Cindy typed 200 words in 5 minutes. At this rate, how many words can she type in 25 minutes?

Answers

Answer 1

Answer: If Cindy can type 200 words in 5 minutes, divide 200 by 5.
200/5=40, so 40x25=1000.

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A manufacturer claims that only 1% of their computers are defective, but in a sample of 600 3% were found to be defective. If the 1% claim were true there would be less than 1 chance in 1000 of getting this number of defects in the sample. Is there statistically significant evidence against the manufacturer's claim? Why or why not?No, because the difference between a 1% and a 3% defect rate is insignificant.

Yes, because the source of the data was unbiased.

Yes, because the results are unlikely to occur by chance.

No, because the sample size was too small to reach a conclusion.

Answers

Answer:

Step-by-step explanation:

Here population parameter p= 1% = 0.01

But sample proportion = 0.03

Sample size = n=600

Std error of the sample = $\sqrt{(pq)/(n) } =\sqrt{(0.1(0.9))/(600) } \n=0.01225\n$

Let us assume significance level as 5%

For proportion z critical for 95% is 1.96

Margin of error = 1.96(std error) = 0.024

Conf interval for proportion lower bound = 0.01-0.024 =- 0.014

Upper bound = 0.01+0.024 = 0.124

Thus conf interval (-0.014, 0.124)

Our sample proportion is 0.03 which does not lie within this interval.

Hence we conclude that

Yes, because the results are unlikely to occur by chance.

Answer:

Yes, because the results are unlikely to occur by chance.

Step-by-step explanation:

We have to remember that when dealing with statistics the larger the sample we are taking, the more the results will tend to the statistical reality, for example, if we flip a coin, the chances or statistics are 50%-50% but if we only toss it two times, theres a singnificant chance that it could be 100% tails, the more we continue to toss the coin, the closer we will get to the 50-50, here we have a really large sample of 600 computers, where 3% of them were defective, so we can assure that it wasn´t by chance, because an increase of 2% on the percetange of the defective devices from the ideal to the reality is not by chance.

NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(15, 0.05). (Round your probabilities to three decimal places.) (a) Determine both P(X ≤ 3) and P(X < 3). P(X ≤ 3) = P(X < 3) = (b) Determine P(X ≥ 4). P(X ≥ 4) = (c) Determine P(1 ≤ X ≤ 3). P(1 ≤ X ≤ 3) = (d) What are E(X) and σX? (Round your answers to two decimal places.) E(X) = σX = (e) In a sample of 90 children, what is the probability that none has a food allergy?

Answers

Answer:

a) P(X ≤ 3) = 0.9946

P(X < 3) = 0.9639

b) P(X ≥ 4) = 0.0054

c) P(1 ≤ X ≤ 3) = 0.5313

d) E(X) = 0.75

σX = 0.84

e) P(X=0) = 0.0099

Step-by-step explanation:

We have x: number in the sample who have a food allergy. As the sample is of n=15 and p=0.05, we have:

$X \sim Bin(15, 0.05)$

a) We have to determine P(X ≤ 3) and P(X < 3)

We can calculate P(X ≤ 3) as the sum of P(0), P(1), P(2) and P(3).

$P(x\leq 3)=\sum_(k=0)^3P(k)\n\n\nP(x=0) = \binom{15}{0} p^(0)q^(15)=1*1*0.4633=0.4633\n\nP(x=1) = \binom{15}{1} p^(1)q^(14)=15*0.05*0.4877=0.3658\n\nP(x=2) = \binom{15}{2} p^(2)q^(13)=105*0.0025*0.5133=0.1348\n\nP(x=3) = \binom{15}{3} p^(3)q^(12)=455*0.0001*0.5404=0.0307\n\n\nP(x\leq 3)=0.4633+0.3658+0.1348+0.0307=0.9946$

P(x<3) can be calculated from the previos result as:

$P(x<3)=P(X\leq3)-P(3)=0.9946-0.0307=0.9639$

b) We can calculate P(X ≥ 4) as:

$P(X\geq4)=1-P(X<4)=1-P(X\leq3)=1-0.9946=0.0054$

c) We can calculate P(1 ≤ X ≤ 3) as:

$P(1 \leq X \leq 3)=P(1)+P(2)+P(3)=0.3658+0.1348+0.0307=0.5313$

d) The expected value of a binomial variable is the product of the sample size n and the probability of success p:

$E(X)=np=15*0.05=0.75$

The standard deviation is calculates as:

$\sigma_x=√(np(1-p))=√(15*0.05*0.95)=√(0.7125) =0.84$

e) In this case, the sample size is n=90.

