Sidney skated for 1 1/10 hours last month and 8 7/10 hours this month. How many
hours did Sidney skate in all?

Here we have a problem of rates of work, we want to know how long will take the 3 ants to build an ant hill if they work together.

We will find that working together, they need to work for 8 hours.

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Let's start by defining the variables that we will use:

Now let's see the given information:

"Aran and Beatrice can build an ant hill in 10 hours"

This can be written as:

(A + B)*10 h = 1 ant hill

"Aran and Charlie can build the ant hill in 12 hours"

This can be written as:

(A + C)*12 h = 1 ant hill

"Beatrice and Charlie can build the ant hill in 15 hours"

This can be written as:

(B + C)*15 h = 1 ant hill.

Then we have 3 equations:

[tex](A + B)*10 h = 1[/tex]

[tex](A + C)*12 h = 1[/tex]

[tex](B + C)*15 h = 1[/tex]

Where for commodity, I removed the "ant hill" unit.

Now we need to solve this system of equations, to do it, we need to isolate one variable in one of the equations and then replace it on another equation.

I will isolate A in the first equation:

[tex]A = \frac{1}{10h} - B[/tex]

Now we can replace it in the second equation to get:

[tex](\frac{1}{10h} - B + C)*12h = 1[/tex]

Now we can isolate C in the last equation to get:

[tex]C = \frac{1}{15h} - B[/tex]

Replacing that in the above equation we get:

[tex](\frac{1}{10h} - B + \frac{1}{15h} - B)*12h = 1\\\\\frac{1}{6h} - \frac{1}{12h}= 2*B\\\\\frac{1}{2}*\frac{1}{12h} = \frac{1}{24h} = B[/tex]

This means that Beatrice alone would construct the hill in 24 hours.

Now that we know the value of B, we can use:

[tex]C = \frac{1}{15h} - B = \frac{1}{15h} - \frac{1}{24h} = \frac{1}{40h}[/tex]

This means that Charlie needs 40 hours to finish the hill alone.

Finally, we can use [tex]A = \frac{1}{10h} - B[/tex] to find the value of A:

[tex]A = \frac{1}{10h} - B = \frac{1}{10h} - \frac{1}{24h} = \frac{7}{120h}[/tex]

Now if the 3 ants work together, the total rate at which they work is:

[tex](A + B + C) = (\frac{7}{120h} + \frac{1}{40h} + \frac{1}{24h} ) = 0.125 h^{-1}[/tex]

This means that they need to work for the inverse of that rate

[tex]\frac{1}{0.125h^{-1}} = 8h[/tex]

Working together, they need to work for 8 hours to complete an ant hill

If you want to learn more, you can read:

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Answer:

16

Step-by-step explanation:

Answer:

I think 16...

Step-by-step explanation:

Answer:

4.09

Step-by-step explanation:

Answer:

25.14kg is the total weight

Step-by-step explanation:

Answer:

The total weight of the dogs is 25.44 kg

The average weight of the dogs are 25 kg

Step-by-step explanation:

It is right on Egenuity comment if you want another answer and have a good day :)    

Answer: Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x=k or y=kx.

9514 1404 393

Answer:

  A = 250

  B = 75

  C = 40

Step-by-step explanation:

Apparently, we're supposed to assume that the "health gained" is proportional to the "time in circle." The constant of proportionality is 100/4 = 25. This means all the numbers in the right column are 25 times those in the left column:

  A = 25·10 = 250

  B = 25·3 = 75

  C·25 = 1000   ⇒   C = 40 . . . . . note these numbers are 10 times those in the first row

Answer: x=40°

Step-by-step explanation:

The two triangles are congruent (I think it’s called the interior angle proof) so the bottom right angle is also 65°. All angles in a Triangle equal 180°, so 180-(75+65)=40

Answer:

huh

Step-by-step explanation:

just multi ply its not hard

Answer:

A realistic budget is hard to come by. All budgets tell you what you should include in your monthly plan, but what about unexpected expenses? Here are some ideas for making a realistic budget, and sticking to it.

daid1784 avatar

Well, the dozens of apps, spreadsheets, and other methods just don’t account for real life and all the expenses we don’t think of. There are plenty of expenses we have that aren’t monthly that take up more of our money than we planned.

Answer:

yes

Step-by-step explanation:

Answer:

Nope, it does not satisfy the equation.

Step-by-step explanation:

2x - 3y > 6

2(5) - 3(6) > 6

10 - 18 > 6

-8 > 6

Hope this helps and I hope u have an Amazing day!

Answer:

56

Step-by-step explanation:

(4+7)²-(4²+7²)=121-65

                     =56

Answer:

56

Step-by-step explanation:

(4 + 7)² - (4² + 7²)  =  11² - (16 + 49)  =  121 - 65  =  56

Answer:

3/10

Step-by-step explanation:

1/5=2/10

2/10+1/10=3/10

Answer:

ITS 3/10 AND CAN SOMEONE PLS ANSWER MY MOST RECENT QUESTION.

Answer:

50%

Step-by-step explanation:

34/68=0.5=50%

Answer:

50%

Step-by-step explanation:

because yes

Answer:

Graph A is increasing more rapidly, so Dan is correct

Answer:

$5,308.42

Step-by-step explanation:

(see attached for reference)

recall that the formula for Depreciation

is given by

A = P ( 1 - r)^t,

where

A = final amount

P = principal amount = given as $6,000

r = depreciation rate = given as 4% = 0.04

t = time in years = given as 3,

Simply substitute these into the equation to get:

A = P ( 1 - r)^t

= 6000( 1 - 0.04) ^ 3

= 6000 (0.96)^3

= $5,308.42

Answer:

21.5%

Step-by-step explanation:

volume of cube: 36x36x36

volume of cylinder: πx18²x36

Cylinder percentage: (πx18²x36) / 36x36x36 = π / 4 = 0.785

percentage  of empty space: 1 - 0.785 = 0.215  (21.5%)

Step-by-step explanation:

[tex] \sin(c) = \frac{36}{45} = 0.8 \\ \cos(c) = \frac{27}{45} = 0.6\\ \tan(c) = \frac{36}{27} = 1.333[/tex]

Answer:

BC = 50

Step-by-step explanation:

Law of Cosines:

c^2 = a^2 + b^2 - 2ab*cosy (c is BC)

c^2 = 30^2 + 21^2 - 2(30)(21)cos123

c^2 = 900 + 441 - 1260*(-0.888)

c^2 = 1341 - (-1118.841)

c^2 = 2459.841

c = 49.597

c = 50

Answer:

10x - 6

Step-by-step explanation:

Answer:

I am not sure if you want it to be a simplified answer but the simplified answer is 10 x - 6

Answer: Kris's bike

Step-by-step explanation:

KRIS 297/4.5 = 66 gallons per mile

JAKE 366/6 = 61 gallons per mile

BEN = 265.2/5.2 = 52 gallons per mile

Answer:

A  76

Step-by-step explanation:

7x+8+7x-2+5x+16+110=360

19x+132=360

19x=228

x=12

∠E=5(12)+16

    =76

Answer:

76. hope it helps.................

Answer:

d. 8 over 15 = 136 over 15 this is the right answer okay

Answer: x = 4

Step-by-step explanation:

since it is showing us that the angles are congruent, we know that the smaller triangle is just a scaled-down version of the larger one. in other words, it is the EXACT SAME triangle, just slightly smaller.

so, i redrew them next to each other, so i could compare them easily.

i looked at the corresponding sides that were given, and realized that the side that is 10 on the larger triangle is equal to 5 on the smaller triangle. the side that is equal to 6 on the larger triangle is equal to 3 on the smaller triangle. this concludes that the smaller triangle is exactly half the size of the larger triangle!

so, i figured (using logic) that x must equal 4, simply dividing its corresponding side (with a measure of 8) in half.

hope this helps! xoxo

Answer:

3. y=-3/4+6

Step-by-step explanation:

The y-int is 6, so you can already cross out the first two answers. Then, you know the slope is negative because the line is going downward, so -3/4 has to be the slope bc it is negative.

Answer:

y=-3/4x+6

Step-by-step explanation:

the y/intercept is (0,6) because that is the point where the line crosses the y-axis

knowing that use the point (0,6) and (4,3) to find the slope use rise over run so it goes up 3 and right 4

using the slope intercept equation y=mx+b  it is y= -3/4+6

it is negative because its going downward

hope this makes sense and helps you guys!

10

Step-by-step explanation:

3x° + 46° +14°

3*10° + 46 + 14° =90

therefore the value of x is 10

The value of x on the given figure is 10.

Option D is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

From the figure,

3x + 46 + 14 = 90

Now,

Simplifying.

3x + 60 = 90

Subtracting 60 on both sides.

3x = 90 - 60

3x = 30

Dividing 3 into both sides.

x = 10

Thus,

The value of x on the given figure is 10.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ3

The complete question is given on the attach image.

Answer:

1. 9 numbers (27, 36, 45, 54, 63, 72, 81, 90, 99)

2. 122 square cm

Step-by-step explanation:

break the shape into 2, find area of each, add those areas together

Answer:

17 students

Step-by-step explanation:

If he started with 37 and ended with 3 we have to subtract those three first so that we know how many we are actually working with so, 37-3=34. 34 balls is the amount distributed among the class. 34/2 is 17.

Answer:

56mm

Step-by-step explanation:

they are parallelograms so the opposite sides are equal.

in the bottom parallelogram the top side length is 4x the side side length so in the top one the top side length must be 4x the side side length to be similar, so 14*4=56mm