a data scientist samples a population by randomly selecting one of the first 100 entries in a telephone directory, as well as every 100th entry after the selected entry. this process is known as:

The initial 50 miles distance from the lighthouse and the N 30° W and N 40° W bearing of the ship before and after traveling due east, using the law of sines, indicates.

The law of sines states that in a triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for each of the three sides of the triangle.

The distance of the ship from the lighthouse = 50 miles

Bearing of the lighthouse from the ship = N 30° W

The direction in which the ship travels = due east

The new bearing to the lighthouse = N 40° W

In the triangle formed by the initial and new locations of the ship and the lighthouse, the interior angles, A, B, C are;

m∠A = 30° + 90° = 120°

m∠B = 90° - 40° = 50°

Therefore; m∠C = 180° - (120° + 50°) = 10°

Angle opposite the initial distance of the ship from the lighthouse = ∠B = 50°

The angle opposite the new distance of the ship from the lighthouse = m∠A = 120°

The law of sines indicate that we have;

\(\dfrac{50}{sin(50^{\circ})} = \dfrac{New \, distance}{sin(120^{\circ})}\)

50 × sin(120°) = The new distance of the lighthouse × sin(50°)

The new distance of the lighthouse = 50 × sin(120°)/(sin(50°)) ≈ 56.53

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Writing linear equations given two points can be a useful skill when graphing linear equations.

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For a standard normal distribution, the approximate value of P(z≤0.42) is 66%.

The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1.

In order to calculate the value of the P(z≤0.42), we need to check the value of 0.42 in the z-table, As the Z-table is already given and in the table, the value of z is 0.6628, therefore,

\(P(z\leq 0.42)\\\\=0.6628 \approx 66\\\\= 66\%\)

Hence, For a standard normal distribution, the approximate value of P(z≤0.42) is 66%.

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Answer:

86% is correct

Step-by-step explanation:

a. Jump with a bobbing motion: Shortest jump  b. Jump from deep knee flexion: Intermediate jump

c. Jump with fully extended knees: Longest jump ,In the long jump activity, three different jumping techniques were observed:

a) The bobbing motion involved bending and extending the knees and arms during the jump.

b) Starting from deep knee flexion meant initiating the jump from a position with knees bent and no motion prior to the jump.

c) Starting with fully extended knees involved jumping with the knees straight and no motion before the jump. During the performance, the lengths of each jump were measured. Trial results consistently indicated that the jump with the bobbing motion had the shortest length, while the jump starting from deep knee flexion had an intermediate length. The jump with fully extended knees consistently achieved the longest distance.

The observations reveal that starting the jump with fully extended knees and no knee motion results in the longest jump. The bobbing motion with knee and arm movements leads to the shortest jump. Deep knee flexion position falls between the two in terms of jump length.

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Answer: Option 3

The male characters are of several races, but there is no representation of female characters of different racial identities.

The standard error of the mean is equal to $3.32.

Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.

SE = SD / √n

where SE = standard error

SD = sample standard deviation

n = sample size

Based on the problem, the sample standard deviation is $21.00 and the sample size is equal to 40. Substitute these values to the equation and solve for the standard error.

SE = SD / √n

SE = $21.00 / √40

SE = 3.32

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Answer:

it takes about 2.79 seconds for the object to hit the ground

Step-by-step explanation:

t√h/4

h=125 feet

t=√125/4=√25×√5/4

t=5√5/4=11.18/4

t=2.79 secs

it takes the object 2.79 seconds to

hit theground

hope this helps. kindly give a feedback if you need more help..

Answer:

Slope= -1

Step-by-step explanation:

Rise over run

2 to the right 2 down = 2/-2

Simplify to -1

Step-by-step explanation:

im sorry if this answer going to like not let more people answer but use math. way it helps a lot

Answer: 4^3, and 5^2. This is the answer.

Step-by-step explanation:

Answer:

I will help you

Step-by-step explanation:

Have a good day

The amount Shirley paid for the Fax machine is $488.

Shirley buys a fax machine and sells it to Devi at a gain of 25% on the cost price.

let the cost Shirley bought the machine = x

Therefore,

selling price = 25% of x + x = 0.25x + x = 1.25x

Devi then sells the fax machine to Amirah at a loss of 250 on the price at which she buys it from Shirley.

Amirah pays $360 for the fax machine.

Therefore,

loss = cost price - selling price

250 = 1.25x - 360

Therefore,

250 + 360 = 1.25x

610 = 1.25x

x = 610 / 1.25

x = $488

Therefore, the amount Shirley paid for the Fax machine is $488.

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Answer:

13

Step-by-step explanation:

We're trying to find the distance between points X and Y. Or the distance of X-Z plus Z-Y.

Lets find the distance of X-Z

6-2=4

Now lets find the distance of Z-Y

15-6=9

Now we add the distances

4+9=13

Answer:

13

Step-by-step explanation:

X = 2 and Y = 15

To find the distance between X and Y, all you have to do is subtract 2 from 15, which is equal to 13.

Answer:

c. 2x.

Step-by-step explanation:

16x2 - 14x

Common factor of 16 and 14 =  2'

for x2 and x it is x,

Answer: 2x.

The population of birds may develop changes in their beak shape and size over time to better adapt to the new food source through the process of evolutionary adaptation.

It appears you'd like to know what would happen to the beaks of a bird population that finds a new type of food that is equally tasty but different in shape and size.
Over time, the beaks of the bird population may undergo adaptation through natural selection.

As the birds start to consume the new type of food, individuals with beak shapes better suited for handling the different shape and size of the new food will have a higher chance of survival and reproduction.

This would lead to the spread of the advantageous beak trait throughout the population.
In summary, the beaks of the bird population may gradually change to better accommodate the new food source, driven by the process of natural selection.

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Let F (n) denote the integral,

∫ x (1 - ln(x))ⁿ dx

We attempt to find a power-reduction formula for F (n) in terms of F (n - 1). Integrate by parts, with

u = (1 - ln(x))ⁿ   →   du = - n/x (1 - ln(x))ⁿ ⁻¹ dx

dv = x dx   →   v = 1/2 x ²

Then

F (n) = u v - ∫ v du

F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2 ∫ x (1 - ln(x))ⁿ ⁻¹ dx

F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2 F (n - 1)

From this relation, we get

F (n - 1) = 1/2 x ² (1 - ln(x))ⁿ ⁻¹ + (n - 1)/2 F (n - 2)

F (n - 2) = 1/2 x ² (1 - ln(x))ⁿ ⁻² + (n - 2)/2 F (n - 3)

F (n - 3) = 1/2 x ² (1 - ln(x))ⁿ ⁻³ + (n - 3)/2 F (n - 4)

and so on, down to

F (1) = 1/2 x ² (1 - ln(x)) + 1/2 F (0)

where

F (0) = ∫ x dx = 1/2 x ² + C

By recursively substituting, we find

→   F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2 [1/2 x ² (1 - ln(x))ⁿ ⁻¹ + (n - 1)/2 F (n - 2)]

… = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2² F (n - 2)

→   F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2² [1/2 x ² (1 - ln(x))ⁿ ⁻² + (n - 2)/2 F (n - 3)]

… = F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2³ x ² (1 - ln(x))ⁿ ⁻² + (n (n - 1) (n - 2))/2³ F (n - 3)

→   F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2³ x ² (1 - ln(x))ⁿ ⁻² + (n (n - 1) (n - 2))/2³ [1/2 x ² (1 - ln(x))ⁿ ⁻³ + (n - 3)/2 F (n - 4)]

… = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + (n (n - 1))/2³ x ² (1 - ln(x))ⁿ ⁻² + (n (n - 1) (n - 2))/2⁴ x ² (1 - ln(x))ⁿ ⁻³ + (n (n - 1) (n - 2) (n - 3))/2⁴ F (n - 4)

and so on, down to

F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + … + (n (n - 1) … 2 × 1)/2ⁿ F (0)

F (n) = 1/2 x ² (1 - ln(x))ⁿ + n/2² x ² (1 - ln(x))ⁿ ⁻¹ + … + (n (n - 1) … 2 × 1)/2ⁿ ⁺¹ x ² + C

We can write this more compactly as the sum,

\(F(n)=\displaystyle\int f_n(x)\,\mathrm dx=x^2\sum_{k=0}^n \frac{n!}{2^{k+1} (n-k)!} (1-\ln(x))^{n-k} + C\)

or

\(F(n)=\displaystyle\int f_n(x)\,\mathrm dx=x^2\sum_{k=0}^n \frac{k!}{2^{k+1}}\binom nk(1-\ln(x))^{n-k} + C\)

where \(\binom nk=\frac{n!}{k!(n-k)!}\) is the binomial coefficient.

No, a Norman window is not a semicircle above a rectangular window.

A Norman window, also known as a "Normandy window" or "Romanesque window," is a specific architectural feature that consists of a rounded arch at the top with a rectangular opening below it. It is characterized by its combination of curved and rectangular elements.

The top portion of a Norman window is indeed a semicircular arch, which reflects the influence of Romanesque architectural styles. The arch is typically constructed using stone or other masonry materials and adds a sense of grandeur and elegance to the window design.

The semicircular arch can vary in size and may feature intricate detailing or decorative elements.

Below the semicircular arch, a rectangular opening is incorporated, which is the main area for letting in light. The rectangular section is usually wider than the arch and can be divided into smaller sections by mullions or transoms.

The rectangular shape of the lower portion provides a practical and functional space for placing glass panes or other materials.

Overall, the combination of the semicircular arch and rectangular opening in a Norman window creates a visually appealing and harmonious design. It is a distinctive feature commonly found in architectural styles inspired by Romanesque and Norman traditions.

In summary, a Norman window consists of a semicircular arch at the top and a rectangular opening below it, rather than a semicircle above a rectangular window.

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The area of the courtroom is the sum of the areas of a rectangle and a triangle equal 45 m².

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

From the given diagram of the courtroom, its total area should be the sum of the area of a rectangle with a length of 9 m and width of 4 m and a triangle with a height of 3m and a base of 6 m.

Therefore,

The area of the courtroom is,

= (9×4) + (1/2)×3×6 m²      [area of triangle = (1/2)×base×height, area of  

                                                          rectangle is (length×width)]

= 36 + 9 m².

= 45m².

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The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).

Given by: The midpoint of the two points is:

M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)

The following vector runs between the two points:

V = (3 - 1, 4 - 0, 0 - (-2)) = (2, 4, 2) (2, 4, 2)

The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.

The normal vector is then provided by:

N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)

The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:

(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2

The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.

12(x - 2) = -8(y - 2) = 4(z + 1) + 2

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Answer:

Step-by-step explanation:

{k - some integer}

2k+1  - the first odd integer (the least)

5(2k+1)  - five times the least

5(2k+1)+3 - three more than five times the least

2k+1+2 = 2k+3  - the odd integer consecutive to 2k+1

2k+3+2 = 2k+5  - the next odd consecutive integer (third)

2k+5+2 = 2k+7  - the last odd consecutive integer (fourth)

2k+1+2k+3+2k+5+2k+7 - the sum of four odd consecutive integers

2k+1 + 2k+3 + 2k+5 + 2k+7 = 5(2k+1) + 3

8k + 16 = 10k + 5 + 3

     - 10k       -10k

-2k + 16 = 8

     -16       - 16    

      -2k = -8  

    ÷(-2)    ÷(-2)  

      k = 4

2k+1 = 2•4+1 = 9

2k+3 = 2•4+3 = 11

2k+5 = 2•4+5 = 13

2k+7 = 2•4+7 = 15  

Check: 9+11+13+15 = 48;  48-3 = 45;  45:5 = 9 = 2k+1

Answer:

\( \huge{ \bold{y - 3 = 7(x +9)}}\)

Step-by-step explanation:

The equation of a line in point-slope form is represented by the formula

\(y - y_1 = m(x - x_1)\)

where

(x1, y1) is the point and m is the slope

From the question the point is (-9,3) and m = 7

So we substitute the given variables into the formula and solve

We have

\(y - 3 = 7(x - - 9) \\ y - 3 = 7(x + 9)\)

Hope this helps you

The probability that the number who have tested is 0.0901.

For a job, 555 candidates are drug tested, and their results are tabulated under four categories.

A candidate is chosen at random from among these.

Probability indicates how likely an event is.

It is written as

\(P(E)=\frac{number\ of\ total\ outcome}{total \ number of \ outcome}\)

Let A represent the event of selecting a drug user.

In this case, the total number of drug users is the sum of the two categories:

The number of people who tested positive for HIV (45)

The number of people who received false negative results (5)

The total number of people tested is 555.

The likelihood of event A is,

\(P(E)=\frac{45+5}{555}=0.0901.\)

The prevalence rate is the number of people in the population who have the condition. The actual estimate is the group of people who use drugs.

The calculated probability does not appear to be a good estimate of the true prevalence level.

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Hi there!

-10-2 is equal to -12, not -8. This changes everything.

The fraction would be -12/16, which simplifies to -3/4.

I hope this helps!

Answer:

1st red box:

-10 - 2 = -12

2nd box above:

-3

3rd box:

4

Answer:

-7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

-3-(-10)/-2+1

-3-5+1

-8+1

-7

Answer:

74.2°

Step-by-step explanation:

Given:

m<A = 60°

a = 18 cm

b = 20 cm

Required:

m<ABC = B

Solution:

Apply the sine rule

\( \frac{sin(B)}{b} = \frac{sin(A)}{a} \)

Plug in the values

\( \frac{sin(B)}{20} = \frac{sin(60)}{18} \)

Multiply both sides by 20

\( \frac{sin(B)}{20}*20 = \frac{sin(60)}{18}*20 \)

\( sin(B) = \frac{sin(60)*20}{18} \)

\( sin(B) = 0.96225 \)

\( B = sin^{-1}(0.96225) \)

\( B = 74.2 degrees \) (approximated to nearest tenth)

Answer:

$585

Step-by-step explanation:

simply find 13% of 4500. 0.13 x 4500 is $585

To find the area under the standard normal curve, follow the following steps: Step 1: Draw the Standard Normal Curve. The standard normal curve is a symmetrical bell-shaped curve. The horizontal axis represents the z-values, which represent the standard deviations from the mean of the curve. The vertical axis represents the probability density, which indicates the likelihood of each z-value occurring. Step 2: Identify the Area of Interest. Under the standard normal curve, the area of interest is the shaded region that represents the probability of an event occurring. The event can be a range of z-values or a specific z-value. The area under the curve represents the probability of the event occurring. Step 3: Use the Standard Normal Table.

The standard normal table is a table of values that corresponds to the area under the curve for different z-values. The table provides the area to the left of a given z-value. To find the area between two z-values, subtract the area to the left of the smaller z-value from the area to the left of the larger z-value. The area to the right of a z-value can be found by subtracting the area to the left of the z-value from 1. To find the area for a specific z-value, use the standard normal table to find the area to the left of the z-value. Step 4: Calculate the Area.

Under the standard normal curve, the area is measured in units of standard deviation. The area between two z-values or to the right of a z-value can be calculated by multiplying the area from the standard normal table by the standard deviation of the curve. For example, if the area to the left of a z-value is 0.35 and the standard deviation of the curve is 2, then the area between the mean and the z-value is 0.35 x 2 = 0.70 square units. The area to the right of the z-value is 1 - 0.35 = 0.65, so the area beyond the z-value is 0.65 x 2 = 1.30 square units.

In summary, to find the area under the standard normal curve, draw the curve, identify the area of interest, use the standard normal table to find the area to the left of the z-value, and calculate the area in units of standard deviation. This calculation helps to interpret the probability of an event occurring in a given population. In about 200 words, this is how to find the area under the standard normal curve.

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Answer:

The solution to the system will be in the point where the two lines intersect.

Step-by-step explanation:

The solution to the system will be in the point where the two lines intersect.

The equation of that is parallel to the graph is y = 1 / 2 x + 3 and the equation perpendicular to the graph is y = -2x + 1

Equation that are parallel have the same slope.

Equation that are perpendicular gives negative 1 when multiplied .

Therefore, using slope intercept equation,

y = mx + b

where

Hence, the equation of the graph can be calculated as follows:

(0, 6)(2, 7)

m = 7 - 6  / 2 - 0 = 1 / 2

Therefore,

y = 1 / 2 x + 6

Therefore, the equation that are parallel to the graph are as follows:

The equation that are perpendicular to the graph is as follows;

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The lengths of the diagonals or "hips" of the trapezoid are:

d1 = 10 cm

d2 = 4 cm

In an inscribed trapezoid, the opposite angles are supplementary, meaning they add up to 180 degrees. Since one of the angles in the trapezoid is 120 degrees, the opposite angle will be 180 - 120 = 60 degrees.

Now, let's label the trapezoid. Let A and B be the endpoints of the longer base, with AB = 10 cm, and let C and D be the endpoints of the shorter base, with CD = 4 cm. Let E be the intersection point of the diagonals, creating two triangles within the trapezoid.

Since the opposite angles at the intersection point of the diagonals are equal, we have angle AEC = angle BDE = 60 degrees.

Since the sum of the angles in a triangle is 180 degrees, we can find angle AED by subtracting the sum of angles AEC and BDE from 180 degrees:

angle AED = 180 - (angle AEC + angle BDE)

angle AED = 180 - (60 + 60)

angle AED = 60 degrees

Now, let's consider triangle AED. It is an isosceles triangle since AE = ED (both are radii of the circle). Thus, angle ADE = angle AED = 60 degrees.

We have angle AED = angle ADE = 60 degrees, and angle AEB = 120 degrees. Therefore, angle ABE = 180 - (angle AED + angle AEB) = 180 - (60 + 120) = 0 degrees.

Angle ABE being 0 degrees means that line AB is parallel to line CD. Hence, the trapezoid is actually a rectangle.

In a rectangle, the diagonals are equal in length. Let's denote the length of the diagonals as d1 and d2.

Since AB and CD are the bases of the trapezoid, d1 is equal to the longer base AB, and d2 is equal to the shorter base CD:

d1 = 10 cm

d2 = 4 cm

Therefore, the lengths of the diagonals or "hips" of the trapezoid are:

d1 = 10 cm

d2 = 4 cm

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