HELP HELP HELP.ASAP PLEASE

Therefore, the truth value of Proposition 2A is False.

To determine the truth value of Proposition 2A, let's substitute the given truth values for the variables:

A = True

B = True

X = False

Y = False

Now let's evaluate the truth value of each component of the proposition:

(X ⊃ A) • (B ⊃ ∼ Y):

(False ⊃ True) • (True ⊃ ∼ False)

(True ⊃ True) • (True ⊃ True)

True • True

True

(B ∨ Y) • (A ⊃ X):

(True ∨ False) • (True ⊃ False)

True • False

False

[(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)]:

True ⊃ False

False

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Answer:

Hope this helps :)

All of these are the answers, the final answer is the simplified one, and the explanation is below.

9/6 (improper fraction)

1 3/6 (mixed number)

1 1/2 (simplified)

Step-by-step explanation:

1. Common denominators which is 6.

7/6 + 1/3

1/3 × 2/2 = 2/6

2. Add the numerators since they already have common denominators.

7/6 + 2/6 = 9/6

3. Change into mixed number and simplify if needed.

9/6 = 1 3/6 = 1 1/2

AB is not perpendicular to CD

Perpendicular lines are two separate lines that cross one other at a right angle, or a 90° angle. Example: Because AB and XY overlap at a 90° angle, AB is perpendicular to XY in this instance.

Lines that cross one other at an angle are known as perpendicular lines. Their slopes are the reciprocal opposites of one another.

Given A (-2, 4, 0),B(1, 1, 1),C(2, 3, 4),D (3, 21, -8)

(-1,3,-1) for AB

(-1,-18,12) for CD

For the lines AB and CD to be perpendicular

a 1a2+b1b2+c1c2=0

-1(-1)+3(-18)+(-1)(12)

=1-54−12=-65not equal to 0

∴ AB not perpendicular to CD

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The problem you're asking about is to create an algorithm that computes x^n, given a real number x and an integer n, in O(log n) time complexity. The solution to this problem is the "Exponentiation by Squaring" algorithm.

Here's a concise explanation of the algorithm in 150 words:

Exponentiation by Squaring is an efficient algorithm that calculates x^n using a divide and conquer approach, which takes advantage of the fact that x^n = (x^2)^(n/2) if n is even, and x^n = x * x^(n-1) if n is odd. The algorithm computes the result recursively or iteratively, and its time complexity is O(log n), making it efficient for large exponents.

To handle negative exponents, we can use the property x^(-n) = 1 / x^n. So, if the given exponent n is negative, we can calculate the reciprocal of x and use the positive value of n in the algorithm. For the base case, when n = 0, the result is always 1, since any non-zero number raised to the power of 0 equals 1.

By using Exponentiation by Squaring, we can quickly compute x^n for any real number x and any positive or negative integer n, in O(log n) time.

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a. The sequence that starts with 5 and ends with 8 is 5, 15, 3, 0, 0, 0, 8.

b. Since 8 is a single-digit number, it can be obtained by starting with any positive integer.

c. By systematically applying the sequence rules, we can construct a sequence that starts with 8 and ends with 999.

(a) To find a sequence that starts with 5 and ends with 8, we can follow these steps:

Start with 5.

Triple the current number: 5 * 3 = 15.

Delete the final digit: 15 -> 1.

Triple the current number: 1 * 3 = 3.

Delete the final digit: 3 -> 0.

Triple the current number: 0 * 3 = 0.

Triple the current number: 0 * 3 = 0.

Triple the current number: 0 * 3 = 0.

Add 8 to the sequence: 0, 0, 0, 8.

Therefore, the sequence that starts with 5 and ends with 8 is 5, 15, 3, 0, 0, 0, 8.

(b) Any positive integer can start a sequence that ends in 8 because of the following reasons:

Tripling a positive integer repeatedly will eventually lead to a number that is divisible by 3.

Dividing a number by 10 removes its final digit. By performing this operation repeatedly on a positive integer, we can reduce it to a single-digit number, at which point we cannot perform the operation anymore.

When a single-digit number is tripled, it becomes a number that is divisible by 3.

Since 8 is a single-digit number, it can be obtained by starting with any positive integer and following the sequence rules outlined above.

(c) To find a sequence that starts with 8 and ends with 999, we can follow this systematic process:

Start with 8.

Triple the current number: 8 * 3 = 24.

Delete the final digit: 24 -> 2.

