A microscope shows you an image of an object that is 8 times the objects actual size, so the scale factor of the enlargement is 8. An insect has a body length of 7 millimeters. What is the body length of the insect under the microscope?

56 centimeters
56 millimeters
560 millimeters
560 centimeters

Answer:

6

Step-by-step explanation:

3/4 x 8 = 3 x 8 / 4 x 1 = 24/4 = 6

The simplified form of the expression (3x² - 4xy + y²)(4x + 3y) is 12x³ - 7x²y + 8xy²  + 3y³.

Given the expression in the question;

(3x² - 4xy + y²)(4x + 3y)

To simplify, apply distributive property by multiplying each term in the first expression by each term in the second expression.

(4x + 3y)(3x² - 4xy + y²)

4x (3x² - 4xy + y²) + 3y(3x² - 4xy + y²)

3x² × 4x - 4xy × 4x  + y² × 4x  + 3x² × 3y - 4xy × 3y  + y² × 3y

12x³ - 16x²y + 4xy²  + 9x²y - 12xy²  + 3y³

Collect like terms

12x³ - 16x²y + 9x²y + 4xy²  - 12xy²  + 3y³

Add -16x²y and 9x²y

12x³ - 7x²y + 4xy² - 12xy²  + 3y³

Add 4xy²  and -12xy²

12x³ - 7x²y + 8xy²  + 3y³

Therefore, the simplified form is 12x³ - 7x²y + 8xy²  + 3y³.

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The height of the figure is 66 m².

Finding the triangle's height can be done in a variety of ways. There are numerous other formulas, but the one that uses a triangle's area is the one that is most widely used. You can determine the triangle's area given its sides using an equation known as Heron's formula. Once you are aware of the region, you can use the fundamental equation to determine the triangle's altitude.

You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.

27.5 × 4.8

= 132

132/2

= 66

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The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

y = ln x

The function is transformed by shifting 8 units left and 12 units up. Then replace x with (x + 8) and y with (y - 12). Then we have

y - 12 = ln (x + 8)

y = ln (x + 8) + 12

The parent function and transformed function will be y = ln x and y = ln (x + 8) + 12, respectively. The graph of the function is given below.

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Based on the information provided, I have analyzed the three options for hosting a dance for the students of CISE, and have come to the following recommendations:

Ancient Abyss: This location charges a flat fee of $200 and $4 per person. This option may be suitable for smaller events with less than 50 attendees, as the flat fee is relatively high. However, for larger events with more than 50 attendees, the per person cost will become more significant and may make this option less cost-effective.

Beautiful Babylon: This location charges a flat fee of $99 and $6 per person. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Ancient Abyss. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.

Crazy Cleopatra: This location charges a flat fee of $280 and $3 per person. This option has the highest flat fee but the lowest per person cost. This option may be more cost-effective for larger events with more than 50 attendees, as the per person cost is lower than Beautiful Babylon. However, for smaller events with less than 50 attendees, the flat fee may be relatively high.

Based on the above analysis, I recommend that the student council consider Beautiful Babylon as the most cost-effective option for hosting the dance. However, I also recommend that the council consider the number of attendees expected at the event and adjust their decision accordingly.

In summary, The council should consider the number of attendees expected, Beautiful Babylon is a good option for larger events, for smaller events, Crazy Cleopatra is the better option.

For the given statement, the domain and range are - Domain : x ,Range : f(x)  40.

In mathematical notation, symbols are used in expressions and formulas to represent operations, unnamed numbers, relations, and any other mathematical objects. In mathematics, science, and engineering, mathematical notation is frequently used to communicate complicated ideas and properties in a clear, unambiguous manner.

A notation is a set of clear guidelines for using symbols to describe numbers and actions.

The sum of numerous linked terms is frequently represented by the sign (capital sigma) in shorthand notation. In statistics, sigma notation is frequently employed.

For each dividend number, the extended notation division method merely repeats the division, multiplication, and subtraction operations.

Given data :

x is the mass of the chicken (in kg)

f(x) : the cooking time ( in minutes )

Domain : x

Range : f(x)  40

f(x) = 15x + 40 - 15 minutes per kg (x) plus 40 more minutes

f (1) = 15 x 1 + 40 = 55

A 1 kg chicken needs 15 min + 40 min = 55 min

f (2) = 15 x 2 + 40 = 70

A 2 kg chicken needs 30min + 40 min = 70 min

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As the value of the ratio of both the quantities are NOT same so the given values .

No, The two rates not form a proportion.

Now, According to the question:

Two ratios are equivalent, if the fractions corresponding to them are equivalent. Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities.

A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:

1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

Now,

0. 4 kilometer for every 15 minutes equals to (0.4/15) = 0.026

So for every minute they travel 0.026km.

0. 6 kilometer for every 20 minutes equals (0.6/20) =  0.03

So for every minute they travel 0.03km.

Here, as the value of the ratio of both the quantities are NOT same so the given values .

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The table for V* n and V/n shows the various answers as

Multiplication is when you take one number and add it together a number of times.

The table appears as follows

Volume(V)       Moles(n)          V*n               V/n

3                       0.145              0.435           20.7

4                        0.193             0.773            20.7

5                        0.242            1.210             20.7

6                       0.290             1.740             20.7

These figures are gotten by the multiplication and division of the numbers in the tables as given by the formulae

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The given expression has sin A = BC/AC=36/85, cos A = AB/AC=77/85, tan A = BC/AB=36/77

In trigonometry, the values of sin, cos, and tan are the main functions we consider when solving trigonometric problems. Using these trigonometric values, the angles and sides of a right-angle triangle are calculated. In addition to sine, cosine, and tangent values, the other three significant values are cotangent, secant, and cosecant.

Normally, when calculating the sin, cos, and tan values for a triangle, the angles of 0°, 30°, 45°, 60°, and 90° are taken into consideration. These specific angles' values are easy to remember. What the trigonometric values are all about is knowing the standard angles for a specific triangle according to the trigonometric ratios (sine, cosine, tangent, cotangent, secant and cosecant).

We have, AB = 77 , BC = 36.and CA=85

When we consider the t-ratios of ∠A, we have

Base = AB = 77, Perpendicular = BC = 36, Hypotenuse = AC =85.

∴sin A = BC/AC=36/85 , cos A = AB/AC=77/85 , tan A = BC/AB=36/77

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Based on the information provided, the two numbers whose HCF is 101 are 1010 and 1313.

The HCF is the highest common factor or in other words, the highest number by which two numbers can be divided. Let's start by listing the four digits numbers that can be the HCF related to 101.

101 x 10 = 1010

101 x 11 = 1111

101 x 12 = 1212

101 x 13 = 1313

Now, from these numbers, there are two numbers whose difference is 303.

1313 - 1010 = 303

Based on this, the two numbers are 1010 and 1313

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The fraction of the circle that would represent food is given as 34.09

The data we have here is given as

Activities = 600

Food = 450

Souvenirs = 270

We would have to sum this up

600 + 450 + 270 = 1320

The proportion that represents food is given as 450

= 450 / 1320

= 0.3409

Then we would have to convert this to percentage

0.341 * 100

= 34.09

34.09 x 360 = 123 degrees

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Answer:

Classify the sequence {1, 6, 11, 16, 21, …}.

The pattern is +5:

1 + 5 = 6

6 + 5 = 11

11 + 5 = 16

16 + 5 = 21

21 + 5 = 26

And so on

Step-by-step explanation:

You're welcome

Answer:

(2.57, -0.07)

Step-by-step explanation:

To solve the system of equations, we can substitute the expression for y in the second equation:

-5x + 4(1/8x - 1) = -13

We can then simplify and solve for x:

-5x + (1/2)x - 4 = -13

-3.5x = -9

x = 2.57

We can then substitute this value of x back into the first equation to find the value of y:

y = 1/8(2.57) - 1

y = -0.07

So the solution of the system of equations is (x, y) = (2.57, -0.07)

According to economists, her opportunity cost of consuming caramel-coated popcorn would be the forgone peanut butter pretzels.

Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them.

Better choices can be made by being aware of the opportunities that might be lost when a company or person chooses one investment over another. It is necessary to weigh the advantages and disadvantages of each choice offered in order to correctly assess opportunity costs.

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Lateral Area = 108 square km

Surface Area = 120 square km

Think of the triangles as the floor and ceiling of this 3D room. The walls are three rectangular sides.

We have a 9 by 4 wall with an area of 9*4 = 36 square km

We have a 9 by 3 wall with an area of 9*3 = 27 square km

We have a 9 by 5 wall with an area of 9*5 = 45 square km

The lateral area is 36+27+45 = 108

The two triangles form the base faces of this prism.

Let's find the area of one of the triangles

area=0.5*base*height = 0.5*3*4 =6

One triangle has an area of 6, so both triangles in total have an area of 2*6 = 12 square km.

The total surface area is therefore 108+12 = 120 square km.

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Answer: 12.5%

(Don't worry!)

1 :1 is the blend as a ratio of corn oil to olive oil.

Now, According to the question:

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)

"Information available from the question"

A chef made a blend of cooking oil.

1/5 of his mix was olive oil

and 4/5 was corn oil.

To find the blend as a ratio of corn oil to olive oil.

Now, Blend Ratio will be:

olive ratio + corn ratio

1/5 + 4/5

= 5/5 = 1/1

Hence, 1:1 is the blend as a ratio of corn oil to olive oil.

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The equation y+2 = 4(x-1) is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this equation, the slope is 4 and the y-intercept is -2.

For a line that is parallel to y+2 = 4(x-1), the slope (m) will be the same, which is 4.

To find the equation of a line that passes through a specific point (1,-3), we can use the point-slope form of a linear equation: y - y1 = m(x - x1)

So, using the point (1,-3) and the slope (4), we can write the equation as:

y - (-3) = 4(x - 1)

Simplifying this equation gives:

y + 3 = 4x - 4

Finally, we can write the equation in slope-intercept form by adding 4 to both sides and dividing both sides by 4:

y = 4x - 1

So the equation for the line that passes through (1,-3) and is parallel to y+2 = 4(x-1) is y = 4x - 1

At 11.5 hours, the red turtle pass the blue turtle. The red turtle won the race. The solution has been obtained by studying graph of the functions.

