What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, which numbers you multiplied to find the volume. You may want to use the formula for volume to find the solution.
Answers
Answer:
[tex]15,000\:\mathrm{mm^3}[/tex]
Step-by-step explanation:
The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.
The volume of the square prism is given by [tex]V=s^2\cdot h[/tex], where [tex]s[/tex] is the base length and [tex]h[/tex] is the height. Substituting given values, we have: [tex]V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}[/tex]
The volume of a trapezoidal prism is given by [tex]V=\frac{b_1+b_2}{2}\cdot l\cdot h[/tex], where [tex]b_1[/tex] and [tex]b_2[/tex] are bases of the trapezoid, [tex]l[/tex] is the length of the height of the trapezoid and [tex]h[/tex] is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ([tex]\frac{b_1+b_2}{2}[/tex]) multiplied by the trapezoid's height ([tex]l[/tex]).
Substituting given values, we get:
[tex]V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}[/tex]
Therefore, the total volume of the composite figure is [tex]5,880+9,120=\boxed{15,000\:\mathrm{mm^3}}[/tex] (ah, perfect)
Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:
[tex]V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark[/tex]
Related Questions
Which of the following estimates at a 95% confidence level most likely comes from a small sample?
A. 60% (±18%)
B. 62% (±6%)
C. 65% (±2%)
D. 71% (±4%)
Answers
Gunther's starting weight is 248 pounds, and he plans to lose 2 pounds each week. Use a linear equation to determine Gunther's weight after 10 weeks
Answers
y = 248 - 2x
good luck :))))
if cos theta is equal to -7/25 and theta (180°;360°) what is the value of 14 tan theta
Answers
Answer:
[tex]14 tan\theta = -48[/tex]
Step-by-step explanation:
[tex]cos \theta = \frac{-7}{25}\\\\cos^2 \theta = \frac{49}{625}\\\\sin^2 \theta = 1 - cos^2 \theta\\\\[/tex]
[tex]=1 - \frac{49}{625}\\\\=\frac{625-49}{625}\\\\=\frac{576}{625}\\\\[/tex]
[tex]sin \theta = \sqrt{\frac{576}{625}} = \frac{24}{25}[/tex]
[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]
[tex]=\frac{\frac{24}{25}}{\frac{-7}{25}}\\\\=\frac{24}{25} \times \frac{25}{-7}\\\\=\frac{-24}{7}[/tex]
[tex]14 tan \theta = 14 \times \frac{-24}{7} = 2 \times -24 = -48[/tex]
An aquarium holds 11.13 cubic feet of water, and is 2.6 feet long and 1.9 feet wide. What is its depth? Round your answer to the nearest whole number.
Answers
Answer:
2.25 feet deep
Step-by-step explanation:
The volume was given as (11.13 cubic feet)
Length as (2.6 feet)
Width as(1.9 feet)
Volume of triangular prism can be written as ( length × width × height)
Volume= ( length × width × height)
Then substitute the values, we have
11.13 = 2.6 × 1.9 × height
Height= 11.13/(2.6×1.9)
= 11.13/4.94
= 2.25 feet
1,9,4,6,8,8 which is the median
Answers
=======================================================
Explanation:
Sort the values from smallest to largest. Doing so leads to the list {1,4,6,8,8,9}
Since the set is small enough, you can probably notice that the middle most number is a tie between the 6 and the first 8. The midpoint is (6+8)/2 = 14/2 = 7.
The median is 7.
---------------
If you wanted, you could cross off the first and last items of the set
That means we go from {1,4,6,8,8,9} to {4,6,8,8}
Then repeat to get the smaller set {6,8}
This shows we have a tie between the 6 and 8 as the middle most item, and why 7 is the median (since 7 is the midpoint between 6 and 8).
Solve -2y+1=y-5
Y=6
Y=-6
Y=-2
Y=3
Answers
Answer:
y=2
Step-by-step explanation:
-2y+1=y-5
Add 2y to each side
-2y+2y+1=y+2y-5
1 = 3y -5
Add 5 to each side
1+5 = 3y-5+5
6 = 3y
Divide each side by 3
6/3 = 3y/3
2 =y
Answer:
y=2
Step-by-step explanation:
Move y to the other side by subtracting by y on both sides:
-y-2y+1=y-y-5
-3y+1=-5
Move the 1 to the other side by subtracting by 1 on both sides:
-3y+1-1=-5-1
-3y=-6
Divide -3 on both sides to eliminate the -3 on y
-3y/-3=-6/-3
y=2
0.6×8 and tell me how you got the answer pls
[tex]0.6 \times 8[/tex]
Answers
Answer:
4.8 is the answer!
Step-by-step explanation:
0.6 x 8 = 4.8
6 x 8 = 48
multiply 6 by 8, and move the decimal to the left one time, and get 4.8
Answer: 4.8
Step-by-step explanation: multiply 6*8 (which is 48) then move the decimal point one forward from the back
48.0 (this is before you move the point)
4.8 (this is after)
basically depending on how much numbers you have after the decimal point, that's how much you move forward!
Let me know if you have more questions!
Good luck!
14.How long will it take a car to go from a complete stop to 44 km/hr if they are accelerating at 5
km/hr2?
Answers
Answer:
8.8
Step-by-step explanation:
What is the value of f(x) when x = -1
f(x) = 2* + 5
Answers
what is the volume of a cube that has a height of 10 inches.
Answers
whats the value of x
5x + 8 + 3x = 26 + 6x
Answers
Answer:
9
Step-by-step explanation:
You are welcome tdydhduyxuhdy
Find the length of the hypotenuse
Answers
Answer:
the answer is b
h^2= a^2+ b^2
h=√a^2+b^2
h=√5^2+3^2
h=√25+9
h=√34
What is the length of the missing leg?
Answers
Answer:
41
Step-by-step explanation:
This is the formula
a^2 + b^2 = c^2
35^2 + 21^2 = 1666
√1666 = 40.81...
Maybe you can estimate it to 41.
answer:
a = 28 millimeters
step-by-step explanation:
since this is a right triangle, we can use the pythagorean theorem a^2 + b^2 = c^2a^2 + 21^2 = 35^2
a^2 + 441 = 1225
a^2 = 784
a = 28 millimeters
ABCD and its image A'B'C'D' in the plane are shown. Which statements describe the type of transformation that occurred?
Answers
giving brainliest to the correct answer !
which product is negative?
• (-3/8)(-5/7)(1/4)
• (3/8)(-5/7)(-1/4)
• (3/8)(5/7)(1/4)
• (-3/8)(-5/7)(-1/4)
Answers
Answer:
33333333333333333333333333333333333333333
Step-by-step explanation:3333333333333333333333333333333333333333
How do you find the area of a circle???
Answers
Answer:
The area of a circle is pi times the radius squared.
[tex]A=\pi r^2[/tex]-----------------------
hope it helps...
have a great day!!
Can someone help me p
Answers
Answer:
(3.5, -2)
Step-by-step explanation:
that point is where the edge if the rectangle is
Express tan W as a fraction in simplest terms.
U
W
24
6
Answers
Answer:
The simplest terms is, tan W=4.
Explanation:
Definition of trigonometry:Trigonometry is a discipline of mathematics that deals with certain angle functions and how to use them in computations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).
Step by step:
Simplest term of tan W are calculated as:
We know that, [tex]tan[/tex]θ [tex]=\frac{opposite}{adjacent}[/tex]
According to the question:
[tex]tan W=\frac{VU}{VW} \\\\tan W=\frac{24}{6} \\\\tan W =4[/tex]
Hence, The simplest form of tan W is 4.
To know more about trigonometry here, https://brainly.com/question/24349828
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A 16-oz bottle of waler costs $2.88. What is the
cost per ounce?
Answers
Answer:
18 cents per ounce
Step-by-step explanation:
Take the total cost and divide by the number of ounces
2.88 /16 =.18
18 cents per ounce
Answer:
.18
Step-by-step explanation:
2.88/16=.18
Talia was born in 2003. What would be her predicted life expectancy? Show how you found this answer.
Is your answer interpolation or extrapolation of the data? Explain your reasoning.
Answers
Please help me out whoever helps I will mark branliest
Answers
Answer:
i'm not too sure myself how to answer the problem.. but that is a translation.. A translation is just moving the shape with really changing its form or anything, just its placement
Help please, it’s multiple choice!
Answers
Answer:
60°
Step-by-step explanation:
Answer:
A) 60
Step-by-step explanation:
Each Angle in a hexagon equals 120
X is supplementary to one of those angels, therefore 180-120 = 60
Giving 15 points! Please help me with these two figures!
Answers
12. A. Cube
Help plz..And No links!! I repeat No links!!
