If the sample space, S = {1, 2, 3, 4, …, 15} and A = the set of odd numbers from the given sample space, find Ac.A.{1, 2, 3, 4, 5, 6, …, 15}B.{1, 3, 5, 7, 9, 11, 13, 15}C.{1, 2, 3, 4, 15}D.{2, 4, 6, 8, 10, 12, 14}

the new equation would be:

if the new rate is changed to 3000. The new equation is:

Answer:

Explanation:

We want to convert 3 gallons to pints.

Recall that;

So, for 3 gallons, we have;

Therefore;

Answer:

To find the area of the polygon with vertices C(5, 3), A(8, -2), S(3, -4), and H(0, -2).

We have that formula for finding the area of the parallelogram with n vertices is,

we get that,

Area of the polygon with 4 vertices that is (x1,y1),(x2,y2),(x3,y3) and (x4,y4) is

Substituting the values we get,

An

income tax = $2572

social security tax = 13.3% of the profit

= 13.3% of $22,150

= 13.3/100 * 22,150 = $2,945.95

So, the total tax =

2572 + 2,945.95 = $5,517.95

Rounding to the nearest dollar

the total tax = $5,518

The answer is option C. $5,518

720x + (-20x)

Remember

(+)(+) = (+)

(+)(-) = (-)

So + (-20x) will equal - 20x, so

720x + (-20x) = 720x - 20x

Subtract 20 from 720

720 - 20 = 700, so

720x + (-20x) = 720x - 20x = 700x

The walk surrounding the pool has an area of 336.66 [tex]ft^{2}[/tex] .

A =  ( Area of semicircle including side walk ) - ( Area of semicircle without side walk )

radius of smaller semicircle = 10 ft and radius of larger semicircle = 10 + 3 = 13 ft

A = [ ( 3.14 * [tex]13^{2}[/tex] ) / 2 ] - [ ( 3.14 * [tex]10^{2}[/tex] ) / 2 ]

            = ( 530.66 - 314 ) / 2

              = 108.33 [tex]ft^{2}[/tex]

Since we take walk on both sides , we will multiply it with 2

A = 2 * 108.33

A = 216.66[tex]ft^{2}[/tex]

One side of bigger rectangle = 20 + 3 + 3 = 26 ft

A = area of rectangle - area of square

A = ( 26 * 20 ) - [tex]20^{2}[/tex]

A = 120 [tex]ft^{2}[/tex]

Therefore ,

A = 216.66 + 120

A = 336.66 [tex]ft^{2}[/tex]

Hence , the walk surrounding the pool has an area of 336.66 [tex]ft^{2}[/tex] .

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Note that parallel lines always have the same slope.

From the problem, the equation is :

and the slope is -1/4

Parallel lines must also have the same slope of -1/4

The answer is -1/4

Answer:

1

Step-by-step explanation:

Answer:

1. Given.

2. Definition of vertical angles.

3. Vertical angles theorem.

4. Definition of corresponding angles.

5. Corresponding angles postulate.

6. Transitive property of congruence.

Explanation:

1. This statement is the given part of the problem

2. vertical angles are the pair of opposite angles that are formed when two line segments intersect. Angles 1 and 3 verify this definition, thus they're vertical angles.

3. The vertical angles theorem states that a pair of two vertical angles have the same measure.

4. Corresponding angles are the angles that are formed in matching corners with the transversal when two parallel lines are intersected by another line. Thus, angles 1 and 5 are corresponding angles.

5. The corresponding angles postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding angles are congruent. Thus, angles 1 and 5 are congruent.

6. The transitive property of congruence states that if a is congruent to b and b is congruent to c, then a is congruent to c.

This means:

The sum of angle in a triangle is 180°

If two of the angles in a triangle is 56° and 6°

Let x be the third angle

56 + 6 + x = 180° (sum of angle in a triangle)

62° + x = 180°

subtract 62° from both-side of the equation

x = 180° - 62°

x = 118°

Hence, the third side is 118°

We are given a function and are asked to determine if it's even, odd or neither. Our approach is to employ the negative test and modify the function to ascertain its status. This will be depicted below.

This is our original function, next, we find h(-x)

Looking at the function h(x) and h(-x), we have to put the polynomial in the correct degree. The input of the negative sign before the h(-x) function is to check if the function will maintain the same format with the original function, h(x). The disparity is what tells us if it is even, odd or neither of the two.

Now we know h(-x), we now use a certain set of conditions to test if function is even, odd or neither.

In this case, based on the above criteria, the function is neither even nor odd.

