The volume of a cuboid is the product of its length, width, and height. Out of the five statements B, C, and E are correct.
What is the volume of a cuboid?The volume of a cuboid is the product of its length, width, and height. It is formulated as:
[tex]\rm \text{Volume of Cuboid} = Length \times Width \times Height[/tex]
As the dimensions of the room are given and a room is mostly in the shape of a cuboid. Therefore, the volume of the room can be written as,
The volume of the room = 10ft × 15ft × 12ft = 1800 ft³
A.)
The heat produced by 3 people in a period of 9 hours will be
= 600 BTU × 3 people × 9 hour
= 16,200 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{16,200\ BTU}{1800\ ft^3} = 9\ BTU/ft^3[/tex]
Hence, the statement that 3 people will produce approximately 8.33 BTUs/ft³ in a 9 hour period is wrong.
B.)
The heat produced by 4 people in a period of 10 hours will be
= 600 BTU × 4 people × 10 hours
= 24,000 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{24,000\ BTU}{1800\ ft^3} = 13.334\ BTU/ft^3[/tex]
Hence, the statement that 4 people will produce approximately 13.334 BTUs/ft³ in a 10 hour period is correct.
C.)
The heat produced by 5 people in a period of 2 hours will be
= 600 BTU × 5 people × 2 hours
= 6,000 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{6,000\ BTU}{1800\ ft^3} = 3.334\ BTU/ft^3[/tex]
Hence, the statement that 5 people will produce approximately 3.334 BTUs/ft³ in a 2 hour period is correct.
D.)
The heat produced by 6 people in a period of 4 hours will be
= 600 BTU × 6 people × 4 hours
= 14,400 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{14,400\ BTU}{1800\ ft^3} = 8\ BTU/ft^3[/tex]
Hence, the statement that 6 people will produce approximately 7.334 BTUs/ft³ in a 4 hour period is wrong.
E.)
The heat produced by 7 people in a period of 4 hours will be
= 600 BTU × 7 people × 4 hours
= 16,800 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{16,800\ BTU}{1800\ ft^3} = 9.334\ BTU/ft^3[/tex]
Hence, the statement that 7 people will produce approximately 9.334 BTUs/ft³ in a 4 hour period is correct.
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Out of 260 racers who started the marathon, 232 completed the race, 25 gave up, and 3 were disqualified. What percentage did not complete the marathon?
Answer:
9
Step-by-step explanation:
You're looking for the percentage that "did not complete the marathon" So take the 25 that gave up and the 3 that were disqualified and add those. Then divide 260 by your sum of those groups. Your expresssion should be 260/28 which gives you the decimal 9.28571429. Your answer would be 9 because this question doesn't ask for a decimal answer.
write 3 in polar form
Answer:
(3,0)
Step-by-step explanation:
I hope this helps. I think this is right.
What is the product of -4 and +6?
Answer:
2
Add negative 4 to positive 6, which is 4 - 6 but backwards, and that gives you 2
Or subtract 0 by 4, then add 2 which is -4 because you are subtracting 4 by 0 instead of 0 by 4, which would be four.
[tex]way~1\\4 - 6 = 2\\\\way~2\\(0 - 4) + 6 = 2[/tex]
I’ll give brainliest
Answer:
After 25 minutes
Step-by-step explanation:
The answer is C
Answer:
Step-by-step explanation:
Louise: Water = 4.6 + 1.2*t gallons of water
Isaac: Water = 54.6 - 0.8 * t t is in minutes.
When will the two amounts of water be equal
When the two waters are the same.
4.6 + 1.2*t = 54.6 - 0.8t Add 0.8t to both sides
4.6 + 1.2*t + 0.8*t = 54.6 Combine the left
4.6 + 2t = 54.6 Subtract 4.6 from both sides.
4.6-4.6 + 2t = 54.6 - 4.6 Combine
2t = 50 Divide by 2
t = 50/2
t = 25
Answer: both aquariums will have the same amount of water in 25 min
Answer: C
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Answer:
can u add a picture cause i dont understand what ur saying at all
Step-by-step explanation:
Write an equation of the circle with center (-5,2) and diameter 6.
