4. Simplify the expression
-22f+8f-15+9

The study would use a simple random sampling because it would be easy to randomly select. The study would use cluster sampling because the of fall into naturally occurring subgroups. The study would use stratified sampling because it would be important to have members from each segment of the population.

The study is a sample survey, because the population is for it to be practical to record all of the responses.

a. The study would use a simple random sampling because it would be easy to randomly select members of the population. Simple random sampling is a type of probability sampling that is used when the population is homogenous and every member has an equal chance of being selected for the sample.

b. The study would use cluster sampling because the members of the population fall into naturally occurring subgroups. Cluster sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into naturally occurring subgroups.

c. The study would use stratified sampling because it would be important to have members from each segment of the population. Stratified sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into segments or strata based on certain characteristics.

d. The study is a sample survey, because the population is too large for it to be practical to record all of the responses. Sample survey is a type of survey that collects data from a sample of the population, rather than the entire population. This is often done when the population is too large or when it is not practical to survey the entire population.

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Answer:

  -1056.87

Step-by-step explanation:

You want to know the number that represents the change in a bank balance from +$708.88 to -$347.99.

The change in a value is found by subtracting the beginning value from the ending value:

  -$347.99 -708.88 = -$1056.87

The number -1056.87 can be used to describe the change in the account balance.

Answer:

Step-by-step explanation:

If you write 1 instead of y, x would be 5/8 so ratio is 1/5:8=8/5

The rocket’s height to the nearest hundredth when the distance between you and the rocket is 100 feet is equal to 96.83 feet.

Based on the information provided, the height h (in feet), of this rocket during its launching with respect to distance d between you and the rocket can be modeled by this quadratic function:

d(h) = √(625 + h²)

Substituting the given parameters into the quadratic function d(h), we have the following;

d(h) = √(625 + h²)

100 = √(625 + h²)

Taking the square of both sides of the quadratic function, we have the following:

100² = [√(625 + h²)]²

10,000 = 625 + h²

Rocket’s height, h² = 10,000 - 625

Rocket’s height, h² = 9,375

Rocket’s height, h = √9,375

Rocket’s height, h = 96.83 feet.

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Answer:

600 and 1200

Step-by-step explanation:

Answer:

62.5%

Step-by-step explanation:

(56 - 62) / 4 = -1.5 z score = 0.0668

(64 - 62) / 4 = 0.5 z score = 0.6915

0.6915 - 0.0668 = 0.6247

Rounded this becomes 62.5%

The probability for the data value in between 56 and 64 is 62.5%.

The z-score of a value is the count of the numbers of standard deviations between the value and the mean of set.

z-score can be calculated by the formula

z = (x - μ)/σ

where,

μ is the mean

σ is the standard deviation

x is the data point

A probability is a number that reflects the chance or likelihood that a particular event will occur.

According to the given question

Mean of a normal distribution, μ = 62

standard deviation of a normal distribution, σ = 4

Now for the data value 56, the z-score will be

z = (56 - 62) / 4 = -1.5 z score = 0.0668

So, the area under normal distribution curve z = -1.5

P(z = -1.5) = 0.0668

Similarly,

For the data value 64, the z-score will be

z-score  = (64 - 62) / 4 = 0.5

The area under normal distribution curve z = 0.5 is given by

P( z = 0.5) = 0.69

Therefore, the probability for the data value in between 56 and 64 is given by

0.6915 - 0.0668 = 0.6247 =  62.5%

Hence, the probability for the data value in between 56 and 64 is 62.5%.

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The area to the right of 0.75 (i.e., the probability that z is greater than 0.75) is: 1 - 0.7734 = 0.2266 This means that the probability of getting a value greater than 4.5 in this non-standard normal distribution is approximately 0.2266.

To answer this question, we need to use the normal distribution table. However, since the distribution is non-standard, we need to standardize the value of 4.5 using the formula: z = (x - μ) / σ where μ is the mean and σ is the standard deviation.

Substituting the given values, we get: z = (4.5 - 3) / 2 z = 0.75 Now, we need to find the probability that z is greater than 0.75. Looking at the normal distribution table, we find that the area to the left of 0.75 is 0.7734.

