Final answer:
The ratio of surface area to volume for the square prism is 4/9 when b = 12 ft and h = 18 ft.
Explanation:
The expression for the ratio of surface area to volume of the square prism is 2b + 4h/bh. To find the ratio when b = 12 ft and h = 18 ft, substitute these values into the expression.
Ratio = 2(12) + 4(18)/(12)(18)
= 24 + 72/216
= 96/216
= 4/9
Therefore, the ratio of surface area to volume for the given square prism is 4/9 when b = 12 ft and h = 18 ft.
The ratio of surface area to volume for a square prism with a base of 12 ft and a height of 18 ft is calculated using the formula 2b + 4h / bh, which results in a ratio of 4 / 9 ft⁻¹.
Explanation:The student has asked to find the ratio of surface area to volume for a square prism when given specific dimensions. The formula provided is 2b + 4h / bh, where b is the base length and h is the height of the prism. To find the ratio for b = 12 ft and h = 18 ft, we substitute these values into the formula:
Ratio = (2 × 12 ft) + (4 × 18 ft) / (12 ft × 18 ft) =
24 ft + 72 ft / 216 ft² =
96 ft / 216 ft².
After performing the calculations, we simplify the expression to get the ratio:
Ratio = 96 ft / 216 ft² = 4 / 9 ft⁻¹.
Thus, the ratio of surface area to volume for a square prism with a base of 12 ft and a height of 18 ft is 4 / 9 ft⁻¹.
Cassie rolls a fair number cube with 6 faces labeled 1 through 6.She rolls the number cube 600 times. Which result is most likely
Answer:
All results are most likely.
Step-by-step explanation:
Each result 1-6 has an equal chance. The probability is the number of chances divided by the total number. The total number of options is 6 since it is a six sided cube. Each options is represented once so 1 out 6 is the likelihood.
1 out of 6 is 1/6 = 0.17 = 17%.
No matter how many times she has rolled it, it's the same likelihood.
suppose that the amount of algae in a pond doubles every 4 hours. if the pond initially contains 90 pounds of algae, how much algae will be in the pound after 12 hours?
720 pounds
360 pounds
1,440 pounds
114 pounds
LCD for 13/4x and 27/3x^2
A hybrid car averages 609 miles on a 12.5 gallon tank of gas. Manuel is planning a 1290- mile vacation in his hybrid car. Find how many gallons of gas he can expect to burn.
Using ratio and proportion, we deduced that Manuel's hybrid car travels 48.72 miles per gallon. Based on this, we estimated that Manuel would need around 26.5 gallons of gas for his 1290-mile vacation.
Explanation:The subject at hand requires the utilization of ratio and proportion in mathematics, specifically in the context of fuel economy of cars. The hybrid car Manuel owns averages 609 miles on a 12.5 gallon tank. This implies that for every one gallon of gas, the car can travel 609 / 12.5 = 48.72 miles.
Now Manuel is planning for a 1290-mile trip. To ascertain how many gallons of gas he might expect to consume, we divide the total distance of the vacation by the miles per gallon for his car: 1290 miles / 48.72 miles/gallon = 26.5 gallons.
Therefore, Manuel can expect to consume approximately 26.5 gallons of gas for his 1290-mile vacation.
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A sporting goods store offers a 40% discount on all golf clubs. Rocco spent 20% of the money in his savings account on a golf putter. He paid $48 for the putter after the discount. How much money did Rocco have in his savings before buyin the putter?
Select the expression for the following word phrase.
12 less than v
For this case, the first thing we are going to assume is that we have the following terms:
Number = 12
Variable = v
We then have the following expression:
12 less than v
Writing the expression in algebraic form we have:
12 <v
Answer:
the expression for the word phrase is:
12 <v
PLEASE HELP!
Which transformations will produce similar, but not congruent, figures?
A)Triangle MNO is reflected across the y-axis and then rotated 180° clockwise to form triangle M"N"O" .
B)Triangle MNO is reflected across the y-axis and then dilated by a scale factor of 1.8 to form triangle M"N"O" .
C) Triangle MNO is reflected across the x-axis and then translated 9 units down to form triangle M"N"O" .
D)Triangle MNO is reflected across the x-axis and then rotated 90° clockwise to form triangle M"N"O" .
what is the answer for Theo is building a garden against his house. He bought two pieces of wood that are each five feet long. He wants to create a triangular garden against his house using the two pieces of wood, without cutting them. His house will be the third side of the triangle. He also wants the perimeter of his garden to be a whole number.
