Answers
First of all, V (prism) = area of base (B) × h
We know that the height (h) of this prism is given, which we'll need later on: h = 5 ft, and area of base (B) is given as 60 ft2
So V = 60 ft2 × 5 ft = 300 ft3
So now for the hard part... how to calculate the SA of this prism
IF YOU DON'T NEED SA FOR THIS TYPE OF PROBLEM, DO NOT PROCEED!!!
[VERY DETAILED]
means solving the dimensions (sides) of that pesky polygon base (B) or lid.
The most important things about polygons are:
1) is it regular (same angle ° and side length)??
2) How many sides or angles??
This has to be regular, because they give you no other info so it has to be, in order to solve. And then it has 5 sides and angles = regular pentagon. ("penta" means 5).
Now there are 360° in any circle, so:
take the central angles of where the sides meet at the center forming triangles (see drawing above), each of those (5) central <'s = 360/5 = 72°
Now the apex of each of these triangles = 72°
but with our 5 triangles, we need to find the height of each triangle -- which is the midpoint of the side (base (b) of triangle), and h is perpendicular to this b. By bisecting that apex angle of 72, it forms 2 equal right triangles of
72/2 = 36°. So each right triangle has 36, 90, and?? 180-36-90 = 90-36 = 54°
let's call the base (b) = 1 side of pentagon
= side (s)
Therefore (see 2nd image drawn above) tangent (tan) of € = opposite/adjacent, or
tan (54) = h÷1/2b --> h = [tan (54)]×(1/2)b
1/2b = h/[tan (54)] = h/1.38
Also the area of each of the larger 5 triangles A(t) = 1/2b×h, and that area A(t) × 5 = area of whole pentagon base A(B)
So now after all that... our A(B) given at beginning = 60ft2. let's put it all together:
1/2b = h/[tan (54)] = h/1.38
A(t) = 1/2b×h, and A(B) = 5×A(t)
which means that A(B) = 5×(1/2b×h)
AND since the other calculation shows that 1/2b = h/1.38, plug that value into the A(B) formula...
.
.
.
now that we have height (h) of each triangle, we can go back to our tan equation for the triangle: tan (54) = 1.38 = h/(1/2b)
--> 1/2×b = h/1.38 --> base (b) = 2h/1.38
b = 2(4.06 ft)/1.38 = 8.12 ft/1.38 = 5.90 ft, for which b us also the width of each rectangular side panel (w)
length (l) of these sides was given as height of the whole prism = 5 ft
NOW FINALLY... THE FINAL SURFACE AREA OF THE PRISM (SA) = (2×A(B)) + (5×rectangular side)
SA = (2×60 ft2) + (5×(l×w)) = 120 ft2 + 5×5ft×5.9ft
SA = 120 ft2 + 147.62 ft2 = 267.62 ft2
Answer:
300 ft³
Step-by-step explanation:
Volume = Area of base × height
Volume = 60ft² × 5ft
Volume = 300 ft³
Related Questions
A restaurant offers 88 appetizers and 99 main courses. in how many ways can a person order a two-course meal
Answers
Answer: 8712
One circle has a circumference half as large as that of a second circle what ratio compares the diameter of the first circle
Answers
These are linear measurements. This means that the ratio of the circumference, distance around, of two circles is the same as the ratio of their diameters, or distance across.
The diameter of first circle is half of the second one.
What is a circle?A circle is a geometric shape, all of which points are equidistant from a fixed point called as the Centre. The centre of the circle does not lie on it. The tangents drawn from the same point outside a circle are equal in length.
The given problem can be solved as follows,
The circumference of a circle is given as C = πd where d is the diameter of the circle.
Suppose, the circumference and diameters for both the circles are C₁, d₁ and C₂,d₂ respectively.
Now, the expression for circumference can be written as,
C₁ = πd₁
And, C₂ = πd₂
As per the question C₁ = 1/2C₂, then the following equations can be written as,
πd₁ = 1/2πd₂
⇒ d₁ = 1/2d₂
Hence, the diameters of the two circles are also in the same ratio.
