Let the random variables X, Y have joint density function

3(2−x)y if0
f(x,y) =

(a) Find the marginal density functions fX and fY.

(b) Calculate the probability that X + Y ≤ 1

The probability of a standard normal variable being less than -2.65 is 0.0040. Therefore, P(x < 979) = 0.0040.

To solve this problem, we use the central limit theorem since we have a large enough sample size.

a) Probability that a single randomly selected value is less than 979 dollars

To find the probability that a single randomly selected value is less than 979 dollars, we standardize the value and use the standard normal distribution:

z = (979 - 1046) / 206 = -0.3233

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than -0.3233 is 0.3736. Therefore, P(X < 979) = 0.3736.

b) Probability that a sample of size n = 66 is randomly selected with a mean less than 979 dollars

To find the probability that a sample of size n = 66 is randomly selected with a mean less than 979 dollars, we use the central limit theorem.

The mean of the sampling distribution of the sample means is the same as the population mean, which is 1046 dollars. The standard deviation of the sampling distribution of the sample means is the standard error, which is:

SE = σ / sqrt(n) = 206 / sqrt(66) = 25.23

To standardize the sample mean, we use the formula:

z = (x - μ) / SE = (979 - 1046) / 25.23 = -2.65

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than -2.65 is 0.0040. Therefore, P(x < 979) = 0.0040.

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To find the temperature of the sun, we'll use the ideal gas law equation, which is PV = nRT. We're given pressure (P), density (ρ), average molecular weight (M), and the gas constant (R). First, we'll find the number of moles (n) and then solve for temperature (T). After the calulation the answer is found out to be option b which is approximately 2.4 x 10^7 K.

1. Calculate the number of moles (n) using the formula n = ρ/M.
  n = 1.4 g/cc / 2 g/mol = 0.7 mol/cc
2. Rearrange the ideal gas law equation to solve for temperature (T): T = PV / nR
3. Plug in the values:
  P = 1.4 x 10^10 atm
  V = 1 cc (since we are considering 1 cc of the gas)
  n = 0.7 mol
  R = 8.4 x 10^7 erg/mol/K
  T = (1.4 x 10^10 atm) x (1 cc) / (0.7 mol) x (8.4 x 10^7 erg/mol/K)
4. Perform the calculation:
  T = 1.4 x 10^10 / (0.7 x 8.4 x 10^7) = 2.38 x 10^7 K
The temperature of the sun is approximately 2.4 x 10^7 K (option b).

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The value of tan C in the figure is 7/24

Information from the question

The value of tan x is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The figure describes a right angle triangle of

hypotenuse = 50

opposite = ?

adjacent = 14

Using cos, CAH for angle C

sin C = Opposite / hypotenuse

sin C = 14 / 50

x = arc sin (14/50)

Solving for tan x

tan (arc sin (14/50)) = 7/24

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Answer:  B

Step-by-step explanation:

If you fold that bottom side up.  the door is not on the closer side to the window. so B is wrong because the door is near the window.

The ONB for the given plane in R3 is ū = [-5/√(26), 1/√(26), 0] and ī = [25/(√(26/13)), -5/(√(26/13)), 0].

To find an orthonormal basis for the plane x + 5y + 4z = 0, we first solve the system and get the parametric solution

x = -5t - 4s

y = t

z = s

Assigning parameters s and t to the free variables and writing the solution in vector form as su + tv, we get

[-5t - 4s, t, s] = t[-5, 1, 0] + s[-4, 0, 1]

Taking u = [-5, 1, 0] and v = [-4, 0, 1], we normalize u to have norm 1 by dividing it by its length

||u|| = √(26)

ū = [-5/√(26), 1/√(26), 0]

To find the component of v orthogonal to u, we take the dot product of v and u, and divide it by the dot product of u and u, and then multiply u by this scalar

v - ((v · u) / (u · u))u

v · u = -5

u · u = 26

v - (-5/26)[-5, 1, 0]

v - [25/26, -5/26, 0]

Finally, we normalize this vector to have norm 1

||v - proj_u v|| = √(26/13)

ī = [25/(2√(26/13)), -5/(2√(26/13)), 0]

Therefore, the orthonormal basis for the plane x + 5y + 4z = 0 is ū = [-5/√(26), 1/√(26), 0] and ī = [25/(√(26/13)), -5/(√(26/13)), 0].

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The value of y when the value of x is 1 would be 60.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using the data points contained in the table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 60/1

Constant of proportionality, k = 60.

Therefore, the required equation is given by;

y = 60x

y = 60(1)

y = 60.

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For the following  equation, L.H.S = R.H.S is proved by solving the left-hand side and equating with it with the right-hand side equation :

[tex]\frac{tan x}{1-cot x} + \frac{cot x }{1-tan x} = 1+ tan x+ cot x[/tex]

L.H.S =  [tex]\frac{tan x}{1- cot x} + \frac{cot x }{1 - tan x}[/tex]

[tex]\frac{- tan^{2}x }{1- tan x} + \frac{cot x }{1 - tan x}[/tex]

[tex]\frac{-tan^{2} x + cot x}{1 - tan x}[/tex]

Multiply [tex]\frac{tan x}{tan x}[/tex] we get,

[tex]\frac{1- tan^{3} x}{tan x (1- tan x)}[/tex]

[tex]\frac{(1 - tan x ) (1 + tan x + tan ^{2}x) }{tan x (1 - tan x )}[/tex]

[tex]\frac{( 1- tan x + tan^{2}x) }{tan x}[/tex]

Divide each term separately,

[tex]\frac{1}{tan x} + \frac{tan x}{tan x} + \frac{tan^{2}x }{tan x}[/tex]

cot x + 1 + tan x

therefore, 1+ tan x + cot x = R.H.S

L.H.S = R.H.S, hence the theory is proved.

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1. The truncation error is 0.66346 (approx)

2. the coefficient of [tex](x - 1)^2[/tex] in the expansion is 1, and the coefficient of [tex](x - 1)^4[/tex] is -1/3!.

3. [tex]H(z) = (1 - 28z^{-1} + z^{-2})/(1 - z^{-1})[/tex]

4. [tex]x(n) = [-1/(n - 5)^3 + 0.375*2^{(n-1)}]u(n-1)[/tex]

What is truncation error?

Truncation error refers to the difference between an exact or ideal mathematical result and an approximation of that result obtained through a numerical method, algorithm, or series expansion, where the approximation is truncated or rounded off at a certain point due to computational limitations.

The Maclaurin series expansion of cot(x) is given by:

[tex]cot(x) = 1/x - (x/3) - (2x^3)/45 - (2x^5)/945 + ...[/tex]

The first four terms are:

cot(x) ≈ 1/x - (x/3)

If x = 0.5, then the exact value of cot(x) is:

cot(0.5) = 1/tan(0.5) = 1/0.546302 = 1.830127

The truncation error is the difference between the exact value and the approximation:

error = cot(0.5) - (1/0.5 - (0.5/3)) = 1.830127 - 1.166667 = 0.66346 (approx)

2. We can expand xsinx - 1 in powers of x - 1 using the Maclaurin series for sin(x):

[tex]sin(x) = x - (x^3)/3! + (x^5)/5! - ...[/tex]

Multiplying by x and subtracting 1 gives:

[tex]x*sin(x) - 1 = x^2 - (x^4)/3! + (x^6)/5! - ...[/tex]

Now, replacing x with (x - 1) gives:

[tex](x - 1)*sin(x - 1) - 1 = (x - 1)^2 - ((x - 1)^4)/3! + ((x - 1)^6)/5! - ...[/tex]

So, the coefficient of [tex](x - 1)^2[/tex] in the expansion is 1, and the coefficient of [tex](x - 1)^4[/tex] is -1/3!.

3. The z-transform of h(n) is given by:

H(z) = Z{h(n)} = Z{S(n)} - 28Z{(n − 1)} + Z{S(n - 2)}

Using the z-transform properties of linearity, time shifting, and the z-transform of the unit step function, we get:

[tex]H(z) = 1/(1 - z^{-1}) - 28z^-{1}/(1 - z^{-1}) + z^{-2}/(1 - z^{-1})[/tex]

Simplifying the expression, we get:

[tex]H(z) = (1 - 28z^{-1} + z^{-2})/(1 - z^{-1})[/tex]

4. To find the sequence x(n) from the given Z-transform, we use partial fraction decomposition:

[tex]-1/(z - 5)^3 + 0.375/(1 - 0.5z)^2[/tex]

Using the z-transform property of the delayed unit step function, we get:

[tex]x(n) = [-1/(n - 5)^3 + 0.375*2^{(n-1)}]u(n-1)[/tex]

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The angles 75° and ∠2 are alternate interior angles.

Option D is the correct answer.

We have,

From the figure,

55°, ∠3, and 75° forms a straight angle.

Alternate angles are pairs of angles formed when a transversal line intersects two parallel lines.

Alternate angles are equal in measure, which means they have the same angle degree value.

So,

75° and ∠2 are alternate angles.

Thus,

75° and ∠2 are alternate angles.

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The net force on a vehicle is directly proportional to its acceleration and mass, according to Newton's Second Law of Motion. Therefore, we can use the equation F = ma, where F is the net force, m is the mass of the vehicle, and a is the acceleration.

We know that the net force on the vehicle is 1800 and its acceleration is 1.5. Substituting these values into the equation, we get:
1800 = m × 1.5

To solve for m, we need to isolate it on one side of the equation. Dividing both sides by 1.5, we get:

m = 1800 ÷ 1.5

m = 1200

Therefore, the mass of the vehicle is 1200 kilograms to the nearest kilogram

Net force = mass × acceleration

In this case, the net force on the vehicle is 1800 N (Newtons), and it is accelerating at a rate of 1.5 m/s² (meters per second squared). We can rearrange the formula to solve for mass:

Mass = net force ÷ acceleration

Now, plug in the given values:

Mass = 1800 N ÷ 1.5 m/s²

Mass ≈ 1200 kg

To the nearest kilogram, the mass of the vehicle is approximately 1200 kg.

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It is proved that if g is not cyclic, all elements of g have order 1, 2, or 3, and there must be an element of order 3.

To prove that if g is not cyclic, all elements of g have order 1, 2, or 3, and show that there must be an element of order 3, follow these steps,

1. Assume that g is a finite group and is not cyclic.
2. Recall that the order of an element a in group g is the smallest positive integer n such that a^n = e, where e is the identity element in g.
3. If g were cyclic, it would have an element a with order equal to the order of the group itself (|g|). However, we are given that g is not cyclic, so the order of any element in g must be less than |g|.
4. We now consider the possibilities for the order of elements in g. If all elements of g have order 1, then g is the trivial group, which is cyclic, contradicting our assumption.
5. If there is an element of order 2, there must be an element of order 3 as well. This is because, according to Cauchy's theorem, if a prime number p divides the order of a finite group g, then g has an element of order p. Since we have assumed that g is not cyclic, |g| must be divisible by at least two prime numbers. The smallest possible case is when |g| is divisible by the primes 2 and 3.
6. By Cauchy's theorem, since 2 and 3 both divide |g|, there must be elements in g of order 2 and order 3.
7. Therefore, if g is not cyclic, all elements of g have order 1, 2, or 3, and there must be an element of order 3.

