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Related Questions
Which show another way to write the ratio 13:9 ?
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26:18 (x2 to both)
39:27 (x3 to both)
hope this helps
An aquarium with a square base has no top. There is a metal frame. Glass costs 8 dollars/m^2 and the frame costs 7 dollars/m. The volume is to be 20 m^3. Express the total cost C in terms of the height h in meters. (Hint: work out the cost of the glass and frame separately.)
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Volume = Area of Base x height
Area of Base = Volume / height = 20/h
Given that the aquarium has a square base.
Area of square = l^2
Thus, the length of the base of the aquarium is [tex] \sqrt{area \ of \ base} = \sqrt{ \frac{20}{h} } [/tex]
The frame is to cover 8 sides with the length equal to the length of the base and 4 sides with the length of the height.
Thus, the total perimeter of the frame is given by [tex]8\sqrt{\frac{20}{h}}+4h= \sqrt{64\left(\frac{20}{h}\right)}+4h = \sqrt{\frac{1,280}{h}}+4h [/tex]
Area of the four side faces of the aquarium is 4 times the length of the base times the height = [tex]4\times\sqrt{ \frac{20}{h} }\times h=\sqrt{16\left(\frac{20}{h}\right)h^2}=\sqrt{320h}[/tex]
Total area to be covered by grass is the base and the four side faces and is given by [tex]\frac{20}{h}+\sqrt{320h}[/tex]
Cost of the entire metal frame = [tex]7\left(\sqrt{\frac{1,280}{h}}+4h\right)= \sqrt{49\left(\frac{1,280}{h}\right)}+7(4h) = \sqrt{\frac{62,720}{h}}+28h [/tex]
Cost of the entire grass = [tex]8\left(\frac{20}{h}+\sqrt{320h}\right)=\frac{160}{h}+\sqrt{64(320h)}=\frac{160}{h}+\sqrt{20,480h[/tex]
Therefore, total cost in terms of the height, h, is given by
[tex]C=\sqrt{\frac{62,720}{h}}+28h+\frac{160}{h}+\sqrt{20,480h[/tex]
the temperature at 6:00AM was 0.8F. BY. 3:00pm the temperature had increased to 2.4 F find the differnce between the two temperatures. Draw models to find the difference
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Mr. Welch bought 24 ft of fencing.
How many yards of fencing did he buy? (1 yd = 3 ft)
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1 yard = 3 feet
divide 24 feet by 3 feet to get yards
24 / 3 = 8 yards
PLEASE HELP 30 points!!!!
what is the slope of this line in the picture?
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because the answer 3/12 = 1/4
Triangle ABC is dilated with a center at the origin and a scale factor of 2. What are the coordinates of triangle A’B’C’?
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The coordinates of triangle A'B'C' are A'(-4, 4), B'(2, 6) and C'(-2, 0).
Given that, triangle ABC is dilated with a center at the origin and a scale factor of 2.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
From the given graph, A(-2,2), B(1, 3) and C(-1, 0)
By using a scale factor of 2, we get
A(-2,2)→2(-2, 2)=A'(-4, 4)
B(1, 3)→2(1, 3)=B'(2, 6)
C(-1, 0)→2(-1, 0)=C'(-2, 0)
Therefore, the coordinates of triangle A'B'C' are A'(-4, 4), B'(2, 6) and C'(-2, 0).
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Is 789 a terminating, Repeating, or Non-repeating Decimal?
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PPPLLLEEEZZZ HHHEEELLLPPP Select from the drop-down menu to correctly identify the property shown.
(−3.4+(−1.5))+6.2=−(3.4+1.5)+6.2
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Use the sequence below to answer parts a and b (8,17,26,35,44,53,...) Create an explicit formula to determine the 12th term of the sequence Create a recursive formula to prove the 7th term is 62.
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The explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...) is 8 + (n-1) * 9, and the 12th term can be found by substituting n = 12. The recursive formula for the sequence is a1 = 8 and an = an-1 + 9. Using this recursive formula, we can verify that the 7th term is indeed 62.
Explanation:To create an explicit formula for the sequence (8, 17, 26, 35, 44, 53, ...), we notice that the difference between each term is 9. So, the explicit formula for the sequence is 8 + (n-1) * 9, where n represents the position of the term in the sequence. Using this formula, we can find the 12th term by substituting n = 12: 8 + (12-1) * 9 = 89.
