A company uses paper cups shaped like cones for its water cooler. Each cup has a height of 14cm, and the base has a radius of 3cm . How much water is needed to fill 125 cups?

Hi Student!

Usually the first step that I take for any problem would be to gather any important information that would be needed in the problem.  However, for this problem, it is pretty straight forward because we just need to solve for the unknown which is x.

Add 3 to both sides

Divide 8 from both sides

For the first equation, we were able to solve for x and get that the solution for the unknown is 1.25

Subtract 5 from both sides

Divide both sides by 7

For the second equation, we are able to solve for x and get that the solution for the unknown is 19/7

Subtract 6 from both sides

Divide both sides by 4

For the final equation, we are able to solve for x and get that the solution for the unknown is -0.25

Answer:

1) [tex]x=\frac{5}{4}=1\frac{1}{4}[/tex]

2) [tex]x=\frac{19}{7}=2\frac{5}{7}[/tex]

3) [tex]x=-\frac{1}{4}[/tex]

Step-by-step explanation:

1) 8x - 3 = 7

1. Group all constants on the right side of the equation

[tex]8x-3=7[/tex]

Add 3 to both sides:

[tex]8x-3+3=7+3[/tex]

Simplify the arithmetic:

[tex]8x=7+3[/tex]

Simplify the arithmetic:

[tex]8x=10[/tex]

2. Isolate the x

[tex]8x=10[/tex]

Divide both sides by 8:

[tex]\frac{8x}{8}=\frac{10}{8}[/tex]

Simplify the fraction:

[tex]x=\frac{10}{8}[/tex]

Find the greatest common factor of the numerator and denominator:

[tex]x=\frac{5\cdot 2}{4\cdot 2}[/tex]

Factor out and cancel the greatest common factor:

[tex]x=\frac{5}{4}[/tex]

2) 5 + 7x = 24

1. Group all constants on the right side of the equation.

[tex]5+7x=24[/tex]

Subtract 5 from both sides:

[tex]5+7x-5=24-5[/tex]

Group like terms:

[tex]7x+5-5=24-5[/tex]

Simplify the arithmetic:

[tex]7x=24-5[/tex]

Simplify the arithmetic:

[tex]7x=19[/tex]

2. Isolate the x

[tex]7x=19[/tex]

Divide both sides by 7:

[tex]\frac{7x}{7}=\frac{19}{7}[/tex]

Simplify the fraction:

[tex]x=\frac{19}{7}[/tex]

3)  5 = 6 + 4x

1. Swap sides

[tex]5=6+4x[/tex]

Swap sides:

[tex]6+4x=5[/tex]

2. Group all constants on the right side of the equation

[tex]6+4x=5[/tex]

Subtract 6 from both sides:

[tex]6+4x-6=5-6[/tex]

Group like terms:

[tex]4x+6-6=5-6[/tex]

Simplify the arithmetic:

[tex]4x=5-6[/tex]

Simplify the arithmetic:

[tex]4x=-1[/tex]

3. Isolate the x

[tex]4x=-1[/tex]

Divide both sides by 4:

[tex]\frac{4x}{4}=\frac{-1}{4}[/tex]

Simplify the fraction:

[tex]x=\frac{-1}{4}[/tex]

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Why learn this:

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

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Terms and topics

The most common use of linear equations is to solve problems involving an unknown variable, generally (but not always) x, and a known constant.

Solving linear equations requires isolating the unknown variable on one side of the equation and simplifying the remainder. Anything done to one side of the equation must also be done to the other when simplifying.

An equation of:

[tex]ax+b=0[/tex]

A typical linear equation with one unknown is in which a and b are constants and x is the unknown variable. In this case, we would isolate x by removing b from both sides of the equation before solving for it. We'd then multiply both sides of the equation by a, yielding the following result:

[tex]x = -\frac{b}{a}[/tex]

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Learn More About Linear Equations With One Unknown

Based on the elements and charges in Copper (II) Oxalate, CuC₂O₄(s), the solubility in pure water is 1.7 x 10⁻⁴ M.

The solubility equilibrium (Ksp) is 2.9 x 10⁻⁸ so the solubility can be found as:

Ksp = [Cu²⁺] [C₂O₄²⁻]

Solving gives:

2.9 x 10⁻⁸ = S x S

S² = 2.9 x 10⁻⁸

S = 1.7 x 10⁻⁴ M

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The value of solubility for cuc2o4(s) in pure water when the value of solubility product, Ksp for it is 2.9 ×10⁻⁸, is 1.703 × 10⁻⁴.

The solubility of a chemical compound or an element is the property or ability of it to be dissolved, specially in water.

