An ice cream store sells 4 drinks, in 5 sizes, and 3 flavors. In how many ways can a customer order a drink?



There are ____ ways that the customer can order a drink.

The standard form of the equation y = 3x + 10 is -3x +y = 10.

To accomplish the given equation and bring it in the standard form for our problem, we first arrange it in standard form and then apply a little algebra to subtract 3x from both sides of the equation.

Given,

y = 3x + 10

Subtract 3x from each side.

Simplify: y - 3x = 3x + 10 - 3x.

y - 3x = 10

The x word should be placed first in the left-hand side arrangement.

-3x + y = 10

We discover that y = 3x + 10 is written as -3x + y = 10.

Ax + By = C is the equation of a line in its standard form, where A, B, and C are constants. There are several possible ways to express a line's equation, and if we are given a line that isn't in standard form, we can apply a little algebra to change the equation.

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The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

500

Step-by-step explanation:

Step-by-step explanation:

55,000 +2,500+62,000+2,000

The linear optimization problem is to maximize the objective function 250x + 150y, subject to the constraints x + y ≤ 60, 3x + y ≤ 90, and 2x + y > 30, where x and y are both greater than or equal to 20.

The feasible region can be determined by graphing the constraints and finding the overlapping region that satisfies all the conditions. In this case, the feasible region is the area where the lines x + y = 60, 3x + y = 90, and 2x + y = 30 intersect. This region can be visually represented on a graph.

To find the corner points of the feasible region, we need to find the points of intersection of the lines that form the constraints. By solving the systems of equations, we can find that the corner points are (20, 40), (20, 60), and (30, 30).

The optimal solution and the optimal objective function value can be determined by evaluating the objective function at each corner point and selecting the point that yields the maximum value. By substituting the coordinates of the corner points into the objective function, we find that the maximum value is achieved at (20, 60) with an objective function value of 10,500.

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Answer:

I believe the answer is -50i

Answer:

sorry dude but should delete account ;-;

Step-by-step explanation:

delete accound pls

i cant open browser so delete accouuunnntt

and report me pls

The displacement of the particle at time t is given by d(t) = 1/3t^3 - 3/2t^2 - 18t, and the total distance traveled up to t = 6 is 72 meters.

To find the displacement at time t, we need to integrate the velocity function v(t).

∫v(t)dt = ∫(t^2 - 3t - 18)dt

= 1/3t^3 - 3/2t^2 - 18t + C

Let's assume that the particle starts at position 0 at time t = 0, so the constant of integration is 0. Therefore, the displacement of the particle at time t is given by:

d(t) = 1/3t^3 - 3/2t^2 - 18t

To find the total distance traveled up to t = 6, we need to calculate the definite integral of the absolute value of the velocity function over the interval [0, 6].

Total distance = ∫|v(t)|dt from 0 to 6

= ∫|t^2 - 3t - 18|dt from 0 to 6

= ∫(t-6)(t+3)dt from 0 to 6 (since t^2 - 3t - 18 = (t-6)(t+3) when t ≤ -3 or t ≥ 6)

= [1/3*(6-6)^3 - 3/2*(6-6)^2 - 18*(6-0)] - [1/3*(0-6)^3 - 3/2*(0-6)^2 - 18*(0-0)]

= 72 meters

Therefore, the displacement of the particle at time t is given by d(t) = 1/3t^3 - 3/2t^2 - 18t, and the total distance traveled up to t = 6 is 72 meters.

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Answer:

600cm2

Step-by-step explanation:

Area of sheet = Length × Breadth

                        = (30 × 20) cm2

                        = 600 cm2

90 seconds does it take to go from the bottom of the wheel to the top of the wheel, so the correct option is option C.

The height above ground for a person riding a ferris wheel after t seconds is modeled by h(t) = 150 sin (π/45 t+67.5) + 160 feet.

To determine the seconds does it take to go from the bottom of the wheel to the top of the wheel.

By the given equation

h(t) = 150 sin (π/45 t+67.5) + 160

This is a sine fraction.

w = λ/45 :period = 2λ/w

period = 2λ/w = 90.

Therefore, 90 seconds does it take to go from the bottom of the wheel to the top of the wheel.

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Answer:

3x1/8x2/5=3/20

Step-by-step explanation:

Let's start by substituting the right-hand side of the equation into the left-hand side:

What does the math equation mean?

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

4y - 3 = 4(y + 1)

4y - 3 = 4y + 4

Now, we can isolate y by subtracting 4y from both sides:

0 = y + 4

-4 = y

So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.

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The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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When you have a system of linear equations, and you identify terms with the same variable and same coefficients, you can use the subtraction method to obtain an equation in which you can obtain the value of one of the variables.

Answer:

\(c \: is \: correct \: \: \: the \: range \: is \: usually \: right \ \\ : and \: they \: are \: x \: \)

The sum of two complementary angles is 90 degrees.

Angle A  +  Angle B = 90

Let Angle B = X

5x + 2 + x = 90

Combine like terms:

6x +2 = 90

Subtract 2 from both sides:

6x = 88

Divide both sides by 6:

x = 88/6

x = 14.67

Angle B = 14.67 degrees ( rounded to the nearest hundredth)

First, we subtract 2x on each side.

Then, we subtract 12 on each side.

We sum 7x on each side.

Then, we add 8 on each side.

At last, we divide the equation by 36.

First, we use the distributive property.

Then, we subtract 8x on each side.

Now, we add 10 on each side.

At last, we divide the equation by -4.