We can calculate the probability that none has a food allergy as:

$P(x=0) = \binom{90}{0} p^(0)q^(90)=0.95^(90)=0.0099$

A sphere that has a diameter of 6 what is the volume of the sphere

Answers

Answer:

36 pi or 113.04

Step-by-step explanation:

The volume of a sphere is given by

V= 4/3 pi r^3

we know the diameter so we need to find the radius

r =d/2

r = 6/2 = 3

V = 4/3 pi (3)^3

V =36 pi

We can approximate pi by 3.14

V is approximately 36 *3.14 or 113.04

Answer:

113.1 (113.0973355...)

Step-by-step explanation:

1. Use the sphere volume formula of $(4)/(3)$ π $r^(3)$ .

2. Divide 6 by 2 in order to get a radius of 3.

3. Substitute 3 in for r.

4. Cube the 3, you'll get 27.

5. Multiply 27 by Pi and 4/3.

6. You get 113.1 as a rough estimate, or 113.0973355... for a more exact number. If you leave it in Pi terms, it's 36π.

SHOW WORK! PLEASE HELP ASAP IF YOU CAN :(A stack of index cards is 3/4 of an inch tall. If each card is 3/160 of an inch thick, how many index cards are in the stack?

Answers

Answer:

so what you have to do first is simplify into variables

S=A 3/4 stack of index cards

C= 3/160

first you can do this with a calculator, divide 3/4 of an inch by 3/160 of an inch.

3/4÷3/160=40

Here is my work shown :)

Male the division into multiplication and swap the numbers in 3/160 to 160/3

3/4 x 160/3

For fraction multiplication, multiply the numerators and then multiply the demoninators to get

3 x 160/4 x 3= 480/12

Divide 480 by 12 which is forty

there you go :) sorry if the answers are messed up and there are spelling errors. but in conclusion the answer is 40

By the way, awesome pfp, I just started watching Toilet Bound Hanako earlier tonight and it's very good so far

The number of bacteria at the beginning of an experiment was 30 and the bacteria grow at an hourly rate of 1.4 percent. Using the model given by () = 0e, estimate the number of bacteria, rounded to the nearest whole number after 20 hours.

Answers

Answer:

The estimated number of bacteria after 20 hours is 40.

Step-by-step explanation:

This is a case where a geometrical progression is reported, which is a particular case of exponential growth and is defined by the following formula:

$n(t) = n_(o)\cdot \left(1+(r)/(100) \right)^(t)$ (1)

Where:

$n_(o)$ - Initial number of bacteria, dimensionless.

$r$ - Increase growth of the experiment, expressed in percentage.

$t$ - Time, measured in hours.

$n(t)$ - Current number of bacteria, dimensionless.

If we know that $n_(o) = 30$ , $r = 1.4$ and $t = 20\,h$ , then the number of bacteria after 20 hours is:

$n(t) = 30\cdot \left(1+(1.4)/(100) \right)^(20)$

$n(t) \approx 39.616$

$n(t) = 40$

The estimated number of bacteria after 20 hours is 40.

Define the first law of thermodynamic with one example.

Answers

Answer:

See explanation below.

Step-by-step explanation:

The first law of thermodynamic states that heat is a form of energy, and as such, is subject to the principle of conservation of energy (Energy is not destroyed or created but remains constant)

For example, when you put an ice cube in water, the ice will melt but the water will get colder, this is because the temperature between the ice cube and the water tends to an equilibrium and the total heat in the system remained the same during this time.

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