Elizabeth,frank,gary, and helen are getting in line to buy lunch in the cafeteria. How many different ways could they line up so that helen is first in line?

Answers

Answer 1

Answer:

Step-by-step explanation: the correct answer is definitely 6

Answer 2

Final answer:

With Helen fixed in the first position, there are 6 different ways Elizabeth, Frank, and Gary can line up behind her, computed by a permutation of the 3 remaining people.

Explanation:

If Helen is always the first in line, we just need to focus on the different ways Elizabeth, Frank, and Gary can line up behind her. For the first spot behind Helen, there are 3 choices (Elizabeth, Frank, or Gary). After choosing one, there are 2 remaining choices for the next spot, and finally, the last person will have no choice but to take the last remaining spot. This is a permutation problem where we multiply the different choices together.

Thus, the number of ways they can line up is 3 (for the second spot)  imes 2 (for the third spot)  imes 1 (for the last spot), which equals 6 different possible lineups.


Related Questions

50% of one-twentieth of the product of 12 and 5z + 5.

Answers

Final answer:

To simplify 50% of one-twentieth of the product of 12 and 5z plus 5, you first calculate the product (60z), take one-twentieth (3z), find 50% of that (1.5z), and then add 5 to get the simplified expression 1.5z + 5.

Explanation:

The question asks to simplify the expression 50% of one-twentieth of the product of 12 and 5z plus 5. Here are the steps to simplify this expression:

Firstly, calculate the product of 12 and 5z, which is 60z.

Then, find one-twentieth of this product, which is 60z / 20 = 3z.

50% of 3z is 1.5z.

Finally, add 5 to 1.5z, which gives you 1.5z + 5 as the simplified expression.

So, the simplified expression is 1.5z + 5.

50% of one-twentieth of the product of (12) and[tex]\(5z + 5\) is \( \frac{3z}{2} + \frac{3}{2} \).[/tex]

To calculate 50% of one-twentieth of the product of [tex]\(12\) and \(5z + 5\)[/tex], we'll follow these steps:

Step 1: Calculate the product of [tex]\(12\) and \(5z + 5\)[/tex].

[tex]\[ \text{Product} = 12 \times (5z + 5) \][/tex]

Step 2: Calculate one-twentieth of the product.

[tex]\[ \text{One-twentieth of the product} = \frac{\text{Product}}{20} \][/tex]

Step 3: Calculate 50% (or half) of one-twentieth of the product.

[tex]{50% of one-twentieth of the product}[/tex] = [tex]\frac{1}{2} \times \frac{\text{Product}}{20} \][/tex]

Now, let's perform the calculations step by step:

Step 1: Calculate the product of [tex]\(12\) and \(5z + 5\):[/tex]

[tex]\[ \text{Product} = 12 \times (5z + 5) \][/tex]

[tex]\[ = 12 \times 5z + 12 \times 5 \][/tex]

[tex]\[ = 60z + 60 \][/tex]

Step 2: Calculate one-twentieth of the product:

[tex]\[ \text{One-twentieth of the product} = \frac{60z + 60}{20} \][/tex]

[tex]\[ = \frac{60z}{20} + \frac{60}{20} \][/tex]

[tex]\[ = 3z + 3 \][/tex]

Step 3: Calculate 50% of one-twentieth of the product:

{50% of one-twentieth of the product} =[tex]\frac{1}{2} \times \left(3z + 3\right) \][/tex]

[tex]\[ = \frac{1}{2} \times 3z + \frac{1}{2} \times 3 \][/tex]

[tex]\[ = \frac{3z}{2} + \frac{3}{2} \][/tex]

So, 50% of one-twentieth of the product of (12) and[tex]\(5z + 5\) is \( \frac{3z}{2} + \frac{3}{2} \).[/tex]

Suppose f(x)=x2 Find the graph of f (x)+1

Answers

You would vertically shift the function up a unit, making it clear that the answer should be graph 3.


Use the image below, red is the original function, and blue is the new function.  


Please answer with calculations

Answers

Answer:


Step-by-step explanation:

Given that a storage rack has dimensions as 25x12x5 ft.

Box has dimensions as 15x8x10 inches

Volume of each box = 15(8)(10) = 1200 inches = 1200x12^(-3) feet^3

Volume of 5000 boxes = 5000 (1200x12^(-3) ) = 3472.22 cubic feet

Volume of storage rack = 25(12)(5) = 1500 cubic feet

Volume of 25 storage racks 1500(25) = 37500 cubic feet.

SInce storage racks have sufficient volume it is concluded that enough storage is there.


Answer:

Yes, we have enough storage space.

Step-by-step explanation:

25 storage racks that are:

Length: Lsr = 25 ft = 25 ft (12 in / 1 ft) → Lsr = 300 in

Width: Wsr = 3 ft = 3 ft (12 in / 1 ft) → Wsr = 36 in

Height: Hsr = 12 ft = 12 ft (12 in / 1 ft) → Hsr = 144 in


5000 boxes 15x8x10 in

Length: Lb = 15 in

Width: Wb = 8 in

Height: Hb = 10 in


In the length of each storage rack we can put:

Nl=Lsr/Lb=300 in / 15 in → Nl = 20

In the width of each storage rack we can put:

Nw=Wsr/Wb=36 in / 8 in = 4.5 → Nw = 4

In the height of each storage rack we can put:

Nh=Hsr/Hb=144 in / 10 in = 14.4 → Nh = 14

Then we can put in each storage rack:

N = Nl Nw Nh = (20)(4)(14) → N=1,120 boxes

And we have 25 storage racks, then we can storage in total:

Nt=25N=25(1,120)→Nt=28,000 boxes

And we have 5,000 boxes, then we have enough storage space

What is the remainder when the polynomial f(x)=3x^3-4x^2+2x+8 is divided by (x-5)

Answers

Answer:

remainder = 290

Step-by-step explanation:

[tex]\frac{3x^3-4x^2+2x+8}{x-5}[/tex]

= 3x² + 11x + 57 + [tex]\frac{290}{x-5}[/tex]

quotient = 3x² + 11x + 57 and remainder = 290


When solving for x what would (8x-46) + (10x-8)

Answers

Answer:

18x - 54  :) :( :) :)

Please help me with number 6

Answers

The answer is C) $250

Answer:

The answer is 250 dollars. to find this do 25 times 1000. the placement is 25 over 100 and x as in the amount were trying find over 1000.

Step-by-step explanation:


a fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges. They also need $12 for 6 apples and 6 oranges. We put information into a system of linear equations.

Answers

Answer:

X = apple

y = orange

4x + 4y = 10

6x + 6y = 12


Step-by-step explanation:


Answer:

4a+4r = 10

6a + 6r = 12

No solutions

Step-by-step explanation:

a = cost of the apple

r = cost of the orange

4a+4r = 10

6a + 6r = 12

Divide the first  equation by 2 and the second equation by 6

2a+2r = 5

a +r = 2

Multiply the second equation by -2 so we can eliminate a

-2a -2r = -4

Add the first equation

2a+2r = 5

-2a -2r = -4

---------------------

0 = 1

This system is inconsistent and has no solutions

you get to pick 8 of your 12 favorite songs to put on a cd . how many ways 8 songs be arranged from a choice of 12 songs

Answers

the answer is 96 ways

Three snacks bars contain 1/5,0.22, and 19 percent of their Calories from fat. Which snack bar contains the least amount of calories from fat?

Answers

Answer:

19 percent

Step-by-step explanation: First we need to convert them all the a similar format. Fractions would be easiest.

.22 = 22/100

1/5 = 20/100

19% = 19/ 100

The one that contains the least is 19/100 or 19%.


Solve using substitution
x=2y-6
y= -3x+17

Answers

Answer:

(x, y) = (4, 5)

Step-by-step explanation:

given the 2 equations

x = 2y - 6 → (1)

y = - 3x + 17 → (2)

Either substitute x = 2y - 6 into (2) or y = - 3x + 17 into (1)

substituting y = - 3x + 17 into (1)

x = 2(- 3x + 17) - 6

x = - 6x + 34 - 6

x = - 6x + 28 ( add 6x to both sides )

7x = 28 ( divide both sides by 7 )

x = 4

substitute x = 4 into (2)

y = - 12 + 17 = 5

solution is (4, 5 )


There are 90 fith-grade students going on a feild trip. Each student gives the teacher $9.25 to cover admission to the theater and for lunch. Admission for all the students will cost $315, and each student will get an equal amount to spend on lunch. How much will each fifth grader get to spend on lunch?

