The NCAA basketball tournament begins with 64
teams, and after each round, half the teams are
eliminated. The number of remaining teams t(n) is
an exponential function of the number n of rounds
already played.

A linear equation can be solved in four steps. First, simplify; next, use the properties of addition and subtraction; then, use the properties of multiplication and division; and last, check your work.

Any equation whose variables' highest powers are all equal to one is said to be a linear equation. This results in a graph with a straight line and is typically written as Ax+By=C. Here, x and y are the variables; A and B are their respective coefficients; and C is a constant.

The steps to solve a linear equation are given by

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The solution is, the cost of each ticket is $21.25.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

each of them bought a game ticket and a $16.50 team jersey.

together, they paid a total of $75.50.

now, we get,

total cost of jersey = 16.50 * 2

                               =33

so, total cost of ticket = 75.50 - 33

                                    =42.50

so, we get,

the cost of each ticket = 42.50 / 2

                                     =21.25

Hence, The solution is, the cost of each ticket is $21.25.

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The greatest volume of mortar mix, she could make, is 1.5 cubic meters.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Mortar mix is made by mixing cement, sand, and quicklime in a ratio of 1:2:3.

Julie has 0.75 m³ of quicklime.

Let the volume of cement, sand, and quicklime be x, 2x, and 3x.

So,

3x = 0.75

Divide by 3 into both sides,

we get,

3x/3 = 0.75/3

x = 0.25

The total volume = the greatest volume of mortar mix

=  x + 2x + 3x

Substituting the value of x to the expression,

we get,

x + 3x + 3x = (0.25) + 2(0.25) + (90.25)

The greatest volume of mortar mix,

= 1.5 cubic meters.

Therefore, the required amount of volume is 1.5 cubic meters.

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The complete question:

Mortar mix is made by mixing cement, sand, and quicklime in a ratio of 1:2:3.

Julie has 0.75 m³ of quicklime.

She has plenty of sand and cement.

Work out the greatest volume of mortar mix she could make.

Yes, 0.5 - 3(-2x - 1 over 3 + 4 + 8x) and -1.5(12x + 7) are equivalent expressions.


To prove this, we can use the distributive property:

0.5 - 3(-2x - 1 over 3 + 4 + 8x)

= 0.5 - 3(-2x/3 - 1/3 + 4/3 + 8x/3)

= 0.5 - (-6x - 1 + 4 + 24x)/3

= (0.5*3 + 6x + 1 - 4 - 24x)/3

= (-1.5*12x - 1.5*7)/3

= -1.5(12x + 7)
No, 0.5 - 3(-2x -1 over 3 +4 + 8x) and -1.5(12x +7) are not equivalent expressions.

To determine if two expressions are equivalent, we can simplify both expressions and compare them.

For the first expression, 0.5 - 3(-2x -1 over 3 +4 + 8x), we can distribute the -3 and combine like terms:

0.5 - 3(-2x) - 3(-1) - 3(3) - 3(4) - 3(8x)
= 0.5 + 6x + 3 - 9 - 12 - 24x
= -18x - 7.5

For the second expression, -1.5(12x +7), we can distribute the -1.5:

-1.5(12x) - 1.5(7)
= -18x - 10.5

As we can see, the simplified expressions are not the same, so they are not equivalent expressions.

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Answer:

Below

Step-by-step explanation:

a = 6 (Real numbers greater than 3)

b = 2 (Real numbers less than 8)

c = 1 (One satisfies this)

If and only if f(a) = 0, a polynomial f(x) has a factor (x-a). It's one of the techniques for factoring a polynomial.

A polynomial is an equation made up of coefficients and in determinates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

The factor theorem can help us determine if a factor is a "root" or "zero" of a polynomial. In other words, if we have a polynomial function, the factor theorem allows us to check if a particular value (usually represented by the variable x) is a solution to the polynomial equation, which means that when we plug in that value for x, the resulting output of the polynomial function will be zero. If it is, then we know that (x - a) is a factor of the polynomial, where "a" is the solution we found.

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x must be a whole number, the maximum whole number of gigabytes of data Piper can use while staying within her budget is 4.

What is the inequality?

An inequality is a mathematical statement that compares two expressions using one of the inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).

Let x be the number of whole gigabytes of data Piper can use while staying within her budget.

Her cost for data usage would be $5 per gigabyte, so her total cost would be:

Total Cost = $38.50 + $5x

The problem states that she wants to keep her bill under $60 per month, so we can set up an inequality:

$38.50 + $5x ≤ $60

Subtracting $38.50 from both sides, we get:

$5x ≤ $21.50

Dividing both sides by $5, we get:

x ≤ 4.3

Hence, x must be a whole number, the maximum whole number of gigabytes of data Piper can use while staying within her budget is 4.

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Answer:

155.744

Step-by-step explanation:

Answer:

p = 29 and q = -3.

Step-by-step explanation:

Using long division, the remainder when we divide by x − 1 is p+q−16.  The remainder when we divide by x + 1 is p−q−20.

The roman numerals of 42 is XLII

Roman numerals are a number system that originated in ancient Rome and remained the standard numbering system throughout Europe until the late Middle Ages. Numbers are written using combinations of letters from the Latin alphabet, each letter has a fixed integer value, and only the following seven are used in modern style:

I V X L C D M

1 5 10 50 100 500 1000

The use of Roman numerals continued long after the fall of the Roman Empire. From the 14th century onwards, Roman numerals were replaced by Arabic numerals. However, this process was gradual and the use of Roman numerals continues to this day in some applications.

The roman numerals of 42 is

42 = 40 +2

for 40 = 50-10 =  XL

and for 2 II

so for 42 = XLII

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Answer:

Step-by-step explanation:

points

The correct inequality written in factored form represents the graphed region is,

⇒ y ≥ (x + 6) (x - 18)

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The graph shows the inequality.

And, The point on the graph is, (- 4, - 44)

Now, By all options;

The correct inequality is satisfy the given point on the graph.

From (i);

The inequality is,

⇒ y ≥ (x + 6) (x - 18)

Put x = - 4, y = - 44

⇒ - 44 ≥ (- 4 + 6) (- 4 - 18)

⇒ - 44 ≥ (2) (- 22)

⇒ - 44 ≥ - 44

Hence, It is the correct inequality written in factored form represents the graphed region.

Thus, The correct inequality written in factored form represents the graphed region is,

⇒ y ≥ (x + 6) (x - 18)

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As per the conversion factor, 50 meters is equal to 54.6805 yards

Before we dive into the mathematical process of converting meters to yards, it is essential to understand the basic concept of these two units of distance. Meters and yards are both units of length used to measure distances, and they are both commonly used in different parts of the world.

Now, to convert 50 meters to yards, we need to know the conversion factor between meters and yards. A conversion factor is a mathematical relationship between two units of measurement. In this case, the conversion factor between meters and yards is 1 meter equals 1.09361 yards.

Using this conversion factor, we can easily convert 50 meters to yards. To do this, we simply multiply the distance in meters by the conversion factor. So,

50 meters x 1.09361 yards/meter = 54.6805 yards.

In conclusion, converting 50 meters to yards involves understanding the conversion factor between these two units of distance and using it to multiply the given distance in meters. With a little bit of practice, you can easily convert distances between meters and yards or any other units of measurement.

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Option a is the correct answer. The patient's description of vivid dreams is most likely occurring during rapid eye movement (REM) sleep.

During fast eye development (REM) rest, the mind is exceptionally dynamic, yet the muscles are loose, bringing about the trademark quick eye developments that give this stage its name. It is during REM rest that most dreaming happens. These fantasies will generally be clear, close to home, and frequently strange, and can be serious to such an extent that they might awaken the sleeper. Interestingly, during non-REM rest, the mind is less dynamic, and dreams are ordinarily less striking and vital. The way that the patient depicted clear dreams is serious areas of strength for a that they were in REM rest, as opposed to one of the non-REM stages.

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Answer:

1. The ball is thrown from a height of 2 ft

Step-by-step explanation:

Since 2 does not have a variable that would be the y-intercept; the y-intercept it where the ball is first getting thrown from.

Answer:

Answered By Unish ©

Verified Answer ✅

Step-by-step explanation:

Multiply the following rational expressions. Remember to fully simplify your answer.

(x^2-1)/(2x-3) ∙ (2x^2+x-6)/(x^2+3x+2)

First, let's factor the expressions in both numerators and denominators to simplify the multiplication:

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(x^2 - 1)/(2x - 3) = (x + 1)(x - 1)/(2x - 3)

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(2x^2 + x - 6)/(x^2 + 3x + 2) = (2x - 3)(x + 2)/(x + 1)(x + 2)

Notice that the factor (x + 2) appears in both the numerator and denominator of the second expression. We can cancel this factor and simplify the expression:

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(x^2 - 1)/(2x - 3) ∙ (2x^2 + x - 6)/(x^2 + 3x + 2)

= [(x + 1)(x - 1)/(2x - 3)] ∙ [(2x - 3)/(x + 1)]

= (x - 1)

Therefore, the simplified product of the two rational expressions is x - 1.

The key feature that is NOT present in the function h(x) is "The x-intercept of h(x) is (5, 0)".

To find the x-intercept of a function, we need to set the y-value to 0 and solve for x. In the case of h(x), we have two different equations for different ranges of x:

h(x) = (x - 5)² when 0 ≤ x ≤ 4

h(x) = -log₄(x + 6) when x > 4

Setting the first equation to 0 and solving for x, we get:

0 = (x - 5)²

0 = x - 5

x = 5

However, this value of x does not fall within the range of 0 ≤ x ≤ 4, so it is not a valid x-intercept for this equation.

Setting the second equation to 0 and solving for x, we get:

0 = -log₄(x + 6)

log₄(x + 6) = 0

4⁰ = x + 6

1 = x + 6

x = -5

This value of x also does not fall within the range of x > 4, so it is not a valid x-intercept for this equation either.

Therefore, the function h(x) does not have an x-intercept of (5, 0), and this is the key feature that is NOT present in the function.

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Answer: x should be equal to 9 (please correct me if i'm wrong)

Step-by-step explanation: Let's say the answer for this problem is equal to x

4 -(-7) + (-2) = x

4 + 7 + (-2) = x

11 + (-2) = x

9 = x

Answer:

Step-by-step explanation:

To solve the problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A is the final amount

P is the principal amount (the initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time in years

We can use this formula for each of the two years and then add the results to find the final amount.

For the first year, we know that the principal (P) is £12000, the time (t) is 1 year, and the final amount (A) is £12336. We do not know the interest rate (r) or the compounding frequency (n), but we can solve for them using the given information.

Using the formula, we have:

£12336 = £12000(1 + r/n)^(n*1)

Dividing both sides by £12000, we get:

1.028 = (1 + r/n)^n

Taking the natural logarithm of both sides, we get:

ln(1.028) = n*ln(1 + r/n)

Solving for n, we get:

n = ln(1.028) / ln(1 + r/n)

For the second year, we know that the principal (P) is £12336 (the final amount from the first year), the time (t) is 1 year, the interest rate (r) is x/2%, and the compounding frequency (n) is the value we just calculated.

Using the formula, we have:

A = £12336(1 + (x/2)/n)^(n*1)

Substituting the value we calculated for n, we get:

A = £12336(1 + (x/2)/ln(1.028))^(ln(1.028)*1)

Simplifying, we get:

A = £12336(1 + (x/2)/ln(1.028))^ln(1.028)

So the value of Jean's investment at the end of 2 years is the result of compounding the interest earned in the first year and second year, which is:

Final amount = £12336(1 + (x/2)/ln(1.028))^ln(1.028) * (1 + x/200)

Note that we use the annual interest rate of x/2% in the second year, but we need to express it as a decimal by dividing by 100. Similarly, we use x/200 instead of x/100 to express the interest rate over the 2-year period.

Answer:

£12 508.70

Step-by-step explanation:

Jean invests £12 000 in an account paying compound interest for 2 years.

In the first year the rate of interest is x%.

At the end of the first year the value of Jean’s investment is £12 336.

​In the second year the rate of interest is: x/2 %

​What is the value of Jean’s investment at the end of 2 years?

First, we find the interest rate for the first year.

Amount at beginning: £12 000

Amount after accruing interest for 1 year: £12 336

Amount of accrued interest in 1 year: £12 336 - £12 000 = £336

Interest rate:

£336 is what percent of £12 000?

percent = part/whole × 100%

percent = £336/£12 000 × 100%

percent = 2.8%

The interest rate of the first year was 2.8%.

The interest rate of the second year is 1/2 × 2.8% = 1.4%.

100% + 1.4% = 101.4% = 0.0104

Value after the second year, which is starting at £12 336 and earning 1.4% for 1 year:

1.0104 × £12 336 = £12 508.70

a) It is a continuous random variable.

b) It is a discrete random variable.

c) It is not a random variable nor discrete.

d) It is a continuous random variable

e)  It is a discrete random variable

f) It is a discrete random variable

A continuous variable has an uncountable range of possible values.

Any value falling inside an interval is acceptable.

They cannot be stated as decimal numbers and can only accept a discrete value. Counting is used to obtain them rather than measuring.

a). The height of a randomly selected giraffe is a continuous random variable.

b). The random variable is discrete. You can count how many people are sitting at a computer.

c). The gender of college students ⇒ Gender is categorical data. It is neither continuous nor discrete.

d). The number of people in a restaurant that has a capacity of 300 is a continuous random variable

e). The number of bald eagles in a country Since the number of people cannot be expressed as decimals, thus it is a discrete random variable

f). it is a discrete random variable as a number of people is a discrete count, which takes values such as 0 or 1 or 2.

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Right triangle trigonometry involves using the relationships between the angles and sides of a right triangle, as defined by the trigonometric functions sine, cosine, and tangent, to solve for missing angles or sides.

To do right triangle trigonometry, you first need to identify which angles and sides are known and which are unknown. You can then use the definitions of sine, cosine, and tangent, as well as the Pythagorean theorem, to set up and solve equations that relate the known and unknown values.

For example, if you know the lengths of two sides of a right triangle, you can use the Pythagorean theorem to find the length of the third side. Alternatively, if you know the measure of one angle and the length of one side, you can use trigonometric functions to find the length of another side or the measure of another angle.

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The Lagrange multipliers fail to solve the problem because  g = 0 at the coordinates (x, y) = (0, 1) where f reaches its minimum on g = 0,

The Italian mathematician Joseph-Louis Lagrange is honoured by having his multiplier method named after him. In order to apply the derivative test of an unconstrained problem to a constrained problem, it is necessary to convert it into a different form.

Moreover, this technique is frequently employed in mathematical optimization. When a function of the form f(x, y, and z) is subject to equality constraints of the form g(x, y, and z) = k or g(x, y, and z) = 0, one useful technique is the method of Lagrange's multipliers. This means that it depends on the values of the desired variable exactly satisfying the terms of one or more equations.

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There are 20 ways to choose 2 letters from the set A, B, C, D, and E if the order of the choices is relevant

If the order of the choices is relevant, we are looking for the number of permutations of 2 letters chosen from a set of 5 letters. We can use the permutation formula to calculate this:

nPr = n! / (n - r)!

where n is the total number of items in the set (5 letters in this case), and r is the number of items we want to choose (2 letters in this case).

nPr = 5! / (5 - 2)!

nPr = 5! / 3!

nPr = 5 x 4 x 3 x 2 x 1 / (3 x 2 x 1)

Divide the numbers

nPr = 20

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The given question is incomplete, the complete question is:

Suppose we want to choose 2 letters, without replacement, from the 5 letters A, B, C, D, and E.

How many ways can this be done, if the order of the choices is relevant?

A system of linear equations can have exactly one solution, infinitely many solutions, or no solutions. It cannot have exactly s solutions, where s is an integer strictly greater than 1.

To see why this is the case, let's consider a system of linear equations with m equations and n variables, where m ≤ n. We can represent the system as an augmented matrix A = [A|B], where A is the coefficient matrix of the system and B is the constant vector.

If the system has exactly one solution, then the rank of the coefficient matrix A is equal to the rank of the augmented matrix A = [A|B], which is n. This means that the number of pivots in the row echelon form of A is equal to n, and there are no free variables.

If the system has infinitely many solutions, then the rank of the coefficient matrix A is less than n, and there are one or more free variables. In this case, the number of solutions is not a fixed number, but rather a family of solutions that can be represented parametrically.

If the system has no solutions, then the rank of the coefficient matrix A is less than the rank of the augmented matrix A = [A|B], which is n + 1. In this case, there is a contradiction in the equations, and there is no solution.

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The sides that cannont be the sides of a triangle are the ones in option B.

2cm, 6cm, 4cm

If A, B, and C are the sides of a triangle, then the triangular inequality says that:

A + B > C

A + C > B

C + B > A

So, any set of 3 sides where the sum of two of the sides is smaller than the other side cannot be the sides of a  triangle.

Then the correct option will be b:

2cm, 4cm, 6cm

If we add the two shorter ones we will get:

2cm + 4cm = 6cm

And that is not larger than the other side, so it isthe correct option.

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A multiplying polynomials calculator is a tool used to multiply two or more polynomials together.

A multiplying polynomials calculator is a tool used to multiply two or more polynomials together. It can be helpful for simplifying algebraic expressions, solving equations, and performing various calculations in mathematics and engineering.

The calculator takes the coefficients of each polynomial as input and uses the distributive property to multiply the terms of each polynomial together. It then combines like terms and arranges the result in descending order of degrees. Multiplying polynomials can be a tedious and error-prone process, especially for large polynomials, so using a calculator can save time and reduce the chances of errors. The multiplying polynomials calculator is commonly used by students, teachers, engineers, and anyone working with algebraic expressions.

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The new coordinates of the triangle after dilation by a scale factor of 0.5 with the origin as the center of dilation are F'(3, 2.5), H'(1, 0.5), and G'(5, 0.5).

To find the coordinates of the triangle after dilation by a scale factor of 0.5 with the origin as the center of dilation, we can use the following formula:

(x', y') = (0.5 × x, 0.5 × y)

where (x, y) are the original coordinates of the point and (x', y') are the new coordinates after dilation.

Let's apply this formula to each point of the triangle:

For point F(6,5):

x' = 0.5 × 6 = 3

y' = 0.5 × 5 = 2.5

The new coordinates of point F are (3, 2.5)

For point H(2,1):

x' = 0.5 × 2 = 1

y' = 0.5 × 1 = 0.5

The new coordinates of point H are (1, 0.5)

For point G(10,1):

x' = 0.5 × 10 = 5

y' = 0.5 × 1 = 0.5

The new coordinates of point G are (5, 0.5)

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The given question is incomplete, the complete question is:

what are the coordinates of triangle by a scale factor of 0.5 with the origin as the center of dilation ?

One U.S. ounce (oz) is equal to 0.0296 litre. Simply multiply any number of oz with the given value of litre to convert and find volume.

Using a volumetric unit of measurement, the three-dimensional extent of an object or space can be determined. Volume is used to determine capacity. The volumetric unit is therefore essentially a unit for measuring the size or extent of an object or space.

The unit is typically used to describe the volume of goods or liquids. Use the International System of Units to calculate a quantity of something. The SI Units are used globally to communicate the measurements used in research settings despite the fact that people speak various languages.

For measuring volume, the three most widely used SI units are cubic meters, liters, and milliliters. specifically, the SI system's cubic meter as the unit of volume.

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