The average full-time faculty member in a post-secondary degree granting institution works an average of 46 hours per week. Round intermediate calculations and final answers to two decimal places as needed.
(a) If we assume the standard deviation is 2.4 hours, then no more than % of faculty members work more than 53.2 hours a week.

Thus, the given sequence is arithmetic, and the common difference is -100

The given sequence is: -18, -118, -218, -318,...To determine whether the sequence is arithmetic or not, we need to check whether the difference between consecutive terms is constant or not.If the difference is constant, then the sequence is arithmetic.

The sequence is not arithmetic.Difference between consecutive terms can be found by subtracting the second term from the first term, the third term from the second term, and so on.

Difference between the first two terms: (-118) - (-18) = -118 + 18 = -100Difference between the second two terms: (-218) - (-118) = -218 + 118 = -100Difference between the third two terms: (-318) - (-218) = -318 + 218 = -100The difference between each of the consecutive terms is -100. Thus, the given sequence is arithmetic, and the common difference is -100.

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Answer:

n = √108

Step-by-step explanation:

Use similar triangles or the right triangle altitude theorem.

18/n = n/6

n^2 = 18 * 6

n^2 = 108

n = √108

Answer:

48^2 =2304 < 2345 < 2401 = 49^2

=> Smallest number should be: 2401 - 2345 = 56

Hope this helps!

:)

Answer:

56

Step-by-step explanation:

sqrt(2345) = 48.425...

Nearest integer is 49

So, the nearest perfect is 49²

49² = 2401

To be added:

2401 - 2345

56

Answer:

He paid $33 dollars for the shoes

Step-by-step explanation:

Answer:

200 a piece bc thats half

The answer is;

62.83

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

The first 6 prime numbers are  2, 3, 5, 7, 11 ,13

The square of 6 prime number

4, 9 ,25, 49 , 121 , 169

The mean difference of these number is

⇒ (4 + 9 + 25 + 49 + 121 + 169) / 6

⇒ 62.83

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The volume of the solid obtained by rotating the region bounded by \(y=x^2\) and \(x=y^2\) about \(x=-4\) is approximately \(-\frac{10\pi}{3}\) cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves \(y = x^2\) and \(x = y^2\) about the line \(x = -4\), we can use the method of cylindrical shells.

First, let's sketch the region to visualize it better. The curves intersect at two points: \((-1,1)\) and \((0,0)\). The region is symmetric with respect to the line \(y = x\), and the rotation axis \(x = -4\) is located to the left of the region.

To set up the integral for the volume, we consider an infinitesimally thin strip of height \(dy\) along the y-axis.

The radius of this strip is \(r = (-4) - y = -4 - y\), and the corresponding infinitesimal volume element is \(dV = 2\pi r \cdot y \, dy\). The factor of \(2\pi\) accounts for the cylindrical shape.

Integrating this expression from \(y = 0\) to \(y = 1\) (the y-coordinate bounds of the region), we get:

\[V = \int_0^1 2\pi (-4 - y) \cdot y \, dy\]

Evaluating this integral gives us the volume \(V\) of the solid obtained by rotating the region bounded by the given curves about the line \(x = -4\).

Certainly! Let's calculate the volume of the solid step by step.

We have the integral expression for the volume:

\[V = \int_0^1 2\pi (-4 - y) \cdot y \, dy\]

To evaluate this integral, we expand and simplify the expression inside the integral:

\[V = \int_0^1 (-8\pi y - 2\pi y^2) \, dy\]

Now, we can integrate term by term:

\[V = -8\pi \int_0^1 y \, dy - 2\pi \int_0^1 y^2 \, dy\]

Integrating, we have:

\[V = -8\pi \left[\frac{y^2}{2}\right]_0^1 - 2\pi \left[\frac{y^3}{3}\right]_0^1\]

Evaluating the limits, we get:

\[V = -8\pi \left(\frac{1^2}{2} - \frac{0^2}{2}\right) - 2\pi \left(\frac{1^3}{3} - \frac{0^3}{3}\right)\]

Simplifying further:

\[V = -8\pi \cdot \frac{1}{2} - 2\pi \cdot \frac{1}{3}\]

\[V = -4\pi - \frac{2\pi}{3}\]

Finally, combining like terms, we get the volume of the solid:

\[V = -\frac{10\pi}{3}\]

Therefore, the volume of the solid obtained by rotating the region bounded by the curves \(y = x^2\) and \(x = y^2\) about the line \(x = -4\) is \(-\frac{10\pi}{3}\) (approximately -10.47 cubic units).

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The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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Answer:

67.50

Step-by-step explanation:

100%-> 450

15%-> 67.50

Answer:

18502.8229198

Answer:

18502.82292

Step-by-step explanation:

calculator

The width of the river at that point can be estimated to be approximately 1,579 feet.

To estimate the width of the river, we can use the concept of similar triangles. Let's consider the situation from a side view perspective. The height of the Gateway Arch, which acts as the vertical leg of a triangle, is given as 630 feet. The angle of depression to the closer bank is 45°, and the angle of depression to the farther bank is 18°.

We can set up two similar triangles: one with the height of the arch as the vertical leg and the distance to the closer bank as the horizontal leg, and another with the height of the arch as the vertical leg and the distance to the farther bank as the horizontal leg.

Using trigonometry, we can find the lengths of the horizontal legs of both triangles. Let's denote the width of the river at the closer bank as x feet and the width of the river at the farther bank as y feet.

For the first triangle:

tan(45°) = 630 / x

Solving for x:

x = 630 / tan(45°) ≈ 630 feet

For the second triangle:

tan(18°) = 630 / y

Solving for y:

y = 630 / tan(18°) ≈ 1,579 feet

Therefore, the estimated width of the river at that point is approximately 1,579 feet.

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Answer:

y=-4/7x+4

Step-by-step explanation:

hope this helps

Answer:

4/7+4=y

Step-by-step explanation:

y=mx+b

Answer:

1. C. The managers used a cluster sample

2.  B)The managers used a systematic sample.

3. The managers used a stratified sample.

Step-by-step explanation:

1. In a cluster sampling method, the population would be divided into several small units called cluster by the researcher. Within these clusters we randomly pick one or more to observe.

2. In systematic sampling we select elements from an ordered sampling frame.

3. In stratified sampling, the population is divided into several stratas and the researcher then selects randomly to complete the sampling process

ANSWER

112

EXPLAINATION

28÷16 = 7

7×16 = answers

The number of students for each favorite sport from the bar graph is:

Cricket = 75

Football = 35

Tennis = 50

Badminton = 30

Swimming = 65

We have,

From the bar graph,

We can find the number of students for each favorite sport.

Now,

Cricket = 75

Football = 35

Tennis = 50

Badminton = 30

Swimming = 65

Now,

The total number of students in the bar graph.

= 75 + 35 + 50 + 30 + 65

= 255

Thus,

The number of students for each favorite sport is:

Cricket = 75

Football = 35

Tennis = 50

Badminton = 30

Swimming = 65

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Answer:

x=-1

Step-by-step explanation:

-2x - 5 = -3

add 5 to both sides

-2x = 2

divide both sides by -2

x = -1

Answer:

x = -1

Step-by-step explanation:

-2x - 5 = -3

Same to both sides:

-2x = -3 + 5

Simplify:

-2x = 2

Divide by -2 on each side to isolate x:

x = -1

Let me know if you have any questions

The correct way to measure the zone of inhibition is to place a known amount of an antimicrobial agent on a solid medium.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The zone of inhibition is then measured as the area surrounding the antimicrobial agent where microbial growth has been inhibited. This area is typically measured in millimeters. To accurately measure the zone of inhibition, it is important to ensure that the size of the inoculum and the amount of antimicrobial agent used remain constant. Additionally, it is important to consider the type of organism being studied, as different organisms can have different levels of susceptibility to the antimicrobial agent. Finally, the medium used should be appropriate for the organism being studied, as different media can produce different results.

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Answer:

-$36

Step-by-step explanation:

Daniel has a starting balance of $259, so anything he spends will be deducted by this amount. To find out how much he spent, we need to add up everything he bought.

He spent $45 + $150 + $100, adding to a grad total of $295.

To find out how much money Daniel has left, we need to subtract his purchases from his funds. This would be $259 - $295. This leaves you with a final answer of -$36 in Daniel's bank account.

Answer:

I think its D

Step-by-step explanation:

You can rule out A and B because he would be able to throw it farther than 30 ft do that leaves C and D but davis Couldn't throw a 9.1 lb ball 30 ft so the answer is D

The value of x is 2.045 by simple algebra.

Use the time formula, t = d/s, which states that time is equal to distance divided by speed, to solve for time. Time is a function of both speed and distance.

Until it reaches its destination 200 miles distant, a car is driving on a little highway at either 55 or 35 miles per hour, depending on the posted speed restrictions.

x is the duration, in hours, that the vehicle is travelling at 55 mph.

Y is the duration, in hours, that the vehicle is travelling at 35 mph.

55x + 35y = 200 is the equation defining the relationship.

We must locate:

If the trip takes the car 2.5 hours at 35 miles per hour, how long does it take to travel at 55 miles per hour?

∵ 55x + 35y = 200

The drive takes the car 2.5 hours at a speed of 35 mph.

Y shows the duration of time for an automobile travelling at 35 mph.

∴ y = 2.5

- To obtain the value of x, substitute the value of y into the equation.

∴ 55x + 35(2.5) = 200

∴ 55x + 87.5 = 200

- Take 87.5 off of both sides.

∴ 55x = 112.5

- Subtract 55 from both sides.

x equals 2.045 hours.

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Answer: I hope I got it right. You can mark brainliest if you want. I don't really care.

Step-by-step explanation:

Well, it seems that for every week, Pragitha swims x + 2 laps. So if she swims x + 2 laps twice, she will get 2x + 4. So x is equal to 4. You add that four and you get three x. So for one week, she swims x + 2 laps and for the second lap, she swims 2x + 4. Which according to the table, is equal to 3x. So for 3 weeks, she clearly swims less, because maybe she's tired or something. So it's 2x+1. And for week 4, it's week one and week 2 combined.

The expression on the other hand is

10x + 9

Answer:

D) 9.2 ft

Step-by-step explanation:

Hope I helped :)

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Answer: i think its the second one

Step-by-step explanation:

Answer:

Square root of 10.

Step-by-step explanation:

To solve, you would find the hypotenuse of a right triangle. the length, which is from -2 to 1, is 3. The height, from 2 to 3, is 1. that means, you square 3, so 9, and square 1, which is 1. You add those which give you 10. The hypotenuse, or the distance from point A to point B is the square root of 10, or 3.16...

Answer:

  30 cm²

Step-by-step explanation:

The shaded area is the difference between the area of the rectangle and the area of the triangle.

The area of the rectangle is ...

  A = LW = (12 cm)(4 cm) = 48 cm²

The area of the triangle is ...

  A = 1/2bh = 1/2(9 cm)(4 cm) = 18 cm²

__

The shaded area is the difference ...

  rectangle area - triangle area = 48 cm² -18 cm² = 30 cm²

The area of the shaded region is 30 square centimeters.

Answer:

Step-by-step explanation:

A(rectangle) - A(triangle)

L×W - ½×B×H

12×4 - ½×(9)×(4)

48 - 2×(9)

48 - 18

= 30cm²

Answer:

A) \(f^{-1}(x)=-\frac{1}{5}x-\frac{4}{5}\)

Step-by-step explanation:

\(f(x)=-5x-4\\y=-5x-4\\x=-5y-4\\x+4=-5y\\-\frac{1}{5}x-\frac{4}{5}=y\\\\f^{-1}(x)=-\frac{1}{5}x-\frac{4}{5}\)

When finding the inverse of a function, we switch the values of x and y, and then solve for y, like in the 3rd-6th steps.

Answer:

512 points altogether.

Step-by-step explanation:

This is a guess hope it helps :D

Answer:

512

Step-by-step explanation:

&:(::6)6/$/):&;!4):$:$:$:&):=512

Answer:

\(\boxed{\sf a=\cfrac{\sqrt{15i} }{3}}\)

\(\boxed{\sf a=-\cfrac{\sqrt{15i} }{3}}\)

Step-by-step explanation:

\(\sf 6a^2 + 10 = 0\)

We'll solve this equation using The Quadratic Formula:

\(\boxed{\sf \frac{-b\pm \sqrt{b^2-4ac} }{2a} }\)

\(\sf 6a^2 + 10 = 0\)

Substitute 6: a, 0: b, 10: c

\(\longmapsto\sf a=\cfrac{0\pm\sqrt{0^2-4\times 6\times 10} }{2\times 6}\)

→ Square 0

→ Multiply -4 * 6= -24

→ Multiply -24 * 10 = -240

\(\longmapsto\sf a=\cfrac{0\pm\sqrt{-240} }{2\times 6}\)

→ Take the square root of -240:

→ Multiply 2 * 6= 12

Now, Separate solutions:

\(\longmapsto\sf a=\cfrac{0\pm 4\sqrt{15i} }{12}\)

Now, Separate solutions:

First, solve the equation when ± is plus:

\(\longmapsto \boxed{\sf a=\cfrac{\sqrt{15i} }{3}}\)

___

Now, solve it when ± is minus:

\(\longmapsto \boxed{\sf a=-\cfrac{\sqrt{15i} }{3}}\)

__________________________________________

\(\sf\longmapsto 6a^2+10=0\)

\(\sf\longmapsto a=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)(This a is root of equation)

\(\sf\longmapsto a=\dfrac{-0\pm\sqrt{0^2-4(6)(10)}}{2(6)}\)

\(\sf\longmapsto a=\dfrac{\pm\sqrt{-240}}{12}\)

\(\sf\longmapsto a=\dfrac{\pm\sqrt{240}i}{12}\)

\(\sf\longmapsto a=\dfrac{\pm 4√15i}{12}\)

\(\sf\longmapsto a=\dfrac{\pm √15i}{3}\)

\(\sf\longmapsto a=\dfrac{\pm √3√5i}{3}\)

\(\sf\longmapsto a=\pm\dfrac{√5i}{\sqrt{3}}\)

\(\sf\longmapsto a=\pm\sqrt{\dfrac{5}{3}}i \)

i stands for iota.

\(\sf\longmapsto i=\sqrt{-1}\)