what is the gcf of 2a³ and a⁶​

an equation to express the relationship between two variables

the equation should be

let the number be x

now product of x and 5. is 5 times x. = 5x

now three less that 5x is given as

5x minus 3

put simply. 5x. - 3

Answer:

rain gauges

Step-by-step explanation:

Answer:

28.26 inches

Step-by-step explanation:

The diameter of the wheel is 3, so the circumference, or distance around the wheel, is 3.14 * 3 (pi times diameter)= 9.42. The wheel goes around 3 times, so 9.42*3=28.26

a) The rate of change of temperature at the point is -1600/√14 °C/m.

b) The direction does the temperature increase fastest at P is by the gradient of T.

c) The maximum rate of increase of temperature at point P is 4200e⁻¹⁴ °C/m.

(a) The rate of change of temperature at point P in the direction towards the point (5, -3, 4) can be found using the directional derivative. The directional derivative is a measure of the rate of change of a function in the direction of a given vector.

To find the directional derivative of T at point P in the direction of the vector v = <5-2, -3-(-1), 4-3> = <3, -2, 1>, we need to take the dot product of the gradient of T at point P with the unit vector in the direction of v:

Evaluating the gradient at P, we get:

∇T(P) = <-1200e⁻¹⁴ , 3600e⁻¹⁴ , -12600e⁻¹⁴ >

The unit vector in the direction of v is:

v/|v| = <3/√14, -2/√14, 1/√14>

So, the directional derivative of T at point P in the direction of v is:

D_v T(P) = ∇T(P) · (v/|v|) = <-1200e⁻¹⁴ , 3600e⁻¹⁴ , -12600e⁻¹⁴ > · <3/√14, -2/√14, 1/√14>

= -1600/√14 °C/m

Therefore, the rate of change of temperature at point P in the direction towards the point (5, -3, 4) is -1600/√14 °C/m.

(b) The temperature increases fastest at point P in the direction of the gradient of T at P. The gradient of T at P gives the direction of steepest ascent of the temperature function at point P.

So, the direction in which the temperature increases fastest at P is given by the gradient of T at P, which is:

∇T(P) = <-1200e⁻¹⁴ , 3600e⁻¹⁴ , -12600e⁻¹⁴

(c) The maximum rate of increase of temperature at point P is given by the magnitude of the gradient of T at P.

So, the maximum rate of increase of temperature at point P is:

|∇T(P)| = √((-1200e⁻¹⁴ )² + (3600e⁻¹⁴ )² + (-12600e⁻¹⁴ )²)

= 4200e^(-14) °C/m

To know more about rate of change here

https://brainly.com/question/29518179

#SPJ4

Answer:

Religion: There were temples and the worship of many gods. Animal sacrifices and complex rituals made some people feel disconnected from Hinduism. Religious beliefs were spread through trade.

Intellectual:

Technology: Gupta metal workers built a huge wrought-iron pillar. Indian doctors practiced Ayurvedic medicine. They could set bones and perform simple surgeries. They also began vaccinating people against smallpox.

Economy:

Buddhism & the Mauryans

Social:

Political: In 321 BCE, Chandragupta Maurya took over the former Magadha kingdom. It became the center of the Mauryan Empire. His government was a highly organized bureaucracy. He worked his way westward to the Indus Valley. The third emperor, Asoka, brought all of India, except the far south, into the empire. He used military strategy to rule.

Religion:

Intellectual: Buddha's teachings and the Four Noble Truths were passed down through oral tradition. Buddhists meditate to find their own truths. Asoka placed stone pillars providing moral guidance all over India (Edicts of Asoka.)

Technology:

Economy: Roads and harbors were built to help trade grow. Royal officials collected taxes.

Step-by-step explanation:

Answer:

= 7×7.5×14.5

= 761.25

800-761.25

= 38.75

so the answer is c

The truck illustrated does not have the space she needs since it has 38.75 cubic feet less space than she needs.

Volume of a three dimensional shape is the space occupied by the shape.

The shape of the truck space is a rectangular prism.

Volume of a rectangular prism = Length × Width × Height

Given that,

Length of the box = 14 1/2 feet = 14.5 feet

Width of the box = 7 feet

Height of the box = 7 1/2 feet = 7.5 feet

Volume = 14.5 feet × 7 feet × 7.5 feet

             = 761.25 feet³

Actual space needed = 800 feet³

Additional space needed = 800 feet³ - 761.25 feet³

                                           = 38.75 feet³

She needs 38.75 feet³ more space than the given truck space.

So the correct option is C.

Hence the truck illustrated does not have the space she needed.

To learn more about Volume, click :

https://brainly.com/question/1578538

#SPJ2

A group contains n men and n women. 2n! number of ways are there to arrange these people in a row if the men and women alternate. Arrangement is known as permutation.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

Learn more about permutation here

https://brainly.com/question/1216161

#SPJ4

The Total weekly revenue of Mae Ling is 570$ with a five percentage commission.  

