Write the recurring decimal 0 32 . o as a fraction. You must show all your working

Answer:

D) 3 i

    \(\frac{Z_{1} }{Z_{2} } = 3 i\)

Step-by-step explanation:

Step(i):-

Given  Z₁ = 9 Cis ( 5π/6) = 9 ( Cos (5π/6) +i Sin (5π/6))

          Z₂ = 3 Cis ( π/3) = 3 ( Cos (π/3) +i Sin (π/3))

  Now  Cos (5π/6) = cos (150°) = cos(90°+60°)   = -sin 60 = \(\frac{-\sqrt{3} }{2}\)

           Sin (5π/6) = Sin (150°) = Sin(90°+60°)   = Cos 60 = \(\frac{1 }{2}\)

    Z₁  = 9 ( Cos (5π/6) +i Sin (5π/6))

          \(= 9(\frac{-\sqrt{3} }{2} + i\frac{1}{2} )\)

   Z₂ = 3 ( Cos (π/3) +i Sin (π/3))    

       \(= 3(\frac{1 }{2} + i\frac{\sqrt{3} }{2} )\)

Step(ii):-

\(\frac{Z_{1} }{Z_{2} } = \frac{ 9(\frac{-\sqrt{3} }{2} + i\frac{1}{2} )}{3(\frac{1 }{2} + i\frac{\sqrt{3} }{2} )}\)

\(\frac{Z_{1} }{Z_{2} } =\frac{3 (-\sqrt{3}+i) }{1+i\sqrt{3}) }\)

Rationalize with 1 - i √3 and we get

\(\frac{Z_{1} }{Z_{2} } =\frac{3 (-\sqrt{3}+i) }{1+i\sqrt{3}) } X\frac{1-i\sqrt{3} }{1-i\sqrt{3} }\)

on simplification , we will use formulas

i² = -1 and    (a+b)(a-b) = a² - b²

\(\frac{Z_{1} }{Z_{2} } =\frac{3(-\sqrt{3} + 3 i + i +\sqrt{3} )}{1 - i^{2} (\sqrt{3} )}\)

\(\frac{Z_{1} }{Z_{2} } =\frac{3(4 i )}{1 - i^{2} (\sqrt{3} )^{2} }\)

\(\frac{Z_{1} }{Z_{2} } =\frac{3(4 i )}{1 - i^{2} (\sqrt{3} )^{2} } = \frac{3(4 i)}{1-(-3)}= \frac{3(4 i)}{4}\)

\(\frac{Z_{1} }{Z_{2} } = 3 i\)

Final answer:-

\(\frac{Z_{1} }{Z_{2} } = 3 i\)

Answer: D. 3i

Step-by-step explanation: I got this right on Edmentum.

Answer:

84

34

27

Step-by-step explanation:

Answer:

he has 720 seconds left

Answer:

The answer is D.

An event D is said to be independent of another event.

Answer: no solution

Step-by-step explanation:

4x² + 17 = 1

4x² + 16 = 0

4x² + 16 - 16 = 0 - 16

4x² = -16

x² = -4 ==> not possible since x² has to be a positive number

Hence, there is no solution for x

Answer:

Well its basically 3 x 4 = 12, so for every lamb add four legs until you get to three

Step-by-step explanation:

Answer:

The radius is 8 inches

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

Assuming you mean 320 pi for the volume

320  pi = pi r^2 ( 5)

320 =5pi r^2

Divide each side by 5pi

320 pi / 5pi = 5 pi r^2 / 5pi

64 = r^2

Take the square root of each side

sqrt(64) = sqrt(r^2)

8 = r

The radius is 8 inches

Answer:

\(\Huge \boxed{\mathrm{4.51 \ inches}}\)

\(\rule[225]{225}{3}\)

Step-by-step explanation:

\(V=\pi r^2 h\)

The volume is 320 in³.

The height is 5 in.

\(320=\pi r^2 * (5)\)

Solving for \(r\).

Dividing both sides by 5.

