simplify 6^5 * 2^3 * 6^4 / 12^3

^ is elevated
* multiplication
/ division

The distance between points A and B is 14 units.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

According to the number line,

Point A lie at - 2 on the number line and point B lie at 12 on the number line.

Now from 0 to point B,

The distance between point 0 and B is 12 units.

And from point A to 0 the distance is 2 units.

Therefore,

The total distance between points A and B will be:

AB = AO + OB

AB = 2 units + 12 units

AB = 14 units

Hence, the correct option is (D) 14 units.

Learn more about number line here:

https://brainly.com/question/25230781

#SPJ9

The number of miles when the cost would be the same is 40 miles.

The equation that represents the total cost for car rentals is a linear function. A linear function is a function with a single variable that is raised to the power of one. A linear function is a straight line when drawn on a graph.

Total cost = constant cost + (cost per mile x number of miles driven)

First rental : $15 + (0.50 x m)

$15 + 0.50m

Second rental : $25 + (0.25 x m)

$25 + 0.25m

When the cost is the same for the car rentals, the two equations would be equal:

$15 + 0.50m = $25 + 0.25m

$25 - $15 = 0.50m - 0.25m

$10 = 0.25m

m = 10 / 0.25

m = 40 miles

To learn more about linear equations, please check: https://brainly.com/question/25711114

#SPJ1

Answer:

70

Step-by-step explanation:

as the discount is 20 thus the original price would be 70

======================================================

Explanation:

E = event space = {1}

The event space is the set of things we want to happen. There's only one outcome and it's the "1" (since it's smaller than 2)

S = sample space = {1,2,3,4,5,6}

There are 6 items in the sample space.

Divide the two counts to get the fraction 1/6 which is the probability of rolling a result less than 2. In other words, the probability of landing on "1" is 1/6 since there's one face with that label out of 6 faces total.

Side note: 1/6 = 0.1667 = 16.67% approximately

There are √34 miles between the house and the library

The given parameters are

Distance between house and market, x = 3 miles

Distance between market and library, y = 5 miles

The number of miles between the house and the library is calculated as

Distance = √x² + y²

Substitute the known values in the above equation

So, we have

Distance = √3² + 5²

Evaluate the exponents in the above equation

So, we have

Distance = √9 + 25

Evaluate the sum in the above equation

So, we have

Distance = √34

Hence, there are √34 miles between the house and the library

Read more about right triangles at

https://brainly.com/question/28757043

#SPJ1

The number of possible combinations of ring and bracelet she has is 78

The given parameters are

Rings = 13

Braceletes = 6

The number of possible combinations of ring and bracelet she has is calculated by multiplying the number of rings and the number of bracelets

This is represented as

Possible combination = Rings x Braceletes

Substitute the known values in the above equation

So, we have

Possible combination = 13 * 6

Evaluate the product in the above equation

So, we have

Possible combination = 78

This means that she has 78 possible combinations of ring and bracelet

Hence, the number of possible combinations of ring and bracelet she has is 78

Read more about combination at

https://brainly.com/question/11732255

#SPJ1

The statement is true that the lines are neither perpendicular nor parallel.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

Slope tells how vertical a line is thus more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

The Slope of parallel lines are same, similarly Slopes of perpendicular lines are negative reciprocal of each other.

Parallel lines have the same slope beacuse the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

If there are two lines perpendicular to each other, then their slopes are negative reciprocal of each other meaning if one line's slope is 'a', then its perpendicular line's slope would be -1/a

We have been given that the slope of line a is 5 and the slope of line b is 1/5.

The statement is true that the lines are neither perpendicular nor parallel.

Learn more about slope here:

https://brainly.com/question/2503591

#SPJ1

Answer:

It would take 5 mechanics to repair 22 cars in 5 hours

Step-by-step explanation:

2 garage mechanics take 3 hours to repair 6 cars.

to repair 1 car, 1 garage mechanics take = (2×3)/6 = 1 hour

So In 1 hour, 1 car can be repaired by 1 mechanic

22 cars can be repaired in 1 hour by = 22/1 = 22 mechanics

22 cars can be repaired in 5 hours by = 22/5 = 4.4 = 5 mechanics

(4.4 mechanics are not possible. There should be 5 mechanics)

Answer:

12 hours

Step-by-step explanation:

First, figure out her hourly rate

Next, divide 252 by the hourly rate to figure out how many hours he will have to work

Multiply the hourly rate by number of hours worked to check your answer

At a rate of $21 per hour, he has to work for 12 hours to make $252.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Ravi made $378 for 18 hours of work.

So, Ravi's unit rate or earnings per hour is $(378/18).

= $21.

Now, In one hour he makes $21.

Therefore, To make $252 he has to work (252/21) hours.

= 12 hours.

So, Ravi has to work for 12 hours to make $252.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ2

It should be noted that when Albert uses a grid to multiply 27 by 13, the product that will be gotten will be 351.

