Expiration dates that establish the shelf lives of pharmaceutical products are determined from stability data in drug formulation studies. In order to measure the rate of decomposition of a particular drug, it is stored under various conditions of temperature, humidity, light intensity, etc., and assayed for intact drug potency at FDA-recommended time intervals of every three months during the first year. In this example, the assay Y (mg) of a certain 500 mg tablet formulation is determined at time X (months) under ambient storage conditions.

X 0 3 6 9 12
Y 500 490 470 430 350

(a) Graph these data points (xi , yi) in a scatterplot, and calculate the sample correlation coefficient r=Sxy/Sx.Sy. Classify the correlation as positive or negative, and as weak, moderate, or strong.
(b) Determine the equation of the least-squares regression line for these data points, and include a 95% confidence interval for the slope β1.
(c) Sketch a graph of this line on the same set of axes as part (a); also calculate and plot the fitted response values y, and the residuals ei= yi - ŷi, on this graph.
(d) Complete an ANOVA table for this linear regression, including the F-ratio and corresponding p-value.

Answer:

cos x = 5

Step-by-step explanation:

[tex] = > sinx.cotx = 5 \\ \\ = > \cancel{sinx}. \frac{cosx}{ \cancel{sinx}} = 5 \\ \\ = > cosx = 5[/tex]

Answer:

Step-by-step explanation:

(a) The figure shows the diameter of the pipe is 4 ft, so its radius is 2 ft. The equation for the volume of a cylinder is ...

  V = πr^2·h

Filling in r=2 and h=18, we have ...

  V = π(2 ft)^2(18 ft) = 72π ft^3

The exact volume is 72π ft³.

__

(b) Using a sufficiently accurate value of pi, the numerical value of the volume is ...

  72π ft^3 ≈ 226.19 ft^3

The approximate volume is 226.19 ft³.

Answer:

  9

Step-by-step explanation:

After 81 passengers get off, only 9 passengers remain on the train of the original 90.

Answer:

The answer to this is both (3,0) and (0,-3). C and B

Step-by-step explanation:

This is because the points in which these two graphs meet is the solution of equations.

Please mark me Brainliest!

Answer:

4

Step-by-step explanation:

20x.2 or 20x(1/5)

Answer:

4

Step-by-step explanation:

Answer:

a) x is the cost of an apple and y is the cost of a banana.

b)

[tex]4x + 3y = 2.59[/tex]

[tex]6x + 5y = 4.11[/tex]

c) An apple costs $0.31 and a banana costs $0.45.

Step-by-step explanation:

We have to find the cost, in dollars, of an apple and of a banana.

We do this solving a system of equations.

a) Decide on pronumeral names for the unknown quantities.

I am going to say that:

x is the cost of an apple.

y is the cost of a banana.

b).write equations involving these pronunerals.work in terms of dollars.

4 apples and 3 bananas for $2.59

This means that [tex]4x + 3y = 2.59[/tex]

6 apples and 5 bananas for $4.11

This means that [tex]6x + 5y = 4.11[/tex]

c). Solve for the unknowns.

I am going to use the addition method, multiplying the first equation by 5 and the second by -3, and then adding them. So

20x + 15y = 12.95

-18x - 15y = -12.33

20x - 18x + 15y - 15y = 12.95 - 12.33

2x = 0.62

x = 0.62/2

x = 0.31

And

4x + 3y = 2.59

3y = 2.59 - 4x

3y = 2.59 - 4*0.31

3y = 1.35

y = 1.35/3

y = 0.45

An apple costs $0.31 and a banana costs $0.45.

Answer:

You can make 27 meatballs.

Step-by-step explanation:

if you add keep subtracting 8.1 by 0.3, then you subtract 27 times to get 0, so you can make 27 meatballs.

Answer:

b) 14°

Step-by-step explanation:

To solve this, you need to make an equation. since a line is equal to 180°, you can add the two angles together. for example, x+96+5x=180. you would write this because these two angles are on a line, which makes the total sum 180°. now you solve: 6x+96=180. 6x=84. x=14°. :)

Answer:

14

Step-by-step explanation:

Answer:

Step-by-step explanation:

Givens

We know that the area of a square is

[tex]A=s^{2}[/tex]

Where [tex]s=12 \ ft[/tex], according to the problem.

Replacing this value, we have

[tex]A=(12 \ ft)^{2} =144 \ ft^{2}[/tex]

Therefore, the area of the square roof is 144 square feet.

Answer: the area of the roof is 144 feet squared for each side (up and down), adding to a total of 288 ft^2

Step-by-step explanation:

If the roof is a square with a side lenght L =  12 feet, then we use the fact that the area of a square is equal to the square of the side lenght of the square, this is:

A = L^2  = (12 ft)^2 = 144 ft^2

Now, Mr. wilson uses the equation A = s, this is because the roof has 2 surfaces, one up and one bottom, then the total area is 2 times the value that we find earlier:

2*144 ft^2 = 288 ft^2

345 cm

this is because cm is the abbreviation of centimeters.

Answer:

   $633.00

Step-by-step explanation:

Decreasing the price 25% makes the new price be 75% of the original:

  $474.75 = 0.75×(original price)

  original price = $474.75/0.75

  original price = $633.00

Answer:

FIRST option is the correct answer

Step-by-step explanation:

First option is the correct answer.

[tex] (x+11)^2 + (y+ 6)^2 = 324\\

(x+11)^2 + (y+ 6)^2 = 18^2 \\[/tex]

Equating it with:

[tex] (x-h)^2 + (y-k)^2 = r^2 \\

- h = 11\implies h = - 11\\

- k= 6\implies k = - 6\\

Center = (-h, \: - k) = (11,\: 6)\\

r^2 = 18^2 \\

Radius= 18\: units [/tex]

Answer:

true

Step-by-step explanation:

Answer: true

Step-by-step explanation:

Answer: c, -3.2 + 1.5n less-than-or-equal-to 8.6

Step-by-step explanation:

I got it right on the quiz

Answer:

the answer is c

Step-by-step explanation:

just did the assignment got 100%

Answer:

X=-2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

1/2(6x-10)=2x-7

(1/2)(6x)+(1/2)(-10)=2x+-7(Distribute)

3x+-5=2x+-7

3x-5=2x-7

Step 2: Subtract 2x from both sides.

3x-5-2x=2x-7-2x

X-5=-7

Step 3: Add 5 to both sides.

X-5+5=-7+5

X=-2

Hope this helps

Answer:

87.5%

Step-by-step explanation:

First we find the number of students that did wear green which is 120-15=105. Then we need to find what percentage of these students who did wear green so we divide 105 by 120 which is .875. To find this number in percent form, we multiply this number by 100 which gives us 87.5%.

Answer:

87.5%

Step-by-step explanation:

Hope this helps have a wonderful day

Answer:

250 hours

Step-by-step explanation:

The first charge is 10 hours, the second charge is 10(0.96) hours, and so on -- the total of these two is 10+10(0.96)  and we need to keep adding our battery usage up until there is no more battery. The third one is 10(0.96)*(0.96), or 10(0.96)².

This can be seen as a geometric series, with 10 as the first tern, or a, and 0.96 as the common ratio, or r. The sum of this is

[tex]a\frac{1-r^{n}}{1-r}[/tex], with n being the number of terms. Since 0.96 to the power of n never actually reaches 0 no matter how high n goes if the number is not infinite, we can say n is infinity. As r^n is really close to 0 when n equals infinity (so close that, for our purposes in this equation, we can just assume it's 0), our equation is then

[tex]10\frac{1}{0.04} =10*25=250[/tex]

Answer: I am pretty confident that the answer to your question is kf(x).

Step-by-step explanation: SO in the graph of f(x) = x^2, one of the coordinates is (1,1). And in the graph of kf(x), it changes to (1,3).

Answer:

We would advise her to choose Country Route because in this route time consistent between 15 and 18 minutes.

Step-by-step explanation:

We are given that Jean lives about 10 miles from the college where she plans to attend a 10-week summer class. There are two main routes she can take to the school, one through the city and one through the countryside.

Jean sets up a randomized experiment where each day she tosses a coin to decide which route to take that day. She records the following data for 5 days of travel on each route.

Country Route - 17, 15, 17, 16, 18  (in minutes)

City Route - 18, 13, 20, 10, 16 (in minutes)

Now, we have to decide which route is better for Jean to go to college.

As we can see from the data that the Country route timings is consistent between 15 to 18 minutes which means most of the times she will reach college between these minutes only.

While on the other hand, we can observe that City route timings are very much consistent as it has a low value of 10 minutes and high value of 20 minutes which means Jean can't be sure that at which time she will reach college.

Hence, we would advise her to choose Country route.

Answer: 91

Step-by-step explanation: I assume you had a typo and mean what did Ana need on the 5th quiz since you only listed 4 quiz scores.

(74 + 92 + 83 + 100 + x)/5 = 88

(349 + x)/5 = 88

((349 +x)/5) x 5 = 88 x 5

349 + x = 440

x = 440-349

x  = 91

Answer:

The radius of the circle with 4 inch diameter is 2 inches

Step-by-step explanation:

This is the formula here:

d = 2r

The radius is solved here:

r = [tex]\frac{d}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 inches

Answer:

13

Step-by-step explanation:

13*4=52

Answer:

10 (positive 10)

Step-by-step explanation:

5 times -2 is equal to -10.

