What is the median of the following numbers?
1, 2, 10, 6, 4, 4, 6, 3, 1,4

Question:

Data were collected over a 10-year timespan from a sample of 100 penguins that were randomly given either metal or electronic tags. One variable examined is the length of foraging trips. Longer foraging trips can jeopardize both breeding success and survival of chicks waiting for food. Mean length of 344 foraging trips was 12.70 days for metal-tagged penguins. Mean length of 512 foraging trips was 11.60 days for electronic-tagged penguins. An estimate of the standard error for this difference of means is SE=0.283.

a) We will address the question of whether foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins. State hypotheses in terms of two means.

b. Calculate the sample statistic xM - xE

c. Calculate a t-test statistic, using the given estimate of SE.

d. What are the correct (conservative) degrees of freedom for a t-distribution for this test?

e. Use t-distribution methods to find the p-value and draw a rough curve with appropriate shaded region. You may give either a precise p-value from software or bounds on a p-value from Table A.

f. State the conclusion of the test in context, using nontechnical language.

Answer:

See explanation below

Step-by-step explanation:

a)  The null and alternative hypotheses are:

H0 : uM - uE = 0

H1 : uM - uE > 0

b) Calculating the sample statistic,

xM-xE, we have:

Given xM = 12.70 days

xE = 11.60 days

xM - xE = 12.70 - 11.60 = 1.10 days

Therefore sample statistic = 1.10

c) Calculating the test statistic, using the given estimate of SE, we have:

Given standard error, SE = 0.283

[tex] \frac{xM - xE}{SE} = \frac{12.70 - 11.60}{0.283} = 3.89 [/tex]

Therefore, t test = 3.89

d) The correct degrees of freedom.

We have:

[tex]Min(n_M-1, n_E-1 ) = Min(344-1, 512-1) = Min(343, 511)[/tex]

df = 343

e) p-value:

Pvalue = P(Z > 3.89) = 0.00000602

Since p value is less than significance level of 0.05, we reject null hypothesis H0.

f) Conclusion:

There is enough evidence to conclude that foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins.

Answer: 8+2x

Step-by-step explanation:

Hi, Perimeter is the distance around a two-dimensional shape.

To calculate it, we have to add all the side lengths of the figure. The missing side  is the ? side (right side). To obtain it we have to subtract the top right side length (2) to the left side length (12)

So, the expression is equal to:

P = 12+ (x-4) + (x-12) +2 +(12-2)

P = 12+ x - 4 +x -12+2 +10

P = 12-4-12+2+10+x+x

P =8+2x

Answer:

  $3,951

Step-by-step explanation:

The growth factor for t years is given as 2^(t/6). Then in 13 years, the account will be multiplied by ...

  2^(13/6) ≈ 4.489848

Its value will be ...

  $880·4.489848 ≈ $3,951

Answer:

16

Step-by-step explanation:

is the the associated

Answer:

1469.52 cm3

Step-by-step explanation:

Area of a circle times the height of the cylinder.

Area of a circle = 3.14*6^2 = 113.04

113.04*13 = 1469.52 cm3

Answer:

3/2

Hope this helps!

Answer:

The area of the quadrilateral ABCD is 114 square units

Step-by-step explanation:

We must calculate the area of each triangle and then add these areas so we calculate the area of the quadrilateral ABCD

First for the BAD right triangle:

AD = sqrt [BD ^ 2 - AB ^ 2]

AD = sqrt [15 ^ 2 - 12 ^ 2]

AD = sqrt [225-144]

AD = sqrt [81]

AD = 9

The area of a triangle is half the product of the base times the height, that is:

A1 = AB * AD / 2 = 12 * 9/2 = 54

Then for the second triangle in the right triangle BDC:

DC = sqrt [BC ^ 2 - BD ^ 2]

DC = sqrt [17 ^ 2 - 15 ^ 2]

DC = sqrt [289 - 225]

DC = sqrt [64] = 8

We calculate the area

A2 = DC * BD / 2 = 8 * 15/2 = 60

The total area then is:

AT = A1 + A2

AT = 54 + 60 = 114

Which means that the area of the quadrilateral ABCD is 114 square units

Answer:

Depende del tipo de prisma del que estés hablando.