Answer:

Step-by-step explanation:

||y + 6|| = 10

Next, we can consider the two possible cases:

Case 1: y + 6 ≥ 0

If y + 6 is non-negative, then the absolute value of y + 6 is just y + 6 itself. So we have:

y + 6 = 10

y = 4

Case 2: y + 6 < 0

If y + 6 is negative, then the absolute value of y + 6 is the opposite of y + 6, which is -(y + 6). So we have:

-(y + 6) = 10

y + 6 = -10

y = -16

Therefore, the solutions to the equation 3||y + 6|| = 30 are y = 4 and y = -16.

The best statement that describes the relationship between lines s and t : (C). Lines s and t are parallel.

A line can be defined as a figure that is one dimensional. It is a trace that is made by the movement of points in opposite direction.

Parallel lines can be defined as a group of lines that are of the same orientation. They face the same direction and are on the same axis.

In conclusion, The best statement that describes the relationship between lines s and t : Lines s and t are parallel.

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Answer: To find the number of liters of water in the first pool after x minutes have passed, we can use the formula:

972 + 17x

To find the number of liters of water in the second pool after x minutes have passed, we can use the formula:

44x

Note that both of these formulas assume that the pools are being filled continuously, without any interruptions. If the flow of water into either pool is interrupted at any point, the actual amount of water in the pools may be different from what these formulas predict.

Answer:

a)

17x + 972

44x

b)

972 + 17x = 44x

Step-by-step explanation:

Answer:

the greatest common factor of 6 and 12 is 6

Step-by-step explanation:

6 can be divided by six, one time. 12 can be divided by six, two times.

The answer is 6.

The factors of 6 are: 1, 2, 3, 6

The factors of 12 are: 1, 2, 3, 4, 6, 12

The GCF of a number is the greatest common factor of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder.

If the end plan changed the length of each side by 9 feet , then the scale factor comparing your original garden to your final result is  0.70 .

in the question ,

it is given that

the length of square garden in original plan = 13 feet .

and

in the end plan the length of the square garden is = 9 feet

So , the scale factor can be calculated using the formula

scale factor = (length of side in end plan) / (length of side in original plan)

On substituting , the values ,

we get ,

scale factor = 9/13

= 0.6923

rounding to the nearest hundredth

we get ,

≈ 0.70

Therefore , If the end plan changed the length of each side by 9 feet , then the scale factor comparing your original garden to your final result is  0.70 .

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There are several reasons why a couple percent error may occur when calculating roots, even if both roots can easily be represented with a float.

These reasons can include rounding errors, numerical instability, algorithm limitations, machine precision, and incorrect input data or model. To minimize the error, it is important to use a stable and accurate algorithm, and to ensure that the input data and model are correct.

The error in the calculation of one of the roots can be due to several reasons, such as:

Rounding errors: In many cases, when performing calculations with floating-point numbers, intermediate results are rounded to a certain number of decimal places. This can result in a small error that accumulates throughout the calculation and leads to an incorrect answer.

Numerical instability: Some mathematical operations, such as division and square roots, can lead to loss of precision or numerical instability. This can result in an incorrect answer, even if the input numbers can be represented as floating-point numbers.

Algorithm limitations: The algorithm used to calculate the roots may have limitations that result in an error, even if the input numbers can be represented as floating-point numbers. For example, some algorithms may not converge to the correct root, or they may converge very slowly.

Machine precision: The precision of the computer used to perform the calculation can also play a role in the error. For example, if the computer uses single-precision floating-point numbers instead of double-precision floating-point numbers, the error will be larger.

Model or input data error: The error could also be due to incorrect input data or an incorrect model. For example, if the mathematical model used to calculate the roots is not an accurate representation of the underlying system, the error will be larger.

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Answer:

x=2.2

Step-by-step explanation:

11%5=2.2 so x=2.2

Answer:

x= 11/5

Step-by-step explanation:

5x=11 .     Divide each side by 5

5x/5 = 11/5 .  Cancel terms

x= 11/5

Answer:

D 2,362 meters

Step-by-step explanation:

2325 - (-37) = 2,362

Answer:

x = 323.65

Step-by-step explanation:

A number can be represented through x.

x + 35% = 324

35% means 0.35

x + 0.35 = 324

   - 0.35    - 0.35

x = 323.65

hope this helps!

The number increased by 35% and the value is 323.65.

We have to determine the result

A number can be represented through x.

A complete search of the internet has found these results. The number is increased. is the most popular phrase on the web.

x + 35% = 324

35% means 0.35

We have to determine the value of x

x + 0.35 = 324

  - 0.35    - 0.35

x = 323.65

Therefore, The number is increased by 35% and the value is 323.65.

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Answer:

a= +1

b= -2

c= +7

Step-by-step explanation:

a= coefficient of xX^2 = +1

b= coefficient of X = -2

c = the constant term= +7

In linear equation, x ≤ 2 is  the maximum number of outfits Nora can purchase while staying within her budget .

What is linear equation ?

$285.41 for the bike, $17.33 (times 4) for the reflectors, and $31.25 for the gloves.

Then you will subtract the costs ($73.43 each) of the outfits that he buys using a variable to solve for the maximum amount he can buy (x).

580 - 285.41 - (17.33 * 4) - 31.25 - 73.43x ≥ 0

1) Parentheses

580 - 285.41 -  69.32 - 31.25 -73.43x ≥ 0

2) Combine like terms

194.02 - 73.43x ≥ 0

3) Get the variable term alone

-73.43x ≥ - 194.02

4) Divide to solve

   x ≥ - 194.02/ -73.43

      x ≤ 2

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