What is the value of x?

The exact value of the minimum of function  f(x) = x^2 e^−x for x ≥ 0 is f(x) = 0

In this question we have been given a function  f(x) = x^2 e^−x

We need to find the exact value of the minimum of function for x ≥ 0.

Consider the first derivative of the function

f'(x) = x^2 f/dx(e^−x) + e^−xd/dx(x^2)

f'(x) = -x^2 e^(-x) + e^-x (2x)

f'(x) = xe^-x (2 - x)

To find the critical points., consider f'(x) = 0

xe^-x (2 - x) = 0

xe^-x = 0,   (2 - x) = 0

x = 0, x = 2

Substitute the value of critical point into the function.

f(0) =  0^2 e^(0)

f(0) = 0

and f(2) =  2^2 e^-2

f(2) = 0.5413

This means, the minimum of the function occurs at x = 0

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A) The value of h, h = 2r.

The height of the can is two times of the radius.

B) The formula for the Can Area is  4πr².

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

For a can with radius r and height h, this goal is reached when

2 πr³= πr²h

a) 2 πr³= πr²h

Solve for 'h'

h= 2 πr³ / πr²

h = 2r

So, the height of the can is two times of the radius.

b) Now, The area of a label for a can is A=2 πrh.

So, putting h= 2r

Area, A = 2 πrh

            = 2πr(2r)

            = 4πr²

So, the formula for the Can Area is  4πr².

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If MX, MY, sX, and sY are known, the additional number that would be the most helpful to know for calculating the regression line for X and Y is r.

In the context of simple linear regression, r means the correlation between the predictor variable, x, and the response variable, y. And r² means the proportion of the variance in the response variable which can be explained by the predictor variable in the regression model.

It is also considered as denotation of the Pearson correlation coefficient, that is a measure of any linear trend between two variables. The value of r ranges between −1 and 1. When r = zero, it means that there is no linear association between the variables.

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The average rate of change of the number of chevy car sales from 1990 to 1992 is 1

What is the average change rate?

The average rate of change is the rate at which one value in a function changes in relation to another. Usually, the average rate of change is used to calculate the slope of a graphed function.

The average rate of change of a function is determined by the slope of the line connecting the two endpoints of a specific interval (known as the secant line).

According to the given question:

The average rate of change of the number of chevy car sales from 1990 to 1992 is (total chevy car sold in 1992- total chevy car sold in 1990)/ Total difference in no. of years

That gives (156-154)/2

So, the average rate of change of the number of chevy car sales from 1990 to 1992 is 1

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The slope of the line is 2/3.

What is a line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

Given coordinates of the points are A(1,-9) and (4,-7).

The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

Here x₁ = 1, y₁ = -9, x₂ = 4, and y₂ = -7

m = (-7 - (-9))/(4 - 1)

m = 2/3

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Answer:

What is scenario 6-9?

Step-by-step explanation:

Yes, the instructor should use linear regression to predict exam scores for a student who studied 10 hours for the final.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Nonlinear regression uses a curve to associate the variables, whereas linear regression uses a straight line.

If a clear linear relationship can be shown on the scatterplot, linear regression may be useful. The use of linear regression is appropriate because there is a high correlation. So, it is concluded that it is beneficial for instructor to use linear regression.

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It is proved that the difference between squares of consecutive even numbers is always a multiple of 4.

Let's consider two consecutive even numbers.

If n = a positive integer

Then the 1st even number would be = 2n

Let the next consecutive even number = 2(n+1)

The consecutive even numbers would be:

2n, 2(n+1)

The square of each consecutive even number is given by -

(2n)² = 2n ×2n = 4n²

[2(n+1)]² = (2n+2)² =(2n+2)(2n+2)

Expanding, we get,

= 4n² +4n +4n+4

[2(n+1)]² = 4n²+8n+4

To determine if the difference between squares of consecutive even numbers is always a multiple of 4, we would substitute values for ' n ' to find the differences between the squares of each consecutive even number.

Let n = 1, 2, 3

For n= 1,

4n² = 4(1)² = 4×1 = 4

4n²+8n+4 = 4(1)² + 8(1) + 4

= 4+8+4 = 16

Thus, the difference between the squares of consecutive even numbers = 16-4 = 12

For n= 2,

4n² = 4(2)² = 4×4 = 16

4n²+8n+4 = 4(2)² + 8(2) + 4

= 16+16+4 = 36

Thus, the difference between the squares of consecutive even numbers = 36-16 = 20

For n= 3

4n² = 4(3)² = 4×9 = 36

4n²+8n+4 = 4(3)² + 8(3) + 4

= 36+24+4 = 64

Thus, the difference between the squares of consecutive even numbers = 64-36 = 28

Clearly, we can see that 12, 20, and 28 are multiples of 4.

Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.

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Answer:

£9.40

Step-by-step explanation:

Given variables:

Defined variables:

1 pound = 100 pence  ⇒  1 pence = 0.01 pounds

Therefore, the equation that models the given scenario is:

[tex]y = 0.01px +f[/tex]

Given:

Substitute the given information into the equation to create two equations:

[tex]\implies f+0.01(4)p=5.40[/tex]

[tex]\implies f+0.01(7)p=7.80[/tex]

Therefore:

[tex]\implies f+0.04p=5.40[/tex]

[tex]\implies f+0.07p=7.80[/tex]

Subtract the first equation from the second to eliminate f:

[tex]\implies 0.03p=2.40[/tex]

Solve for p:

[tex]\implies \dfrac{0.03p}{0.03}=\dfrac{2.40}{0.03}[/tex]

[tex]\implies p=80[/tex]

Substitute the found value of p into one of the equations and solve for f:

[tex]\implies f+0.04(80)=5.40[/tex]

[tex]\implies f+3.20=5.40[/tex]

[tex]\implies f=2.20[/tex]

Substitute the found values of p and f into the equation to create an equation for the cost of x miles:

[tex]\implies y=0.8x+2.2[/tex]

To find the cost of a 9-mile journey, substitute x = 9 into the found equation:

[tex]\implies 0.8(9)+2.2=9.40[/tex]

Therefore, the cost of a 9-mile journey is £9.40.

Answer: A

Step-by-step explanation:

:D

the answer is A. because x² is quardatic function and x³ is cubic function

The lines a and b are parallel. The proof is given.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given:

Statement 1:

∠1 and ∠6 are supplementary.

Justification:

If two angles sum up to 180 degrees, they are referred to as supplementary angles.

That means,

∠1 + ∠6 = 180°  

∠1 = 180°- ∠6

∠1 =∠5, given that the angles are made by intersecting lines.

Statement 2:

∠1 ≅∠4

Justification:

Vertical angles are also congruent angles, meaning they are equal or have the same measurement.

Two crossing lines actually create two sets of opposite angles that, when the measures of their angles, are added all together.

Since, ∠1 ≅∠4

That means, ∠4 and ∠6 are supplementary.

Statement 3:

∠4 and ∠6 are supplementary.

Justification:

If two angles sum up to 180 degrees, they are referred to as supplementary angles.

Statement 4:

a and b are parallel lines.

Justification:

This means that lines a and b make the same angle with the intersecting line, meaning they don't intersect each other at any point.

a and b are parallel lines.

Therefore, the all statements are true.

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Answer:

360 cm³

Step-by-step explanation:

height of bottom layer = 7 - 2 = 5cm

Volume = 9 · 8 · 5 = 360 cm³

Answer:

B.  X = 8 degree

Step-by-step explanation:

8x - 4 = 60 degree

8x = 64 degree

x = 8 degree

So, the answer is B

Answer:

x = 8°

Step-by-step explanation:

The angle that say 60° and the angle that says 8x -4 ARE BOTH EQUAL.

