A dolphin ate 2604 pounds of fish during the 31 days in march. What is the average amount of fish the dolphin ate per day.

Answers

Answer 1

Answer:

To find the average of something you add up all of the data points (in this case it would be how many pounds offish were eaten per day but this is already done for us) then you would divide by the number of points you have (the number of days which is 31). So all you have to do is 2604/31. This equals 84 pounds of fish per day on average.

Answer 2

Answer:

the dolphin ate

2604 lbs of fish in 31 days

this can also be written as

2604/31

we want the denominator to be 1, since the denominator represents days

to do this, we can divide 31 by 31. but we must do the same to the numerator

2604 ÷ 31 = 84

so our new fraction is

84/1

so per day, the dolphin ate 84 pounds of fish

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What is the slope of a line segment with endpoints at (-1, 1) and (1, 5)

Answers

The slope(m) of the line segment whose endpoints are (-1, 1) and (1, 5) is: 2.

Recall:

Slope (m) = rate of change of y / rate of change of x
Slope (m) = $\mathbf{(y_2 - y_1)/(x_2 - x_1)}$

Given the endpoints of a line as:

(-1, 1) and (1, 5)

Let,

$(-1, 1) = (x_1, y_1)\n\n(1, 5) = (x_2, y_2)$

Plug in the values

Slope (m) = $(5-1)/(1-(-1))$

Slope (m) = $(4)/(2)$

Slope (m) = 2

In summary, the slope(m) of the line segment whose endpoints are (-1, 1) and (1, 5) is: 2.

Learn more here:

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Answer:

Slope = 2

Step-by-step explanation:

(x,y) ->(-1,1)
(x,y) -> (1,5)

5 - 1 = 4

1 - (-1) = 2

4/2 = 2

Find the perimeter of this quarter circle with radius, r
= 2mm.
Give your answer as an expression in terms of
π
.

Answers

Answer:

Step-by-step explanation:

First find the circumference of the circle

C = 2 * pi*r

C = 2 * pi *2

C = 4pi

A quarter circle is 1/4 of a circle

1/4 C = 1/4 (4pi)

1/4C = pi

Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally distributed. You randomly catch and weigh 17 such salmon. The mean weight from your sample is 19.2pounds with a standard deviation of 4.4 pounds. You want to construct a 90% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River.(a) What is the point estimate for the mean weight of all spawning Chinook salmon in the Columbia River?
pounds

(b) Construct the 90% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River. Round your answers to 1 decimal place.
< ? <

(c) Are you 90% confident that the mean weight of all spawning Chinook salmon in the Columbia River is greater than 18 pounds and why?

No, because 18 is above the lower limit of the confidence interval.

Yes, because 18 is below the lower limit of the confidence interval.

No, because 18 is below the lower limit of the confidence interval.

Yes, because 18 is above the lower limit of the confidence interval.

(d) Recognizing the sample size is less than 30, why could we use the above method to find the confidence interval?

Because the sample size is greater than 10.

Because we do not know the distribution of the parent population.

Because the parent population is assumed to be normally distributed.

Because the sample size is less than 100.

Answers

Answer:

a) $\bar X= 19.2$ represent the sample mean. And that represent the best estimator for the population mean since $\hat \mu =\bar X=19.2$ b) The 90% confidence interval is given by (17.3;21.1)

c) No, because 18 is above the lower limit of the confidence interval.

d) Because the parent population is assumed to be normally distributed.

The reason of this is because the t distribution is an special case of the normal distribution when the degrees of freedom increase.

Step-by-step explanation:

1) Notation and definitions

n=17 represent the sample size

Part a

$\bar X= 19.2$ represent the sample mean. And that represent the best estimator for the population mean since $\hat \mu =\bar X=19.2$ Part b

$s=4.4$ represent the sample standard deviation

m represent the margin of error

Confidence =90% or 0.90

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

2) Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . The degrees of freedom are given by:

$df=n-1=17-1=16$

We can find the critical values in excel using the following formulas:

"=T.INV(0.05,16)" for $t_(\alpha/2)=-1.75$

"=T.INV(1-0.05,16)" for $t_(1-\alpha/2)=1.75$

The critical value $tc=\pm 1.75$

3) Calculate the margin of error (m)

The margin of error for the sample mean is given by this formula:

$m=t_c (s)/(√(n))$

$m=1.75 (4.4)/(√(17))=1.868$

4) Calculate the confidence interval

The interval for the mean is given by this formula:

$\bar X \pm t_(c) (s)/(√(n))$

And calculating the limits we got:

$19.2 - 1.75 (4.4)/(√(17))=17.332$

$19.2 + 1.75 (4.4)/(√(17))=21.068$

The 90% confidence interval is given by (17.332;21.068) and rounded would be: (17.3;21.1)

Part c

No, because 18 is above the lower limit of the confidence interval.

