What is the probability that a patient shows improvement
if it is known that the patient was given the drug?

Answer:

Can you please write the question given to answer the graph

Answer:

[tex]\dfrac{d^2y}{dx^2} = 5e^{3x} \sin (2x)+12e^{3x} \cos (2x)[/tex]

Step-by-step explanation:

[tex]\large \boxed{\begin{minipage}{5 cm}\textsf{\underline{Product Rule}}\\\\$ \textsf{When } \:y=uv\\\\\dfrac{dy}{dx}=u\dfrac{dv}{dx}+v \dfrac{du}{dx}$\\\end{minipage}}[/tex]

Given:

[tex]y=e^{3x} \sin(2x)[/tex]

First Derivative

[tex]\textsf{let } u=e^{3x} \implies \dfrac{du}{dx}=3e^{3x}[/tex]

[tex]\textsf{let } v= \sin(2x) \implies \dfrac{dv}{dx}=2 \cos (2x)[/tex]

Using the Product Rule:

[tex]\begin{aligned}\dfrac{dy}{dx} & =e^{3x}\cdot 2 \cos (2x) + \sin (2x) \cdot 3e^{3x}\\& = 2e^{3x} \cos (2x) + 3e^{3x} \sin (2x)\\& = e^{3x}(2 \cos (2x) + 3 \sin (2x))\end{aligned}[/tex]

Second Derivative

[tex]\textsf{let } u=e^{3x} \implies \dfrac{du}{dx}=3e^{3x}[/tex]

[tex]\textsf{let } v= 2 \cos (2x)+3 \sin (2x) \implies \dfrac{dv}{dx}=-4 \sin (2x) +6 \cos (2x)[/tex]

Using the Product Rule:

[tex]\begin{aligned}\dfrac{d^2y}{dx^2} & =e^{3x}(-4 \sin (2x) +6 \cos (2x)) +3e^{3x} (2 \cos (2x)+3 \sin (2x))\\& = e^{3x}[-4 \sin (2x) +6 \cos (2x)+6 \cos (2x)+9 \sin (2x)]\\& = e^{3x}[5 \sin (2x) +12 \cos (2x)]\\& = 5e^{3x} \sin (2x)+12e^{3x} \cos (2x)\end{aligned}[/tex]

Answer:

[tex] \tt{ \frac{ {d}^{2} y}{d {x}^{2} } = 5 {e}^{3x} \sin(2x) + 12 {e}^{3x} \cos(2x)}[/tex]

Step-by-step explanation:

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[tex]y = {e}^{3x} \sin(2x) \\ { \sf{To \: find}} \: \frac{ {d}^{2}y }{d {x}^{2} } [/tex]

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[tex] \sf using \: \frac{d}{dx} uv = u \frac{d}{dx} v + v \frac{d}{dx} u \: formula[/tex]

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[tex] \bold{ \frac{dy}{dx} = {e}^{3x} \frac{d}{dx} \sin(2x) + \sin(2x) \frac{d}{dx} {e}^{3x} } \\ \\ \bold{ \frac{dy}{dx} = {e}^{3x} \cos(2x) \frac{d}{dx} 2x + \sin(2x) {e}^{3x} \frac{d}{dx} 3x}[/tex]

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[tex] \bold{ \frac{dy}{dx} = {e}^{3x} \times 2 \cos(2x) + \sin(3x) \times 3 {e}^{3x} }[/tex]

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[tex] \bold{ \frac{dy}{dx} = 2 {e}^{3x} \cos(2x) + 3 {e}^{3x} \sin(2x) }[/tex]

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⠀⠀● First solving 2e^3x cos(2x)

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[tex] \bold{ 2( {e}^{3x} \frac{d}{dx} \cos(2x) + \cos(2x) \frac{d}{dx} {e}^{3x}) }[/tex]

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[tex] \bold{2( {e}^{3x} - \sin(2x) \frac{d}{dx} 2x + \cos(2x) {e}^{3x} \frac{d}{dx} 3x)} \\ \\ \bold{ - 4 {e}^{3x} \sin(2x) + 6 {e}^{3x} \cos(2x) }[/tex]

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⠀⠀● Now solving 3e^3x sin(2x)

