1. Find a counterexample.

If two angles are complementary, then they are not congruent.

area = 13+9=22

22/2 = 11

11x 4 = 44 square units

Answer:

44 square units

Step-by-step explanation:

Area of the trapezoid formula is [tex]\frac{base1 +  base2}{2} \cdot height[/tex]

To find the base and the height we count the number of units in the graph

Base 1= 13

Base 2= 9 and height = 4

Now plug in all the values in the formula and find the area of the trapezoid

Area of the trapezoid=[tex]\frac{base1 +  base2}{2} \cdot height[/tex]

=[tex]\frac{13+9}{2} \cdot 4[/tex]

=[tex]\frac{22}{2} \cdot 4[/tex]

=44 square units

When two dice are rolled, there are 6 feasible outcomes out of 36 that will sum to '7', hence the probability is 1 out of 6, or approximately 0.167.

In the field of probability, when you roll two dice, there are 6 possible outcomes for each die, hence giving us 36 possible outcomes altogether (6*6=36). Out of these 36 possible outcomes, there are 6 combinations that can total to '7'. These combinations are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). Therefore, the probability of rolling a '7' with two dice is 6 out of 36, which simplifies to 1 out of 6, or approximately 0.167, when rounded to three decimal places.

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Answer:

1. D. 30

2. C. [tex]\frac{5}{14}[/tex]

3.  [tex]\frac{5}{9}[/tex]

4. D. [tex]\frac{8}{15}[/tex]

5. A. [tex]\frac{12}{9}, \frac{11}{9}[/tex]

Step-by-step explanation:

1. LCD or lowest common denominator for a set of fractions is lowest common multiple of all the denominators in that set of fractions

∴ for [tex]\frac{3}{5}[/tex] and [tex]\frac{1}{6}[/tex] LCD will be 5×6 = 30

2. [tex]\frac{3}{7} - \frac{1}{14}  = \frac{6-1}{14} = \frac{5}{14}[/tex]

3. [tex]\frac{1}{3} - \frac{2}{9}  = \frac{3+2}{9} = \frac{5}{9}[/tex] = [tex]\frac{5}{9}[/tex]

4. [tex]\frac{2}{15} + \frac{1}{15} = \frac{1}{5}\\\\\frac{2}{15} + \frac{8}{30} = \frac{2}{5}\\\\\frac{2}{15} + \frac{5}{15} = \frac{7}{15}\\\\\frac{2}{15} + \frac{8}{15} = \frac{2}{3}[/tex]

5. [tex]\frac{12}{9} - \frac{11}{9} = \frac{1}{9} \\\\\frac{34}{7} - \frac{21}{7} = \frac{13}{7} \\\\\frac{24}{5} - \frac{11}{3} = \frac{17}{15}\\\\\frac{27}{9} - \frac{11}{3} = \frac{-6}{9}[/tex]

The value of ( g o f ) (0) is -3.

Here,

The function is given as;

[tex]f (x) = x^{2}[/tex] and [tex]g (x) = x-3[/tex]

We have to find the value of ( g o f ) (0).

What is Composite function?

Composite function is an operation that takes two functions f and g and produces a function k such that k (x) = g(f(x)).

Now,

The function are;

[tex]f (x) = x^{2}[/tex] and [tex]g (x) = x-3[/tex]

Simplify ( g o f ) (0) as;

⇒ [tex]( g o f ) (0) = g ( f (0)) = g (0) = 0-3 = -3[/tex]

Hence, The value of ( g o f ) (0) is -3.

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Answer:

If a staff member notices behavioral changes in the child it could improve the situation if a staff member subtly questioned the child not alarming anything and if the child is aware of abuse the staff member could quickly respond and seek help from a higher person.

We are given that:

fabric required = 3 3/5 yards

costumes = 5

We can write fabric required as a fraction in the form of:

(3 * 5) + 3 = 18

fabric required = 18 / 5 yards

So total fabric required is = (18 / 5 yards) * 5 = 18 yards

Answer:

18 yards

If the area of one face of a cube is 25 cm2 . what the surface area of the cube will be is: 150cm²

Let x represent the surface area of the cube

Hence:

Surface area of a cube of edge x =6x²  

Surface area of the cube =6(25cm)²

Surface area of the cube=150cm²

Inconclusion if the area of one face of a cube is 25 cm2 . what the surface area of the cube will be is: 150cm²

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The original statement, 'If a number is a natural number, then it is also a whole number' is true because every natural number falls into the set of whole numbers. However, its converse is not true, as whole numbers include 0, which is not a natural number, making the inverse and the bi-conditional false. The contrapositive of the statement is true, maintaining logical consistency.

If a number is a natural number, then it is indeed also a whole number. The relationship between natural numbers and whole numbers is an inclusive one, where all natural numbers (1, 2, 3, ...) are also whole numbers (0, 1, 2, 3, ...). The original statement can be expressed in logical form as: If P, then Q, where P is 'a number is a natural number,' and Q is 'it is also a whole number.'

Here is how the other forms of the statement look:

The inverse negates both the hypothesis and the conclusion: If not P, then not Q. So, 'If a number is not a natural number, then it is not a whole number.'

The converse switches the hypothesis and the conclusion: If Q, then P. For our statement, 'If a number is a whole number, then it is also a natural number.'

The contrapositive negates and switches the hypothesis and conclusion: If not Q, then not P. Therefore, 'If a number is not a whole number, then it is not a natural number.'

The bi-conditional states that P if and only if Q: A number is a natural number if and only if it is a whole number.'

The truth value of the original statement is true since all natural numbers are whole numbers. However, the converse is not true because whole numbers also include 0, which is not a natural number. Consequently, the inverse and the bi-conditional are false. The contrapositive is true because if it is not a whole number, then it can't be a natural number (considering that whole numbers include all natural numbers).

The sum of the probabilities of any event and its complement is always 1.

The student's question involves probability and arrangement of objects, which falls under the subject of mathematics. More specifically, the problem relates to permutations and the fundamental counting principle, combined with basic probability concepts.

Statement 36: The sample space is the set of all possible outcomes that can occur. Since there are 12 different books, the sample space consists of these 12 unique titles, where 8 are fiction (F1 to F8) and 4 are nonfiction (N1 to N4). The sample space is therefore: {F1, F2, F3, F4, F5, F6, F7, F8, N1, N2, N3, N4}.

Statement 37: The sum of the probabilities of an event and its complement is always 1. This is because an event and its complement together cover all possible outcomes in the sample space.

The number of pounds that she received in exchange for $500 cash will be 299.40 pounds.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Angela lives in the United States. She went on a trip, flying first to London, then to Paris, then back to the United States. Assume that currency rates remained constant during her trip. If the currency rate was $1.67 per English pound.

The dollar is directly proportional to the pound.

Let p be the number of the pound.

p / 500 = 1 / 1.67

p = 500 / 1.67

p = 299.40 pounds.

The number of pounds that she received in exchange for $500 cash will be 299.40 pounds.

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The coordinates of the midpoint of segment VW are (x/2, (y-3)/2).

To find the coordinates of the midpoint of segment VW, we can use the midpoint formula.

The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.

Given the endpoints V(-2, -6) and W(x+2, y+3), we can find the x-coordinate of the midpoint by taking the average of the x-coordinates: (-2 + (x+2))/2.

Similarly, we can find the y-coordinate of the midpoint: (-6 + (y+3))/2.

So the coordinates of the midpoint are (x/2, (y-3)/2).

The simplified form of cos C is sqrt(2)/2.

"Cos is the cosine function of a right triangle in trigonometry. Cos function is the ratio of adjacent side and hypotenuse. It helps us to find the length of the sides of the triangle, irrespective of given angle.

Suppose we have a right triangle and α is the angle between adjacent side and hypotenuse, then as per the cos function, we can write

Cos α = Adjacent Side/Hypotenuse"

Here, given the base of the triangle is = 5

and hypotenuse is = 5sqrt2

So, [tex]cos C = 5/5\sqrt2 = 1/\sqrt2[/tex]

Multiplying both numerator and denominator by sqrt2

We get [tex]\sqrt2/2[/tex].

Hence, the value of cos C is [tex]\sqrt2/2[/tex]

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Answer:

Cost of living is the amount of money needed for fixed expenses such as housing, food, taxes, and health care, as well as variable expenses. Big cities tend to have a higher cost of living than smaller cities.

Step-by-step explanation:

The function g(x) = –7x² + x³ is the reflection of the function f(x) = 7x² – x³ about the x-axis. This is observed by the change in signs of each term in the function's equation after performing the reflection.

By observing the given equation, f(x) = 7x² – x³ and g(x) = –7x² + x³, it is clear that the function f(x) reflects about the x-axis to create function g(x). This is indicated by the change of signs of each term in the equation of the function.

To elaborate, a reflection about the x-axis sees a function's equation change y(x) to -y(x). In our example, f(x) becomes -f(x) or –(7x² – x³), which after simplifying gives us –7x² + x³ = g(x). Therefore, g(x) is the reflection of f(x) about the x-axis.

Furthermore, to identify a reflection about the y-axis, observe if the equation changes from f(x) to f(-x). An even function or a function symmetric about the y-axis would not change with this transformation. Conversely, an odd function would change signs, just like our function did when reflecting over the x-axis.

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Final answer:

The probability of obtaining at least one concert ticket through both the internet and by telephone is 0.9984.

Explanation:

The probability that someone who tries to buy tickets both through the internet and by telephone will obtain at least one ticket is 0.9984.

To calculate this, we first find the probability of not getting any tickets through either method: P(no tickets) = P(no tickets by phone) * P(no tickets online). Then, subtract this probability from 1 to get the probability of obtaining at least one ticket: P(at least one ticket) = 1 - P(no tickets).

Using mathematical operations, the total no. of singles Jordan hit during his baseball career = 67.

Understanding the distinction between Operators and Operands will be made easier if we are aware of the differences between and purposes for Numbers/Values, Symbols, and Functions.

Understanding mathematical operations will be aided by being aware of the distinction between Operators and Operands as well as their function.

In the given statistics,

The number of Home Runs = 3

The number of Doubles = 17

The number of Triples = 1

The total no. of hits = 88

Now, to calculate the total no. of singles hit = 88 - (3+17+1)

= 67

Therefore, the total no. of singles Jordan hit during his baseball career = 67.

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Billy drives 171 miles in 3 hours, so he could drive 256.5 miles in 4.5 hours.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

The number of miles driven varies directly with the number of hours in the car.

Billy drives 171 miles in 3 hours.

Then the number of miles he can drive in 4.5 hours will be

Let x be the number of miles covered in 4.5 hours.

The speed remains constant.

Then we have

x / 4.5 = 171 / 3

x = 256.5 miles

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Billy could drive 256.5 miles in 4.5 hours.

To find the number of miles Billy could drive in 4.5 hours, we will use the concept of direct variation. Direct variation states that when two variables are directly proportional, their ratio is constant.

Given that Billy drives 171 miles in 3 hours, we can set up a proportion:

Miles driven / Hours in the car = Miles driven / Hours in the car

Using the given values, we have:

171 / 3 = x / 4.5

To solve for x, cross multiply:

3x = 171 * 4.5

Divide both sides by 3:

x = (171 * 4.5) / 3

Simplifying the right side of the equation gives us:

x = 256.5

Therefore, Billy could drive 256.5 miles in 4.5 hours.