\(64=\pi r^2\)

Dividing both sides by \(\pi\).

\(20.371833=r^2\)

Taking the square root of both sides.

\(r= 4.513517\)

The radius is 4.51 inches.

\(\rule[225]{225}{3}\)

Therefore, the correct statement is:" D corresponds to E." that is option B.

A rectangle is a four-sided flat shape with four right angles (90-degree angles) between its sides. It is a type of parallelogram that has two pairs of opposite sides that are parallel and congruent (equal in length), and all four angles are right angles. In a rectangle, the opposite sides are equal in length, which means that the width (or height) of the rectangle is the same throughout. The length of a rectangle is the longer side, while the width (or height) is the shorter side. The perimeter of a rectangle is the sum of the lengths of all its sides, while the area is the product of its length and width. These formulas are often used to calculate the dimensions of a rectangle or to solve problems related to its area or perimeter. Rectangles are used in many applications such as architecture, engineering, mathematics, and art, and they are commonly found in everyday objects such as books, windows, doors, and computer screens.

Here,

In a translation, every point on the preimage (the original figure) moves the same distance and in the same direction to become a point on the image (the translated figure).

To determine which statement is true, we can look at the corresponding vertices of the rectangle ABCD and its image EFGH.

A corresponds to E, B corresponds to F, C corresponds to G, and D corresponds to H.

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Considering the expression of a line, the slope of line that passes through points (-2,7) and (-3,3) is 4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m can be calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (-2, 7) and (x₂, y₂)= (-3, 3), the slope can be calculated as:

m= (3 -7)÷ (-3 -(-2))

m= (3 -7)÷ (-3 +2)

m= (-4)÷ (-1)

m= 4

Finally, the slope is 4.

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The relationship between the quantities shown in the table is +10. The values in column 2 (y) are obtained by adding 10 to the corresponding values in column 1 (x).

In the given table, the values in column 1 (labeled "x") are 1, 2, 3, and 4. The values in column 2 (labeled "y") are 11, 22, 33, and 44.

To determine the relationship between the quantities in the table, we can compare the values in column 2 (y) with the corresponding values in column 1 (x).

If we subtract each value in column 1 from the corresponding value in column 2, we find that:

11 - 1 = 10

22 - 2 = 20

33 - 3 = 30

44 - 4 = 40

By observing these results, we can see that the difference between each value in column 2 and its corresponding value in column 1 is always 10.

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The graph of function is,

⇒ f (x) = (x + 2) / (x + 1)

Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here, We have to given that;

The graph of function is shown in figure.

Hence, By options we get;

The graph of function is,

⇒ f (x) = (x + 2) / (x + 1)

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The ending inventory cost on December 31 for 21 units, under the three inventory methods, is as follows:

a) first-in, first-out (FIFO) method: $719

b) last-in, first-out (LIFO) method: $661

c) weighted average cost method: $690

The ending inventory cost is the difference between the cost of goods available for sale and the cost of goods sold determined by the various inventory methods.

Some of the inventory methods include:

Date       Activities         Units     Unit Cost   Total

Jan. 1      Inventory           16            $31       $496

Aug. 13   Purchase           14           $33         462

Nov. 30  Purchase           13           $35         455

Available for sale            43                       $1,413

Average cost = $32.86 ($1,413 ÷ 43)

Ending inventory             21

Units sold =                     22 (43 - 21)

a) FIFO:

Ending inventory = $719 (13 x $35 + 8 x $33)

Cost of goods sold = $694 ($1,413 - $719)

b) LIFO:

Ending inventory = $661 (16 x $31 + 5 x $33)

Cost of goods sold = $752 ($1,413 - $661)

c) Weighted Average:

Ending inventory = $690 (21 x $32.86)

Cost of goods sold = $723 (22 x $32.86)

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Answer: 52

Step-by-step explanation: x=7, so in the equation, it would be put as

(6)(7)+10. So (6)(7)+10=52.