To know more about circle click on,
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Find the quotient of -36x^3-6x^2+12x/-6x
Answers
Answer:
6x² + x - 2
Explanation:
To find the quotient of a polynomial expression divided by a monomial, divide each term by the monomial.
[tex]\frac{-36x^3-6x^2 + 12x}{-6x}[/tex] becomes [tex]\frac{-36x^3}{-6x} + \frac{(-6x^2)}{(-6x)} + \frac{12x}{(-6x)}[/tex]
-36x³ / (-6x) = 6x²
(-6x²) / (-6x) = 1x = x
12x / -6x = -2
Place each of these terms together into an polynomial expression once more and the quotient is: 6x² + x - 2
What is the volume of the cone to the nearest tenth?
1,244.1 m^3
829.4 m^3
552.9 m^3
1,520.5 m^3
Answers
V = (1/3)π*r^2*h
Of course, the radius is half the diameter, so is 11 m. Substituting the given values, you have
V = (1/3)π(11 m)^2*(12 m)
V = 484π m^3
V ≈ 1520.5 m^3
The volume of the cone to the nearest tenth is ...
1520.5 m³
The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. What is the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim? Show your work.
Answers
circumference=2*pi*r-------> r=circumference/(2*pi)
circumference=30 in
r=circumference/(2*pi)------> 30/(2*pi)-----> 4.7746 in
the radius of a standard basketball is 4.77 in
the distance between the ball and the rim is equal to
radius of a basketball rim minus radius of a a standard basketball
radius of a basketball rim =18/2------> 9 in
radius of a a standard basketball=4.77 in
the distance between the ball and the rim=[9-4.77]------> 4.23 in
the answer is
4.23 in
1. You have the following information given in the problem above:
- The diameter of a basketball rim is 18 inches.
- A standard basketball has a circumference of 30 inches.
2. Therefore, the diameter of the standard basketball is:
D=30 inches/π
D=9.54 inches
3. Therefore you have:
(18 inches-9.54 inches)=8.45 inches on both sides
4. Then, the distance the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim, is:
d=8.45 inches/2
d=4.22 inches
The answer is: 4.22 inches
a catering company needs to know how much roast beef to slice for sandwiches for an event.They are making 30 club sandwich, which requires 1/8lb of roast beef each. They are also making 20 french dip sandwiches, which require 1/5lb each. How many pounds of roast beef should they slice in total?
Answers
You should slice 7 and 3/4 lbs of roast beef
To find this you'd multiply 30/1 (30 as a fraction) by 1/8. To do so, you multiply straight across which gives you 30/8 or 3 3/4 when simplified. You repeat this process for the next two numbers too (20/1*1/5 = 20/5. Simplified it equals 4). Finally you add 4 and 3 3/4 together to get your answer of 7 3/4. Round up to 8 if needed.
I hope this helps!
Consider the equation . how many different solutions does this equation have if all the variables must be positive integers? enter the exact numeric answer.
Answers
Find the center, vertices, and foci of the ellipse with equation 2x2 + 9y2 = 18.
Answers
1. You have the following equation:
2x^2+9y^2=18
2. Dividing the equation by 18, you have:
(x^2/9)+(y^2/2)=1
3. The center is:
[(x-0)^2/9]3^2[(y-0)^2/√2]=1
(h,k)=(0,0)
The center is (0,0)
4. The vertices are:
a^2=9
a=3
Vertices: (-3,0) and (3,0)
5. The foci is:
c^2=a^2-b^2
c=√7
The foci is: (-√7,0) and (√7,0)
Tabby Soft believes that it will need new equipment in 5 years. The equipment will cost $26,000. What lump sum should be invested today at 6%, compounded semiannually, to yield $26,000? a. $22,558.87 c. $22,390.94 b. $23,948.47 d. $19,346.44
Answers
A = P (1+R/2)^2t
Where, A = Amount after 5 years = $26,000; P = Amount invested now; R = Annual rate of earning = 6% = 0.06; t = time = 5 years.
Substituting;
26000 = P(1+0.06/2)^2*5 = P(1.3439)
Therefore, P = 26000/1.3439 = $19,346.44
The correct answer is d.
