At a wedding​ reception, the bride and groom and five attendants will form a receiving line. How many ways can they be arranged in each of following​ cases? ​a) Any order will do. ​b) The bride and groom must be the last two in line. ​c) The groom must be last in line with the bride next to him.

Explanation:

It is convenient to regroup the numbers, and adjust two of them to "make a ten".

  = 13 + 17 + 19 . . . . rearrange (swap the order of 17 and 19)

  = (10 + 3) + (-3 + 20) + 19 . . . . "make a ten" by adding or subtracting a small number. Here, those adjustments cancel—which is the point of doing it.

  = 10 + 20 + 19

  = 30 + 19

  = 49

Gio should first complete the square by adding and subtracting [tex]\((\frac{3}{2})^2\)[/tex], leading to the equation [tex]\((x + \frac{3}{2})^2 = \frac{25}{4}\).[/tex]

To solve the quadratic equation [tex]\(5x^2 + 15x - 4 = 0\)[/tex] by completing the square, Gio should follow these steps:

1. Make the Coefficient of [tex]\(x^2\) 1:[/tex]

Divide the entire equation by the coefficient of [tex]\(x^2\)[/tex] to make it equal to 1. In this case, divide the equation by 5:

[tex]\[x^2 + 3x - \frac{4}{5} = 0.\][/tex]

2. Move the Constant to the Other Side:

Move the constant term to the other side of the equation:

[tex]\[x^2 + 3x = \frac{4}{5}.\][/tex]

3. Complete the Square:

  Add and subtract [tex]\((\frac{3}{2})^2\)[/tex] inside the parentheses to complete the square:

 [tex]\[x^2 + 3x + (\frac{3}{2})^2 = \frac{4}{5} + (\frac{3}{2})^2.\][/tex]

4. Factor the Perfect Square Trinomial:

  Factor the left side, which now is a perfect square trinomial:

 [tex]\[(x + \frac{3}{2})^2 = \frac{25}{4}.\][/tex]

5. Solve for (x):

  Take the square root of both sides and solve for (x):

[tex]\[x + \frac{3}{2} = \pm \frac{5}{2}.\][/tex]

6. Isolate (x):

  Isolate (x) on one side to find the solutions:

  [tex]\[x = -\frac{3}{2} \pm \frac{5}{2}.\][/tex]

Therefore, Gio should first complete the square by adding and subtracting [tex]\((\frac{3}{2})^2\)[/tex], leading to the equation [tex]\((x + \frac{3}{2})^2 = \frac{25}{4}\).[/tex]

Answer:

The correct answer to this question is C: x > 0

Step-by-step explanation:

Compound interest is the interest generated overtime on a sum of money invested. The time it will take for the amount of money to double is 5.9 years

Compound interest is the interest generated overtime on a sum of money invested. The formula for calculating compound interest is expressed as:
V(t) = P(1+r/n)^nt

where:

Given the following

V(t) = 2P
r = 0.12
n = 4

Substitute
2P = P(1+0.12/4)^4t
2 =  (1.03)^4t
ln2 = 4t ln(1.03)
0.6931 = 0.1182t
t = 0.6931/0.1182
t = 5.9 years

Hence the time it will take for the amount of money to double is 5.9 years

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Answer:

[tex]155,850 \leq  x \leq 415,850[/tex]

Step-by-step explanation:

A publisher estimates their costs of publishing a book is from $980,000 to $1,240,000.

Let x be the amount publisher can spend

So, [tex]980000\leq x \leq 1240000[/tex]

Now we are given that  So far, they have spent $824,000

So, [tex](980000-824000)\leq x \leq (1240000-824000)[/tex]

[tex]156000\leq x \leq 416000[/tex]

So, Option D is true

Hence compound inequality correctly expresses how much more the publisher can spend is [tex]155,850 \leq  x \leq 415,850[/tex]

The absolute value inequality which relates to the expression n is less than 6 units from 0 is |n|< 6

The absolute value which stand for 6 units From 0 can be expressed as :

This means that, the number n is less than 6

Therefore, the expression can be written as :

|n| < 6. This means that the absolute value of n is less than 6.

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To write an absolute value inequality when a number n is less than 6 units from 0, use the notation |n| < 6.

To write an absolute value inequality, we need to express the distance between the number n and 0 as less than 6 units. This can be done by using the absolute value notation: |n| < 6. In this inequality, the absolute value of n must be less than 6 units.

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The equation that can be used to determine how long after Car X leaves Car Y will catch up is D. 55x = 60(x - 1).

To determine when Car Y will catch up to Car X, we need to find the time it takes for Car Y to cover the same distance as Car X. Since Car Y leaves 1 hour later, it will travel for (x - 1) hours, where x represents the time Car X has been traveling. So, the equation would be:

D. 55x = 60(x - 1)

This equation accounts for the distance traveled by both cars over the same time frame, considering Car Y started an hour later.

Complete question : Car X leaves Northtown traveling at a steady rate of 55 mph. Car Y leaves 1 hour later following Car X, traveling at a steady rate of 60 mph. Which equation can be used to determine how long after Car X leaves Car Y will catch up? A. 55x=60x-1 B.55x=60x C.60x=55x(x-1) D.55x=60(x-1).

Answer:

140 button pep club makes per hour.        

Step-by-step explanation:

Given : Pep club members are making spirit buttons. They make 490 spirit buttons in [tex]3\frac{1}{2}[/tex] hours.

To find : The number of button pep club makes per hour ?

Solution :

In  [tex]3\frac{1}{2}[/tex] hours they make 490 buttons.

i.e. In 3.5 hours they make 490 buttons.

So, In 1 hours they make [tex]\frac{490}{3.5}[/tex] buttons.

In 1 hours they make 140 buttons.

Therefore, 140 button pep club makes per hour.

The statements, 4.02>4.1, 4.181<4.118 and 4.665>4.67 are true. Therefore, options A, B and D are the correct answers.

Comparing decimals involves starting with the digits having the highest place value, just like when comparing other whole numbers. We begin the comparison by putting the provided decimal numbers in a place value table. We move on to the digits in the next place to the right if the digits on the biggest place value match. Up till the digits that are different are reached, we continue comparing digits.

A) 4.02>4.1

Here, the statement is true.

B) 4.181<4.118

The statement 4.181<4.118 is true.

C) 4.5>4.49

The statement 4.5>4.49 is not true.

D) 4.665>4.67

The statement 4.665>4.67 is true.

Therefore, options A, B and D are the correct answers.

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Answer:

C ) 35 in2

Step-by-step explanation:

i did the test

To make 30 cupcakes Margaret needs 4.375 cups of vanilla.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

Margaret uses 1 3/4 teaspoon of vanilla to make 12 cupcakes

So,

1 3/4 teaspoon vanilla ⇒ 12 cupcakes

(4×1 + 3)/4 teaspoon ⇒ 12 cupcakes

7/4 teaspoon vanilla ⇒  12 cupcakes

Divide by 12 into both sides,

7/(4×12)  teaspoon vanilla ⇒ 1 cupcake

Now multiply by 30 on both sides,

(7 × 30)/(4 × 12)teaspoon vanilla ⇒ 30 cupcake

30 cupcakes ⇒ 4.375 teaspoon vanilla.

Hence "To make 30 cupcakes Margaret needs 4.375 cups of vanilla".

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To find the number of miles traveled when the total cost is $51.25, subtract the base cost from the total and divide by the per-mile rate, resulting in 65 miles traveled.

The question asks how many miles were traveled if the total cost for renting a car was $51.25. According to the equation y = 35 + 0.25x, where y represents the total cost and x represents the miles traveled, we first need to subtract the base cost of $35 from the total cost to find out how much is charged for the mileage.

Here is how you calculate it:

Therefore, you were charged for traveling 65 miles.