Answer:
[tex](x+5)^2+(y-2)^2=36[/tex]
Step-by-step explanation:
The equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius, thus:
[tex](x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-2)^2=6^2\\(x+5)^2+(y-2)^2=36[/tex]
This means that our equation for the given circle is [tex](x+5)^2+(y-2)^2=36[/tex]
Pls answerrrrrrrrrrrrrrrrrrrrrrrrrrr
Answer:
The answer should be 2
Step-by-step explanation:
P
r
=
n
!
(
n
−
r
)
!Subtract
1
from
2
.Simplify
2
!
(
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.
At the school carnival, the student council sold
temporary tattoos of the school mascot. They
purchased a batch of the tattoos for $10, and sold
each one for $4.
Define a unit for the amount of money made.
1. How much money did the student council make
by selling five tattoos?
Answer:
$10
Step-by-step explanation:
4 x 5 = 20
But then we need to subtract the $10 the tattoos cost.
So the amount of money they made was $10.
Hope this helps!
Answer:
$20
Step-by-step explanation:
$4 × 5 = $20
basically just multiply 4 by 5
Find the distance between A(3, 2) and B(8,2) a. 2 units b. √5 units c. 3 units d. 5 units
Answer:
[tex]\boxed{\sf{5 \quad units}}[/tex]Step-by-step explanation:
Use the slope formula.
[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
Use the distance formula.
[tex]: \Longrightarrow \sf{\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}}[/tex]
[tex]\sf{x_2=8}\\\\\\\sf{x_1=3}\\\\\\\sf{y_2=2}\\\\\\\sf{y_1=2}[/tex]
Rewrite the problem down.
[tex]\sf{\sqrt{\left(8-3\right)^2+\left(2-2\right)^2}}[/tex]
Solve.
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract⇒ (8-3)²+(2-2)²Solve parentheses, first.
⇒ (8-3)²
⇒ 8-3=5
⇒ 5²+(2-2)²
⇒ (2-2)=0
⇒ 0²
Rewrite the problem down.
⇒ 5²+0²
Do exponents next.
⇒ 5²=5*5=25
⇒ 0²=0*0=0
⇒ 25+0
Add.
⇒ 25+0=25
You can also divide the numbers from left to right.
→ 25/5=5
Therefore, the distance between (3, 2) and (8,2) is "5 units", which is our answer.I hope this helps. Let me know if you have any questions.
Easy math help picture below 2 problems
Answer:
One line of symmetry.Both rotational and bilateral symmetry.My reasoning for saying both is because the shape is a unique plane. Bilateral symmetry is the term used for when a unqiue shape is folded in any direction and looks the same, while rotational symmetry is when a shape looks the same after a rotated half-turn.
Trick: Fold the shape by the bottom diagonal left side, folding the top left end, then do a rotational turn on the top right corner, fold in the bottom, and it shapes like a rectangle.
Decompose 5/6
How can you solve this problem?
Answer:
3/6+2/6 or 1/6+1/6+1/6+1/6+1/6
Step-by-step explanation:
when you decompose a fraction ask yourself "what will add up to the numerator of the fraction?" when decomposing keep denominator the same.
3+2=5. answer 5/6
What is the discriminant of the polynomial below?
2x^2 + 3x - 7
A. -5
B. -47
C. 23
D. 65
Answer:
2x^2 + 3x - 7 (a= 2 , b= 3 , c= -7)
discriminant= b^2 - 4ac
= (3)^2 - 4(2)(-7)
= 9 + 56 = 65
The answer is D. 65
Hope this helps :)
What is the missing vertex of a rectangle that has (0, 0), (0, 6), and (8, 0) as three of its vertices?
Answer:
(8,6)
Step-by-step explanation:
Refer to the graph below
PLEASE HELP PLEASE PLEASE HELP
Answer:
B. 12 days
Step-by-step explanation:
This can be set up as an equation:
64x = 768, where x represents the days it will take to achieve 768 doughnuts.
Divide both sides by 64.
x = 12.
It will take 12 days to make an additional 768 doughnuts.
Type the correct answer in each box.
