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liubo4ka [24]
2 years ago
9

1.

Mathematics
1 answer:
Kobotan [32]2 years ago
6 0

Using the Central Limit Theorem, it is found that a larger sample size reduces the variability, that is, the experimental probabilities will be closer to the theoretical probabilities, which explains why the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times.

<h3>What does the Central Limit Theorem states?</h3>

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \mu = p and standard error s = \sqrt{\frac{p(1 - p)}{n}}, as long as np \geq 10 and n(1 - p) \geq 10.

That is, the standard error is inverse proportional to the square root of the sample size, hence a larger sample size reduces the variability, that is, the experimental probabilities will be closer to the theoretical probabilities, which explains why the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times.

More can be learned about the Central Limit Theorem at brainly.com/question/16695444

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A bacteria population experiences continuous growth. If there were 2,000 bacteria present at the start of an experiment, how lon
allochka39001 [22]

Answer:

D. About 15.69 hours.

Step-by-step explanation:

Let x be the number of hours.

We have been given that there  were 2,000 bacteria present at the start of an experiment and the growth rate was 7% per hour.

Since number of bacteria is growing exponentially, so we will use exponential growth function to solve our given problem.

The continuous exponential growth formula is in form: y=e^{kx}, where,

e= mathematical constant,

k = Growth rate in decimal form.

Let us convert our given rate in decimal form.

7\%=\frac{7}{100}=0.07

Upon substituting our given values we will get exponential function for bacteria growth as: y=2,000*e^{0.07x}, where, y represents number of bacteria after x hours.

Since we need to figure out the number of hours it will take for there to be 6,000 bacteria, so we will substitute y= 6,000 in our function.

6,000=2,000*e^{0.07x}

Let us divide both sides of our equation by 2,000.

\frac{6,000}{2,000}=\frac{2,000*e^{0.07x}}{2,000}

3=e^{0.07x}

Let us take natural log of both sides of our equation.

\text{ln}(3)=ln(e^{0.07x})

\text{ln}(3)=0.07x

1.0986122=0.07x  

x=\frac{1.0986122}{0.07}  

x=15.69446\approx 15.69  

Therefore, it will take about 15.69 hours to be 6,000 bacteria and option D is the correct choice.




3 0
3 years ago
The length of ZX is 2 units. What is the perimeter of triangle XYZ?
dezoksy [38]

Keywords

triangle,perimeter,distance, length, side, points

we know that

The <u>perimeter</u> of a<u> triangle</u> is the sum of the three <u>length</u> <u>side</u>

To find the<u> length</u> <u>side</u> calculate the <u>distance</u> between two <u>points</u>

The formula to calculate the <u>distance</u> between to <u>points</u> is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}


Step 1

Find the <u>distance</u> ZY

Z(1,0)\\Y(3,1)  

substitute the values


d=\sqrt{(1-0)^{2}+(3-1)^{2}}


dZY=\sqrt{5}\ units


Step 2

Find the <u>distance</u> XY

X(-1,4)\\Y(3,1)  

substitute the values


d=\sqrt{(1-4)^{2}+(3+1)^{2}}


dXY=\sqrt{25}=5\ units  

Step 3

Find the <u>perimeter</u> of the <u>triangle</u>

P=ZX+ZY+XY

we have

dZX=2\sqrt{5}\ units


dZY=\sqrt{5}\ units


dXY=5\ units  

Substitute

P=(2\sqrt{5}+\sqrt{5}+5)\ units

therefore

the answer is

P=(3\sqrt{5}+5)\ units

4 0
3 years ago
Read 2 more answers
Solve for x<br><br>4x+6-7+9=18​
Alla [95]

here is your ans have a nice day

6 0
3 years ago
Read 2 more answers
I am thinking of an animal whose name starts with the letter e. Guess the<br> animal.
laiz [17]

Answer:

elk

Step-by-step explanation:

4 0
3 years ago
angle A is a compliment of angle b and m angle b = (6-5x) degrees and m angle a =(7-2x)degrees find m angle a
Anuta_ua [19.1K]

Answer:

61

Step-by-step explanation:

A + B = 90

6 - 5x + 7 - 2x = 90

13 - 7x = 90

- 7x = 90 - 13

- 7x = 77

- x = 77 / 7

x = - 11

A: 6 - (5 * - 11) = 6 + 55 = 61

B: 7 - (2 * -11)  = 7 + 22 = 29

Together they equal 90 as they should.

7 0
3 years ago
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