Triple the current number: 2 * 3 = 6.

Delete the final digit: 6 -> 0.

Triple the current number: 0 * 3 = 0.

Add 9 to the sequence: 0, 0, 0, 9.

Triple the current number: 9 * 3 = 27.

Delete the final digit: 27 -> 2.

Triple the current number: 2 * 3 = 6.

Delete the final digit: 6 -> 0.

Triple the current number: 0 * 3 = 0.

Add 9 to the sequence: 0, 0, 0, 9, 0, 0, 0, 9.

Repeat steps 8-13 until the desired number is reached: 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, ..., 0, 0, 0, 9, 99, 999.

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Answer:

scale factor is 3, k=3

Step-by-step explanation:

everything is being multiplied by 3

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

To determine the tension in each of the three vertical wires supporting the rectangular plate, we can apply the principle of equilibrium. By considering the forces acting on the plate, we can calculate the tension in each wire.

Since the plate is in equilibrium, the sum of the vertical forces acting on it must be zero. The weight of the plate is acting downward with a magnitude of 60 lb. The tension in each wire can be considered as a vertical force acting upward.

Let's label the wires as A, B, and C, from left to right. Considering the forces acting on the plate, we have the following equation:

Tension in wire A - Tension in wire B - Tension in wire C = 60 lb.

To find the tension in each wire, we need additional information. For example, if the plate is symmetric, we can assume that the tension in wire B is equal to the tension in wire C. In that case, we can rewrite the equation as:

Tension in wire A - 2 * Tension in wire B = 60 lb.

Since there are no additional details or measurements provided about the plate or the wires, we cannot determine the specific values of the tensions in each wire without further information. The solution would depend on the specific configuration and characteristics of the plate and the wires.

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The area of the triangle is 19.5 square units.

To find the area of the triangle, we can use the formula:

Area = (1/2) * base * height

where the base and height are the distance between two of the vertices of the triangle. We can choose any two vertices to use as the base and height, as long as we use the same units for both. Let's choose (-3,2) and (6,-2) as our base.

The distance between (-3,2) and (6,-2) can be found using the distance formula:

d = \(\sqrt((6 - (-3))^2 + (-2 - 2)^2)\)
d = \(\sqrt(81 + 16)\)
d = \(\sqrt(97)\)

Now we need to find the height of the triangle. The height is the perpendicular distance from the third vertex (3,5) to the line containing the base (-3,2) and (6,-2). We can use the formula:

height = \(|Ax + By + C| / \sqrt(A^2 + B^2)\)

where A, B, and C are the coefficients of the line in the standard form Ax + By + C = 0, and x and y are the coordinates of the third vertex. We can find the coefficients of the line by using the two points (-3,2) and (6,-2):

A = 2 - (-2) = 4
B = (-3) - 6 = -9
C = 6*(-2) - (-3)*2 = -18

Now we can plug in the values to find the height:

height = \(|4*3 - 9*5 - 18| / \sqrt(4^2 + (-9)^2)\)
height = \(39 / \sqrt(97)\)

Finally, we can plug in the base and height to find the area:

Area = \((1/2) * \sqrt(97) * (39 / \sqrt(97))\)
Area = 19.5

Therefore, the area of the triangle is 19.5 square units.

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The mean number of number of people in passengers cars on the highway is given as follows:

E. 6.28.

The expected value of a discrete distribution is calculated as the sum of each value multiplied by it's respective probability.

The distribution in this problem is given as follows:

Then the expected value before the transformation is given as follows:

E(X) = 0.56 x 1 + 0.28 x 2 + 0.08 x 3 + 0.06 x 4 + 0.02 x 5 = 1.7.

The transformation is given as follows:

Y = 0.75x + 5.

Thus the expected value after the transformation is of:

E(X) = 0.75(1.7) + 5 = 6.28.

Meaning that option E is correct.

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Step-by-step explanation:

since there is triangle , you use the formula

1/2 × b × h

as you can see the base is 6 and the height is 4, so

1/2 × b × h

= 1/2 × 6 × 4

=12

12 × 2 = 24 , you times by 2 because there is 2 triangle

There is also rectangle in the diagram, so you use the formula , length × breadth , the length is 8 and the breadth is 5, so

length x breath

= 5 × 8

=35

35 × 2 = 70 , times by 2 because you can see 2 rectangles with the same length and breadth

length x breath

= 8 × 6

= 48

this one is different because the length is 8 and the breadth is 6.

