1. Which point represents a value that is less
than -1 and greater than -5?

In September 2021, the approximate number of citizens incarcerated in jails and prisons is around 2.3 million.

It is important to note that this figure can vary over time due to changes in policies, criminal justice reforms, and other factors. The incarcerated population includes individuals who have been convicted of crimes and are serving their sentences, as well as those who are awaiting trial or have been sentenced but not yet transferred to a correctional facility.

These numbers can vary between different countries and jurisdictions. To obtain the most accurate and up-to-date information on current incarceration rates, it is advisable to refer to official sources such as the U.S. Bureau of Justice Statistics or relevant governmental organizations in your country.

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The estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we can use the right Riemann sum method.

The width of each rectangle, Δx, is given by the interval width divided by the number of rectangles.

In this case, Δx = (π/2 - 0)/4 = π/8.

To calculate the right endpoint values, we evaluate f(x) at the right endpoint of each rectangle.

For the first rectangle, the right endpoint is x = π/8.

For the second rectangle, the right endpoint is x = π/4.

For the third rectangle, the right endpoint is x = 3π/8.

And for the fourth rectangle, the right endpoint is x = π/2.

Now, let's calculate the area for each rectangle by multiplying the width (Δx) by the corresponding height (f(x)):

Rectangle 1: Area = f(π/8) * Δx = 5cos(π/8) * π/8

Rectangle 2: Area = f(π/4) * Δx = 5cos(π/4) * π/8

Rectangle 3: Area = f(3π/8) * Δx = 5cos(3π/8) * π/8

Rectangle 4: Area = f(π/2) * Δx = 5cos(π/2) * π/8

Now, let's calculate the values:

Rectangle 1: Area = 5cos(π/8) * π/8 ≈ 0.2887

Rectangle 2: Area = 5cos(π/4) * π/8 ≈ 0.3142

Rectangle 3: Area = 5cos(3π/8) * π/8 ≈ 0.2887

Rectangle 4: Area = 5cos(π/2) * π/8 ≈ 0

Finally, to estimate the total area, we sum up the areas of all four rectangles:

Total Area ≈ 0.2887 + 0.3142 + 0.2887 + 0 ≈ 0.8916

Therefore, the estimated area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 0.8916.

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Answer:

2.

Step-by-step explanation:

He started with 50, so that must be the initial sum, and since it increases by 65 each week, 65 must be the common difference.

Expression represents the total number of pages Saul has read is 50+65w.

An expression or mathematical expression is a finite combination of symbols that is well-formed.

Given :

Saul reads, first week = 50 pages.

Saul reads, second week =65 pages

If he started from 50 pages for first week, then each week he read 65  pages and continued to read 65 pages for the few next weeks.

So, expression will be , if he reads for w weeks

50+65w

Hence, expression represents the total number of pages Saul has read is 50+65w.

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The number of apple in each basket is as follows:

First basket = 25 apples

Second basket = 37 apples

Third basket = 16 apples

Fourth basket = 29 apples

Fifth basket = 13 apples

total apples = 120

let

the number of apples in the first basket = a

the number of apples in the second basket = b

the number of apples in the third basket = c

the number of apples in the fourth basket = d

the number of apples in the fifth basket = e

Therefore,

a + b = 62

b + c = 53

c + d = 45

d + e = 42

a + b + c + d + e = 120

62 + 45 + e = 120

e = 120 - 62 - 45

e = 13

d = 42 - 13

d = 29

c = 45 - 29

c = 16

b = 53 - 16

b = 37

a = 62 - 37

a = 25

Therefore,

the number of apples in the first basket = 25

the number of apples in the second basket = 37

the number of apples in the third basket = 16

the number of apples in the fourth basket = 29

the number of apples in the fifth basket = 13

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Answer:

( 3x + 5y) • (3x - 5y)

Step-by-step explanation:

hope this helps:))

Answer:

( 3x + 5y)  (3x - 5y)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 200

x = 34

p = 34/200 = 0.17

q = 1 - 0.17 = 0.83

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.82 = 0.18

α/2 = 0.18/2 = 0.09

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.09 = 0.91

The z score corresponding to the area on the z table is 1.35. Thus, the z score for a confidence level of 82% is 1.35

Therefore, the 82% confidence interval is

0.17 ± 1.35√(0.17)(0.83)/200

Confidence interval is 0.17 ± 0.036

Answer:

z  ∗  = 1.341

Step-by-step explanation:

Its right on khan academy

Answer:

If a researcher cannot gain access to a target population, snowball sampling procedures can assist in locating subjects. In regard to sampling procedures, if a researcher wants to be able to generalize results to the total population of interest, then a purposeful sampling technique is the best approach.

Answer:

Non-probability sampling

Step-by-step explanation:

Non-probability sampling is a method of selecting units from a population using a subjective  method.

A lifeline in a sequence diagram is a line that is used to represent an active object, such as a class, interface, or object, and is typically identified by a solid line.

A lifeline in a sequence diagram is a graphical element used to depict the active objects in an interaction or sequence diagram. The lifeline is typically represented as a solid line running from the top of the diagram to the bottom, which represents the object's lifetime. The lifeline is used to show the messages that are sent and received between objects, as well as the sequence in which they occur. Additionally, the lifeline is often used to represent any changes of state in the objects, such as method calls, data values, and more. By depicting the lifelines of the active objects in a sequence diagram, it is possible to gain a better understanding of the interactions between the objects, and how they are related.

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Answer:

b good luck with the answer

The two triangles are similar If they have the same shape, but their sizes are different.

Similar triangles are triangles that have the same shape, but their sizes may be same or different. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. The similarity of triangles are denoted by ‘~’ symbol

AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then those two triangles are similar to each other.

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed between those two sides in both the triangle are equal, then two triangles are said to be similar.

SSS or Side-Side-Side Similarity

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Therefore, two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

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The frequency of revision times is given by the product of the frequency

density value and the class width.

Correct response:

The estimate of the number of students who revised for less than 45

minutes is given by the area, A, under the histogram to the left of the 45

minute mark as follows;

Frequency, f = Frequency density × Class width

Number of students = ∑f

Therefore;

A = 5 × 2 + 10 × 2.2 + 20 × 1.6 + 10 × 0.8 = 72

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Answer:

0

Step-by-step explanation:

The negative would just cancel the positives out. Therefore, since they are both adding together the same things the negatives would make the outcome 0.

Answer:

parallel lines are two lines drawn next to each other without a intersection

Answer:

  $340

Step-by-step explanation:

You want to know the original price of a desk priced such that $272 is 80% of its original price.

We can write the relation as an equation. If p represents the original price, then we have ...

  $272 = 80% × p

  p = $272/0.80 = $340 . . . . . . . divide by the coefficient of p

The original price is $340.

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Answer:

Below in bold.

Step-by-step explanation:

4.   y = x^5 - 7x

Finding the derivative:

y' = 5x^4 - 7

This is the formula for the slope at any point on the curve.

At (1, -6) the slope = 5(1)^4 - 7= 5 - 7 = -2.

5.  y = 4x - 1/x

y = 4x - x^-1

y' = 4 - (-1x^-2)

y' = 4 + 1/x^2

The slope at (-1,-3)

=  4 + 1/ (-1)^2

= 4 + 1

= 5.

The distance between the bottom end of the rope and the wall at the moment when it breaks is 4 meters.

The rope forms a right triangle with the ground and the wall. If we denote the distance between the wall and the bottom end of the rope by x,  :

L² = x² + 9 (because the rope is fixed at a height of 3 meters)

Use the implicit differentiation of the Pythagorean equation with respect to time, t:

2L x (dL/dt) = 2x x (dx/dt)

dL/dt = (x/L) x dx/dt                        dL/dt = 4 and dx/dt = 5

4 = (x/L) x 5

x/L = 4/5

Substitute x/L = 4/5 into the Pythagorean equation:

L² = (4/5L)² + 9

L =  √ [(16/25)L² + 9]

L = 5 meters

Then, substitute L = 5 into the equation x/L = 4/5 to find x:

x = (4/5) x 5

= 4 meters

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Using the interquartile range (IQR) method, the value 2 is considered an outlier in the given data.

To determine if there is an outlier in the given data, we need to calculate the lower and upper bounds using the interquartile range (IQR) method.

First, we need to calculate the first quartile (Q1), second quartile (Q2 or median), and third quartile (Q3) of the data.

Arranging the data in ascending order

2, 9, 13, 17, 18, 20, 23, 24, 33, 34, 43, 45, 53, 53

Q1 = 17

Q2 = 24

Q3 = 43

Next, we can calculate the IQR by subtracting Q1 from Q3

IQR = Q3 - Q1 = 43 - 17 = 26

Now we can calculate the lower and upper bounds

Lower bound = Q1 - 1.5 × IQR = 17 - 1.5 × 26 = -8

Upper bound = Q3 + 1.5 × IQR = 43 + 1.5 × 26 = 79

Any values outside the lower and upper bounds are considered outliers.

In this case, we have a value of 2 that is outside the lower bound of -8. Therefore, 2 is considered an outlier in the given data.

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Answer:

The correct equation is D

The standard deviation of ages in the room increases, while the median of ages stays approximately the same.

Standard deviation is a measure of the variability of a set of data points. The addition of a 30-year-old mother and an infant to the group of ten five- and six-year-olds increases the spread of the ages, thus increasing the standard deviation.

