Problem Solving in Santa's Workshop
Clifford works in the gift-wrapping department of Santa's
workshop. His job is to finish all the packages with a bow.
He is running low on bows and only has 100 bows left. He
begins working at 5:00 a.m. During the first half-hour, he
uses 12 bows. In the second half-hour, he uses 9 bows.
During the third half-hour, he uses 14 bows and in the
fourth half-hour, he uses 11 bows. Clifford uses 16 bows
during the fifth half-hour. If the pattern continues, during
which half-hour will Clifford run out of bows?

Answers

Answer 1

Answer:

Eighth half-hour

Step-by-step explanation:

Given pattern:

1st half hour = 12 bows used2nd half hour = 9 bows used3rd half hour = 14 bows used4th half hour = 11 bows used5th half hour = 16 bows used

Calculate the differences between the number of bows used:

[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16[/tex]

Therefore, the pattern for the bows used is:

-3, +5, -3, +5, etc...

If the pattern continues:

[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16\underbrace{}_{-3}13\underbrace{}_{+5}18\underbrace{}_{-3}15\underbrace{}_{+5}20[/tex]

6th half hour = 16 - 3 = 13 bows used7th half hour = 13 + 5 = 18 bows used8th half hour = 18 - 3 = 15 bows used9th half hour = 15 + 5 = 20 bows used

Create a table with the given and found data, and add a cumulative total column:

[tex]\begin{array}{c|c|c}\vphantom{\dfrac12} \textsf{Half Hour} & \textsf{Bows used per half hour} & \sf Cumulative\; total\\\cline{1-3} \vphantom{\dfrac12} \sf 1st & 12 & 12\\\vphantom{\dfrac12} \sf 2nd &9 &21 \\\vphantom{\dfrac12} \sf 3rd & 14&35 \\\vphantom{\dfrac12} \sf 4th & 11& 46\\\vphantom{\dfrac12} \sf 5th & 16& 62\\\vphantom{\dfrac12} \sf 6th & 13& 75\\\vphantom{\dfrac12} \sf 7th &18 & 93\\\vphantom{\dfrac12} \sf 8th & 15& 108\\\vphantom{\dfrac12} \sf 9th & 20& 128\\\end{array}[/tex]

If Clifford has a total of 100 bows, he will run out of bows during the eighth half-hour.


Related Questions

Solve for for n. 10(n+4) = 63

Answers

Answer:

n=23/10

Step-by-step explanation:

10(n+4)=63

n+4=63/10

n=63/10-4

n=23/10

decimal form: 2.3

Identify three pythagorean triples using the known triple 8, 15, 17. What does this mean?​

Answers

Answer:

yes

Step-by-step explanation:

8² + 15² = 17²

64 + 225 = 289

289 = 289

Find the distance between the points (2, 4) and (8,-8) on a coordinate plane, to the nearest whole number.

Answers

Answer:

2,5

Step-by-step explanation:

2 to the right and 5 up

Lin and Noah are solving the equation `7(x+2)=91`. Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like.

HELPPP

Answers

Answer:

Step-by-step explanation:

Lin’s method

- multiply both x and 2 by  7

7x+14 = 91

- add -14 at both members

7x+14-14 = 91-14

7x = 77

- divide the two members by 7

x = 11

Noah’s method

- divide the two members by 7

x+2 = 13

- add -2 at both members

x+2-2 = 13-2

x = 11

Answer:

The solution is x=11

Step-by-step explanation:

The original equation is

7(x+2)=91

Lin uses the distributive property, which states that

a (x+y) = ax + ay

By applying the property to this case,

7(x+2)=91

7x+14=91

Then we subtract  14 on both sides:

7x+14 - 14 = 91-14

7x=77

Finally, we divide by 7 on both sides:

7x÷7 = 77÷7

x=11

Noah starts by dividing each side by 7, so he gets:

7(x+2)÷7 = 91÷7

x+2= 13

Then he can subtract +2 from both sides:

x+2-2 =13 - 2

x=11

So, they get the same result. The similarity between the two methods is that  they both divide by 7, while the difference is that Lin has to subtract 14, while Noah has to subtract 2.

14. Which numbers below are rational numbers?
2
-3.45
0.8989
All of the above

Answers

Answer:

All of them.

Step-by-step explanation:

They can all be written as a fraction a/b.

x^2+2x=4 Can someone help me complete the square I forgot how to do it. pls show steps​

Answers

Answer:

First of all , you need to make the standard form of equation out of datas . In order to do that transfer (4) to the left side of equation and put 0 instead of it .

The next levels are shown in the above pics , sorry i coulden't write them here .

Step-by-step explanation:

Hope it was helpful dear .

Maria and Juan are married, filing jointly. Their taxable income is $154,849. Use the table below to write an equation to determine their tax. Then calculate their tax.

Answers

Answer:

The right answer is "$31,399.75".

Step-by-step explanation:

The given value is:

Taxable income,

= $154,849

According to the question,

The tax amount will be:

=  [tex]8,962.50 + (154,849 - 65,100)\times 25 \ percent[/tex]

=  [tex]8,962.50+(89,749)\times 25 \ percent[/tex]

=  [tex]8,962.50+22,437.25[/tex]

=  [tex]31,399.75[/tex] ($)

Hey guys!
Please help me out with these questions. Tmrw I have an exam... Will mark BRAINILIEST for the answer explaining proper steps. If I sound rude, please forgive me, I'm just stressed out.....

Thanks ​

Answers

Answer:

Step-by-step explanation:

Solve for x

x^2 + x - 6 = 0

Answers

Answer:

X = 2 and -3

Step-by-step explanation:

I  hope this helps :)

which is greater ? | -5| or 4

Answers

Answer:

4

Step-by-step explanation:

Answer:

|-5|

Step-by-step explanation:

|-5| = 5

5 > 4

|-5| > 4

The value of y varies directly with x. If x=4, then y=10. a. Find the constant of proportionality. b. Write an equation to represent the situation.

Answers

Answer:

aaaa

Step-by-step explanation:

In a short paragraph, describe how you would determine the amount of work needed to pull a toboggan the length of a football field. Be sure to include the equipment list and describe the measurements that you will take.

The Thompson Family has a garden in their backyard. They take the produce each week to a local farmers market. Use the graph to answer question. What percent of the garden is tomatoes? Show work for full credit.

Answers

Answer: 20%

Step-by-step explanation:

The total # of plants is 30, so what you do is take the # of tomatoes over 30. (6/30) and then x/100 so the formula would be 6/30=x/100. Then you would cross multiply and solve! so your answer is 20%

I need the answer please

Answers

Answer:

Parallel

Step-by-step explanation:

Because it is

need some help rq....

Answers

Answer:

work will be explained in the explanation portion

1. x = 3

2. y = 5

3. x = 13

4. y = 2

5. c = 7

6. a = 34

7. unsure but -5/12

8. 16

Step-by-step explanation:

1. 11 - 8 = 3

2. 16 + 9 = 25      5 x 5 = 25

3. 9 + 4 = 13

4. 10 - 4 = 6          3 x 2 = 6

5. 45 - 3 = 42       6 x 7 = 42

6. 23 + 11 = 34

7. 2/3 = 8/12          1/4 = 3/12            8/12 - 3/12 = 5/12

8. 14 divided by 7/8 = 16 (use keep change flip)

HOPE THIS HELPS!! <33

Answer:

1.x=3

2.y=5

3.x=13

4.y=2

5.c=7

6.a=34

7.y=-5/12

8.w=16

Step-by-step explanation:

x+8=11

x=11-8

x=3

5y-9=16

5y=16+9

5y=25

y=25/5

y=5

x-4=9

x=9+4

x=13

3y+4=10

3y=10-4

3y=6

y=6/3

y=2

6c+3=45

6c=45-3

6c=42

c=42/6

c=7

11-a=-23

-a=-23-11

-a=-34

a=34

2/3+y=1/4

y=1/4-2/3

y=-5/12

7/8w=14

7w/8=14

7w=14×8

7w=112

w=112/7

w=16

The three townships of Springfield, Wyandot, and
Johnsonville form an equilateral triangle as shown
below. Write and solve an equation to determine the
value of x.
Wyandot
(62) mi
18.6 mi
Johnsonville
Springfield
X=

Answers

Answer:

x=23 miles

Step-by-step explanation:

heart if it helped

Answer:

X=23jkhhhhjhggguhhgyfv

11. Which could be the table of values that was used to graph the function of x shown below?

Answers

Answer:

D

Step-by-step explanation:

Here, we want to select the possible table of the given line

Let us look at the intercepts

On the x-axis, we have an intercept at x = 2

On the y-axis, we have an intercept at y = -4

This means that when y = 0, x = 2 and when x = 0, y = -4

Looking at the options, the table that supports this answer is the table of option D

A set of cards is numbered 1,2,3,4,5,6,7,8,9,10,11,12. Suppose you pick a card at random without looking. Find the probability of each event. Write as a fraction in simplest form for each questions.

P(3) =

P(a number that starts with the letter T) =

P(odd number) =

P(multiple of 4) =

P(3 or 5) =

P(13) =

Answers

Answer:

3= 1/12

a number with the letter T= 1/3

odd number= 1/2

multiple of 4= 1/6

3 or 5= 1/6

13= 0

Answer:

p(3)=1/3

p(a number that starts with the letter T)=1/3

p(odd number)=1/2

p(multiple of 4)=1/4

p(3 or 5)=1/6

p(13)=0

\large f\left(x\right)=2\left(x+5\right)^2-7

Answers

Which word could you use to describe the author's purpose in an argument?

Convince

Describe

Entertain

Inform

PLEASE HELP HELP HELP HELP

Answers

Answer: 12

Step-by-step explanation:

A polynomial is an expression that contains more than one number, letter, etc. so 12 is a monomial, because it only has one number. Hope this helps!!

I NEED HELP WITH MY MATH NOWWW PLSSS HELP ME

Answers

Answer:

no

Step-by-step explanation:

she still has to multiply by two because there are 2 each of the rectangles that she is calculating the area of. the correct formula would be 2(8*16+8*12+16*12)

Answer:

No.

Step-by-step explanation:

The surface area formula of a right rectangular prism is 2(wl * hl * hw). The height is 12, width is 8, and length is 16. (these sides don't matter, the area will always be 832.) Anyway, our dear Muna did all the steps right, except she has to multiply all that she did by 2. She forgot to do that part

in Joe's fish tank, there are 6 goldfish and 12 snails. How does the ratio 6:18 describe Joe's fish
tank?

Answers

Hey there!

The ratio 6:18 describes Joe's fish tank, certainly. But how?

Note that this ratio can be written as 6 to 18, 6/18, and 6 out of 18.

This ratio can show this: For every 6 goldfish in Joe's tank, there are 12 snails.

Great question!

Hope I helped, please feel free to comment below should you have any questions/comments/concerns!

The correct option is C.

Given that,

in Joe's fish tank, there are 6 goldfish and 12 snails.

Here 6:18 denotes that the number of goldfish to the total no of animals.

Here total no of animals could be

= 6 + 12

= 18

Learn more: brainly.com/question/17429689

Help me with 8,9,10 please I really need help with this!!! Just real answers please

Answers

Answer:

The measure of side CD is 18cm

The measure of side BD is 15+15= 30cm

The perimeter of triangle CDE is 15+15+18 = 48cm

QUADRATIC EQUATIONS HELP(no link or im reporting)

Answers

Answer:

D

Step-by-step explanation:

Given

x² - 8x +

To complete the square

add ( half the coefficient of the x- term )² to x² - 8x

x² + 2(- 4)x + (- 4)²

= x² - 8x + 16 → D

= (x - 4)² ← perfect square

A student used f ( x ) = 5.00(1.012) x to show how the balance in a savings account will increase over time. What does the 5.00 represent?
A: The annual interest rate of the savings account
B: The interest the savings account earned for the first year
C: The starting balance of the savings account
D: The number of years the savings account has earned interest

Answers

Answer:

A student used f(x) = 5.00(1.012)* to show how the balance in a savings ... A student used f(x) = 5.00(1.012)* to show how the balance in a savings increase over time. What does the 5.00 represent? A The interest the savings account earned for the first year. B ... kamyawright is waiting for your help.

Step-by-step explanation:

Which expression is equivalent to -4(2k - 6) - 4k

Answers

Answer:

Factor and Simplfy

12k+24

Answer:

-12k+24

Step-by-step explanation:

-4(2k-6)-4k

do distributive property

-8k+24-4k

simplify

-12k+24

I think this is what the question is asking

really confused on what to do, please help!

Answers

Answer:

6/1 · 11/4 = 66/4 = 16 1/2

-10/3 · (-17/5) = 170/15 = 11 1/3

-9/2 · 26/3 = -234/6 = -39

11/6 · (-9/1) = -99/6 = -16 1/2

someone please help with this math question! ill give brainly if its correct

Answers

Answer:

x = 50, y = 61

Step-by-step explanation:

y + 8 + 2x + 11 = 180°

y + 2x = 161°

the total of the interior angles of the 5 sided polygon is:

(180 x 5) - 360 = 540°

540 = 98 + 98 + 125 + 108 + 2x + 11

2x = 100

x = 50°

y + 2(50) = 161

y = 61°

Solve the equation using Order of Operations. (It's in the picture)
A) 87
B) 101
C) 68
D) 99

I am not allowed to use a calculator, by the way.

Answers

Step-by-step explanation:

(38+45)+9*2+3-59+((4/2)*3+8*5)=

83+18+3-59+(6+40)=

83+18+3-59+(6+40)=

83+18+3-59+46=

(83+18+3+46)-59=

150-59=91

I'm not sure if this is correct but it should be. Is it 4/2*3 or (4/2)³?If it is (4/2)³ the result would be 93.

16.BONUS:
A lamp produced a shadow of a man standing in the middle of a stage.
21° 19°
25 meters
How long is the shadow?
;

Answers

Answer: 11.38

Step-by-step explanation:

I just did this math nation question and that’s what they said the answer was

The solution is, Length of the shadow = 11.4 m.

What are trigonometric relations?

Trigonometry can be stated as the study of the relationships between the angles and the lengths of the sides of triangles.

here, we have,

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

here, we have,

Given the graph:

The length of the shadow = y - x.

• To find x:

tan 21 = x/25

so, we get,

x = 25 * tan 21

  =9.6m

• To find y:

tan 40 = y/25

so, we get,

y = 25* tan40

  = 21m

Length of the shadow:

length = 21 - 9.6 m

           = 11.4m

so, we get,

Length of the shadow = 11.4 m

To learn more about trigonometric relations click :

brainly.com/question/14450671

#SPJ7

HELP

Can some one help me with these 4 problems, I need to find the area, and con you pls explain how you got the answer so I can understand and practice.

Answers

Answer:

1. 380.13

2. 254.47

3. 254.47

4. 153.94

Step-by-step explanation:

Since its a hassle to explain how to solve all 4 problems I'll explain how to solve one of them

For example #1

To solve this:

Use formula A=πr2

Input the radius into the equation

A=π·11²

Multiply all the values

A= 380.13

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