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Answer:

x/2x+3 + 2x +3/x = 184 /65

x(2x + 3)–1 + (2x+3)x-1 = 184/65

(2x + 3)x / (2x +3)x = 184/65

2x² + 3x / 2x² + 3x = 184/65

1x= 184/64

x = 184/64

Step-by-step explanation:

Given that: {x/(2x+3)} + {(2x+3)/x} = 184/65

⇛[{(x*x) + (2x+3)(2x+3)}/{(x)(2x+3)}] = 184/65

⇛[{x² + 2x(2x+3) + 3(2x+3)}/(2x²+3x)] = 184/65

⇛[{x² + 4x² + 6x + 6x + 9}/(2x²+3x)] = 184/65

⇛[{x² + 4x² + 12x + 9}/(2x² + 3x)] = 184/65

⇛{(5x² + 12x + 9)/(2x² + 3x)} = 184/65

On applying cross multiplication then

⇛184(2x² + 3x) = 65(5x² + 12x + 9)

Multiply the number outside of the brackets with numbers and variables in the brackets on LHS and RHS.

⇛388x² + 582x = 325x² + 780x + 584

⇛388x² + 582x -325x² - 780x - 584 = 0

⇛388x²-325x² + 582x-780x - 584 = 0

⇛63x² - 198x - 584 = 0

⇛8(7x² - 22x - 65) = 0

⇛7x² - 22x - 65 = 0

Now,

This is of the form ax² + bx + c = 0, Where, a = 7, b = -22 and c = -65

Using the quadratic formula x = [{-b±√(b²-4ac)}/2a] , we get

x = [{-(-22)±√(-22)² - 4(7)(-65)}/{2(7)]

x = [{-(-22)±√(-22*-22) - 4(7)(-65)}/{2(7)]

x = [{22 ± √(484 + 1820)}/14]

x = [{22 ± √(2304)}/14]

x = {(22 ± 48)/14}

x = {(22 + 48)/14} or {(22 - 48)/14}

x = (70/14) or (-26/14)

x = 5 or x = -13/7

Therefore, x = 5 or -13/7

Answer: Hence, the value of x for the given equation is 5 or -13/7.

Please let me know if you have any other questions.

A particle moving along the x-axis with velocity given by the function v(t) = t^2 In(t + 2). The acceleration of the particle at time t = 6 is approximately 29.453.

To find the acceleration of the particle at time t = 6, we need to calculate the derivative of the velocity function v(t).

Given: v(t) = t^2 * ln(t + 2)

To find the derivative, we use the product rule and the chain rule. The derivative of v(t) is denoted as a(t) (acceleration):

a(t) = (2t * ln(t + 2)) + (t^2 * (1/(t + 2)))

Now, substitute t = 6 into the acceleration function to find the acceleration at time t = 6:

a(6) = (2 * 6 * ln(6 + 2)) + (6^2 * (1/(6 + 2)))

    = (12 * ln(8)) + (36 * (1/8))

    = 12 * ln(8) + 4.5

Calculating this expression, we find that a(6) is approximately 29.453.

Therefore, the acceleration of the particle at time t = 6 is approximately 29.453.

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\(\\ \sf\longmapsto V=1610.82\)

\(\\ \sf\longmapsto \dfrac{1}{3}\pi r^2h=1610.82\)

\(\\ \sf\longmapsto \pi r^2(19)=1610.82(3)=4832.36\)

\(\\ \sf\longmapsto 3.14r^2=254.34\)

\(\\ \sf\longmapsto r^2=81\)

\(\\ \sf\longmapsto r=9m\)

The function f(x, y) satisfies the conditions that its limit approaches zero as x approaches zero along two different paths: y = x and y = x^2. This implies that as x approaches zero, the function f(x, y) must approach zero regardless of whether y varies linearly or quadratically with x.

The given conditions state that the limit of f(x, y) as x approaches zero along the path y = x is zero. This means that as x gets arbitrarily close to zero, the function f(x, y) approaches zero when y varies linearly with x. Similarly, the second condition states that the limit of f(x, y) as x approaches zero along the path y = x^2 is also zero. This implies that when y varies quadratically with x, the function f(x, y) still approaches zero as x approaches zero. Therefore, the function f(x, y) must satisfy both conditions by converging to zero as x approaches zero along both paths.

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The area of the rectangle is found to be 20 - 2·√(10) sq. units.

Let x be the length of the rectangle.

Let y be the width of rectangle.