Jimmy is trying to figure out how many pennies are in his bank. He asked his mother to help him figure out the total. He tells her to let the amount in the bank equal 21x^3+18x^2+9x and each penny equal 3x. Can you help them figure out how many pennies are in the bank?
Which reason best describes why you can divide any number by 100 by moving the decimal point two places to the left?
Dividing a number by 100 is the same as subtracting the number 100 times.
Dividing by 100 is the same as removing a zero.
Moving the decimal point makes the number smaller.
Moving the decimal point two places to the left makes the number 1/100 of its original value.
Answer:
Option D, Moving the decimal point two places to the left makes the number 1/100 of its original value.
Step-by-step explanation:
Step 1: Find the answer
I believe that it is the last choice because a number divide by 100 gives 1/100 of the value.
Example: Find 4 / 100
[tex]\frac{4}{100} = 0.04[/tex]
[tex]4*\frac{1}{100} = \frac{4}{100}=0.04[/tex]
Answer: Option D, Moving the decimal point two places to the left makes the number 1/100 of its original value.
PLEASE HELP
7.02
1. Determine whether the sequence converges or diverges. If it converges, give the limit.
60, 10, five divided by three , five divided by eighteen , ...
A) Converges; 72
B) Converges; 0
C) Diverges
D) Converges; -15540
2. Find an explicit rule for the nth term of the sequence.
1, 3, 9, 27, ...
A) an = 1 • 3n + 1
B) an = 3 • 1n - 1
C) an = 1 • 3n - 1
D) an = 1 • 3n
3. Find an explicit rule for the nth term of the sequence.
-5, -25, -125, -625, ...
A) an = -5 • 5n
B) an = 5 • -5n + 1
C) an = 5 • -5n
D) an = -5 • 5n - 1
4. Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
A) an = 2 • 3n - 1
B) an = 2 • (-3)n - 1
C) an = 2 • 3n
D) an = 2 • (-3)n + 1
5. A certain radioactive isotope has a half-life of 11 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?
Cylinder A has a volume of 360 cm3. Cylinder B has a base and height identical to that of cylinder B, but leans to the right in such a way that its slant length is greater by 4 cm. What is the volume of cylinder B? V = 270 cm3 V = 360 cm3 V = 480 cm3 V = 600 cm3
Step-by-step explanation:
ndkfkasdjfkjdasl;fkjalksdfjlasdjf
Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
The first five terms of a complex sequence are 4, 7, 10, 16, and 28.
Let's consider a non-trivial sequence.
Let's say the first term of our sequence, a1, is 4.
From then on, the sequence increases by 3 times the previous term, but instead of simply multiplying by 3, we will multiply by 3 raised to the power of one less than the term's position in the sequence. However, we are given that the general expression for the nth term is 4 + 3 x 2(n-2), except for the first term which remains 4.
This gives us a starting point for both our formulas.
To find the first five terms of this sequence, we can manually calculate them using the explicit formula given:
a1 = 4 (by definition)a2 = 4 + 3 x 2(2-2) = 4 + 3 x 1 = 7a3 = 4 + 3 x 2(3-2) = 4 + 3 x 2 = 10a4 = 4 + 3 x 2(4-2) = 4 + 3 x 4 = 16a5 = 4 + 3 x2(5-2) = 4 + 3 x 8 = 28Therefore, the first five terms are 4, 7, 10, 16, and 28.
Explicit Formula:
The explicit formula for any term an in the sequence is:
an = 4 + 3 x 2(n-2) for n > 1, with a1 = 4.
Recursive Formula:
The recursive formula builds each term based on the preceding term. For n > 1, the recursive formula is an = an-1 + 3 imes 2(n-2), with a1 still equal to 4.
4.2(3.9r – 5.9s) + 7.9s – 9.53r
A.
16.88r + 6.85s
B.
10.82r + 31.15s
C.
10.82r – 31.15s
D.
6.85r – 16.88s
Answer:
D. 6.85r – 16.88s
Step-by-step explanation:
Use the distributive property to eliminate parentheses, then collect terms.
