The different of two numbers is 18
and the difference of six times
the larger number and two times
the smaller number is 156. Find the
two numbers​

(a) Propositional form:

(A ∨ M) → ¬(A ∨ M)

(c) The truth table reveals that, regardless of the truth values of A and M, the assertion "(A M) (A M)" is always true. Therefore, the argument is valid.

(a) Propositional form:

(H ∧ ¬H) → S

(c) From the truth table, we can see that the statement "(H ∧ ¬H) → S" is always true regardless of the truth values of H and ¬H. Therefore, the argument is invalid.

Argument: The attack on Pearl Harbour did not result in the sinking of either the USS Arizona (A) or the USS Missouri (M). Therefore, it is not the case that either the USS Arizona or the USS Missouri was sunk in the attack on Pearl Harbor.

(a) Propositional form:

(A ∨ M) → ¬(A ∨ M)

(b) Truth table:

A               M                 (A ∨ M) → ¬(A ∨ M)

True    True                         False

True    False                         False

False    True                         False

False    False                            True

(c) From the truth table, we can see that the statement "(A ∨ M) → ¬(A ∨ M)" is always true regardless of the truth values of A and M. Therefore, the argument is valid. This means that if the premise is true (either the USS Arizona or the USS Missouri was not sunk), then the conclusion (neither the USS Arizona nor the USS Missouri was sunk) must also be true.

Argument: I am hungry (H) and I am not hungry. Therefore, I will eat my shoe (S).

(a) Propositional form:

(H ∧ ¬H) → S

(b) Truth table:

H                  ¬H             (H ∧ ¬H) → S

True          False         True

False          True         True

True          True         True

False         False         True

(c) From the truth table, we can see that the statement "(H ∧ ¬H) → S" is always true regardless of the truth values of H and ¬H. However, the conclusion of the argument (I will eat my shoe) does not logically follow from the premises (I am hungry and I am not hungry). Therefore, the argument is invalid.

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ANSWER:

500.5 m²

STEP-BY-STEP EXPLANATION:

To know how much artificial grass should be purchased to cover the athletic field, we must calculate the area corresponding to the figure.

The area of a trapezoid has the following formula:

Where b is the small base, B is the large base and h is the height, we substitute and calculate the area, like this:

It is necessary to purchase the amount of 500.5 m² to be able to cover the athletic field

Probability that the diameter of a randomly selected pipe will exceed 0.36 inch = 0.023

What is Probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here, Normal distribution of probability is used

Mean of the distribution = 0.3 inch

Standard Deviation of the distribution = \(\sqrt{0.009} = 0.03\)

Probability that the diameter of a randomly selected pipe will exceed 0.36 inch = P(X > 0.36)

       = 1 - P(X \(\leq\) 0.36)

          1 - P(z \(\leq\) \(\frac{0.36 - 0.3}{0.03}\))

          1 - P(z \(\leq\) 2)

          1 - 0.9772

           0.023

Probability that the diameter of a randomly selected pipe will exceed 0.36 inch = 0.023

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The teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

In order to help the students understand that the triangle is equivalent to half a square, the teacher can adopt different methods, including the following:

1. Drawing diagrams of the triangle and the square to show the comparison. The teacher can draw diagrams of a triangle and a square on the board and label the different parts.

They can then show the students that a triangle can be created by halving the square diagonally. This way, the students will be able to visualize the comparison and understand it better.

2. Demonstrating the concept practically. The teacher can also demonstrate the concept by using physical objects such as paper or cardboard.

They can show the students how to create a triangle by folding a square diagonally and cutting it along the fold. This way, the students will be able to see the practical application of the concept.

3. Using real-world examples. The teacher can also use real-world examples to help the students understand the concept better.

For example, they can show the students pictures of tents or rooftops that are shaped like triangles and explain how they are related to squares.

4. Conducting group discussions. The teacher can conduct group discussions where the students can share their understanding of the concept and ask questions.

This way, the students will be able to learn from each other and clarify any doubts they may have.

Overall, the teacher can use a combination of these methods to help the students understand that a triangle is equivalent to half a square.

The key is to use different approaches that cater to different learning styles and to encourage the students to participate actively in the learning process.

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On solving the provided question, we can say that - polynomial has the binomial (3x+2) as a component, then the root of that polynomial is x = -2/3.

