Answers
9514 1404 393
Answer:
rectangular prism: 288 ft³triangular prism: 72 ft³total: 360 ft³Step-by-step explanation:
The volume of a rectangular prism is given by the formula ...
V = LWH . . . . . the product of length, width, height
This rectangular prism has a volume of ...
V = (12 ft)(6 ft)(4 ft) = 288 ft³ . . . . rectangular prism volume
__
The volume of a triangular prism is found from the formula ...
V = Bh
where B is the area of the triangular base, and h is the height of the prism (distance between the triangular bases). The triangular base area is found from ...
A = 1/2bh . . . . .where b is the base of the triangle, and h is its height.
Here, we have ...
B = 1/2(6 ft)(4 ft) = 12 ft²
V = Bh = (12 ft²)(6 ft) = 72 ft³ . . . . triangular prism volume
__
The total volume of the given geometry is the sum of the volumes of the parts:
aquarium volume = 288 ft³ +72 ft³ = 360 ft³
Related Questions
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x 49 x dx
Answers
Answer:
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =2\sqrt{x + 49} +49\ln|\frac{\sqrt{x + 49}-7}{\sqrt{x + 49}+7}|+c[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {\frac{\sqrt{x + 49}}{x}} \, dx[/tex]
Required
Solve by substitution
Let:
[tex]u = \sqrt{x + 49}[/tex]
Square both sides
[tex]u^2 = x + 49[/tex]
Differentiate
[tex]2udu = dx[/tex]
Also notice that:
[tex]x = u^2 - 49[/tex]
So, we have:
[tex]\int\limits {\frac{\sqrt{x + 49}}{x}} \, dx =\int\limits {\frac{u}{u^2 - 49}} \, 2udu[/tex]
[tex]\int\limits {\frac{\sqrt{x + 49}}{x}} \, dx =\int\limits {\frac{2u^2}{u^2 - 49}} \, du[/tex]
Add 0 to the numerator
[tex]\int\limits {\frac{\sqrt{x + 49}}{x}} \, dx =\int\limits {\frac{2u^2+0}{u^2 - 49}} \, du[/tex]
Express 0 as 98 -98
[tex]\int\limits {\frac{\sqrt{x + 49}}{x}} \, dx =\int\limits {\frac{2u^2-98+98}{u^2 - 49}} \, du[/tex]
Split the fraction
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =\int( \frac{2u^2-98}{u^2 - 49}+\frac{98}{u^2 - 49} )\, du[/tex]
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =\int( \frac{2(u^2-49)}{u^2 - 49}+\frac{98}{u^2 - 49} )\, du[/tex]
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =\int( 2+\frac{98}{u^2 - 49} )\, du[/tex]
Rewrite as:
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =\int( 2+\frac{98}{u^2 - 7^2} )\, du[/tex]
Integrate
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =2u +\int\frac{98}{u^2 - 7^2} \, du[/tex]
Remove constant (98)
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =2u +98\int\frac{1}{u^2 - 7^2} \, du[/tex]
As a general rule,
[tex]\int \frac{1}{x^2 - a^2} \, dx = \frac{1}{2}\ln|\frac{x-a}{x+a}|[/tex]
So, we have:
[tex]\int \frac{1}{u^2 - 7^2} \, du = \frac{1}{2}\ln|\frac{u-7}{u+7}|[/tex]
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =2u +98\frac{1}{u^2 - 7^2} \, du[/tex] becomes
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =2u +98*\frac{1}{2}\ln|\frac{u-7}{u+7}|+c[/tex]
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =2u +49\ln|\frac{u-7}{u+7}|+c[/tex]
Substitute values for u
[tex]\int{\frac{\sqrt{x + 49}}{x}} \, dx =2\sqrt{x + 49} +49\ln|\frac{\sqrt{x + 49}-7}{\sqrt{x + 49}+7}|+c[/tex]
differentiate loge(x/x^2+7)
Answers
Answer:
1+1=11 2+2=22 ok na yan kuya or ate
you arrive in Mexico City with $360 how many pesos can you buy?
Answers
Answer:
7 442,84
Step-by-step explanation:
Multiply 2x(5x+8y+3)
Answers
Answer:
10x² + 16xy + 6x
Step-by-step explanation:
2x(5x+8y+3)
10x² + 16xy + 6x
Answer:
[tex]10x^{2} + 16xy + 6x[/tex]
Hope this helped!
3. Write the ones digit in the square of each of the following numbers
a.13
b. 27
c.46
d.20
e.75
f.31
g.42
h.64
i.38
j.79
Answers
Answer:
a.9
b.9
c.6
d.0
e.5
f. 1
g.4
h.6
i.4
j.1
ASAP!!! There are three marbles in a bag. One is red and two are black. What is the probability of picking a red marble first, putting it back in the bag and then picking a black marble? Use the following probably need to find the answer.
Answers
Answer:
The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)
Step-by-step explanation:
Hey there!
The probability of first getting a red marble is 1/3 since we have 1 red marble out of 2 + 1 = 3 total.
We put the marble back. The probability of then choosing a black marble is 2/3, since we have 2 black marbles out of 3 total.
So we get 1/3 * 2/3 = 2/9
The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)
Hope this helps, please mark brainliest if possible. Have a nice day. :)
What are the solutions to this equation?
-7 + (x2 – 19) = 20
-10
5.6
There are no solutions.
10
-5.6
Answers
If ABC~DEF what is the length of BC?
If ABC~DEF what is the length of EF?
Answers
BC would equal the same as EF, they are similar. All you would have to do is figure out the pre image (BC) of EF.
Answer: 8
Step-by-step explanation:
16. Rachael teaches at the college and it pays $3000 per month. She spends $50 on groceries per
week. Netflix costs $9 per month. She pays $50/month for internet. Utilities cost $200 per
month. Rachael's phone bill is $82 per month. Find the net monthly cash flow. (assume 1 month
= 4 weeks).
Answers
Answer: Rachel gets a total of 2459 dollars to save each month.
Step-by-step explanation:
200+9+50+200+82=541
3000-541=2459
What was the original price? Explain how you arrived at this answer.
ONLY ANSWER IF YOU KNOW THE ANSWER
Answers
Answer:
180
Step-by-step explanation:
120 divide by 2
then times by 3
Answer all question
1.There is a circular path around a sports field. Erica takes 18 minutes to drive one round of the field.
Harriet takes 12 minutes. Suppose they both start at the same point and at the same time and go in
the same direction, after how many minutes will they meet?
2. Round the following to four significant figures.
i. 0.00095897
ii. 24596
Answers
Answer:
1. LCM of 18 & 12 = 36 minutes
2. 0.00095897
explanation.
2 18 2 12
____I______ ___l_________
3 9 2 6
____l_______. ___I_________
3 3 3 3
_____l________. ___l_________
l 1
18= 2×3×3 12=2×2×3
1 2 2 1
=1 × 3 =2 × 3
L.C.M= product of greatest power of each prime factor.
2 2
= 2 × 3
=4×9 = 36
hence, time taken by both to meet again
LCM of 18 & 12 =36 minutes
A right rectangular container is 10 cm wide and 24 cm long and contains water to a depth of 7cm. A stone is placed in the water and the water rises 2.7 cm. Find the volume of the stone.
Answers
Answer:
The volume of the rock is 648 cm^3
Step-by-step explanation:
Likely the only dimension that is free to move is the depth of 7 cm.
Volume of the Rock = L * W * h1
L = 24
W = 10
h1 = 2.7
V = 24 * 10 * 2.7
V = 648 cm^3
What is the volume of a cone that has a radius of 11.2 cm and a height of 25.3 cm?
Your Answer:
Sim
Answers
Step-by-step explanation:
V≈3323.42cm³
r Radius
11.2
cm
h Height
25.3
cm
Solution
V=πr2h
3=π·11.22·25.3
3≈3323.41966cm³
hope it is helpful
[tex]\sqrt{160000}[/tex]
what is the value of this
Answers
Answer:
400
Step-by-step explanation:
sqrt(160000)=sqrt(16)*sqrt(10000)=4*100
Have a stack of quarters
from the floor to the top of
your head OR $225?