4.2(3.9r -5.9s) +7.9s -9.53r
= 16.38r -24.78s +7.9s -9.53r
= (16.38 -9.53)r +(-24.78 +7.9)s
= 6.85r -16.88s
PLEASSE HELLP! // 99 points // look at the picture below
Parallelogram is your answer
The opposite sides are parallel to each other, and are congruent.
hope this helps
A toy plush weighed 1/5 of a pound. a flimsy box can hold 3 pounds. how many toy plushes could the box hold?
what is the solution of the equation x^2-1=0
A toy manufacturer ships a toy in one of two different size boxes. The small box contains 6 of the toy and the large box contains 10 of the toy.
A client orders no fewer than 100 of the toy. Based on his storage and sales needs, the client requires that he receive no more than 8 of the large boxes and no fewer than 6 of the small boxes.
The cost to the client for a small box is $4 and the cost to the client for a large box is $6. The client does not wish to exceed $200 for his order of toys.
Let x represent the number of small boxes and y represent the number of large boxes.
What constraints are placed on the variables in this situation?
Answer:
Let x represent the number of small boxes.
Let y represent the number of large boxes.
The client receive no more than 8 of the large boxes and no fewer than 6 of the small boxes.
[tex]x \geq 6[/tex]
[tex]y \leq 8[/tex]
The cost of small box is $4 and the cost to the client for a large box is $6. The client does not wish to exceed $200.
[tex]4x+ 6y \leq 200[/tex]
The small box contains 6 of the toy and the large box contains 10 of the toy. A client orders no fewer than 100 of the toy.
[tex]6x+10y \geq 100[/tex]
Two armies face each other for battle. One army has 1220 soldiers and the other has 549 soldiers. Both armies are divided into smaller groups of equal size called platoons. Find the largest possible number of soldiers in a platoon if the platoon size is equal for the two armies.
The largest possible number of soldiers in a platoon is 61.
What is the greatest common factor?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.
Given that, two armies face each other for battle. One army has 1220 soldiers and the other has 549 soldiers.
Factors of 1220 and 549 are
1220 = 2×2×5×61
549 = 3×3×61
So, GCF is 61
Therefore, the largest possible number of soldiers in a platoon is 61.
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I really need help ASAP
plzz hellp :( i will mark you the brainlist if some on helps (A rectangular prism has a length of 1 1/4 yards, a width of 2 1/2 yards, and a height of 4 yards.
Enter the volume of the prism as a mixed number in simplest form in the box.
The ratio of two supplementary angles is 6:3. what is the measure of the smaller angle?
Solving quadratics by factoring 3x^2+33x+30=0
The radius and height of a right cylinder are each multiplied by 2. what is that change in the total surface area of the cylinder
When both the radius and height of a right cylinder are multiplied by 2, the change in the total surface area is 4 times the original surface area.
Explanation:
The total surface area of a right cylinder is given by the formula A = 2πrh + 2πr², where r is the radius and h is the height. When both the radius and height are multiplied by 2, we can calculate the change in the total surface area:
The new radius is 2r, so the new area of the bases is 4πr².The new height is 2h, so the new area of the lateral surface is 2π(2r)(2h) = 8πrh.Therefore, the total surface area of the new cylinder is A' = 4πr² + 8πrh = 4(πr² + 2πrh) = 4A.Learn more about Total surface area of a cylinder here:https://brainly.com/question/35459045
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What is the volume of a rectangular prism with a length of 81\2 centimeters, width of 9 1\3 centimeters, and a height of 12 2\5 centimeters?
Matias stacked his cubes to make this rectangular prism.
rectangular prism with grid lines
How many cubes did Matias use?
cubes
Answer:
The answer is 80
Which are reasonable solutions for this situation if x represents the number of hot dogs sold and y represents the number of bottles of water sold? Check all that apply.
(–1, 5)
(0, 6)
(2, 1)
(1, 1.5)
(1, 3)
(2, 2)
its actually c, and e
Step-by-step explanation:
A) –2n + 9m – 17p
B) –2n – 9mn + 17np
C) –2n + 9mn – 17np
D) –18n + 81mn – 153np
Give the values a, b, and c needed to write the equations standard form. 2/3(x-4)(x+5)=1
Answer:I agree
Step-by-step explanation:
Give the coordinates of the points after a reflection over the line y=-4
A( 4,5) A' (_,_)
B(0,4) B' (_,_)
C(-2,1) C' (_,_)
use algebraic representation and please show your work !