Which of these r-values represents the weakest correlation?

A. –0.75
B. –0.15
C. –0.55
D. –0.35

Answer:

Its -0.2 Because time cannot be a negative value.

Step-by-step explanation:

The correct value would be the 2.7 sec. one.

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Here, Indicated when h(t) = 0, we are to find for the time where the football has reached a certain height.

⇒ - 16t² + 40t + 7 = 0

Then, the values of t would be -0.2 and 2.7.

Since,  we are to look for the time, it is impossible for us to have an answer that has a negative value.

So based from our answer, the solution that we will eliminate is the -0.2 one. Since its value is negative.

Thus, the correct value would be the 2.7 sec. one.

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Answer:

The LA theorem is a special case of the AAS theorem and the ASA postulate.

Step-by-step explanation:

The LA theorem is a special case of the AAS theorem and the ASA postulate.

LA(Leg - Acute) theorem states that if the leg and one acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.

AAS (Angle Angle Side) states that if two angles and the non included side of one triangle are congruent to two angles and the non included side of another triangle, then these two triangles are congruent.

ASA (Angle Side Angle) postulate states that if two angles and one included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

A double integral of Sin(x^2 + y^2) over a region between two circles with radii 2 and 5 is transformed into polar coordinates for simplification. The limits of the polar coordinates correspond to this region, and the integral becomes ∫ ∫ rSin(r^2) dr dθ, with r ranging from 2 to 5, and θ from 0 to π/2.

The student asked about the calculation of a double integral over a region between two circles, presented in polar coordinates, where the function is Sin(x^2 + y^2). For simplification, we can change to polar coordinates. In polar coordinates, x = rcosθ and y = rsinθ. Thus, x^2 + y^2 becomes r^2, and the function becomes Sin(r^2).

For a region between two circles of radii 2 and 5 in the first quadrant, we can describe the limits of the polar coordinates. r will range from 2 to 5, and θ from 0 to π/2. Thus, the integral will be ∫(from 0 to π/2) ∫(from 2 to 5) rSin(r^2) dr dθ. Evaluation of the integral will require techniques of polar integration.

It's important to note that this is a theoretical discussion and the actual integration may have complex results depending on the function to integrate.

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We need solve the given integral, convert coordinates to polar form and integrate step by step. First we will solve the inner integral from 2 to 5 and then the outer integral from 0 to π/2

We need to evaluate the double integral of Sin(x² + y²) over the region between the circles with radii 2 and 5.

In polar coordinates, where x = r cos(θ) and y = r sin(θ), this integral becomes:

∫(from 0 to π/2) ∫(from 2 to 5) sin(r²) r dr dθ

Let's solve the inner integral first, with respect to r:

Firstly, set up the integral: ∫(from 2 to 5) sin(r²) r dr.

Then Use the substitution u = r², then du = 2r dr.

Now Rewriting the integral: (1/2) ∫(from 4 to 25) sin(u) du = (1/2) [-cos(u)] (from 4 to 25).

and evaluating this: (1/2) [-cos(25) + cos(4)].

Next, integrate the result with respect to θ:

Set up the outer integral: (1/2) ∫(from 0 to π/2) [-cos(25) + cos(4)] dθ.

Now since [-cos(25) + cos(4)] is constant, the integral is straightforward: (1/2) [-cos(25) + cos(4)] * (π/2).

Hence the final answer: (π/4) [-cos(25) + cos(4)].

Therefore, the integral evaluates to (π/4) [-cos(25) + cos(4)].

EDITED QUESTION

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Find the double integral  Sin(x² + y²) over the region between the circles with radii 2 and 5.

Using simple mathematical operations, we know that 201 bolts are produced in 21 minutes.

So, the bolts produced in 21 minutes are:

Calculate as follows:

Therefore, using simple mathematical operations, we know that 201 bolts are produced in 21 minutes.

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Final answer:

To find the number of bolts produced in 21 minutes, set up a proportion using the given information: 268 bolts / 28 minutes = x bolts / 21 minutes. Simplifying, we find that x = 201 bolts.

Explanation:

To find the number of bolts produced in 21 minutes, we can set up a proportion using the given information. We know that the machine produces 268 bolts in 28 minutes. Let x be the number of bolts produced in 21 minutes.

Using the proportion:

268 bolts / 28 minutes = x bolts / 21 minutes

Multiplying both sides by 21, we get:

(268 bolts / 28 minutes) * 21 minutes = x bolts

Simplifying, we find that x = 201 bolts.

