For the following exercises, solve the inequality and express the solution using interval notation.
71. |3x − 2 | < 7

Statistical analyses are least likely to be found in a (D) qualitative research.

Therefore, statistical analyses are least likely to be found in a (D) qualitative research.

Know more about qualitative research here:

https://brainly.com/question/24492737

#SPJ4

Conservation of number, which is the understanding that the quantity of an object remains the same even if its appearance or arrangement changes.

Four-year-old Dimitri has not acquired the concept of conservation.

Conservation refers to the understanding that certain properties of objects, such as quantity, remain the same even when their appearance changes, as long as nothing is added or removed.

In this case,

Dimitri incorrectly believes that increasing the spacing between nickels in one row results in more nickels, failing to understand that the quantity remains the same.

For similar question on appearance.

https://brainly.com/question/28998583

#SPJ11

Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.

One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.

Learn more about chess: https://brainly.com/question/29897063

#SPJ11

Answer:

5x^2 - 2x - 3

Step-by-step explanation:

(x-1) (5x+3)

5x^2 + 3x - 5x - 3

5x^2 - 2x - 3

So, the answer is 5x^2 - 2x - 3

Answer:

Step-by-step explanation:

I would say B

To maximize the area of the rectangular corral, the farmer should construct a square corral with dimensions of 50 yards by 50 yards using the 200 yards of fencing available.

Let's assume the length of the corral is l yards and the width is w yards. Since the farmer only needs to fence three sides (two widths and one length), the total length of fencing required is 2w + l yards.

Given that the farmer has 200 yards of fencing, we can write the equation:

2w + l = 200

To maximize the area of the corral, we need to find the dimensions that will result in the largest possible area. The area of a rectangle is given by the formula A = lw.

We can solve the equation for l in terms of w:

l = 200 - 2w

Substituting this into the area formula, we get:

A = w(200 - 2w)

To find the maximum area, we can take the derivative of A with respect to w, set it equal to zero, and solve for w. Taking the second derivative will confirm that it is a maximum.

By solving the derivative and second derivative, we find that w = 50 yards, l = 100 - 2(50) = 50 yards.

Therefore, the dimensions of the corral that maximize the area are 50 yards by 50 yards, resulting in a square shape.

Learn more about rectangular here:

https://brainly.com/question/21416050

#SPJ11

The value of p in the binomial expansion is 1920.

Here we have been given

\((a-kx^m)^n = \frac{243}{32} - \frac{405}{4}x^{\frac{3}{2}} + 540x^3 - 1440x^\frac{9}{2} + px^6 - qx^\frac{15}{2}\)

Now to calculate the value of p we need to calculate the values of n, m, k, and a using the Binomial Expansion formula.

Now we have 6 terms over here. According to the rule, the power of an expression is

no. of terms in expansion - 1

= 6 - 1

= 5

Now the first term is

\(C^5_0 a^5 = \frac{243}{32}\)

\(or, a^5 = \frac{3^5}{2^5}\)

Hence we get

a = 3/2

Now the second term should be

\(C^5_1 a^4 (-kx^m) =- \frac{405}{4}x^\frac{3}{2}\)

\(-5k\frac{81}{16}x^m =- \frac{405}{4}x^\frac{3}{2}\)

\(or, kx^m = 4x^\frac{3}{2}\)

Hence here we see that k = 4 and m = 3/2

Now we can calculate p by

\(C^5_4 a^1 (-kx^m)^4 = px^6\)

\(5 X \frac{3}{2} X 256x^6 = px^6\)

\(or, 1920x^6 = px^6\)

Hence the value of p is 1920

To learn more about Binomial Expansion visit

https://brainly.com/question/2165968

#SPJ4

Answer:

7 4/5

Step-by-step explanation:

2 1/10 + 5 7/10 = 2 + 5 + 1/10 + 7/10 = 7 8/10 = 7 4/5

(a) The equation for the tangent plane at point P₀(2,0,2) on the surface 2z−x²=0 can be found by taking the partial derivatives of the surface equation with respect to x, y, and z at point P₀.

Then we can use these derivatives to construct the equation of a plane in the form of Ax + By + Cz + D = 0.

(b) To find the equations for the normal line, we first need to determine the normal vector to the tangent plane at point P₀. The normal vector will have components equal to the coefficients of x, y, and z in the equation of the tangent plane. Once we have the normal vector, we can write the parametric equations of the normal line using the coordinates of point P₀.

It seems that the equation for the tangent plane and the equations for the normal line are missing from the provided options. Without the specific equations, it is not possible to provide the exact values for x, y, and z in the equations for the normal line.

To learn more about derivatives  click here

brainly.com/question/29144258

#SPJ11

The minimum labor cost is $74/3, or approximately $24.67. To find the values of x and y that minimize the labor cost, we need to find the critical points of the function L(x,y).

To do this, we need to find the partial derivatives of L with respect to x and y, and set them equal to zero:

∂L/∂x = 3x - 5 - 2y = 0
∂L/∂y = 2y - 2x - 2 = 0

Solving these two equations simultaneously, we get:

x = 5/3
y = 2/3

To confirm that this is indeed a minimum, we need to check the second partial derivatives:

∂²L/∂x² = 3 > 0 (positive, so minimum)
∂²L/∂y² = 2 > 0 (positive, so minimum)
∂²L/∂x∂y = -2 < 0 (negative, so minimum)

Therefore, the values of x and y that minimize the labor cost are x = 5/3 and y = 2/3.

To find the minimum labor cost, we substitute these values into the original function:

L(5/3, 2/3) = 3/2 (5/3)^2 + (2/3)^2 - 5(5/3) - 2(2/3) - 2(5/3)(2/3) + 93

L(5/3, 2/3) = 75/9 + 4/9 - 25/3 - 4/3 - 20/9 + 93

L(5/3, 2/3) = 74/3

Know more about minimum labor cost here:

https://brainly.com/question/29959145

#SPJ11

The set of arrows that best represents the change in momentum for balls A and B is the set of arrows labeled "C". This is because the arrows are pointing in opposite directions, indicating that the momentum of ball A is decreasing while the momentum of ball B is increasing.

This is consistent with the principle of conservation of momentum, which states that the total momentum of a closed system remains constant unless acted upon by an external force.

B) The arrow that indicates the direction of the impulse applied to ball A by ball B is the arrow labeled "D". This is because the impulse is defined as the change in momentum, and the change in momentum of ball A is in the direction of the arrow labeled "D". This means that ball B exerted an impulse on ball A in the direction of the arrow labeled "D" during the collision. The magnitude of the impulse is equal to the change in momentum of ball A, which is equal to the area under the curve of the force-time graph during the collision.

To know more about momentum visit:-

https://brainly.com/question/30677308

#SPJ11

To solve the equation in part a and determine the mystery weight, we used the following properties of equality:

Addition property: This property states that if we add the same number to both sides of an equation, the equality is preserved. In this case, we added 23 grams to both sides of the equation to isolate the variable.

Subtraction property: This property states that if we subtract the same number from both sides of an equation, the equality is preserved. In this case, we subtracted 8 grams from both sides of the equation to isolate the variable.

Multiplication property: This property states that if we multiply both sides of an equation by the same number, the equality is preserved. In this case, we multiplied both sides of the equation by 3 to isolate the variable.

Division property: This property states that if we divide both sides of an equation by the same number (excluding 0), the equality is preserved. In this case, we divided both sides of the equation by 2 to isolate the variable.

By using these properties of equality, we were able to manipulate the equation and isolate the variable to determine the mystery weight.

To learn more about equations from given link

https://brainly.com/question/22688504

#SPJ1

Answer:

b= 4.260

Step-by-step explanation:

28^3=2165

divide both sides by 28

x^3= 2165/28

x=(2165/28)^(1/3)

x= 4.260232

Answer:

-2137

Step-by-step explanation:

     you have to subtract the two numbers then you get your answer

Hypothesis test for µ1 – µ2 can be used to test whether borrowers from this particular bank who receive hamp modifications are more likely to re-default than those who receive non-hamp modifications.

The Independent Samples t Test analyses the means of two separate groups to see if there is statistical support that the population mean values are statistically substantially different. Independent Samples t Test is known as parametric test.

The population means are deemed to be different if the two-sample means are sufficiently dissimilar from one another.

The null and alternative hypothesis for the programs is

H0: μ1 - μ2=0

H1: μ1 - μ2  ≠0        

To learn more about hypothesis refer here

https://brainly.com/question/29519577#

#SPJ4

Answer:

Step-by-step explanation:

Its in right form. It cant be reduced. I think. If wrong sorry.

Answer:

A

Step-by-step explanation:

The constant 4 is positive so the graph is shifted up by 4 units. If it was instead -4, then the graph would have been shifted down 4 units

The probability that a randomly selected car had automatic transmission or air conditioning or both is 0.92517.

Total number of cars sold, n = 147

Let A denotes the car is air conditioning.

And B denotes the car is automatic message transmission.

A = 81

B = 82

Number of cars that neither of these extras = 11

Only A = 54

Only B = 55

Now,

P(A ∩ B') = A/n

P(A ∩ B') = 81/147

P(A ∩ B') = 0.551

P(A' ∩ B') = 11/147

P(A' ∩ B') = 0.07483

The probability that a randomly selected car had automatic transmission or air conditioning or both is:

P(A ∪ B) = 1 - P(A' ∩ B')

P(A ∪ B) = 1 - 0.07483

P(A ∪ B) = 0.92517

The likelihood that an automobile chosen at random has either an automatic gearbox, air conditioning, or both is 0.92517.