SA = 48 + 35 + 24

= 107 cm ²

Sorry for my bad eng ,its not my first language.

Answer:

0.375

Step-by-step explanation:

You mean 3/8 right?

3/8=0.375

Answer:

0.375

Step-by-step explanation:

(✿◡‿◡) <-- she wants brainliest

Given the matrix expression A = (a 0 3(a-b) b) = (1 0 3 1) (a 0 0 b) (1 0 -3 1), we want to compute the matrix power Ak using the factorization A = PDP^-1.

First, we need to find the matrices P and D. The matrix D is a diagonal matrix consisting of the eigenvalues of A, which are a, b+3a, and b-3a. The matrix P is the matrix whose columns are the eigenvectors of A, which can be found by solving the system (A - λI)x = 0 for each eigenvalue λ.

Solving for each eigenvalue, we get λ1 = a with eigenvector (0,1), λ2 = b+3a with eigenvector (-3,1), and λ3 = b-3a with eigenvector (1,1). Thus, we have:

D = (a 0 0

0 b+3a 0

0 0 b-3a)

P = (0 -3 1

1 1 1

0 0 1)

To compute Ak, we can use the formula A^k = PD^kP^-1. Since D is a diagonal matrix, we can easily compute D^k by raising each diagonal entry to the power of k. Thus, we get:

D^k = (a^k 0 0

0 (b+3a)^k 0

0 0 (b-3a)^k)

Multiplying out the matrices P and P^-1, we get:

P^-1 = (1/3 -1/3 0

-1/3 2/3 -1/3

0 -1/3 1/3)

P^-1AP = D

Multiplying both sides by P^-1, we get:

A = PDP^-1

Now, substituting D^k into the formula A^k = PD^kP^-1, we get:

A^k = P D^k P^-1

Substituting the matrices P, P^-1, and D^k, we get the expression for Ak as:

Ak = (1/3)((b+3a)^k - (b-3a)^k) (1 -3(b-3a)^k/(b+3a)^k - 3(b+3a)^k/(b-3a)^k 1) (a 0 0 b)

Therefore, we have the expression for Ak.

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The required probability for the given event is given as 0.5.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

The probability of a door being locked is 70% = 0.7

Total number of keys is 10.

The number of keys being carried is 2.

Thus, there can be two cases for getting through the door.

Case 1: The door is locked.

The probability to open the door by 1 key is 1/10.

Then, the probability to open the door by 2 keys is 2/10 = 1/5.

Case 2: The door is open.

In this case no keys are needed which means the chance of getting through is the probability of door not being locked which is given as,

1 - 0.7 = 0.3.

Now, the overall probability should consider both the cases as,

P(getting through the door) = P(Door is closed and keys open it)

+ P(The door is open)

= 0.3 + 1/5

= 0.3 + 0.2

= 0.5.

Hence, the probability to get through the door without returning for more keys is 0.5.

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Answer:

The answer would be 5h+45

Step-by-step explanation

5 (h+9)

You need to convert this equation into the equation

you multiply 5 by h and get 5h

Then multiply the same number outside the parenthesis, 5, by 9 which will give you the answer 45

Once you have 5h and 45 just put it together with the addition symbol which will will equal:

5 (h+9) = 5h + 45

Your Welcome! (hopefully this answers your question)

Answer:

X = 4

Step-by-step explanation:

We have to add like variables, so all the x variables will be added together. We get this:
-x + 35 = 31

Get x by itself.
-x = -4

Get rid of the negatives since what you do on one side you do to both sides.

x = 4

I hope this was able to help you out :D

16 (-x +x ) +19 + x = 31

16+19+x = 31

35+x = 31

x= -4

hey buddy i hope uh got an answer

Answer:

Step-by-step explanation:

5

Discrete - Whole days spent on holiday, Number of sheep in a field

Continuous - Length of a fish, Height of a wardrobe

Data that can only take on particular values or categories is referred to as discrete data. There are distinct, independent, and countable data points in it. Discrete data cannot be broken into smaller units because it is often based on categories, labels, or full numbers.

Thus it follows that Whole days spent on holiday and  Number of sheep in a field are examples of discreet data while Length of a fish and  Height of a wardrobe are examples of continuous data.

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Answer:

r = - \(\frac{1}{3}\)

Step-by-step explanation:

The n th term of a GP is

\(a_{n}\) = a₁ \(r^{n-1}\)

where a₁ is the first term and r the common ratio

Here a₁ = 18 and a₆ = - \(\frac{2}{27}\) , then

18 \(r^{5}\) = - \(\frac{2}{27}\) ( divide both sides by 18 )

\(r^{5}\) = - \(\frac{1}{243}\) ( take the fifth root of both sides )

r = \(\sqrt[5]{-\frac{1}{243} }\) = - \(\frac{1}{3}\)

Donna is not correct, as the mean is of 7.1 kg, which is greater than 7 kg.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

The sum of the data-set in this problem is given as follows:

4 x 5 + 5 x 9 + 1 x 6 = 71 kg.

The number of observations is given as follows:

10.

Hence the mean is given as follows:

71/10 = 7.1 kg > 7 kg.

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Answer:

It will take 5.68 seconds to cover a distance of 100 meters.

Step-by-step explanation:

Given that:

A greyhound dog runs with a top speed of 17.6 m/s

Distance to cover = 100 meters

We know that:

Distance = Speed * Time

Putting the values in formula

100 = 17.6 * Time

Time = \(\frac{100}{17.6}\)

Time = 5.68 seconds

Hence,

It will take 5.68 seconds to cover a distance of 100 meters.

Option B. The null hypothesis is that the mean weight of men in the population is equal to 191 pounds.

The investigator hypothesized that the mean weight of men in the population is higher than the mean weight reported by the CDC, which is 191 pounds. To test this hypothesis, the investigator took a random sample of 100 men and found that the average weight of men in the sample was 197.1 pounds with a standard deviation of 25.6 pounds.

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Answer:

t= -15/2       or       t= -7.5

Step-by-step explanation:

We are given the equation:

\(\frac{-6}{5}t=9\)

and asked to solve for t. Therefore, we must isolate t on one side of the equation.

t is being multiplied by -6/5. The inverse of multiplication is division. We should divided both sides by -6/5, but we are dividing by a fraction. Instead, we can multiply by the reciprocal.

To find the reciprocal, flip the numerator (top number)  and denominator (bottom number).

-6/5 ----> -5/6

Multiply both sides of the equation by -5/6

\(\frac{-5}{6} *\frac{-6}{5}t=9 *\frac{-5}{6}\)

\(t=9 *\frac{-5}{6}\)

\(t=\frac{9}1 *\frac{-5}{6}\)

Multiply across the numerator and denominator.

\(t= \frac{9*-5}{1*6}\)

\(t=\frac{-45}{6}\)

Simplify the fraction. Both the numerator and denominator can be divided by 3.

\(t=\frac{-45/3}{6/3}\)

\(t=\frac{-15}{2}\)

\(t= -7.5\)

t is equal to -15/2 or -7.5

The Economic Order Quantity (EOQ) is calculated to be 547.72 units. The number of orders placed per year is 5.84, and the reorder point (ROP) is 32.01.

The total holding cost of lawnmowers is R1369.30, and the total ordering cost of lawnmowers is R876.00. These calculations provide valuable insights for efficient inventory management.

The Economic Order Quantity (EOQ) can be calculated by using the formula: EOQ = √2DS / H,

where D = Total Demand = 3200 units,

S = Ordering cost per order = R150,

and H = Annual holding cost per unit = R5.

Therefore, EOQ = √ (2 x 3200 x 150) / 5 = 547.72 units.

4.2 Number of orders placed per year: No of orders per year = D / Q,

where D = Total Demand = 3200 units and Q = EOQ = 547.72 units.

Therefore, No of orders per year = D / Q = 3200 / 547.72 = 5.84 orders.

4.4 Total holding cost of lawnmowers:

Total holding cost of lawnmowers = (Average inventory level) x (Annual holding cost per unit),

where (Average inventory level) = EOQ / 2 = 547.72 / 2 = 273.86 units and Annual holding cost per unit = R5.

Thus, the Total holding cost of lawnmowers = 273.86 x R5 = R1369.30.

4.1 Reorder Point (ROP): ROP can be calculated by using the formula:

ROP = dL, where d = Daily demand = D / Number of working days

= 3200 / 300 = 10.67 and L = Lead time = 3 days.

Hence, ROP = dL = 10.67 x 3 = 32.01.

4.5 Total ordering cost of lawnmowers:

Total ordering cost of lawnmowers = (Number of orders placed per year) x (Ordering cost per order),

where (Number of orders placed per year) = 5.84 orders and Ordering cost per order = R150.

