Independent Practice : Rectangular Prism
GRAHAM CRACKERS A manufacturer wants to double the volume of the graham cracker box.
The manufacturer will either double the height or double the width.
GRAHAM
CRACKERS
a. Which option uses less cardboard? Justify your answer.
h 9 in
w 2 in
16 in.
b. What is the volume of the new graham cracker box?
Answers
Answer:
a). Amount of cardboard required will be less when manufacturer doubles the width.
b). Volume of the new cracker box = 216 in³
Step-by-step explanation:
Volume of the Graham cracker box = volume of the rectangular prism formed
= Length × Width × Height
= 6 × 2 × 9
= 108 in³
a). To double the volume of the rectangular prism, manufacturer either doubles the height or doubles the width.
When manufacturer doubles the height,
Amount of cardboard required = surface area of the rectangular prism
= 2(lw + wh + hl)
= 2(6×2 + 2×18 + 18×6)
= 2(12 + 36 + 108)
= 2(66)
= 132 in²
When manufacturer doubles the width,
Surface area of the rectangular prism = 2(6×4 + 4×9 + 9×6)
= 2(24 + 36 + 54)
= 2(114)
= 228 in²
Therefore, amount of cardboard required will be less when manufacturer doubles the width.
b). Volume of the new Graham box = 2(Volume of the old box)
= 2 × 108
= 216 in³
Related Questions
70 is 30% of what number?
Answers
Answer: 233.33.
Step-by-step explanation: Consider marking this answer as brainliest if it helped you out.
Answer:
Step-by-step explanation:
233.33
Hope this helps =)
Solve as y=mx+b
Write an equation of the line below.
Answers
Answer:
y = 2x
Step-by-step explanation:
Since the line passes through the origin or (0,0), adding + 0 is irrelevant so we are just looking for slope.
Since there is a rise of 2 units every one unit, the slope or m = 2.
Since we know two points by observing the graph (0,0) and (3,6). m = y2-y1/x2-x1 = 6-0/3-0 = 6/3 = 2/1 = 2
Find the Domain of the function y = 5x - 3
Answers
Answer:
y=5x+3y=5x+3
im not sure
9514 1404 393
Answer:
all real numbers
Step-by-step explanation:
The domain of any polynomial function is all real numbers.
Factor this expression into primes.
22x
Answers
(11x) (2)
this is supposed to look like a factor tree where 11x and 2x are circled :)
The factors of expression into prime numbers is 2 and 11.
We are given that;
The expression= 22x
Now,
Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
To factor an expression into primes, we need to find the prime factors of each term and then write the expression as a product of those factors.
For example, 22x can be written as:
[tex]$22x = 2 \times 11 \times x$[/tex]
The prime factors of 22 are 2 and 11, and x is already a prime factor.
Therefore, by factorization answer will be 2 and 11.
Learn more about factorization here:
https://brainly.com/question/10454590
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For the situation described.
a) Write an equation in the form y = mx + b.
b) Then, solve the problem.
"A water tank holds 24,000 gallons. How many days will it take for all of the water to
be used if the water is used at an average rate of 650 gallons per day? (round to the
nearest whole number)"
a) y =
X +
b)
days
Answers
Answer:
a) y=650x+0
b) 24,000=650x
24,000/650=x
x=37
I hope this is good enough:
if you can you don't have to put the +0 its just to fill it all out
Which equation represents this number sentence? Fourteen more than the quotient of a number and 5 is 23.
5/n+14=23
n+14/5=23
5/n+14=23
n/5+14=23
Answers
Answer:
D) n/5+14=23
Step-by-step explanation:
A) cannot be the right answer because the question states "quotient of a number and 5", which means that it has to be "n/5"B) cannot be the right answer because the question states "fourteen more than the quotient", which means that it has to be "n/5 + 14"C) cannot be the right answer because it's the same as A), it has to be "n/5"D) is the correct answer- this is because the question states "fourteen more than...", which means that "14" has to be added to the quotient; the question also says the "quotient of a number and 5", which means it should be "n/5"The CEO of a company wants to determine whether taking the employees to a company retreat would boost their morale. He decides to survey a simple random sample of 50 of the 250 employees. Which of the following options would guarantee a simple random sample? asking the first 50 employees who come to work on Monday morning to take the survey telling the managers in each of the 5 departments to randomly select 10 people to take the survey giving each employee a unique number from 1 to 250 and randomly selecting 50 people to take the survey sending an email to all 250 employees asking them to complete the survey within the next couple of days
Answers
Answer:
b
Step-by-step explanation:
Among all the given options, the one that would guarantee a simple random sample is: “telling the managers in each of the 5 departments to randomly select 10 people to take the survey.” Hence, Option B is correct.