-10 times -1 is equal to 10.

Answer:

postive 10

Step-by-step explanation:

Answer:

he will pay

Step-by-step explanation:

2962.25 is the total weight of the bricks

Answer:

  [tex]\dfrac{\sqrt[3]{95^2}}{17\cdot95^4}=\dfrac{\sqrt[3]{9\,025}}{1\,384\,660\,625}[/tex]

Step-by-step explanation:

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)/(a^c) = a^(b-c)

__

  [tex]\dfrac{190^3}{68^2}\times\dfrac{34}{95^{\frac{19}{3}}}=\dfrac{(2\cdot 95)^3}{(2\cdot 34)^2}\cdot\dfrac{34}{95^6\cdot 95^{\frac{1}{3}}}=2^{3-2}95^{3-6-\frac{1}{3}}34^{1-2}\\\\=2\cdot 95^{-3\frac{1}{3}}\cdot 34^{-1}=2\cdot 95^{-4+\frac{2}{3}}\cdot 34^{-1}\\\\=\dfrac{2\sqrt[3]{95^2}}{95^4\cdot 34}=\dfrac{\sqrt[3]{95^2}}{17\cdot95^4}\\\\=\dfrac{\sqrt[3]{9\,025}}{1\,384\,660\,625}[/tex]

Answer:

x=-6

Step-by-step explanation:

substitute f(x)=0

0=1/3x+2

solve for x

x=-6

Answer:

x >= -6

Step-by-step explanation:

edg 2020

Answer:

a)  The yield for the circular area is the triple of the original yield so it is 1,050 bushels.

Average yield for the square plot= 899 bushels.

b) The ratio of irrigated area to the total area of the square plot is the same if we put the sprinkler in the center (with half side as the ratio) or in the corner (with ratio of the side of the square).

Step-by-step explanation:

The arm of the sprinkler goes half the length of the square plot, so the area irrigated is the circumscribed circle. See the picture attached (irrigated area).

The yield will triple in the irrigated area and the same as before in the non-irrigated area. The irrigated area is the area of the circle with radius equal to half the side of the square.

[tex]Y_c=3Y_0=3\cdot350=1,050[/tex]

The non-irrigated area is the area of the square less the area of the circle.

We can calculate the yield as:

[tex]Y=\dfrac{(3Y_o)\cdot A_c}{A_s}+\dfrac{Y_0(A_s-A_c)}{A_s}[/tex]

where Y0: original yield (350 bushels), Ac: area of the circle, and As: area of the square.

The ratio between the area of the circle and the area of the square is:

[tex]\dfrac{A_c}{A_s}=\dfrac{\pi r^2}{l^2}\\\\\\r=l/2\\\\\\\dfrac{A_c}{A_s}=\dfrac{\pi (l/2)^2}{l^2}=\dfrac{\pi l^2}{4l^2}=\dfrac{\pi}{4}\approx0.78[/tex]

We can now solve for the yield:

[tex]Y=\dfrac{(3Y_o)\cdot A_c}{A_s}+\dfrac{Y_0(A_s-A_c)}{A_s}\\\\\\Y=3Y_0\dfrac{\pi}{4}+Y_0(1-\dfrac{\pi}{4})=Y_0\left(\dfrac{3\pi}{4}+1-\dfrac{\pi}{4}\right)=Y_0\left(\dfrac{\pi}{2}+1\right)\\\\\\Y\approx2.57Y_0=2.57\cdot350=899.5[/tex]

b) If the arm is located in one corner of the square and the arm has a length of the side of the square, we have an irrigated area that is a quarter of a circle with radius l.

We can calculate the proportion of irrigated area in the square plot, and if it is bigger than the proportion of irrigated area when we have the sprinkler in the center (proportion of 0.78 of irrigated area), then it is better to put the sprinkler in the corner.

The ratio of the irrigated area to the total area is:

[tex]\dfrac{Aq}{A_s}=\dfrac{\pi r^2/4}{l^2}\\\\\\r=l\\\\\dfrac{Aq}{A_s}=\dfrac{\pi l^2/4}{l^2}=\dfrac{\pi}{4}\approx 0.78[/tex]

The ratio of irrigated area to the total area of the square plot is the same if we put the sprinkler in the center (with half side as the ratio) or in the corner (with ratio of the side of the square).

Answer:

question 7 is 9

question 8 is 11

Step-by-step explanation:

7) the square root of 81 is 9

8) the square root of 25 is 5 and the square root of 36 is 6

5+6=11

Answer:

7) 9

8) 11

Step-by-step explanation:

√81=9

√25=5           √36=6

5+6=11

Answer: Jordan is sad about how the story ends

Step-by-step explanation:

The story is sad

Jordans POV