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a.   (-∞,3) - f(x) is decreasing

   (3,∞) - f(x) is rising.

b. Local minima at x=3. No local Minima

c. The function f(x)=x²-6x is always concave upwards.

d. Concave up and does not change concavity, so, No Inflection points.

f(x)= x²-6x

f'(x) = 2x-6

f"(x) = 2

Critical point f'(x)=0

2x-6=0

x=3

Thus, we have two sub intervals over the entire number line. (-∞,3) , (3,∞)

a) sub-interval      x-value           f'(x)                           verdict

         (-∞,3)                1             2(1)-6=-4<0             f(x) is decreasing  

          (3,∞)                4            2(4)-6=2>0              f(x) is increasing

b) At x=3; Before x=3, f(x) decreasing and after x=3, f(x)

is increasing, thus Local minima at x=3.

No local Minima

c) Since f"(x)=2 Always, the function f(x)=x²-6x is always concave upwards

d) Inflection points

Since graph of function f(x)=x²-6x have only been concave up and does not change concavity,

No Inflection points.

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(a) Since a healthy person would not have excess insulin, their glucose level would not be too low. Therefore, the probability of a healthy person being suggested medication after a single test is very low, almost negligible.

(b) If each healthy person has completed two tests, then the expectation of the distribution of X would be the average of the two test results, denoted as E(X) = μ = (X1 + X2)/2, where X1 and X2 are the results of the first and second tests, respectively. Since the two test results are independent, the variance of the distribution of X would be the sum of the variances of the two tests, denoted as Var(X) = σ^2 = Var(X1) + Var(X2). The standard error of the distribution of X would be the square root of the variance, denoted as SE(X) = σ/√2.

(c) The probability that a healthy person will be suggested medication after 2 tests can be calculated as follows:
P(X1 < 40 and X2 < 40) = P(X1 < 40) * P(X2 < 40 | X1 < 40)
Since the two test results are independent, we can use the distribution from part (b) to find these probabilities.
P(X1 < 40) = P(Z < (40-μ)/σ) = P(Z < (40-(E(X))/SE(X)))
P(X2 < 40 | X1 < 40) = P(Z < (40-μ)/σ) = P(Z < (40-(E(X))/SE(X)))
Substituting the values of E(X) and SE(X), we get
P(X1 < 40) = P(Z < (40- X1 - X2)/ (2*SE(X1)))
P(X2 < 40 | X1 < 40) = P(Z < (40- X1 - X2)/ (2*SE(X2)))
Therefore, the probability of a healthy person being suggested medication after 2 tests to verify the doctor's theory can be calculated using the above formulas.

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We reject the null hypothesis and conclude that there is strong evidence to support the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

The null and alternative hypotheses are:

H_0: mu <= 42

H_a: mu > 42

Using the sample mean, sample size, and population standard deviation given, we can calculate the test statistic:

z = (x - mu) / (sigma / sqrt(n))

z = (42.85 - 42) / (2.65 / sqrt(68))

z = 2.56

Using a standard normal distribution table or calculator, we can find the critical values for each significance level:

a = 0.10: z_crit = 1.28

a = 0.05: z_crit = 1.645

a = 0.01: z_crit = 2.33

a = 0.001: z_crit = 3.09

Since our test statistic is greater than the critical value at a = 0.10 and a = 0.05, we reject the null hypothesis at these levels. However, we fail to reject the null hypothesis at a = 0.01 and a = 0.001.

To calculate the p-value, we can use a standard normal distribution table or calculator to find the probability that a z-score is greater than or equal to our test statistic:

p-value = P(Z >= 2.56)

p-value = 0.0052

Since the p-value is less than all of the given significance levels, we reject the null hypothesis and conclude that there is strong evidence to support the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

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Answer:

Step-by-step explanation:

Solve for x.

4x - 9 = 2x + 5

4x - 2x = 5 + 9

2x = 14

x = 14 : 2

x = 7

-----------------

check   (replace "x" with "7")

4 * 7 - 9 = 2 * 7 + 5                  (remember PEMDAS)

28 - 9 = 14 + 5

19 = 19

the answer is good

Answer:

hence the required value of x is 7.