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Mae Ling earns a weekly salary of $355 plus a 5.0% commission on sales at a gift shop.

Since she sold $4,300 worth of merchandise

Her commission would be = 4300 * 5%

Commission = 4300 * 5/100

Commission = 215$

Her total salary = commission + weekly wage

Her total salary = 215 + 355 = 570

Therefore, the Total weekly salary of Mae Ling is 570$ with a 5 percent commission.

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ1

Answer:

B. The sample proportion would less closely model the population proportion.

Step-by-step explanation:

if they chose 10% and changed it to 5% theres gonna be less data to go by.

The sample proportion would less closely model the population proportion.

Option A is the correct answer.

Random sampling is a statistical method of selecting a sample from a larger population in a way that every individual in the population has an equal chance of being selected.

In other words, random sampling is a process of selecting a subset of individuals from a population in which every member of the population has an equal chance of being chosen.

This helps to reduce bias and increase the likelihood that the sample represents the population accurately.

Random sampling is commonly used in research studies, opinion polls, and market research to draw conclusions about a population based on a smaller sample.

We have,

When the sample size is smaller, there is a higher chance of the sample being unrepresentative of the population, resulting in a larger sampling error.

Therefore, if the student council decided to sample only 5% of the student body instead of 10%, it is more likely that the sample proportion would be less accurate and less closely model the population proportion.

Thus,

The sample proportion would less closely model the population proportion.

Learn more about random sampling here:

https://brainly.com/question/12719656

#SPJ7

Answer:

r=-36

Step-by-step explanation:

The evaluated value of the function f(x) = 3e^(-x+2) - 2 for x = 4 is approximately 0.045.

To evaluate the function, we substitute x = 4 into the given equation and simplify the expression. Plugging in x = 4, we have f(4) = 3e^(-4+2) - 2. Simplifying further, we get f(4) = 3e^(-2) - 2.

Using the approximate value of e as 2.71828, we can calculate the evaluated value. Evaluating 3e^(-2) - 2, we find that f(4) is approximately equal to 0.045 when rounded to three decimal places.

Therefore, when x is 4, the function f(x) = 3e^(-x+2) - 2 evaluates to approximately 0.045.

Learn more about Function

brainly.com/question/30721594

#SPJ11

Answer:

7 over 8

Step-by-step explanation:

Change all the numerators over the least common denominator. 1+4+2 over 8.

Answer:

Step-by-step explanation:

20 miles

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

Learn more about integration :

https://brainly.com/question/18125359

#SPJ4

To find the answer:

1. Remove parenthesis by multiplying the number outside parenthesis

Answer:

Step-by-step explanation:

According to triangle inequality, any side is less than the sum of the other two:

We see contradiction with above when values substituted:

It means we can't form a triangle with given sides

The statement that is not true of unnormalized data is option (d) unnormalized data is multivalued data.

Unnormalized data refers to raw data that has not been organized or processed in any way. It may contain redundancies, inconsistencies, and other issues that make it difficult to work with. However, it does not necessarily involve multivalued data.

Multivalued data refers to data that has multiple values for a single attribute. For example, if a customer can have multiple phone numbers, that data would be considered multivalued. Unnormalized data may or may not have multivalued data, depending on the nature of the data itself.

Therefore, the correct option is (d) unnormalized data is multivalued data

Learn more about raw data here

brainly.com/question/30557329

#SPJ4

The shapes are a cone and cylinder. The surface area of the cylinder is 107 ft² and the approximate surface area of the cone is 254 ft² approximately.

The appropriate shape to model the trunk of the tree is a cylinder and the appropriate shape to model the rest of the tree is a cone.

The surface area of the cylinder can be estimated as:

Surface area of cylinder = 2πr h + 2πr²

where r = radius of the cylinder (half of width of trunk) and h = height of the cylinder (height of tree minus length of branches).

Using the given measurements, estimate the surface area of the cylinder as:

Surface area of cylinder = 2π(1) (30 - 10 - 4) + 2π(1)² = 2π(16) + 2π = 34π ≈ 107 ft²

The surface area of the cone can be estimated as:

Surface area of cone = πr s + πr²

where r = radius of the base of the cone and s = slant height of the cone.

Using the given measurements, estimate the radius of the cone as:

radius = 10/2 = 5 feet

Estimate the slant height of the cone using the Pythagorean theorem:

s² = r² + h²

where h = height of the cone (length of branches) and r = radius of the base.

Using the given measurements, estimate the slant height of the cone as:

s² = (5)² + (10)²

s² = 125

s ≈ 11.2 feet

Using these estimates, estimate the surface area of the cone as:

Surface area of cone = π(5)(11.2) + π(5)² = 56π + 25π = 81π ≈ 254 ft²

Therefore, the approximate surface area of the cylinder is 107 ft² and the approximate surface area of the cone is 254 ft².

Find out more on surface area here: https://brainly.com/question/26403859

#SPJ1

Answer:

Explanation: Im built different

You answer would be mate it would be x=66

Answer:

The width of the tank is approximately 7.9 feet.

Step-by-step explanation:

The pool is a rectangular prism with the following dimensions:

length = 2*x feet

width = x feet

height = 4 feet

With volume equal to 500 cubic feet, therefore:

volume = length*width*height = 500

(2*x)*(x)*(4) = 500

8*x² = 500

x = sqrt(500 / 8)

x = sqrt(62.5)

x = 7.90569 feet

The width of the tank is 7.9 feet.

Answer:

D

Step-by-step explanation:

Area of triangle= ½ ×base ×height

Since the length of the base and the height of the triangle is equivalent to the length of a side of the square, s,

area of triangle

= ½ ×s ×s

= ½s²

Given that the area of the triangle is 12.5 units²,

½s²= 12.5

Multiply both sides by 2:

s²= 12.5(2)

s²= 25

Square root both sides:

\(s = \sqrt{25} \)

s= 5 units

(reject negative value since s > 0)

The exponential model is the most appropriate model for the given data.

The table of values is given as:

x  0  1  2      3    4     5

y  4  8 15.9 32 65.2 128

From the above table, we have the following highlights:

The above highlights is similar to an exponential model, because an exponential model has a constant multiplicative rate

Hence, the appropriate model is the exponential model

Read more about exponential models at:

https://brainly.com/question/11464095

#SPJ1

To complete the table for the cards that Simon picks, we need to express the probabilities in terms of the given variables r and t. Since Simon is picking a card from each box, we have two independent events: picking a shape (triangle or square) and picking a color (red or blue).

The table can be completed as follows:
The probability of picking a triangle and a red card is given by tr, as these are independent events.
The probability of picking a triangle and a blue card is given by t(1 - r), as we are picking a triangle (t) and a card that is not red (1 - r).
The probability of picking a square and a red card is given by (1 - t)r, as we are picking a card that is not a triangle (1 - t) and a red card (r).
The probability of picking a square and a blue card is given by (1 - t)(1 - r), as we are picking a card that is not a triangle (1 - t) and a card that is not red (1 - r).
In summary, the probabilities in the table can be expressed in terms of r and t as follows:
Triangle and red card: tr
Triangle and blue card: t(1 - r)
Square and red card: (1 - t)r
Square and blue card: (1 - t)(1 - r)

Learn more about probabilities here
https://brainly.com/question/30034780

#SPJ11

Answer:

the answer would be a % because of the divisibility rule

After considering the given data we conclude that the given width of the rectangle is 5x - 8, under the condition that the given area of the rectangle is 35x²-36x-32 and length of the rectangle is 7x + 4.

To evaluate the width of a rectangle given its area and length, we can apply the formula:
width = area / length
As we all know the area of the rectangle is 35x²-36x-32 square inches and its length is 7x + 4 inches.
So, staging these values in the formula above, we get:
width = (35x²-36x-32) / (7x + 4)
Here we have to perform polynomial division.  
(35x²-36x-32) / (7x + 4)
= (5x - 8)(7x + 4) / (7x + 4)
= 5x - 8
Therefore, the measure of the width is  5x - 8.
To learn more about polynomial division
https://brainly.com/question/12520197
#SPJ1

Answer:

2.3333333333333333333333333333333 sec

A window cleaner charges £0.55 pence to clean each window.

Replace the variable inside the equation with the given integer. Words on both of the equation's sides should be made simpler. Check to see whether the resultant equation is correct. The figure is a solution if it is accurate.

Any value of a variable that makes both Left Hand Sides (LHS) as well as the Right Thumb Half (RHS) of the solution equal is considered a solution to the problem. To solve an equation, one must identify its solution or solutions.

A window cleaner assigns n pence to wash each window, and for a cottage, with 9 windows, he arrests £4.95.

Then the equation is given as,

9n = £4.95

Simplify the equation, then we have

9n = £4.95

n = £4.95 / 9

n = £0.55 per window

A window cleaner charges £0.55 pence to clean each window.

To know more about Solution of the equation visit:

https://brainly.com/question/29964751

#SPJ1

The amount of money Rashon would need to invest is equal to $8,300.46.

Mathematically, the compound interest on an investment can be calculated by using this mathematical expression:

A(t) = P(1 + r/n)^{nt}

Where:

In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:

Quarterly interest rate = 0.069/4

Quarterly interest rate = 0.01725%

20,200 = P(1 + 0.01725)^{4 × 13}

20,200 = P(1.01725)^52

20,200 = 2.4336P

Principal, P = 20,200/2.4336

Principal, P = $8,300.46.

Read more on interest rate here: brainly.com/question/26343258

#SPJ1

Answer:

In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:

Quarterly interest rate = 0.069/4

Quarterly interest rate = 0.01725%

20,200 = P(1 + 0.01725)^{4 × 13}

20,200 = P(1.01725)^52

20,200 = 2.4336P

Principal, P = 20,200/2.4336

Principal, P = $8,300.46.

Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.