Answer:
a = 7, b = 9, c = 4
Step-by-step explanation:
Hope it helps you in your learning process.
[tex]7^{\frac{9}{4}}= \sqrt[4]7^{9}\implies\sqrt[c]a^{b}[/tex]
On comparing, we find:
a = 7, b = 9, c = 4
Answer:
[tex] \sf \: a = 7,\: b = 9,\: c = 4[/tex]
Step-by-step explanation:
[tex] {7}^{\frac{9}{4}} [/tex] we have to write in the form [tex] \sf \: {}^{c} \sqrt{ {a}^{b} } [/tex]
[tex] {a}^{ \frac{1}{b} } = {}^{b} \sqrt{a} [/tex]
[tex] {a}^{b} = {a}^{b}[/tex]
from there we can write.
[tex] {7}^{3 \times \frac{1}{4} } = {}^{4} \sqrt{ {7}^{9} } [/tex]
Comparing with [tex] \sf \: {}^{c} \sqrt{ {a}^{b} } [/tex]
c = 4 , b = 9, a = 7
A bookstore has 36 copies of the latest bestseller and they fit exactly on 3 shelves. The bookstore ordered another 120 copies. How many shelves do they need to fit all their copies of the book?
Answer:
13
Step-by-step explanation:
First, to find out how many book fit on one shelf, you will need to divide the total number of books by the toal number of shelves:
36 books / 3 shelves = 12 books/shelf
Because the question says that the bookstore order another 120 copies, this is means that the 120 books is in addition to the original 36 books.
Because we already know that the 36 books require 3 shelves, we still need to find how many shelves 120 books needs. So, we can divide books by number of how many books can fit on a shelf:
120 books / 12 books per shelf = 10 shelves
So to find the total number of shelves needed, add the number of shelves together:
3 + 10 = 13 shelves
HELP WITH THE FORMULA PLEASE!
It was reported in 2007 that there were 7,234,000 people age 16 or older who had a "go outside the home" disability and that this was 22.4% of the population (of this age group). These are people who cannot go outside the home without help. How large was the total population (of this age group) in 2007?
Answer:
32294643
Step-by-step explanation:
You can first set up a proportion.
22.4/100 = 7234000/x
723400000 = 22.4x
x = 32294642.8571 ≈ 32294643
I hope this is correct and that it helps!
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
This is because of the slope and amount of earnings Tatiana has.
Tatiana gets 26 dollars added to her earnings every 2 hours
Sample: 16 + 26 = 42
The 16 represents the number of earnings that Tatiana gets/earns for hour 0.
If we were to graph the earnings of Tatiana meaning her time represents X and the earnings represent Y. We could clearly see that Tatiana earns more money than Darryl.
factor 1-2sin^2(x)+sin^4(x)
Answer:
[tex]\left(1 - \sin^{2}(x)\right)^{2}[/tex].
Step-by-step explanation:
Notice that "[tex]1[/tex]" is equal to "[tex]1^{2}[/tex]" whereas [tex]\sin^{4}(x) = {\left(\sin^{2}(x)\right)}^{2}[/tex]. Therefore:
[tex]\begin{aligned} & 1 - 2\, \sin^{2}(x) + \sin^{4}(x) \\ =\; & 1^{2} - 2\, \sin^{2}(x) + {\left(\sin^{2}(x)\right)}^{2}\end{aligned}[/tex].
Make use of the identity [tex](a - b)^{2} = a^{2} - 2\, a\, b + b^{2}[/tex]. In this case, set [tex]a = 1[/tex] whereas [tex]b = \sin^{2}(x)[/tex]. Therefore:
[tex]\begin{aligned} & 1^{2} - 2\, \sin^{2}(x) + {\left(\sin^{2}(x)\right)}^{2} \\ =\; & a^{2} - 2\, a\, b + b^{2} \\ =\; & (a - b)^{2} \\ =\; & {\left(1 - \sin^{2}(x)\right)}^{2}\end{aligned}[/tex].
A square has side length 3.4 cm. The side length of the enlargement is 17 cm. Determine the scale factor.
Answer:
The scale factor is 5
Step-by-step explanation:
To find the scale factor, we divide 17 by 3.4 to find how much it was enlarged by.