Answers

Answer:

they each get $5.75 for lunch

Step-by-step explanation:

9.25 x 90 students = 832.50

832.50 -315 = 517.50

517.50 / 90 = 5.75

5. State whether the number 91 is prime, composite, or neither.

Answers

Answer:

91 is a composite number

Step-by-step explanation:

A prime number is the positive number, which has factors 1 and itself.

Example : 1,3,5,7

Clearly 91 is not a prime number, as its factors are:

91 = 1,7,13,91

It has more than 2 factors (1 and itself), hence 91 is a composite number.

Composite number is the number which has factors other than 1 and itself.

Answer:

91 is composite

Step-by-step explanation:

its factors are 1, 7, 13, 91

Amelia and Brianna work at a furniture store. Amelia is paid $240 per week plus 6% of her total sales in dollars, xx, which can be represented by g(x)=240+0.06xg(x)=240+0.06x. Brianna is paid $130 per week plus 8.5% of her total sales in dollars, xx, which can be represented by f(x)=130+0.085xf(x)=130+0.085x. Determine the value of xx, in dollars, that will make their weekly pay the same.

Answers

Answer:

x = $4400

Step-by-step explanation:

If we want their pay to be the same, the equations have to be equal

g(x)=240+0.06x = f(x)=130+0.085x

240 + .06x = 130+0.085x

Subtract .06x from each side.

240 + .06x - .06x = 130+0.085x-.06x

240 = 130 +.025x

Subtract 130 from each side

240-130 = 130-130 +.025x

110 = .025x

Divide each side by .025 to isolate x

110/.025 = .025x/.025

4400 =x



the product of p and 9

Answers

Answer:

The answer is p · 9

Step-by-step explanation:

Product means multiplication

Answer:

The answer is p · 9

but, on gradpoint the answer is 9p

Step-by-step explanation:

What is the sum of 4a^2 − 7a − 5 and −8a^2 − 2a + 7?

Answers


[tex]{ - 4a}^{2} - 5a + 2 [/tex]
steps:
1. gather like terms
all terms with a squared are like, all terms with a are like, all constants are like
2. solve

If 9 is added to twice a number and this sum is multiplied by 6​, the result is the same as if the number is multiplied by 7 and 14 is added to the product. What is the​ number?

Answers

Answer:

The number is -1.

Step-by-step explanation:

Let the number be represented by n.

Then "9 is added to twice a number and this sum is multiplied by 6" is represented by 2n + 9, and

" the number is multiplied by 7 and 14 is added to the product" is

7n + 14.

Then the complete equation is 2n + 9 = 7n + 14.

We must solve this for n.  To accomplish this, subtract 2n from both sides, obtaining 9 = 5n + 14.  Then subtract 14 from both sides, obtaining

-5 = 5n.  Then n must be -1.

Answer:

The number is -8

Step-by-step explanation:

Developing an equation

Read these phrases a little a time.

9 is added to twice a number = 2x + 9This sum is multiplied by 6 = 6* sum = 6 * (2x + 9) Note the brackets.is the same thing as means = the number multiplied by 7 = 7xand 14 is added to the product 7x + 14So what you have is equation: 6*(2x + 9) = 7x + 14

Solution

6*(2x + 9) = 7x + 14               Remove the brackets on the left12x + 54 = 7x + 14                 Subtract 14 from both sides12x + 54 - 14 = 7x + 14 - 14    Collect terms12x + 40 = 7x                         Subtract 12x from both sides.12x - 12x + 40 = 7x - 12x        Combine40 = -5x                                 Divide by - 540/-5 = x                                Do the division- 8 = x

D-I are the measurements of the lengths of the sides of triangles. Identify the types of
triangles

d. 45 cm 61 cm 60 cm e. 30 cm, 31cm, 30 cm f. 4 cm, 5ft, 4 cm
g. 89mm, 89mm, 89mm h. 9 in, 5in, 3 in i. 22cm, 22cm, 22in


J-O are the measurements of the angles of triangles. Identify the type of triangle.
j. 900, 350, 550 k. 600, 600, 600 l. 700, 550, 550
m. 350, 400, 1000 n. 460, 460, 440 o. 1200, 300, 300,

Answers


Answer:

The sum of the interior angles of a triangle is 180 degrees.

d. Scalene

e. Isosceles

f. Isosceles

g. Equilateral

h. Scalene

i. Equilateral

j. Right

l. Acute

m. Obtuse - doesn't add to 180 not a triangle

n. Acute - doesn't add to 180 not a triangle

o. Obtuse

Step-by-step explanation:

The interior angles of a triangle add to 180 degrees. There are two ways we classify triangle by side lengths and angle measures.

Side lengths: Compare the side lengths and see if any are equal to determine the type.

Scalene: 3 different lengthsIsosceles: 2 equal lengths and 1 differentEquilateral : 3 equal sides

Angle Measures: Compare the angles measures to 90 degrees.

Right: If one angle is equal to 90Acute: All angles are less than 90 degreesObtuse: One angle is greater than 90 degrees

Answer please ?!?!?!

Answers

Answer: -9

Step-by-step explanation: -91/6 ≈ -9.167

21/3 ≈ 2.33333

-17/8 ≈ -1.875

-9.167 + 2.3333 + -1.875 = -8.71

Rounded, the answer is -9.

Will give brainliest please help ASAP

Answers

Answer:

D

Step-by-step explanation:

y>-3x+1                                 Negative slope

y<x+2                                   Positive slope

< or > have dotted line

< or > have a solid line

> or > means solutions are above the line

< or < means solutions are below the line

The one with negative slope has a dotted line and solutions above it.

The one with positive slope has a solid line and solutions below it.

At the art fair, 95 artists exhibited their work. Of those 95 artists, 25 showed sculptures and 48 showed paintings. If 12 showed both sculptures and paintings, how many artists showed only sculptures or paintings?

Answers

Final answer:

To determine the number of artists who showed only sculptures or paintings at the art fair, we use the formula for the principle of inclusion-exclusion, resulting in 61 artists.

Explanation:

To find out how many artists showed only sculptures or paintings at the art fair, we apply the principle of inclusion-exclusion. First, we add the number of artists who showed sculptures (25) to those who showed paintings (48), which gives us a total of 73 artists. However, this counts the 12 artists who showed both sculptures and paintings twice, so we subtract 12 from this total to correct for the double counting. Therefore, the number of artists who showed only sculptures or paintings is 73 - 12, which equals 61 artists.

Linda received a $ 90 gift card for a coffee store. She used it in buying some coffee that cost $ 7.63 per pound. After buying the coffee, she had $ 51.85 left on her card. How many pounds of coffee did she buy?

Answers

Answer:

5 pounds

Step-by-step explanation:

:'>

Answer:

She bought 5 pounds of coffee.

Step-by-step explanation:


solve and simplify, typing the final answer as a fraction 1/4 ÷ 3/8

Answers

[ Answer ]

2 / 3


[ Explanation ]


1 * 8 / 4 * 3


8 / 12


Simplify:

2 / 3


<> Arsenal <>


2/3 that is the answer

At the beginning of the week Fayez writes down the mileage of his limo at 2529 at the end of the week the mileage is 2834, Fayez knows he used 75.2 litres of petrol during this week. The handbook states the limo uses 1 gallon of petrol for every 20 miles. Fayez wants to know if his limo uses 1 gallon of petrol for every 20 miles that week. 1 gallon = 4.54 litres . Did his limo use 1 gallon of petrol every 20miles that week. Show your answer clearly

Answers

Answer:

No. It used  1 gallon in 18.41 miles.

Step-by-step explanation:

He travelled 2834 - 2529 = 305 miles.

So his consumption is  305 / 75.2 = 4.056 miles/litre.

This equals 4.056*4.54 = 18.41 miles / gallon.

So this is less than the 1 gallon  every 20 miles stated by the handbook.

Answer: His limo used 1 gallon fuel for 18.4136 miles.


Step-by-step explanation:

Fayez covered distance:

2834 - 2529 = 305 miles.

He used fuel = 75.2 litres

75.2/4.54 = 16.5638 gallons petrol used.

His limo covered distance / total petrol used = 305 miles / 16.5638 gallons petrol = 18.4136 miles per gallon.

That is less than 20 miles per gallon

You are making sets of pens and pencils to sell. You want each set to contain the same combination of pens and pencils. You have 28 pens and 80 pencils, and you want to use them all. What is the greatest number of these sets you can make?

Answers

Final answer:

The greatest number of sets of pens and pencils that can be made, using all of the given 28 pens and 80 pencils in each set, is 4. Each set would contain 7 pens and 20 pencils.

Explanation:

In the problem, we are looking to find the Greatest Common Divisor (GCD), which is the greatest number that can evenly divide both the number of pens (28) and the number of pencils (80). The GCD between 28 and 80 is 4.

Thus, the most sets of pens and pencils you can make would be equal to the GCD, which in this case is 4.

This means you can put together 4 sets with an equal number of pens and pencils in each set. In each of these sets, there would be 7 pens (28 pens ÷ 4 sets) and 20 pencils (80 pencils ÷ 4 sets).

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Final answer:

To maximize the number of sets with 28 pens and 80 pencils, find the greatest common divisor and divide the total by it. You can create 27 sets of 4 pens and 10 pencils each.

Explanation:

To find the greatest number of sets you can make with 28 pens and 80 pencils, you need to determine the highest common factor of the two quantities.

Calculate the greatest common divisor (GCD) of 28 and 80, which is 4.

Divide the total number of pens and pencils by the GCD: (28 + 80) ÷ 4 = 27.

You can make 27 sets, each consisting of 4 pens and 10 pencils.

I don’t understand all 3 of them

Answers

me neither sorry
But maybe someone will know it later

How do you solve for a²+b²=289 when b+a=23

Answers

Answer:


1 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

​a

​​ x

​b

​​ =x

​a+b

​​  

{a}^{2}+bb=289a

​2

​​ +bb=289

2 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x

​a

​​ x

​b

​​ =x

​a+b

​​  

{a}^{2}+{b}^{2}=289a

​2

​​ +b

​2

​​ =289

3 Subtract {b}^{2}b

​2

​​  from both sides

{a}^{2}=289-{b}^{2}a

​2

​​ =289−b

​2

​​  

4 Take the square root of both sides

a=\pm \sqrt{289-{b}^{2}}a=±√

​289−b

​2

​​  

​​  

5 Rewrite 289-{b}^{2}289−b

​2

​​  in the form {a}^{2}-{b}^{2}a

​2

​​ −b

​2

​​ , where a=17a=17 and b=bb=b

a=\pm \sqrt{{17}^{2}-{b}^{2}}a=±√

​17

​2

​​ −b

​2

​​

6 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a

​2

​​ −b

​2

​​ =(a+b)(a−b)

a=\pm \sqrt{(17+b)(17-b)}a=±√

​(17+b)(17−b)


If quadrilateral ABCD is congruent to quadrilateral EFGH, then what corresponding side is congruent to side EF? (5 points)

Answers

Answer:

Side AB

Step-by-step explanation:

Draw two congruent quadrilaterals.

Label the sides of one A,B,C,and D.

Label the sides of the other E,F,G,and H

Because the sides match up with the order in which they appear in if they are congruent, The first two letters(E and F) should be equivalent to the first two letters of the other shape(A and B).

jordan is chopping wood for the winter. for 10 days on a row he follows the same process: in the morning he chops 20 pieces of wood and in the evening he chops an additional 30 pieces of wood on the 11th day jordan chops only 5 pices of wood write a numerical expression with parentheses for the total number of pieces of wood jordan chopped. (do not simplify your expression)

Answers


[tex](20 + 30) \times 10 + 5[/tex]
I'm 90% sure that's right, sorry if I'm wrong :/

i dont understand this help me :( What is the equation of a line with a slope of ​3​ and a point (3, 1) on the line?

Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.

Answers

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{1})~\hspace{10em} slope = m\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=3(x-3) \\\\\\ y-1=3x-9\implies y=3x-8[/tex]

explain whether a quadratic function can have both a maximum value and a minimum value

Answers

A quadratic function can not have a maximum and minimum value. It can only take on one of those. The quadratic only makes one turn, so if the quadratic opens upwards, there is a minimum. If the quadratic opens downwards, there is a maximum.


Final answer:

A quadratic function can have either a maximum value or a minimum value, but not both.

Explanation:

A quadratic function can have either a maximum value or a minimum value, but not both. Whether it has a maximum or minimum value depends on the coefficient of the quadratic term (a) in the function. If a is positive, the graph of the quadratic function opens upwards and has a minimum value. If a is negative, the graph opens downwards and has a maximum value.

For example, the function y = x² has a minimum value of 0 at the vertex of the parabola, while the function y = -x^2 has a maximum value of 0 at the vertex.

Therefore, a quadratic function cannot have both a maximum value and a minimum value.

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