Answers
Answer:
402.124
Step-by-step explanation:
2pirL = 2 x π x 8 x 8
Answer: 804.08
Step-by-step explanation:
Which equation is equivalent to 5= 4/3 (6y +9)?
A) 5 = 8y +3
B) 5= 8y +9
C) 5 = 8y + 12 D) 5 = 8y + 36
Answers
Answer:
option C
Step-by-step explanation:
[tex]5 = \frac{4}{3}(6y + 9)\\\\5 = \frac{4\times6y}{3} +\frac{4 \times 9}{3}\\\\5= 8y + 12[/tex]
Just tell me the answer plz and thank you
Answers
Answer:
6 - 14t
Step-by-step explanation:
2(3-7t)
Distribute
2*3 - 2*7t
6 - 14t
Answer:
6 - 14t
Step-by-step explanation:
PLEASE HELP‼️‼️
i suck at slope
Answers
Answer:
m= -1/3
Step-by-step explanation:
to find the slope you have to go from any point on the line to a second point on the line.
for example go from point located at (-4, 2) to point (2,0)
slope = how much you moved vertical / how much you moved horizontal
look at the graph at (-4, 2)
move down 2 and then
move right 6 you should be at (2, 0)
which means that the slope m= -2/ 6 = -1/3
The most Brendan can afford to pay per year in mortgage payments is $10,500, and his credit score is currently 544. According to the following table for a $150,000 mortgage, by how many points would he need to improve his credit score in order to take a mortgage for $150,000? FICO Interest Monthly Score Rate Payment 720-850 700-719 675-699 620-674 560-619 500-559 5.59% 5.71% 6.25% 7.40% 8.53% 9.29% $860 $872 $924 $1039 $1157 $1238 O A. 16 points B. 156 points C. 76 points D. 131 points
Answers
Answer:
B. 156
Step-by-step explanation:
Brendan would need to improve his credit score by 75 points to qualify for a $150,000 mortgage with a monthly payment of $875 or less.
We have,
To determine Brendan's interest rate and monthly payment for a $150,000 mortgage, we need to find which range his FICO score falls in.
From the table, we see that his score of 544 falls in the range of 500-559, which corresponds to an interest rate of 9.29% and a monthly payment of $1238.
Next, we can use the mortgage payment of $10,500 per year to determine the maximum monthly payment Brendan can afford.
i.e
$10,500 per year / 12 months
= $875 per month
Since this amount is less than the monthly payment for the 500-559 FICO score range, Brendan would need to improve his credit score to qualify for a $150,000 mortgage.
To determine how many points he needs to improve, we can look at the next lowest interest rate and payment in the table, which corresponds to a FICO score range of 560-619.
The monthly payment for this range is $1157, which is below Brendan's maximum payment of $875.
So, he needs to improve his credit score to fall into this range.
To determine how many points he needs to improve,
we can subtract the minimum FICO score in the 560-619 range (560) from his current FICO score (544), and then add that difference to the maximum FICO score in the 560-619 range (619).
i.e
(619 - 560) + (560 - 544)
= 59 + 16
= 75
Therefore,
Brendan would need to improve his credit score by 75 points to qualify for a $150,000 mortgage with a monthly payment of $875 or less.
Learn more about credit scores here:
https://brainly.com/question/25668115
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which of the following statements are true about solving equations
Answers
Answer:
u need to provide the statement
Step-by-step explanation:
Kyle pours 3/4 liter of a liquid from a beaker. Then he puts another 1/2 liter of liquid. What is the overall change in the amount of liquid in the beaker
Answers
Answer:
1 and 1/4
Step-by-step explanation:
add 3/4 and 1/2, divide 1/2 into 2/4 and when you add 2/4 to 3/4 you have an extra quarter. therefor you have 4/4 and 1/4 which is 1 and 1/4.
hope this helps <3
Answer:
[tex]1\frac{1}{4}[/tex]
Step-by-step explanation:
Step 1: Add the given values (Since we don't know the original amount and we are given the amount of which is changed with, we need to add those amounts together to know by how much the liquid beaker changed.)
[tex]\frac{3}{4} = 0.75\\\\\frac{1}{2} = 0.5\\\\0.5 + 0.75 = 1.25\\\\\frac{3}{4} + \frac{1}{2} = 1\frac{1}{4}[/tex]
Therefore, the overall change in the amount of liquid in the beaker is [tex]1\frac{1}{4}[/tex] liters.