An art teacher has 2,532 crayons. He plans to give 12 crayons to each student who takes his class. How many students take his art class?

The translations performed are

From the question, we have the following function that can be used in our computation:

f(x) = ln(x)

g(x) = -ln(x + 1) - 3

First, we have the transformation to be:

From f(x) = ln(x) to f(x) = -ln(x)

This means a reflection across the x-axis

Next, we have

From f(x) = -ln(x) to f(x) = -ln(x + 3)

This means the function is translated left by 3 units

Next, we have:

From f(x) = -ln(x + 3) to f(x) = -ln(x + 3) - 3

This means the function is translated down by 3 units

Hence, the translation is 3 units left and 3 units down

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The area of the figure is 75  + 25π/4 squared unit. The value of the blank is 75

(Consider the image I attached)

The area of the figure = Area of rectangle A + Area of square B + Area of sector C

The area of the figure = (L×W) + (L²) + (θ/360 × πr²)

Note: Area of sector = θ/360 × πr². The sector has an angle of 90° and a radius of 5

The area of the figure = (10×5) + (5²) + (90/360 × π×5²)

The area of the figure = 50 + 25 + 25π/4 = 75  + 25π/4 squared unit

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3±2√3 much longer is the longer leg when in a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.

Given that,

In a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.

We have to find how much longer is the longer leg.

We know that,

Let the one side of the triangle be x

The other side we get x-1 and x+2

From Pythagoras theorem,

x²+(x-1)²=(x+2)²

x²+x²-2x+1=x²+4x+4

2x²-2x+1-x²-4x-4=0

x²-6x-3=0

To find the value of x we have a formula that is

x=-b±√(b²-4ac)/2a

Here, a=1, b=-6 c=-3

x=6±√(-6²-4(1)(-3))/2(1)

x=6±√36+12/2

x=6±√48/2

x=6±4√3/2

x=3±2√3
Therefore, 3±2√3 much longer is the longer leg when in a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.

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By using regression, it can be calculated that-

The response variable is a dependent variable

Option a is correct

What is regression?

The process which is used to find a relationship between a dependent variable and one or more independent variables is called regression

In regression analysis, the variable which is to be predicted is called response variable.

Since response variable is the variable to be predicted, response variable is dependent on other variables

So response variable is a dependent variable

Option a is correct

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The ladder is 13.15 feet long.

"Information available from the question"

In the question:

A ladder is placed against the side of a house.

The base of the ladder rests 2 feet from the house

and, the top of the ladder meets a window sill that is 13 feet up from the ground.

To find the how long is the ladder?

Now, According to the question:

Let's Know:

What is Pythagoras theorem?

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle), algebraic notation,

a² + b² = c².

The set is making a right triangle, so using Pythagoras theorem,

base² + (wall length)² = (length of ladder)²

2²+13² = (length of ladder)²

169+4 = (length of ladder)²

173 = (length of ladder)²

(length of ladder) = √173

(length of ladder) = 13.15

Hence, The ladder is 13.15 feet long

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Answer:

173

Step-by-step explanation:

Did it

The solution to the equation -2.5(4x - 4) = -6 is x = 1.6

From the question, we have the following parameters that can be used in our computation:

-2.5(4x - 4) = -6

Open the bracket using the Distributive Property

So, we have the following representation

-10x + 10 = -6

Subtract 10 from both sides of the equation

-10x = -16

Divide both sides by -10

x = 1.6

Hence, the solution is x = 1.6

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Answer:

72 seconds I think I am sorry if it is wrong

1. The actual differences that researchers imply causality come from randomized experiments.

2.  That the sample selected represents the population.

3. Confidence level clearly stated.

Population values, also called parameters, are calculated from all values ​​in the entire population.

A representative sample is a subset of the population that attempts to accurately reflect the characteristics of the larger group. For example, in a classroom of her 30 students, 15 boys and 15 girls, you can create a representative sample of her 6 students, 3 boys and 3 girls.

Probable sampling is defined as a sampling technique in which the researcher selects samples based on the researcher's subjective judgment rather than at random. This is a less rigorous method. This sampling method relies heavily on the researcher's expertise. This is done through observation and is often used by researchers for qualitative research.

A confidence interval (CI) is the range of estimated values ​​for an unknown parameter. Confidence intervals are computed at the specified confidence level. A 95% confidence level is the most common, but other levels such as 90% and 99% are sometimes used. The confidence level represents the proportion of corresponding CIs over time that contain the true value of the parameter. For example, 95% of all intervals computed at the 95% level must contain the true value of the parameter.

Factors that affect the width of the CI include confidence level, sample size, and intra-sample variation. All other things being equal, the larger the sample, the narrower the confidence interval. Similarly, the greater the sample variability, the wider the confidence interval, and the higher the confidence level, the wider the confidence interval should be.

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Based on the observation the appropriate domain of the function is 12.5.

A relation is a function if it has only One y-value for each x-value.

Given, a company manufactures and sells shirts.

The daily profit the company makes depends on how many shirts they sell.

The company sell x shirts can be found by function f(x)=7x-80

The given function is f(x)=7x-80

f(-7)=7(-7)-80=-49-80

=-129

The value is negative so it is not the answer.

f(8)=7(8)-80

=56-80=-24

The value is negative so it is not the answer.

f(12.5)=7(12.5)-80

=87.5-80

7.5

The company sells 12.5 shirts.

Hence, based on the observation the appropriate domain of the function is 12.5.

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Identifying Correlation helps in presenting solutions to be explored.

What is Correlation?

Correlation is a statistical metric (a number) that represents the magnitude and direction of a link between two or more variables. A correlation between variables, on the other hand, does not imply that a change in one variable is the cause of a change in the values of the other variable.

Solution:

Identifying Correlation helps in presenting solutions to be explored.

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Answer:

i got 6.6, 2.9, and 50 but i don't think it's right

Step-by-step explanation:

The equation of the function in vertex form is y = -(x + 5)² + 4

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

Given that the quadratic function has roots at -3 and -7 and a vertex at (-5,4).

We need to find the equation of the function in vertex form

equation of the function in vertex form.

As per the information given in the question,

The given roots of the function are -3 and -7,

y = a (x + 3) (x + 7)

y = a (x² + 10x + 21)

y = a (x² + 10x + 25 − 4)

y = a (x² + 10x + 25) − 4a

y = a (x + 5)² − 4a

The vertex is (-5, 4),

So, a = -1.

y = -(x + 5)² + 4

Hence, y = -(x + 5)² + 4  is the equation of the function in vertex form

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Answer:

[tex]5x \geq 15\\x\geq 3[/tex]

Step-by-step explanation:

5 times x must be greater than or equal to 15, thus the inequality is

[tex]5x \geq 15[/tex]

To solve, pretend the [tex]\geq \\[/tex] is an = and solve, putting back the [tex]\geq[/tex] for the final answer

[tex]5x \geq 15\\5x = 15\\5x/5 = 15/5\\x = 3 \\x \geq 3[/tex]

However, it’s possible to notice clouds moving vertically. That is, at one point you might see a cloud much lower slightly rise up further in the sky. This is due to convection, which is rising hot air from the ground moving upwards. This hot air can cause clouds to move upwards where the air is colder.

Answer:

Physical change

Step-by-step explanation:

Answer:

y - 14 = -0.5(x + 9)

By using function, it can be concluded that-

The predictor variables are bed, bath, floor

What is function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

In a function y = f(x), x is the independent variable and y is the dependent variable.

The price of an apartment is dependent on the number of bedrooms, bathrooms and the floor of the apartment

So the required function is p = f(bed, bath, floor) where p is the price of the apartment

The predictor variables are bed, bath, floor

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Answer:

y=-9

Step-by-step explanation:

If  equation y = 6200x represents the number of miles, y, that the satellite Space Explorer flies in a hours then 6200 is the rate of change.

