function N that models the number of bact

Tpy6a [65]

Answer: a) $N(t)=1500(2)^t$

b) 25165824000

Step-by-step explanation:

The exponential equation for growth is given by :-

$y= ab^t$ , where a= initial value , b =multiplicative growth factor and t = time.

Given : A bacteria culture contains 1500 bacteria initially and doubles every hour.

i.e. a = 1500 and b= 2

Then, the function N that models the number of bacteria after t hours will be :

$N(t)=1500(2)^t$

To find , the number of bacteria after 24 hours , we put t= 24 in above equation , we get

$N(24)=1500(2)^{24}\\\\=1500(16777216)=25165824000$

Hence, the number of bacteria after 24 hours is 25165824000.

7 0

3 years ago

What is the sum or difference?

dlinn [17]

1. Ans: Option (B) $-6x^4$

Explanation:
Given: $2x^4 - 8x^4$
Take the common out:
=> $x^4(2 - 8)$

Hence: => $[tex]-6x^4$ [/tex] (Option B)

2. Ans: Option (D) $-3y^5$

Explanation:
Given: $6y^5 - 9y^5$
Take the common term(s) out:
=> $y^5(6-9)$

Hence: => $-3y^5$ (Option D)

3. Ans: Option (B) $9x^2 - 12x + 6$ quadratic trinomial

Explanation:
Given: $6 - 12x + 13x^2 - 4x^2$

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> $13x^2 - 4x^2 - 12x + 6$
=> $9x^2 - 12x + 6$ (Option B)

4. Ans: Option (C) $7.3x^2 + 0.8x + 1.3$

Explanation:
In order to find the total number of Common and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

Common guppies: $3.1x^2 +6.0x + 0.3$ 
Endler's guppies: $4.2x^2 - 5.2x + 1.0$
(add both)
-----------------------------------------------------------------
Total number: $7.3x^2 +0.8x + 1.3$
-----------------------------------------------------------------
Hence the ans is Option(C) $7.3x^2 + 0.8x + 1.3$

5. Ans: Option (D) $2x^2(133 - 18 \pi )$

Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = $266x^2$

Now the area of the circular fountain:
Area of the Circular Fountain = $\pi r^2$
Since, r=6x
Therefore,
Area of the Circular Fountain = $\pi (6x)^2 = 36 \pi x^2$

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = $266x^2$ - $36 \pi x^2$
=> Final area of the Yard = $2x^2(133 - 18 \pi)$ (Option D)

6. Ans: Option (A) $56x^2$

Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x = $60x^2$

Now the area of the stadium:
Area of the stadium = 1x * 4x = $4x^2$

Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= $60x^2$ - $4x^2$
=> Final area of the lot = $56x^2$ (Option A)

-i

4 0

3 years ago

Read 2 more answers

Simplify ‐19 ‐ 7( ‐17z + 13) 4n ‐ 3( ‐9n + 13)

nataly862011 [7]

Answer:

for the first one it's 119z−110

the second one is 31n−39

i'm not sure if you wanted both together

so here just incase

31n+119z−149

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

X 2 +(y−7.5) 2 = 49 9 What is the radius?

Flura [38]

50 is the answer hugnfgh

8 0

4 years ago

Read 2 more answers

Box of 15 gadgets is known to contain 5 defective gadgets if 4 gadgets are drawn at random what is the probability of finding no

baherus [9]

To solve this problem, we make use of the Binomial Probability equation which is mathematically expressed as:

P = [n! / r! (n – r)!] p^r * q^(n – r)

where,

n = the total number of gadgets = 4

r = number of samples = 1 and 2 (since not more than 2)

p = probability of success of getting a defective gadget

q = probability of failure = 1 – p

Calculating for p:

p = 5 / 15 = 0.33

So,

q = 1 – 0.33 = 0.67

Calculating for P when r = 1:

P (r = 1) = [4! / 1! 3!] 0.33^1 * 0.67^3

P (r = 1) = 0.3970

Calculating for P when r = 2:

P (r = 2) = [4! / 2! 2!] 0.33^2 * 0.67^2

P (r = 2) = 0.2933

Therefore the total probability of not getting more than 2 defective gadgets is:

P = 0.3970 + 0.2933

P = 0.6903

Hence there is a 0.6903 chance or 69.03% probability of not getting more than 2 defective gadgets.

5 0

4 years ago