Therefore, the Total ordering cost of lawnmowers = 5.84 x R150 = R876.00.

The Economic Order Quantity (EOQ) is calculated to be 547.72 units.

The number of orders placed per year is 5.84, and the reorder point (ROP) is 32.01.

The total holding cost of lawnmowers is R1369.30, and the total ordering cost of lawnmowers is R876.00.

These calculations provide valuable insights for efficient inventory management.

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Answer:

Here is the ans...Hope it helps :)

a) The sample mean home sale amount is $660,500 and the sample median home sale amount is $582,500.

b) The new sample mean home sale amount would be $617,500 and the new sample median home sale amount would be $575,000.

c) The 20% trimmed mean home sale amount is $573,600.

d) The 15% trimmed mean home sale amount is $601,400.

In a group of numerical data, the median serves as a gauge of central tendency. When the values are ordered in order of magnitude, it is the median value in the dataset. In other words, the median is the value in the middle when a dataset has an odd number of variables. The median is the average of the two middle values when the dataset has an even number of values. Because it is unaffected by extreme numbers or outliers that can influence the mean, the median is helpful in these situations. To indicate the typical value of a dataset, it is frequently employed.

a. To calculate the sample mean, we add up all the home sale amounts and divide by the total number of homes in the sample:

(590 + 815 + 575 + 608 + 350 + 1285 + 408 + 540 + 555 + 679) / 10 = 660.5

So the sample mean home sale amount is $660,500.

To find the sample median, we first need to order the home sale amounts from lowest to highest:

350, 408, 540, 555, 575, 590, 608, 679, 815, 1285

There are 10 homes in the sample, so the median is the middle value. Since there are an even number of homes, we take the average of the two middle values:

(575 + 590) / 2 = 582.5

So the sample median home sale amount is $582,500.

b. If the 6th observation had been 985 rather than 1285, the sample mean would change as follows:

(590 + 815 + 575 + 608 + 350 + 985 + 408 + 540 + 555 + 679) / 10 = 617.5

So the new sample mean home sale amount would be $617,500.

To find the new sample median, we first need to order the home sale amounts from lowest to highest:

350, 408, 540, 555, 575, 590, 608, 679, 815, 985

There are 10 homes in the sample, so the median is the middle value. Since there are an odd number of homes, the median is simply the middle value:

575

So the new sample median home sale amount would be $575,000.

c. To calculate a 20% trimmed mean, we first need to remove the two smallest and two largest observations:

(540, 555, 575, 590, 608)

Then, we calculate the mean of the remaining observations:

(540 + 555 + 575 + 590 + 608) / 5 = 573.6

So the 20% trimmed mean home sale amount is $573,600.

d. To calculate a 15% trimmed mean, we need to remove the 1.5 smallest and 1.5 largest observations. Since we can't remove half an observation, we need to remove 1 observation from each end of the list. This gives us:

(555, 575, 590, 608, 679)

Then, we calculate the mean of the remaining observations:

(555 + 575 + 590 + 608 + 679) / 5 = 601.4

So the 15% trimmed mean home sale amount is $601,400.

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Answer:

Step-by-step explanation:

For the slope of a line formula to be used,

Slope (m) of a line = \(\frac{\triangle y}{\triangle x}\)

1). \(-\frac{3}{4}=\frac{\triangle y}{4}\)

  Δy = -3

2). \(\frac{2}{3}=\frac{\triangle y}{6}\)

   Δy = \(\frac{2\times 6}{3}\)

   Δy = 4

3). \(-\frac{3}{2}=\frac{\triangle y}{8}\)

    Δy = \(-\frac{3}{2}\times 8\)

    Δy = -12

4). \(\frac{3}{4}=\frac{\triangle y}{4}\)

     Δy = 3

The equation of the her earnings is 0.4(x + $200) = $900 and the Ashley's had earned last summer is 2050 dollars.

Let x be Ashley's earnings last summer. Then her earnings this summer would be (x + $200).

Ashley saves 40% of her earnings, 40% is equivalent to the 0.4.

Thus ,according to the given condition in the question the equation ogf the

Ashley's earnings given as :

so the amount she saved this summer is 0.4(x + $200) = $900.

Expanding the equation and solving for x, we get:

0.4x + $80 = $900

0.4x = $820

x = $2050

Therefore, Ashley earned $2050 last summer and $2250 this summer.

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