For problem 1, the solution is an = n.

For problem 2, the solution is an = 3n - 1.

For problem 3 (the hard problem), we can solve for the values of a, b, and c in the quadratic equation: [tex]an^2 + bn + c = 0[/tex], where a = 5, b = 6n - 1, and c = -2.

Using the quadratic formula, we get:

[tex]n= \frac{-b±\sqrt{b^{2}-4ac }  }{2a}[/tex]

Substituting the values of a, b, and c, we get:

[tex]n= \frac{-(6n-1)±\sqrt{(6n-1)^{2}-4(5)(-2) }  }{2(5)}[/tex]

Simplifying, we get:

[tex]n = \frac{(-6n+1 ± \sqrt{36n^{2}-48n+49 } ) }{10}[/tex]

Therefore, the solution for problem 3 is:

[tex]an= 5n^{2} + \frac{-6n+1 + \sqrt{36n^{2}-48n+49 } }{10}[/tex]

or

[tex]an= 5n^{2} + \frac{-6n+1 - \sqrt{36n^{2}-48n+49 } }{10}[/tex]

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The value of x in the parallelogram is 1/3.

PQRT is a parallelogram

PT = 8x, TR = 6y, QT = 2x + 2, TS = 2y

We have to find the value of x

In a parallelogram the opposite sides are equal

8x=2x+2

Subtract 2x from both sides

6x=2

Divide both sides by 6

x=2/6

x=1/3

Hence, the value of x in the parallelogram is 1/3.

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The distance of the jot air balloon to ground is 21.62 ft.

Here, we have,

In triangle ACB:

tan36° = x/y

x  = y tan36°

In triangle ADB:

tan25° = x/y + 12

x  = y+12 * tan25°

Therefore equating both equations gives:

y tan36°  =  y+12 * tan25°

y tan36°  =  y tan25° + 12tan25°

so, we get,

y = 21.50 ft

Therefore x = 21.50*tan(36) = 15.62 ft

The distance of the jot air balloon to ground = 15.62 + 6 = 21.62 ft

Hence, The distance of the jot air balloon to ground is 21.62 ft.

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The value of j is equal to -9.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

10 = (-5 - 5)/(-10 - j)

10(-10 - j) = -10

(-10 - j) = -1

j = -10 + 1

j = -9

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Complete Question:

A line with a slope of 10 passes through the points (j, 5) and (-10,-5). What is the value of j?

If a woman pays $2.78 for some bananas and eggs. If each banana costs $0.69 and each egg costs $0.35, then she bought 4 bananas and 6 eggs.

Let's assume the woman bought x bananas and y eggs.

According to the problem, each banana costs $0.69 and each egg costs $0.35.

So the cost of x bananas would be 0.69x and the cost of y eggs would be 0.35y.

The total cost of the bananas and eggs is given as $2.78. So we can write the equation:

0.69x + 0.35y = 2.78

Now we need to solve for x and y.

We can start by multiplying the entire equation by 100 to get rid of the decimals:

69x + 35y = 278

We can also simplify the equation by dividing both sides by 1 (which doesn't change the equation):

69x/1 + 35y/1 = 278/1

Now we can use a system of equations to solve for x and y.

Let's solve for y in terms of x by isolating y on one side of the equation:

35y = 278 - 69x

y = (278 - 69x)/35

Now we can substitute this expression for y into the original equation:

0.69x + 0.35((278 - 69x)/35) = 2.78

Simplifying this equation, we get:

0.69x + 8 - 2x = 2.78

Solving for x, we get:

0.69x - 2x = 2.78 - 8

-1.31x = -5.22

x = 4

So the woman bought 4 bananas.

Now we can substitute this value for x into the expression we derived for y:

y = (278 - 69(4))/35

y = 6

So the woman bought 6 eggs.

Therefore, the woman bought 4 bananas and 6 eggs.

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The perimeter of the square based on the dimensions of the diagonal is 145.27 millimeters.

We will begin with calculating the side of square from the diagonal of square. It will form right angled triangle and hence the formula will be represented as -

diagonal² = 2× side²

Keep the value of diagonal

(37✓2)² = 2× side²

Side² = 2638/2

Side² = 1319

Side = ✓1319

Side = 36.32 millimetres

Perimeter of the square = 4 × side

Perimeter = 145.27 millimeters

Thus, the perimeter of the square is 145.27 millimeters.

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The x-coordinate of the point that the line passes through is x = 0.

We can use the point-slope form of a linear equation to solve this problem.

The slope of the line can be found using the two given points:

slope  (change in y) / (change in x)

slope = (-3 - (-9)) / (12 - x)

slope = 6 / (x - 12)

Now we can use the point-slope form of the linear equation, with the y-intercept of 6:

y - 6 = slope * (x - 0)

Substituting the slope we just found:

y - 6 = (6 / (x - 12)) * x

Simplifying:

y - 6 = 6x / (x - 12)

Multiplying both sides by (x - 12):

y(x - 12) - 6(x - 12) = 6x

Distributing:

xy - 12y - 6x + 72 = 6x

Moving the x terms to one side:

xy - 12y - 12x + 72 = 0

Now we can substitute the y-coordinate of the other given point, (-9), and solve for x:

x(-9) - 12(6) - 12x + 72 = 0

Simplifying:

-9x - 72 - 12x + 72 = 0

-21x = 0

x = 0

Therefore, the x-coordinate of the point that the line passes through is x = 0.

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Before deciding which type of business might be the most successful, you would need to gather a variety of information, including Market demand, Competitors, Industry trend, Financial projections and Target market:

Market demand: You need to identify the needs and wants of the target customers in the market.

Competitors: Analyze the competition in the market and determine what they offer, what their strengths and weaknesses are, and how you can differentiate your business from them.

Industry trends: Keep up with industry trends and identify any new or emerging technologies or trends that could affect your business.

Financial projections: Estimate the initial and ongoing costs of running your business, including overhead, staffing, marketing, and inventory. Create a financial projection that includes cash flow, income statements, and balance sheets to help determine if your business can be profitable.

Target market: Identify your target market and understand their demographics, preferences, and buying habits.

Legal requirements: Determine the legal and regulatory requirements for starting and operating a business in your location, including permits, licenses, and taxes.

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The surface area of the given cylinder is 200.96 square centimeters.

Given that the radius of the cylinder is 4 cm and the height of the cylinder is also 4 cm,

The surface area of the cylinder can be found using the formula:

SA = 2πr² + 2πrh, where r is the radius of the circular base and h is the height of the cylinder.

Substitute given values into the formula to get:

SA = 2π(4)² + 2π(4)(4)

= 2π(16) + 2π(16)

= 32π + 32π

= 64π

= 64(3.14)

= 200.96

Therefore, the surface area of the cylinder is 200.96 square centimeters.

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The complete question is as follows

What is the surface area of the cylinder?

Here, the radius of the cylinder is 4 cm and the height of the cylinder is 4 cm

Apply the formula SA = 2πr² + 2πrh.

In a direct proof, evidence is used to support a claim, On the other hand, a counterexamples is a single example that show the contradictions in a claim.

Evidence means any piece of information that supports the argument being made in a proof which could include mathematical formulas, logic, or theorems that have been previously proven.

Counterexamples are specific examples that disprove a statement made in a proof and are used to show that a proof is not valid and that the argument being made is flawed.

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Answer: (1, 5)

Step-by-step explanation:

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For a right angled triangle with known measure of sides 11.2 units and 8.5 units, the unknown value of third side, i.e, x is equals to the 7.3 units.

A right triangle or right-angled triangle is defined as a triangle in which one angle is a right angle. Therefore, one of the angles must be 90 degrees and sum all interior angles is equals to 180°. See the triangle present in above figure. It is a right angled triangle because measure of one angle is 90°.

Height of triangle = x units

Base of triangle, b = x

Length of hypotenuse of triangle = 11.2

We have to determine the value of x. Using payathagaros theorem of sides in a right angled triangle, (hypothenuse)² = (base)² + (height)²

Substitute all known values in above formula,

=> (11.2)² = x² + (8.5)²

=> 125.44 = x² + 72.25

=> x² = 125.44 - 72.25

=> x² = 53.19

=> x = 7.2931 ~ 7.3

Hence, required value is 7.3 units.

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Complete question:

The above figure complete the question. Solve for x. Round your answer to the nearest tenth.

X

8. 5

11. 2

A. The 95% confidence interval is 0.291 < p < 0.435. B. The 80% confidence interval is (0.303, 0.397). C. A 99% confidence interval is 0.613 < p < 0.703.

A. Using the formula:

CI = p ± zsqrt(p(1-p)/n)

where p is the sample proportion, n is the sample size, and z is the critical value from the standard normal distribution. For a 95% confidence level, z is 1.96.

Putting the values:

CI = 131/396 ± 1.96sqrt((131/396)(265/396)/396)

Simplifying:

CI = 0.291 < p < 0.435

Therefore, the 95% confidence interval for the population proportion p is 0.291 to 0.435.

B. For an 80% confidence level, z is 1.282.

Putting the values:

CI = 0.35 ± 1.282sqrt((0.35)(0.65)/367)

Simplifying:

CI = (0.303, 0.397)

Therefore, the 80% confidence interval for the population proportion p is (0.303, 0.397).

C. For a 99% confidence level, z is 2.576.

Putting the values:

CI = 384/600 ± 2.576sqrt((384/600)(216/600)/600)

Simplifying:

CI = 0.613 < p < 0.703

Therefore, the 99% confidence interval for the population proportion p is 0.613 to 0.703. Writing it in tri-inequality form, we get:

0.613 < p < 0.703

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The steps in order to solve the equation  5x + 4y = -14 and 3x + 6y =6 are step 1, 2, 3, and 4 respectively.

The equations 5x + 4y = -14 and 3x + 6y = 6, we have to use the steps 1, 2, 3 and 4 in the same order as stated in the question.

First, multiply Equation 1 by -3 and Equation 2 by 5, respectively, to obtain -15x - 12y = -42 and 15x + 30y = 30.

Step 2: Combine Equations 1 and 2 to take the x-variable out, resulting in 15y=-12.

Step 3: Calculate y by multiplying both sides by 15, which results in y=-4/5.

Step 4: To solve for x, enter y=-4/5 into Equation 1 or Equation 2, which will result in x = 2.

So, the correct order of the steps to eliminate x from the given equations is 1, 2, 3 and 4 respectively.

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The answer is not one of the choices provided.

The distribution of sample means follows a normal distribution with a mean equal to the population mean (11) and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

So, for a sample size of 35, the distribution of sample means is normal with a mean of 11 and a standard deviation of 4.7/sqrt(35) = 0.795.

We need to find the probability that the mean blood pressure of the 35 people will be less than 122. We can standardize the distribution of sample means to a standard normal distribution with mean 0 and standard deviation 1 using the z-score formula:

z = (x - mu) / (sigma / sqrt(n))

where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = (122 - 11) / (4.7 / sqrt(35)) = 37.98

We can then use a standard normal distribution table or calculator to find the probability of z being less than 37.98. Since the standard normal distribution is symmetric, we can also find this probability as 1 minus the probability of z being greater than 37.98.

Using a standard normal distribution table or calculator, we get:

P(z < 37.98) = 1 (to a very high degree of precision)

Therefore, the probability that the mean blood pressure of 35 people will be less than 122 is essentially 1, or 100%. The answer is not one of the choices provided.

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