Part d

Because the parent population is assumed to be normally distributed.

The reason of this is because the t distribution is an special case of the normal distribution when the degrees of freedom increase.

The lifetime of a certain type of battery is normally distributed with a mean value of 10 hours and standard deviation of 2 hours. Find the probability that a randomly selected battery has a lifetime greater than 12 hou g

Answers

Answer:

$P(X>12)=P((X-\mu)/(\sigma)>(12-\mu)/(\sigma))=P(Z>(12-10)/(2))=P(z>1)$

And we can find this probability using the complement rule:

$P(z>1)=1-P(z<1)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>1)=1-P(z<1)=1-0.841=0.159$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the lifetime of a certain type of battery of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,2)$

Where $\mu=10$ and $\sigma=2$

We are interested on this probability

$P(X>12)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=(x-\mu)/(\sigma)$

If we apply this formula to our probability we got this:

$P(X>12)=P((X-\mu)/(\sigma)>(12-\mu)/(\sigma))=P(Z>(12-10)/(2))=P(z>1)$

And we can find this probability using the complement rule:

$P(z>1)=1-P(z<1)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>1)=1-P(z<1)=1-0.841=0.159$

#7: Twenty-three more than 10 times a number is the same as 5 more than 1 pointthe number. *
Your answer
26 more than twice the

Answers

Answer:

23+10r= 5+r

Step-by-step explanation:

let r be the number

Set up and evaluate the optimization problems. (Enter your answers as comma-separated lists.) Find two positive integers such that their sum is 14, and the sum of their squares is minimized. Find two positive integers such that their sum is 14, and the sum of their squares is maximized.

Answers

Answer and Step-by-step explanation:

Let x and y be two positive integers and their sum is 14:

X + y = 14

And the sum of square of this number is:

f = x2 + y2

= x2+ (14 – x)2

Differentiate with respect to x, we get:

F’(x) = [ x2 + (14 – x)2]’ = 0

2x + 2(14-x)(-1) = 0

2x +( 28 – 2x)(-1) = 0

2x – 28 +2x = 0

2x + 2x = 28

4x = 28

X = 7

Hence, y = 14 – x = 14 -7 = 7

Now taking second derivative test:

F”(x) > 0

For x = y = 7,f reaches its maximum value:

(7)2 + (7)2 = 49 + 49

= 98

F at endpoints x Є [ 0, 14]

F(0) = 02 + (14 – 0)2

= 196

F(14) = (14)2 + (14 – 14)2

= 196

Hence the sum of squares of these numbers is minimum when x = y = 7

And maximum when numbers are 0 and 14.

Final answer:

To find two positive integers such that their sum is 14, and the sum of their squares is minimized, we need to consider all possible pairs of positive integers and calculate their sums of squares. The pair (6, 8) has the minimum sum of squares of 100. To find two positive integers such that their sum is 14, and the sum of their squares is maximized, the pairs (1, 13) and (2, 12) both have the maximum sum of squares of 170. Since we need to find two positive integers, the pair (1, 13) is the answer.

Explanation:

To find two positive integers such that their sum is 14 and the sum of their squares is minimized, we need to consider all possible pairs of positive integers that add up to 14 and calculate their sums of squares. Let's list all the pairs:

1 and 13: 1^2 + 13^2 = 170
2 and 12: 2^2 + 12^2 = 148
3 and 11: 3^2 + 11^2 = 130
4 and 10: 4^2 + 10^2 = 116
5 and 9: 5^2 + 9^2 = 106
6 and 8: 6^2 + 8^2 = 100
7 and 7: 7^2 + 7^2 = 98

From the list, we can see that the pair (6, 8) has the minimum sum of squares, which is 100.

Similarly, to find two positive integers such that their sum is 14 and the sum of their squares is maximized, we need to again consider all possible pairs and calculate their sums of squares. Let's list the pairs:

1 and 13: 1^2 + 13^2 = 170
2 and 12: 2^2 + 12^2 = 148
3 and 11: 3^2 + 11^2 = 130
4 and 10: 4^2 + 10^2 = 116
5 and 9: 5^2 + 9^2 = 106
6 and 8: 6^2 + 8^2 = 100
7 and 7: 7^2 + 7^2 = 98

From the list, we can see that the pair (1, 13) and the pair (2, 12) both have the maximum sum of squares, which is 170. Since we need to find two positive integers, the pair (1, 13) is the answer.

Learn more about Optimization Problems here:

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