Step-by-step explanation:

Un  el prisma rectangular tiene 6 bases y un prisma triangular tiene 5 bases. Un prisma triangular sólo tiene dos bases.

Answer:

x = -3

y = -3

Step-by-step explanation:

To solve this system of equations, you can use the elimination method, which is to have one of the variables match, but be the opposite sign of the other:

- x + y = 0

4x - 3y = -3

The easier one to match is the 1st equation, and to make it match oppositely, you multiply the whole equation by 4:

4(-x + y = 0)

-4x + 4y = 0

4x - 3y = -3

-4x and 4x cancel each other out:

4y = 0

-3y = -3

_______

y = -3

Then plug in -3 for y, into one of the equations:

- x + y = 0

- x - 3 = 0

Add 3 to both sides:

- x = 3

Divide both sides by -1:

x = -3

Answer:

[tex]\dfrac{40}{42}[/tex]

Step-by-step explanation:

Let the numerator of the fraction=x

Since the denominator of a fraction is two more than the numerator.

Denominator=x+2

The fraction is therefore:

[tex]\dfrac{x}{x+2}[/tex]

If both numerator and denominator are decreased by six, the fraction becomes:

[tex]\dfrac{x-6}{x+2-6}[/tex]

The simplified result is [tex]\dfrac{17}{18}[/tex]

Therefore:

[tex]\dfrac{x-6}{x+2-6}=\dfrac{17}{18}\\$Next, we solve for x\\Cross multiply\\18(x-6)=17(x+2-6)\\18(x-6)=17(x-4)\\Expand the bracket\\18x-108=17x-68\\Collect like terms\\18x-17x=-68+108\\x=40[/tex]

Substituting x=40 into the initial fraction

[tex]\dfrac{x}{x+2}=\dfrac{40}{40+2}=\dfrac{40}{42}[/tex]

Therefore, the original fraction is [tex]\dfrac{40}{42}[/tex]

Answer: [tex]129.42m[/tex]

Step-by-step explanation:

We can use a trigonometric function to find x.

In this case, sine works.

[tex]sin=\frac{opposite}{hypothenuse}[/tex]

Solve for hypothenuse.

[tex]hypothenuse=\frac{opposite}{sin}[/tex]

[tex]h=\frac{120}{sin68}[/tex]

[tex]h=129.42m[/tex]

Answer:

Yes

Step-by-step explanation:

6z > 15

z > 15/6

z > 2.5

So all numbers greater than 2.5 is in the solution set of the inequality 6z > 15.

Answer:

The brown house has the longer driveway

Step-by-step explanation:

So we would need to convert both of these units of measurements to feet in order to compare them.

Converting yards to feet, wee need to multiply the number of yards by 3

Since the red house has a driveway of 7 yards and 9 feet, we can rewrite this to 21 feet + 9 feet, which is equivalent to 30 feet

Now comparing the two driveways, the 35 ft-long brown driveway is 5 feet longer than the 30 ft-long red driveway.

The brown house has the longer driveway

Answer:

Step-by-step explanation:

Answer:

>

Step-by-step explanation:

-3+7= 4

-10-2= -12

4> -12

Answer:

It's popular and hard

Step-by-step explanation:

Answer:

the moon blocks light from the sun by coming between the earth and the sun

Answer:

They lost a total of -12 yards.

Step-by-step explanation:

Do the calculation.

5- 13= -8

-8 + 2 + 6= 0

0 - 12 = -12

Answer:  4

Step-by-step explanation:

Answer:   the domain of f/g is every real number except 1 which can be conventionally expressed as {(x,y): x ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.

Step-by-step explanation:

since f(x) = x + 4 and g(x) = x -  1

then f/g = x + 4/x - 1

the denominator of a function cannot be zero since a fraction with a denominator of zero is undefined.