To create a recursive formula to prove that the 7th term is 62, we observe that each term is the previous term plus 9. So, the recursive formula for the sequence is:
a1 = 8an = an-1 + 9Using this recursive formula and starting with a1 = 8, we can find the 7th term as follows:
a1 = 8a2 = a1 + 9 = 8 + 9 = 17a3 = a2 + 9 = 17 + 9 = 26a4 = a3 + 9 = 26 + 9 = 35a5 = a4 + 9 = 35 + 9 = 44a6 = a5 + 9 = 44 + 9 = 53a7 = a6 + 9 = 53 + 9 = 62Therefore, the 7th term in the sequence is indeed 62.
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Rewrite the expression with parentheses to equal the given value 12+6÷2+4 value 13
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you buy 12 apples. you also buy a box of cereal for $3.35. the bill is 8.75. how much does each apple cost
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Total 12 apple = $5.40
I got this by
8.75-3.35=5.40
5.40/12
Each apple cost $0.45
PLEASE HELP ME.
Show Work.
Use two unit multipliers to convert 70 meters to inches.
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.
Rough check, 1 m = 39.36 in approx , 70*39.36 = 2755.2
I think that's how it's done. As far as explaining it goes, I can't do that. I had to ask my math teacher and she wrote the calculations down.
To convert 70 meters to inches, use the unit multiplier method. 70 meters is equal to 2755.91 inches.
Explanation:To convert meters to inches, we can use the unit multiplier method. There are two unit multipliers we can use:
1 meter = 39.37 inches and 1 inch = 0.0254 meters.
Start with the given quantity of 70 meters.Multiply by the unit multiplier 39.37 inches / 1 meter. This will cancel out the meters and leave us with the equivalent value in inches.Multiply the result by the unit multiplier 1 meter / 0.0254 inches. This will cancel out the inches and convert the value back to meters.Simplify the expression to find the final answer.Therefore, 70 meters is equal to 2755.91 inches.
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The amount of money Kelly earns is proportional to the number of hours she works. Kelly earns $32.40 working 4 hours. Create an equation that models the relationship between the amount of money Kelly earns, in dollars, and h, the number of hours she works.
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y = 8.10h...where y is the amount of money earned and h is the number of hrs worked
Working together , 5 friends collected 40 5/8 bags of food for the homeless . On a average how many bags of food did each friend collect ?
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(20 points)
What is the perimeter of the figure?
229-4/9 ft
229-2/3 ft
230-2/3 ft
231 ft
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60 5/6 + 56 1/6 = 117
59 1/3 + 54 1/3 = 113 2/3
117 + 113 2/3 = 230 2/3 feet
Rotate 180 around the origin, and then translate 6 units to the left. (-2, -8) (-6, -8) (-11, -1) (-7, -3)
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What is the best way to 7x7 in expanded form?
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Answer: Add 7 7 times
Step-by-step explanation: if you add 7 7 times like this 7+7+7+7+7+7+7 then that is your answer easy way too.
There is 1/4 ounce of yeast in every 2 and 1/4 teaspoons of yeast. A recipe for bread calls for 2 teaspoons of yeast. How many ounces of yeast are needed for this recipe?
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1. What events led to the attack at Pearl Harbor?
I know that this isn't math but I just need help please. :(
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If there are 1000 grams in a kilogram and 454 grams in a pound, how many pounds are there per kilogram?
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Answer:2.2 pounds per kilogram
Step-by-step explanation:
454gram = 1 pound
since; 1000g = 1kg
454g = x
x= 454/1000
x=0.454kg
there is 0.454kg in 1 pound
but the question says how many pound is in 1kg
0.454kg = 1 pound
1 kg = x
cross multiply
0.454x = 1
Divide bothside by 0.454
x = 1/0.454
x = 2.2 pound
Therefore; there are 2.2pounds in 1 kilogram.
There are 2.20 pounds are there per kilogram
Given that,
1 kg = 1000 gm
1 pound = 454 gm
Since we know that,
A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Since,
1 pound = 454 gm
Therefore,
⇒ 454 gm = 1 pound
⇒ 1 gm = 1/454 pound
And since,
1 kg = 1000 gm
= 1000x(1/454) pound
= 2.20 pounds
Hence,
1 kg = 2.20 pounds
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Rodney bought a 25- pound bag of dog food . His dog ate 10 2/5 pounds of the food in the first month and 10 4/5 pounds of the food in the second month. How much dog food , in pounds, was remaining in the bag at the end of the two months ? Show your work ..... How many pounds
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There is 3 4/5 pounds left!
