which of these triangle pairs can be mapped to each other usijng a translation and rotation about point a

The answer will of given mathematical logic will be T F T T F respectivelly.

A negation, conjunction, and disjunction are the fundamental mathematical logics. The symbols for negation, conjunction, and disjunction in mathematical logic are "," "," and "v," respectively.

Logical proofs frequently employ mathematical logic. Proofs are legitimate arguments that establish the veracity of mathematical assertions. A series of statements make up an argument. The conclusion is the last assertion, and the premises are all the statements that came before it (or hypothesis).

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The complete truth table is shown in the below diagram.

≈ q → ≈ p: True  False  True  True

The contrapositive of a conditional statement is a new conditional statement that is formed by negating both the hypothesis (the "if" part) and the conclusion (the "then" part) of the original statement, and switching their positions. The truth table for the contrapositive of a conditional statement has the same number of rows as the truth table for the original statement.

For example, if the original statement is "If it is raining, then the ground is wet", then the contrapositive would be "If the ground is not wet, then it is not raining."

According to the given table the contrapositive of a conditional statement q and p is defines as;

True

False

True

True

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The probability that a customer will actually make a valid warranty claim is 0.075.

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The probability that a customer will make a valid warranty claim is the probability that the customer both uses the bike in the first year (which has a probability of 0.75) and discovers a defect (which has a probability of 0.10).

Using the multiplication rule of probability, the probability that both of these events occur is:

0.75 x 0.10 = 0.075

Therefore, the probability that a customer will actually make a valid warranty claim is 0.075.

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Roberto needs 4 square yards of fabric to make his costume.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. For instance, the fraction 7/3 is incorrect since 7 is bigger than 3. Mixed numbers, which combine a whole number and a correct fraction, can be created from improper fractions.

Given that, piece of fabric that is 2 2/3 yards long and 1 1/2 yard wide.

Convert the length from a mixed number to an improper fraction:

2 2/3 = (2 x 3 + 2)/3 = 8/3

1 1/2 = 3/2

The area of the rectangle is:

Area = Length x Width

Substituting the values we have:

Area = (8/3) x (3/2) = 4

Hence, Roberto needs 4 square yards of fabric to make his costume.

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Answer:

w = 1

Step-by-step explanation:

If we read the problem, we are given the instructional steps to solve this problem. Lets do it anyway without any help.

[tex]11w+3=14[/tex]

We, subtract 3 on both sides (3 - 3, 14 - 3)

[tex]11w=11[/tex]

Divide by 11w (11w/11w, 11/11w)

[tex]w=1[/tex]

Answer:

Let x be the amount invested in Treasury bonds and y be the amount invested in mutual funds. Then we have the following constraints:

x + y ≤ 40 (total investment cannot exceed $40 million) x ≥ 5 (at least $5 million must be invested in Treasury bonds) y ≥ 15 (at least $15 million must be invested in mutual funds) 100x + 200y ≤ 7000 (total fees cannot exceed $7000)

The objective is to maximize the annual interest, which is given by:

0.06x + 0.08y

We can solve this problem using linear programming. The feasible region is a polygon with vertices at (5, 15), (5, 35), (30, 10), and (40, 0). We evaluate the objective function at each vertex:

At (5, 15): 0.06(5) + 0.08(15) = 1.2At (5, 35): 0.06(5) + 0.08(35) = 2.6At (30, 10): 0.06(30) + 0.08(10) = 2.8At (40, 0): 0.06(40) + 0.08(0) = 2.4

The maximum value of the objective function is 2.8, which occurs at (30, 10). Therefore, the amount that should be invested in Treasury bonds is $30 million and the amount that should be invested in mutual funds is $10 million.

The annual interest earned is 0.06(30) + 0.08(10) = $2.8 million.

Step-by-step explanation:

Preparation of a Corrected set of Financial Statements :

Income Statements :

PARTY WAGON .INC

INCOME STATEMENT

FOR THE YEAR ENDED DECEMBER 31

CURRENT YEAR

Party Revenue Earned

156,000

Total Revenue

156,000

Expenses :

Insurance Expenses

2,160

Office Rent Expense

14,400

Supplies Expense

1,440

Salary Expense

90,000

Repair and Maintainence expense

2,400

Travel Expense

7,200

Miscellaneous Expense

4,320

Interest Expense

5,280

Depreciation - Van

9,600

Depreciation -Music and Equipment

8,400

Total Expenses

145,200

Income Before Income Tax

10,800

Less : Income Tax Expense

2,400

Net Income

8,400

Jack included balance sheet accounts in the income statement, therefore the corrected income statement consisting of revenue and expenses accounts is provided above.

Statement of Retained Earnings :

Retained Earnings (As per adjusted trial balance)  18,000

Add : Net Income  8,400

Less : Dividends  (1,200)

Retained Earnings Dec 31, Current Year  25,200

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The marginal profit at the following expenditures for $8000 is 0 for $6000 is 8 for $12,000 is -16 and for $20,000 is -48.

When one more unit is produced and sold, a company or individual will make a profit known as marginal profit. The additional expense or profit made while manufacturing the next unit is referred to be marginal. Whereas marginal cost is the additional expense for manufacturing one extra unit, marginal product is the additional income received.

The difference between marginal cost and marginal product is known as marginal profit (also known as marginal revenue). Managers can utilise margin analysis to help them decide whether to increase output, reduce production, or halt production completely, a decision known as the shutdown point.

we have,

P(x)= 1000+32x - 2x²

Formula for derivative of function:

[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

Finding the derivative,

P(x+h) = 1000 + 32(x+h) - 2(x+h)²

P(x+h) = -2x² -4xh - 2h² + 32x + 32h + 1000

P(x+h) - P(x) = h(-4x - 2h + 32)

P'(x) = -4x + 32

Finding derivatives for given values of x is,

P'(8) = -4(8) + 32 = 0

P'(6) = -4(6) + 32 = 8

P'(12) = -4(12) + 32 = -16

P'(20) = -4(20) + 32 = -48

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Complete question:

The profit (in thousands of dollars) from the expenditure of x thousand dollars on advertising is given by P(x)= 1000+32x - 2x². Find the marginal profit at the following expenditures.

a. $8000

b. $6000

c. $12,000

d. $20,000

Answer:

(2, -4)

Step-by-step explanation:

[tex]{ \sf{f(x) = {x}^{3} - {3x}^{2} }} \\ { \sf{ {f}^{l}(x) = {3x}^{2} - 6x }} \\ \\ { \sf{0 = x(3x - 6)}} \\ { \sf{0 = 3x - 6}} \: \: \: \: \: \\ { \sf{3x = 6}} \\ { \sf{x = 2}}[/tex]

For x = 2

[tex]{ \sf{f(2) = {2}^{3} - 3 {(2)}^{2} }} \\ { \sf{f(2) = 8 - 12}} \\ { \sf{f(2) = - 4}}[/tex]

Point is (2, -4)

Answer:

D. y = -2x

Step-by-step explanation:

slope = rise/run = 2/-1 = -2

y-intercept = (0,0)

y = mx + b

y = -2x + 0

y = -2x

Answer:

p=O-12

Step-by-step explanation:

original price:O

12 less than O is "O-12"

therefore p=O-12

If x is an integer, the least possible value of x is 4. So the option D is correct.

The triangle's third side should be less than the sum of the other two sides and more than the difference of the other two sides.

11 - 7.5 < x < 11 + 7.5

Simplify

3.5 < x < 18.5

So the value of the x is between 3.5 and 18.5.

From the option the value 4 and 5 lies between 3.5 and 18.5.

As we have to determine the least possible value of x, so the value of x should be 4. So the option D is correct.

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The complete question is:

The sides of a triangle have lengths 7.5, 11, and x. If x is an integer, what is the least possible value of x?

A. 1

B. 2

C. 3

D. 4

E. 5

Answer:

I'm pretty confident that the answer is E

The value of y in the given isosceles triangle is 140°.

A triangle with two equal edges is said to be isosceles. Also equal are the two angles that face the two identical sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.

If the sides AB and AC of a triangle ABC are equivalent, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is also congruent," states the theorem that explains the isosceles triangle.

An angle is a shape created by two lines that share an endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two beams are in the plane where the rays are located. The meeting of two surfaces also creates angles.

In the given question,

∠P=∠Q

2x+10=x+15

x=5

Therefore,

∠P=2(5)+10=20°

∠Q=5+15= 20°

∠P+∠Q+∠R= 180°

20+20+∠R= 180°

∠R= 140°

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Step-by-step explanation:

Set it up as a ratio:

14 is to (14 +6)   as   21 is to  ?

14/20 = 21/?

? = 21 * 20 / 14 = 30 units

By analyzing the relationship between the distance traveled and the time taken from the given graph, we determined that the cruising speed of the airplane is 567 units of distance per 1 unit of time.

To find the cruising speed of the airplane, we can analyze the given graph and observe the relationship between the distance traveled and the time taken.

Looking at the data points provided, we see that the distance traveled is directly proportional to the time taken. This means that for every unit increase in time, there is a corresponding increase in the distance traveled.

Let's consider the first two data points: (1,567) and (2,1134). The time difference between these two points is 2 - 1 = 1, and the distance traveled difference is 1134 - 567 = 567.

Since the distance traveled is directly proportional to time, we can conclude that the speed of the airplane is equal to the distance traveled divided by the time taken. In this case, the speed would be 567 units of distance per 1 unit of time.

Now, let's calculate the cruising speed using the other data points as well:

(2,1134) - (1,567) = 1134 - 567 = 567 units of distance per 1 unit of time

(3,1701) - (2,1134) = 1701 - 1134 = 567 units of distance per 1 unit of time

(4,2268) - (3,1701) = 2268 - 1701 = 567 units of distance per 1 unit of time

(5,2268) - (4,2268) = 2268 - 2268 = 0 units of distance per 1 unit of time

We can see that for each time interval, the distance traveled is always 567 units. Therefore, we can conclude that the cruising speed of the airplane is 567 units of distance per 1 unit of time.

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Answer:

No.

Step-by-step explanation:

Given two triangles on a coordinate plane, you can check whether they are congruent by using the distance formula to find the lengths of their sides. If three pairs of sides are congruent, then the triangles are congruent by the above theorem.

Over here, they aren't congruent by the SSS.

The concept of Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different theorems and axioms.

The concept of Euclidean geometry as required to be discussed is basically introduced for flat surfaces or plane surfaces. The postulates of the Euclidean geometry are as follows!

1 : A straight line may be drawn from any one point to any other point.

2 :A terminated line can be produced indefinitely.

3 : A circle can be drawn with any centre and any radius.

4 : All right angles are equal to one another (Congruent).

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The intersection of two parallel lines; x = 10 metres.

Alternate angles are created when two parallel lines are intersected by a transversal. Have a look at the given illustration; the two parallel lines are EF and GH. When a transversal splits two parallel lines, the alternate angles are equal.

The alternate interior angles are equal because of the parallel lines characteristic.

Angle STQ (denoted as 2x+10) and angle RQS are hence equal. Angle QRP (shown as x+20) and angle RQS are likewise equal.

Setting these two angles equal to each other, we can get:

x+20 = 2x+10

Simplifying this equation, we get:

x = 10.

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A vector x orthogonal to the row space of A, and a vector y orthogonal to column space, and a vector z orthogonal to the null space. The orthogonal vector is :

A = [tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]

The orthogonal complement of the subspace V contains any vector perpendicular to V. This orthogonal subspace is denoted V⊥. (pronounced "V perp").

By this definition, null space is the orthogonal complement of row space. Every x perpendicular to the line satisfies Ax = 0 and lies in null space.

vice versa. If v is orthogonal to null space, it must be in row space. Otherwise, we can add this v as an extra row of the matrix without changing its null space. The rice space will become larger, breaking the rule of r+(n−r) = n.

The column space extent of A. These two vectors are the basis of col(A) , but they are not normalized.

In this case, the columns of A are already orthonormal, so you don't need to use the Gram-Schmidt procedure. To normalize a vector and then divide it by its norm:

                   [tex]\left[\begin{array}{ccc}1&2&1\\2&4&3\\3&6&4\end{array}\right][/tex]

and the vector after orthogonal process is:

                  [tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\1&-2&2\end{array}\right][/tex]

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After answering the provided question, we can conclude that slant height  of pyramid  [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The edges of the base form triangle faces known as sides, which connect to the top.

            /\

          /    \

        /         \

      /______\

         5

         |

         |

         |

         |

         |

         2

The square pyramid in the diagram above has a two-unit-long square base and four five-unit-high triangular faces. The Pythagorean theorem can be used to calculate the slant height of each triangular face:

slant height [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]

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Answer: y = 3x-2 (for first question)

Step-by-step explanation:

Equation of the line: y = mx+c. For A, it passes through (0, -2) and has a gradient of 3. So, you substitute the values inside the equation.

x = 0

y = -2

m = 3

-2 = 0+c

c= -2

ans: y = 3x-2

Use the same method to complete the rest of the questions. GL

Note: I am just a student, if I get this wrong I hope someone corrects me, thanks

The base of the triangle is decreasing at a rate of 36/19 cm/min when the altitude is 9.5 cm and the area is 94 sq cm.

We can differentiate composite functions using the chain rule in calculus. Any function that is created by fusing two or more other functions is referred to as a composite function. According to the chain rule, if y = f(g(x)), and f and g are both differentiable functions, then the derivative of y with respect to x is given by:

dy/dx = f'(g(x)) * g'(x)

Given that, the altitude is 9.5 cm and the area is 94 sq cm.

The area of the triangle is given as:

A = 1/2(b)(h)

Differentiating both sides with respect to time we have:

dA/dt = 1/2[(db/dt)(h) + b(dh/dt)

Now,

dA/dt = 2 and dh/dt = 2.

Substituting the values we have:

2 = (1/2) * (db/dt * 9.5 + b * 2)

4 = db/dt * 9.5 + 2b......(1)

Using the area of triangle we know that:

Area = (1/2) * b * h

94 = (1/2) * b * 9.5

b = 20

Substituting the value of b in equation 1 we have:

4 = db/dt * 9.5 + 40

db/dt = - 36/19 cm/min

Hence, the base of the triangle is decreasing at a rate of 36/19 cm/min when the altitude is 9.5 cm and the area is 94 sq cm.

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The difference between the two formulas is that nPr takes order into account, while nCr does not. To determine which formula to use, consider whether order matters in the problem. If order matters, use nPr. If order does not matter, use nCr.

a) An example of an application problem that uses nPr could be the following: In how many ways can a committee of 3 people be chosen from a group of 7 if the order of selection matters?

b) An example of an application problem that uses nCr could be the following: In how many ways can a committee of 3 people be chosen from a group of 7 if the order of selection does not matter?

c) The formula for nPr is n!/(n-r)!, where n is the total number of items and r is the number of items being selected in a specific order. The formula for nCr is n!/r!(n-r)!, where n is the total number of items and r is the number of items being selected without regard to order.

a) The tree diagram for the problem is:

     H          T

    / \        / \

   H   T      H   T

  / \ / \    / \ / \

 H  T H  T  H  T H  T

b) The probability that all the coins will turn up heads is 1/8 or 0.125, since there is only one outcome out of the eight possible outcomes that satisfies this condition.

c) The probability that there will be at least one tails is 7/8 or 0.875, since there are seven outcomes out of the eight possible outcomes that satisfy this condition (all except HHH).

Therefore, All the possible outcomes are:  [tex]HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.[/tex]

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Step-by-step explanation:

(a) Let the original price of each 6-day ski pass be x. Then, the sale price of each pass is 0.85x = 272. Solving for x, we have:

0.85x = 272

x = 320

Therefore, the original price of each 6-day ski pass was $320.

(b) Two 3-day ski passes cost 2 x £110 = £220. Converting to US dollars using the exchange rate, we have:

£220 x 1.70 = $374

Therefore, Andrew would save:

$374 - $272 = $102

by buying one 6-day ski pass in the sale rather than two 3-day ski passes.

Answer:

Step-by-step explanation:

y2-y1/x2-x1

-7-(-19)/-2-1

12/-2

-6

The slope is -6

Answer:

g(5)=69

Step-by-step explanation:

g(5)=3(5)^2-2(5)+4

g(5)=75-10+4

g(5)=69

Answer:

B is correct

Step-by-step explanation:

If it is spun twice then the probability of it landing on 2 and then an odd number is:

Pr(2,1) or Pr(2,3) or Pr(2,5) or Pr(2,7)

1/49 * 4

4/49

the probability of indentifying at least 11 shirts correctly by random guessing is 0.0002

The ratio of favaourable outcomes to all possible outcomes of an event is known as the probability. The total number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

Total no.of event=12

the probability that Joy will identify at least 11 shirts correctly by random guessing=

P(X≥11)=P(X=11)+P(X=12)

=¹²C₁₁(½)¹(½)¹¹+¹²C₁₂×(½)¹²(½)⁰

=12×½×(1/2)¹¹+(½)¹²

=0.00024414062≈0.0002

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