William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with some water until its comepletly full. If he uses 85 marbles, he will have to add 20.9 liters of water. What is the volume of each marble? and How much water is necessary if William uses 200 Marbles?

Answers

Answer 1

Total capacity = 26 liters

He added in 20.9 liters of water, so if we take out the water …
26 – 20.9 = 5.1 liters
The 5.1 liters volume was made up by the 85 marbles

85 marbles = 5.1 liters
1 marble = 5.1 ÷ 85
1 marble = 0.06 liter

If he uses 200 marbles
200 x 0.06 = 12 liters
The 200 marbles will take up 12 liters

Amount of water needed = 26 - 12
Amount of water needed = 14 liters

Answer 2

Answer:

Volume of each Marble: 0.06 liters

Water required for the marbles and water: 14 Liters

Related Questions

Melissa had a balance of $104 in her checking account at the beginning of the month. She made one additional deposi of $216 and wrote checks $78 , $119 , and $105. What was the balance in her checking account at end of the month

Answers

Do you deposit or cash the checks?

Answer:

She only had $18 left

Step-by-step explanation:

if tyrone works 40 hours per week and has no other sources of income what is his total monthly cash inflow

Answers

[tex]18 \times 40 = 720[/tex]

[tex]720 \times 4 = 2880[/tex]

[tex]2880 - 1800 = 1080[/tex]

~~

Answer : B

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

Find the values of a b and c for which the quadratic equation ax^2+bx+c=0 has the solutions -3 and 1

Answers

It may be easier to start from

.. a(x +3)(x -1) = 0
.. a(x^2 +2x -3) = 0

The quadratic
.. ax^2 +bx +c = 0 will have solutions -3 and 1 for ...

.. a ≠ 0
.. b = 2a
.. c = -3a

Write an equation that involves multiplication,addition, contains a variable and has a solution of 8.

Answers

is there a photo with this

Hi there!

Here's an equation:

(Solve for x.)
x=(4+1)*2-2

Hope this helps!

What is the factored form of x2 - 4x - 5 ?

Answers

(X-5)(x+1)

Two factors of five that subtract to four

5) If f(x) = 4x2 - 5x + 7 and g(x) = 3x2 - 2x + 8, find f(x) + g(x).

Answers

Simply put this just means add the like terms together.
f(x) + g(x) = 4x^2 - 5x +7 + 3x^2 - 2x + 8
f(x) + g(x) = 7x^2 - 7x + 15. Don't go any further.

Which operation is performed in the derivation of the quadratic formula moving from Step 6 to Step 7? subtracting from both sides of the equation squaring both sides of the equation taking the square root of both sides of the equation taking the square root of the discriminant

Answers

it's "taking square root of both sides of the equation"

as the power 2 from the right side of the equation disappeared
it means that the it's square root has been taken as square root is the opposite of power 2
and it's easily identifiable that it is been square rooted from the right side of the equation as well

Answer:

Step-by-step explanation:

116=0.0625. Which calculation is NOT a way to find 1516?

Answers

we have that
1/16=0.0625

we know that
Multiply (0.0625) by 15 is a way to find (15/16)--------> 0.0625*15=0.9375
so
any operation that results in any other value is not a way to find (15/16)

Answer: 16 divided by 15

Step-by-step explanation:

I got it right.

2x+5y=-6 , wht is the x intercept, what is the y intercept

Answers

Final answer:

The x-intercept is (-3,0) and the y-intercept is (0,-6/5).

Explanation:

The x-intercept is the point where the line crosses the x-axis. To find the x-intercept, we set y=0 and solve for x. In the equation 2x+5y=-6, we substitute 0 for y and solve for x:

2x + 5(0) = -6

2x = -6

x = -3

So, the x-intercept is the point (-3,0).

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we set x=0 and solve for y. In the equation 2x+5y=-6, we substitute 0 for x and solve for y:

2(0) + 5y = -6

5y = -6

y = -6/5

So, the y-intercept is the point (0,-6/5).

A triangle has sides with lengths of 6 millimeters, 8 millimeters, and 10 millimeters. Is it a right triangle?