Answer:
D
Step-by-step explanation just put D
sigma notation 2+ (-8)+32+(-128)+...
Answers
At the zoo on Monday, 65 percent of the people in attendance were children. If 520 children were in attendance, how many people in total were visiting the zoo on Monday?
Answers
Answer:
800+
Step-by-step explanation:
The length of a rectangle is twice the width. the area is 256 squared. find the length and the width.
Answers
First, draw a rectangle. Label two opposite sides as "w", representing the width. Label the other two sides as "2w", since the length is twice the width.
Next, write an equation. In this case, the equation would be 256=2w*w.
Simplify the equation to 2w^2=256. Divide both sides by two to get w^2=128. The width would be the square root of 128. The length would be twice that, so it would be the square root of 256. That would be 16, so the length is 16.
The diameter of a circle has endpoints (-3, 2) and (3, -2) which is closest to the length of the diameter of the circle?
Answers
D=√((x2-x1)²+(y2-y1)²) = √(3-(-3))²+(-2-2)²) = √(6² + 4²)=√(36+16)=√52
D=2√13≈7.21
Answer: Diameter = 7.21 units
The weight of a mandarin orange is about 6 ounces. A basket that weighs 4 ounces will hold m mandarin oranges, the total weight is 70 ounces. Which equation represents the basket of oranges?1. 4 + 6m = 70 2. 6 + 4m = 70 3. 70 + 4m = 6 4.70 + 6m = 4
Answers
Answer:
A is the answer on Edgen.
Step-by-step explanation:
4 + 6m = 70
6 + 4m = 70
70 + 4m = 6
70 + 6m = 4
24 MIN LEFT anyone know the answer?
Answers
A+B+E+F=360
A+152+82+98=360
Angle A=28 degrees
A bage contains 5 blue marbles, 3 red marbles, and 2 yellow marbles. You select a marble at radom. What is p(yellow)
Answers
Total yellow marbles = 2
P(yellow) = 2/10 = 1/5
Answer: 1/5
Find the mean, median, and interquartile for the data set below. Round your answer to the nearest tenth. 27,16,8,5,19,14,22,31,13,5,23,16,8 Mean: Median: Interquartile range:
Answers
Median: 26
interquartile range: 14-16
The mean of the data set is 15.9, the median is 16, and the interquartile range is 14.5 after rounding to the nearest tenth.
To find the mean, median, and interquartile range for the data set 27, 16, 8, 5, 19, 14, 22, 31, 13, 5, 23, 16, 8, we need to follow these steps:
Organize the data in ascending order: 5, 5, 8, 8, 13, 14, 16, 16, 19, 22, 23, 27, 31.
Calculate the mean by adding all numbers and divide by the total count. Mean: (5+5+8+8+13+14+16+16+19+22+23+27+31)/13 = 207/13 ≈ 15.9.
Find the median which is the middle number. Since there are 13 values, the median is the 7th number: Median: 16.
For the first quartile (Q1) and third quartile (Q3), divide the list into two halves. The Q1 is the median of the first half, and Q3 is the median of the second half. Q1: Median of 5, 5, 8, 8, 13, 14 ≈ 8.5; Q3: Median of 19, 22, 23, 27, 31 ≈ 23.
Calculate the interquartile range (IQR) by subtracting Q1 from Q3. Interquartile range: IQR = Q3 - Q1 = 23 - 8.5 = 14.5.
The mean is approximately 15.9, the median is 16, and the interquartile range is 14.5.