What is a random sample?An unprejudiced portion of a population is chosen in a simple random sampling. With this sampling technique, the possibility of selection bias is reduced because every person of the population has an exact equal probability of being chosen.
A simple random sample is a group of people chosen at random, all with the same probability, from a larger group of people in statistics. It involves a method of randomly choosing a sample.
Random sampling assures that the results of sample should be close to those that would have been found if the complete population had been measured. With the simplest random sample, each unit in the population has an equal probability of being chosen.
Therefore, Option B is correct.
Learn more about random sample from here:
https://brainly.com/question/12719645
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Oliver estimates the weight of of his cat to be 16 pounds. The actual weight of the cat is 14.25 pounds. What is the percent error of Oliver's estimate rounded to the nearest tenth of a percent.
Answers
Given:
Estimated weight of a cat = 16 pounds
Actual weight of that cat = 14.25 pounds
To find:
The percent error to the nearest tenth of a percent.
Solution:
We know that,
[tex]\text{Percent error}=\dfrac{\text{Estimated value - Actual value}}{\text{Actual value}}\times 100[/tex]
Using the above formula, we get
[tex]\text{Percent error}=\dfrac{16-14.25}{14.25}\times 100[/tex]
[tex]\text{Percent error}=\dfrac{1.75}{14.25}\times 100[/tex]
[tex]\text{Percent error}=0.122807\times 100[/tex]
[tex]\text{Percent error}=12.2807[/tex]
Round the percent error to the nearest tenth of a percent.
[tex]\text{Percent error}\approx 12.3[/tex]
Therefore, the percent error is 12.3%.
Answer:22
Step-by-step explanation:
Juan jogs each day from his house to a local park, and then he jogs back along the same route. On his way to the park, he averages 4 miles per hour. On his way home, he averages 6 miles per hour. If the total trip takes 1 and one-half hours, which equation can be used to find x, the distance in miles from Juan’s house to the park? Distance (mi) Rate (mi/hr) Time (hr) Trip to Park x 4 mph Trip to Home x 6 mph StartFraction x Over 4 EndFraction + StartFraction x Over 6 EndFraction = 1 StartFraction x Over 4 EndFraction + StartFraction x Over 6 EndFraction = 1 and one-half 4 x + 6 x = 1 and one-half 4 x + 6 x = 1
Answers
Answer:
The distance traveled equals the speed v multiplied by the time t
:
Since the speed varies, and we only know the total time, we must rewrite this as:
If we separate this in the two 'directions', it should add up to one and a half:
That would lead me to answer b
Step-by-step explanation:
have a nice day :)
Answer:
B. x/4+x/6=1,1/2
96 is the product of 6 and Raj's height.
Answers
Answer:
Raj's height is 16.
Step-by-step explanation:
The answer is 16 because if you multiply 6 with 16 you would get 96. Thanks and if you could mark me as brainliest.
20% of the total candy in a basket is Reese's chocolate. There are 8 Reese's in the basket. What is the total number of pieces of candy in the basket?
Answers
Answer:
I believe it is 40. I'm not 100% sure though
Step-by-step explanation:
If 20% of the candy is reese's and there are 8 reese's in the basket, to find the answer you must multiply 8 by 5. You multiply 8 by 5 because to get 100% you have to multiply 20% by 5 to get 100%.
Brianna invested $990 in an account paying an interest rate of 9 3 4 9 4 3 % compounded continuously. Penelope invested $990 in an account paying an interest rate of 9 1 2 9 2 1 % compounded monthly. After 16 years, how much more money would Brianna have in her account than Penelope, to the nearest dollar?
Answers
Answer:
Brianna would have $177 more in her account than Penelope after 16 years.
Step-by-step explanation:
Note: There are errors in the question especially in how the interest rates are stated. These are therefore fixed before answering the question. The complete question with the fixed errors is given as follows:
Brianna invested $990 in an account paying an interest rate of 9.34943% compounded continuously. Penelope invested $990 in an account paying an interest rate of 9.12921% compounded monthly. After 16 years, how much more money would Brianna have in her account than Penelope, to the nearest dollar?
The explanation to the answers is now provided as follows:
Step 1: Calculation of the amount of money Brianna would have in her account after 16 years
Since the interest rate is compounded continuously, the amount can be calculated using the formula for calculating the future of value (FV) with a continuous compounding interest rate as follows:
FVB = Pe^(rt) …………………………. (1)
Where;
FVB = Future value or the amount of money Brianna would have in her account after 16 years = ?
P = Amount invested = $990
e = exponential function
r = interest rate = 9.34943%, or 0.0934943
t = number of years = 16
Substituting the values into equation (1), we have:
FVB = $990 * e^(0.0934943 * 16)
FVB = $990 * e^(1.4959088)
FVB = $990 * 4.46339103998695
FVB = $4,418.75712958708
Rounding to the nearest dollar, we have:
FVB = $4,419
Therefore, Brianna would have $4,419 in her account after 16 years.
Step 2: Calculation of the amount of money Penelope would have in her account after 16 years
Since the interest rate is compounded monthly, the amount is calculated using the normal formula for calculating the future value as follows:
FVP = P * (1 + R)^n …………………………. (2)
Where;
FVP = Future value or the amount of money Penelope would have in her account after 16 years = ?
P = Amount invested = $990
R = monthly interest rate = Interest rate / 12 months = 9.12921% / 12 = 0.0912921 / 12 = 0.007607675
t = number of months = number of years * 12 months = 16 * 12 = 192
Substituting the values into equation (2), we have:
FVP = $990 * (1 + 0.007607675)^192
FVP = $990 * 1.007607675^192
FVP = $990 * 4.28510670976906
FVP = $4,242.25564267137
Rounding to the nearest dollar, we have:
FVP = $4,242
Therefore, Penelope would have $4,242 in her account after 16 years.
Step 3: Calculation of the amount of money Brianna would have more in her account than Penelope after 16 years
From Step 1 above, we have:
FVB = Future value or the amount of money Brianna would have in her account after 16 years = $4,419
From Step 2 above, we have:
FVP = Future value or the amount of money Penelope would have in her account after 16 years = $2,242
The amount of money Brianna would have more in her account than Penelope after 16 years can be calculated by deducting FVP from FVB to obtain the difference as follows:
Difference = FVB - FVP = $4,419 - $4,242 = $177
Therefore, Brianna would have $177 more in her account than Penelope after 16 years.
Answer:
$212
Step-by-step explanation:
trust me
Helppp mehhhh please!!!!!!!! :)
Answers
Answer:I think it is 82.5
Step-by-step explanation:
Answer:
82.5
Step-by-step explanation:
2 hours= $165
1 hour= 2 hours/ 2.
so 1 hour of pay= 165/2= 82.5
perpendicular to the line y = x - 4 passing through (- 1, - 2)
Answers
Answer:
Y= -x-3
Step-by-step explanation:
which best describes how to slove the equation below? 26x=74
Answers
Answer:
Step-by-step explanation:
Simplifying
26x = 74
Solving
26x = 74
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '26'.
x = 2.846153846
Simplifying
x = 2.846153846x
this is google respond
=74/26
x=37/13 this is mines mak me brainest plz
-1/6 times (-9/7) and if you answer correctly i’ll mark your answer brainly and 60 points
Answers
Answer:
3/14
Step-by-step explanation:
(−1/6)(−9/7)
= (−1)(−9)
(6)(7)
=9/42
Answer:
3/14
Step-by-step explanation:
Or 14/3
a climber starts descending from 504 feet above sea level and keeps going until she gets to 40 feet below sea level, how may feet did she descend?
Answers
Answer:
544 feet.
Step-by-step explanation:
|504| +|-40|=544
Math!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!3
Answers
Answer:
may you please mark me as brainliest? I will mark you it if you answer on mine
Step-by-step explanation:
10
8
7
6
5
4
3
2
1
х
0 1 2
3
4
5
6
7
8
9
10
What is the slope?
Answers
Answer:
d
Step-by-step explanation:
d trust
thanks for all of you guys' help!!! this is the fourth one nowww
Answers
Answer: The answer should be C. y = 5.5x. Good luck! :)
Answer:
C
Step-by-step explanation:
Admission to a concert is $20. It costs an additional $7.50 for each T-shirt you bought. You spent a total of $57.50 at the concert. How many T-shirts did you purchase at concert?
Answers
Answer:
you bought 5 T-shirts
Step-by-step explanation:
If x+y=1 and x/y=1 , what is the product of x and y?
F. 1/4
G. 1/2
H. 3/4
J. 1
K. 4
Answers
Answer: g
Step-by-step explanation: 1
2
1
2
=(
1
2
)(
2
1
)
=
(1)(2)
(2)(1)
=
2
2
=1
Use the image to help you answer these question slides 2. Angles g and f are:
a) consecutive interior angles
b) alternate interior angles
c) vertical angles
d) corresponding angles
Answers
Answer:
alternate interior angles
Step-by-step explanation:
They are on alternate sides of the line and they are equal
Jody works at the finish line and gets $36 each day he works plus $1.50 for each pair of shoes he sells. Write a function to represent the total (y) he will make in one day in relation to the number of shoes he sells.
Answers
Answer: y=36+1.50x
Step-by-step explanation:
Given: Daily wages = $36
Commission per pair of shoes he sells = $1.50
Let y= Total he will make in one day by selling x shoes .
Total earnings per day = Daily wages + Commission (Number of shoes)
y=36+1.50x
Hence, a function to represent the total (y) he will make in one day in relation to the number of shoes he sells: y=36+1.50x
What are the zeros of the function?
f(x)=x^3−2x^2−3x
A. 3, 0, and 2
B. 2, 0, and 3
C. 1, 0, and 3
D. 3, 0, and 1
Answers
Answer:
C
−1, 0, and 3
Step-by-step explanation:
f(x) factors as
f(x)=x(x+1)(x-3)
so has zeros of x = -1, 0, 3 because these values make the factors be zero.
Can I have brainliest please.
Michael wants tto start a garmets business. He borrowed 50000 for 5 years at 14% from his friend. The intrest is compoudee semi-annually from his friend. What is the total amount he will have to pay back to his friend?Round to the nearest cent
Answers
Answer:
98,357.57
Step-by-step explanation:
The formula to find the total amount obtained using compound interest is given as:
A = P(1 + r/n)^nt
Where:
A = Amount returned or payed back.
P = Amount borrowed = 50,000
R = Interest rate = 14% = 0.14
T = Time = 5 years
n = number of time compounded = semi annually = 2
Hence,
A = 50,000(1 + 0.14/2)^2 ×5
A = 50,000(1 +0.07)^10
A = 98,357.57
The amount he is paying back to his friend is 98,357.57.
A recipe calls for 2 cups of milk. The recipe makes 10 servings. How many cups of milk are needed to make 8 servings?
Answers
Answer:
1.6 Cups of Milk
Step-by-step explanation:
1 serving = 0.2 cups of milk
8 servings= 0.2*8 which equals 1.6
I hope i helped you :)
HELP PLEASE
Which number sentence is true
O A) 12 < |-12|
OB) |-121 <|-48|
C) |-48|< |48|
OD) |12| > |-48|
Answers
Answer:
A
Step-by-step explanation:
Is PRB congruent to QSB? Justify your answer.
This problem requires you to show your work and explain your reasoning.
Be sure to -
• Mark given information on the diagram
• Answer the question
• Provide justification statements that are mathematically correct
Answers
Answer:
When looking at this model, and asking yourself the question, is PRB congruent to QSB? PRB is in fact congruent to QSB. Congruent means that two figures have the same shape/size, no matter if it's mirrioring or not it is congruent. In this image, PRB is one shape, and QSB is another. They have the exact same points and they're also the same shape, but one is flipped the right side up. It was also stated PQ and RS bisect eachother at point B, <p is congruent to <Q, and <R is congruent to <S proving all these connections make this figure conguent.
Step-by-step explanation:
Gerald and his dog Spike get on the scale together. Their combined weight is 128 pounds. If the ratio of Gerald's weight to Spike's weight is 3:1, how much does Gerald weigh?
Answers
Answer:
96lbs
Step-by-step explanation:
g + s = 128
g = 3s
3s + s = 4s = 128
s = 128/4 = 32
g = 3s = 96