Answers
Answer:
225 quarters are easy to loose and who will accept that many quarters
Step-by-step explanation:
Answer:
quarters
You will get more money
Can someone help me please
Answers
Answer:0.02
Step-by-step explanation:
I WILL MARK BRANLIEST IF YOU ANSWER CORRECTLY
Answers
Answer:
ok what is your question.
A swimming pool is circular with a 40-ft diameter. The depth is constant along east-west lines and increases linearly from 3 ft at the south end to 8 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.)
Answers
Answer:
[tex]V=6912ft^3[/tex]
Step-by-step explanation:
From the question we are told that:
Diameter [tex]D=40ft[/tex]
Radius [tex]r=d/2=>20ft[/tex]
Depth at south [tex]d_s=3ft[/tex]
Depth at north [tex]d_n=8ft[/tex]
Average depth of the pool
[tex]d_a=\frac{3+8}{2}[/tex]
[tex]d_a=5.5ft[/tex]
Generally the equation for Volume is mathematically given by
[tex]V=\pi r^2h[/tex]
[tex]V=3.142*(20)^25.5[/tex]
[tex]V=6912ft^3[/tex]
PLEASE HELP URGENT Give evidence and proof no links
1/What is the correct written expression for the variable expression: (3 - x)/7 *
the difference of 3 and x divided by 7
3 divided by the difference of 7 and x
the sum of 3 and x divided by 7
the difference of 3 divided by 7 and x
2.Johnny is 5 less than 3 times the age of Elizabeth. If Elizabeth is e years old, which expression shows Johnny's age? *
3e - 5
3e + 5
5 - 3e
5 + 3e
3.What is the value of 4a - 7b - 8, when a = 7 and b = 3? *
1
15
-1
-45
4.Jose has g video games. Tony has 8 fewer games than Jose. What variable expressions represents the total number of video games Jose and Tony have? *
g + 8
2g + 8
g - 8
g + (g - 8)
5. Which written expression represents the variable expression 1/2 (8 - y) *
One half of eight less than a number y
A number y less than half of eight
One half the difference between eight and a number y
the difference of one half of eight and a number y
Answers
A1/ the difference of 3 and x divided by 7
A2/ 3e - 5
A3/ -1
A4/ g + (g - 8)
A5/ One half the difference between eight and a number y
I'm not sure, but I hope it helps :)
factor the polynomial by grouping
[tex]5 {x}^{2} - 11x + 6[/tex]
Answers
Factor
−
11
-
11
out of
−
11
x
-
11
x
.
5
x
2
−
11
(
x
)
+
6
5
x
2
-
11
(
x
)
+
6
Rewrite
−
11
-
11
as
−
5
-
5
plus
−
6
-
6
5
x
2
+
(
−
5
−
6
)
x
+
6
5
x
2
+
(
-
5
-
6
)
x
+
6
Apply the distributive property.
5
x
2
−
5
x
−
6
x
+
6
Find the slope of the line that passes through the following points. Simplify answer (-6,8)and(-1,8)
Answers
Answer:
m = 0
General Formulas and Concepts
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify points
Point (-6, 8)
Point (-1, 8)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{8 - 8}{-1 - -6}[/tex][Fraction] Subtract: [tex]\displaystyle m = \frac{0}{5}[/tex]Divide: [tex]\displaystyle m = 0[/tex]Pluto is 3,647,720,000 miles from the sun. what is that distance in AU?
1. 3.4
2. 39.2
3. 0.25
4. 26.3
Answers
Answer:
39.2 AU.
Step-by-step explanation:
If my memory serves me right an astronomical unit is 93,000,000 miles.
So the answer is 3647720000/93000000
= 39.2 AU.
5.3x-4=15.61 solve for x please
Answers
Answer:
x = 3.7
Step-by-step explanation:
15.61 + 4 = 19.61
19.61 divided by 5.3 = 3.7
Therefore, x = 3.7
Also because it syas "5.3x", it means you have to times that number and x to get the total number; so we can do the equation.
The answer is written above these are filler words for explaining the answer you’re welcome :)
The product of ______________ and (-1) is -35.
Answers
Answer:
35Step-by-step explanation:
The product of 35 and (-1) is -35.
As,
35 × (-1) = -35
Which statement is true about the end behavior of the
graphed function?
• As the x-values go to positive infinity, the function's
values go to negative infinity.
O As the x-values go to zero, the function's values go to
positive infinity.
• As the x-values go to negative infinity, the function's
values are equal to zero
As the x-values go to positive infinity, the function's
values go to positive infinity.
Answers
Answer:
I believe it is the first choice
Step-by-step explanation:
As the x-values go to positive infinity, the function's
values go to negative infinity is the answer because the x-valures are in the first coordinate which is positive but the functions is going negative because of the line in the 3rd coordinate.
I tried my best, i hope you get it correct.
Please let me know if this is correct or not, if not i will edit my answer.
Please mark brainliest :)
Please can someone help quick and now 115 students choose to attend one of three after school activities: football, tennis or running.
There are 54 boys.
52 students choose football, of which 25 are girls.
43 students choose tennis.
10 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
Answers
Answer:
only 20 students would
Step-by-step explanation:
the probability would be very since it is 20 out of 115. i hope this helped
A road has a scale of 1:50 000 The length of a road on the map is 8.5cm.Work out the length of the real road in kilometres
Answers
The answer is 2.1 Km. Hope this helps!
Enlarge the triangle by scale factor -1/3 with centre (-1,2)
PLEASE CAN SOMEONE HELP?????????????/
Answers
The coordinates of the image after a dilation by scale factor -1/3 with center (-1, 2) are (0, 2), (0, 4), and (-1, 4).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of -1/3 centered at the point (-1, 2) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate A, we have;
Coordinate A = (-4, 2) → (-1/3(-4 - (-1)) + (-1), -1/3(2 - 2) + 2)
Coordinate A = (-4, 2) → (-1/3(-4 + 1) - 1, -1/3(2 - 2) + 2)
Coordinate A' = (1, 1) → (0, 2)
For coordinate B, we have;
Coordinate B = (-4, -4) → (-1/3(-4 - (-1)) + (-1), -1/3(-4 - 2) + 2)
Coordinate B = (-4, -4) → (-1/3(-4 + 1) - 1, -1/3(-4 - 2) + 2)
Coordinate B' = (1, 1) → (0, 4)
For coordinate C, we have;
Coordinate C = (-1, -4) → (-1/3(-1 - (-1)) + (-1), -1/3(-4 - 2) + 2)
Coordinate C = (-1, -4) → (-1/3(-1 + 1) - 1, -1/3(-4 - 2) + 2)
Coordinate C' = (1, 1) → (-1, 4).
Read more on dilation here: brainly.com/question/20482938
#SPJ1
In an all boys school, the heights of the student body are normally distributed with a mean of 68 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be taller than 72 inches tall, to the nearest thousandth?
Answers
Answer: 0%?
Step-by-step explanation: there isn't much to this problem because if it had a deviation of 3 from 68, it could be 7 digits from 65 to 71, but since 72 is out of the range, i can only say that this answer is not very correct if it has answer choices other than 0.
The probability is 0.160
What is probability?
'Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.'
mean (μ) = 68 inches
Standard Deviation (σ) = 3
We know,
Z = [tex]\frac{x - mean}{standard deviation}[/tex]
From the normal distribution bell curve, we can see that the percentage of students taller than 72 inches = 14% + 2%
= 16%
The probability that a randomly selected student will be taller than 72 inches = 16/100
= 4/25
= 0.16
= 16%
Hence, we can conclude, that the probability that a randomly selected student will be taller than 72 inches is 0.160
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ2
Joe drives for 3 hours and covers 201 miles. In miles per hour, how fast was he driving?
Answers
Answer:
67 mph
Step-by-step explanation:
201/3 = 67