Answers

If it is a right triangle, then a^2 + b^2 = c^2
6^2 + 8^2 = 100^2
36 + 64 = 100
100 = 100

Yes, the triangle is a right triangle.

Hope this helps =)

The sides 6 mm, 8 mm and 10 mm forms a right angles triangle.

We have,

The sides of the triangle are of lengths 6 mm, 8 mm and 10 mm.

The longest side length is 10 mm.

Now, the sum of squares of the smaller sides is given as:

6² + 8² = 36 + 64 = 100 = 10²

As, the sum of squares of the smaller sides is equal to the square of the longer side.

So, by the Pythagorean Theorem, the sides form a right triangle.

Learn more about Pythagoras theorem here:

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5 plus 500% of 10 is the same as 110% of what number?

Answers

5+10×500%=5+50=55
55÷110%=50
so 5 plus 500% of 10 is the same as 110% of 50

1) Which two lines are parallel?

I. 5y = -3x-5
II. 5y = -1 - 3x
III. 3y - 2x = -1

a. I. and II.
b. I. and III.
c. II. and III.
d. No two of the lines are parallel.

2) Which do lines are parallel?

I. 3y = -2x - 3
II. 3y = 1 - 2x
III. 4y - 3x = -1

a. I. and II.
c. II. and III.
b. I. and III.
d. No two of the lines are parallel.

Answers

1)a

2)a
hope this helps

Which of the following is a monomial?
A. 2xyz2
B. 2x + yz
C. 2 + xyz
D. 2x − yz

Answers

A monomial has one term, even if it has multiple variables.
So your answer would be A. 2xyz2. Hope it helps! :)

Please explain how you worked the problem to find x!

1/x +1/(x+4) =1/5

Answers

[tex]\frac{1}{x} +\frac{1}{x+4}[/tex] (by taking the common factor for the two elements of the equation
[tex]\frac{1]{x} *\frac{x+4}{x+4} +\frac{1}{x+4}*\frac{x}{x}=\frac{x+4}{x*(x+4)}+\frac{x}{x*(x+4)}[/tex] now we can add both of the equation as the denominators have the same value.
[tex]\frac{x+4+x}{x*(x+4)}=\frac{2x+4}{x^{2}+4x} = \frac{1}{5}[/tex] by multiplying both sides by [tex]5*(x^{2}+4x)[/tex]
[tex] 5*(2x+4)=x^{2} +4x[/tex]
[tex] 10x+20=x^{2}+4x[/tex] by subtracting both sides by (10x+20)
[tex] x^{2} -6x -20 = 0[/tex] (by using the quadratic formula)
we will find two answers for this equation
x={[tex]\frac{-6- \sqrt{116}}{-2}[/tex] and [tex] \frac{-6+\sqrt{116}}{-2}[/tex]

Let u = (1,0,2) , v = (0,-1,2) and w = (2,1,0). Compute

(i) the area of the parallelogram bounded by u and v (5)

(ii) the equation of the plane parallel to v and w pass through the tip of u

Answers

Answers:

(i) 3
(ii) [tex]-2x + 4y + 2z = 2[/tex]

Explanation:

(i) The area of the parallelogram bounded by vectors u and v is given by:

[tex]\text{Area} = \left \| u \times v \right \|[/tex]

Note that if [tex]u = (u_1, u_2, u_3) = (1, 0, 2), v = (v_1, v_2, v_3) = (0, -1, 2) [/tex],

[tex]u \times v \\ = \left(u_2v_3-u_3v_2, u_3v_1-u_1v_3, u_1v_2-u_2v_1\right) \\ = \left((0)(2)-(2)(-1), (2)(0)-(1)(2), (1)(-1)-(0)(0)\right) \\ \boxed{u \times v = \left(2, -2, -1 \right)}[/tex]

Thus, the area of the parallelogram formed by vectors u and v is calculated as

[tex]\text{Area} = \left \| u \times v \right \| \\ = \left \| \left(2, -2, -1 \right) \right \| \\ = \sqrt{(2)^2 + (-2)^2 + (1)^2} \\ \boxed{\text{Area} = 3}[/tex]

Hence, the area of the parallelogram is 3.

(ii) To obtain the equation of the plane, we must get its normal vector and a point in the plane.

As calculated in (i), the normal vector to the plane is [tex]v \times w[/tex] because the plane is parallel to vectors v and w. Note that if [tex]v = (v_1, v_2, v_3) = (0, -1, 2), w = (w_1, w_2, w_3) = (2, 1, 0)[/tex],

[tex]v \times w \\ = \left(v_2w_3-v_3w_2, v_3w_1-v_1w_3, v_1w_2-v_2w_1\right) \\ = \left((-2)(0)-(2)(1), (2)(2)-(0)(0), (0)(1)-(-1)(2)\right) \\ \boxed{v \times w = \left(-2, 4, 2 \right)}[/tex]

Thus, a normal vector to the plane is [tex]\left(-2, 4, 2 \right)[/tex].

To get a point in the plane, note that vector u can be represented by any pairs of points. So, we can take (0, 0, 0) to be the starting point of vector u. Since [tex]u = (1, 0, 2)[/tex], the tip of vector u is [tex](0 + 1, 0, 0 + 2) = (1, 0, 2)[/tex]. Because the plane passes thru the tip of vector u, a point in the plane has coordinates [tex] (1, 0, 2)[/tex].

So for any point [tex](x, y, z)[/tex] in the plane, the equation is given by

[tex]n \cdot (x - 1, y - 0, z - 2) = 0[/tex]

Where n is the normal vector to the plane.

Since [tex]n = \left(-2, 4, 2 \right)[/tex], the equation becomes

[tex]\left(-2, 4, 2 \right) \cdot (x - 1, y - 0, z - 2) = 0 \\ \left(-2, 4, 2 \right) \cdot (x - 1, y, z - 2) = 0 \\ -2(x - 1) + 4y + 2(z - 2) = 0 \\ -2x + 2 + 4y + 2z - 4 = 0 \\ -2x + 4y + 2z - 2 = 0 \\ \boxed{-2x + 4y + 2z = 2 }[/tex]

How do I solve this equation for n? (6x2n)÷8=15

Answers

multiply 8 on both sides so we have no division so 8 multiplied by 15 = 120
now we know (6x2n) = 120
so if we re-write this you can make it 6x(2n) = 120
Now we divide by 6 on both sides that gives us (2n) = 20
divide by two and you have your answer

hope this helps

To solve the equation (6x2n)÷8=15 for n, you must perform algebraic operations to isolate n. This involves multiplying by 8, then dividing by 6x, and finally by 2, to arrive at n = 20 / x.

To solve the equation (6x2n)÷8=15 for n, we need to follow several steps. This involves manipulating the equation using algebraic operations until we isolate the variable n on one side. Here is the step-by-step process:

Multiply both sides of the equation by 8 to get rid of the fraction: 6x2n = 15 × 8.Simplify the right side: 6x2n = 120.Divide both sides by 6x to isolate n: 2n = 120 / 6x.Further simplify the right side to get n on its own: n = (120 / 6x) / 2.Complete the calculation based on the values of x that are given: n = 20 / x.

If x is known, you can substitute the value of x into the equation to find the value of n. If x is not given, then this is the simplified form of the equation in terms of n and x.

is possible to have a shape with different dimensions while having the same volume?

Answers

Yes, they could be different and still have the same volume

yes,

a cuboid with dimensions 2, 4, 8 has volume = 64 unit^3

a cube with side 4 has volume = 64 unit^3

so, they have different shapes but same volume

Which terms accurately classify this triangle? Choose exactly two answers that are correct. A. right B. acute C. isosceles D. scalene

Answers

The answer is (C isosceles) hope it helps and have a great day!

Jim goes to the store and buy 6 apples for 25 cent each and 10 bananas for 10 cent each Jim has a 10% off coupon Jim will own the store $2. 25 truє σr fαlѕє

Answers

I believe the answer is true

Analyze the following budget, with an income of $750, to determine how much can be spent on food for the month. Month________ Budgeted Amount Food $___ Personal Items $20 Cell Phone $75 Entertainment $85 Car Expenses – Gas, Insurance $260 College Savings $250 a. No more than $70 can be spent on food. b. No more than $75 can be spent on food. c. No more than $80 can be spent on food. d. No more than $60 can be spent on food.