HOPE I HELPED!!!!!!!!!!!!!
What is the sum of the Linear expression 2n+6 and 6n-2
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To solve, do the following.
2n + 6 = 8n and 6n - 2 = 4n
I think you can take it from here ;)
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does it matter whether you remove x tiles or 1 tiles first
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is 3 yds less than 21 ft
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21 feet > 3 yd
hope this helps
-4.2 (-2.8+4.5) what is the value of the expression
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Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 7 liters of natural oil for every 5 liters of synthetic oil. If 355 liters of synthetic oil are used, how many liters of petrolyn oil will be made?
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Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 7 liters of natural oil for every 5 liters of synthetic oil.
What we need to find:
If 355 liters of synthetic oil are used, how many liters of petrolyn oil will be made?
Set up a proportion to find how much natural oil is used.
7L natural oil/5L synthetic oil = x/355 synthetic oil where x=natural oil
7/5=x/355
(5)(x)=(7)(355) cross multiplied
5x=2485 simplified
5/5x=2485/5 multiplicative inverse
x=497L
Now, add both synthetic oil and natural oil to find amount of petrolyn oil.
355 L synthetic oil + 497 L natural oil= 852 L of petrolyn oil
ASAP please help me
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For the part above the rectangle, you can see that the 2 triangles and the irregular shape make one large triangle so take the area of that. (I’m going to refer to this as the BIG triangle).
.5*40*120=2,400
The base of the triangle is equal to the base of the rectangle. The height of the triangle you get by subtracting the height of the WHOLE lawn by the height of the rectangle. (88-48=40).
Inside that large triangle made up of three shapes, you can see another triangle that’s made up of one triangle and the irregular shape. I’ll refer to this triangle as triangle 1.
Take the area of that triangle.
.5*25*75=937.5
The base of the triangle you get by adding the base of the smaller triangle and the irregular shape. (51+24=75)
Inside the triangle you just took the area of (triangle 1) is another triangle (which I’ll refer to as triangle 2). Take the area of triangle 2.
.5*51*17=433.5
Subtract the area of triangle 1 by the area of triangle 2 and that’ll give you the area of the irregular shape.
937.5-433.5=504
So now you add the areas of the BIG triangle and the rectangle.
5760+2,400=8160
Make sure you subtract the irregular shape since it isn’t part of the lawn’s area.
8160-504=7656
So the lawn is 7656 square feet. Multiply it by .005. That equals 38.28. That’s how much fertilizer he needs to use.
Multiply 1.25 to 38.28 to get the amount of money he needs to spend.
47.85 dollars
I might’ve made a few mistakes but I hope my reasoning was at least understandable
1) A large trapezoid with sides 48 ft and 88 ft, and non-parallel sides 136 ft and the top side that includes the dashed part.
2) A small trapezoid with parallel sides 17 ft and 25 ft, and non-parallel sides 24 ft and the dashed segment on top.
The area of the lawn is the area of the large trapezoid minus the area of the small trapezoid.
Area of trapezoid = (B + b)h/2
where B = large base, b = small base, and h = height.
(The height is perpendicular to both bases.)
Large trapezoid:
A = (88 ft + 48 ft)(120 ft)/2 = 8160 ft^2
Small trapezoid:
A = (25 ft + 17 ft)(24 ft)/2 = 504 ft^2
Area of lawn = area of large trapezoid - area of small trapezoid
Area of lawn = 8160 ft^2 - 504 ft^2
Area of lawn = 7656 ft^2
Weight of fertilizer:
0.005 * 7656 = 38.28 lb
Cost of fertilizer:
1.25 * 38.28 = $47.85
5 different mixed numbers that add up to 10 with only 3rds and 4ths
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2 2/3
1 2/4
3 1/4
1 1/4
the exact radius of a circle with circumference 36 meters
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Bruno's hourly salary is 6.75. Last Week he worked a 20 hour week. How Much did he earn
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Bruno makes 6.75 per hour that can be represented by the following; h being the variable for "hours" hence, the h.
6.75h
Las week he worked 20 hours, so plug that in for h
Like so ;
6.75(20) = How much $ Bruno made
135 = how much $ Bruno made
So Bruno made 135$ last week.