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.

The formula of the function, where x is entered in radians is   y = -3sin(πx/5) -6

The key components: amplitude, period, phase shift, and vertical shift.

Amplitude is the distance between the midline and max/min points. Midline at (0, -6), so distance to min point (2.5, -9) is 3. Amplitude: 3.

Vertical shift: Displacement along y-axis. Midline at y = -6, vertical shift is -6. Period: distance between max/min points. Graph intersects midline at (0, -6) and minimum point at (2.5, -9).  Period is 5 (2 * 2.5). Freq: Reciprocal of period, 1/5.

Phase shift: Horizontal shift of graph. Graph intersects midline at x=0, no phase shift.

Hence:

The general form of the sinusoidal function is y = A sin (B(x-C)) + D

So, Substituting the known values into the general formula:

y = 3 x  sin((1/5)x - 0) - 6

Hence: Simplifying it will be:

y = 3 x sin(πx/5) - 6

Then, the formula of the function, where x is entered in radians, is: y = -3sin(πx/5) - 6

Based on the image attached, the first given point is one that informs one that the function is a sine (not a cosine) function, and that it is one that has its offset as -6.

Also, the second given point is one that informs you of the first peak is at x=2.5, hence the argument of the sine function is π/2 if x=2.5: (πx/5).

Based on the fact that the peak is 3 units smaller than the midline, the amplitude is said to be -3.

Therefore the  formula for the function is  seen as:  y = -3·sin(πx/5) -6

Learn more about sinusoidal function from

https://brainly.com/question/16300816

#SPJ1

Answer:

i think the answer is C

Step-by-step explanation:

i normally just do length divided by width to figure this out

Answer:

Volume is the measure of how big an object is in three dimensions, so the volume of a box measure how much room there is inside of the box. To find it, you need to make a few simple measurements of length, width, and height, and then multiply them.

Step-by-step explanation:

Answer:

Equivalent

Step-by-step explanation:

4/5=12/15

4*15=12*4( cross multipication)

60=60

Hence,

PROVED

Answer:

D. Bank charges a large fee for bouncing a check is not an example of overdraft protection.

Step-by-step explanation:

Overdraft protection is a service offered by banks that allows you to link your checking account to another account, such as a savings account or a line of credit. If you overdraw your checking account, the bank will automatically transfer funds from the linked account to cover the shortfall, which helps you avoid overdraft fees and other penalties.

Option A is not an example of overdraft protection as it refers to earning interest on money in your savings account, which is a separate service.

Option B refers to additional fees collected by the bank when you bounce a check, which is a penalty for not having sufficient funds in your account to cover the check.

Option C refers to an ATM machine providing you with cash, which is a basic function of an ATM and is not related to overdraft protection.

The area of triangle DEF, in square units, is given as follows:

4.08 units squared.

The area of a triangle is given by half the multiplication of it's base by it's height, as follows:

Area = 0.5 x base x height.

We consider the base as the segment DE, hence it's length is given by the distance between these two points, obtained as follows:

\(b = \sqrt{(8 - 3)^2 + (-6 - (-5))^2}\)

\(b = \sqrt{26}\)

b = 5.1 units.

The midpoint of the base is given as follows:

(5.5, -5.5).

As it is obtained with the mean of the coordinates.

The height is the distance between the midpoint of the base and the other vertex, hence:

\(h = \sqrt{(5.5 - 4)^2 + (-5.5 - (-5))^2}\)

h = 1.6 units.

Hence the area of the triangle is obtained as follows:

Area = 0.5 x 5.1 x 1.6 = 4.08 units squared.

The problem asks for the area of the triangle, as shown in the image given at the end of the answer.

More can be learned about the area of a triangle at https://brainly.com/question/21735282

#SPJ1

Constructing an angle bisector using only a straightedge and compass involves drawing the Angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle.

To construct an angle bisector using a straightedge and compass, there are several steps that you need to follow. The correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass are listed below:

Step 1: Draw the angle ABC with a straightedge.

Step 2: Place the point of the compass on point B and swing an arc that intersects both lines that make up the angle. Label the two points where the arc intersects the angle as points D and E.

Step 3: Without changing the compass width, place the point of the compass on point D and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point F.

Step 4: Without changing the compass width, place the point of the compass on point E and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point G.

Step 5: Draw the line segment FG with a straightedge. This line segment is the angle bisector of angle ABC.

In summary, constructing an angle bisector using only a straightedge and compass involves drawing the angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle. Following these steps will allow you to construct the angle bisector of ABC accurately.

For more questions on Angle.

https://brainly.com/question/31615777

#SPJ8

solve simultaneously

Step-by-step explanation:

make one of the equations x subject of the formula and the other equation y subject of the formula

y=8+2/5x....1

x=-5/3 + 2/3y.....2

substitute equation 1 into equation 2

x=5

y=10

Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

<95141404393>

Answer:

2 dogs/ 3 cats and 10 dogs/ 15 cats are an example of

Equivalent ratios.

The mean of a distribution is 217, while the median is 217.The statements is likely to be true about the distribution is  option  D. It is not symmetrical.

The distribution is likely to be asymmetrical if the mean and median have different values. If the mean and median of a distribution are equal, it is likely that the distribution is symmetrical, which means it has equal tail sizes on both sides. However, if the mean and median are not equal, it indicates that the distribution is skewed.

A negatively skewed distribution means that the mean is less than the median, whereas a positively skewed distribution means that the mean is greater than the median.In this case, since the mean and median of the distribution are equal, it is likely to be symmetrical. Since none of the options say "symmetrical," option D, "It is not symmetrical," is the correct answer.

Know more about  symmetrical   here:

https://brainly.com/question/31331083

#SPJ8

Given:

So the value of:

Answer:

Step-by-step explanation:

From the given picture,

AD and BE are the lines intersecting at a point C.

Point C is the midpoint of these lines.

From ΔABC and ΔDEC,

AC ≅ CD

CE ≅ CB

And ∠ABC ≅ ∠DEC [Vertical angles]

Therefore, ΔABC ≅ ΔDEC [By SAS property of congruence]

And AB ≅ ED [Since, ΔABC ≅ ΔDEC]

Answer:

3x²+6x+10 is your answer

Step-by-step explanation:

(x^2+6x-5)+(2x^2+15)

open bracket

x²+6x-5+2x²+15

add or subtract common

3x²+6x+10

Answer:

1 1/2 + 2/5

3/2 + 2/5 I changed the first fraction from a mixed fraction to an improper fraction

5/5( 3/2 ) + 2/2(2/5)  I did this to make the denominators the same

15/10 + 4/10

19/10

1 9/10 = Answer

Step-by-step explanation:

Answer:

It is explained below

Step-by-step explanation:

Taking into account the required points we can say the following:

In this case measuring the duration of hair is reliable. The purpose for my opinion is that regardless of how often Joni will degree a persons hair the effects will always be more or less the same. There fore, we are able to rely on the fact that the outcomes may be similar this method is reliable. On the other hand, this technique isn't valid, due to the fact the length of a persons' hair has nothing to do with political opinion. The prediction theory that occurs to me with respect to the model is that the longer the person's hair is, the more they tend to be liberal, due to the rebellious thinking of the left-wing.

Answer:

See image below for answer:)

Step-by-step explanation:

You can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps.

Answer:

3. I would say shop one because it's at a lower price.  Although, it is up to you.

Step-by-step explanation:

Roger wants 400 copies; First print shop; $21.50 for first 200 copies + $10 for every 100 additional copies. Second print shop; $0.15 per copy + no deals on bulk  

1. how much will cost roger at the first print shop?  

$21.50 + $20 = $41.50 for 400 copies  

2. how much will it cost roger at the second print shop?  

$0.15 x 400 = $60

Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

Answer:

X+7 < 40 is the answer

x can equal anything less than 33

Step-by-step explanation:

The Square root of 225 is 15

The act of repeatedly subtracting is called division. It functions in the opposite way to how multiplication works. Forming equal groups is how it is described. When dividing numbers, we split a larger number into smaller ones so that the product of the multiplication of those smaller numbers equals the larger number that was divided. As an illustration, 4 2 = 2. This knowledge can be expressed as the multiplication 2 x 2 = 4.

Given that :Square root of 225

225  = 3 × 75

225 = 3 × 3 ×25

225 = 3 ×3 × 5 ×5

225 = 3² × 5²

225 = (3 × 5)²

225 = 15²

√225 = 15

To learn more about division method visit :

brainly.in/question/7698504

#SPJ9

Answer: The answer to your question is C. Brainliest?

Step-by-step explanation:

For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:

2/12 = (2 x 5) / (12 x 5) = 10/60

For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:

2/15 = (2 x 4) / (15 x 4) = 8/60

Now, we can add the two fractions:

10/60 + 8/60 = 18/60

Simplifying this fraction by dividing both numerator and denominator by 6, we get:

18/60 = 3/10

Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.

The answer is C. 0.3.

Answer:

BC, DE, CD

let me  know if that helps

Step-by-step explanation:

Answer:

35/3

Step-by-step explanation:

\(\frac{x+6 + 6x+2+x+6}{3} =4x-7\)

Simplify to get

9x+14=3(4x-7)

35=3x

x=35/3 or 11.66

76

Step-by-step explanation:

just divide 6080 by 80 and you get 76

Answer:

14

Step-by-step explanation: