O Assignment is
eBookwork
Consider the conjecture, "Any number divisible by 2 is also divisible by 4." Is each of the numbers 12, 19, 22, 28, and 30 a counterexample of the conjecture?
Complete the following table.

Answer:

  38%

Step-by-step explanation:

You want to know the percentage of students not wearing a hat if 800 did not wear a hat and 1300 did wear a hat.

The fraction of students not wearing a hat is their number divided by the total number of students:

  800/(800 +1300) = 800/2100 = 8/21

The percentage of students not wearing a hat is the fraction multiplied by 100%.

  8/21 · 100% ≈ 38.1% ≈ 38%

About 38% of students did not wear a hat.

The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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There is a very small chance (less than 1%) that a randomly selected baby from this sample was born on Tuesday OR on Friday.

To find the probability that a randomly selected baby from this sample was born on Tuesday OR on Friday, we need to add the number of babies born on Tuesday to the number of babies born on Friday, and then divide by the total number of babies in the sample.

The number of babies born on Tuesday is 202020, and the number of babies born on Friday is 151515. Therefore, the total number of babies born on Tuesday or on Friday is 202020 + 151515 = 353535.

The total number of babies in the sample is 500500500. Therefore, the probability that a randomly selected baby from this sample was born on Tuesday OR on Friday is:

353535 / 500500500 = 0.0007061

It is interesting to note that the number of babies born on different days of the week varies in this sample. For example, there are more babies born on weekdays (Monday-Friday) than on weekends (Saturday and Sunday), and there are more babies born on Tuesday than on Wednesday or Thursday.

The number of scheduled deliveries is higher than the number of unscheduled deliveries overall, but there are some days (e.g., Friday and Saturday) where there are more unscheduled deliveries than scheduled deliveries. These patterns could be explored further to understand the factors that influence the timing and scheduling of deliveries.

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The correct response is C. 0.0036 Square degrees The field of vision of the Hubble Space Telescope is only 0.006 degrees, which is around 100 times less than that of the Micro Observatory telescopes. But it has a 100 times better angular resolution!

Skywatchers can readily view planets with just a modest or medium-sized telescope. How much of our solar system is visible will wow you! Additionally, you don't need a completely dark sky to see all of the planets in our solar system; a telescope can still make Venus, Mars, Jupiter, and Saturn easily visible even when viewed in a city. From $100 to well over $10,000, a telescope can be purchased. In 2022, you can anticipate that a good telescope for visual observing will start around $300 and a telescope capable of deep-sky astrophotography would start around $800. With a 25x telescope, even the tiniest telescope should be able to see Saturn's rings.

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Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST's) advanced camera has a field of view that is roughly square and about 0.06 degree on a side. Calculate the angular area of the HST's field of view in square degrees.

A. 0.006 Square degrees

B. 0.36 Square degrees

C. 0.0036 Square degrees

D. 0.06 Square degrees

..............36.8 dm

Jack has a total of 35 different combinations of fruits to choose from at the store.

To calculate the number of combinations Jack can choose, we need to use the concept of combinations in mathematics. Since Jack can buy any three fruits out of the seven available options, we need to calculate the number of combinations of 7 fruits taken 3 at a time.

The formula to calculate combinations is C(n, r) = n! / (r! * (n - r)!), where n is the total number of options and r is the number of options to be chosen.

In this case, n = 7 (total number of fruits) and r = 3 (fruits to be chosen). Plugging these values into the formula, we get:

C(7, 3) = 7! / (3! * (7 - 3)!)

        = (7 * 6 * 5 * 4!) / (3 * 2 * 1 * 4!)

        = (7 * 6 * 5) / (3 * 2 * 1)

        = 35

Jack has a total of 35 different combinations of fruits to choose from at the store. He can select any three fruits out of the available options, which include apples, oranges, pears, bananas, plums, grapefruit, and kiwis.

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Latesha should compare the values 5 (from 4x - 3) and 9 (from one-half (4x - 6) - 2x(1 - 3)). If both values are equal, it would justify that the expressions are equivalent.

To determine if the expressions 4x - 3 and one-half (4x - 6) - 2x(1 - 3) are equivalent, Latesha can compare the values of the expressions when x = 2. By substituting x = 2 into both expressions, Latesha can calculate the numerical values and compare them.

For the expression 4x - 3:

- Substitute x = 2: 4(2) - 3 = 8 - 3 = 5.

For the expression one-half (4x - 6) - 2x(1 - 3):

- Substitute x = 2: 0.5(4(2) - 6) - 2(2)(1 - 3) = 0.5(8 - 6) - 2(2)(-2) = 0.5(2) - 2(-4) = 1 - (-8) = 1 + 8 = 9.

Latesha should compare the values 5 (from 4x - 3) and 9 (from one-half (4x - 6) - 2x(1 - 3)). If both values are equal, it would justify that the expressions are equivalent.

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The equation of a circle with center (a, b) and radius r is:

(x - a)^2 + (y - b)^2 = r^2

(x, y) represents any point on the circle

A circle is described as a shape consisting of all points in a plane that are at a given distance from a given point, the center.

The properties of the circle are as follows:

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The provider has prescribed ibuprofen 800 mg po tid. the unit dose is 400 mg tablets.6 tablets will be administered to the client.

To calculate the number of tablets that will be administered to the client when the provider has prescribed ibuprofen 800 mg po tid and the unit dose is 400 mg tablets, the following steps can be used:

Step 1: Determine the total daily dose

To determine the total daily dose, the 800 mg dose prescribed three times daily can be added up.

800 mg + 800 mg + 800 mg = 2400 mg/day

Step 2: Calculate the number of tablets needed to achieve the daily dose

The total daily dose can be divided by the strength of the tablet to determine the number of tablets needed to achieve the daily dose.

2400 mg/day ÷ 400 mg/tablet = 6 tablets/day

Therefore, 6 tablets will be administered to the client.

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Answer:

irrational

Step-by-step explanation:

pi itself is an irrational number, pi/2 will also be an irrational number

Answer:

irrational

Step-by-step explanation:

it's an irrational number divided by a rational so therefore it is irrational

a. there must be at least two pairs of these integers with the sum 11. b. The conclusion in part (a) is not true if six integers are selected instead of seven.

a) To show that if seven integers are selected from the first 10 positive integers, there must be at least two pairs of these integers with the sum 11, we can use the pigeonhole principle.

In this case, we have 10 positive integers to choose from. If we select seven integers, we can think of each integer as a pigeonhole. Since we have more pigeons (selected integers) than pigeonholes (possible sums), by the pigeonhole principle, there must be at least one pigeonhole with at least two pigeons.

Let's consider the possible pairs of integers with a sum of 11:

(1, 10), (2, 9), (3, 8), (4, 7), (5, 6)

If we select seven integers, at least two of them must belong to the same pair, and their sum will be 11. Therefore, there must be at least two pairs of these integers with the sum 11.

b) If six integers are selected rather than seven, the conclusion in part (a) may not be true. Let's consider a scenario where we select the integers 1, 2, 3, 4, 5, and 6. In this case, there are no two pairs of integers with a sum of 11. The possible sums of pairs from these integers are:

(1, 10): Not selected

(2, 9): Selected

(3, 8): Not selected

(4, 7): Selected

(5, 6): Not selected

As we can see, with only six integers selected, we can choose them in such a way that there are no two pairs with a sum of 11. Therefore, the conclusion in part (a) is not true if six integers are selected instead of seven.

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Answer:

The awnser is 31

Step-by-step explanation:

47 minus 16 = 31

Answer:

$31

Step-by-step explanation:

Since he earned $16 an now has $47, all you need to do is subtract 16 from 47 to get 31.

47 - 16 = 31

The value of the expression, \((-r-10)-(-4r^2+r+7)\) is \(4r^2-2r-17\) such that \((-r-10)-(-4r^2+r+7)\).

The difference between the two numbers \(a\), and \(b\) is \((a-b)\).

Simplify the given expression as-

\((-r-10)-(-4r^2+r+7)=-r-10+4r^2-r-7\\=4r^2-2r-17\)

Thus, the value of the expression, \((-r-10)-(-4r^2+r+7)\) is \(4r^2-2r-17\).

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The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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The equation of the parabola with focus at f(0 -4) and directrix x = 4 is

y² = 16x.

A parabola is a quadratic function graph. A parabola, according to Pascal, is a circle's projection. Galileo demonstrated that projectiles falling under the influence of uniform gravity have a path known as a parabolic path. Many bodily motions follow a curvilinear route that is shaped like a parabola. In mathematics, a parabola is any mirror-symmetrical planar curve that has an approximate U shape. The goal of this section is to comprehend the derivation of a parabola's standard formula, the several standard forms of a parabola, and the properties of a parabola.

Given

Focus at f(0, -4)

Directrix x = 4

As we know, the equation of a parabola with focus (a, 0) and directrix x = a

y² = 4ax.

y² = 4(4)x

y² = 16x

The equation of the parabola with focus at f(0 -4) and directrix x = 4 is

y² = 16x.

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Yes, $9 for 4 visitors and $18 for 8 site visitors are proportional.

To determine whether or not $9 for 4 visitors and $18 for 8 visitors are proportional, we need to test if the ratio of the value to the number of visitors is the equal for both cases.

The ratio of cost to the quantity of visitors for $9 and four visitors is:

$9/4 visitors = $2.25/ visitors

The ratio of value to the quantity of visitors for $18 and eight visitors is:

$18/8 visitors = $2.25/ visitors

We are able to see that both ratios are equal to $2.25 per visitor.

Therefore, $9 for 4 visitors and $18 for 8 site visitors are proportional.

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Answer: A and D

Step-by-step explanation: The centimeters of the triangles are the same, therefore congruent.

The surface area of the closed cylinder is  \(2πrh + 2πr^2\). The lateral surface area of a cylinder can be calculated using the formula 2πrh, where r is the radius and h is the height of the cylinder.

This formula represents the area of the curved surface that wraps around the cylinder.

The surface area of the two circular bases can be calculated using the formula 2πr^2, where r is the radius of the cylinder.

To find the total surface area, we add the lateral surface area and the area of the two bases. Therefore, the formula for the total surface area of a closed cylinder is:

Surface Area = \(2πrh + 2πr^2\).

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The total surface area is \(\[ A_{\text{total}} = 2 \times 16\pi + 48\pi = 80\pi \text{ square units} \]\).  A closed cylinder is a three-dimensional shape with two circular bases and a curved surface connecting them.

The term "positively-oriented" or "outward-oriented" means that the normal vectors on the surface of the cylinder are pointing away from the center of the cylinder. It has a radius (r) and a finite height (h).

To calculate the surface area of the cylinder, we need to find the area of each circular base and the area of the curved surface.

1. The area of each circular base is given by the formula \(\[ A_{\text{base}} = \pi r^2 \]\). Since there are two bases, the total base area is 2 * A_base.

2. The curved surface area can be calculated using the formula \(\[ A_{\text{curved}} = 2\pi r h \]\). This represents the area of the rectangle that wraps around the cylinder.

3. Finally, we can find the total surface area by adding the base area and the curved surface area: \(\[ A_{\text{total}} = 2 \cdot A_{\text{base}} + A_{\text{curved}} \]\).

For example, let's consider a cylinder with a radius of 4 units and a height of 6 units.

The base area is \(\[ A_{\text{base}} = \pi \times (4^2) = 16\pi \text{ square units} \]\).
The curved surface area is \(\[ A_{\text{curved}} = 2\pi \times 4 \times 6 = 48\pi \text{ square units} \]\) .


In conclusion, the surface area of a positively-oriented closed cylinder with a radius (r) and height (h) is given by the formula \(\[ A_{\text{total}} = 2 \pi r^2 + 2\pi r h \]\)

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Complete Question :  1. Suppose that S is a positively-oriented (or outward-oriented) closed cylinder of radius R and finite height h. (a) Determine div Ě, where F = (xy, y +z, x – yz). (b) Use the Divergence Theorem to compute the flux of Ę across S (Hint: you should not need to actually compute a triple integral here - instead, think about what it represents).

The pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay is represented in dollars per hour, and it ranges from $12 per hour for a new employee in a low-level position to $60 per hour for a senior developer with extensive experience.

For example, if we look at the table created in part a, we can see that a junior developer with less than a year of experience will earn $18 per hour, while a senior developer with more than 10 years of experience will earn $60 per hour. This means that the pay at the Digital Source is directly related to the employee's experience and job position.

Additionally, the table also shows that the pay rate increases as the employee gains more experience and moves up the career ladder. For instance, a junior developer with less than a year of experience will earn $18 per hour, but a mid-level developer with 3-5 years of experience will earn $35 per hour. This shows that employees are rewarded for their skills and experience, and they have the opportunity to advance their careers and earn higher pay rates.

In summary, the pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay rate ranges from $12 per hour to $60 per hour, and it increases as the employee gains more experience and moves up the career ladder. The company values the skills and expertise of their employees and rewards them accordingly.

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Answer: x < 5

Step-by-step explanation:

4 - 4x + 5 + 5x > 3x - 1

9 + x > 3x - 1

10 > 2x

x < 5

The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.

The probability of renting exactly three apartments in a week is given by the Poisson probability function:

\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)

Substituting the values, we get:

\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)

P(X = 3) = (0.09963 * 12.167) / 6

P(X = 3) = 0.2018

Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

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Given:

The perimeter of a rectangle is 84cm.

The length is 12 cm longer than the width.

Required:

We need to find the length and width of the rectangle.

Explanation:

Let l be the length of the rectangle and w be the width of the rectangle.

The length is 12 cm longer than the width.

Add 12 to the width to get the length.

Consider the perimeter of the rectangle formula.

Substitute l=12+w and P =84 in the formula.

Subtract 24 from both sides of the equation.

Divide both sides of the equation by 4.

Substitute w =15 in the equation l=12+w.

Final answer:

The length of the rectangle is 27 cm.

The width of the rectangle is 15 cm.

The equation to determine p, which is the total number of player at the basketball game, is 12 = p x 3 / 4 .

The number of players at the basketball game is 16 players .

The equation to find the number of players is;

Players who chose water = total players x proportion of players who chose water

12 = p x 3 / 4

This means that solving for p gives :

12 = p x 3 / 4

12 ÷ 3 / 4 = p

p = 12 ÷  3 / 4

p = 12 / 0.75

p = 16 players

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Answer: area of triangle = 1/2 base*height  = 1/2  * 2 x 10   = 10 ft2   each

then you are left with a rectangle   13 ft x 10 ft = 130 ft^2

130 + 10 + 10 = 150 ft2

Step-by-step explanation: Hope it helps

Answer:

Below

Step-by-step explanation:

First let's determine the slope if thus function

Let m be the slope of this function

m = [0-(-4)]/ 2-0 = 4/2 =2

So our equation is:

y = 3x +b

b is the y-intercept wich is given by the image of 0

Here it's -4

So the equation is:

y = 2x-4 wich is also y = x-2 after simplifying

●●●●●●●●●●●●●●●●●●●●●●●●

A line that is parallel to this one will have the same slope.

Examples:

● y= 2x+3

● y = 2x-7

■■■■■■■■■■■■■■■■■■■■■■■■■■

A line that is perpendicular to this one and has a slope m' satisfy this condition:

m*m'= -1

m'= -1/m

m' = -1/2

So this line should have a slope that is equal to -1/2

Answers from the choices:

y = -1/2 x +1/2

y+1= -1/2 (x-3)

The value of dz/dt, using the chain rule, is (-3t^2 + 7t + 12)e^(3t). (The expression is obtained by substituting the given values and differentiating with respect to t using the chain rule.)

We are given:

z = (x + y)e^x

x = 3t

y = 4 - t^2

To find dz/dt, we need to differentiate z with respect to t using the chain rule. Let's substitute the given expressions into z:

z = ((3t) + (4 - t^2))e^(3t)

Now, we differentiate z with respect to t, applying the chain rule:

\(dz/dt = (d/dt)((3t + 4 - t^2)e^(3t))\)

\(= ((3 + (-2t))e^(3t)) + ((3t + 4 - t^2)(d/dt)(e^(3t)))\)

\(= (3 - 2t)e^(3t) + (3t + 4 - t^2)(3e^(3t))\)

\(= (3 - 2t)e^{(3t)} + 3(3t + 4 - t^2)e^{(3t)\)

\(= (3 - 2t + 9t + 12 - 3t^2)e^(3t)= (-3t^2 + 7t + 12)e^(3t)\)

Therefore, dz/dt is given by (-3t^2 + 7t + 12)e^(3t) based on the given values and applying the chain rule.

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The experimental probability the next 4 customers will order a salad is 12.96%

The experimental probability of the next 4 customers ordering a salad can be calculated by multiplying the individual probabilities of each customer ordering a salad.

Given that 60% of customers typically order a salad, the probability of a customer ordering a salad is 0.6, or 60% expressed as a decimal.

To find the probability of all 4 customers ordering a salad, we multiply the probabilities together:

P(4 customers ordering a salad) = 0.6 * 0.6 * 0.6 * 0.6 = 0.6^4 = 0.1296

Therefore, the experimental probability of the next 4 customers ordering a salad is 0.1296, or 12.96% expressed as a percentage.

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