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1 year ago

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A department within an agency is randomly chosen each week for auditing. If there are 25 departments, what is the chance that an

y single department is chosen for auditing in a given week?

1 answer:

Alexandra [31]1 year ago

8 0

<u>Answer:</u>

The chance that any single department is chosen for auditing in a given week is 0.04%

<u>Explanation:</u>

Given that a department within an agency is randomly chosen per week for auditing and we are given total number of departments are 25 departments of which 1 is to be chosen.

Now chance of any single department to be chosen in any particular week will be given by 1 dividing by total no. of departments

which is equal to 1/25

1/25 = 0.04%

which is the chance of percentage of choosing a department

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Consider the graph of the line y = x – 4 and the point (−4, 2). The slope of a line parallel to the given line is . A point on t

Harman [31]

The given line is y = x - 4, and the given point is (-4, 2).

The slope of the given line is 1, and its y-intercept is (0, -4).

Part a.
The slope of a line parallel to the given line is 1.

Part b.
Let the equation of a line parallel to the given line be
y = x + c
Let (x,y) be a point on a parallel line which passes through (-4,2).
Then, in point-slope form,
(y - 2)/(x + 4) = 1
That is,
y - 2 = x + 4
y = x + 6

If x = 0, then
y - 2 = 0 + 4
y - 2 = 4
y = 6
Therefore the point (0, 6) is one of many points that lies on this line.

Part c.
The slope of a line perpendicular to the given line is -1.
The product of the slopes of perpendicular lines is -1.

Let (x,y) be a point on the perpendicular line which passes through (-4,2).
In point-slope form, its equation is
(y - 2)/(x + 4) = -1
That is,
y - 2 = -x - 4
y = -x - 2
Wneh x = 0, then y = -2.
A point on the perpendicular line that passes through (-4,2) is (0, -2).

Answers:
1. The slope is 1.
2. The point (0, 6) falls on the parallel line passing through (-4, 2).
3. The slope of a perpendicular line is -1.
4. The point (0, -2) falls on the perpendicular line passing through (-4, 2).

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2 years ago

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What is the quotient (3x4 – 4x2 + 8x – 1) ÷ (x – 2) brainly

Karolina [17]

To find our quotient we are going to perform long division.

Long division step by step:

Step 1. Write the polynomial (dividend) in descending order (from highest to least exponent). If you encounter a missing term, use zero to fill the space of the term in the descending sequence.

Notice that even tough our polynomial is written in descending form, $x^3$ is missing, so we are going to use $0x^3$ to fill the gap:

$3x^4-4x^2+8x-1$

$3x^4+0x^3-4x^2+8x-1$

Step 2. Divide the first term of the polynomial (dividend) by the first term of the divisor.

In our case the first term of the dividend is $3x^4$ and the first term of the divisor is $x$ , so $\frac{3x^4}{x} =3x^3$ . Notice that $3x^3$ is the first term of the quotient.

Step 3. Multiply the first term of the quotient by the terms of the divisor and subtract them from the respective term of the dividend.

The first term of our quotient (from the previous step) is $3x^3$ and the divisor is $(x-1)$ , so $3x^3(x-2)=3x^4-6x^3$ . Now, we are going to subtract them from the respective term (the term with the same power) of the dividend. The respective terms of the dividend are $3x^4$ and $0x^3$ , so $3x^4-3x^4=0$ and $0x^3-(-6x^3)=0x^3+6x^3=6x^3$

Step 4. Bring down the next term in the dividend and repeat the process for the remaining terms.

After finish the process (check the attached picture), we can conclude that the quotient of $3x^4-4x^2+8x-1$ ÷ $(x-2)$ is $3x^3+6x^2+8x+24$ with a remainder of $47$ , or in a different notation: $3x^3+6x^2+8x+24+\frac{47}{x-2}$

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2 years ago

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In a study of the progeny of rabbits, Fibonacci (ca. 1170-ca. 1240) encountered the sequence now bearing his name. The sequence

expeople1 [14]

The question in part c is not clear, nevertheless, part a and part b would be solved.

Answer:

a. The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

b. The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Step-by-step explanation:

a. Given

an + 2 = an + an + 1

where a1 = 1 and a2 = 1.

a3 = a1 + a2

= 2

a4 = a2 + a3

= 3

a5 = a3 + a4

= 5

a6 = a5 + a4

= 8

a7 = a6 + a5

= 13

a8 = a7 + a6

= 21

a9 = a8 + a7

= 34

a10 = a9 + a8

= 55

a11 = a10 + a9

= 89

a12 = a11 + a10

= 144

The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

(b)

Given

bn = an+1/an

b1 = a2/a1

= 1/1 = 1.000

b2 = a3/a2

= 2/1 = 1.000

b3 = a4/a3

= 3/2 = 1.500

b4 = a5/a4

= 5/3 = 1.667

b5 = a6/a5

= 8/5 = 1.600

b6 = a7/a6

= 13/8 = 1.625

b7 = a8/a7

= 21/13 = 1.615

b8 = a9/a8

= 34/21 = 1.619

b9 = a10/a9

= 55/34 = 1.618

b10 = a11/a10

= 89/55 = 1.618

The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

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1 year ago

Matthew manages the packaging department of his company. Yesterday, the department operated for only 4 hours due to a company pi

yKpoI14uk [10]

Alright, lets get started.

If Matthew wants to complete packages at an average rate of at least 39 packages per hour.

And they worked 4 hrs only due to picnic, yesterday, it means they have to make $39*4 = 156$ packages.

But they made only 112 packages means they are short of $156 - 112 = 44$ packages.

Suppose they are working today t hrs, and his department will complete 43 packages per hour today.

It means they are going to make 43 t packages today.

This 43 t packages includes those 44 too , which they are short of yesterday due to picnic.

So, average will be

$\frac{43 t - 44}{t} = 39$ (39 average given in question)

Cross multiplying

$39 t = 43 t - 44$

Adding 44 in both sides

$39 t + 44 = 43 t - 44 + 44$

$43 t = 39 t + 44$

Subtracting 39 t in both sides

$43 t - 39 t = 39 t + 44 - 39 t$

$4t = 44$

Dividing 4 in both sides

t = 11 hrs

Hence they have to woth 11 hrs today : Answer

Hope it will help :)

3 0

2 years ago

Read 2 more answers

The histogram shows the number of cell phone calls received by Medera, a middle school student, one Saturday from 10 a.m. to 10

Anni [7]

Answer:

The hours when zero calls were received were most possibly when Madera turned the phone off while playing in a soccer game.

Step-by-step explanation:

According to the question,

Madera, a middle school student, received some phone calls on one Saturday from 10 a.m. to 10 p.m.

The hours when zero calls were received were most possibly when Madera turned the phone off while playing in a soccer game.

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2 years ago

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