If I Helped, Please Mark Me As Brainliest, Have A Great Day :D

Answer:

  \(a=\dfrac{\Delta v}{t}\)

Step-by-step explanation:

Acceleration is the change in velocity per unit time. It is usually represented by the letter "a". An appropriate formula is ...

  \(\boxed{a=\dfrac{\Delta v}{t}}\)

The required equation for determining the acceleration from a velocity-time graph is \(a=\dfrac{\Delta v}{t}\)equation is a=delta v over t.

We know that,

Acceleration is known as the rate of change of velocity per unit time.

The velocity vs time graph is the graph plotted between the change in velocity with the change in time.

\(a=\dfrac{\Delta v}{t}\)

Hence the required equation for determining the acceleration from a velocity-time graph is \(a=\dfrac{\Delta v}{t}\).

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Answer:

The first quartile is: 0-25

second quartile is 26-50 (median is 50)

third quartile is: 51-75

Range: 100

Hope this helps!

Step-by-step explanation:

Answer:

This relation is not a function.

Step-by-step explanation:

Function

A relation is a function when each input (x-value) has a single output (y-value).

A function is one-to-one if each output (y-values) corresponds to exactly one input (x-values).

A function is many-to-one if some outputs (y-values) correspond to more than one (many) inputs (x-values).

In the given relation, one input value (x = 4) corresponds to two output values.  Therefore, this relation is not a function.

(See attached Relation Arrow Diagram).

The exact perimeter of the triangle is: 8+3√17 units.

what is perimeter ?

Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.

Given by the question:
The distance formula between two points (x1, y1) and (x2, y2) is:

\(d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

So, to find the lengths of the sides of the triangle with vertices (-3, 5), (-3, 2), and (-1, -3), we can use the distance formula as follows:

Between (-3, 5) and (-3, 2):

\(d =\sqrt{[(y2 - y1)^2 + (x2 - x1)^2]}\)

= \(\sqrt{[(2 - 5)^2 + (-3 - (-3))^2]}\)

= \(\sqrt{[(-3)^2 + 0^2]}\)

= \(\sqrt{9}\)

= 3

Between (-3, 2) and (-1, -3):

\(d = \sqrt{[(y2 - y1)^2 + (x2 - x1)^2]}\)

= \(\sqrt{[(-3 - 2)^2 + (-1 - (-3))^2]}\)

= \(\sqrt{[(-5)^2 + 2^2]}\)

= \(\sqrt{29}\)

Between (-1, -3) and (-3, 5):

\(d = \sqrt{[(y2 - y1)^2 + (x2 - x1)^2]}\)

= \(\sqrt{[(5 - (-3))^2 + (-3 - (-1))^2]}\)

= \(\sqrt{[8^2 + (-2)^2]}\)

= \(\sqrt{68}\)

Now we can add up the lengths of the sides to get the perimeter:

\(P = 3 + \sqrt{29} + \sqrt{68}\)

So the exact perimeter of the triangle is:

8 + 3√17 units.

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The answer to the given question is length is 17m and width is 6m

Given that a rectangle's length is 7 meters less than its width.

And also given the perimeter of the rectangle is 46 meters.

We know that the rectangle's perimeter is twice the sum of its length and width.

l - length of the rectangle

w - width of the rectangle

P - perimeter of the rectangle

Then we have P = 2 × (l + w)

Given that a rectangle's length is 7 meters less than its width.

⇒ l = 4 × w - 7

Given the perimeter of the rectangle is 46 centimeters.

⇒ 2 × ( l + w) = 46

⇒ 2 × (4w - 7 + w) = 46 (using the value of length given in terms of width)

⇒ 4w - 7 + w = 23 (dividing by 2 on both the sides)

⇒ 5w - 7 = 23

⇒ 5w = 23 + 7

⇒ 5w = 30

⇒ w = 6 (dividing both sides by 5)

Using the width value in the length equation, we get

l = 4 × 6 - 7

⇒ l = 24 - 7

⇒ l = 17

Therefore, The rectangle is 17 meters in length and 6 meters in width.

