Of five letters (a, b, c, d, and e), two letters are to be selected at random. how many possible selections are there

Answer:

Distributive property

Step-by-step explanation:

convert 2 2/5 into a fraction

2 2/5 = 12/5

12/5 * 1/9 =12/45 reduces to 4/15

The arithmetic sequence A(n) = –3 + (n – 1)(–2.2) yields the first, fourth, and tenth terms as -3, -9.6, and -22.8 respectively when n is substituted with the corresponding term number.

The arithmetic sequence described by the rule A(n) = –3 + (n – 1)(–2.2) can be used to find specific terms of the sequence. To find the first term, plug in n = 1 into the formula to get A(1) = -3 + (1 - 1)(-2.2) = -3. The fourth term can be found by plugging in n = 4 which yields A(4) = -3 + (4 - 1)(-2.2) = -9.6. The tenth term is calculated as A(10) = -3 + (10 - 1)(-2.2) = -22.8. Therefore, the first, fourth, and tenth terms are -3, -9.6, and -22.8 respectively.

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Answer:

A. [tex]g(x)=-\frac{2}{5}(10)^x[/tex].

Step-by-step explanation:

We are given the function [tex]f(x)=\frac{2}{5}(10)^x[/tex].

Now, g(x) is obtained by reflecting the function f(x) over x-axis.

Reflection of f(x) over x-axis changes f(x) to -f(x).

So, we get,

[tex]g(x)=-f(x)[/tex]

i.e. [tex]g(x)=-\frac{2}{5}(10)^x[/tex]

Thus, the reflected function is [tex]g(x)=-\frac{2}{5}(10)^x[/tex].

So, option A is correct.

The choice which is a counterexample to the statement is 2.

"It is a number that is divisible only by itself and 1 "

For given question,

We have been given a statement 'All prime numbers are odd. '

We need to select a counterexample to given statement.

Consider a number 2.

2 is divisible only by itself and 1

This means, 2 is a prime number.

We know that 2 is an even number.

Therefore, the choice which is a counterexample to the statement is 2.

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Answer:

Value of x is:

20

Step-by-step explanation:

Clearly, the two angles are vertically opposite

and vertically opposite angles are always equal

So, x+40=3x

Subtracting both sides by x, we get

x+40-x=3x-x

i.e. 40= 2x

Dividing both sides by 2, we get

x = 20

Hence, Value of x is:

20

390-150 = 240 cars were sold in November & December

 ratio is 3:5

240/8 = 30

30*3 = 90

3*5 = 150

90 cars sold in November

150 cars sold in December

To comply with the triangle inequality theorem, the smallest possible length of the congruent sides in an acute isosceles triangle with the longest side being 8 centimeters, would be slightly greater than 4 centimeters, rounded to the nearest tenth (4.1 centimeters).

In the context of an acute isosceles triangle, the longest side is the base and the other two sides are congruent or have equal length. The smallest possible length of the congruent sides comes into play in respect of the triangle inequality theorem, stating that the sum of the lengths of any two sides must be greater than the length of the third side. Thus, for the smallest possible length, each of the congruent sides must hence be just slightly larger than half the length of the longest side. So for an 8 centimeter base, the smallest length for the congruent sides should be slightly more than 4 centimeters, let's call it 4.1 centimeters, when rounded to the nearest tenth.

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The equation that has the solution x = all real numbers is given by option a) (4(3 - x) + 6x = 3x + 12 - x) and this can be determined by using the arithmetic operations.

Check all the options in order to determine which of the following equations has the solution x = all real numbers.

A) 4(3 - x) + 6x = 3x + 12 - x

Simplify the above equation separately that is:

LHS = 12 - 4x + 6x

       = 12 + 2x

RHS = 3x + 12 - x

       = 2x + 12

LHS = RHS means there is an infinite number of solutions.

B) 4(3 - x) + 6x = 3x + 10 - x

Simplify the above equation separately that is:

LHS = 12 - 4x + 6x

       = 12 + 2x

RHS = 2x + 10

LHS [tex]\neq[/tex] RHS means that there are no solutions.

C) 4(3 - x) + 6x = 3x + 12 + 2x

Simplify the above equation separately that is:

LHS = 12 - 4x + 6x

       = 12 + 2x

RHS = 5x + 12

LHS [tex]\neq[/tex] RHS means that there are no solutions.

D) 4(3 - x) + 6x = x + 12 - 3x

Simplify the above equation separately that is:

LHS = 12 + 2x

RHS = 12 - 2x

LHS [tex]\neq[/tex] RHS means that there are no solutions.

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Answer:

$245

Step-by-step explanation:

Given : My past due bill is $585.00, and I just made payment arrangements for the next 3 months to keep my account from being suspended. My normal monthly bill is $50.00 per month.

To Find:  How much will I need to pay each month?"

Solution:

Past due bill = $585

Now  just made payment arrangements for the next 3 months to keep my account from being suspended

So, Payment each month of past bill = [tex]\frac{585}{3}=195[/tex]

My normal monthly bill is $50.00 per month.

So, I need to pay per month = $50+$195= $245

Thus ,I need to pay $245 per month .

Answer:

Volume of the gas is 20 cubic inches.

Step-by-step explanation:

Inverse proportion: Let x and y be two quantities are said to be inverse proportion or inversely proportional if one quantity increases at the same rate the other decreases.

[tex]x \propto \frac{1}{y}[/tex] or

[tex]x = \frac{k}{y}[/tex] ⇒[tex]k =xy[/tex]   where k is constant.

Since, it is given that the volume of gas is inversely propotional to its pressure.

Given the function:  

[tex]v = \frac{18000}{p}[/tex]           ......[1] ; where volume in cubic inches and pressure in pounds per square.

To find the volume in cubic inches.

The pressure (p) = 900 pounds per square inch.

Substitute the value of p in [1];

[tex]v = \frac{18000}{900}= 20 in^3[/tex]

Therefore, the volume(v) = 20 cubic inches when the pressure is 900 pounds per square inch.

The volume when the pressure is 900 pounds per square inch is [tex]20 in^3.[/tex]

proportionality can be explained as equality between two ratios, it gives relationship that is always in the same ratio.

We were given the function as[tex]v= \frac{18000}{p}[/tex]

But the pressure is given as pressure (p) = 900 pounds per square inch.

We can get volume, if we substitute "p" as;

[tex]v=\frac{18000}{p}[/tex]

[tex]V= \frac{18000}{900} =20 in^3.[/tex]

Hence, the volume when the pressure is 900 pounds per square inch is [tex]20 in^3.[/tex]

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Hello there! :)

This equation is written in slope-intercept form. which means we can easily idenify the slope and the y-intercept.

First of all, slope-intercept form looks like this:

y=mx+b

The letter m represents the slope, while the letter b represents the y-intercept.

Now, let's look at the values that we have.

We are given the equation of the line:

y=6x-9

We know that m is the slope; therefore, in this equation, 6 is the slope.

-9 is the y-intercept (the letter b)

Therefore, 6 is the slope and b is the y-intercept.

I hope it helps you. Let me know if you have any queries.

~A smiley teen

[tex]MagicalNature[/tex] here to help

Final answer:

The square root of 26 in simplest radical form is just √26, as 26 has no perfect square factor. It can also be expressed as 26 raised to the power of 0.5 based on the concept of fractional powers corresponding to roots.

Explanation:

The square root of 26 in its simplest radical form cannot be simplified further as a perfect square factor because 26 is not a perfect square. However, if we apply the concept of expressing numbers as fractional powers, we can say that any number 'x' squared, written as x², is equivalent to the square root of 'x'. Thus, the square root of 26 can also be written as 26 to the power of 0.5 or 26⁰.⁵.

Expressing the concept mathematically, we can write the square root of any number 'x' as x to the power of 0.5, which is a helpful way to solve for unknown values in various equations. This idea is useful in scenarios where different roots of a number or expressions involving fractional exponents are to be calculated, and it is essential to remember that the square root is just another form of an exponent.