Answer:

Approximately 83 bags each carrying 50 pounds of soil will carry 1 cubic yard of soil or 4,128 pounds of soil.

Step-by-step explanation:

We are given the following information in the question:

1 cubic yards is equal to 4128 pounds that is

[tex]1~yard^3 = 4,128~pounds[/tex]

Amount of soil 1 bag can hold = 50 pounds

Number of bags to hold 1 cubic yard of soil or 4,128 pounds of soil:

Formula:

[tex]\text{Number of bags} = \displaystyle\frac{\text{Total amount of soil}}{\text{Amount of soil 1 bag can hold}}[/tex]

[tex]= \displaystyle\frac{4128}{50} = 82.56[/tex]

Thus, approximately 83 bags each carrying 50 pounds of soil will carry 1 cubic yard of soil or 4,128 pounds of soil.

[tex]\frac{1}{132}[/tex] part of the golf course is in the trees.

To find out what part of the golf course is in the trees, we need to add the fractions of the golf course that are in the fairways and the greens, and then subtract that sum from 1 (which represents the whole golf course).

First, we add the fractions of the golf course that are in the fairways and greens:

To add these fractions, we must first find a common denominator. The denominators are 12 and 11, so the common denominator is 12 x 11 = 132.

Convert each fraction to have this common denominator:

Now, add these converted fractions together:

[tex]\frac{121}{132}[/tex] + [tex]\frac{12}{132}[/tex] = [tex]\frac{133}{132}[/tex]

Since the sum [tex]\frac{133}{132}[/tex] is greater than 1, we convert it to a whole number plus a fraction. [tex]\frac{133}{132}[/tex] = 1 + [tex]\frac{1}{132}[/tex].

Now, to find the part of the golf course in the trees, subtract this sum from the whole golf course:

1 - 1 + [tex]\frac{1}{132}[/tex] = [tex]\frac{1}{132}[/tex]

So, [tex]\frac{1}{132}[/tex] of the golf course is in the trees.

Complete question:

About [tex]\frac{11}{12}[/tex] of a golf course is in the fairways, [tex]\frac{1}{11}[/tex] in the greens, and the rest in the trees. What part of the golf course is in the trees?

The 15/26 fraction of the students is hearing​ impaired if in an American Sign Language​ (A.S.L) class of 26 ​students, 15 are hearing impaired.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

In an American Sign Language​ (A.S.L) class of 26 ​students, 15 are hearing impaired.

The fraction:

= 15/26

We can convert the above value in the percentage as follows:

The best method for obtaining this answer is to divide 15 by 26 to obtain the number 0.5769, multiply that number by 100 to obtain the number 57.69; and then round it to the closest full number if necessary.

15/26 in percentage will be 57.69

Thus, the 15/26 fraction of the students is hearing​ impaired if in an American Sign Language​ (A.S.L) class of 26 ​students, 15 are hearing impaired.

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The required measure of the length of the given line is 8.6 units.

Distance is defined as the object traveling at a particular speed in time, from one point to another.

here,
Locate the end point of line in the graph,
end point of the line from the graph is given as (0, 8) and (7, 3)

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂ - y₁]²]

Substitute the point in the above equation,

D = √[[7]² + [3 - 8]²]
D = √49 + 25
D = √74
D = 8.6

Thus, the required measure of the length of the given line is 8.6 units.

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Answer:

c

Step-by-step explanation:

Answer:

The sum is fraction therefore rational

Step-by-step explanation:

Given two numbers

[tex]-2\frac{3}{4}\text{ and }\frac{5}{9}[/tex]

we have to tell that how their sum is rational.

we add the above two number

[tex]-2\frac{3}{4}+\frac{5}{9}[/tex]

[tex]\frac{-11}{4}+\frac{5}{9}[/tex]

[tex]\frac{-99+20}{36}=\frac{-79}{36}=-2.194444...[/tex]

Hence, the sum is we can say fraction or non-terminating but repeating which is the definition of a rational number.

∴ from the given options answer C is correct.

The sum is fraction therefore rational.

The number in which the 6 has a value that is one-tenth the value of the 6 in 34,761 is 3,476.1

In the number 34,761, the digit 6 is in the tens place, giving it a value of 60. To find a number where the value of 6 is one-tenth of 60, we look for a place value that is one position to the right.

In 3,476.1, the 6 is in the ones place, making its value 6, which is one-tenth of 60. This shift from the tens place to the ones place decreases the value by a factor of ten.