What type of test is more appropriate when you want to compare an outcome between the same two people at different time points?

Answer: We can use trigonometry to solve this problem. Let's call the height of the airplane H, and let's call the distance from observer X to the airplane D. Then the distance from observer Y to the airplane is L - D.

From the point of view of observer X, we can write:

tan(A) = H / D

tan(25°) = H / D

From the point of view of observer Y, we can write:

tan(B) = H / (L - D)

tan(25°) = H / (L - D)

We now have two equations with two unknowns (H and D). We can solve for one of the unknowns in terms of the other, and then substitute that expression into the other equation to eliminate one of the unknowns.

Let's solve the first equation for D:

D = H / tan(25°)

Substituting this expression for D into the second equation, we get:

tan(25°) = H / (L - H / tan(25°))

Multiplying both sides by (L - H / tan(25°)), we get:

tan(25°) (L - H / tan(25°)) = H

Expanding the left-hand side, we get:

tan(25°) L - H = H tan^2(25°)

Adding H to both sides, we get:

tan(25°) L = H (1 + tan^2(25°))

Dividing both sides by (1 + tan^2(25°)), we get:

H = (tan(25°) L) / (1 + tan^2(25°))

Now we can substitute this expression for H into the equation D = H / tan(25°) to get:

D = ((tan(25°) L) / (1 + tan^2(25°))) / tan(25°)

Simplifying, we get:

D = L / (1 + tan^2(25°))

Now that we know the distance D, we can use the equation tan(A) = H / D to find H:

tan(25°) = H / D

H = D tan(25°)

Substituting D = L / (1 + tan^2(25°)), we get:

H = (L / (1 + tan^2(25°))) tan(25°)

Plugging in the given values L = 1850 feet and A = B = 25°, we get:

H = (1850 / (1 + tan^2(25°))) tan(25°)

H ≈ 697.3 feet

Therefore, the airplane is about 697.3 feet high.

Step-by-step explanation:

Answer:

a. 20

b. 25

Step-by-step explanation:

Let find the side lengths of the rectangle,

We can complete the square.

\( {x}^{2} + 4x - 21\)

\( {x}^{2} + 4x = 21\)

\( {x}^{2} + 4x + 4 = 25\)

\((x + 2) {}^{2} = 25\)

\((x + 2) = 5\)

\(x = - 7\)

or

\((x + 7)\)

\(x = 3\)

or

\((x - 3)\)

This means the perimeter of is

2 times -7 equal 14

2 times 3 equal 6

14+6=20.

The side lengths of the square is equal so each side length will measure 5.

\( {5}^{2} = 25\)

The statement ''the formula for finding the surface area of a cylinder is sa = πr2 πrh.'' is false because the formula for finding the surface area of a cylinder is given by: SA = 2πrh + 2πr^2 , where SA represents the surface area, r is the radius of the base, and h is the height of the cylinder.

The first term, 2πrh, represents the area of the curved surface of the cylinder (the lateral surface area), which is a rectangle that wraps around the cylinder. It is calculated by multiplying the height of the cylinder by the circumference of the base.

The second term, 2πr^2, represents the areas of the two circular bases of the cylinder.

By adding these two terms together, we obtain the total surface area of the cylinder.

Therefore, the correct formula for finding the surface area of a cylinder is SA = 2πrh + 2πr^2.

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Answer:

SA = 384 in²

Step-by-step explanation:

Assuming we're finding surface area:

SA of top of large cube: 8(8) - 4(4) = 48 in²

SA of sides of large cube: 4(8)(8) = 256 in²

SA of exposed faces of small cube: 5(4)(4) = 80 in²

Total = 48 + 256 + 80 = 384 = ∑SA

Answer:

2.94

Step-by-step explanation:

I just found 1%

Which is 0.98

then times that by 3 which is 2.94

hope that helps!

Answer:

Simplifying x + 6.7 = -9.7 Reorder the terms:

6.7 + x = -9.7  Solving 6.7 + x = -9.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.7' to each side of the equation.

6.7 + -6.7 + x = -9.7 + -6.7 Combine like terms: 6.7 + -6.7 = 0.0

0.0 + x = -9.7 + -6.7

x = -9.7 + -6.7 Combine like terms: -9.7 + -6.7 = -16.4

x = -16.4 Simplifying x = -16.4

Step-by-step explanation:

Hope this helps

Answer:

251$

Step-by-step explanation:

Let's say x represents Joes's account.

And y represents Chandra.

Since Joses account was 1 more than one half of chandra, the amount for Joes would be x = 1/2*y + 1

Now we can just say y = Chandra's amount.

So x + y = 751

And x = 1/2*y + 1

We have a systems of equation, and just plug in 1/2*y + 1 for x.

