An educational researcher is studying two similar high schools in different states. Suppose that 50% of all
425 students at high school A have taken a college-level course, while 40% of all 525 students from hig
school B have taken such a course. The researcher plans on taking separate random samples of 50 students
from each high school to look at the difference (A - B) between the proportions of students who have
taken a college-level course in each sample.
Consider the formula:
OPA-js =
PA (1 - PA) PB (1 - PB)
+
ПА
NB
Why is it not appropriate for the researcher to use this formula for the standard deviation of PA - PB?
Choose 1 answer:

slope = rise / run

2 + 0 / 12 + 14

2 / 26 = 1 / 13 slope

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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Answer:

60kph

Step-by-step explanation:

Distance = Rate X Time

640 = r x 4+ (r+5) x 7

640 = 4r + 7r + 35

640=11r + 35

640 - 35 = 11r

605 = 11r

r = 605 / 11

r= 55 kph

r=55 =5 =60 kph is the speed of the train

To see if the answer is right: 55 x 4 + 60 x 7 = 220 + 420 = 640 km

Answer: It would be the first option. 15√​6

​

Step-by-step explanation:

5√3 = 5x3=15

√18= √9x2

√9=3

√3x2= √6

15√6

Answer:

- 12(x + 2)

Step-by-step explanation:

- 12x - 24 ← factor out the common factor of - 12 from each term

= - 12(x + 2)

Answer:

The chemistry of class 11th includes the basic rules and concepts that is required in daily life, for further educational purposes, it also helps to get some knowledge about the topics on which the work will be done further.

It includes some basic concepts of chemistry which helps to know the concepts of organic compound, in organic compound, metals, non metals.

The class 11th chemistry also helps the person know about some other compounds like radioactive compounds and its application in research field.

The basic reactions, types of reaction and compounds that takes place in our daily life.

This subject also helps individual in better understanding of the other subjects related to chemistry.

Answer:

II, III and IV.

You can construct similar figure for I.

Answer:

\((13,-23)\)

Step-by-step explanation:

Given

Translation: \((x,y) -> (x-4,y+15)\)

Required

Determine the pre-image of (9,-8)

In (9,8)

\(x = 9\) and \(y = -8\)

So:

\((x,y) -> (x-4,y+15)\)

Becomes

\((9,8) ->(x-4,y+15)\)

By comparison:

\(x - 4 = 9\)

\(y + 15 = 8\)

Solving for (x):

\(x - 4 = 9\)

\(x = 9 + 4\)

\(x = 13\)

Solving for (y):

\(y + 15 = -8\)

\(y = -8 - 15\)

\(y = -23\)

Hence, the pre -image has a coordinate of \((13,-23)\)

Answer:

A.true

Step-by-step explanation:

The domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.

Answer:

5

Step-by-step explanation:

Answer:

7.9%

Step-by-step explanation:

The formula is P=x time 100, divided by y

the x is $0.25

the y is $3.15

0.25x100=25

25/3.15=7.936

rounded to the tenths place it's 7.9

Answer:

x = 46

Step-by-step explanation:

130 is the exterior angle of the triangle,

Its interior angle

= 180 - 130

= 50

96 is the exterior angle of the triangle,

Its interior angle

= 180 - 96

= 84

Now,

x, 50 and 84 are the interior angles,

Sum of interior angles of a triangle is 180,

50 + 84 + x = 180

134 + x = 180

x = 180 - 134

x = 46

Answer:

x = 46 degrees.

Step-by-step explanation:

The  base angles are 180 - 96 = 84 degrees

and 180 - 130 = 50 degrees.

As there are 180 degrees in a triangle x = 180 - (84 + 50)

= 180 - 134

= 46 degrees,

The stem and leaf for the data values is

0       | 3   8

1        | 2  2   4

2       | 0  1   3  6

3       | 4

From the question, we have the following parameters that can be used in our computation:

Data values:

3 8 12 12 14 20 21 23 26 34

Sort in order of tens

So, we have

3 8

12 12 14

20 21 23 26

34

Next, we draw the stem and leaf as follows:

a | b

Where

a = stem and b = leave

number = ab

Using the above as a guide, we have the following:

0       | 3   8

1        | 2  2   4

2       | 0  1   3  6

3       | 4

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Answer:

you have it correct sir

Step-by-step explanation:

Answer:

Step-by-step explanation:1) Find the domain of the given function. f(x) = square root of quantity x plus three divided by quantity x plus eight times quantity x minus two.

using a graphical tool    see the attachment  

the answer is C) x ≥ -3, x ≠ 2  

2. Identify intervals on which the function is increasing, decreasing, or constant.

g(x) = 2 - (x - 7)2

using a graphical tool    

see the attachment

the answer is  C) Increasing: x < 7; decreasing: x > 7

3. Perform the requested operation or operations.

f(x) = 4x + 7, g(x) = 3x2

Find (f + g)(x).

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 4x + 7 + 3x^2

(f + g)(x) = 3x^2 + 4x + 7

The answer is  C) 4x + 7 + 3x2

4. Perform the requested operation or operations.

f(x) = x minus five divided by eight. ; g(x) = 8x + 5, find g(f(x)).

f(x)=(x-5)/8    g(x)=8x+5

g(f(x))=8((x-5)/8)+5=x-5+5=x

the answer is  B) g(f(x)) = x  

5. Find f(x) and g(x) so that the function can be described as y = f(g(x)).y = nine divided by square root of quantity five x plus five.

y=f(g(x))=9/((5x+5) ^1/2)

let do

g(x)=5x+5...........so

f(x)= 9/( x^1/2)

the answer is  A) f(x) = nine divided by square root of x. , g(x) = 5x + 5

6. A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?

Original size- >4km*4km=16 km2

4 times its original size---------------4*(16km2)-----64 Km2----------- > 8 km by 8 Km

Therefore

3km----------------------------- 1 sec

(8km-4km)---------------------x

X=4/3=1.33 sec

The answer is D) 1.33 sec

7. Find the inverse of the function.

f(x) = the cube root of quantity x divided by seven. - 9

to solve, replace f(x) with y , switch x and y, solve for y and replace y with f⁻¹(x)

f(x)=((x/7)-9) ^(1/3)

replace f(x) with y

y=((x/7)-9) ^(1/3)

switch x and y

x=((y/7)-9) ^(1/3)

solve for y

x^3=((y/7)-9)

x^3+9=y/7

y=7(x^3+9)

the answer is C) f-1(x) = 7(x3 + 9)  

8. Describe how the graph of y= x2 can be transformed to the graph of the given equation.y = (x - 14)2 – 9

using a graphical tool     see the attachment  the answer is C) Shift the graph of y = x2 right 14 units and then down 9 units  

9. Describe how to transform the graph of f into the graph of g. f(x) = alt='square root of quantity x minus nine.' and g(x) = alt='square root of quantity x plus five. '

f(x)=(x-9) ^1/2  g(x)=(x+5) ^1/2

using a graphical tool     see the attachment

the answer is C) Shift the graph of f left 14 units

10. If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.

f(x) = -16x5 - 7x4 – 6

The answer is B) Degree: 5; leading coefficient: -16

11. Write the quadratic function in vertex form.y = x2 + 4x + 7

Complete the square on the right side of the equation

Use the form ax2+bx+cax2+bx+c, to find the values of a, b, and c.

a=1,b=4,c=7

Consider the vertex form of a parabola.

a(x+d)2+e

Find the value of dd using the formula d=b/2a

d=4/(2*1)=2

Find the value of e using the formula e=c−b2/4a

e=7−4=3

Substitute the values of a, d, and e into the vertex form a(x+d)2+e

(x+2)2+3

The answer is A) y = (x + 2)2+ 3

12. Find the zeros of the function.

f(x) = 3x3 - 12x2 - 15x

using a graphical tool   (see the attachment)x1=-1

x2=0

x3=5

The answer is C) 0, -1, and 5

13. Find a cubic function with the given zeros.7, -3, 2

X1=7

X2=-3

X3=2

f(x)=(x-7)(x+3)(x-2)=(x2-4x-21)(x-2)=x3-6x2-13x+42

the answer is C) f(x) = x3 - 6x2 - 13x + 42  

14. Find the remainder when f(x) is divided by (x - k).f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3

f(x)=7(3)4+12(3)3+6(3)2-5(3)+16=946

 The answer is the B) 946

15.  Use the Rational Zeros Theorem to write a list of all potential rational zerosf(x) = x3 - 10x2 + 4x - 24

The constant term of () is -24

The leading coefficient is 1.

We have to only consider the factors of the constant (leading coefficient = 1)

The factors are 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24

The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

Answer:

2.5 minutes per quesiton

Step-by-step explanation:

75 minutes to take 30 quesitons means you divide the time equally so

75/30

Answer:

If you need help with questions I'd be happy to help.

Step-by-step explanation:

The estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

To estimate the monthly average daily radiation on a horizontal surface H in June in Amman, we can use the following equation:

\([H = S \times H_s \times \frac{\sin(\phi)\sin(\delta)+\cos(\phi)\cos(\delta)\cos(H_a)}{\pi}]\)

where:

S is the solar constant, which is approximately equal to 1367 W/m(^2);

\(H(_s)\) is the average number of sunshine hours per day in Amman in June, which is given as 10 hours;

(\(\phi\)) is the latitude of the location, which for Amman is approximately 31.9 degrees North;

(\(\delta\)) is the solar declination angle, which is a function of the day of the year and can be calculated using various methods such as the one given in the answer to Q1;

\(H(_a)\) is the hour angle, which is the difference between the local solar time and solar noon, and can also be calculated using various methods such as the one given in the answer to Q1.

Substituting the given values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(\delta)+\cos(31.9)\cos(\delta)\cos(H_a)}{\pi}]\)

Since we are only interested in the monthly average daily radiation, we can assume an average value for the solar declination angle and the hour angle over the month of June. For simplicity, we can assume that the solar declination angle (\(\delta\)) is constant at the value it has on June 21, which is approximately 23.5 degrees North. We can also assume that the hour angle \(H(_a)\) varies linearly from -15 degrees at sunrise to +15 degrees at sunset, with an average value of 0 degrees over the day.

Substituting these values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(23.5)+\cos(31.9)\cos(23.5)\cos(0)}{\pi}]\)

Simplifying the equation, we get:

\([H \approx 7.35 \text{ kWh/m}^2\text{/day}]\)

Therefore, the estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

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Answer:

Step-by-step explanation:

The domain is:

The range is:

Correct choice is C

The domain is:

The range is:

Correct choice is E

Answer:

A= 90 , b= 12 , c=60,

Step-by-step explanation:

cuz im smart like that

Answer:

1.0625 seconds

Step-by-step explanation:

Given that:

Initial velocity of Belinda, \(v_0=17\ ft/sec\)

Height in feet of Belinda above the trampoline is given as the formula:

\(d(t) = v_0t-16t^2\)

Where \(t\) is the time in seconds.

To find:

Time taken by Belinda to come back to trampoline = ?

Solution:

When Belinda will come back to trampoline, the height will be zero.

Putting \(d(t) =0\)

We have the equation as:

\(0 = 17t-16t^2\\\Rightarrow 16t^2-17t=0\\\because t\neq0\\\Rightarrow 16t=17\\\Rightarrow t=\dfrac{17}{16}\\\Rightarrow t =1.0625\ seconds\)

Therefore, the answer is: 1.0625 seconds

Answer:

Step-by-step explanation:

Answer:  Factors of 44: 1, 2, 4, 11, 22, 44

Step-by-step explanation: coz I juss know

Answer:

\(\sf P(A \cap B)=\dfrac{1}{4}\)

Step-by-step explanation:

\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)

Event A - spinning violet or yellow

Assuming that the spinner has 4 different colors (red, orange, violet and yellow) - see attachment.

\(\implies \sf P(A) = \dfrac{2}{4}=\dfrac{1}{2}\)

Event B - rolling an even number

Assuming the number cube has 6 sides numbered 1, 2, 3, 4, 5 and 6.  Therefore, the even numbers are 2, 4 and 6.

\(\implies \sf P(B)=\dfrac{3}{6}=\dfrac{1}{2}\)

Events A and B are independent events as the outcome of one event does not affect the outcome of the other event.

For independent events A and B:

\(\implies \sf P(A \cap B)=P(A)P(B)\)

To find P(A and B), substitute the found values of P(A) and P(B):

\(\implies \sf P(A \cap B)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}\)

P(A)

P(B)

3 even nos are 2,4,6

P(A\(\cap\))

Answer:

b. x = -2

Step-by-step explanation:

x - 8 = -10

x = -10 + 8

x = -2

The expression does not have like terms that can be combined, so it remains as is:

4g² + 7ab - 2b²

5x8 - 5 can be simplified as follows:

5x8 - 5 = 40 - 5 = 35

x² - x² - x + 1 can be simplified as follows:

The x² terms cancel out:

x² - x² - x + 1 = -x + 1

6413 - 1 is a subtraction of two numbers:

6413 - 1 = 6412

4g² + 7ab - 2b² can be simplified further:

The expression does not have like terms that can be combined, so it remains as is:

4g² + 7ab - 2b²

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The measure of the arc KL and MJ in the given attached figure is equal to = 20° and 80°.

Measure of angle MEJ = 30 degrees

Measure of angle MFJ = 50 degrees

In the attached figure apply angle intersecting secant theorem we get,

m∠MEJ = 1/2(MJ - KL)

Substitute the value of m∠MEJ = 30 degrees we get,

⇒30° = 1/2(MJ - KL)

Multiply both the side by 2 we get,

⇒60° = MJ - KL

⇒ KL = MJ - 60°

Now , we have from the attached figure,

m∠MFJ = 1/2(MJ + KL)

⇒50° = 1/2(MJ + MJ - 60°)

⇒100° = 2MJ - 60°

⇒2MJ = 100° + 60°

⇒2MJ = 160°

⇒MJ = 160°/2

⇒MJ = 80°

⇒KL = MJ - 60°

       = 80° - 60°

This implies that,

KL = 20°

Therefore, the measures of the arcs are equal to measure of arc KL = 20° and MJ = 80°.

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The above question is incomplete, the complete question is:

Given: m∠MEJ=30, m∠MFJ=50

Find the measure of the arc KL, MJ.

Attached figure.

Answer:  sin(2tan^-1(u/6)) = (2u) / [(u² + 36) * √(u² + 36)]

Step-by-step explanation:  We can use the trigonometric identity:

tan(2θ) = (2 tan θ) / (1 - tan² θ)

to rewrite sin(2tan^-1(u/6)) as an algebraic expression.

Step 1: Let θ = tan^-1(u/6). Then we have:

tan θ = u/6

Step 2: Substitute θ into the formula for tan(2θ):

tan(2θ) = (2 tan θ) / (1 - tan² θ)

tan(2 tan^-1(u/6)) = (2 tan(tan^-1(u/6))) / [1 - tan²(tan^-1(u/6))]

tan(2 tan^-1(u/6)) = (2u/6) / [1 - (u/6)²]

tan(2 tan^-1(u/6)) = (u/3) / [(36 - u²) / 36]

Step 3: Simplify the expression by using the Pythagorean identity:

1 + tan² θ = sec² θ

tan² θ = sec² θ - 1

1 - tan² θ = 1 / sec² θ

tan(2 tan^-1(u/6)) = (u/3) / [(36 - u²) / 36]

tan(2 tan^-1(u/6)) = (u/3) * (6 / √(36 - u²))²

tan(2 tan^-1(u/6)) = (u/3) * (36 / (36 - u²))

Step 4: Rewrite the expression in terms of sine.

Recall that:

tan θ = sin θ / cos θ

sin θ = tan θ * cos θ

cos θ = 1 / √(1 + tan² θ)

Using this identity, we can rewrite the expression for tan(2tan^-1(u/6)) as:

sin(2tan^-1(u/6)) = tan(2tan^-1(u/6)) * cos(2tan^-1(u/6))

sin(2tan^-1(u/6)) = [(u/3) * (36 / (36 - u²))] * [1 / √(1 + [(u/6)²])]

simplify to get:

sin(2tan^-1(u/6)) = (2u) / [(u² + 36) * √(u² + 36)]

Answer:

  x = 2+1/3i or 2-1/3i

Step-by-step explanation:

The equation of interest can be written in vertex form as ...

  9(x -2)² +1 = 0

so its solutions can be found by subtracting 1, dividing by 9, taking the square root, then adding 2.

  x = 2 ± √(-1/9)

In the desired form, the zeros of the given expression are ...

  x = 2 +1/3i or 2 -1/3i

Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)