The solubility for CuC₂O₄(s) in pure water has to be found out.  The solubility product is,

[tex]K_{sp}=2. 9 \times 10^{-8}[/tex]

Let suppose x is the molar solubility of CuC₂O₄(s). From the ICE approach solution,

[tex]K_{sp}=x^2\\2. 9 \times 10^{-8}=x^2\\x=\sqrt{2. 9 \times 10^{-8}}\\x=1.703 \times 10^{-4}\rm\; M[/tex]

Thus, the value of solubility for cuc2o4(s) in pure water when the value of solubility product, Ksp for it is 2.9 ×10⁻⁸, is 1.703 × 10⁻⁴.

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Step-by-step explanation:

4(5 + x) = 2x + 2

that is my understanding of the given problem.

if you made a typo, please adapt the following solution.

4×5 + 4×x = 2x + 2

20 + 4x = 2x + 2

20 + 2x = 2

2x = -18

x = -9

The dice will show a sum of 7 if you roll

• 1 and 6

• 2 and 5 (2 ways)

• 3 and 4 (3 ways)

so there are 6 ways of rolling a sum of 7. Out of 6 × 6 = 36 possible outcomes, the probability of rolling a sum of 7 is 6/36 = 1/6.

Answer:

40%

Step-by-step explanation:

Answer:

right triangle

Step-by-step explanation:

it has a 90 degree sign by the base of the triangle

By definition of coterminal angles, the angle 2π/3 has two coterminal angles: θ' = 14π/3 and θ' = - 4π/3. The angle - 11π/7 has no coterminal angles.

Two angles are coterminal when their terminal ends have the same direction. By the fact that two consecutive coterminal angles have a difference of 2π, we find the following definition:

θ' = θ ± 2π · i, i ∈ [tex]\mathbb{N}_{O}[/tex]     (1)

Now we proceed to determine the coterminal angles for each case:

a) θ = 2π/3

θ' = 14π/3, θ' = - 4π/3

b) θ = - 11π/7

There are no coterminal angles.

By definition of coterminal angles, the angle 2π/3 has two coterminal angles: θ' = 14π/3 and θ' = - 4π/3. The angle - 11π/7 has no coterminal angles.

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Answer:

D. 1/3

Step-by-step explanation:

Answer:

A 1/3

Step-by-step explanation:

Event e either will take place or not. The probability that it'll take place is already given as 2/3.this means that 1/3 is the probability that it won't take place

Answer:

50%

Step-by-step explanation:theres only 2 sides on a coin

Answer: 50% , as likely as not .

Step-by-step explanation:

The probability of a 2 on the die is 1/6. The probability of a heads on the coin is 1/2. That means that (on average) half the time you roll a 2 you'll also get heads and the other half you'll get tails. What's half of 1/6?

The possibilities are:

1H 2H 3H 4H 5H 6H

1T 2T 3T 4T 5T 6T

So, it's 1/12 that you'll get a 2 and heads (on average).

HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST . THANKS .

Since the straw is 6 inches long, the approximate length of the cylinder's radius is 3.32 in

To find the radius of the cylinder, we need to apply Pythagoras' theorem.

Pythagoras' theorem states that in any right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other two sides.

Mathematically, c² = a² + b² where

Now, since the 6 inch straw inclined at an angle forms a right angle with the radius,r and length of the cylinder, h.

Since the length of the straw is the hypotenuse side, L we have that

L² = h² + r²

Making r the radius of the cylinder subject of the formula, we have

r = √(L² - h²)

Given that

Substituting the values of the variables into the equation,we have

r = √(L² - h²)

r = √(6² - 5²)

r = √(36 - 25)

r = √11

r = 3.316 in

r ≅ 3.32 in

So, the approximate length of the cylinder's radius is 3.32 in

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Answer:

the leading coefficient of a polynomial is the coefficient of the term with the highest degree of the polynomial

so the answer should be the second one -7+6x+5x^2

Answer:

D

Step-by-step explanation:

Range = Y coordinats of a the points

Hi Student!

In the problem statement we are given a number of 0.38 meters which it then tells us to write and solve an equation to convert that to centimeters.  The first step would be to write an equation that would perfectly incapsulate what we are trying to do.

[tex]x = meters\ *\ \frac{100\ centimeters}{1\ meter}[/tex]

This equation can now be used for any amount of meters where we can input the amount of meters that we have and that will cancel with the meters on the bottom while multiplying by 100 to which we then will receive our value of x in centimeters.  Let's solve the equation using 0.38 meters.

Input the values

Cancel the meters

Simplify the expression

Therefore, our final answer is that 0.38 meters can be converted to centimeters which would then get 38 cm as the result.

Answer:

The answer is 13, 9 and (-1)

Step-by-step explanation:

For x = (-2)

h(x) = (-2x + 9)

h(-2) = [-2(-2) + 9]

h(-2) = (4 + 9)

h(-2) = 13

For x = 0

h(x) = (-2x + 9)

h(0) = [-2(0) + 9]

h(0) = (0 + 9)

h(0) = 9

For x = 5

h(x) = (-2x + 9)

h(5) = [-2(5) + 9]

h(5) = [(-10) + 9]

h(5) = (-1)

Thus, The answer is 13, 9 and (-1) when x = (-2), 0 and 5 respectively.

