A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 0.989 0.978 0.927 0.167 0.530

The preparation of the Cash Flow Statement for Nikea Inc. for the year ended December 31, 2013, is as follows:

Direct Method:

Nikea Inc.

Cash received from customers  $600,000

Cash paid to suppliers of goods (400,000)

Cash paid to vendors of servides (30,000)

Cash from operating activities    $170,000

Indirect Method:

Nikea Inc.

For the year ended December 31, 2013

Net income                                $150,000

Add non-cash expenses:

Depreciation                                 20,000

Cash from operating activities $170,000

The direct method of preparing the Cash Flow Statement starts with the operating income and adds the non-cash expenses to obtain the cash flow from operating activities.

On the other hand, the indirect method reconciles the accounts receivable and payable to extract the exact cash flows received from customers or paid to suppliers of goods and services.

Both methods of determining the cash flow from operating activities yield the same result.

Nikea’s income statement for the year 2013

Sales                          $600,000

Cost of Goods Sold   (400,000)

Gross Profit                 200,000

Operating Expenses   (30,000)

Deprecation                (20,000)

Net Income                 150,000

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Answer:

That may or may not be true, depending one the ship size.

Step-by-step explanation:

'Can't really give a proper answer, to somethings that's not a q. *shrug*

Answer:

f(x) = x^2 - x + 1

g(x) = 3x-5

Step-by-step explanation:

The vertices of the feasible region is (4, 3)

From the question, we have the following parameters that can be used in our computation:

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

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On solving the provided question related to rectangle we can say that the Perimeter, P = 2(10+20); P = 60 cm

The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth The perimeter of a shape is always calculated by adding up the length of each of the sides. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width.

In order to find the perimeter, or distance around the rectangle, we need to add up all four side lengths.

This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length. Perimeter=(length+width)×2 is the formula for perimeter

here,

we have length, L = 10

and breadth, B = 20

Perimeter, P = 2(10+20)

P = 60 cm

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The time take to fill the pool will be 494 hours.

Inlet pipe fills in  38 hours = 1 pool

Inlet pipe fills in 1 hours = 1/38

Drain pipe empty in 39 hours = 1 pool

Drain pipe empty in 1 hour = 1/39

If both pipes are opened together then in pool fills in 1 hour =  1/38 - 1/39

= 1/1482

Therefore, 1/1482 fills in 1 hour.

. Therefore, 1/3 will be:

= 1/3 × 1482

= 494 hours.

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The amount of edging trim needed will be equal to the circumference of the given circle, so it will be 31.4ft

We know that the circumference of a circle of diameter D is given by:

C = 3.14*D

Here, we have a circular garden with a diameter of 10ft, and we want to place edging trim along its circumference, so the amount of edging trim that we need is given by:

C = 3.14*10ft = 31.4 ft

You need 31.4ft of edging trim to surround the garden by placing the trim all along the garden's circumference.

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Answer:

|5x+12| when x=5

I5*5=12I

I37I

37

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

X=5

5x=(5×5)=25

25+12=37

Answer:

\(\textsf{Area}=\dfrac{5\pi -3}{12} \approx 1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}\)

Step-by-step explanation:

To find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector.

An isosceles triangle is made up of two congruent right triangles.

To find the height of the right triangles (and thus the height of the isosceles triangle), use the cosine trigonometric ratio.

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

Given values:

Substitute these values into the cosine ratio to calculate the height of the right triangles (and thus the height of the isosceles triangle):

\(\cos \left(\dfrac{5\pi}{12}\right)=\dfrac{x}{1}\)

\(x=\cos \left(\dfrac{5\pi}{12}\right)\)

\(x=\dfrac{\sqrt{6}-\sqrt{2}}{4}\)

The base of one of the right triangles can be found by using the sine trigonometric ratio.

\(\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

Given values:

Substitute these values into the sine ratio to determine the base of the right triangle:

\(\sin \left(\dfrac{5\pi}{12}\right)=\dfrac{y}{1}\)

\(y=\sin \left(\dfrac{5\pi}{12}\right)\)

\(y=\dfrac{\sqrt{6}+\sqrt{2}}{4}\)

The base of the isosceles triangle is twice the base of the right triangle, so the base of the isosceles triangle = 2y.

Therefore the area of the isosceles triangle is:

\(\begin{aligned}\textsf{Area of isosceles triangle}&=\dfrac{1}{2} \cdot \sf base \cdot height\\\\&=\dfrac{1}{2}\cdot 2y \cdot x\\\\&=\dfrac{1}{2} \cdot 2\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\left(\dfrac{\sqrt{6}+\sqrt{2}}{4}\right) \cdot \left(\dfrac{\sqrt{6}-\sqrt{2}}{4}\right)\\\\&=\dfrac{4}{16}\\\\&=\dfrac{1}{4}\sf \;square\;units\end{aligned}\)

To find the area of the sector of the circle, use the area of a sector formula (where the angle is measured in radians).

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}\)

Given values:

Substitute the values into the formula:

\(\begin{aligned}\textsf{Area of the sector}&=\dfrac{1}{2} \cdot (1)^2 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot 1 \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{1}{2} \cdot \dfrac{5\pi}{6}\\\\&=\dfrac{5\pi}{12}\;\; \sf square\;units\end{aligned}\)

Finally, to find the area of the shaded region, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Area of the shaded region}&=\sf Area_{sector}-Area_{isosceles\;triangle}\\\\&=\dfrac{5\pi}{12}-\dfrac{1}{4}\\\\&=\dfrac{5\pi}{12}-\dfrac{3}{12}\\\\&=\dfrac{5\pi -3}{12}\\\\&=1.05899693...\\\\&=1.06\; \sf square\;units \;(3\;s.f.)\end{aligned}\)

Therefore, the area of the shaded region is (5π - 3)/12 or approximately 1.06 square units (3 significant figures).

\(\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &5918\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &8\\ \end{cases} \\\\\\ A = 5918(1 - 0.06)^{8} \implies A = 5918( 0.94 )^{8}\implies A \approx 3607.43\)

Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

You can write the quadratic function y = ax^2 + bx + c in the vertex form y = a(x - h)^2 + k

The standard form of the quadratic function is

y = ax^2 + bx + c

Where a, b and c are numbers not equal to zero

The graph of the quadratic function is parabola.

Therefore the parabola or the quadratic function can be expressed in terms of vertex form

The standard from of vertex from is

y = a(x - h)^2 + k

Where a is the constant that tell the whether the parabola is facing up or down

(h, k) is the coordinates of the vertex of the parabola

h = -b / 2a

k = f(h)

Therefore, it is possible to write a quadratic function in vertex form

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The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.

7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.

8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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Answer:

He would be 15 years old.

Step-by-step explanation:

If the difference is 15, and sarah is double the age, whatever age the youngest brother is, that number if multiplied by 2 or added to 15 needs to be the same answer. You could make a equation by writing those two on either side of the equation and making the unknown sum “x”. This would look like “2x=x+15”. Then to get the final product you would subtract the x on the right side from both side, ending up to be “x=15” in this scenario, that would be the final answer.

If a, b, c, and d are four different numbers and the proportion. The given statement is true.

We take one example,

When you split them, they will all equal the same thing.

A = 5 ,B = 20 20 divided by 5 equals 4

C = 28 ,D = 7 28 divided by 7 equals 4

The ratio is used to compare two amounts of the same type. For two numbers, a and b, the ratio formula is written as a: b or a/b. The ratio and proportion concepts are based on fractions. Ratio and proportion are the fundamental building blocks for many other notions in mathematics. Ratio and proportion are useful in addressing many everyday difficulties, such as comparing heights, weights, distance, or time, or when combining ingredients in cookery, and so on.

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G:{3,4,6}->{0,9}

The pairs represent the input (first number in each pair) and the result (second nu.ber in each pair) for the relation G. for example G(3)=9.

The domain is the set of values that the relation can act upon. The range is the set of the values the results can take

Answer:

(f - g) = 2x - 3

Step-by-step explanation:

Simply distribute the negative and add like terms together:

(f - g) = 3x - 1 - (x + 2)

(f - g) = 3x - 1 - x - 2

(f - g) = 2x -  3

Answer:

40 shirts.

Step-by-step explanation:

The budget is $170.
There's a one time fee of $10.
A T-shirt costs $4.
Put that in an equation with x, where x is the amount of t-shirts that can be made, to solve for it.
170 - (4x + 10) = 0
170 = 4x + 10
-10
160 = 4x
/4
40 = x
So, 40 shirts can be made at most.

Answer:

a number is correct watch it clearly

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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Answer:

12 pesos

Step-by-step explanation:

Answer:

Sergio added 2 instead of multiplying 2

Step-by-step explanation:

If Sergio's sister found 6 pennies that means that Sergio should've found 3 but instead of multiplying 2 he added 2.

The result of expanding the trigonometry expression \(\sin^2(\theta) * (1 + \cos(\theta))\) is \(cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)\)

The expression is given as:

\(\sin^2(\theta) * (1 + \cos(\theta))\)

Express \(\sin^2(\theta)\) as \(1 - \cos^2(\theta)\).

So, we have:

\(\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))\)

Open the bracket

\(\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)\)

Express 1 as cos°(Ф)

\(\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)\)

Hence, the result of expanding the trigonometry expression \(\sin^2(\theta) * (1 + \cos(\theta))\) is \(cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)\)

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Answer:

x=2y-4

Step-by-step explanation:

Of the 250 total shirts about, the quantity of shirts that should be red would be = 125.

The total quantity of shirts that was ordered by Mr. Torres = 250 school t-shirts

The total quantity of red shirt selected at random = 5

The total quantity of blue shirt selected at random = 13

The total quantity of grey shirt selected at random = 12

Total selected at random = 30

Now if 5 red shirts = 30

X red shirts = 250

make X the subject of formula;

X = 15× 250/30

X = 3750/30

X = 125 red shirts.

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The argument of the polar coordinate is -45 degrees, which can be converted as,

Thus, the required point is D.

Answer:did you end up figuring it out?

Step-by-step explanation:

I rly need it I’m on a test

The total number of players on team A 24 is and on the team, B is 20.

The comparison of two quantities of constant units illustrates the quantitative relationship by showing what percentage of one quantity is a gift inside the other.

Team A's total player count should be "x" and Team B's total player count should be "y.".

Assuming that 3 players on Team A (or 1/8 of the players) have scored goals, this can be represented by,

1/8(x) = 3

x = 3 × 8

x = 24

Given that 4 players on Team B have scored goals, 1/5 of the players have scored a goal, which can be represented by,

1/5(y) = 4

y = 4 × 5

y = 20

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The equation of the line in slope-intercept form is: C. y = -3/2x - 9/2

If we determine the slope value, m, and the y-intercept value of the line, b, we can write the equation of a line in slope-intercept form as y = mx + b by substituting the values.

Slope of a line (m) = change in y / change in x.

y-intercept of a line is the point on the y-axis where the value of x = 0, and the line cuts the y-axis.

Slope of the line in the diagram, m = -3/2

y-intercept of the line, b = -9/2.

Substitute m = -3/2 and b = -9/2 into y = mx + b:

y = -3/2x - 9/2 [equation in slope-intercept form]

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Here is your Answer

Step-by-step explanation:

Ravi bought rice = 50kg

Rate it =40kg

Sold it at the rate = = 44kg

Answer:

42 m

Step-by-step explanation:

First, find <S

<S = 180 - (41+113) [ sum of angles in a triangle)

<S = 180 - 154 = 26°

Next is to find length of ST, using the law of sines: a/sin A = b/sinc B = c/sin C

Let a = RT = 28m

A = <S = 26°

b = ST

B = <R = 41°

Thus, we have:

28/sin(26°) = b/sin(41°)

Cross multiply

28*sin(41°) = b*sin(26°)

28*0.6561 = b*0.4384

18.3708 = b*0.4384

Divide both sides by 0.4384 to make b the subject of formula

18.3708/0.4384 = b

41.9041971 = b

b ≈ 42m (rounded to nearest meter)

Length of ST to nearest meter = 42 meters

Answer:

-24+6=

Step-by-step explanation:

select the correct rule, then solve the equation

Complete Question

Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum=7, maximum = 83, 6 classes ​

What is the class width? (whole number)

We have that the Class Width is given as

7-19

20-32

33-45

46-58

59-71

72-84

Generally

\(Class\ width =\frac{83-7}{6}\)

Class width =12.67

Class width =13

Hence

Lower class limit is

7,7+13=20...33,46,59,72

Upper class limit is

7+13-1=19,32,45,58,71,84

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