Lipids provide much of the dietary energy in the bodies of infants and young children. There is a growing interest in the quality of the dietary lipid supply during infancy as a major determinant of growth, visual and neural development, and long-term health. An article reported the following data on total polyunsaturated fats (%) for infants who were randomized to four different feeding regimens: breast milk, corn-oil-based formula, soy-oil-based formula, or soy-and-marine-oil-based formula. (Use i= 1, 2, 3, and 4 respectively.)
Sample Regimen Sample Size Sample Mean Sample SD
Breast milk 15 42.9 1.3
CO 17 43.1 1.5
SO 8 43.7 1.2
SMO 14 43.9 1.2
What assumptions must be made about the four total polyunsaturated fat distributions before carrying out a single-factor ANOVA to decide whether there are any differences in true average fat content?
a. The distribution of polyunsaturated fat percentages for each of the four regimens must be uniform with equal variances.
b. The distribution of polyunsaturated fat percentages for each of the four regimens must be normal with unequal variances.
c. The distribution of polyunsaturated fat percentages for each of the four regimens must be normal with equal variances.
d. The distribution of polyunsaturated fat percentages for each of the four regimens must be binomial with unequal variances.

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Answer:

  R(p) = -3500p^2 +48000p . . . revenue function

  $6.86 . . . price for maximum revenue

Step-by-step explanation:

The 2-point form of the equation for a line can be used to find the attendance function.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (27000 -20000)/(6 -8)(x -8) +20000

  y = -3500(x -8) +20000

  y = 48000 -3500x . . . . y seats sold at price x

The per-game revenue is the product of price and quantity sold. In functional form, this is ...

  R(p) = p(48000-3500p)

  R(p) = -3500p^2 +48000p . . . per game revenue

__

Revenue is maximized when its derivative is zero.

  R'(p) = -7000p +48000

  p = 48/7 ≈ 6.86

A ticket price of $6.86 would maximize revenue.

Answer:

1.25p

Step-by-step explanation:

p = amount raised last year

amount raised this year = p +(25% of p)

=1 p+0.25p

=p(1+0.25)

=1.25p

Answer:

(2, - 1 )

Step-by-step explanation:

Given the 2 equations

2x - 5y = 9 → (1)

3x + 4y = 2 → (2)

Multiplying (1) by 4 and (2) by 5 and adding the result will eliminate the y- term

8x - 20y = 36 → (3)

15x + 20y = 10 → (4)

Add (3) and (4) term by term to eliminate y

23x + 0 = 46

23x = 46 ( divide both sides by 23 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (2)

3(2) + 4y = 2

6 + 4y = 2 ( subtract 6 from both sides )

4y = - 4 ( divide both sides by 4 )

y = - 1

solution is (2, - 1 )

Answer: 5x-15

Outer numbers multiply with both inside the parentheses.

Answer:

-12 is the common differences

Answer:

expanded form: 5 * 5 * 5

value: 125

Step-by-step explanation:

Answer:

seniors: 780

juniors: 1170

sophomores: 975

freshmen: 585

Step-by-step explanation:

4 + 6 + 5 + 3 = 18

3510/18 = 195

195(4) = 780

195(6) = 1170

195(5) = 975

195(3) = 585

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Answer:

[tex]C = (2,-1)[/tex]

Step-by-step explanation:

Given

[tex]A = (-5,-1)[/tex]

[tex]B = (-5,3)[/tex]

[tex]D = (2,3)[/tex]

Required

The coordinate of the fourth point (C)

The given coordinates indicate the rectangle is vertical/horizontal because it has similar x and y values.

The coordinate of such rectangle can be represented as:

[tex]A = (x_1,y_1)[/tex]

[tex]B = (x_1,y_2)[/tex]

[tex]C = (x_2,y_1)[/tex]

[tex]D = (x_2,y_2)[/tex]

By comparing the general coordinates with the given coordinates, we have:

[tex]x_1 = -5[/tex] --- see A and B

[tex]y_1 = -1[/tex] --- see A and C

[tex]x_2 = 2[/tex] ---- see C and D

[tex]y_2 = 3[/tex] --- see B and D

So, we have:

[tex]C = (x_2,y_1)[/tex]

[tex]C = (2,-1)[/tex]

Answer:

25km/h

Step-by-step explanation:

It would be helpful to understand the 24 hour clock in this case so you don't get confused by the AM and PM. For reference, 5 AM is technically 17AM, since 5 + 12 = 17.

The ship departed at 9pm, subtract that from 17 and you'll get 8 hours.

17 - 9 = 8

We know that there are 8 hours total, and since the ship traveled 200km, we set up a fraction, which is 8hr/200km. Since we want the average speed, we'll go by km/hr. To do this, we need to set the hrs to 1.

8/x = 1

x = 8

200/8 = 25

Your answer is 25km/hr

Answer:

13 + 3x = 34

Variables:

x = random number

Answer:

AB = 5

Step-by-step explanation:

The side opposite the 30 degree angle will have the shortest length. The side opposite the 60 degree angle will be  √3  times as long, and the side opposite the 90 degree angle will be twice as long.

In this case we just divide 10 by 2

Answer:

5 cm

Step-by-step explanation:

Sin 30° = opposite / hypothenus

= AB / 10cm

AB = sin 30° × 10 cm

= 5 cm

Answer:

66 students prefer the zoo

Step-by-step explanation:

I got it correct :)

Answer:

150658743

Step-by-step explanation:

(301 317 167+319)÷2=150658743

Answer:

the awnser is D) $41.25.

Answer: the answer is r=7.5%

Step-by-step explanation:

You get the formula A=P(1+nr) where A is the accumulated amount: 5750, P is the principal: 5000, n is the amount of years: 2, and r is the rate: unknown

Now you plug in what you know:

5750=5000(1+2r)

Divide 5000 on both sides

Decimal form: 1.15=1+2r

Subtract -1 on both sides

0.15=2r

And lastly divide by 2 on both sides

0.075=r

BUT WHEN FINDING THE RATE ALWAYS MAKE IT A PERCENTAGE

r=0.075*100=7.5%

Answer:

Let x be the variable for a t-shirt for $8.

Let y be the variable for shorts for $12.

Let z be the variable for the hats that cost $10 each.

We have the expression 1 below:

$464 = $8x + $12y + $10z

other expressions:

3z = x

2z =y

By substitution we can solve each variable:

464 = 8(3z) + 12(2z) + 10z

464 = 24z +24z +10z

464 = 58z

z = 8

Solve for x andy:

3z=x

3*8 = 24=x

2z=y

2*8 = 16 = y

The t-shirts are 24 pieces, the shorts are 16 pieces and hats are 8 pieces.

Step-by-step explanation:

Answer:

The answer is C because the largest mode is the longest set with the biggest numbers

Step-by-step explanation:

Answer:

9.045 grams

Step-by-step explanation:

You add the 42.68+19.125=61.805

Then take 61.805- 52.76=9.045

The number of grams of mixture that the baker still has is 9.045 grams.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Given that,

A baker mixes 42.68 grams of flour and 19.125 grams of sugar in a bowl.

Total grams of flour and sugar = 42.68 + 19.125 = 61.805 grams

So,

Total weight of the mixture = 61.805 grams

The baker then uses 52.76 grams of the mixture in a cake.

Remaining grams of the mixture = 61.805 grams - 52.76 grams

                                                      = 9.045 grams

Hence the remaining mixture is 9.045 grams.

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Answer:

[tex]\bar x =29.7[/tex]

[tex]\sigma = 6.81[/tex]

[tex]Median = 30.5[/tex]

Step-by-step explanation:

Given

[tex]Data:20,38,24,39,27,40,28,37,29,35,30,31,32,19,33,18,34,21,36,23[/tex]

[tex]n = 20[/tex]

Solving (a): The sample mean

This is calculated as:

[tex]\bar x =\frac{\sum x}{n}[/tex]

[tex]\bar x =\frac{20+38+24+39+27+40+28+37+29+35+30+31+32+19+33+18+34+21+36+23}{20}[/tex]

[tex]\bar x =\frac{594}{20}[/tex]

[tex]\bar x =29.7[/tex]

Solving (b): The standard deviation

This is calculated as;

[tex]\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n}}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{928.2}{20}}[/tex]

[tex]\sigma = \sqrt{46.41}[/tex]

[tex]\sigma = 6.81[/tex]

Solving (c): The median

First, sort the data in ascending order

[tex]Sorted:18,19,20,21,23,24,27,28,29,30,31,32,33,34,35,36,37,38,39,40[/tex]

The position of the median is calculated as:

[tex]Median = \frac{n+1}{2}[/tex]

[tex]Median = \frac{20+1}{2}[/tex]

[tex]Median = \frac{21}{2}[/tex]

[tex]Median = 10.5th[/tex]

The 10.5th item represents the mean of the 10th and 11th item.

So, median is:

[tex]Median = \frac{30+31}{2}[/tex]

[tex]Median = \frac{61}{2}[/tex]

[tex]Median = 30.5[/tex]

Answer:

A) Decreasing

Step-by-step explanation:

By graphing the logarithmic equation, we can see that as the x value increases, the y value decreases. Therefore, we say that the graph is decreasing.

Answer:

decreasing

Step-by-step explanation:

Step-by-step explanation:

Volume of Cylinder =

[tex]\pi {r}^{2} h[/tex]

given r = 10 in

h = 30 in

Volume of Cylinder =

[tex]\pi( {10}^{2} )(30) \\ = \pi(100)(30) \\ = 3000\pi \: {in}^{3} \\ = 9424.8 {in}^{3} [/tex]

Please take note in this case choose the answer closest to the answer calculated.

Answer:

9,420 in^3

Step-by-step explanation:

V = π r^2 h

V = 3.14 · 10^2 · 30

V = 3.14 · 100 · 30

V = 3.14 · 3,000

V ≈ 9,420

Answer:

10 1/18

Step-by-step explanation:

3 2/6 + 8 2/9 - 1 1/2 = ?

First, we need to find the common denominator, which I will choose to be 18, which means I will need to convert all the fractions.

3 6/18 + 8 4/18 - 1 9/18 = ?

Now, we solve.

3 6/18 + 8 4/18 - 1 9/18 = 10 1/18

Answer:

H0 : u ≥ 10  against the claim Ha: u < 10

Step-by-step explanation:

The mean breaking strength of a ceramic insulator must be at least 10 psi.

(At least means greater or equal to ). As it is already given in the data the null and alternate hypotheses will be formulated according to it.

H0 : u ≥ 10  against the claim Ha: u < 10

The null hypothesis is the mean breaking strength of a ceramic insulator must be at least 10 psi

and the alternate hypothesis is

the mean breaking strength of a ceramic insulator is less than 10 psi

Answer: C. 85

Step-by-step explanation: subtract 125 from 40

Answer:

The answer is 16% I just took the test

Step-by-step explanation:

Answer:

360 mi^3

Step-by-step explanation:

The figure is composed by two parallelepipeds. For find the volume we have to find the volume of both the solids and the added up the two values

solid  1

length = 11 - 4 = 7 mi

base area = length x width = 7 x 4 = 28 mi^2

V = base area x height = 28 x 6 = 168 mi^3

solid 2

base area = 8 x 4 = 32 mi^2

V = 32 x 6 = 192 mi^3

total volume: 168 + 192 = 360 mi^3

The volume of the figure is 360 mi³.

Volume of a three dimensional shape is the space occupied by the shape.

Given is a figure where two rectangular boxes are put on top of each other.

Volume of a rectangular prism = L × W × H

Here L is the length, W is the width and H is the height.

The dimensions of the rectangular prism are :

Larger one having L = 11 mi, W = 6 mi and H = 4 mi

Smaller one on top having L = 4 mi, W = 6 mi and H = 8 - 4 = 4 mi.

Volume of the figure = volume of larger box + Volume of smaller box

                                  = (11 × 6 × 4) + (4 × 6 × 4)

                                  = 264 + 96

                                  = 360 mi³

Hence the volume of the figure is 360 mi³.

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