in a certain area of Brazil, deforestation is currently the most critical Socio economic problem. The area of a certain rain forest is currently 1156.25 square miles. after every year, the area of this rain force decreases by 2% which of the following statements is correct
A- deforestation problem is an example of exponential growth
B- The growth or decay rate for the area of the rainforest is 0.2
C- The function of equals 1156.25(1 -0.02 )^t
D- in less than a century the rain forest will be completely wiped out
E- in about 35 years the area of the rain forest will be cut by more than half
F-The domain of the function that model the deforestation problem above is 0<_t<_100 (less than or equal to <_)
Answers
A is INCORRECT because here we have degrowth and growth
B is INCORRECT because the decay factor is 2% or 0.02 , not 0.2
C is CORRECT, the function is which is used to calculated the area of rainforest at time t is given by 1156.25(1 -0.02 )^t
D is INCORRECT, if we plug in t=100 in the above equation , we get = 1156*(1-0.02)^100 = 153 square miles of forest. So it will not be wiped out
E is CORRECT, if we plug in t =35, we get = 1156*(1-0.02)^35 = 570 square miles. So more than half will be cut in 35 years
F is INCORRECT becuase domain goes beyond 100 years as shown by option D
So, correct options are C and E
Whst is the remainder when f(x)=x^3+3x^2-10x-4 is diveded by x-3
Answers
The remainder of f(x) divided by (x-k) equals f(k).
Thus
f(x)=x^3+3x^2-10x-4 divided by x-3
gives a remainder of
f(3)=27+3(9)-10(3)-4=27+27-30-4=20
Therefore the remainder required is 20.
The remainder when the polynomial [tex]f(x)=x^3+3x^2-10x-4[/tex] is divided by x-3 is found using the Remainder Theorem and is 20.
The remainder when a polynomial f(x) is divided by a linear divisor such as x - 3 can be found using the Remainder Theorem, which states that the remainder is simply f(3). To find the remainder for [tex]f(x)=x^3+3x^2-10x-4[/tex], we substitute x = 3 into the polynomial.
Calculate f(3):
[tex]f(3) = (3)^3 + 3*(3)^2 - 10*(3) - 4[/tex]
f(3) = 27 + 27 - 30 - 4
f(3) = 54 - 34
f(3) = 20
Therefore, the remainder when f(x) is divided by x - 3 is 20.
A boat traveled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average of (v+3) miles per hour. if the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?
Answers
90v−3−90v+3=1290v−3−90v+3=12 --> 90(v+3)−90(v−3)v2−9=1290(v+3)−90(v−3)v2−9=12 --> 90∗6v2−9=1290∗6v2−9=12 --> v2=90∗6∗2+9v2=90∗6∗2+9 --> v2=9∗(10∗6∗2+1)v2=9∗(10∗6∗2+1) --> v2=9∗121v2=9∗121 --> v=3∗11=33v=3∗11=33;
Trip downstream took 90v+3=9033+3=2.590v+3=9033+3=2.5 hours.
40 POINTS!
Find the exact value by using a half-angle identity.
⬇️⬇️⬇️
Answers
[tex]Use: \cos(\alpha-\beta)=\cos\alpha \cos\beta+\sin\alpha \cos\beta[/tex]
[tex](*)=\cos\dfrac{\pi}{2} \cos\dfrac{\pi}{12}+\sin\dfrac{\pi}{2} \sin\dfrac{\pi}{12}\\\\=0\cdot\cos\dfrac{\pi}{12}+1\cdot\sin\dfrac{\pi}{12}=\sin\dfrac{\pi}{12}[/tex]
[tex]\dfrac{\pi}{12}=\dfrac{\dfrac{\pi}{6}}{2}[/tex]
[tex]The\ half-angle\ identity\ \sin^2\dfrac{\alpha}{2}=\dfrac{1}{2}\left(1-\cos\alpha\right)[/tex]
[tex]Using\ the\ above\ formulas,\ we\ get:\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}\left(1-\cos\dfrac{\pi}{6}\right)\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}\left(1-\dfrac{\sqrt3}{2}\right)\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}-\dfrac{\sqrt3}{4}[/tex]
[tex]Since\ 0 \ \textless \ \dfrac{\pi}{12} \ \textless \ \pi,\ then\ \sin\dfrac{\pi}{12}\ is\ a\ positive\ number.\\\\ Therefore,\ we\ have:\\\\\sin\dfrac{\pi}{12}=\sqrt{\dfrac{1}{2}-\dfrac{\sqrt3}{4}}=\sqrt{\dfrac{2-\sqrt3}{4}}=\dfrac{\sqrt{2-\sqrt3}}{2}[/tex]
[tex]Answer:\ \boxed{\cos\dfrac{5\pi}{12}=\dfrac{\sqrt{2-\sqrt3}}{2}}[/tex]
I agree with him because it's correct and makes sense!