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To draw a conclusion, a statistical analysis with a significance level (alpha) of 0.02 can be applied to compare the results.treated samples consistently show lower shrinkage temperatures compared to the control samples

In this study, the aim is to prove that electrical stimulation improves meat tenderness. Connective tissue (collagen) from beef steaks was examined, as lower collagen shrinkage temperature indicates higher tenderness.

The beef carcasses were split, with one side subjected to electrical current and the other side untreated as a control. Steak samples were cut from each side and tested for tenderness by determining the collagen shrinkage temperature.

I, it suggests that electrical stimulation does improve meat tenderness.

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394 subscribers are represented in the venn diagram.

Venn diagrams are charts that are used to visually represent relationships between sets, operations on those relationships, and set relationships. The Venn diagram, which uses circles that are overlapped, intersected, and not intersected to depict the relationship between sets, was created by John Venn. A set diagram or a logic diagram is another name for a Venn diagram, which shows a variety of set operations such the intersection, union, and difference of sets.

Additionally, it can be used to set items. a depiction of each relationship between several sets. Any closed figure, such as a circle or a polygon (square, hexagon, etc.), can be used to represent a Venn diagram. However, each group is typically represented as a circle.

according to the venn diagram

196+41+21+52+84 = 394

There are 394 subscribers

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2 1/4 miles => 1 week

1 mile => 1 ÷ 9/4

( 9/4 is an improper fraction of 2 1/4 )

12 1/2 miles => ( 1 ÷ 9/4 ) × 25/2

= 50/9

= 5 5/9 weeks

( 25/2 is an improper fraction of 12 1/2 )

Therefore, it will take 5 5/9 weeks for the company to replace the stretch of road.

( you can round it off to 6 weeks if the qn specify to give to the nearest whole number )

Answer:

D

Step-by-step explanation:

4X =2 X +6

=>X =  3

Required two transformations are translated according to the rule (x, y) → (x + 8, y + 2) reflected across the x-axis.

How to find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″?

To find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″, we can compare the coordinates of corresponding vertices of both pentagons.

Starting with point A, we see that it has been translated 8 units to the right and 2 units up to become A″. Therefore, the first transformation is a translation according to the rule (x, y) → (x + 8, y + 2).

Next, we can compare the y-coordinates of point A and A″ to see if a reflection has been applied. We see that the y-coordinate of A has changed from 5 to -7 in A″, indicating that a reflection has been applied across the x-axis.

Therefore, the two transformations applied to pentagon ABCDE to create A″B″C″D″E″ are:

Translated according to the rule (x, y) → (x + 8, y + 2)

Reflected across the x-axis.

The other options can be ruled out as they do not correctly reflect the transformation that was applied.

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Answer:

The designed life should be of 21,840 vehicle miles.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles.

This means that \(\mu = 35000, \sigma = 7000\)

Find its designed life if a .97 reliability is desired.

The designed life should be the 100 - 97 = 3rd percentile(we want only 3% of the vehicles to fail within this time), which is X when Z has a p-value of 0.03, so X when Z = -1.88.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.88 = \frac{X - 35000}{7000}\)

\(X - 35000 = -1.88*7000\)

\(X = 21840\)

The designed life should be of 21,840 vehicle miles.

The coordinates of the reflected point P' will be (4, -3).

When a point is reflected over the x-axis, its y-coordinate changes sign.

In this case, the point P has coordinates (4,3).

To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.

So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.

Therefore, the coordinates of the reflected point P will be (4, -3).

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

45

Answer:

C. 15

Step-by-step explanation:

3 is 3/5 of 5

so x-6 should be 3/5 of x?

-6 would be 5/5 - 2/5

2/5 = 6

1/5 = 3

5/5 = x = 15

Step-by-step explanation:

The cost of a cup of tea is t cents.

The cost of a cup of coffee is (t + 5) cents.

The total cost of 7 cups of tea and 11 cups of coffee is 2215 cents.

Therefore,

7t+11t+55=2215

18t=2160

t=120