17/3.4 = 5
We do this becuase when finding the scale factor, we take the dilated shape/side length and divide it by the original shape/side length.
1. The width of a rectangular table is 7 - 2x feet and the length is 5x + 2 feet. Write a polynomial that represents the perimeter.
2. Base from problem number 10, what is the perimeter of the rectangular table if x is 3.
Answer:
perimeter is 36
Step-by-step explanation:
if x=3
then it turns into
Width 7-2(3)
length 5(3)+2
which equals
width 1
length 17
since it's a perimeter you add all four corners
which is 1+1+17+17=36
Maya is building a model of her city's downtown area. She is constructing part of an office building, as shown below. Each cube has an edge length of 1/6 foot.
The height of the model building is foot?
A.3/4
B.1/2
C.1/6
D.3/18
E.1/4
Answer: the answer is 1 over 2 which is e
Step-by-step explanation: 4 and 2 and 3 equal 9 so 1 over 6 times 9 cubes equal 1.5 which is 1 over 2
What is the end behavior of h(x)=-5x^4+13x/x^3
Answer:
Both ends point down
Step-by-step explanation:
SInce this function is even, and the leading coefficient is negative, both ends will point in the negative direction.
Fill in each blank of the table shown by converting
given form of a number into the missing form of the
number.PICTURE BELOW
IM SO CONFUSED PLEASE HELP THANK YOU
Answer:
A. 0.11111
B. 17/100
C.0.232323
D. 6/9 or 2/3
E. 1.8888889
F. 4/11
G. 1.45454545
H. 3/100
Step-by-step explanation:
Convert them to fractions and decimals
a bathing suit is on sale for 40% off including 7% sales tax the final price is $57.78 what was the original cost without tax or discount
Answer:
38.7126
step-by-step explanantion:
so it's technically 33 percent off because the taxes is 7 percent.
and 33 percent of 57.78 is 19.0674. so 57.78-19.0674 will equal 38.7126
The original cost of the bathing suit without tax or the discount is $38.72.
DiscountThe term "discount" refers to a pricing scheme in which a commodity's (goods or services) price is lower than its marked price. Simply said, a discount is a proportion of the advertised price.
How to find the original cost?The bathing suit is 40%off including 7% tax.This means that the discount of 40% includes the tax of 7%.Thus the discount without tax will be calculated by: 40%-7%=33%
Now we will calculate the discount without tax on the final cost of the bathing suit, i.e, 33% of the final cost.
[tex]\frac{33}{100} \times 57.78=19.06[/tex]
So, we get a discount of $19.06 on the final cost.Then the original cost of the bathing suit without the tax or the discount will be the final cost less than the discount: $57.78-$19.06=$38.72
So, the original cost of the bathing suit without tax or the discount is $38.72.
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3.6 is 90% of what number
Answer:
4
Step-by-step explanation:
Answer:
90% of 4 = 3.6 I believe that this is the answer
2a+2b=360 degrees
a) a= 60 degrees
b) a = 75 degrees
use algebra to solve for b, find the unknown angles for the parallelogram
Answer:
2a+2b=360
2(60)+2b=360
120+2b=360
2b=360-120
2b/2=240/2 divide by 2
b=120
step 2
2a+2b=360
2(60)+2(120)=360
120+240=360
360=360
part two b)2a+2b=360
2(75)+2b= 360
150+2b=360
2b=360-150
2b/2=210/2
b=105
step 2
2a+2b=360
2(75)+2(105)=360
150+210=360
360=360
An online video streaming service offers two plans for unlimited streaming. Plan A has a one-time $25 membership fee and is $8 per month. Plan B has a $5 membership fee and is $12 per month. how many months till they cost the same amount?
what is 1/2 - 3/10 in simplest form
Answer: 1/5
Step-by-step explanation:
Help pls I am confused
Answer:
A. 25 books
Step-by-step explanation:
James has 100 comic books and sells 1/4 of his collection. This means that the amount of comic books that he sold is 1/4 of 100 since 100 is the total amount of comic books that he has. To calculate that, we divide 100 by 4 to get 25. Therefore, James sells 25 books.