∴  x - 1 ≠ 0

the value of x when g(x) = 0 is

       x - 1 = 0

       x = 1

∴ x ≠ 1

Therefore the domain of f/g is every real number except 1 which can be conventionally expressed as {(x,y): x ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.

Answer:

x=13, y=2

Step-by-step explanation:

for this equation you can use a variety of solutions, but you have to choose one (obviously). if you substitute 2 for y, the equation will be 2x-16=10. to make this true, 2x must be equal to 26, so x will be 13 :)

Answer:

b =-2

Step-by-step explanation:

-3b+7=13

Subtract 7 from each side

-3b+7-7=13-7

-3b = 6

Divide each side by -3

-3b/-3 = 6/-3

b = -2

Answer:

b=-2

Step-by-step explanation:

-3b+7=13

     -7  -7

-3b=6

/-3   /-3

b=-2

Answer:

x=(-4+√-200)/-2

x=(-4-√-200)/-2

Step-by-step explanation:

Answer:

No real solutions is correct

Step-by-step explanation:

−x^2+4x=54

Move 54 over

−x^2+4x-54=0

Pull out -2

-2(x^2-4x+54)

Solve for the factors

It must multiply to 54 and add to -4

There are no whole number answers.

Hope this helps! Please mark brainliest :)

Answer:

I am not I understand the game but

1. 17 doesn't belong cause it a prime number and doesn't dived with any of the other numbers and double digit

2. 4 divides with 216 and 8 and single digit similar to 8

Step-by-step explanation:

Answer:

Five

Step-by-step explanation:

A quart is 4 cups

4x5 is 20

Answer:

I think the answer is 18 hope it helps

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

To find the slope

m = (y2-y1)/(x2-x1)

    = (-8 - -3)/(9-9)

    = (-8+3)/(9-9)

     = -5/0

When we divide by 0, we get a slope of undefined

Answer:

  1/2

Step-by-step explanation:

This can be done several ways. Perhaps the easiest is to use the decimal equivalents:

  (2 3/4)/(5 1/2) = 2.75/5.5 = 0.5

__

If you want to use the numbers given, the usual procedure is to convert them to improper fractions and do the division that way:

  2 3/4 = (4·2 +3)/4 = 11/4

  5 1/2 = (2·5 +1)/2 = 11/2

Now, the problem can be written as ...

  (2 3/4) / (5 1/2) = (11/4) / (11/2)

This sort of division problem can be solved two ways:

  invert and multiply (the denominator is inverted)

  = (11/4) × (2/11) = (11·2)/(11·4) = 2/4 = 1/2

  use a common denominator (for the two fractions)

  = (11/4) / (11/2) = (11/4) / (22/4) = 11/22 = 1/2

The quotient is 1/2.

_____

Additional comments

It is helpful in many cases to just use decimal equivalents for the calculation. To do that, you need to be familiar with the equivalents of commonly used fractions. I find it is usually sufficient to know the unit fractions in each case. Then you can multiply or add to find the others.

1/9 = 0.1...(1-digit repeat), 1/8 = 0.125, 1/7 = 0.142857...(6-digit repeat), 1/6 = 0.16...(1-digit repeat), 1/5 = 0.2, 1/4 = 0.25, 1/3 = 0.3...(1-digit repeat), 1/2 = 0.5

__

I learned the "invert and multiply" method for dividing fractions when I was in school. The Common Core math apparently also teaches the method of matching the denominators of a compound fraction. Then the result is the ratio of numerators. (A variation not taught is that you can match the numerators and use the inverse of the ratio of denominators. Both of these methods can be validated using the "invert and multiply" method. (11/4)/(11/2) = 2/4)

"Invert and multiply" is another way of saying that division is the same as multiplication by the reciprocal. This applies everywhere, not just in fraction problems.

Answer:constant is 2/33

Step-by-step explanation:

1 min to fill 16.50 gallons

Time(t) varies directly as volume(v)

t α v

t =k x v Where k is constant

1=k x 16.50

k=1/16.50

k=2/33

Constant is 2/33