Then, length is reduced by 4 and with is increased by 5.

x - 4 = y + 5 , (becomes square) ....eq 1

Area of square = 40 cm²

Then,

(x - 4) × (y + 5) = 40 cm²

From eq 1

(y + 5) × (y + 5) = 40 cm²

y² + 10y + 25 = 40

y² + 10y + 25 - 40 = 0

y² + 10y - 15 = 0

Solving equation by quadratic formula:

y = -5 + 2·√(10)

Then, for x:

x - 4 = 5 + -5 + 2·√(10) = 2·√(10)

x = 4 + 2·√(10)

Now,

Area of the rectangle, A = x × y

Put the values:

A = (-5 + 2·√(10)) × (4 + 2·√(10))

A = 20 - 2·√(10)

Thus, the area of the rectangle is found to be 20 - 2·√(10) sq. units.

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Answer: 360cm^2

Step-by-step explanation: the rectangle is 24 by 15

The time required to compute f(x) = ∑^n _i=0 a_ix^i depends on the routine used to perform exponentiation.

a. Using a simple routine to perform exponentiation, the time required to compute f(x) would be O(n), since we would have to perform exponentiation n times for each term in the sum.

b. Using the routine in 2.4.4, the time required to compute f(x) would be O(log n), since the routine uses a divide-and-conquer approach to perform exponentiation, which reduces the number of computations required.

Therefore, the time required to compute f(x) depends on the routine used to perform exponentiation. Using a simple routine, the time required would be O(n), while using the routine in 2.4.4, the time required would be O(log n).

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Answer:

x = 9

Step-by-step explanation:

12^2+x^2 = 15^2

==> x = 9

Answer:

9

Step-by-step explanation:

x = \(\sqrt{c^{2} - a^{2} }\)

x = \(\sqrt{15^{2} - 12^{2} }\)

x = \(\sqrt{225 - 144}\)

x = \(\sqrt{81}\)

x = 9

Among the given events, A and C are independent.

Two events are considered independent if the occurrence or non-occurrence of one event does not affect the probability of the other event happening. Let's analyze the given events:

A = {1, 3, 5}: This event consists of the outcomes of rolling an odd number on the fair die.

B = {2, 4, 6}: This event consists of the outcomes of rolling an even number on the fair die.

C = {1, 2, 3, 4}: This event consists of the outcomes of rolling a number from 1 to 4 on the fair die.

To determine if events A and C are independent, we need to check if the probability of A intersection C (the outcomes that satisfy both A and C) is equal to the product of their individual probabilities.

P(A) = 3/6 = 1/2 (since there are 3 favorable outcomes out of 6 possibilities)

P(C) = 4/6 = 2/3 (since there are 4 favorable outcomes out of 6 possibilities)

P(A intersection C) = 2/6 = 1/3 (since there are 2 outcomes common to both A and C: {1, 3})

Since P(A) * P(C) = (1/2) * (2/3) = 1/3 = P(A intersection C), we can conclude that events A and C are independent.

However, events B and C are not independent because the occurrence of B (rolling an even number) affects the probability of C (rolling a number from 1 to 4) since the outcomes in B are not part of C. Similarly, events A and B are also not independent because the occurrence of A (rolling an odd number) affects the probability of B (rolling an even number).

Therefore, the correct answer is that A and C are the two independent events among the given options.

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Answer:

(0, 1)

Step-by-step explanation:

y > 3x - 1

When x = 0:   y > (3 x 0) - 1  ⇒  y > -1

When x = 1:    y > (3 x 1) - 1  ⇒   y > 2

When x = 2:   y > (3 x 2) - 1  ⇒  y > 5

Therefore the only point that satisfies this is (0, 1)

Answer:

Step-by-step explanation:

Attached is the graphical solution.

We can see one point is within the shaded area -  (0, 1), all the others are outside.

the derivative of the function y = (ln(x + 4))x using logarithmic differentiation is given by y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))].

To find the derivative of the function y = (ln(x + 4))x using logarithmic differentiation, we can follow these steps:

Step 1: Take the natural logarithm of both sides of the equation:

  ln(y) = ln((ln(x + 4))x)

Step 2: Use the logarithmic property ln(a^b) = b ln(a) to simplify the right-hand side of the equation:

  ln(y) = x ln(ln(x + 4))

Step 3: Differentiate both sides of the equation implicitly with respect to x:

  (1/y) * y' = ln(ln(x + 4)) + x * (1/ln(x + 4)) * (1/(x + 4))

Step 4: Simplify the expression on the right-hand side:

  y' = y * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))]

Step 5: Substitute the original expression of y = (ln(x + 4))x back into the equation:

  y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))]

Therefore, the derivative of the function y = (ln(x + 4))x using logarithmic differentiation is given by y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))].