What isn't a product?

It should be noted that in mathematics, a product or an expression that specifies factors to be multiplied is the outcome of multiplication.

The multiplicand, multiplier, and product are the components of a multiplication sentence. The first number is the multiplicand, the second number is the multiplier, and the result is the product.

It should be noted that based on the information, we want to multiply 27 and 13. This will be illustrated thus:

= 27 × 13

= 351

Therefore, when when Albert uses a grid to multiply 27 by 13, the product that will be gotten will be 351.

Note that the information is incomplete and was solved based on the available information given.

Learn more about multiplication on:

https://brainly.com/question/10873737

#SPJ1

Answer:

[-2,infinitysymbol)

Step-by-step explanation:

If you have a graph to look at, the domain is like you are walking up and down the x-axis (which is actually not up/down but left/right) and you're stating where this graph exists.

If you walked all the way over to -10 and looked up or down, the graph just doesn't exist over there.

The graph exists from -2, including -2, so use the SQUARE bracket [.

On the right side there's an arrow on the graph so it keeps going forever. Thats infinitysymbol.

Always wrap a parenthesis ), around the infinity symbol.

Interval notation uses the [SQUARE] brackets or (parenthesis) and even though it looks like a point, its not. It means

[FromHere, ToHere) and answers the question, where is the graph?

Answer:

y = 1.2x

Step-by-step explanation:

The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is

y = 1.2x

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 4 is an equation.

We have,

Pilar:

Cost of 2 cans of dog food = $2,40

We can write this as an equation:

2 = 2.40 ____(1)

Leo:

Cost of 3 cans of dog food = $3.60

We can write this as an equation:

3 = 3.60 ____(2)

From (1) and (2) we get,

The cost of dog food y is proportional to 1.2 of the cans of dog food x.

y = 1.2x

Thus,

The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is

y = 1.2x

Learn more about equations here:

https://brainly.com/question/27996921

#SPJ2

In the equation b = a -2, which variable is the independent variable and which is the dependent variable ? Explain.

In the given equation b=a-2, a is an independent variable and b is an dependent variable.

Independent variable is variable whose values are unaffected by changes is referred to as an independent variable.

The dependent variable is defined as the variable whose evaluation of the independent variable determines the quality of the dependent variable.

For example, y=x+5

Here, According to changes in the evaluation of the variable "x," the estimation of the variable "y" also varies. The variable "y" is referred to as an dependent variable and the "x" is referred to as an independent variable.

Therefore, In the equation b=a-2, "a" is an independent variable and "b" is an dependent variable.

To learn more about independent variable visit: https://brainly.com/question/1479694

#SPJ9

Answer:

1.55 is the correct answer

Answer:

If you like to round 1.553 to the nearest hundredth, leaving only two numbers after the decimal point, then ask your teacher for help instead of letting yourself down. The result you'll get is 1.55

Step-by-step explanation:

Number Rounded to Nearest 100th

1.553 1.55

1.554 1.55

1.555 1.56

1.556 1.56

1.557 1.56

1.558 1.56

1.559 1.56

1.56          1.56

1.561 1.56

1.562 1.56

Based on the given numbers, the number that is divisible by 4 are: 152, 76, and 4,788.

The numbers that are divisible by four need to meet certain requirements and the first one is that they should end in an even number.

The numbers divisible by 4 are:

= 152/4 = 38

= 76 / 4 = 19

= 4,788 / 4

= 1,197

This shows that these numbers are divisible by 4.

In conclusion, the numbers that are divisible by 4 are 152, 76, and 4,788.

Find out more on numbers divisible by 4 at https://brainly.com/question/207338

#SPJ1

Based on the given values in the table that shows different speed-distance-time relationships, the value of A is 140 meters and the value of B is 3 hours.

To find the distance, the formula is:
= Speed x time

The distance of A is:

= 35 x 4

= 140 meters

To find the time taken, the formula is:
= Distance / speed

The time in B is:

= 81 / 27

= 3 hours

Find out more on finding distance at https://brainly.com/question/26046491

#SPJ1

The scatter plot is shown in attached images and the line of best fit for the data set is y=24.6607x+24.7637.

The given data set is (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396).

Plot the points on a coordinate plane.

Calculate the mean of the x -values and the y -values.

[tex]\begin{aligned}\bar{X}&=\frac{3+5+7+9+11+13+15}{7}\\ &=\frac{63}{7} \text{ or } 9\\ \bar{Y}&=\frac{100+150+195+244+296+346+396}{7}\\ &=\frac{1727}{7}\text{ or }246.71\end[/tex]

Now, we will calculate the [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})[/tex] and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}[/tex], we get

[tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}=112[/tex]

and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})=2762[/tex]

Calculate the slope.

[tex]\begin{aligned}m&=\frac{\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})}{\sum_{i=1}^{n}(x_{i}-\bar{X})}\\ &=\frac{2762}{112}\\ &=24.6607\end[/tex]

Calculate the y -intercept.

Use the formula to compute the y -intercept.

[tex]\begin{aligned}b&=\bar{Y}-m\bar{X}\\ &=246.71-(24.6607\times 9)\\ &=246.71-221.9463\\ &=24.7637\end[/tex]

Use the slope and y -intercept to form to find the equation of the line of best fit.

The slope of the line is 24.6607 and the y -intercept is 24.7637 .

Therefore, the equation is y=24.6607x+24.7637.

Draw the line on the scatter plot.

Hence, the scatter plot is shown in attached image and the line of best fit for given data set (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396) is y=24.6607x+24.7637.

Learn more about the scatter plot from here brainly.com/question/27841050

#SPJ4

Answer:
x= 7+y/2

The slope is 2

Step-by-step explanation:

A) 0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is

left-handed.

B) 0.10 is part of this interval and as such we can say that it is a plausible estimate for the proportion of the population that is

left-handed.

C) 0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is

left-handed.

We are given that;

Population that is left-handed = 0.10

Margin of error =0.02.

A) Confidence interval = 0.07 ± 0.02

CL = (0.05, 0.09)

0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is

left-handed.

b) Confidence interval = 0.087 ± 0.02

CL = (0.067, 0.107)

0.10 is part of this interval and as such we can say that it is a plausible estimate for the proportion of the population that is

left-handed.

c) Confidence interval = 0.128 ± 0.02

CL = (0.108, 0.148)

0.1 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is

left-handed.

Read more about Confidence Interval at; https://brainly.com/question/17097944

#SPJ1

According to the question, the given rational expression can be simplified and as shown below:

Rational expression = [tex]\frac{4x^{2} }{5y}.\frac{7y}{12x^{4} }[/tex]

To simplify the given rational expression, calculate the factors of the numerator as well as denominator. And later divide it from each other. These expressions are also called as polynomial expressions.

Rational expression = [tex]\frac{1}{5}.\frac{7}{3x^{2} }= \frac{7}{15x^{2} }[/tex]

The final expression of the given equation is [tex]\frac{7}{15x^{2} }[/tex].

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

To learn more about the polynomial expression from the given link:

https://brainly.com/question/1280754

#SPJ4

In mathematics, an inverse function is one that "reverses" another function. The inverse of the function y = 5 - 2x²  is f ⁻¹(x) = √2(−x+5)/2, −√2(−x+5)/2

The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f exists bijective.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

Interchange the variables.

x = 5 − 2y²x = 5 - 2y²

Solving for y

y = √2(−x+5)²y = 2(-x+5)²

y = −√2(−x+5)²y = -2(-x+5)²

Replace y with f ⁻¹(x)

f ⁻¹(x)=√2(−x+5)²,−√2(−x+5)² f ⁻¹(x)=2(-x+5)²,-2(-x+5)²

The inverse of the function y = 5 - 2x²  is f ⁻¹(x) = √2(−x+5)/2, −√2(−x+5)/2.

To learn more about inverse function, refer to:

brainly.com/question/11735394

#SPJ4

There is no solution for the equation 2 + √x + 5 = 4 for x ∈ R.

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Consider the equation,

2 + √x + 5 = 4

√x + 7 = 4

Subtracting 7 from each side of the equation.

√x + 7 - 7 = 4 - 7

√x = - 3

Since √f(x) cannot be negative for x ∈ R.

Hence, there is no solution for x ∈ R of the equation.

Learn more about equations here:

https://brainly.com/question/2972832

#SPJ9

Answer:

9,

Step-by-step explanation:

The equation to find the volume in terms of P, n, R , and T is:

[tex]V=\frac{n R T}{P}[/tex]

The ideal gas law is the general gas equation. It is a good approximation to find behavior of gases under different conditions. This law says that the product of pressure in the atmosphere and volume is equal to product of moles and temperature. We generally use an equation to define these relations.

Equation of ideal gas law

P V=n R T

where,

P = pressure measured in atmosphere

V = volume measured in liters

n = number of moles present in gas

T = temperature

R = gas constant

Ideal gas equation shows several direct and indirect variations between the different elements ,  such as in the equation pressure (P) shows direct variation with n and T , and inverse variation with volume (V).

To know more about ideal gas equation, visit :

brainly.com/question/4147359

#SPJ4

Answer:

It is not a function because the number 4 (input) is being used more then once

Based on the total cost of making hamburgers, and the cost per hamburger the equation to find the number of hamburgers made is 13,025 = 2.05x + 2,000

The cost of a single hamburger is $2.05 and this is in addition to a fixed cost of $2,000 for fixed costs.

This means that the number of hamburgers x, can be found by the formula:
Total cost of hamburgers = Cost per hamburger x Number of hamburgers + Fixed costs

Using x and the given figures gives:
13,025 = 2.05x + 2,000

Find out more on the total cost at https://brainly.com/question/21305974

#SPJ1