You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rule, but your friends tells you to use 5!. Who is correct? Explain.

Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.

Your friend is correct because applying the permutations rule in this setting would be inappropriate.

Neither method is correct. The combinations rule should be applied in this setting.

Your method is correct because you are applying the permutations rule in the appropriate setting.

To find the purchase price at which the $5 off coupon and the 20% off coupon have the same value, solve the equation x - $5 = 0.8x by isolating x.

To find the purchase price at which the $5 off coupon and the 20% off coupon have the same value, we need to set up an equation and solve for the purchase price.

Let's assume the purchase price is x dollars. The $5 off coupon would give us a discount of $5, so the price after the discount would be x - $5. The 20% off coupon would give us a discount of 20% of x, so the price after the discount would be 0.8x.

We can set up the equation:

x - $5 = 0.8x

Now we can solve for x:

x - 0.8x = $5

0.2x = $5

x = $25

Therefore, the coupons will have the same value at a purchase price of $25.

https://brainly.com/question/34673987

#SPJ12

Fuel in aeroplane when tank was full =  40,000 gallons.

Fuel left after flying for 8 hours = 14,000 gallons

Fuel consumed in 8 hours flight =40,000-14,000= 26000 gallons.

Fuel consumed in 1 hour time =  26000÷8= 3250 gallons.

Fuel consumed in remaining 3.5 hours = 3250x3.5=11375 gallons.

Total fuel consumed = 26000+11375 =37375 gallons.

Fuel left after landing =40,000 -37375=2625 gallons.

The second part is asking us to find total distance of the flight.

Total time of flight= 8+3.5=11.5 hrs

Speed of aeroplane = 550 miles per hour.

Distance covered = speed x time

Distance (Total ) covered = 550x11.5=6325 miles.

The answer is B.) $210

The question is asking for the value of h(g(1.5)) using given functions h(x) and g(x). First, find g(1.5) by substituting 1.5 into g(x) to get 3.5. Then, substitute 3.5 into h(x) to get the final answer of 12.

Firstly, identify the functions h(x) and g(x) given to you. h(x) =

2x+5

and g(x)=

8-3x

. The question requires you to find h(g(1.5)). This means that you need to plug g(1.5) into h(x).

Start by calculating g(1.5). In the function g(x), replace x with 1.5. g(1.5) = 8 - 3*1.5 = 3.5.

Now, substitute the value obtained, which is 3.5, into h(x). So, h(g(1.5)) turns into h(3.5) = 2*3.5 + 5 = 12. Therefore, the value of h(g(1.5)) is

12

.

https://brainly.com/question/30143914

#SPJ12

To calculate the composite function h(g(1.5)), first calculate the value of g(1.5) which is 3.5, then substitute this value into the function h(x) to get the answer, which is 12.

The question is asking us to find the value of h(g(1.5)). This means we need to first find the value of g(1.5) and then substitute that value into the function h(x).

So, let's first determine g(1.5). We know that g(x)=8-3x. Substituting 1.5 in place of x in g(x), we get: g(1.5) = 8 - 3*(1.5) = 8 - 4.5 = 3.5.

Next, to find h(g(1.5)), we substitute the value of g(1.5) which is 3.5 into h(x) to get: h(3.5) = 2*(3.5) + 5 = 7 + 5 = 12. Thus, the value of h(g(1.5)) is 12.

https://brainly.com/question/30143914

#SPJ12

Answer:

[tex]\frac{1}{64}[/tex]  makes the statement true.

Step-by-step explanation:

Given expression,

[tex]8^{-2}[/tex]

By using the property of exponent, i.e. [tex]a^m=\frac{1}{a^{-m}}[/tex]

[tex]\implies 8^{-2}=\frac{1}{8^{2}}[/tex]

[tex]=\frac{1}{64}[/tex]

Hence, the true statement would be,

[tex]8^{-2}=\frac{1}{64}[/tex]

The simplified form of 2√3 - 2√3 is 0, which is a rational number.

In order to determine if the simplified form of 2√3 - 2√3 is rational, we first need to simplify the expression. Since we have the same terms being subtracted from each other, the expression will simplify to 0. Therefore, the simplified form is 0, and 0 is considered to be a rational number since it can be written as 0/1.

Answer:

degree of the polynomial is 11.

C is the correct option.

Step-by-step explanation:

We have been given the polynomial

[tex]7x^7+10x^4+4x^3-5x^{11}-10x^6-6x^7[/tex]

Rewrite this polynomial in standard form i.e from descending exponents

[tex]-5x^{11}-6x^7+7x^7-10x^6+10x^4+4x^3[/tex]

On simplifying, we get

[tex]-5x^{11}+x^7-10x^6+10x^4+4x^3[/tex]

Now, we know that the degree of the polynomial is the highest exponent.

Here, the highest exponent is 11.

Therefore, the degree of the polynomial is 11.

C is the correct option.

Yes, the placement of parentheses can affect the value of an expression even when only multiplication is used. This is because parentheses can change the grouping of factors, which can in turn change the order of operations.

The order of operations is a set of rules that dictate the order in which operations should be performed in an expression. When there are no parentheses, the order of operations is as follows:

Exponents

Multiplication and division (from left to right)

Addition and subtraction (from left to right)

However, when there are parentheses, the operations inside the parentheses are performed first. This means that the order of operations is not always followed strictly from left to right.

For example, consider the following expression:

3 * 2 * 4

According to the order of operations, this expression should be evaluated as follows:

3 * 2 = 6

6 * 4 = 24

However, if we add parentheses to the expression, we can change the value:

(3 * 2) * 4

In this case, the parentheses tell us to evaluate the expression inside the parentheses first. So, we have:

(3 * 2) = 6

6 * 4 = 24

Therefore, the value of the expression is different depending on the placement of the parentheses.

This is because the parentheses change the grouping of factors. In the first expression, the factors are grouped as (3)(2)(4). In the second expression, the factors are grouped as ((3)(2))(4). This change in grouping changes the order in which the operations are performed, which can in turn change the value of the expression.

You have to subtract the 11% that you are putting into your 401k to find out how much you are earning and that you're not putting into retirement.

67,200*0.11 = 7,392

67,200 - 7,392 = 59,808

Mustafa's pretax income after contributing 11% to his 401(k) plan is 59808 dollars.

A percentage is a value per hundredth.

Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given Mustafa contributes 11% of his $67,200 annual salary to his 401(k) plan.

∴ 11% of $67200 is = (11/100)×67200 dollars.

= 7392 dollars.

So, his pretax income is (67200 - 7392) dollars.

= 59808 dollars.

learn more about percentages here :

https://brainly.com/question/14801224

#SPJ5

You need to know how to use it propeller to also use it at all

To solve the system of equations, rewrite them in standard form, eliminate x, solve for y, and substitute the value of y into the equations to solve for x. The solution to the system of equations is x = 4 and y = 2.

To solve the system of equations:

The solution to the system of equations is x = 4 and y = 2.

To solve the provided system of linear equations, the elimination method can be used. The solution to the equations 3x - 2y = 14 and 5x + 6y = 42 is x = 6 and y = 2.

The student has provided two linear equations which form a system of equations:

To solve this system, we can use either the substitution method, the elimination method, or graphical method. In this case, the elimination method may be more straightforward. Here's a step-by-step explanation:

Therefore, the solution to the system of equations is x = 6, y = 2.

Answer:

The value of the f (3 +h) is  h² + 9h + 23 .

Option (B) is correct.

Step-by-step explanation:

As the function given in the question be

f(x)= x² + 3x + 5

Now

f(3 +h )= (3 +h )²+3(3 + h)+5

Now by using the formula

(a + b)² = a² +  b² + 2ab

f(3 +h )= 3² + h² + 2 × 3 × h +3 × 3 + 3 ×h +5

f(3 +h )= 9 + h² + 6h  + 9  + 3h +5

f(3 +h )=  h² + 9  + 9 + 5 + 3h + 6h

f(3 +h )=  h² + 9h + 23

Therefore the value of the f (3 +h) is  h² + 9h + 23 .

Option (B) is correct.

Answer:  The circumference of the patio is 21.98 meters.

Step-by-step explanation:  Given that there is a circular patio with a diameter of 7 meters. Greg is going to put a titled edge around the patio.

We are to find the circumference of the patio.

If 'r' units is the radius of a circle, then the circumference of the circle is given by

[tex]C=2\pi r.[/tex]

Since the diameter of the circular patio is 7 meters, so the radius 'r' will be given by

[tex]\textup{radius}=\dfrac{1}{2}\textup{ of the diameter}\\\\\Rightarrow r=\dfrac{1}{2}\times 7\\\\\Rightarrow r=3.5~\textup{meters.}[/tex]

Therefore, the circumference of the patio is given by

[tex]C=2\pi r=2\times 3.14\times 3.5=21.98~\textup{meters}.[/tex]

Thus, the circumference of the patio is 21.98 meters.

Answer: The answer is (c) - 5, (e) 0 and (f) - 200.

Step-by-step explanation:  We are to select the correct numbers from the given options that cannot represent the area of a polygon.

We know that the area of any figure cannot be a negative number or zero.

So, the numbers which cannot represent the area of a polygon are - 5, 0 and - 200.

Thus, (c), (e) and (f) are the correct options.

The required 3 5/8 as a decimal is 3.625, as of the given mixed fraction.

Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,

Here,

To convert 3 5/8 to a decimal, we can first convert the mixed number to an improper fraction and then divide the numerator by the denominator using a long division or a calculator. Here are the steps,

3 5/8 = (3 x 8 + 5)/8 = 29/8

Dividing 29 by 8 using long division, we get:

3 5/8 =  3.625

Therefore, 3 5/8 as a decimal is 3.625.

Learn more about decimal values here,

brainly.com/question/19802955

#SPJ5

If the point (8,4) is on the graph of an even function, the point (-8,4) must also be on the graph.

An even function is a function that satisfies the property f(x) = f(-x) for all values of x in the domain of the function. If the point (8,4) is on the graph of an even function, then the point (-8,4) must also be on the graph. This is because substituting x = -8 into the function would give the same y-value as when x = 8.

The expanded form of the number 2015473 is  2,000,000 + 10,000 + 5,000 + 400 + 70 + 3.

The division of numbers into groups according to place value, such as ones, tens, hundreds, thousands, ten thousand, and so forth, results in the expanded form of the number.

The expanded form of the number is the one that is represented by the sum of each digit times its place value.

The given number is 2015473. The given number in the expanded form will be written as,

2015473 = 2,000,000 + 10,000 + 5,000 + 400 + 70 + 3.

Therefore, the expanded form of the number 2015473 is  2,000,000 + 10,000 + 5,000 + 400 + 70 + 3.

To know more about an expanded form of the number follow

https://brainly.com/question/16802852

#SPJ2