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[tex] \bold{ 3( {e}^{3x} \frac{d}{dx} \sin(2x) + \sin(2x) \frac{d}{dx} {e}^{3x} )}[/tex]

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[tex] \bold{ 3( {e}^{3x} \cos(2x) \frac{d}{dx} 2x + \sin(2x) {e}^{3x} \frac{d}{dx} 3x)} \\ \\ \bold{ 6 {e}^{3x} \cos(2x) + 9 {e}^{3x} \sin(2x) }[/tex]

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[tex] \bold{ \frac{ {d}^{2}y }{d {x}^{2} } = - 4 {e}^{3x} \sin(2x) + 6 {e}^{3x} \cos(2x) + 6 {e}^{3x} \cos(2x) + 9 {e}^{3x} \sin(2x) } \\ \\ \bold{ \frac{ {d}^{2} y}{d {x}^{2} } = 5 {e}^{3x} \sin(2x) + 12 {e}^{3x} \cos(2x) }[/tex]

Answer:

write an article for publication in the daily graphic on the topic every school must have a library

Answer:

Unfortunately they are not simmilar because 9 is not similar to 80 but to 90, they would be similar if the triangle was 40, 70 and 90, know what I mean?

Step-by-step explanation:

Answer:

Original price = t = $24

Expression = t + 0.05t

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New price = t + 0.05t = 24 + (0.05*24) = $25.20

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Have a nice day!!

Answer:

$25.20

Step-by-step explanation:

Original price = t = $ 24

New price = 1.05*24

                 = 25.20

Just multiply 1.05 by 24

Answer:

B

Step-by-step explanation:

B is the answer to your question

Answer:

see below

Step-by-step explanation:

6!    is    six factorial

   =   6 x 5 x 4 x 3 x 2 x 1  = 720

Answer:

5/21.

Step-by-step explanation:

Total number of balls = 7.

Prob(Blue on first pick) = 3/7

Prob(Blue on second pick) = 2/6 = 1/3

So Prob( 2 Blue's) = 3/7 * 1/3 = 3/21 = 1/7.

Prob(Red on first pick) = 2/7

Prob(Red on second pick) =  1/6

So Prob( 2 Red's) = 2/7 * 1/6 = 1/21.

Now the Probability of getting 2 white balls is the same as for the red balls

= 1/21.

Finally, the probability of 2 balls of the same colour

= 1/7 + 1/21 + 1/21

= 3/21 + 1/21 + 1/21

= 5/21.

the probability of picking two balls of the same color is 5/21.

To calculate the probability of picking two balls of the same color, we need to consider all the possible combinations of drawing two balls from the bag and then determine how many of those combinations result in both balls being the same color.

Total number of balls in the bag = 7

1. Probability of picking two blue balls:

Number of blue balls = 3

Probability of picking the first blue ball = 3/7

Probability of picking the second blue ball (after one blue ball has been picked) = 2/6 (since there are 2 blue balls left after one has been picked)

Total probability of picking two blue balls = (3/7) * (2/6) = 6/42 = 1/7

2. Probability of picking two red balls:

Number of red balls = 2

Probability of picking the first red ball = 2/7

Probability of picking the second red ball (after one red ball has been picked) = 1/6 (since there is 1 red ball left after one has been picked)

Total probability of picking two red balls = (2/7) * (1/6) = 2/42 = 1/21

3. Probability of picking two white balls:

Number of white balls = 2

Probability of picking the first white ball = 2/7

Probability of picking the second white ball (after one white ball has been picked) = 1/6 (since there is 1 white ball left after one has been picked)

Total probability of picking two white balls = (2/7) * (1/6) = 2/42 = 1/21

Now, we add up the probabilities of picking two balls of the same color:

Total probability = Probability of two blue balls + Probability of two red balls + Probability of two white balls

Total probability = 1/7 + 1/21 + 1/21

Total probability = (3 + 1 + 1)/21

Total probability = 5/21

Therefore, the probability of picking two balls of the same color is 5/21.

Learn more about probability here

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Answer:

Given:

As the exponent of Sample A is negative, this means that the mass of Sample A is smaller than that of Sample B.

Therefore, to find the proportional relationship between the samples, divide the mass of the larger sample (B) by the mass of the smaller sample (A):

[tex]\begin{aligned}\implies \dfrac{\textsf{Sample B}}{\textsf{Sample A}}=\dfrac{3.6 \times 10^2}{2.4 \times 10^{-2}} & =\dfrac{3.6}{2.4} \times \dfrac{10^2}{10^{-2}}\\\\ & =1.5 \times 10^{(2-(-2))}\\\\& = 1.5 \times 10^4 \end{aligned}[/tex]

To convert the scientific notation [tex]1.5 \times 10^4[/tex] to a decimal, move the decimal point to the right 4 places:

[tex]\implies 1.5000 \times 10^4=15000[/tex]

(If the exponent is positive, move the decimal point to the right.  If the exponent is negative, move the decimal point to the left. The number of places to move the decimal point is the numerical value of the exponent).

Therefore, the mass of sample B is 15,000 times the mass of sample A, so Narissa is correct.

Answer:

Step-by-step explanation:

next multiply 12 and 35. and get 420

finally subtract the two and get 345

Answer:

3rd option (bottom left)

Step-by-step explanation:

Answer:

  4.0%

Step-by-step explanation:

If we assume that potential impact sites are uniformly distributed over the area, the probability of interest is the ratio of the area of Connecticut to the area of the circle within 200 miles of Hartford.

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The area of a circle with radius 200 miles is ...

  A = πr²

  A = π(200 mi)² = 40000π mi² ≈ 125,664 mi²

The area of a rectangle 100 miles by 50 miles is ...

  A = LW

  A = (100 mi)(50 mi) = 5000 mi²

The probability of interest is the ratio of these areas:

  p(impact in CT) = (5000 mi²)/(125664 mi²) ≈ 0.03979

The probability the meteor landed in Connecticut is about 4.0%.

Answer:

v = 29647.79 cu.ft.

Step-by-step explanation:

[tex]v=\frac{4}{3} \pi r^{3}\\ r=19.2[/tex]

[tex]v=\frac{4}{3} \pi (19.2)^{3} =29,647.79 cu.ft[/tex]

Hope this helps

Answer:

29632.76 cubic feet

Explanation:

volume of sphere: 4/3 π(radius)³

Here given:

Volume:

insert values

simplify

rounded to nearest hundredth

Answer:

x = 7 and the degree of other two angles is 69.

Step-by-step explanation:

As we can see it is an isosceles triangle so base angles of an isosceles triangle are equal so

9x + 6 + 9x + 6 + 42 = 180 (being sum of angles of triangle )

18x + 54 = 180

18x = 180 - 54

18x = 126

x = 126/18

x = 7

the degree of the other two angle is

= 9*7 + 6

= 69

Hope it helps :)

Answer: radius: 28.5

area: 2551.76

Step-by-step explanation:

radius is always half of the diameter and area is pi(r^2)

A parallelogram is a quadrilateral or a flat shape with opposite sides parallel. Squares, Rhombuses, and Rectangles are few example of Parallelogram.

Explanation:

There are six important properties of a parallelograms:

The answer to the above question is (D) Diagonals Congruent

Answer:

D

Step-by-step explanation:

Because these are the 7 properties of a parralelgrom

Opposite sides are parallel.

Opposite sides are congruent.

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary. .

Each diagonal of a parallelogram separates it into two congruent triangles.

The diagonals of a parallelogram bisect each other.

Answer:

∠ e = 20°

Step-by-step explanation:

you should have also subtracted 2e from the 360

since UV is a straight line, the angles lying on it sum to 180° , that is

90° + e + 70° = 180°

e + 160° = 180° ( subtract 160° from both sides )

e = 20°

Answer:

Step-by-step explanation:

First step is to solve the numerator

so the fraction is 29/10/29

so the whole expression is 1/10

Answer: Solve the numerator, numerator and denominator are equal, expression equals 13

Step-by-step explanation:

13 x (5.6-2.7/2.9)

1. The first step; solve the numerator (5.6-2.7=2.9)

2. The numerator and dominator are equal, so the whole expression equals 13 (2.9/2.9 = 1 --> 1*13 = 13)

well, tis noteworthy that the equation of the parabola above is already in vertex form, which means its vertex is at (3 , 6) and its focus point is at (3 , 1).

now, the focus point is below the vertex, meaning is a vertical parabola opening downwards, like a hump.

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]y=-\cfrac{1}{20}(x-3)^2+6\implies y-6=-\cfrac{1}{20}(x-3)^2\implies \stackrel{4p}{-20}(y-\stackrel{k}{6})=(x-\stackrel{h}{3})^2 \\\\\\ 4p=-20\implies p=-\cfrac{20}{4}\implies p=-5[/tex]

the focus point must be a negative distance since the parabola is opening downwards, and the directrix is across the vertex at "p" distance, Check the picture below.

Answer: 25/8

Step-by-step explanation:

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

Change 3+1/8 to an improper fraction.

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

First, multiply the whole part (3) times the denominator (8):-

[tex]\bold{3\times8=24}[/tex]

Now add the numerator:-

[tex]\bold{25}[/tex]

That's the numerator of the improper fraction, and the denominator stays the same.

[tex]\bigstar[/tex] Therefore, the fraction is

[tex]\bold{\dfrac{25}{24}}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

$ 199.56 per sq ft

Step-by-step explanation:

price / ft^2    =    450 000 / 2255 = 199.56

Answer:

$0.65

Step-by-step explanation:

Given:

Books cost $6.95 each.

Mary had a $5 bill, a $1 bill, and 3 dimes.

To Find:

How much more money does she need to buy one book?

Solve:

Add all Mary money:

5+1+.30

6+.30

=6.30

Now subtract the book cost  by Mary total money.

$6.95-$6.30

=$.65

Hence, Mary needs .65 cents to buy one book.

Kavinsky

Answer: 65 cents 0.65

Step-by-step explanation:

$5 + $1=$6

3dimes= 30 cents

$6 + 30 cents=$6.30

$6.95-$6.30=0.65

Answer:

60cm²

Step-by-step explanation:

2(1/2×4×3)+(3×6)+(5×6)

The skewness of the plot is positive skewness, and the equation of the regression line is y = -0.052x + 2.706

To do this, we make use of the following data values

15, 16, 16, 17, 17, 17, 20, 22, 22, 30

The mean is calculated using:

Mean = Sum/Count

So, we have:

Mean = (15+ 16+ 16+ 17+ 17+ 17+ 20+ 22+ 22+30)/10

Evaluate

Mean = 19.2

Using a graphing calculator, we have:

Standard Deviation, σ = 4.30

The min and the max are:

Min = 15

Max = 30

See attachment for the histogram.

From the attached histogram, we can see that the skewness of the plot is positive skewness

The min and the max values are the range of the normal plot.

So, the percentage area between these values is 100%

Let the three samples be

16, 17, and 30

The sample mean is:

Mean = Sum/Count

So, we have:

Mean = (16 + 17 + 30)/3

Evaluate

Mean = 21

The sample mean is different from the population mean

Since the means are not equal, then we fail to accept the Null hypothesis.

To do this, we make use of a graphing calculator with the following calculation summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -8 / √((154)(3.333)) = -0.3531

The correlation coefficient -0.3531 means that there is a negative correlation between the data values

To do this, we make use of a graphing calculator with the following calculation summary:

So, we have:

y = -0.052x + 2.706

Hence, the equation of the regression line is y = -0.052x + 2.706

See attachment 2 for the scatter plot.

Read more about scatter plots and histograms at:

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Answer:

  (b) both powers should be in the denominator with positive exponents

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

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The correct simplification is ...

  [tex]x^{-3}y^{-9}=\dfrac{1}{x^3}\cdot\dfrac{1}{y^9}=\boxed{\dfrac{1}{x^3y^9}}[/tex]

Both variables should have positive exponents in the denominator.

Answer:

39cm

Step-by-step explanation:

area of square = side^2 =169

side = 13cm

Perimeter of triangle = 3*side

=3 * 13 = 39cm

Answer:

52

Step-by-step explanation:

√169 =13

13*4= 52 because the perimeter of the square is equal to the perimeter of the triangle