The median, on the other hand, is the middle value in a set of data points. Since the median only depends on the order of the values, not their magnitude, adding a mother and an infant to the group of children does not significantly affect the median age in the room, which would still be close to 5 or 6 years old.

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So, the matrix representation of the given system of linear first-order differential equations is: X' = [1 2; 3 0] X + [ -4e^(2t); 0 ].

To write the given system of linear first-order differential equations in matrix form, we can define the vector of variables X as X = [x, y].

The system can then be represented as:

X' = AX + B

where X' is the derivative of X with respect to the independent variable, A is the coefficient matrix, X is the vector of variables, and B is the vector of constant terms.

For the given system:

x' = x + 2y - 4e^(2t)

y' = 3x

The matrix form of the system becomes:

X' = [1 2; 3 0] X + [ -4e^(2t); 0 ]

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Answer:

8x+7

Step-by-step explanation:

Use the given functions to set up and simplify  

(f+g)(x)

Answer:

8x + 7

Step-by-step explanation:

(f+g)(x)= f(x) +g(x) = 3x + 10 + 5x - 3 = 8x + 7

Answer:

Your answer is 5/12.

Step-by-step explanation:

Hope this helps!

any nonzero vector in R^3 can be an eigenvector of T with eigenvalue λ = -1. For example, the vector (1, 0, 0) is an eigenvector of T with eigenvalue λ = -1, since T sends it to its negative (-1, 0, 0). Similarly, (0, 1, 0) and (0, 0, 1) are also eigenvectors of T with eigenvalue λ = -1.

To find the matrix for the linear transformation T that reflects all vectors in R^3 through the xy plane, we first need to determine how T affects the standard basis vectors.

T sends the vector (1, 0, 0) to (-1, 0, 0), since reflecting across the xy-plane negates the z-coordinate. Similarly, T sends (0, 1, 0) to (0, -1, 0), and (0, 0, 1) to (0, 0, -1). Therefore, the matrix for T with respect to the standard basis is:

[T] = [ -1  0  0 ]

     [  0 -1  0 ]

     [  0  0 -1 ]

To find the eigenvalues and eigenvectors of T, we can solve the characteristic equation:

det([T] - λ[I]) = 0

where I is the 3x3 identity matrix. Substituting the matrix for T and expanding the determinant, we get:

det([T] - λ[I]) = det([ -1-λ   0     0   ])

                 det([  0    -1-λ   0   ])

                 det([  0     0   -1-λ ])

               = (-1-λ)(-1-λ)(-1-λ)

               = -(λ+1)^3

Therefore, the only eigenvalue of T is λ = -1, and we need to find its eigenvectors. To do this, we need to solve the system of equations:

([T] - (-1)[I])v = 0

Substituting the matrix for T and the eigenvalue λ = -1, we get:

[   0    0    0 ][x]   [0]

[   0    0    0 ][y] = [0]

[   0    0    0 ][z]   [0]

This system of equations has a rank of 0, which means that there are infinitely many solutions.

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Answer:

The answer is zero

Step-by-step explanation:

Answer:

This is a translation considering that it moved and, didnt change size or form.

Step-by-step explanation:

Answer:

1/7

Step-by-step explanation:

6 + 5 + 4 = 15

There are 15 marbles to start with.

p(event) = (number of desired outcomes)/(total number of outcomes)

First pick (there are 6 desired outcomes out of a total of 15 possible outcomes):

p(r) = 6/15

Now there are 5 red marbles left and a total of 14 marbles left.

Second pick (there are 5 desired outcomes out of a total of 14 possible outcomes):

p(r) = 5/14

These events are independent, so we multiply the two probabilities.

p(r, r) = 6/15 × 5/14

p(r, r) = 3/7 × 1/3

p(r, r) = 1/7

The soccer ball reaches a maximum height of approximately 34.8 feet.

The parametric equations for the motion of the soccer ball are:

x(t) = 39*cos(44°)t ≈ 26.9t

y(t) = \(39\sin(44)*t - 16t^2\) ≈ \(22.7t - 16t^2\)

where t is the time elapsed since the ball was kicked.

To find the maximum height of the ball, we need to find the vertex of the parabolic trajectory given by y(t).

The maximum height occurs at the vertex, which is at the time t = -b/2a, where a = -16 and b = 39*sin(44°).

So, t = -b/2a ≈ 1.1 seconds.

Substituting this value of t into the equation for y(t), we get the maximum height:

y(max) = \(39*\sin(44)1.1 - 16(1.1)^2 = 34.8 feet.\)

Therefore, the soccer ball reaches a maximum height of approximately 34.8 feet.

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