Two or more expressions with an Equal sign is called as Equation.

The given equation is y = 6200x

y equal to six thousand two hundred times of x.

y = 6200x represents the number of miles, y, that the satellite Space

Explorer flies in a hours.

We need to find the rate of change.

Rate of change means how quickly something changes over time.

Differentiate the equation with respect to x

dy/dx=6200

Hence, the rate of change is 6200.

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Answer:

Step-by-step explanation:

I think it's B or C because if you look closely u see that the line goes up then straight on 4. Go for an educational guess.

Equation which represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced is 7w=20t

Two or more expressions with an Equal sign is called as Equation.

Given that Seven out of every twenty soda bottles produced have caps indicating that the purchaser has won a prize.

We need to find the equation which  represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced.

Let w represent the number of bottles with winning caps, and

let t represent the total number of bottles produced.

t=7/20w

7w=20t.

Hence, 7w=20t is the equation represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced.

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Answer:

Step-by-step explanation:

A Commission

The extra 2% of the sales dollars that Padma receives each month is called a commission.

The commission is a payment made to an employee in addition to their regular salary or wages, based on the number of sales or business they bring in. Another popular definition of commission is the amount of money earned by an employee when they sell something: He receives a 1% commission on each sale in addition to his pay.

As per the question, Padma receives a commission of 2% of the sales dollars she brings in each month. The commission is a common form of compensation in sales and customer service jobs, where employees are often paid a base salary plus a commission based on their sales or performance.

Thus, the required fill-in-the-blank will be "commission".

Hence, the extra 2 percent of the sales dollars that Padma receives each month is called a commission.

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The surface area of that part of the plane 6x+10y+z=9 that lies inside the elliptic cylinder [tex]x^{2}/49 + y^{2}/9 =1\\[/tex] is 21 [tex]\pi[/tex] [tex]\sqrt{137\\[/tex].

Given:

6x + 10y + z = 9  ..... (1)

[tex]x^{2}/49 + y^{2}/9 =1\\[/tex] ..... (2)

Equation (1) can also be written as:

z = 9 - 6x - 10y ...... (3)

The surface area is given by the equation:

SA = ∫∫[tex]\sqrt{((df/dx)^2) + (df/dy)^2 + 1} )dA[/tex]

[tex]\sqrt{df}/dx = -6[/tex]

[tex]\sqrt{df}/dy = -10[/tex]

Now, substitute the known values in equation (4).

SA = ∫∫[tex]\sqrt{(-6)^2 + (-10)^2 + 1} dA[/tex]

SA =[tex]\sqrt{137}[/tex]  ∫∫dA

Now the area enclosed by an ellipse is given by:

[tex]x^{2}/49 + y^{2}/9 =1\\x^{2}/a^2 + y^2/b^2=1\\[/tex]

By comparing the above equation:

a = 7

b = 3

The area is given by:

SA = [tex]\sqrt{137}[/tex] [tex]\pi[/tex] (7 x 3)

SA = 21 [tex]\pi[/tex] [tex]\sqrt{137\\[/tex]

The surface area of an elliptic cylinder is 21 [tex]\pi[/tex] [tex]\sqrt{137\\[/tex].

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Answer:

Step-by-step explanation:

f+5

The required explanation of null hypothesis and alternate hypothesis for given question is below.

Hypothesis testing is a type of measurable derivation that utilizes information from an example to make inferences about a populace boundary or a populace likelihood circulation. Initial, a speculative supposition that is made about the boundary or dissemination.

Connection is a factual measure that communicates the degree to which two factors are directly related (meaning they change together at a consistent rate).

It's a typical device for portraying basic connections without saying something about circumstances and logical results.

As indicated by the inquiry,

A gathering of researcher haphazardly chose 20 Piknits from the ocean bottom and estimated their particular loads in grams.

Likewise, They were curious as to whether the weight of the Piknits can be utilized to foresee the quantity of Gogles.

From the given data,

Null hypothesis : H0 : There is no direct connection between the heaviness of piknits and the quantity of gogles

Alternative hypothesis : Ha: There is a direct connection between the heaviness of piknits and the quantity of gogles

Choice 4 is right about Null hypothesis and Alternative hypothesis.

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The number met between the town are

mitten = 67,137

kittens = 50

cats = 1680

rats = 67,200

bags = 56

nags = 7

Browns = 8

From the given information it can be deduced that

John Brown, and seven daughters

Browns = 1 + 7 = 8

everyone had seven bags

number of bags = 8 * 7 = 56 bags

In every bag there were thirty cats

number of cats = 56 * 30 = 1680 cats

the number of kittens = 50

every cat had forty rats

number of rats = 1680 * 40 = 67,200 rats

all but the nags and bags wore mittens.

number of mittens = 67 200 - the nags (Brown's daughters) - the bags

number of mittens = 67 200 - 7 - 56 = 67 137

The number of mittens is 67,137

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The sample size would be required is 400.

What is standard deviation?

A measure of a group of values' variance or dispersion in statistics is called the standard deviation. When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.

The lowercase Greek letter sigma, which stands for the population standard deviation, or the Latin letter s, which stands for the sample standard deviation, are most frequently used in mathematical equations and texts to represent standard deviation. Standard deviation is also sometimes referred to as SD.

suppose that in a random sample of size 100, the standard deviation of the sampling distribution of the sample proportion is 0.08.

Since we know the weights from the population, we can find the population mean.

μ = 0.08

if a researcher wanted to reduce the standard deviation to 0.04.

Hence, The sample size would be required is 400.

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Square 1 is so named because of the shape of the puzzle: it is a cube with four sides, each with nine squares, creating a square shape

The puzzle is also sometimes referred to as a "magic cube" because it can be rearranged into different shapes and configurations.Square 1 is a 3-dimensional puzzle that consists of nine squares on each side of a cube. The puzzle is made up of four layers of nine colored squares that can be rotated around the center axis. This creates a square-like shape, hence the name “Square 1”. The object of the game is to arrange the nine squares on each side so that all of the colors match up. This requires the player to manipulate and rotate the pieces in order to achieve the desired outcome.

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Mario left 65 miles to reach his goal and m + 65 = 130 is the equation to show how many miles Mario has left to run this month to reach his goal

Two or more expressions with an Equal sign is called as Equation.

Given that the Mario set a goal to run 130 miles this month to prepare for a marathon.

He has run 65 miles in this month.

We need to find the equation to show how many miles Mario has left to run this month to reach his goal.

m+65=130

We can find the left out distance in miles.

Subtract 65 from both sides.

m=130-65

m=65

Hence, m + 65 = 130 is the equation to show how many miles Mario has left to run this month to reach his goal and Mario left 65 miles to reach his goal.

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Answer:

it's b

Step-by-step explanation:

Total 83 numbers that are positive perfect squares less than [tex]10^6[/tex] are multiples of 24.

What is perfect Square?

A perfect square is a number that can be written as the second exponent of an integer or as the product of an integer by itself.

For instance, the number 25 is a perfect square since it is the product of the integer 5 multiplied by itself, 5*5 = 25.

21 cannot be expressed as the product of two identical integers, so it is not a perfect square number.

Prime Factorization of 24 is 2^3*3.

There must be at least 3 factors of number 2 and 1 factor of number 3 in each square.

its square root must have 2 factors of number 2 and 1 factor of number 3.

This means each square should be in the from [tex](12*c)^2[/tex]. where 12 is a positive numbers less than [tex]\sqrt{10^6}[/tex]  = 1000.

So total numbers of positive perfect squares.

= 1000/12 = 83.

Total 83 numbers that are positive perfect squares less than [tex]10^6[/tex] are multiples of 24.

Given question is incomplete Complete Question here

How many perfect squares less than 10^6 are multiples of 24.

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