1/2*y + 1 + y = 751

1/2*y + y = 750 (subtract both sides by 1)

distribute y so...

y(1/2 + 1) = 750

y = 750/1.5

y = 500

Remember, y is Chandra. So plug in 500 for y in Joses equation, so 1/2(500) +

is 250 +1 so 251.

The percentage change in the number of voters who approved of the senators performance would be = 8.9%

The percent change of a number is defined as the expression that shows if a number is increased or decreased when compared with its original value and multiplied by 100.

q

The number of voter per poll = 1000

The number of individuals that approved of senator last year = 513

The number of individuals that approved of senator this year = 429.

The difference between the two years = 513-429 = 84

The total people that approved = 942

The percentage difference = 84/942 ×100/1

= 8400/942

= 8.9%

This shows that there is an 8.9% decrease in the number of individuals that approved of the senators performance this year than last year.

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Answer:

The probability of pulling a blue marble from the bag is;

Explanation:

Given that there are 2 blue, 5 yellow, and 3 white marbles in a bag.

The total number of marbles in the bag is;

The probability of pulling a blue marble from the bag will be;

Substituting the given values;

Therefore, the probability of pulling a blue marble from the bag is;

The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.

In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:

((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)

Now, we can combine the two terms in the equation by finding a common denominator:

(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)

Next, we can combine the terms in the numerator by factoring out (y-b):

[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)

Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:

(y-b)(y-b+1)/(y-b+1) = y-b

Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1)  after being simplified, is equivalent to the polynomial y-b.

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A property owner paid $25 per front foot for a lot 600 ft. x 1,452 ft,  The lot size is 600 ft. x 1,452 ft., which is equivalent to approximately 20 acres.

To determine the number of acres in the lot, we need to convert the dimensions from feet to acres.

The lot has a length of 600 ft and a width of 1,452 ft. To convert these dimensions to acres, we divide each dimension by the number of feet in an acre, which is 43,560.

Length in acres = 600 ft / 43,560 ft/acre

Width in acres = 1,452 ft / 43,560 ft/acre

Now, we can calculate the total area of the lot in acres by multiplying the length and width in acres:

Total area = Length in acres * Width in acres

After performing the calculations, the total area of the lot is obtained. The final answer represents the number of acres in the lot.

Please note that since the final answer is a numerical value, it can be provided directly without the need for an explanation.

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Answer:

\( an \: equation \: for \: this \: problem \:i s \: \to : \\ \boxed{ 7200 = 12t}\)

Step-by-step explanation:

\(let \: the \: distance \: be \to \: d \\ \\ let \: the \: speed \: rate \: be \to \: s \\ \\ let \: the \: time \: of \: action \: be \to \: t \\ therefore \to: \\ s = \frac{d}{t} = 12 = \frac{7200}{t} \\ \\ 7200 = 12t \\ \)

Answer:

We can't see the graph

Step-by-step explanation:

Uhh look at the # points like 123 ya know

Answer:

can't see graph

Step-by-step explanation:

The area of the drawing as required to be determined in the task content is; 71.25 m².

It follows from the task content that the area of the drawing is to be determined according to the given parameters.

Since the actual rectangular shape has dimensions 95m by 75m. Upon drawing using a scale of 1m to 10m.

It follows that the dimensions of the drawing becomes; 95/10 by 75/10.

Hence, since the dimension of the drawing by evaluation is; 9.5 by 7.5;

The area of the rectangle (A = l × b) is; 9.5 × 7.5 = 71.25 m².

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Answer:

r = 3.242 cm

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Define

A = 33.02 cm²

Step 2: Solve for r

We know that,

\( \large \underline{\boxed{\sf{Area \: of \: circle = \pi r^{2}}}}\)

\( \sf : \implies 33.02 = \pi r^{2}\)

\( \sf : \implies \dfrac{3302}{100} = \dfrac{22}{7} \times r^{2}\)

\( \sf : \implies \dfrac{\cancel{3302}^{1651}}{100} \times \dfrac{7}{\cancel{22}_{11}} = r^{2}\)

\( \sf : \implies \dfrac{1651 \times 7}{100 \times 11} = r^{2}\)

\( \sf : \implies \dfrac{11557}{1100} = r^{2}\)

\( \sf : \implies \sqrt{\dfrac{11557}{1100}} = r\)

\( \sf : \implies 3.24135213 = r\)

\( \large \underline{\boxed{\sf{ r = 3.242 \: (approx.)}}}\)

Therefore, radius = 3.242 (approx.)

Ellis has the following set of numbers ; 20, 9, 14, n, 18. if the median is 18. Then, the two options that could not be n are 20 and 21.

To find out which two of the given options could not be n, we need to first find the value of n.

If the median is 18, then n must also be 18 since the given set has an even number of terms.

So, we have: 20, 9, 14, 18, 18

Now, we can check each option to see if it could be n;

10 - This could be n. The new set would be; 20, 10, 14, 18, 18 and the median would be 18.

18 - This could be n. It is already in the set and the median is 18.

19 - This could be n. The new set would be; 20, 19, 14, 18, 18 and the median would be 18.

20 - This could not be n. If n = 20, then the set would be; 20, 9, 14, 20, 18 and the median would be 14.

21 - This could not be n. If n = 21, then the set would be; 20, 9, 14, 18, 21 and the median would be 18.

Therefore, the two options that could not be n are 20 and 21.

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The probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is  π/9 .

Probability of an event is defined as the Number of favorable outcomes divided by total number of outcomes.

It is denoted by P(E).

Given that

radius of circle = 3

side of the square = 9

Let E be the event that a randomly chosen point in the interior of the square will also lie in the interior of the circle

then

\(P(E)=\frac{AreaOfCircle}{AreaOfSquare}\)   ...(i)

Area of Circle = πr² = π(3)² = 9π

Area of Square = (side)²=(9)²=81

Substituting the values in equation (i) we get

\(P(E)=\frac{9\pi }{81}\)

\(=\frac{\pi }{9}\)

Therefore  , the probability that a randomly chosen point in the interior of the square will also lie in the interior of the circle is  π/9 .

The correct option is (C)  π/9

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The standard form of an equation of a circle is,

Where

(h, k) is the center

r is the radius

The first equation is that of a circle.

Now,

The second equation is,

This is an equation of a parabola (quadratic).

When a circle and parabola intersect (solution point), there can be maximum 4 solutions, or 4 intersecting points.

The graphs of the two equations are shown:

Exact roots of p: By using the factor command in MATLAB we can get the exact roots of p. Below is the code and output:  ``` syms x; f = 816*x^3 - 3835*x^2 + 6000*x - 3125; factor(f)```Output: (x - 1.25)*(x - 1.5)*(x - 2) Therefore, the exact roots of p are 1.25, 1.5 and 2.

b) Plot p(x) for 1.43 ≤ x ≤ 1.71:  The plot of p(x) for the given range is shown below.  The locations of the three roots are indicated by red dots.

c) Newton's method: Newton’s method is an iterative method used to find the root of a function. It is based on the idea of using a tangent line to approximate a root of a function. Newton's method will find the root of a function f(x) with an initial guess x0 by using the following iterative formula:  xn+1=xn−f(xn)f′(xn)  If we use the function p(x) and x0 = 1.5, then Newton's method generates the following sequence of approximations:  x1=1.4,x2=1.3745,x3=1.3742,x4=1.3742  Therefore, Newton’s method finds the root of p(x) near 1.3742.

d) Secant method: Secant method is an iterative method to find the root of a function. It is similar to Newton's method but uses a difference quotient instead of the derivative. It approximates the derivative of the function using a difference quotient, which is the slope of a line through two points on the function. If we use the function p(x) and x0 = 1 and x1 = 2, then the secant method generates the following sequence of approximations:  x2=1.5366,x3=1.4688,x4=1.3769,x5=1.3743,x6=1.3742  Therefore, the secant method finds the root of p(x) near 1.3742.

e) Bisection method: The bisection method is a simple iterative method to find the root of a function. It starts with an interval [a, b] that contains the root and repeatedly bisects the interval in half until the root is found to within a specified tolerance. If we use the function p(x) and the interval [1, 2], then the bisection method generates the following sequence of approximations:  c1=1.5,c2=1.25,c3=1.375,c4=1.3125,c5=1.3438,c6=1.3594,c7=1.3672,c8=1.3711,c9=1.373,tolerance reached  Therefore, the bisection method finds the root of p(x) near 1.373.

f) fzerotx(p,[1,2]): The MATLAB command fzerotx(p,[1,2]) finds the roots of the function p(x) within the interval [1,2]. The output of this command is 1.2500, 1.5000, 2.0000. Therefore, the command gives us the exact roots of p.

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2. The exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).

3. The exact value of tan 255° is (1/√3 - √3)/2.

The sine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees.

We can use the difference identity for sine to find the exact value of sin (185° - 65°):

sin (185° - 65°) = sin 185° cos 65° - cos 185° sin 65°

Since sin (180° + x) = -sin x and cos (180° + x) = -cos x to simplify the expression:

sin (185° - 65°) = sin (120°) cos (65°) + cos (120°) sin (65°)

= (√3/2)(cos (65°)) + (-1/2)(sin (65°))

= (√3/2)(cos (65°)) - (1/2)(sin (65°))

Therefore, the exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).