What is graph of the function?

The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. The graph of f is also known as the graph of

y = f(x).

In the graph, it is seen that from 6 to 13 hours, the blue turtle is at the same place whereas the red turtle is moving.

Therefore, at 11.5 hours the red turtle passes the blue turtle.

The red turtle won the race in 16 hours because in the graph it is observed that the blue turtle did not complete the entire km. The graph of blue turtle is a little less than that of red turtle.

Hence, at 11.5 hours, the red turtle pass the blue turtle and wins the race.

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Since there are multiple questions, so the question answered above is attached below.

The area of the roof is 157.5 .

It is given that the roof of a clock tower is a pentagonal pyramid.

Each side of the base is 7 ft long.

The slant height is 9 ft.

we know that, to find area we have,

Area=1/2 × 7 × 9 × 5

= 315/2

= 157.5

Hence, 157.5 square feet is the area of the roof.

Pentagonal pyramid

A pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point.

It is a three  dimensional figure, it is a solid figure or an object or shape that has three dimensions—length, width, and height.

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When we simplify the expression (4x⁴y⁵ / 3xy²)⁵, the result obtained is 1024x¹⁵y¹⁵ / 243

To simplify the expression (4x⁴y⁵ / 3xy²)⁵, the laws of indices must be applied as illustrated below:

(4x⁴y⁵ / 3xy²)⁵

Recall

(Aᵐ)ⁿ = Aᵐⁿ

Thus,

(4x⁴y⁵ / 3xy²)⁵ = 1024x²⁰y²⁵ / 243x⁵y¹⁰

Recall

Aᵐ / Aⁿ = Aᵐ⁻ⁿ

Thus,

1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x²⁰⁻⁵y²⁵⁻¹⁰

1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x¹⁵y¹⁵

1024x²⁰y²⁵ / 243x⁵y¹⁰ = 1024x¹⁵y¹⁵ / 243

Therefore,

(4x⁴y⁵ / 3xy²)⁵ = 1024x¹⁵y¹⁵ / 243

From the above illustration, we can conclude that the simplified form of (4x⁴y⁵ / 3xy²)⁵ is 1024x¹⁵y¹⁵ / 243

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A per the measurement, there is only form exactly 1 unique triangle.

The term triangle in math is known as a two-dimensional shape with three sides, three interior angles, and three vertices.

Here we have know that a rope 10 units in length, if side lengths must be in whole units.

And we need to find the number of different triangles can be made.

Here we know that length is 10 units, and the side length are whole units.

Which means that here we have 3 distinct value.

So as we all know that all of the triangles you make are the same triangle. Which means that if your three side lengths can form a triangle, then they can only form exactly 1 unique triangle.

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The equation is 2m + 3.10 = 21.10

And, the number of miles in the taxi ride is m = 9.

Now, According to the question:

Joseph took a taxi from his house to the airport. The taxi company charged a pick-up fee $3.10 plus $2 per mile. The total fare was $21.10.

Now,

The equation is written as,

2m + 3.10 = 21.10

Subtract 3.10 from both sides

2m = 18

Divide 2 from both sides

m = 9

Hence, The equation is 2m + 3.10 = 21.10

And, the number of miles in the taxi ride is m = 9.

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Area swept by minute hand of a clock is 66cm².

Given that length of the minute hand of clock is 6cm.

We know that, total angle covered by the minute hand of clock is 360° in 60 minutes.

Total time interval = 7:45 PM – 7:05 PM = 35 minutes

In 60 minutes 360° angle covered

Then, in 1 minute 360/60 angle covered

So, in 35 minutes

total angle covered = 360/60 * 35 = 210°

Total area covered = sectional area of circle with radius 6cm

Total area covered = Ф/360 * πr²

= 210/360 * 22/7 * 6² = 66 cm²

Therefore, total area swept by minute hand of a clock is 66cm².

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Jade's mother is the sun of Jade because she motivated Jade against race and gender, class and privilege, and fear and courage. Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, Jade's mother is the sun. So the option 3 is correct.

While expressing the complicated emotions of an aspirational, devoted girl, Jade's narrative voice offers riveting insights on the intricacies of race and gender, class and privilege, and fear and courage. Watson's story, which brims with empathy and wisdom, extols the ability of creative expression to reimagine and transform the world.

The many individuals who find themselves in the world looking for themselves are addressed in Watson's exquisitely written book. Piecing Me Together is a novel about how young people deal with the struggles and pain of daily life while remaining entire and true to themselves. It is both timely and timeless.

The reason why Jade's mother is said to as the sun of Jade is because she inspired Jade to overcome prejudices related to class, privilege, and fear.

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The complete question is:

Consider this excerpt from chapter 39:

Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, who is the sun?

1. The tour guide

2. Maxine

3. Jade's mother

4. The symphony members

Answer:

I don't know

Step-by-step explanation:

Answer:

4 2/9

Step-by-step explanation:

7 5/9 -3 1/3

68/9 -10/3

(68-30)/9

38/9

4 2/9