A useful rule of thumb called the "rule of 70" states that if something grows at a constant rate of z percent per year, it doubles in size approximately every __________ years.
a. z/70
b. 70/z
c. 70 - z
d. 70 × (z/100)

Answer:

12

Step-by-step explanation:

=1x60

5x1

=60

5

12

Answer:

I believe the answer is 1/8 hour per mile

Step-by-step:

I don't know. I  just believe that that is the most reasonable answer to this question and I have this question as well, it might seem hard it's really not.

Answer:

A) -4 over 9

Step-by-step explanation:

We have the fraction [tex]\frac{4}{-9}[/tex] the equivalent of this fraction is [tex]\frac{-4}{9}[/tex]

[tex]\frac{4}{-9}= \frac{-4}{9} =-\frac{4}{9}[/tex]

Both fractions are the same and equivalent, the negative sign makes the whole fraction negative regardless of whether it is in the numerator or denominator.

Final answer:

To find the number of pizza combinations available using 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, one multiplies the number of topping choices by the number of cheese choices, giving 8 x 3 = 24 possible combinations.

Explanation:

Calculating Pizza Combinations

When calculating the number of possible pizza combinations with 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, we use basic counting principles. Each pizza can be thought of as a combination of one topping and one cheese. Since these choices are independent, we multiply the number of options for toppings by the number of options for cheeses to find the total combination possibilities. This results in 8 toppings multiplied by 3 cheeses, giving 24 possible combinations.

The formula used is straightforward: Number of combinations = Number of toppings × Number of cheeses.

Pizza Combination Calculation Example

For instance, if you were at a pizza parlor where you could choose from pepperoni, mushrooms, onions, and 5 other toppings, along with mozzarella, cheddar, and one other cheese, you could create 24 unique pizzas. Just pick one topping and one cheese, and that's your combination.

Answer:

The answer is only one piece of candy

Step-by-step explanation:

Firstly, we have to determine the total amount of pieces of candy:

There are three bags with 75 pieces in each one, so the total is:

[tex]75+75+75=225[/tex]

Then, in order to determine the amount of pieces of candy for every friend,

we have to divide the total amount by 7, where the remainder of the division is the answer.

[tex]\frac{225}{7}=32*7+1[/tex]

Remainder=1

Finally, every friend of Scott receive 32 pieces of candy evenly and Scott is left with only one piece of candy.

The solution is, the value of x is 7.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

(10x-20)=(6x+8)

We simplify the equation to the form, which is simple to understand

(10x-20)=(6x+8)

Remove unnecessary parentheses

10x-20=(6x+8)

Remove unnecessary parentheses

10x-20=6x+8

We move all terms containing x to the left and all other terms to the right.

+10x-6x=+8+20

We simplify left and right side of the equation.

+4x=+28

We divide both sides of the equation by 4 to get x.

x=7

Hence, The solution is, the value of x is 7.

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Answer:

Answer is 31,

Step-by-step explanation:

PLATO Confirmed

As modeled by the function below: t=0.007x^2+0.003x. The time it will  take the computer to sort 15 objects is 1.62sec

What is Time?

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Given:

t = 0.007x^2+0.003x

x = 15

Substituting the value in the equation we get,

t = 0.007(15)^2+0.003(15)

t = 0.007(225) + 0.045

t = 1.575 + 0.045

t = 1.62sec

Hence, It will take 1.65sec to sort 15 objects

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The radians that are contained in a central angle that is 2/3 of a circle will be 4π / 3 radians.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The central angle that is 2/3 of a circle will be given as,

⇒ 2π × (2 / 3)

Simplify the expression, then we have

⇒ 2π × (2 / 3)

⇒ 4π / 3 radian

The radians that are contained in a central angle that is 2/3 of a circle will be 4π / 3 radians.

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The remainder obtained by dividing on [tex]{x^7} + {x^5} + 1[/tex] the generator polynomial [tex]{x^3} + 1[/tex] is [tex]\boxed{{-x^2} + {x} +1}[/tex]

Given:

The generator polynomial is [tex]{x^3} + 1.[/tex]

The polynomial is [tex]{x^7} + {x^5} + 1[/tex]

Explanation:

There are two methods of dividing the two polynomials.

(1). Synthetic division

(2). Long division method

The fraction can be expressed as,

[tex]{\text{Fraction}}= \dfrac{{{x^7} + {x^5} + 1}}{{{x^3} + 1}}[/tex]

The denominator of the fraction is [tex]{x^3} + 1[/tex] and the numerator of the fraction is [tex]{x^7} + {x^5} + 1.[/tex]

Divide [tex]{x^7} + {x^5} + 1[/tex] by [tex]{x^3} + 1[/tex] to obtain the remainder and the quotient of the polynomial.

The remainder obtained by dividing on [tex]{x^7} + {x^5} + 1[/tex] the generator polynomial [tex]{x^3} + 1[/tex] is [tex]\boxed{{-x^2} + {x} +1}[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Long division method

Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree, cubic polynomial, quadratic equation.

Final answer:

To find the remainder of the polynomial division of x^7 + x^5 + 1 by x^3 + 1, one would perform polynomial long division or synthetic division, continuing until the degree of the remainder is less than the divisor.

Explanation:

The student is asking how to find the remainder of a polynomial division. Specifically, they want to know the remainder when dividing x^7 + x^5 + 1 by the polynomial x^3 + 1. To solve this, one would typically use long division of polynomials or synthetic division. The process is similar to long division with numbers. We would start by looking at the highest degree terms of both polynomials and divide them, then multiply the divisor by the result and subtract from the dividend. Repeat this process until the degree of the remainder is less than the degree of the divisor. Since finding the remainder requires us to consider terms up to x^2, we are essentially looking for the result of division that does not perfectly divide, similar to how 7 divided by 3 leaves a remainder.

Final answer:

The number 46 can be written as 'forty-six', 'XLVI' in Roman numerals, '101110' in binary, '56' in octal, '2E' in hexadecimal, a sum or product of other numbers, or in scientific notation as 4.6 x 10ⁱ.

Explanation:

There are several ways to write the number 46 in mathematics. One alternative way to express the number is by using words, such as 'forty-six'. Another method is to use Roman numerals, which would be 'XLVI'. Additionally, 46 can be represented in other numerical bases; for example, in binary, it is '101110', in octal, it is '56', and in hexadecimal, it is '2E'. If we dive into mathematics, 46 can also be written as a sum of other numbers, such as 23 + 23, or a product of primes, which for 46 is 2 x 23. Lastly, 46 can be expressed in scientific notation as 4.6 x 10±, though this form is more commonly used for very large or very small numbers.

Final answer:

The constant of proportionality when y = 18 and x = 60 is calculated by dividing y by x, which results in a constant of 0.3.

Explanation:

To find the constant of proportionality when y = 18 and x = 60, we must assume that the relationship between y and x is directly proportional. This means that as x increases, y increases at a constant rate, and vice versa. If the relationship is directly proportional, we can write y = kx, where k is the constant of proportionality.

To calculate k, we simply divide y by x. So we have:

k = y / x
k = 18 / 60
k = 0.3

Therefore, the constant of proportionality is 0.3.

The given equation y = 4 - 2x is a linear equation, however, it is not in standard form. The standard form is 2x + y = 4.

The equation y = 4 - 2x is indeed a linear equation. A linear equation is an equation that represents a straight line when graphed. It generally has the form 'y = mx + b' where 'm' represents the slope of the line, and 'b' represents the y-intercept. Here, 'm' is -2 and 'b' is 4.

However, it is not currently in standard form. The standard form of a linear equation is 'Ax + By = C', where A, B, and C are integers, and A and B are not both zero. To write the equation in standard form, we can re-arrange it as 2x + y = 4.

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The machine lays cable at a rate of 25 meters per minute. This is calculated by dividing 125 meters by 5 minutes.

To determine how quickly the machine can lay underground cable, we need to calculate the rate of cable it places per minute. We start by noting that the machine can lay 125 meters of cable in 5 minutes.

We calculate the rate as follows:

This means the machine lays cable at a rate of 25 meters per minute.

Complete Question: A machine laying underground cable can place 125 meters of cable in 5 minutes. What is the rate per minute?

Answer:

(0, 139) and (139/35, 0)

Step-by-step explanation:

To graph a line, two points are needed. Taking x = 0 and replacing this value in the equation, we get:

y+1=−35(0−4)

y = 140 - 1

y = 139

Then, the point (0, 139) is on the line.

Taking y = 0 and replacing this value in the equation, we get:

0+1=−35(x−4)

1/(-35) = x -4

1/(-35) + 4 = x

139/35 = x

3.971 = x

Then, the point (139/35, 0) is on the line.

To solve the given differential equation, variables need to be separated, followed by integration of both sides. Since the equation involves both exponential and inverse square terms, separation of variables and integration are key steps. A specific solution also requires substituting a given function of y into the found general solution to determine any integration constants.

The question involves solving a differential equation 3e^(3x)dy/dx = -9x/y^2. First, we need to recognize this as a separable differential equation, which can be solved by isolating all terms involving y on one side and all terms involving x on the other side. After separation, we integrate both sides with respect to their respective variables.

Step 1: Separate the variables. We get dy/y^2 = -3x e^(-3x) dx.

Step 2: Integrate both sides. The integration of dy/y^2 with respect to y is -1/y, and the integration of -3x e^(-3x) with respect to x requires integration by parts or a table of integrals.

Step 3: Upon integration, we would find an implicit solution involving y and x, combined with an integration constant that needs to be determined based on initial conditions or additional information. Since specific initial conditions are not provided in the initial question, we'd include a constant C in our final expression.

For a specific solution when y(x) = cos(3x), additional steps are required to substitute this y expression into our general solution and solve for the constant.

The number of gazelles will the park have next year will be 126 if An animal park has 120 gazelles. If the population increase 5% in on year.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

An animal park has 120 gazelles. If the population increase 5% in on year,

= 5% of 120

= 6

= 6 + 120

= 126

Thus, the number of gazelles will the park have next year will be 126 if An animal park has 120 gazelles. If the population increase 5% in on year.

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