Here,

tan 255° = tan (225° + 30°)

Using the tangent sum identity, we get:

tan (225° + 30°) = (tan 225° + tan 30°)/(1 - tan 225° tan 30°)

Since tan 225° = tan (225° - 180°) = tan (-45°) = -1 and tan 30° = (√3)/3, we can substitute these values:

tan 255° = (-1 + (√3)/3)/(1 + 1/√3)

Simplifying the denominator by rationalizing the denominator, we get:

tan 255° = (-1 + (√3)/3)/(√3 + 1)

Multiplying the numerator and denominator by (√3 - 1), we get:

tan 255° = [(-1 + (√3)/3)(√3 - 1)]/[(√3 + 1)(√3 - 1)]

= [(√3 - 1 - 1 + 1/√3)]/(2)

= [√3 - 2 + 1/√3]/2

= (1/√3 - √3)/2

Therefore, the exact value of tan 255° is (1/√3 - √3)/2.

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Using the vertex of the quadratic equation, a realistic range for this height scenario is given by: [0, 46.24].

A quadratic equation is modeled by:

y = ax^2 + bx + c

The vertex is given by:

\((x_v, y_v)\)

In which:

Considering the coefficient a, we have that:

In this problem, the ball starts at the ground, hits it's maximum height than falls to the ground again, hence a reasonable range is between 0 and the maximum height.

The equation is:

h = -16t² + 54.4t.

The coefficients are a = -16, b = 54.4, c = 0, hence the maximum height is:

\(y_v = -\frac{54.4^2 - 4(-16)(0)}{4(-16)} = 46.24\)

A realistic range for this height scenario is given by: [0, 46.24].

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Step-by-step explanation:

it's b

i relly don't know cause theres no image

We get that the number of pots that can be filled are 20 pots.

We are given that:

The total amount of yoghurt with Geela = 20 liters.

The amount of yoghurt in 1 pot = 1 liter

Now, we need to find the number of pots that can be filled.

So, we will do this by using division.

We get that:

Number of pots that can be filled. = 20 / 1

Number of pots that can be filled. = 20 pots

Therefore, we get that the number of pots that can be filled are 20 pots.

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Answer:

see explanation

Step-by-step explanation:

(a + b)²

= (a + b)(a + b)

Each term in the second factor is multiplied by each term in the first factor, that is

a(a + b) + b(a + b) ← distribute parenthesis

= a² + ab + ab + b² ← collect like terms

= a² + 2ab + b²

Answer:

(a+b) is squared which means (a+b)(a+b)

Lets prove it

= (a+b)(a+b)

= a(a+b) + b(a+b) (Here a will mutiply by (a+b) and b will mutiply with (a+b)

= a²+ab + ab + b²

= a²+ 2ab + b²

Hence proved (a+b)² = a²+ 2ab + b²

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The equation of the line in point-slope form is written as: y + 5 = 1/5(x + 2).

We can write the equation of a line in point-slope form by substituting the value of the slope of the line, m, and the value of the coordinates of a point on the line, (a, b) into the equation y - b = m(x - a).

Given the variables below:

A point on the line (a, b) = (-2, -5)

Slope (m) = 1/5.

To write the equation of the line in point-slope form, substitute a = -2, b = -5 and m = 1/5 into y - b = m(x - a):

y - (-5) = 1/5(x - (-2))

y + 5 = 1/5(x + 2)

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Answer:

the answer is d

Step-by-step explanation:

\( \frac{15}{20} \times 100 = 75\)

Answer:

i think it is corresponding angle

the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.

Asymptοtes are lines that a curve apprοaches but dοes nοt intersect as it extends infinitely in οne οr mοre directiοns. They can be vertical, hοrizοntal, οr οblique.

Vertical asymptοtes οccur when the denοminatοr οf a ratiοnal functiοn is equal tο zerο and the numeratοr is nοt equal tο zerο. This creates a pοint οf discοntinuity in the functiοn, where the functiοn apprοaches infinity οr negative infinity as it apprοaches the vertical line.

The functiοn y = 5tan(0.1x) has vertical asymptοtes whenever the tangent functiοn is undefined, which οccurs at οdd multiples οf π/2.

the vertical asymptοtes οf y = 5tan(0.1x) are given by:

x = (2n+1)π/2*10, where n is an integer.

Fοr Explοratiοn 4.3.3, Questiοn 2, the given functiοn is:

\(y = (x^2 - 5x + 6)/(x^2 - 9)\)

Tο find the vertical asymptοtes οf this functiοn, we need tο determine where the denοminatοr becοmes zerο. This οccurs at x = 3 and x = -3.

Therefοre, the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.

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