The time to complete a project varies inversely with the number of employees. If 6 people can complete the project in 4 days, how long will it take 8 people?

Answer: B)28

Step-by-step explanation:

The Breakeven revenue for the retail business is Birr 12,500

Breakeven is the point at which the revenue is equals to the cost, hence the profit is zero.

Revenue = Cost

Let x represent the number of items sold, hence:

Revenue = (100% + 25%) of x = 1.25x

Cost = 5% of x + 12000 = 0.05x + 12000

At breakeven:

1.25x = 0.05x + 12000

x = 10000

Hence:

Revenue = 1.25(10000) = Birr 12,500

The Breakeven revenue for the retail business is Birr 12,500

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Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

First, identify the three vectors in component form (remember to have the direction angle for each vector account for the quadrants they are in!):

[tex]u=\langle90\cos220^\circ,90\sin220^\circ\rangle\\v=\langle 60\cos110^\circ,60\sin110^\circ\rangle\\w=\langle 40\cos30^\circ,40\sin30^\circ\rangle[/tex]

Secondly, we add them:

[tex]u+v+w=\langle90\cos220^\circ+60\cos110^\circ+40\cos30^\circ,90\sin220^\circ+60\sin110^\circ+40\sin30^\circ\rangle\approx\langle-54.824,18.531\rangle[/tex]

Thirdly, find the magnitude of the new vector:

[tex]||u+v+w||=\sqrt{(-54.824)^2+(18.531)^2}\\||u+v+w||\approx57.871[/tex]

And finally, find the direction of the new vector:

[tex]\theta=tan^{-1}(\frac{18.531}{-54.824})\\\theta\approx-18.675^\circ\approx-19^\circ[/tex]

Because our new vector is in Quadrant II, our found direction angle is a reference angle, telling us that the actual direction of our vector is 19° clockwise from the negative x-axis, which would be 180°-19°=161°

Thus, B is the best answer

Problem 2

To find the component form of a vector, we simply subtract the initial point from the terminal point. In this case, our initial point is at (7,-1) and our terminal point is at (1,6). We subtract the horizontal and vertical components separately:

[tex]\langle1-7,6-(-1)\rangle=\langle-6,7\rangle[/tex]

Thus, A is the correct answer

Problem 3

Again, subtract the initial point from the terminal point to find the vector, and then apply scalar multiplication:

[tex]-\frac{1}{2}v=-\frac{1}{2} \langle-8-8,10-4\rangle=-\frac{1}{2}\langle-16,6\rangle=\langle8,-3\rangle[/tex]

Thus, C is the correct answer

Problem 4 (top one in 4th image)

Remember that scalar multiplication only affects the magnitude of the vector and not the direction. Thus, [tex]-3u=-3\bigr[20\langle\cos30^\circ,\sin30^\circ\rangle\bigr]=-60\langle\cos30^\circ,\sin30^\circ\rangle[/tex], which means our magnitude is -60 and our direction remains 30°.

Thus, B is the correct answer

Problem 5 (fake #6, bottom one in 4th image)

Basically, whatever is in front of the i represents the horizontal component, and whatever is in front of the j represents the vertical component, so:

[tex]u=-3i+8j=\langle-3,8\rangle[/tex]

Thus, B is the correct answer

Problem 6 (real one, 5th image)

Recall:

Knowing these facts, let us compute the dot product:

[tex]u\cdot v=(-4*28)+(7*-49)=(-112)+(-343)=-455[/tex]

Since the dot product of the two vectors is not 0, then the vectors are not orthogonal, so we can eliminate choices A and B

To check if the vectors are parallel, find the angle between them:

[tex]\displaystyle\theta=cos^{-1}\biggr(\frac{u\cdot v}{||u||\:||v||}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{(-4)^2+(7)^2}\sqrt{(28)^2+(-49)^2}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{16+49}\sqrt{784+2401}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{65}\sqrt{3185}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{207025}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{455}\biggr)\\\\\theta=cos^{-1}(-1)\\\\\theta=180^\circ[/tex]

So, since the angle between the two vectors is 180°, this implies that cosθ=-1, and the two vectors must be parallel.

Thus, D is the correct answer

Circle One:

No

Explain:

The chart shows that teenagers get roughly between 7 - 8 and 1/2 hours of sleep every night. It shows that no teenagers get 9 and 9 and 1/2 hours of sleep. This is why their data does not support the delay to starting time.

Answer: ( -[tex]\sqrt{5}[/tex] / 3)

Step-by-step explanation:

sin(angle) = opposite/hypotenuse

opposite =2

hypotenuse = 3

solve for adjacent side with pythagorean theorum

opposite^2 + adjacent^2 = hypotenuse^2

2^2 + adjacent^2 = 3^2

4 + adjacent^2 = 9

adjacent^2 = 9 - 4

adjacent^2 = 5

adjacent = [tex]\sqrt{5}[/tex]

-[tex]\sqrt{5}[/tex] since it is in the second quadrant

cosx = (adjacent/hypotenuse)

cosx = (-[tex]\sqrt{5}[/tex]/3)

(-[tex]\sqrt{5}[/tex]/3)

Question 3

Let the number of times an odd number was chosen be x. Then, the number of times an even number was chosen is x+4.

[tex]x+x+4=50\\\\2x+4=50\\\\2x=46\\\\x=23[/tex]

So, the answer is 23 times.

Question 4

If 8 ordered pizza, 4 did not order pizza.

[tex]\frac{4}{12}=\frac{1}{3}[/tex]

So, the answer is 1 out of 3.

r = 50/2.5 = 20 cm

------------------------

Clock pendulums swing 8 degrees or less, which is an included angle of ~0.28 radians

Answer:

5 and -5

Step-by-step explanation:

3x² = 75

x² = 75/3

x² = √25

x = 5 and - 5

The mode of the data in the line plot is the data with the highest number of marks

The mode of the data is 8

From the line plot, we have the following frequency table:

Number        Frequency

5                       2 marks

6                       4 marks.

7                        3 marks

8                        6 marks

9                         2 marks

10                         4 marks

11                         2 marks

The number with the highest mark is 9

Hence, the mode of the data is 8

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Answer: The mode is 8

Step-by-step explanation: Mode means the number that shows up must in the graph and since 8 is the highest that goes the mode is 8. Also I did the k12 quiz.

Answer:

C  69

Step-by-step explanation:

The correct option for Which confidence level would produce the widest interval when estimating the mean of a population based on the mean and standard deviation of a sample of that population is C. 69%

A population is the number of living people that live together in the same place. A city's population is the number of people living in that city. These people are called inhabitants or residents. The population includes all individuals that live in that certain area.

Conclusion: It can be a group of people, objects, events corporations, and so forth. you use populations to attract conclusions. determine 1: population. An example of a population would be the complete scholar body at a faculty. it'd consist of all of the college students who examine in that university at the time of statistics collection.

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Answer:

5 feet

Step-by-step explanation:

[tex]f(t) = 3 cos \bigg( \frac{\pi}{6} t\bigg) + 5 \\ \\ plug \: t = 9 \\ \\ \implies \: f(9) = 3 cos \bigg( \frac{\pi}{6} \times 9 \bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \frac{3\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \pi + \frac{\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = - 3 cos \bigg( \frac{\pi}{2}\bigg) + 5 \\ [ \because \: cos ({\pi}+\theta) = -\cos \theta]\\\\\implies \: f(9) = - 3 (0) + 5 \\ ( \because \: cos \frac{\pi}{2} = 0) \\ \\ \implies \: f(9) = 0 + 5 \\ \\ \implies \: \huge{ \orange{f(9) = 5 }}[/tex]

Answer:

  (x, y) = (3, 8)

Step-by-step explanation:

The graph for y is a translation upward 4 units of the graph of f(x).

__

A point on the graph of f(x) is given as ...

  (x, f(x)) = (3, f(3)) = (3, 4)

Then a point on the graph of y will be ...

  (x, y) = (x, f(x) +4)) = (3, f(3)+4) = (3, 4 +4)

  (x, y) = (3, 8)

Answer:

arc sr

Step-by-step explanation:

i can't see the options for the question so lol

im gonna say its sr arc

Answer:four hundred and thirty nine thousand five hundred and thirty two

Step-by-step explanation:

Answer:

four hundred thirty nine thousand, five hundred thirty two

Step-by-step explanation:

Hope this helps :)

Answer:

is TURNS

Step-by-step explanation:

A figure but does not change its shape and size is Turns.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items.

A flip is a geometric movement that involves turning an object over in a straight line to create a mirror image. The distance between each point on an object and its corresponding point on the picture is equal. A reflection is another name for a flip.

Thus, thus required transformation is Turns.

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Answer:

The product of a rational number with an irrational number is an irrational number. To see this assume that x is a rational number and y an irrational number. Then let us assume that the product xy is rational, which means that there are integers a,b such that xy=a/b. But then we obtain y=(1/x)(a/b) which is also rational since the set of rational numbers is closed under multiplication. But this is a contradiction since y was assumed to be an irrational number.

Step-by-step explanation:

Question:Now consider the product of a nonzero rational number and an irrational number. Again, assume x =a/b , where a and b are integers and b ≠ 0. This time let y be an irrational number. If we assume the product x · y is rational, we can set the product equal to m/n, where m and n are integers and n ≠ 0. The steps for solving this equation for y are shown. Based on what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of number y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number?

Answer:2

Answer:

y = -3x + 2

Step-by-step explanation:

use the slope formula to find the slope

replace x and y into slope intercept form with the slope you just found

Base on the equidistant chords theorem, chords FB and DA are congruent because they are equidistant from C.

The equidistant chords theorem states that two chords in the same circle are congruent to each other, if they are equidistant from the center of the circle.

Thus, based on the information given we can conclude that chords FB and DA are congruent because they are equidistant from C based on the equidistant chords theorem.

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Answer:

Its D The one at the top is incorrect.

Step-by-step explanation:

I got A 100% which means i got it right...

= 5^-3 × 7⁰

= 1/5³ × 1. ( a^-m = 1/a^m ), ( a⁰ = 1 )

= 1/125 × 1

= 1/125 ANSWER

Answer:

see explanation

Step-by-step explanation:

the area (A) of a trpezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

b₁, b₂ are the parallel bases and h the perpendicular height between them

(1)

b₁ = 12, b₂ = 8 , h = 5

A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 8) = 2.5 × 20 = 50 cm²

(2)

b₁ = 6 , b₂ = 4 , h = 3

A = [tex]\frac{1}{2}[/tex] × 3 × (6 + 4) = 1.5 × 10 = 15 cm²

(3)

b₁ = 7 , b₂ = 4 , h = 4

A = [tex]\frac{1}{2}[/tex] × 4 × (7 + 4) = 2 × 11 = 22 cm²

Answer:

see explanation

Step-by-step explanation:

the area (A) of a trpezoid is calculated as

A = \frac{1}{2}21 h (b₁ + b₂ )

b₁, b₂ are the parallel bases and h the perpendicular height between them

(1)

b₁ = 12, b₂ = 8 , h = 5

A = \frac{1}{2}21 × 5 × (12 + 8) = 2.5 × 20 = 50 cm²

(2)

Answer:

$83,333

Step-by-step explanation:

1 000 000*1/4

250 000

250 000*1/3 = 83 333.33

Answer:

9

Step-by-step explanation:

Raising a number to the second means multiplying that number.  3 * 3 = 9

Answer:

Split brackets method see below

Step-by-step explanation:

Answer:

i) 66

ii) 536

Step-by-step explanation:

Check attachement(s) for solution.

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

We should solve according to the order of operations, PEMDAS.

#1) Parentheses

#2) Subtraction

#3) Addition

circumference = 12.57m

hope it helps...!!!

Answer:

Your Answer is A.

Step-by-step explanation:

Looking at the picture the LM is the original and wants to translate it to L'M'.

So Right 5 and 2 up.

Answer:

A

Step-by-step explanation:

LM is 5 units away from LM'

LM is 2 units down from LM'

Answer:

Step-by-step explanation:

If the function f(x) is change to g(x) what transformation has occurred?

(5 Points)

f (x) = 3x - 7 and g (x) = 3x + 3

The graph of g is a vertical strecth.

The graph of g is 3 units above f

• The graph of g is 10 units above f