So the numbers we have are:

-2, 3/4, -1/3, 0.2, -1, 1/2 & -0.8

So the numbers from least to greatest go as follows:

-2, -1, -0.8, -1/3, 0.2, 1/2, 3/4

Given the equation of the function f(x):

We will use the following rules of the exponents:

So, we can rewrite f(x) as follows:

So, the answer will be option B

We know that 5 lbs of apples cost $2.99

To know how much do 3 lbs of apple cost, you can use cross multiplication

If 5 lbs cost $2.99

Then 3 lbs cost $x

The proportion between the price and the number of apples is the same, you have to calculate it as:

3 lbs of apples cost $1.79

3xy²(x - 5)

The equation: 3x²y²-15xy²

x is common to both expression, we factorise it:

x(3xy² - 15y²)

y² is common to both expression, we factorise it:

xy²(3x - 15)

3 is common to both expression, we factorise it:

3xy²(x - 5)

Solution:

Given:

From the probability, it can be deduced that as the number of trials increases, the observed frequency will get closer to the expected frequency.

Therefore, if the number of trials increases significantly, then the observed frequency of landing heads up gets closer to the expected frequency based on the probability of the coin landing heads up.

For a sample space for rolling a six-sided die and then an eight-sided die is constructed as

We just change the probable events of the second die up to 8 and then combine it with the possible combinations with a normal six die, which is shown in the table above.

range = ? -2 < y < 4 According to the directions this is the inequality

Letter A is the right answer

SOLUTION

Now, 9 and 51 are not compatible because 51 cannot divide 9 without a remaider.

The compatible number with 9 that is close to 51 is 54.

Hence,

9 and 54 are compatible.

This will give us

Hence,

The estimate is 600

Answer: A

Step-by-step explanation:

B is wrong A is right.

Given:

Derivative and sope of tangent

Required:

We want to define relation

Explanation:

The derivative of a function gives us the slope of the line tangent to the function at any point on the graph. This can be used to find the equation of that tangent line for example

and the slope of that tangent is the derivative of function at point P

Now to find equation of a tangent line

1) Find the first derivative of f(x).

2) Plug x value of the indicated point into f '(x) to find the slope at x.

3) Plug x value into f(x) to find the y coordinate of the tangent point.

4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

Step 1

The meaning of QUADRATIC EQUATION is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Step 2

We are required to Identify the two tables which represent quadratic relationships.

In a quadratic equation, we have a polynomial in x with degree 2. Hence the result in y or P(x) do get repeated as a polynomial contains x² in it.

Looking at the tables we will observe that;

The answers will be;

Notice that the factor x is a common factor for all three terms. Then, factor out x:

Notice that the factor x²-2x-35 is a quadratic expression.

Find two numbers whose sum is -2 and whose product is -35 to factor out the quadratic expression. Since 5-7 = -2 and (5)(-7)=-35, those two numbers are -7 and 5. Then, the quadratic expression can be factored out as:

Then:

Then, the factorization of the given trinomial is:

Therefore, the correct choice is option C) x(x-7)(x+5)

At first, we will find the volume of the cone and the volume of the sphere, then subtract them to find the answer

The rule of the volume of the cone is

Since the height of the cone is 1 cm and its radius is 3 cm, then

h = 1 and r = 3

Substitute them in the rule above

The formula of the volume of the sphere is

Since the diameter of the sphere is 3 cm, then

Substitute it in the formula above

Noe subtract them to find the answer

The amount of the extra soap is

Let L be the amount of hours that Kylie works on raking leaves and W the amount of hours that she works on cleaning windows (on a week).

Since she cannot work more than 30 hours a week, and the total time spent working is L+W, then:

Since one month has 4 weeks, she should win $25 a week to earn $100 in a month. Since she gets paid $7 per hour for raking leaves, after L hours she would have won a total amount of 7L, and since she gets paid $6 for cleaning windows, she would have won 6W after W hours. The total amount of money earned would be 7L+6W, which should be greater than 25:

Therefore, the system of inequalities that represents the situation, is:

Solution:

To find square feet, multiply the length measurement in feet by the width measurement in feet.

Hence, the standard formula to calculate square foot is;

Chicken salad costs more

Cost of Hamburger = $ 4.30

Cost of hot Dog = $ 2.35

Cost of Chicken salad = $ 4.49

Cost of pizza = $2.49​

$4.49 is greater than $4.30

Cost of of Chicken salad is greater than Cost of Hamburger

Hence, Chicken salad costs more

An inequality that shows the answer:

4.49 > 4.30

cost = $699

Discount = 15% = 15/100 = 0.15 (decimal form)

Multiply the cost by the discount in decimal form

699 x 0.15 = 104.85

Subtract the discount amount

699-104.85 = $594.15

1) Assuming this is a quadrilateral, then the area is width times length

So

A =10 x 7

A= 70 m²

It's an area of 70 m²