To learn more about probability link is here

brainly.com/question/11034287

#SPJ4

Answer with Step-by-step explanation:

\(a) {n}^{2} + 3 \\ \\ n = 1 \\ {1}^{2} + 3 \\ 1 + 3 \\ = 4 \\ \\ n = 2 \\ {2}^{2} + 3 \\ 4 + 3 \\ = 7 \\ \\ n = 3 \\ {3}^{2} + 3 \\ 9 + 3 \\ = 12 \\ \\ n = 4 \\ {4}^{2} + 3 \\ 16 + 3 \\ = 19 \\ \\ n = 10 \\ {10}^{2} + 3 \\ 100 + 3 \\ = 103\)

In this sequence,

1st term = 4

2nd term = 7

3rd term = 12

4th term = 19

10th term = 103

\(b)2 {n}^{2} \\ \\ n = 1 \\ 2 \times {1}^{2} \\ 2 \times 1 \\ = 2 \\ \\ n = 2 \\ 2 \times {2}^{2} \\ 2 \times 4 \\ = 8 \\ \\ n = 3 \\ 2 \times {3}^{2} \\ 2 \times 9 \\ = 18 \\ \\ n = 4 \\ 2 \times {4}^{2} \\ 2 \times 16 \\ = 32 \\ \\ n = 10 \\ 2 \times {10}^{2} \\ 2 \times 100 \\ = 200\)

in this sequence,

1st term = 2

2nd term =8

3rd term = 18

4th term =32

10th term = 200

Answer:

9.5

Step-by-step explanation:

The correct answer is 9.5 because 9.49 is closer to 9.5 than 9.4

Answer:

9.5

Step-by-step explanation:

9.492 to the nearest tenth

First you would round 0.092, which would just be 0.09 because 2 is less than 5. You would then have 9.49. You would then round the 0.49, and since 9 is greater than 5, it would be 9.5 because 9 would round to 10.

Answer:

Option D

Step-by-step explanation:

If (1, 6) is the only solution of the system of equations and one of system of equations is,

y = 2x + 4

Then solution of the system will satisfy both the equations.

Option A

y = 4x - 7

By satisfying this equation by (1, 6),

6 = 4(1) - 7

6 = -3

False.

Therefore, given equation is not the answer.

Option B

y = 2x + 8

By satisfying this equation by (1, 6),

6 = 2(1) + 8

6 = 10

False.

Therefore, given equation is not the answer.

Option C

y = -2(x + 2)

By satisfying this equation by (1, 6),

6 = -2(1 + 2)

6 = -6

False.

Therefore, given equation is not the answer.

Option D

y = 5x + 1

By satisfying this equation by (1, 6),

6 = 5(1) + 1

6 = 6

True.

Therefore, this is one of the equations of the system of equations.

Option D is the answer.

In geometry, a transversal is a line that intersects two or more other lines. When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .

It is given that <1 = <2

Then m<3 = m<4, since

Therefore, m<3 = m<4.

Answer: 8.3 m

Step-by-step explanation:

Given

The angle of declination is \(50^{\circ}\)

Earthworm is \(7\ m\) away from the base of the tree

Suppose h is the height of the tree

from the figure, we can write

\(\Rightarrow \tan 50^{\circ}=\dfrac{h}{7}\\\\\Rightarrow h=7\tan 50^{\circ}=8.3\ m\)

The domain of the function f(x) = (3 - 2x)/(9 - 4x) is equal to (-∞, 9/4) U (9/4, ∞) or (-∞, 2.25) U (2.25, ∞).

In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined.

In order to determine the domain of this rational function, we would use an online graphing calculator to plot it and then write its domain in interval notation based on the values on the x-coordinate of the graph as follows:

Domain = (-∞, 9/4) U (9/4, ∞) or (-∞, 2.25) U (2.25, ∞)

By using set builder notation, the domain of this rational function f(x) = (3 - 2x)/(9 - 4x) can be re-written as follows;

Domain = {x|x ≠ 9/4} or {x|x ≠ 2.25}.

Read more on domain here: brainly.com/question/4685947

#SPJ1

hope this helped buddy

Peace

A triangle has 3 sides

Answer:

x = 5, -5, 3, -3

Step-by-step explanation:

First, substitute u = x^2 into the equation, and we have

u^2 - 34u + 225 = 0

u = x^2

Factor u^2 −34u +225 using the AC method, and we get

( u - 25) ( u - 9) = 0

We know If any individual factor on the left side of the equation is equal to

0, the entire expression will be equal to 0, so

u - 25 = 0

u - 9 = 0

Next, we set u - 25 equal to 0  and solve for u, and we get

u = 25

Then set u - 9 equal to 0 and solve for u, and we get

u = 9

The final solution is all the values that make (u−25)(u−9) = 0  true.

u =25,9

Substitute the real value of u=x^2 back into the solved equation.

x^2 = 25

(x^2)^1 = 9

x^2 = 25

x = 5, -5

Now we solve the second equation

(x^2)^1 = 9

x = 3, -3

So, the answers are: 5, -5, 3, -3

The integration is as follow

Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.

Given:

first, \(\int\limits {e^{4x} / 19 - e^{8x}} \, dx\)

= \(\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx\)

let \(e^{4x}\) = z

4\(e^{4x}\) dx = dz

= 1/4 \(\int\limits {dz / \sqrt{19} ^2 -z^2} \,\)

= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C

= 1/8√19 log|(\(e^{4x}\) + √19)/ (\(e^{4x}\) - √19)| + C

Second,

\(\int\limits {33 sec^5 (x)} \, dx\)

= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]

= 33/4  tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]

=  33/4  tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C

Learn more about integration here:

https://brainly.com/question/18125359

#SPJ4