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Answer:

1558.99

Step-by-step explanation:

The value l = 3 is not arbitrary and is indeed a result of some aspect of the structure of the floating rate tranche. This value is determined by the specific terms and conditions outlined in the tranche agreement.

In a floating rate tranche, the interest rate is adjusted periodically according to a reference index, such as LIBOR or EURIBOR, plus a margin or spread (l). In this case, l = 3 represents the margin added to the reference index to determine the overall interest rate payable.

This value is established by the issuer based on various factors such as credit quality, market conditions, and the issuer's own funding costs.


1. The floating rate tranche's interest rate is determined by a reference index plus a margin (l).
2. In this case, l = 3 is the margin added to the reference index.
3. The value of l is established by the issuer, considering credit quality, market conditions, and funding costs.
4. Therefore, l = 3 is not arbitrary and is a result of the structure of the floating rate tranche.

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When summarizing heavily skewed data, the best measure of central tendency is the median.

In situations where the data distribution is heavily skewed, the mean may not accurately represent the central tendency of the data. Skewness refers to the asymmetry of the data distribution, where the tail of the distribution extends more to one side. When data is heavily skewed, it can be influenced by extreme values, leading to an unbalanced representation of central tendency if the mean is used.

The median, on the other hand, is less affected by extreme values and provides a better measure of central tendency for skewed data. The median represents the middle value in a data set when the observations are arranged in ascending or descending order. Unlike the mean, it is not influenced by extreme values, making it a robust measure for summarizing skewed data.

By using the median, we can capture the central value that is more representative of the majority of the data points, even in the presence of outliers or skewed distributions. It provides a better understanding of the typical value or position within the data set, regardless of extreme values or asymmetric distributions.

Therefore, when summarizing heavily skewed data, the median is considered the best measure of central tendency as it provides a more accurate representation of the center of the distribution and is less influenced by extreme values.

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Answer:

B and D

Step-by-step explanation:

When you subtract a negative number, you are adding.

7-(-7)=7+7=14

Adding goes right on a number line.

Answer:

y=3−x

(−2,0,3)

Solution set of the given system of equations is {(-11/3, -1/3, 1)}.Hence, this is the solution set to the given system of equations using Gaussian elimination.

Gaussian Elimination method: The system of equations can be transformed into an equivalent system of equations through a sequence of operations such as switching rows, multiplying rows, or adding a multiple of one row to another row.

These operations do not affect the solution set of the original system.

These steps are repeated until the system of equations is in a simpler form that can be solved by substitution method.

Here is the main answer to the given problem:

3x₁ +5x₂ + x3 = 32x1 + 6x2 + 7x3

= 13x₁ - x₂ + x₃ = 15x₁ + 2x₂ + 8x₃ = -2.

Add (-1/3) * R₁ to R₂Add (-3) * R₁ to R₃R₁ remains the same

5x₂ + 20/3 x₃ = -62x₂ + 2/3 x₃

= 1R₃ = 0x₂ + 14/3 x₃

Hence, Solution set of the given system of equations is {(-11/3, -1/3, 1)}.Hence, this is the solution set to the given system of equations using Gaussian elimination.

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Answer:

13

Step-by-step explanation:

416/96 = 4.33333

416 is 4.333 times 96, so he needs 4.333 times 3 bundles.

4.3333 × 3 = 13

Answer: 13

Answer:

13

Step-by-step explanation:

you see how much it covers initially. (96/3=32) then 416/32=13

Steps to solve:

4x + 6 = 10 - 4

~Simplify

4x + 6 = 6

~Subtract 6 to both sides

4x = 0

~Divide 4 to both sides

x = 0

Best of Luck!

Answer:

\(\large\boxed{x = 0}\)

Step-by-step explanation:

4x + 6 = 10 - 4

Subtract 10 - 4

4x + 6 = 6

Subtract 6 from both sides of the equation

4x = 0

Divide both sides of the equation by 4

\(\large\boxed{x = 0}\)

Hope this helps :)

Answer:

You cannot combine -5x^2 and 2x.

Step-by-step explanation:

You cannot combine -5x^2 and 2x.  They are not like terms

x^2 and x are not the same

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

All real numbers is the answer

Answer:

All real numbers is the Answer

Step-by-step explanation: