Suppose a number from 1 to 100 is selected at random. what is the probability that a multiple of 4 or 5 is chosen?

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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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]

These numbers are called power of ten. A power of ten is 10 multiplied by itself the exponent number of times. For example:

We can write 10 as 10¹

100 as 10²

1000 as 10³

The exponent is equal to the number of zeros in the number like 100 has 2 zeros so the exponent is 2 and write it as 10²

If the absolute value of a nonzero real number is equal to the opposite of the number then the number is negative.

A number system is defined as a system of writing to express numbers.

We have to find the number for the absolute value of a nonzero real number is equal to the opposite of the number

The absolute value of a number is its numerical value without regard to its sign.

So if the absolute value of a number is equal to the opposite of the number, it means that the sign of the number must be negative.

Hence, if the absolute value of a nonzero real number is equal to the opposite of the number then the number is negative.

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The value of 'x' in a triangle is determined by using the Pythagoras theorem, while in a rectangle, it's determined by algebraic equations.

In order to find the value of 'x' in both cases, we need to understand that two different concepts potentially apply; Pythagoras theorem for the triangle, and algebra for the rectangle. The Pythagorean theorem applies to right angle triangles and is expressed as x² + y² = h² where 'x' and 'y' are sides and 'h' is the hypotenuse. In a rectangle, to find 'x' related to an equation like y = 9 + 3x, you substitute values for 'y' and solve for 'x'. An example is given in Table A1 where we see an instance of substituting values for 'x' and then calculating what value of 'y' results. These points are then plotted on a graph.

Answer: If adding exponents, they have to the same value or same coefficient.

For example:

1) 2x^2+2x^2= 4x^2

1L = 1000ml

 14L = 14000ml

14000-9500 = 4500ml left

Answer: the guy above is right for anyone looking at this and was sceptical

Step-by-step explanation:

Martha can ensure she has money to pay for college by starting or adding to a college savings account, maintaining high grades, getting involved in extracurricular activities, and filling out the FAFSA immediately.

Martha can take the following steps to ensure she has money to pay for college:

The steps Martha should take to ensure she has money to pay for college are as follows:

1. She should start or add to a college savings account so it can grow with deposits and earned interest. This is a proactive step that allows the money to benefit from compound interest over time.

2. She should ask her parents if they have a college savings account set up for her. It's important to know if there are existing funds that can be used for her education.

3. She should work to maintain high grades throughout school so she can qualify for scholarships. Many scholarships are merit-based, and good grades are often a key criterion.

4. She should get involved in extracurricular activities like clubs and sports so she can discover what she enjoys and qualify for scholarships. Participation in these activities can make her a well-rounded candidate for scholarships that value leadership and community involvement.

5. She should fill out the FAFSA (Free Application for Federal Student Aid) when she is eligible, which is typically during her senior year of high school. This form is crucial for accessing federal grants, loans, and work-study opportunities, as well as some state and college-specific aid.

6. While asking friends and neighbors to contribute to her college savings account could potentially help the account grow faster, it is not a conventional or reliable method for funding college education. Therefore, it is not a primary step she should take.

In summary, Martha should focus on saving money, exploring existing savings, maintaining good grades, engaging in extracurricular activities, and preparing to fill out the FAFSA. These steps will help her secure funding for college through savings, scholarships, and financial aid.

To get the perfect square when a is greater than 1 divide the whole equation by a.

When a given expression is simplified to the square of a sub-function is called a perfect square.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let's presume with an example,
ax² + bx + c =0
In order to get the perfect square the whole equation must be divided by a for a greater than 1

x² + b/a x + c/a = 0

Thus, to get the perfect square when a is greater than 1 divide the whole equation by a.

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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 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:

$18,000

Step-by-step explanation:

It is given that the interest amount $6,300

We will calculate the principal amount.

So we use the formula

I = prt

P = Principal amount

r = rate of interest 7% ( 0.07 )

t = time in years 60 months ( [tex]\frac{60}{12}[/tex] years )

6,300 = P × 0.07 × [tex]\frac{60}{12}[/tex]

6,300 = P × 0.07 × 5

6,300 = 0.35P

[tex]\frac{6,300}{0.35}[/tex] = P

P = $18000

The original loan amount was $18,000.  

The density of the cube is calculated to be 2 g/cm³ by dividing the mass (250 grams) by the volume of the cube (125 cm³).

To calculate the density of a substance, you divide its mass by its volume. In the given problem, the cube has a mass of 250 grams and each side of the cube is 5 cm. The volume of a cube is calculated by taking the cube of the side length, which in this case is 5^3 = 125 cm³.

By substituting the given mass and computed volume in the formula, we find that the density of the cube is 250 grams ÷ 125 cm³ = 2 g/cm³.

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Answer:

The value of [tex]\frac{b}{a}=4[/tex] .

Step-by-step explanation:

As given in the question

[tex]\frac{2a}{b}=\frac{1}{2}[/tex]  

Now find out the value of [tex]\frac{b}{a}.[/tex]

[tex]\frac{b}{a}=\frac{2\times 2}{1}[/tex]

[tex]\frac{b}{a}=2\times 2[/tex]

[tex]\frac{b}{a}=4[/tex]

Therefore the value of [tex]\frac{b}{a}=4[/tex] .

The value of b/a from the equation; 2a/b=1/2 is; 4

The given equation is;

Divide both sides of the equation by 2; we have;

Hence, the inverse of a/b is b/a and;

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