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial in mathematics is an expression made up of variables (also known as indeterminates), coefficients, addition, subtraction, multiplication, and non-negative integer powers of variables.

If a polynomial has the binomial (3x+2) as a component, then the root of that polynomial is x = -2/3.

\(6(-2/3)^3 + 3(-2/3)^2 + 4(/2/3) + 2 = -16/9 +4/3 - 8/3 + 2 = -10/9\)

\(12(-2/3)^2 + 23(-2/3) + 10 = 0\)

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I assume you meant h(t) = 160t - 16t^2, as h(t) = 160t - 16t2 has no maximum.

There's two ways of solving this:

(i) By completing the square and finding the maximum turning point.

(ii) By using Calculus methods to find derivative and equating it to 0 in order to find maximum turning point.

(i) h(t) = 160t - 16t^2

h(t) = -16t^2 +160t

h(t) = -16(t^2-10t) (by taking out a common factor of -16)

h(t) = -16[(t-5)^2 - 25] (by completing the square)

h(t) = -16(t-5)^2 + 400 (on multiplying out by -16)

From this we see that the turning point is at (5;400), therefore the maximum height is 400 feet and is reached after 5 seconds.

Or...

(ii) h(t) = 160t - 16t^2

h`(t) = 160 - 32t (where h`(t) = derivative of h(t))

Now to find maximum of h(t), we set h`(t) = 0 and solve for t:

0 = 160 - 32t (on substituting h`(t) = 0)

32t = 160 (on solving for t)

t = 160/32 (on dividing both sides by 5)

t= 5

Now we have found that at 5 seconds, we will reach our maximum height. So to find this maximum height, we'll have to substitute t=5 into h(t) = 160t - 16t^2.

h(5) = 160(5) -16(5)^2

h(5) = 800 - 400

h(5) = 400 feet

So, once again we have shown that maximum height is 400 feet and is reached after 5 seconds.

Answer:

x = -3

Step-by-step explanation:

-22 = 5x - 7

-15 = 5x

x = -3

Answer:

X=3 or -3 i am not sure which but am positive it is one of those

Step-by-step explanation:

the optimal solution to maximize Z is x1 = 25 and x2 = 0, with Z = 3000.

To solve the given linear programming model graphically, we need to plot the feasible region and identify the corner points to find the optimal solution. Here's the step-by-step process:

1. Plot the constraints:

  - Plot the line x1 = 40 (vertical line at x1 = 40).

  - Plot the line x2 = 10 (horizontal line at x2 = 10).

  - Plot the line 20x1 + 10x2 = 500 (which can be rewritten as 2x1 + x2 = 50).

  - Shade the feasible region that satisfies all the constraints.

2. Identify the corner points:

  - Determine the coordinates of the corner points where the boundary lines intersect.

3. Evaluate the objective function:

  - Calculate the value of the objective function Z = 120x1 + 80x2 for each corner point.

4. Determine the optimal solution:

  - Select the corner point that maximizes the objective function Z.

Here's the graphical representation of the feasible region:

      |

 40   |           C

      |          /

      |         /

      |        /

      |       /

      |      /

      |     /    Feasible Region

 10   |_____/_________________

      0   10  20  30  40  50

            0`

The corner points of the feasible region are:

A: (0, 0)

B: (0, 10)

C: (25, 0)

D: (20, 5)

Now, we evaluate the objective function Z = 120x1 + 80x2 for each corner point:

Z(A) = 120(0) + 80(0) = 0

Z(B) = 120(0) + 80(10) = 800

Z(C) = 120(25) + 80(0) = 3000

Z(D) = 120(20) + 80(5) = 2400

From the above calculations, we can see that the maximum value of Z occurs at point C: (25, 0).

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(i) For function f(x) = x² - 2x + 2 over interval [-1, 2]: f(-1) = 5, f(2) = 2.

(ii) For function f(x) = x² + x over interval [0, 1]: f(0) = 0, f(1) = 2.

(iii) For function f(x) = 1/x² over interval [1, 2]: f(1) = 1, f(2) = 1/4.

To find the value of the function at the end-points of the interval, we substitute the values of the endpoints into the given functions.

Part (a) : f(x) = x² - 2x + 2; [-1, 2]

At x = -1:

f(-1) = (-1)² - 2(-1) + 2 = 1 + 2 + 2 = 5,

At x = 2:

f(2) = (2)² - 2(2) + 2 = 4 - 4 + 2 = 2,

So, values of function at the endpoints of the interval [-1, 2] are f(-1) = 5 and f(2) = 2.

Part (b) : f(x) = x² + x; [0, 1]

At x = 0:

f(0) = (0)² + 0 = 0.

At x = 1:

f(1) = (1)² + 1 = 1 + 1 = 2.

So, values of function at the endpoints of the interval [0, 1] are f(0) = 0 and f(1) = 2.

Part (c) : f(x) = 1/x²; [1, 2]

At x = 1:

f(1) = 1/(1)² = 1/1 = 1.

At x = 2:

f(2) = 1/(2)² = 1/4.

Therefore, the values of the function at the endpoints of the interval [1, 2] are f(1) = 1 and f(2) = 1/4.

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The given question is incomplete, the complete question is

Find the value of the function at the end points of the interval.

f(x) = x² - 2x + 2;   [-1, 2]

f(x) = x² + x;   [0,1]

f(x) = 1/x² ;    [1,2]

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approx b). 0.9428.

The intelligence quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. The standard deviation of the mean of a sample of 50 adults can be calculated as the population standard deviation divided by the square root of the sample size, or 15/√50 = 1.58.

Using a standard normal distribution table, the probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 can be calculated as the area under the standard normal curve between the z-scores corresponding to 98 and 103. These z-scores can be calculated using the formula z = (x - mean) / standard deviation, where x is the value of interest and mean is the population mean. The z-score for 98 is (98 - 100) / 1.58 = -1.27, and the z-score for 103 is (103 - 100) / 1.58 = 2.53.

The area under the standard normal curve between -1.27 and 2.53 can be found using a standard normal distribution table or a calculator with normal distribution functions. The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approximately 0.9228, which is closest to the answer choice b. 0.9428.

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Answer:-18 and +2

Step-by-step explanation:18*2=36

-18++2=-18+2=-16

Answer:

3:2

Step-by-step explanation:

42:28

21:14

3:2

Answer:

  3x +4y = 25

Step-by-step explanation:

You want the equation of the tangent to the graph of x² +y² = 25 at the point (3, 4).

The given equation is that of a circle of radius 5 centered at the origin. For some point (x, y) on the circle, the radius to that point will have a slope of m = y/x. This means the tangent will have a slope of ...

  -1/m = -1/(y/x) = -x/y

For the given point, the slope of the tangent is -3/4.

The y-intercept in the slope-intercept form equation for a line is 'b'. We can solve for that ...

  y = mx +b

  b = y - mx

For (x, y) = (3, 4) and m = -3/4, the y-intercept is ...

  b = 4 -(-3/4)·3 = 4 +9/4 = 25/4

Using the values of m and b we found, the slope-intercept form equation for the tangent is ...

  y = -3/4x +25/4

In standard form, the equation becomes ...

  4y = -3x +25

  3x +4y = 25

__

Additional comment

If you work through this process for point (a, b) on the circle of radius r centered at the origin, you find the equation of the tangent at that point is ...

  ax +by = r²

If the center of the circle is at (h, k), then the equation will be the same thing translated to the new center:

  (a -h)(x -h) +(b -k)(y -k) = r²

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The algebraic expression for half of a number is x/2.

When we are working in algebra and we want to represent "a number", we use a variable for it.

We do this because "a number" can be any real number.

For example, we can say that a number is represented by the variable x.

Now, to write half of a number, we just need to divide our variable by 2, then we will get:

x/2

That is the algebraic expression.

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Answer:

X equals 3 so that will be C?

Answer:

Only C

Step-by-step explanation:

Simple multiplication that can be checked using a calculator.

Answer:

A) 5927

B) 13

C) 8

D) cannot read expression

Step-by-step explanation:

A) (77^2)-2 = 5927

B) (1+4)*3-2 = 13

C) 2(1+3) = 8

Answer:

The common difference is 1/5.

Step-by-step explanation:

Each new term is equal to the previous term, plus the common difference 1/5.

-2 + 1/5 = -10/5 + 1/5 = -9/5  = -1 4/5, and so on.

Answer:

Step-by-step explanation:

\(c.d.=-1\frac{4}{5} -(-2)\\=-\frac{9}{5} +2\\=\frac{-9+10}{5} \\=\frac{1}{5}\)

Answer:

X=12

Step-by-step explanation:

70+25+9x-23=180°

95+9x-23=180°

9x+72=180°

9x=180°-72

9x=108°

x=12.