What is the sun made of (by mass)?
a. 50 percent hydrogen, 25 percent helium, 25 percent other elements
b. 70 percent hydrogen, 28 percent helium, 2 percent other elements
c. 90 percent dark matter, 10 percent ordinary matter
d. 100 percent hydrogen and helium?
Answers
A. 0
B. 1
C. 2
D. 3
Answers
19 to 15 = 4 this would be a -4 difference
3 to 7 is a positive 4 difference
-3 to 7 is a difference of 10
so there is 1 with a -4 difference
answer is B.
How many ways could the students Amy, Ben, and Lorenzo, come in 1st, 2nd, and 3rd place?
Answers
A1, L2, B3
L1, B2, A3
L1, A2, B3
B1, A2, L3
B1, L2, A3
[tex] 3!=6 [/tex]
..........
How to solve x in a trapezoid
Answers
Mary has 7 1/4 yard of fabric. she cuts off 3/4 foot fabric to make the edge even. Mary wants to end up with 3 pieces of fabric that are the same size. how long will each piece be?
Answers
6 2/4 ÷ 3 = 26/4 ÷ 3 = 26/4 x 1/3 = 2 1/6
Answer: 2 1/6 yd
Final answer:
Mary has 7 1/4 yards of fabric, and after cutting off 3/4 foot (which is 1/4 yard), she is left with 7 yards. When she divides this equally into 3 pieces, each piece will be 2 1/3 yards long.
Explanation:
Mary has 7 1/4 yards of fabric. To convert the fabric she cuts off, which is 3/4 foot, to yards, we use the fact that 1 yard = 3 feet. Thus, 3/4 foot is 1/4 yard. After cutting off 1/4 yard from her fabric, she is left with 7 yards (7 1/4 yards - 1/4 yard). Mary wants to divide this into 3 equal pieces. To find the length of each piece, we divide 7 yards by 3, which is 2 1/3 yards for each piece.
A truck tire has a diameter of 4 feet and is revolving at a rate of 45 rpm. at t = 0, a certain point is at height 0. what is the height of the point above the ground after 15 seconds?
Answers
radius=1.5 ft
axle at 2 ft and up and down from there:
thus
y=2-1.5cos(1.5πt)
to make y=0 at 0
at 15 sec
y=2-1.5cos(15*1.5π)
y=2-0
y=2 ft
Jeff drinks 2/3 of a glass of juice. Write
a fraction equivalent to 2/3
Answers
To find this, you can simply multiple both the numerator and denominator (top and bottom) by any number as long as it's the same number for both top and bottom.
In this case, we used 2 as the number, and multipled it to the top and bottom of 2/3, to get 4/6.
I hope this helps!
sam had four test last month his scores were 81 94 83 and 91 what is the median of his scores
Answers
Final answer:
The median of Sam's test scores (81, 83, 91, 94) is 87, calculated by averaging the two middle numbers after arranging the scores in ascending order.
Explanation:
To find the median of Sam's test scores, we first list the scores in numerical order: 81, 83, 91, 94. Since there are an even number of scores, the median will be the average of the two middle numbers, which are 83 and 91. To find the median, you add those two middle scores and divide by 2: (83 + 91) / 2 = 174 / 2 = 87. Therefore, the median of Sam's scores is 87.
Calculating the median of a set of values involves organizing them in ascending order, as done with Sam's test scores. In cases where there is an even number of values, the median is determined by averaging the two middle numbers. This method ensures a representative central value for the dataset, providing insight into the typical test performance. In Sam's case, with test scores 81, 83, 91, and 94, the median is computed as 87, offering a balanced perspective on his overall performance.
A right triangle has legs that measure 7cm and 3cm. What is the length of the Hypotenuse?
Answers
49 + 9 = c²
58 = c²
c = √58
Answer:
square root of 58
Step-by-step explanation:
If its wrong e2020 says its right