They are called Alternate Interior Angles

Let's write an equation to represent this relationship, then we solve it to find x

8x - 4 = 60

SOLVE

8x = 60 + 4

8x = 64

x = 64 / 8

x = 8 °

Answer:

3m

Step-by-step explanation:

hope this helps :D

Answer:

7.5 joules

Step-by-step explanation:

The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the box is 5 newtons and the distance over which the force is applied is 1.5 meters.

The amount of work done on the box is therefore 5 newtons * 1.5 meters = 7.5 joules. This is the amount of energy that has been transferred to or from the box as a result of the force applied to it.

Answer:

The relationship between the number of gems and the number of chests can be represented by an equation in the form of g = kc, where g is the number of gems, c is the number of chests, and k is a constant.

To find the value of the constant k, we can substitute the values from one of the adventures into the equation and solve for k. For example, using the values from Adventure A:

g = 600

c = 2

Substituting these values into the equation, we get:

600 = k * 2

Solving for k, we get:

k = 600 / 2 = 300

Therefore, the equation that describes the relationship between the number of gems and the number of chests is:

g = 300c

Using the information provided in the table, we know that for Adventure B, Lulu received 1500 gems and needed 5 chests to hold them. Substituting these values into the equation, we get:

g = 1500

c = 5

Substituting these values into the equation g = 300c, we get:

1500 = 300 * 5

This equation can be used to determine the number of chests needed to hold a given number of gems, or vice versa. For example, to find the number of chests needed to hold 1200 gems, we can substitute 1200 for g and solve for c:

g = 1200

c = 1200 / 300 = 4

Thus, 4 chests would be needed to hold 1200 gems.

The researcher can use two categorical variables or two values from a contingency table to perform chi - squared test.

A standard hypothesis test used to analyze contingency tables with large sample sizes is the chi-squared approach. This test is designed to examine if two categorical factors influence the test statistic independently. Pearson's chi-squared test and its variants are true when the test statistic equals chi-squared under the null hypothesis.

Pearson's chi-squared test is used to determine whether there is a statistically significant difference between expected and observed frequencies for one or more contingency table categories. For contingency tables with fewer samples, a Fisher's exact test is employed instead.

In the traditional application of this exam, observations are classified into mutually exclusive kinds. If the null hypothesis is correct and there are no variations in the population between classes, the test statistic generated by the data has a two-frequency distribution.

The test's purpose is to estimate how likely observed observed frequencies are if the null hypothesis is true.

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Answer:

63

Step-by-step explanation:

using the ratio

[tex] \frac{4}{1} = \frac{252}{x} [/tex]

cross multiply

[tex]4x = 252[/tex]

divide both sides by (4)

[tex] \frac{4x}{4} = \frac{252}{4} [/tex]

x = 63

i hope this helps

The correct answer is x = 63

[tex]\boxed{\frac{4}{1}=\frac{252}{x}4x=252\frac{4x}{4} =\frac{252}{4}x=63 }\\\huge\boxed{\underline_ So, \frac{4}{1}=\frac{252}{\bold{63}} }[/tex]

Therefore, the correct answer is x = 63

4 quarts in a gallon, 8 quarts in 2 gallons, so 32.40 divided by 8 is $4.05..

each quart cost 4 dollars and 5 cents

Step-by-step explanation:

The price per quart will be $4.05.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

It should be noted that 4 quarts are in a gallon. Therefore, since the 2-gallon container of laundry detergent costs $22.00. The price per quart will be:

= $22.00 / (4 × 2)

= $4.05

The price is $4.05.

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Answer:

--------------------------------------------

The distance traveled in each minute is a speed.

Find the speed per min for each distance:

Since the speed is not same over the total distance, the first choice is correct.