The equation 11x + 10y = 32 is a linear equation, and the solution to the linear equation 11x + 10y = 32 is [tex]y = \frac{32 - 11x}{10}[/tex]

The equation is given as:

11x + 10y = 32

Subtract 11x from both sides

10y = 32 - 11x

Divide both sides by 10

[tex]y = \frac{32 - 11x}{10}[/tex]

Hence, the solution to the linear equation 11x + 10y = 32 is [tex]y = \frac{32 - 11x}{10}[/tex]

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Answer:

I do not know I am very sorry brother now begone

Answer:

5y + 6 = 9

Step-by-step explanation:

If you want to take it a step further and solve it:

5y = 3

y = 3/5

Answer:

About 26.67 percent.

The Maximum number of hours available for unskilled labour

= 400 hours

Maximum number of hours available for skilled labour be, = 320 hours

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

The company employs 10 unskilled workers and each worker provides 40 hours of labour per week.

The company also employs 8 skilled workers and each worker provides 40 hours of labour per week.

Maximum number of hours available for unskilled labour be,

= 40  × 10

= 400 hours

Maximum number of hours available for skilled labour be,

= 40 × 8

= 320 hours

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Answer:

A, (-2,2)

Step-by-step explanation:

Answer: [tex]2x+4y[/tex]

Step-by-step explanation:

[tex]2*(x+2y)[/tex]

[tex](2x+3y)+y[/tex]

Apply rule: [tex](a)=a[/tex]

[tex](2x+3y)=2x+3y[/tex]

[tex]=2x+3y+y[/tex]

Add similar elements: [tex]3y+y=4y[/tex]

[tex]=2x+4y[/tex]

[tex]2x+4y~is~the~answer[/tex]

Answer:

1. unknow

2. mean median range spread average

3. the bike Ville is more expensive in everything

Using Average, the prices of bicycles at two stores are compared.

Average is the" sum of observations divided by total number of observations".

According to the question,

The price of bicycles at two stores are shown.

Bikeville:                  140 160 800 235   250 450 80 115 220 250 96  290

Discount Bicycles:   50  180  300  110   120  150 155 285 120 200 70 175 95

Average of bikeville = [tex]\frac{sum of observations}{Total number of observation}[/tex]

= 140 + 160 + 800 + 235 + 250 + 450 + 80 + 115 + 220+250+96+29

= 3086

Average of bikeville= 3086/12

= 257.167

Average of Discount of bicycles:

( 50 +180+100+110+120+150+155+285+

120+150+155+285+120+200+70+175+95)     =2720

= 2720/15

=181.33

Average of Discount of bicycles is 181.33.

Hence, using Average the prices of bicycles at two stores are compared.

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Answer:

30%

Step-by-step explanation:

percent decrease = (new - old) / old * 100 = (3934-5620)/5620 * 100 = 30%

The objective function of the printing company in a bid to minimize cost is; p = 25x + 20y.

The objective function in a linear programming problem is the real-valued function whose value is to be either minimized or maximized dependent on the constraints defined on the given linear programming problem over the set of feasible solutions. The objective function of a LPP is a linear function of the form z = ax + by in which case, z is the parameter to be optimised.

It therefore follows from the complete question that the objective function is; p = 25x + 20y. This follows from the fact that Supplier X charges $25 per case. Supplier Y charges $20 per case and the parameter to be optimised is price.

Remarks;

The complete question is as follows;

A printing company orders paper from two different suppliers. Supplier X charges $25 per case. Supplier Y charges $20 per case. The company needs to order at least 45 cases per day to meet demand and can order no more than 30 cases from Supplier X. The company needs no more than 2 times as many cases from Supplier Y as from Supplier X. Let x = the number of cases from Supplier X and y = the number of cases from Supplier Y.

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Answer:

D

Step-by-step explanation:

right on edge

[tex]\text{Apply Pythagorean theorem,}\\ \\~~~~~~~x^2 = 25^2 +75^2\\\\\implies x =\sqrt{25^2 +75^2}\\ \\\implies x = \sqrt{625+5625}\\\\\implies x = \sqrt{6250}\\\\\implies x =\sqrt{625 \times 10}\\\\\implies x = \sqrt{25^2 \times 10}\\\\\implies x = 25\sqrt{10}[/tex]

Answer:

$7650.44

Step-by-step explanation:

Annual interest rate = 4.02%

but compound 4 times per year, means quarterly compound

quarterly interest rate = 4.02%/4 = 1.005%

Account balance = 4734 * (1.01005)^48 [compound 4 times a year for 12 years]

= 4734 * 1.616

= 7650.44

Answer:

D) $7,650.44

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]

where:

Given:

Substituting the given values into the formula and solving for A:

[tex]\large \text{$ \sf \implies 4734\left(1+\frac{0.0402}{4}\right)^{4 \times 12} =7650.435473$}[/tex]

Answer:

0.833

Step-by-step explanation: