A randomized study compared two drugs that are designed fo lower a person's serotonin level. It was found that over a 1-year period, those receiving Drug A decreased their serotonin level by a mean of 36 nanograms per millimeter. Those receiving Drug B decreased their serotonin level by a mean of 20 nanograms per millimeter. To determine whether the results are significant, the data are randomized and the difference of the means is shown in the dot plot. What is the best conclusion to make based on the data?

A. The difference of the means is significant because the rerandomizations show that it is outside the range of what likely happens by chance.

B. The difference of the means is not significant because the rerandomizations show that it is outside the range of what likely happens by chance.

C. The difference of the means is not significant because the rerandomizations show that it is within the range of what likely happens by chance.

D. The difference of the means is significant because the rerandomizations show that it is within the range of what likely happens by chance.

Answer:

[tex]35.36,44.64[/tex]

Step-by-step explanation:

Sample size [tex]n=40[/tex]

Mean weight [tex]\=x =67[/tex]

Standard deviation [tex]\sigma=11.4[/tex]

Confidence Interval [tex]CI=0.99[/tex]

\alpha==0.01

Therefore

[tex]Z_{\frac{\alpha}{2}}=Z_[0.005][/tex]

From table

[tex]Z_{\frac{\alpha}{2}}=2.576[/tex]

Generally, the equation for Margin of error is mathematically given by

[tex]M.E=Z_{\frac{\alpha}{2}}*(\frac{\sigma}{sqrt{n}}[/tex]

[tex]M.E=2.576*(\frac{11.4}{\sqrt{40}}[/tex]

[tex]M.E=4.64[/tex]

Therefore Estimated mean is

[tex]\=x-M.E<\mu <\=x +E[/tex]

[tex]40-4.64<\mu< 40+4.64[/tex]

[tex]35.36<\mu < 44.64[/tex]

[tex]35.36,44.64[/tex]

Let it be x

[tex]\\ \sf\longmapsto \dfrac{3}{5}=\dfrac{x}{x+4}[/tex]

[tex]\\ \sf\longmapsto 3(x+4)=5x[/tex]

[tex]\\ \sf\longmapsto 3x+12=5x[/tex]

[tex]\\ \sf\longmapsto 5x-3x=12[/tex]

[tex]\\ \sf\longmapsto 2x=12[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{12}{2}[/tex]

[tex]\\ \sf\longmapsto x=6[/tex]

Answer:

D

Step-by-step explanation:

8 and 3/5 = 8.2 and 8.2 is between 8 and 9 so the answer is D.

Answer:

c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.

Step-by-step explanation:

Given :

Groups:

x1 = 69 ; s1 = 19 ; n1 = 38

x2 = 32 ; s2 = 14 ; n2 = 37

1 - α = 1 - 0.95 = 0.05

Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :

The confidence interval obtained is :

(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between

(24.32 ; 39.68) .

Answer:

how many times should u use the metal rod ??

Answer:

obtuse                    

aniuhafjhnfajfnha

Answer:

x = 1/5

Step-by-step explanation:

5(3x + 4) = 23

Distribute

15x+20 = 23

Subtract 20 from each side

15x+20-20 = 23-20

15x = 3

Divide by 15

15x/15 = 3/15

x = 1/5

Answer:

[tex]x = 0.2[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex]5(3x + 4) = 23[/tex]

[tex](5 * 3x) + (5 * 4) = 23[/tex]

[tex](15x) + 20 = 23[/tex]

Step 2:  Subtract 20 from both sides

[tex](15x) + 20 - 20 = 23 - 20[/tex]

[tex]15x = 3[/tex]

Step 3:  Divide both sides by 15

[tex]\frac{15x}{15} = \frac{3}{15}[/tex]

[tex]x = \frac{1}{5}[/tex]

[tex]x = 0.2[/tex]

Answer:  [tex]x = 0.2[/tex]

Answer:

162.4 miles

Step-by-step explanation:

We can write a ratio to solve

116 miles            x miles

----------------- = ------------

5 gallons           7 gallons

Using cross products

116*7 = 5x

Divide by 5

812 /5 = 5x/5

162.4 =x

162.4 miles

Answer:

there are infinite solutions

Step-by-step explanation:

if you add y-3 to both sides of the first equation, you will see that it is equal to the second equation, so they are the same line. Therefore, there are infinite solutions to this system

9514 1404 393

Answer:

  x = 14 cm

Step-by-step explanation:

We can only solve for x if the triangles are similar. The arrows on the left and right legs say those are parallel. Since alternate interior angles at each of the transversals are congruent, the triangles are AA similar.

ΔABC ~ ΔDEC, so we have ...

  EC/ED = BC/BA

  x/(18 cm) = (35 cm)/(45 cm)

  x = (18 cm)(7/9) = 14 cm

Answer:

17 units

Step-by-step explanation:

Use the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Plug in the points and simplify:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

[tex]d = \sqrt{(-8 - 7)^2 + (0-8)^2}[/tex]

[tex]d = \sqrt{(-15)^2 + (-8)^2}[/tex]

[tex]d = \sqrt{225 + 64[/tex]

[tex]d = \sqrt{289[/tex]

[tex]d = 17[/tex]

So, the distance between the points is 17 units

Answer:

[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex]

[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex]

[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex]

Step-by-step explanation:

Given

[tex]x^\frac{3}{5}[/tex]

Required

The equivalent expressions

We have:

[tex]x^\frac{3}{5}[/tex]

Expand the exponent

[tex]x^\frac{3}{5} = x^{ 3 * \frac{1}{5}}[/tex]

So, we have:

[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex] ----- this is equivalent

Express 1/5 as roots (law of indices)

[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex] ------ this is equivalent

The above can be rewritten as:

[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex] ------ this is equivalent

= 2025

When you are told to find the smallest length possible, you perform L.C.M(Least common multiples)

For this, you divide the given lengths using the numbers that divides all through.

I have added an image to this answer. Go through it for more explanation

Answer:

The original height of the plant was 2 mm

Step-by-step explanation:

Given

[tex]y = 2 + 4x[/tex]

Required

Interpret the y-intercept

The y-intercept is when [tex]x = 0[/tex]

So, we have:

[tex]y = 2 + 4 *0[/tex]

[tex]y = 2 + 0[/tex]

[tex]y = 2[/tex]

This implies that the original or initial height was 2 mm

Answer:

1250 supermarkets

Step-by-step explanation:

Given

[tex]\frac{dN}{dt} = N(1 - 0.0008N)[/tex]

[tex]N(0) = 1[/tex]

Required

Number of supermarkets over a long period of time

To do this, we simply set

[tex]\frac{dN}{dt} = 0[/tex]

So, we have:

[tex]N(1 - 0.0008N) = 0[/tex]

Split

[tex]N = 0\ or\ 1 - 0.0008N = 0[/tex]

Solve: [tex]1 - 0.0008N = 0[/tex]

Collect like terms

[tex]0.0008N = 1[/tex]

Make N the subject

[tex]N = \frac{1}{0.0008}[/tex]

[tex]N = 1250[/tex]

So:

[tex]\lim_{t \to \infty} N(t) = 1250[/tex]

Answer:

Step-by-step explanation:

a) categorical

b) add all of the numbers and divide by how many numbers there were.

c) outliers means any that were far away from the rest of the data

d) not entirely, you can make an estimate based on it, but nat an exact answer.

Answer:

The zeroes of the function are: 3 and 4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The graph is a square root function

Answer:

The rate at which the distance between the two cars is increasing is 30 mi/h

Step-by-step explanation:

Given;

speed of the first car, v₁ = 24 mi/h

speed of the second car, v₂ = 18 mi/h

Two hours later, the position of the cars is calculated as;

position of the first car, d₁ = 24 mi/h  x 2 h  = 48 mi

position of the second car, d₂ = 18 mi/h  x 2 h = 36 mi

The displacement of the two car is calculated as;

displacement, d² = 48² + 36²

                        d² = 3600

                        d = √3600

                        d = 60 mi

The rate at which this displacement is changing = (60 mi) / (2h)

                                                                                 = 30 mi/h

Answer:

17.637 ounces

Step-by-step explanation:

35.274 ounces is 1 kilogram so divide 35.274 by 2

Answer:

isosceles acute

Step-by-step explanation:

We have two sides that are equal so the triangle is isosceles

None of the angles are larger than 90 degrees so non of the angles are obtuse,  and none of the angles are 90 degrees, so the triangle is acute ( which means the angles are all less than 90 degrees)

Step-by-step explanation:

Area ABC=1/2ab×sin C

=1/2 ×20×10 ×Sin C

Sin C =100

Step-by-step explanation:

1. In an arithmetic sequence, the general term can be written as

xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.

Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =

x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get

x₅-x₃ = 2d

divide by 2 to isolate d

(x₅-x₃)/2 = d

This lets us solve for d. Given d, we can say that

x₃ = y+d(2)

subtract 2*d from both sides to isolate the y

x₃ -2*d = y

Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of

xₙ = y + d(a-1)

2.

Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is

x₃* r * r

= x₃*r² = x₅

divide both sides by x₃ to isolate the r²

x₅/x₃ = r²

square root both sides

√(x₅/x₃) = ±r

One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.

Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence

Answer:

absolutely yes, because pythagorean theorem is used in a right triangle

and when we match a line from the tee to the hole, we have a right triangle

Step-by-step explanation:

Answer:

x = - 10

Step-by-step explanation:

(6x -5x) / 10 = - 1

x = - 10

Answer:

C

Step-by-step explanation:

Answer:

B. The question may not be directly stated.

Answer:

x = 5 and -6

Step-by-step explanation:

Using the intersecting chord theorem which states that the products of the lengths of the line segments on each chord are equal.

Hence:

let

a = 6, b = 5, c = x+1 and d = x

Therefore, ab = cd

6*5 = x(x+1)

30 = x²+x

x²+x - 30 = 0

x²+ 6x - 5x - 30 = 0

x(x+6) - 5(x+6) =0

(x-5)(x+6) = 0

x-5 =0 and x+6 = 0

x = 5 and -6