Answers

The answer is D
Hope it helps

A monthly of $60 can be spent for food after all the expenses and savings

are sorted.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The numerical form of the given information can be formed as,

$(750 - 20 - 75 - 85 - 260 - 25).

= $60.

So, With an income of $750 and all the expenses including saving for for college worth of $250 the amount that can be spent on food is $60.

learn more about numerical expressions here :

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Charlie reads quickly. He reads 1 and 3 seventh pages every 2 third minutes. Charlie reads at a constant rate. How many pages does charlie read per minute?

Answers

The unit rate would be 1 3/7 ÷ 2/3 10/7 ÷ 2/3 10/7 · 3/2 separate by division, rearrange and multiply 15/7

Charlies reads 15/7, or 2 1/7, page per minute.

Hope this helps a bit.

A candy maker buys a bar of chocolate weighing 162 ounces. About how many pounds does the bar weigh?

Answers

For this case, the first thing you should keep in mind is the following conversion:
1 pound = 16 ounces
Applying the comversion we have:
(162) * (1/16) = 10,125 pounds
Therefore, the weight of the chocolate bar in pounds is 10,125
Answer:
the bar does weigh 10,125 pounds

15% of the toddlers in a preschool class drink water with their lunch. How many toddlers
are in the class if 3 toddlers drink water with their lunch?
(a) Draw a model for the situation (if you prefer to use a 100-grid model or ratio table
model, that’s fine too!) and label the “part,” “whole,” and “percent.”

Answers

15/100 = 3/x

15x = 300
x = 300/15
x = 20 kids

Use the data to create a scatter plot. Year 0 1 2 3 4 Population 3 4 6 11 15 Use the point tool to plot the points from the table in the coordinate grid to create a scatter plot.

Answers

In order to create the scatter plot in your point tool, mark the points one by one on the coordinate grid. The first point will be (0,3). This means for location 0 on x-axis the value on y axis is 3. First point goes there. The second point is (1, 4). Move one unit on the x-axis and 4 units on y-axis. Second point goes there. Do this process for all the points to complete the scatter plot. I used Microsoft excel to create the scatter plot. Your plot will be similar to the plot shown below.

Enter the values in the first two columns of MS excel. Then go on the insert tab and click insert scatter plot. A scatter plot will be made as shown below in the attached picture.

The same plot can be made by hand by simply inserting the correct points on the graph. From the scatter plot we can observe that a positive correlation occurs in the given variables. A straight line can be used to approximate the trend of the data.

Answer:

Refer the attached figure.

Step-by-step explanation:

Given : Data of population

To find : Use the data to create a scatter plot?

Solution :

Data :

Year(x) Population(y)

0 3

1 4

2 6

3 11

4 15

A Scatter Plot has points that show the relationship between two sets of data.

With the help of scatter plot graph,

We plot the points of the data.

Refer the attached figure below.

What is the constant term in the expression 4x3y + 8x2 + 6x + 5?

Answers

Answer:

Step-by-step explanation:

The constant term is the one with no variables in it: +5.

Answer:

i took the test and its 5.

how many time does 2 go into 19

Answers

Hello There @Diamondinthesky123 (Cute Username)

When you state the question, "How many times does 2 go into 19", I assume your talking about Long Division. (Not so long in this case)

In this case, we would divide 19 by 2, resulting in 9 with a remainder of 1.
Thats It! :)

I hope I helped, Have a great Day!

Thank you,
Darian D.

Final answer:

In basic division, 2 goes into 19 a total of 9 times with 1 leftover. This demonstrates division and the concept of remainders in mathematics.

Explanation:

The student is asking about basic division in mathematics, specifically how many times 2 goes into 19. To find this, we divide 19 by 2.

Doing the division, we get:

19 divided by 2 equals 9 with a remainder of 1.

Therefore, 2 goes into 19 9 times with 1 left over.

It's worth noting that there's also a mathematics technique called estimation that might be considered here. If we estimate to the nearest whole number, 2 would go into 19 approximately 9 times since 2 times 9 is 18, which is very close to 19.

Answer and how you get then answer

Answers

Percent Change = ((new value)/(old value) -1) * 100%
= (480/540 -1)*100%
≈ -11.11%

The number of calories in a child's meal was reduced about 11%.

solve the proportion
[tex] \frac{3}{4} = \frac{x}{6} [/tex]

Answers

To solve a problem like this, you can use a method called cross-multiplying. This is when you multiply the denominator of the first fraction by the numerator of the other and then multiply the two remaining numbers.

[tex] \frac{3}{4} = \frac{x}{6} [/tex] Multiply 3 by 6 and multiply 4 by x.
4x = 18 Divide by 4.
x = [tex] \frac{18}{4} [/tex] Simplify!
x = [tex] \frac{9}{2} [/tex]

You can check this by comparing the fractions with [tex] \frac{9}{2} [/tex] in the place of x.

[tex] \frac{3}{4} = \frac{ \frac{9}{2} }{6} [/tex] Divide [tex] \frac{9}{2} [/tex] by 6 ( [tex] \frac{9}{2} [/tex] times [tex] \frac{1}{6} [/tex]).
[tex] \frac{3}{4} = \frac{9}{12} [/tex] Simplify!
[tex] \frac{3}{4} = \frac{3}{4} [/tex]

The fractions are equal, so x = [tex] \frac{9}{2} [/tex] .

$8000 invested at an APR of 6% for 10 years.
If interest is compounded annually, what is the amount of money after 10 years?

Answers

The formula in finding the maturity value is the following:

A = P (1 + r) ^t

Where A = Maturity value

P = principal amount

r = Annual percentage rate

t = time in years

Substituting the given amount to the formula:

A = $8,000 (1 + 6%) ^10

= $8,000 (1.7908)

= $14,326.40

Therefore, the amount of $8,000 after 10 years compounded annually at 6% is $14,326.40

In a circle with a radius of 36 3/5 cm, an arc is intercepted by a central angle of 2π7 radians.

What is the arc length?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.

cm

Answers

Answer:

The arc length is [tex]32.84\ cm[/tex]

Step-by-step explanation:

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=36\frac{3}{5}\ cm=\frac{36*5+3}{5}=\frac{183}{5}\ cm[/tex]

substitute

[tex]C=2(3.14)(\frac{183}{5})=229.848\ cm[/tex]

Remember that

[tex]2\pi[/tex] radians subtends the complete circle of length [tex]229.848\ cm[/tex]

by proportion

Find the arc length by a central angle of [tex]2\pi/7[/tex] radians

[tex]\frac{229.848}{2\pi}=\frac{x}{2\pi/7}\\ \\x=229.848*(2\pi/7)/(2\pi)\\ \\x=`32.84\ cm[/tex]

The arc length is approximately 32.81 cm.

Step 1

To find the arc length intercepted by a central angle, we can use the formula:

[tex]\[ \text{Arc Length} = \text{radius} \times \text{central angle} \][/tex]

Given:

- Radius [tex]($ r $[/tex]) = 36 3/5 cm

- Central angle [tex]($ \theta $) = $ \frac{2\pi}{7} $[/tex] radians

First, let's convert the radius to a decimal:

[tex]\[ \text{Radius} = 36 \frac{3}{5} \text{ cm} = 36.6 \text{ cm} \][/tex]

Step 2

Now, we can use the formula to find the arc length:

[tex]\[ \text{Arc Length} = 36.6 \times \frac{2\pi}{7} \]\[ \text{Arc Length} = 36.6 \times \frac{2 \times 3.14}{7} \]\[ \text{Arc Length} = 36.6 \times \frac{6.28}{7} \]\[ \text{Arc Length} = 36.6 \times 0.897 \]\[ \text{Arc Length} \approx 32.808 \][/tex]

Rounded to the nearest hundredth, the arc length is approximately 32.81 cm.

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