In some division problems, a number or pattern of number that continues indefinitely is a?

Answers

Answer 1
Answer: my guess would be a repeating decimal or an infinite decimal.


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A giant fish tank at the zoo contains z Halibut. The tank contains 4times as many Bluefin Tuna as Halibut. Write an equation that
represents the total number of Bluefin Tuna, y in the tank.

Answers

Answer:

Y=4Z

Step-by-step explanation:

The table on the left is that of a linear function, and the one on the right is that of an exponential function. Can you tell which function has the higher rate of growth? How?

Answers

The correct answer is D.

As you can see, the exponential function grows by doubling the previous output with each increment of the input: start with 1, you double it to get 2, then you double it to get 4, 8 and so on.

On the other hand, the linear function adds 7 with each step. This means that the exponential function will eventually reach and pass the linear one, and will definitely be grater from that point on. In fact, if we continue the table, we get

\begin{array}{c|c|c}\text{x value}&\text{linear}&\text{exponential}\n4&28&8\n5&35&16\n6&42&32\n7&49&64\n8&56&128\n9&63&256\end{array}

and you can see how the exponential growth is much faster than the linear one.

The residents of a certain dormitory have collected the following data: People who live in the dorm can be classified as either involved in a relationship or uninvolved. Among involved people, 10 percent experience a breakup of their relationship every month. Among uninvolved people, 15 percent will enter into a relationship every month. What is the steady-state fraction of residents who are uninvolved

Answers

Answer:

The steady state proportion for the U (uninvolved) fraction is 0.4.

Step-by-step explanation:

This can be modeled as a Markov chain, with two states:

U: uninvolved

M: matched

The transitions probability matrix is:

\begin{pmatrix} &U&M\nU&0.85&0.15\nM&0.10&0.90\end{pmatrix}

The steady state is that satisfies this product of matrixs:

[\pi] \cdot [P]=[\pi]

being π the matrix of steady-state proportions and P the transition matrix.

If we multiply, we have:

(\pi_U,\pi_M)*\begin{pmatrix}0.85&0.15\n0.10&0.90\end{pmatrix}=(\pi_U,\pi_M)

Now we have to solve this equations

0.85\pi_U+0.10\pi_M=\pi_U\n\n0.15\pi_U+0.90\pi_M=\pi_M

We choose one of the equations and solve:

0.85\pi_U+0.10\pi_M=\pi_U\n\n\pi_M=((1-0.85)/0.10)\pi_U=1.5\pi_U\n\n\n\pi_M+\pi_U=1\n\n1.5\pi_U+\pi_U=1\n\n\pi_U=1/2.5=0.4 \n\n \pi_M=1.5\pi_U=1.5*0.4=0.6

Then, the steady state proportion for the U (uninvolved) fraction is 0.4.

A survey in Men’s Health magazine reported that 39% of cardiologists said that they took vitamin E supplements. To see if this is still true, a researcher randomly selected 100 cardiologists and found that 36 said that they took vitamin E supplements. At α = 0.05, test the claim that 39% of the cardiologists took vitamin E supplements. A recent study said that taking too much vitamin e might be harmful how might this study make the results of the previous study invalid?

Answers

Answer:

z=\frac{0.36 -0.39}{\sqrt{(0.39(1-0.39))/(100)}}=-0.615  

The p value for this case would be:

p_v =2*P(z<-0.615)=0.539  

For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not different from 0.39

Step-by-step explanation:

Information given

n=100 represent the random sample taken

X=36 represent the number of people that take E supplement

\hat p=(36)/(100)=0.36 estimated proportion of people who take R supplement

p_o=0.39 is the value that we want to test

\alpha=0.05 represent the significance level

z would represent the statistic

p_v represent the p value

Hypothesis to test

We want to test if the true proportion is equatl to 0.39 or not, the system of hypothesis are.:  

Null hypothesis:p=0.39  

Alternative hypothesis:p \neq 0.39  

The statistic is given by:

z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}} (1)  

Replacing the info we got:

z=\frac{0.36 -0.39}{\sqrt{(0.39(1-0.39))/(100)}}=-0.615  

The p value for this case would be:

p_v =2*P(z<-0.615)=0.539  

For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not different from 0.39

The weights of adobe bricks used for construction are normally distributed with a mean of 3 pounds and a standard deviation of 0.25 pound. Assume that the weights of the bricks are independent and that a random sample of 28 bricks is selected. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that all the bricks in the sample exceed 2.75 pounds? (b) What is the probability that the heaviest brick in the sample exceeds 3.75 pounds?

Answers

Answer:  a) 0.8413, b) 0.9987.

Step-by-step explanation:

Since we have given that

Mean = 3 pounds

Standard deviation = 0.25 pounds

n = 28 bricks

So, (a) What is the probability that all the bricks in the sample exceed 2.75 pounds?

P(X>2.75)\n\n=P(z>(2.75-3)/(0.25)\n\n=P(z>(-0.25)/(0.25))\n\n=P(z>-1)\n\n=0.8413

b) What is the probability that the heaviest brick in the sample exceeds 3.75 pounds?

P(X>3.75)\n\n=P(z>(3.75-3)/(0.25))\n\n=P(z>(0.75)/(0.25))\n\n=P(z>3)\n\n=0.9987

Hence, a) 0.8413, b) 0.9987.

How does the quotient compare to the dividend when the divisor is less than 1

Answers

Final answer:

When a dividend is divided by a divisor that is less than 1, the resulting quotient is greater than the original dividend. This is equivalent to multiplying the dividend by the reciprocal of the divisor.

Explanation:

In mathematics, when we divide any number (the dividend) by a number that is less than 1 (the divisor), the quotient will be greater than the dividend. This is because dividing by a number less than 1 is equivalent to multiplying by its reciprocate which is more than 1. For example, let's consider 10 divided by 0.5 (which is less than 1); the quotient is 20, which is greater than the dividend (10). Therefore, in relation to your question, the quotient is larger than the dividend when the divisor is less than 1.

Learn more about Division here:

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Answer:

Greater provided the divisor is positive.

It would be more accurate and clearer to say that when dividing a number which is greater than zero by a number between 0 and 1, then the quotient is greater than the dividend.

If the divisor is negative and the dividend is positive, then the quotient is negative (and so less than the dividend).