Find the average speed over the given distance:

Find the predicted time to travel 30 km:

Answer: 300 miles

Step-by-step explanation:

Let x be the number of miles

We have the equation below

20 + 0.35x = 35 + 0.30x

Subtract 20 from both sides

0.35x = 15 + 0.30x

Then subtract 0.30x from both sides

0.05x = 15

Then divide by 0.05 from both sides

x = 300 miles

Answer:

130 ft

Step-by-step explanation:

The distance across the canyon is 130 feet.

When Christian moved 100 feet from the tree on his side, the angle formed by the tree on his side and the tree on the other side was 70°. This means that the distance across the canyon is the length of the opposite side of the right triangle formed by Christian's position, the tree on his side, and the tree on the other side.

To find the length of the opposite side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the distance across the canyon, and the other two sides are 100 feet and the length of the opposite side of the triangle.

We can write this as an equation: (distance across the canyon)^2 = (100 feet)^2 + (opposite side of the triangle)^2.

To solve for the distance across the canyon, we can take the square root of both sides of the equation: distance across the canyon = √((100 feet)^2 + (opposite side of the triangle)^2).

Since the length of the opposite side of the triangle is equal to the length of the adjacent side (100 feet) divided by the tangent of the angle formed by the tree on his side and the tree on the other side, we can substitute this value into the equation above: distance across the canyon = √((100 feet)^2 + (100 feet / tan 70°)^2).

To calculate the value of tan 70°, we can use a calculator or look up the value in a table of trigonometric functions. The value of tan 70° is approximately 1.73. We can substitute this value into the equation above to get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2).

We can now use a calculator to evaluate this expression and find the distance across the canyon. When we do this, we get: distance across the canyon = √((100 feet)^2 + (100 feet / 1.73)^2) ≈ 130 feet.

Therefore, the distance across the canyon is approximately 130 feet.

Option A is the correct answer

A polynomial function is made up of terms called monomials; If the expression has exactly two monomials it’s called a binomial. A third-degree polynomial is of the form f(x) = ax³ + bx²+ cx + d where is not equal to zero. It is also called a cubic polynomial as it has a degree of 3.

Given here the polynomial as g(x) = f(2x)

                                                         =8ax³ + 4bx²+2cx + d

Both the polynomial have the same constant d and therefore the same y-intercept.

Hence, the correct option is B

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940 is the initial value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

Given that,

An amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

We have to find what is the quantity's value, to the closest hundredth, after 30 minutes.

We know that,

Formula is

S=a(r+1)ⁿ

Here,

S is initial value

a is 800

r is 5.5%

n is time 30/10

800×(5.5%+1[tex])^{30\div10}[/tex]

=939.3931

Therefore, 940 is the quantity's value, to the closest hundredth, after 30 minutes when amount that starts out at 800 increases exponentially at a rate of 5.5% every 10 minutes.

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Answer:

939.39

Step-by-step explanation:

The Density of object is 10,490 kg/m³

What is Density, Mass and Volume ?

Given,

Mass = 73,430 Kg

Volume = 7 m³

We know,

Density = Mass / volume

Now, plug in the values

Density = 73430/7

             = 10, 490 kg/m³

Hence, the Density of object is 10,490 kg/m³

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Answer:

A. Eight-four percent of 6th grade girls surveyed prefer cereal A

Step-by-step explanation:

Out of 100 6th grade students, 50 were girls and 50 were boys.

42% of the 100 students i. e. 42 were girls who preferred cereal A

Percentage of girls who liked cereal A = (42/50)x100%

= 84%

Answer:

A

Step-by-step explanation:

42% of entire 6th grade girls were surveyed

it means that 84% of ONLY the 6th grade girls liked Cereal A

Answer:

433 pizzas

Step-by-step explanation:

6062 / 14 = 433

Answer:

So the answer is A and D

Step-by-step explanation:

I think it is A and D cause it is 3 and -3 its a bigger number and smaller number

Answer:

12

Step-by-step explanation: