Unit 3 Closing Activity
Your task is to package 36 cans of tennis balls for shipping. Each tennis ball can contain 3 tennis balls.
You must box them in two rows of 18 cans.
When you go to the box store to purchase a box, you notice that the boxes come in a variety of sizes. All dimensions are in multiples of 6” (ie. 6”, 12”, 18”, etc.). Assume the diameter of one tennis ball is 3 inches. Use 3.14 as the value of .
When talking to the shipping clerk, you find out that there is an extra charge for any extra space in the shipping box that is not taken up by the cans because they have to fill that space in with a filler. Since you are on a tight budget, you want to spend the least amount of money as possible to ship this box.
Your task:
Choose the size box that fits the cans for your shipment.
L= W= H=
2) Determine how much extra space there is in your box after you have put the cans in
Answer:
1) L = 54", W = 6", H = 9"
2) Extra Space = 1389.96 in³
Step-by-step explanation:
1)
LENGTH:
Since, there will be 18 balls along the length of box. Therefore,
Length = L = (18 balls)(Diameter of 1 ball) = (18)(3'')
L = 54"
WIDTH:
Since, there will be 2 rows of cans, and hence, 2 balls along the width of box. Therefore,
Width = W = (2 balls)(Diameter of 1 ball) = (2)(3'')
W = 6"
HEIGHT:
Since, each can can hold 3 balls along the height of box. Therefore,
Height = H = (3 balls)(Diameter of 1 ball) = (3)(3'')
H = 9"
2)
First we calculate the total volume of box:
Total Volume = L*W*H = (54")(6")(9") = 2916 in³
Now, we calculate volume of one ball:
Volume of 1 Ball = (4/3)π(d/2)³ = (4/3)π(3"/2)³ = 14.13 in³
Now, we calculate the total number of balls in box:
No. of Balls = (Balls along length)(Balls along width)(Balls along height)
No. of Balls = (18)(2)(3) = 108 balls
Now, we calculate the total volume of box occupied by balls:
Total Volume occupied by Balls = (No. of balls)(Volume of 1 Ball)
Total Volume occupied by Balls = (108)(14.13 in³)
Total Volume occupied by Balls = 1526.04 in³
Hence, the extra space will be:
Extra Space = Total Volume of Box - Total Volume Occupied by Balls
Extra Space = 2916 in³ - 1526.04 in³
Extra Space = 1389.96 in³
help me with this??
What’s the answer??????
Answer:
720 gallons
Step-by-step explanation:
First, find how many gallons are cleaned per hour.
You can use a ratio:
36 gallons = x gallons
1/4 hour 1 hour
Cross multiply:
36 (1) = 1/4x
36 = 1/4x
(36 = 1/4x) (4/1)
144 = x
x = 144
Then, use this info to find how many gallons per 5 hours.
You can use a ratio:
144 gallons = y gallons
1 hour 5 hour
Cross multiply:
144 (5) = 1y
720 = y
y = 720
There are 720 gallons cleaned per 5 hours.
sorry if it’s hard to read but can anyone help me with number 18?
Answer:
14
Step-by-step explanation:
i need help with this also. (homework due tomorrow)
Answer:
Using Pyhagoras theoram,
(H)^2 = (B)^2 + (P)^2
B = 13 in
P = 5 in
[tex](h)^{2} = (13)^{2} + {(5)}^{2} \\ = > (h)^{2} = 169 + 25 \\ = > (h)^{2} = 194 \\ = > h = \sqrt{194} \\ = > h = 13.92[/tex]
Hence, the missing side is 13.92 inhes.
Answer:
13.93
Step-by-step explanation:
[tex]5^{2} + 13^{2} = c^{2}[/tex]
[tex]25 + 169 = 194 = c^{2}[/tex]
[tex]\sqrt{194} = c^{2}[/tex]
[tex]13.92838827718 = c[/tex]
then round up to 13.93
HELP!!!! :( I will give 5 stars!
1,11,111,1111 what is the next to terms in the sequence and is it geometric or Arithmetic
Tim's mother, using the odometer in the car,
measured the distance between their house and
Tim's school to be 12.8 miles. Tim then
converted the distance in miles to inches, there
are 63,360 inches in each mile.
Which of the following values would be an
approximate and appropriate representation of
the distance in inches that Tim calculated?
A. 811,008 inches
B. 811,000 inches
C. 810,000 inches
D. 800,000 inches
Answer:
A
Step-by-step explanation:
the reason for this equations answer to be A is because if you take the inches in one mile 63,360 and multiple it by the miles that it takes to get the school 12.8 you'll get 811,008.
Lines e and m are intersected by transversalt and ei m.
e
m
1
3
2.
5
4
7
6
8
If m_2 = 112, what is m_7?
Create three different expressions that are each equal to 20. Each expression should include only these three numbers: 4, -2, and 10.
Answer:
Step-by-step explanation:
you could do;
10 x -2 = 20
-2 x (-2) x 10 divided by (-2) + 10 + 10 + 10 +10 =20
4 + 4 - 10 x -2 - 4 - 4 = 20
What is the range of this quadratic function?
Answer:
(negative infinity, 4]
Step-by-step explanation:
Reminder: the range is all the possible y values the function can get by plugging in x values.
Since this is a downward opening parabola, it won't have a lower boundary, which means that the answer must be (negative infinity, 4]
We can further check that's correct by seeing that the parabola has its vertex at 4, which is written in the answer.
That means the correct answer must be (negative infinity, 4]
11) The sum of three consecutive integers is 13 greater than twice the smallest of the three integers. Find the integers.
Answer:
The sum of 3 consecutive integers is 13 more than twice the smallest integer. Find the integer.
x + (x+1) + (x+2) = 2x + 13
3x + 3 = 2x + 13:
3x - 2x = 13 - 3
x = 10 is the smallest integer:
Check: 10 + 11 + 12 = 2(10) + 13
The integers will be equal to 10, 11, and 12 respectively.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The sum of 3 consecutive integers is 13 more than twice the smallest integer. The integer will be calculated as below:-
x + (x+1) + (x+2) = 2x + 13
3x + 3 = 2x + 13:
3x - 2x = 13 - 3
x = 10 is the smallest integer:
Check: 10 + 11 + 12 = 2(10) + 13 = 33
Therefore, the integers will be equal to 10, 11, and 12 respectively.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ2
Please help me with my homework
A) 1st one
B) 2nd one
C) and im too lazy to do c
Answer:
6 x 10^-6 is a greater value
2 x 10^-8 is the lesser value
I'm not sure about the third one
According to cell theory, all cells come from:
A.
water.
B.
soil.
C.
chemical reactions.
D.
pre-existing cells.
Answer:
pre-existing cells
Step-by-step explanation:
Answer:
D. pre-existing cells
Step-by-step explanation:
According to the cell theory all living cells arise from pre-existing cells by division. The cell is the fundamental unit of structure and function in all living organisms. I hope this helps!
Find the measure of each angle. Assume the lines are parallel.
Answer:
2 = 67
3 = 113
4 = 67
5 = 113
6 = 67
7 = 113
8 = 67
Step-by-step explanation:
opposite angle have to equal 180 because if you combine them they just become the line.
since the lines are parallel, measurements will be the same for the bottom set of angles as they are the top set of angles.
Anyone know how to do??
Answer:
30°
Step-by-step explanation:
Step 1:
2x + 10 + 4x + 80 = 180 Sum of a line
Step 2:
6x + 90 = 180 Combine Like Terms
Step 3:
6x = 90 Subtract 90 on both sides
Answer:
x = 30° Divide
Hope This Helps :)
y=1/2(x+4)(x-2) vertex
Answer:
(-1, -4.5)Step-by-step explanation:
[tex]y=\frac12(x+4)(x-2)\quad\implies\quad x_1=-4\,,\ \ x_2=2[/tex]
vertex is (p, q) where:
[tex]p=\dfrac{x_1+x_2}2=\dfrac{-4+2}2=\dfrac{-2}2=-1\\\\q=f(p)=\frac12(-1+4)(-1-2)=\frac12(3)(-3)=-\frac92=-4.5[/tex]
So the vertex is: (-1, -4.5)
If I || m, identify the angle pair as congruent or supplementary.
Justify your reasoning by classifying the angle pair.
Angle Pair
Congruent or
Supplementary?
Classify
10. 21 and 28
11. 25 and 26
12. Z6 and 28
13. 22 and 23
14. 24 and 27
15. 23 and 26
Answer/Step-by-step explanation:
10. <1 and <8 are congruent.
Reason/classification: alternate exterior angles
11. <5 and <6 are supplementary.
Reason/classification: linear pair
12. <6 and <8 are congruent.
Reason/classification: corresponding angles
13. <2 and <3 are supplementary.
Reason/classification: same side interior angles
14. <4 and <7 are congruent.
Reason/classification: vertical angles
15. <3 and <6 are congruent.
Reason/classification: alternate interior angles
pls help me out its needed
Answer:
150 students
Step-by-step explanation:
30%+60%=90%
15=10%
multiply by 100 on both sides then simplify
Which equation correctly applies the distributive property?
70+2.028=(70⋅2)+(70⋅0.02)+(70⋅0.008)
Answer:
70.2
Step-by-step explanation:
Anwhat wht
Step-by-step explanation:
ithinkithink ok sure
Solve
(6x + 5) - (x + 3)
Answer:
5x+2
Step-by-step explanation:
6x-x=5x and 5-3=2
so 5x+2 is the answer.
The IQ scores for students at a certain school follow a bell-shaped distribution with mean 102 and standard deviation
10. Kyla, a student at this school, had a standardized IQ score of 1.2. What was her actual IQ score?
104
107
111
114
120
Answer:
104
Step-by-step explanation:
If the standard deviation is 10, multiply it by .2 to get 2. Add 102 and you get 104.
A frozen yogurt shop offers a rewards system for frequent customers. The graph below represents how much a rewards customer pays based on the number of ounces of frozen yogurt purchased.
A graph titled Customer Rewards. The horizontal axis shows ounces of yogurt purchased, numbered 2 to 22, and the vertical axis shows Total Spent (dollars) numbered 1 to 11. A line begins at 0, extends to 5 dollars spent at 10 to 12 ounces, and ends at 9 dollars spent at 20 ounces.
Which statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt?
A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.
A rewards customer pays $5 per ounce because the total amount paid is always increasing.
A rewards customer pays $20 for 10 or 12 ounces of yogurt because the total amount paid is increasing.
A rewards customer earns 5 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.
Answer:
A rewards customer earns 2 free ounces of yogurt because the total amount paid for 10 ounces and 12 ounces is the same.
did the test on edge
Which fraction is equivalent to
2/-6?
Answer:
-2/6
Step-by-step explanation:
Please help me with this
Answer:
B.
[tex](x + 2) ^{3} - 9 [/tex]
Line p is parallel to side B and C
What is the measure of angle 1 in degrees?
Answer:
73 degrees
Step-by-step explanation:
The interior angle equals to 180. 73+37+ m<2 = 180. That means angle 2 is 70 degrees.
m<1 and m<C and equal due to alternate interior angles. That means angle 1 is 37 degrees.
We know angles 1 and 2 equal to 37 and 73. That means the angles are equal to the interior triangle. 70+37= 107. 180-107= 73 Degrees
Which value of x makes the equation -5x-(-7-4x) =-2(3x-4 true?
Answer:
x = 1/5
Step-by-step explanation:
Step 1: Write equation
-5x - (-7 - 4x) = -2(3x - 4)
Step 2: Solve for x
Distribute: -5x + 7 + 4x = -6x + 8Combine like terms: -x + 7 = -6x + 8Add 6x to both sides: 5x + 7 = 8Subtract 7 on both sides: 5x = 1Divide by 5 on both sides: x = 1/5Step 3: Check
Plug in x to verify it's a solution.
-5(1/5) - (-7 - 4(1/5)) = -2(3(1/5) - 4)
-1 - (-7 - 4/5) = -2(3/5 - 4)
-1 - (-39/5) = -2(-17/5)
-1 + 39/5 = 34/5
34/5 = 34/5
Given the equation of a linear function in standard form 2x + 3y = 12, solve for y. Select all that apply
which function represents the graph below?
Y=1/2x+1
The answer is
Ye is riding home from a friend's house. After 5 minutes he is 4 miles from home, after 15 minutes Ye is 2 miles from home. Which equation models his distance from home y, in terms of minutes, x?
Answer:
[tex]y = -\frac{1}{5}x + 5[/tex]
Step-by-step explanation:
Given
[tex]5\ minutes = 4\ miles[/tex]
[tex]15\ minutes = 2\ miles[/tex]
Required
Determine the equation
y represents distance
x represents time
So, the given parameters can be modeled (x,y) as:
[tex](x_1,y_1) = (5,4)[/tex]
[tex](x_2,y_2) = (15,2)[/tex]
First, we need to determine the slope of the function.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 - 4}{15 - 5}[/tex]
[tex]m = \frac{-2}{10}[/tex]
[tex]m = -\frac{1}{5}[/tex]
The equation can be determined using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = -\frac{1}{5}[/tex]
[tex](x_1,y_1) = (5,4)[/tex]
[tex]y - y_1 = m(x - x_1)[/tex]
becomes
[tex]y - 4 = \frac{-1}{5}(x - 5)[/tex]
Open bracket
[tex]y - 4 = -\frac{1}{5}x + 1[/tex]
Solve for y
[tex]y = -\frac{1}{5}x + 1 + 4[/tex]
[tex]y = -\frac{1}{5}x + 5[/tex]