Answer:

31122

Step-by-step explanation:

Hope this helps.

Answer:

the answer is 31,122

The value of P(X < 120) is also 0.8413.So, the required probability is 0.8413 (rounded to 4 decimals).

Given that a normal random variable X has a mean = 100

Standard deviation = 20 and we have to find P(X < 120).

The z-score formula for the random variable X is given by:

z = (X - µ)/σ

Where,

z is the z-score,

µ is the mean,

X is the normal random variable, and

σ is the standard deviation.

Substituting the given values in the z-score formula,

we get:

z = (120 - 100)/20z

= 1

Now we have to find the value of P(X < 120) using the standard normal distribution table.

In the standard normal distribution table, the value of P(Z < 1) is 0.8413.

Therefore, the value of P(X < 120) is also 0.8413.So, the required probability is 0.8413 (rounded to 4 decimals).

Hence, the answer is 0.8413.

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The cost when two plans cost the same amount is $90, and the amount of calling for which the two plans cost the same is 650 minutes.

An algebraic expression is an equation made up of variables and arithmetic operations like multiplication and division.

Assume that the two plans have the same costs when x minutes are called.

Therefore, the algebraic statement can be expressed as 26 + (0.10) = 0 + (0.14),

or Plan A Equals Plan B.

By solving this, we can determine how many minutes each of the two plans will cost:

650 minutes are equal to 26 = 0.10x - 0.14x 0.04x.

B) The price when two plans have the same price:

Plan A = 26 + 0.10 x 650

           = 26 + 65 = $90,

or Plan A Equals Plan B = $90.

The following are the answers:

A) Calling for 650 minutes will be equal in price between the two plans.

B) The price is $90 when two plans have the same price.

Hence, The cost when two plans cost the same amount is $90, and the amount of calling for which the two plans cost the same is 650 minutes.

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Answer:

3255

Step-by-step explanation:

Answer: The answer is 3255

Step-by-step explanation: It just is.

Answer:

3*2 = 6+9 = 15

Step-by-step explanation:

The required number is 2.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, nine more than three times a number is fifteen

Let the number be a

Converting the statement into mathematical expression,

9+3a = 15

3a = 6

a = 2

Hence, The required number is 2.

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Answer:

Step-by-step explanation:

We can factor by grouping like so

3v^2 + 16v + 5

3v^2 + 15v + v + 5

3v(v + 5) + 1(v + 5)

(3v+1)(v+5)

---------

Check:

(3v+1)(v+5)

w(v+5) ... let w = 3v+1

vw + 5w

v(w) + 5(w)

v(3v+1) + 5(3v+1) .... plug in w = 3v+1

3v^2+v + 15v + 5

3v^2 + 16v + 5

We get the original expression again, which confirms the answer.

Sonji choses the pieces that can be used to construct a triangle.

Given the question is shown in attached image.

We have to find which student chose pieces that can be used to construct a triangle.

Here, we will use the third important property of triangles is the triangle inequality rule, which states that the one length of a side of a triangle is always less than the sum of the lengths of the other two sides which are left and greater than the difference of the lengths of the other two sides.

So, applying this property in each case:

Case 1. Don’s uses the wires which measure 3 inches, 5 inches, and 12 inches.

Now using property

since sum of two sides = 3+5 =8

As we see here the third side 12 is not less than 8

So, Don’s wire cannot be used .

Case 2. Margo’s uses the wires which measure 6 inches, 8 inches, and 14 inches.

Now using property

since sum of two side :8+6=14

But third side 14 is not less than 14

So, Margo’s wire cannot be used .

Case 3. Sonji’s uses the wires which measure 12 inches, 8 inches, and 17 inches.

Now using property

since sum of two side :12+8=20

third side 17 is  less than 20

Now , difference of two sides : 12-8=4

third side 17 is greater than 4

So, Sonji’s wire can be used .

Case 4. Liam’s uses the wires which measure 16 inches, 8 inches, and 27 inches.

Now using property

since sum of two side :16+8 =24

But third side 27 is not less than 24

So, Liam’s wire cannot be used .

Hence, according to the question sonji choses the pieces that can be used to construct a triangle which is shown in attached image.

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Answer:

El ángulo conjugado de 145 grados es 35 grados.

hope it helps you....