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erma4kov [3.2K]
3 years ago
5

For a class experiment, Hilda places different colored marbles in a bag. She pulls a marble at random from the bag, records its

color, and then puts the marble back in the bag. She repeats this process 25 times. The overall results are shown in the table. Result Blue Red Yellow Orange Frequency 6 4 8 7 What is the relative frequency that Hilda pulled a red marble? Enter your answer in the box.
Mathematics
1 answer:
vodomira [7]3 years ago
3 0

Answer:

4/25 or 16 percent of the time

Step-by-step explanation:

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The number of bacteria after t hours is given by N(t)=250 e^0.15t a) Find the initial number of bacteria and the rate of growth
Art [367]

Answer:

a) N_0=250\; k=0.15

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies t=0. And N(0)=N_0. The process is:

N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250

b) After 2 days means t=48. So, we just replace and operate:

N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}

c) N(t_1)=4000; \;t_1=?

N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\  \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h

d) t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)

N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h

6 0
3 years ago
a web designer charges a $200 fee plus $50 per hour to build a website. which equation represents the total cost, y, to a custom
dezoksy [38]
Y = 50x + 200 <=== ur equation
6 0
3 years ago
Read 2 more answers
NEED HELP FAST!!! Find the percent of increase from 260 to 430. Round to the nearest tenth of a percent if necessary.
a_sh-v [17]

You started out with 260, and increased to 430.
The amount you increased was (430 - 260) = 170

170 is  (170/260) = <em>65.4%</em> of what you started with.

============================

Another way:

The new amount is  (430/260) of the old amount.

 430 / 260 = 1.654 = 165.4%

The original amount was  260.
You started with  100%  of it.
You ended up with  165.4%  of it.
That's an increase of  65.4% .

5 0
3 years ago
Please need help with this assignment… thx
Citrus2011 [14]

Answer:

1.length = 15, width = 12, height = 13

2. 13 × 12 × 15 = 2340

Step-by-step explanation:

3 ÷ 1/4 = 12

3 3/4 = 15/4

15/4 ÷ 1/4 = 15

3 1/4 ÷ 1/4 = 13

length = 15

width = 12

height = 13

13 × 12 × 15 = 2340

5 0
2 years ago
A machine starts dumping sand at the rate of 35 m3/min, forming a pile in the shape of a cone. The height of the pile is always
juin [17]
We are given with the following given
dV/dt = 35 m3/min
h = (3/2)D

What is asked is
dr/dt at t = 7 min

The volume of a cone is
V = (1/3)πr²h

From the given
h = (3/2)D
since D = 2r
h = 3r

Subsituting
V = πr³

At t = 7 min, the volume is
V = 35(7)
V = 245
and the radius is
245 = πr³
r = 4.27

Differentiating the volume
dV/dt = 3πr² dr/dt
From the given
dV/dt = 35

Subsituting
35 = 3πr² dr/dt
So,
dr/dt = 0.20 m/s
and
dh/dt = 0.60 m/s
6 0
3 years ago
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