Express 486 as a product of its prime factors, leaving your answer in index notation.

The simplified form of the numerical expression  (9² - 4 - 4) - (- 2³ - + 12) is 93.

Numerical expression is a combination of the words numerical, which refers to numbers, and expression, which denotes a statement. Consequently, it is a statement that uses numbers.

Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.

By mixing numbers with different mathematical operators, we can create a numerical expression. There is no restriction on how many operators can be used in a numerical expression. Between two numbers, some mathematical expressions utilize just one operator, whereas others may use multiple operators.

Given, An expression (9² - 4 - 4) - (- 2³ - + 12).

= (9×9 - 8) - (- 2×2×2 - 12).

= (81 - 8) - (- 8 - 12).

= (73) - (- 20).

= 73 + 20.

= 93.

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For the digits -5/4, -2 1/2, and -0.1, the correct inequality is -

Option D: -0.1 > -5/4 > -2 1/2

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The values for the inequality are -

A fractional number = -5/4

A mixed fractional number = -2 1/2

A decimal number -0.1

Convert the fraction number into decimal value using arithmetic operation of division -

-5/4 = -1.25

Convert the mixed fraction number into decimal value using arithmetic operation of multiplication and division -

-2 1/2 = -5/2 = -2.5

Here the greatest value is -0.1.

Then the second greatest value is -1.25 or -5/4.

The lowest value is -2.5 or -2 1/2.

So, the inequality obtained is = -0.1 > -5/4 > -2 1/2

Therefore, the inequality is -0.1 > -5/4 > -2 1/2.

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The statement is false.

O(nlogn), commonly known as loglinear complexity, denotes that n times will be required to perform logn operations.

The term "1 half n (n space plus log space n )space" is equivalent to O(n log n) which is a class of functions that grow asymptotically no faster than n log n.

On the other hand, the term "omicron (n squared)" is equivalent to o(n^2), which is a class of functions that grow asymptotically slower than n^2.

As a result, it is untrue to say that there is a single half-n (n space plus log n)space element in the omicron (n squared) space.

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a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

A relation is a function if it has only One y-value for each x-value.

Given that a  Function G takes a student's first name for its input and gives the number of letters in the first name for its output.

a.

Given that G(Jada) = 4

In the above function Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. We need to find the value of G(Diego)

In the above function Diego is the input and 5 will be output, the output is 5 because there are 5 letters in Diego word.

G(Diego) =5

Hence, a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

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For the given matrix A, a 3x2 matrix B such that AB=I, where I is the 2x2 matrix B =  [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex] when AB=I

Given matrix A = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₂ₓ₃

B = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₃ₓ₂

In such a way we know that, that AB = I ₂ₓ₂

therefore = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

we can say that [tex]\left[\begin{array}{ccc}a+2c+e&b+2d+f\\a+c+e&b+d+f\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

then, a+2c+e=1

then, when elaborated we get, a+2(-a-e)+e=1

a-2a-2e+e=1

-a-e=1

a+e = -1

2c-c = 1, c = 1 hence we get the value for c

similarly we can do the same steps for the other values

b+2d+f=0

1-d+2d=0

1+d = 0

d = -1

we get the value of d as well now for the value of a and e we can proceed as shown below:

a+c+e=0

c= -a-e

a+e= -c

a+e= -1

a= -2, e=1

similarly we can proceed as shownfor the values of b and f

b+d+f=1

b+f=1-d

b+f=2

b=1, f=1

when we put these values in the correct order and place we get the value for matrix b such as shown below,

therefore, matrix B =  [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex]

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I agree with Kofi that the circumference of a circle equals pi times the diameter. This is because the formula for the circumference of a circle is given by:

C = 2πr

Where C is the circumference, π is pi, and r is the radius of the circle. To find the diameter, we can double the radius, so we can write:

C = 2π(r) = π(2r) = πd

Where d is the diameter of the circle.

So, the formula for the circumference of a circle is indeed pi times the diameter, not just pi times the radius.

1. The area of the marble is 6.6m² and the cost is

$3491.4

2. The area of the marble is 42.84m² and the cost is $22662.36

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

1. The area of the marble is

A=( 3.7 × 1.2 ) + 0.9 × 2.4

A= 4.44 + 2.16

A= 6.6m²

if the cost is 23 dollars /meter

per meter square = 23² = $ 529 / meter square

1 meter square = 529

6.6 meter square = 529 × 6.6 = $3491.4

2. The area of the marble is obtained by cutting it into rectangle and trapezium

A= ½(8.8+4.8) 3.9 + 4.8 × 3.4

A= ½(13.6× 3.9) + 16.32

A= 26.52+ 16.32

A= 42.84 m²

The cost will be 529 × 42.84

= $22662.36

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The total number of each type of bill and coin are

$5 bills x 5,

$1 bills x 10,

quarters x 16,

dimes x 9.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) sign on either side. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.

Now in the given question,

$5 bills = x, total = 5x

$1 bills = 2x, total = x

Quarters = 3x + 1, total = 0.25(3x + 1)

Dimes = 3x + 1 - 7= 3x - 6, total = 0.1(3x - 6)

Equation below as the sum, solve for x:

5x + 2x + 0.25(3x + 1) + 0.1(3x - 6) = 39.9

7x + 0.75x + 0.25 + 0.3x - 0.6 = 39.9

8.05x  - 0.35 = 39.9

8.05x = 40.25

x = 40.25/8.05

x = 5

Number of each bill and coin:

$5 bills = 5

$1 bills = 2*5 = 10

Quarters = 3*5 + 1 = 16

Dimes = 3*5 - 6 = 9

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The company must make 100 X-ray machines to minimize the unit cost.

A differential equation is an equation that contains one or more functions with its derivatives.

To minimize the unit cost, we need to find the value of x that minimizes the function C(x) = 0.9x² - 180x + 20985.

We can start by taking the derivative of C(x) with respect to x and setting it equal to zero:

C'(x) = 1.8x - 180 = 0

Solving for x, we get:

x = 100

Therefore, the company must make 100 X-ray machines to minimize the unit cost.

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The p-value is a measure of the evidence against the null hypothesis (H0)

The correct answer is (a) greater the evidence against H0.

It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming that the null hypothesis is true.

The smaller the p-value, the less likely it is that the observed result is due to chance alone, and the stronger the evidence against the null hypothesis. This means that if the p-value is very small (e.g., less than 0.05), we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis.

In contrast, a large p-value indicates weak evidence against the null hypothesis, and we may not have enough evidence to reject H0. Therefore, the smaller the p-value, the greater the evidence against H0.

Option (b) is incorrect because the chance of committing a Type I error (rejecting the null hypothesis when it is actually true) is related to the level of significance (alpha) and not the p-value. Option (c) is also incorrect because the chance of committing a Type II error (failing to reject the null hypothesis when it is actually false) is related to the power of the test and not the p-value. Option (d) is incorrect because a smaller p-value actually makes it more likely that one will reject H0, assuming that the level of significance is held constant.

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The Equivalent Fraction of -117 / 63 is -13/7.

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½.

A rule that says the outcome of multiplying the numerator and denominator of a fraction by the same nonzero number is a fraction equal to the original fraction.

Given:

We have the Fraction -117 / 63

As, Equivalent fraction can have different numerators but the denominators should be necessarily same.

Now, simplifying the fraction

= -117/ 63

= - (13 x 9) / (7 x 9)

= -13 / 7

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Answer:

angle a = 122°

Step-by-step explanation:

since the opposite angles in a parallelogram are equal, therefore,

Angle a = angle c

therefore,

14x -4 = 15x - 13

-4 +13 = 15x - 14x

x = 9

therefore angle a = 14 x 9 - 4 = 122°

The approximate solutions to the equation is (0.655, -2.618)

From the question, we have the following parameters that can be used in our computation:

-2x

|-3 + 1| =

-2√x - 1

Express the equation properly

So, we have the following representation

-2x|-3 + 1| = -2√x - 1

This gives

-4x = -2√x - 1

Next, we split the equation

y = -4x

y = -2√x - 1

To solve graphically, we plot the equation and write out the point of intersection

Hence, the solution is (0.655, -2.618)

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A scatter plot would best display the relationship between the number of hours a student spent studying for several tests and the student's grade on each test.

A scatter plot is a graph that displays the relationship between two continuous variables. In this case, the number of hours a student spent studying is the independent variable, which would be plotted on the x-axis. The student's grade on each test is the dependent variable, which would be plotted on the y-axis. Each data point would represent a single test, with the x-coordinate indicating the number of hours studied for that test and the y-coordinate indicating the grade received.

By using a scatter plot, you can easily identify any patterns or relationships between the number of hours studied and the student's grades on each test. It can also help to identify any outliers or anomalies in the data.

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There are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers. Hence, the accurate answer is option (b) 28.

To determine the number of ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers, we will use the formula for combinations, which is given by -

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items to be selected, and ! denotes the factorial function (the product of all positive integers up to a given number).

Here, we are given n = 8 fish and k = 2 fish.

Thus, the number of ways to select and place 2 fish from 8 fish will be -

8C2 = 8! / (2!(8-2)!) = (8 x 7) / (2 x 1) = 28

Therefore, there are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers.

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The answer choices  50(1.15)  and 57.5 below are equivalent to 50(1+0.15)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).

50(1+0.15)

Add the numbers

= 50(1.15)

Multiply the  numbers

= 57.5

The answer choices  50(1.15)  and 57.5 below are equivalent to 50(1+0.15)

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Answer:

25.85 cubic feet

Step-by-step explanation:

Volume of a cylinder is

Base Area • height

The Base Area of a cylinder is a circle. The area of a circle is pi•r^2.

Vol = pi•r^2•h

They gave the diameter of the circle as 2.8, so the radius is half of that.

r = 1.4

The height was given

h = 4.2

Fill in radius and height and 3.14 for pi. Square the radius and then multiply everything.

see image.

Round to two decimal places.

hi i just did the test and the answer is 25.85 cubic feet

and it was correct btw other person deserves brainly have a nice day!

Doubling the down payment reduces the total cost of the vehicle, and increasing the down payment or extending the loan term are two ways to lower the monthly payment.

Let's assume that you're planning to buy a car worth $20,000. The down payment is the initial amount you pay towards the purchase of the car, and it is usually expressed as a percentage of the total cost of the car. Let's assume that the down payment is 10% of the total cost, which means you have to pay $2,000 initially.

If you double the down payment from 10% to 20%, you will have to pay $4,000 initially. This means that the amount you borrow from the bank to buy the car will be reduced. As a result, the total cost of the vehicle will decrease because the interest on the loan will also decrease.

Now, let's move on to ways to lower your monthly payment.

Increase the down payment: As we discussed earlier, making a higher down payment reduces the loan amount, which, in turn, reduces the monthly payment. So, if you can increase the down payment, you can lower the monthly payment.

Increase the loan term: The loan term is the length of time you have to repay the loan. If you extend the loan term, the monthly payment will be lower. However, keep in mind that a longer loan term means you'll end up paying more interest over the life of the loan, which will increase the total cost of the vehicle.

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Answer:

to help navigate the answer

A regular polygon with 18 sides has a central angle that is 20 degrees in size.

A polygon's total number of central angles equals 360 degrees.

As a result, the regular polygon's centre angle has a ratio of 360 to its number of sides. It may be expressed as,

[tex]$C_a=\frac{360}{n}[/tex]

Here, (n) denotes the regular polygon's number of sides.

The polygon in the provided issue has an overall total of 18 sides. Using the method above, it is possible to determine the polygon's centre angle, which has 18 sides. Thus,

[tex]$& C_a=\frac{360}{18} \\[/tex]

[tex]$& C_a=20^{\circ}[/tex]

Therefore, a regular polygon with 18 sides has a central angle that is 20 degrees in size.

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Using the ratio formula the unknown numbers are found to be 6 and 9.

What is ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

The original ratio value is 2 : 3.

Three is added to the ratio.

The new ratio value is 3 : 4.

Let the unknown numbers be 2x and 3x.

The equation will be -

2x + 3 / 3x + 3 = 3/4

Solve the equation -

4(2x + 3) = 3(3x + 3)

8x + 12 = 9x + 9

8x - 9x = 9 - 12

-x = -3

x = 3

Substitute the value of x in the unknown numbers -

2x = 2(3) = 6

3x = 3(3) = 9

Therefore, the numbers are 6 and 9.

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Answer:

SOLVE IT!

Step-by-step explanation:

A. 45.50+0.11= answer

B. 65.50+0.17= answer

Minus A plus B to get answer!

Answer:

x = 3

Step-by-step explanation:

Take the first equation-  x + 2y = (-1)

Multiply both sides by 2

2(x + 2y) = 2(-1)
2x + 4y = -2

Add first and second equations

(2x + 4y = -2)

+(4x -4y = 20)
= 6x = 18

x = 18/6

x= 3

Extra info- This method is also called as Elimination method in which Elimination (whether by addition of equations or subtraction) of any variable is done.

Hope it helps

======================================================

Explanation:

Let's label the sides of the triangle a, b, and c.

Furthermore, let's have 'a' & b represent known sides and  [tex]b \ge a[/tex] be the case. For a triangle to be possible, the missing side c must have these restrictions placed on it:

b-a < c < b+a

This inequality is valid because of a modification to the Triangle Inequality Theorem. I'll leave the proof to the reader.

-------

In this case we have a = 3 and b = 8 which lead to...

b-a < c < b+a

8-3 < x < 8+3

5 < x < 11

The third side is between 5 and 11, excluding both endpoints. We cannot have x = 5. Furthermore, we cannot have x = 11 either. If x were either of those endpoints, then we'd form a straight line rather than a triangle.

Having x be an integer leads to the roster set notation {6,7,8,9,10} to represent all possible values of x. For instance, we could have a triangle with side lengths 3, 8, and 6. I recommend getting slips of paper of these lengths to try it out yourself. Or you can use software such as GeoGebra to see why this works.

The value of the function expression evaluation; f (x) + g (x) - h (x) as required is; 3x² + 6x + 2.

It follows from the task content that the expression which represents f (x) + g (x) - h (x) be determined.

Since;

F(x) = 3x + 5

G(x) = 4x² - 2

H(x) = x² - 3x + 1

Therefore,

f (x) + g (x) - h (x) = 3x + 5 + 4x² - 2 - (x² -3x + 1)

= 3x² + 6x + 2

Ultimately, the value of f (x) + g (x) - h (x) is; 3x² + 6x + 2.

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Step-by-step explanation:

We know all angles on a traingle equal 180

We also know one angle is a right angle which is 90

180 - 90 = 90, indicating the other two angles equal 90

[tex](2x - 1) + (3x + 6) = 90[/tex]

Now we will combine the X's and constants

[tex]5x +5 = 90[/tex]

Now to subtract 7

[tex]5x = 85[/tex]

Lastly, divide by 5

[tex]x = 17[/tex]

Using the diagram in the problem angle TQU is solved to be

The angle at U is 90 degrees, Using the concept of adjacent angles the three angles at U is solved

Using the trigonometry relations of right triangle we solve for angle PQT'

tan (angle PQT) = 1 / 3

angle PQT = arc tan (1 / 3)  

angle PQT = 18.43

angle PQT = angle UQS and

angle PQT + angle UQS  + angle TQU = 90 degrees adjacent angles

2 * 18.43 * angle TQU = 90

angle TQU = 90 - 2 * 18.43

angle TQU = 53.14 degrees

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A solution (6.5, 17.50) does not make sense in the context of the problem, as the number of movies watched must be a non-negative integer.

The general format of an ordered pair is given as follows:

(x,y).

The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.

The variables for this problem are given as follows:

You can watch 1, 2, 3, ... and so on movies, a countable amount, hence 6.5 movies watched does not make sense in the context of this problem as decimal numbers are outside the function's domain.

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