The amount of light reflected up through the top of a
diamond (brilliancy) can be maximized using the ratio between the width of the
diamond and the depth of the diamond. A gemologist has a diamond with a width of
80 millimeters. If x represents the depth of the diamond, then 80/x
represents the
brilliancy ratio y. Describe the reasonable domain and range values. Graph the function.

Answer:

y = 4/5x + 3

Step-by-step explanation:

The equation y + 1 = 4/5(x + 5) can be solved by first isolating the y variable on one side of the equation. To do this, we'll first distribute the 4/5 across the parenthesis:

y + 1 = 4/5x + 4

Next, we'll subtract 1 from both sides of the equation:

y = 4/5x + 3

This is the equation in standard form, with the y variable on the left side and the x variable on the right side, and the constants added and subtracted.

Answer: The summer monsoon rains are a crucial source of rainfall for India, bringing in 80% of the country's annual rainfall. These rains are essential for the country's agriculture as they provide the necessary water for crops to grow and thrive. The monsoon season typically runs from June to September, and the amount of rainfall received during this time period can greatly impact the success of the agricultural season. With the majority of the rainfall coming during this season, farmers and agricultural experts closely monitor the monsoon forecast to ensure that enough rainfall is received to support the crops. Without the summer monsoon rains, the agricultural production of the country would be greatly impacted and the livelihoods of many farmers would be at risk.

Step-by-step explanation:

a) The percentage change in nominal GDP between 2010 and 2019 is;

47.54%

b)  Real GDP in 2019 at prices of 2010 is; 20,597.113 billions

c)  The percentage change in real GDP between 2010 and 2019; 72.4%

d)  The percentage change in nominal GDP between 2010 and 2019 attributed to changing prices is; 24.45%

The formula to calculate percentage change is;

Percentage change = (Final Value - Original Value)/Original Value * 100%

a) The percentage change in nominal GDP between 2010 and 2019 is;

(21433 - 14527)/14527 * 100%

= 47.54%

b) Real GDP in 2019 at prices of 2010 is;

21433 * 0.961

= 20,597.113 billions

c)  The percentage change in real GDP between 2010 and 2019;

real GDP in 2010 = 14527 * 0.961

= 13,960.447 billion

Real GDP in 2019 = 21433 * 1.123

= 24,069.259 billion

Percentage change =  (24069.259 - 13960.447)/13960.447 * 100%

= 72.4%

d)  The percentage change in nominal GDP between 2010 and 2019 attributed to changing prices is;

Percentage change = [(21433/1.123) - (14527/0.961)]/(14527/0.961) * 100%

= 24.45%

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The measure of ∠EFJ is 60°. Option B is the correct option.

What is a linear pair?

When two lines cross at one point, a linear pair of angles are created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles.

∠EFG is a linear pair of angle.

This means ∠E F G = 180°

Given that ∠J F K = 90° and ∠E F J = 2∠K F G.

∠E F G is the sum of angles ∠E F J, ∠J F K  and ∠K F G

∠E F G = ∠E F J + ∠J F K + ∠K F G

Now putting the value of ∠E F G, ∠J F K

180° = ∠E F J +  90° + ∠K F G

Again putting ∠K F G = 1/2∠E F J:

180° = ∠E F J +  90° + 1/2∠E F J

180° -  90° = 3/2 ∠E F J

90° = 3/2 ∠E F J

∠E F J = 90° ×(2/3)

∠E F J = 60°.

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As the value of a decreases the graph will expand.

In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.

Given that consider the quadratic function y = ax². When the function is plotted on the for the value of an increases the graph contracts and if the value a decreases the graph expands.

The graph is attached with the answer below. In the graph, the quadratic function is shown at the two values of a.

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Based on the given derivative function, the function f is decreasing for a < x < b, because f'(x) < 0 for a < x < b (A).

The given derivative function is the first derivative of function f(x), where:

f'(x) = x² - (a+b) x + ab = (x - a) (x - b)

a < b

Since the first derivative function f'(x) is still in the form of x²  function, we can deduce that the original function f(x) has 2 extreme points, the maximum and the minimum. Those extreme points are (x = a) and (x = b).

However we cannot determine which one is the maximum point and which is the minimum one. We need to do another derivative work and check the second derivative function for each extreme points relevant to zero (0).

f'(x) = x²  - (a+b) x + ab

f''(x) = 2x - (a+b)

(x = a)

f''(a) = 2(a) - (a+b)

f''(a) = 2a - a - b

f''(a) = a - b < 0 --> because a < b

(x = b)

f''(b) = 2(b) - (a+b)

f''(b) = 2b - a - b

f''(b) = b - a > 0 --> because a < b

Based on the second derivative function, we can define that (x = a) is the maximum point because f''(a) < 0 and (x = b) is the minimum point because f''(b) > 0. Then the value of f(x) between a < x < b should be on a downward slope.

However wee need to reconfirm this statement by choosing one set of random number that meet the rules of a < x < b. For this time, we use:

a = 1

b = 3

x = 2

Then:

f'(x) = x² - (1 + 3) x + (1) (3)

f'(x) = x²  - 4x + 4

(x = 2)

f'(2) = (2)²  - 4(2) + 3

f'(2) = 4 - 8 + 3

f'(2) = -1 < 0 --> supported statement A

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Answer:

31=3+x

31=-3+x

28=x

28/7

$4

Each Candy bar cost $4 each

Step-by-step explanation:

Answer:

  (f/g)(x) = -(x²+7x)/(x²-9)

Step-by-step explanation:

Given f(x) = x^2 +7x and g(x) = 9 -x^2, you want f/g(x).

The rational function (f/g)(x) is ...

  [tex](f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{x^2+7x}{9-x^2}\\\\\\\boxed{(f/g)(x)=-\dfrac{x^2+7x}{x^2-9}}[/tex]

__

Additional comment

We simply use the values of f(x) and g(x) in the desired ratio. No simplification is possible.

Based on the given figure, we refer to angle a as the length of the side opposite to the angle θ, b as the length of the side adjacent to the angle θ and c as the length of the hypotenuse.

A right triangle is composed by two sides, that form a right angle = angle of 90º between them, plus the hypotenuse, which is the segment connecting these two sides.

The angles are classified as adjacent and opposite as follows:

The problem is given by the image presented at the end of the answer.

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the number of students going

$12.50 is the cost of the STUDENT ticket, so that knocks 2 answers down then, would you times the total by 12.5 to get the actual cost. no so it has to be the number of students going

When a number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.

The sample space describing all possible outcomes is {1, 2, 3, 4, 5, 6}

Then outcomes for the event of rolling an even number. {2, 4, 6}

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to foretell the likelihood of many events.

In probability, sample space refers to the list of all potential outcomes of an experiment. Regardless of the number of ways an event could occur, each potential result is represented by a single point in the sample space.

The sample space is the numbers from 1 to 6 while event of rolling an even number is 3/6 = 1/2

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Answer:

Step-by-step explanation:

Is there enough evidence to reject the researcher claim?

To determine if there is enough evidence to reject the researcher's claim, we can perform a hypothesis test with a null hypothesis of p <= 0.05 (at most 5% of working college students are employed as teachers or teaching assistants) and an alternative hypothesis of p > 0.05 (more than 5% of working college students are employed as teachers or teaching assistants).

Find the critical values and identify the rejection.

For a one-tailed test with a significance level of alpha = 0.05, the critical value for a z-test would be 1.645. This means that if the calculated z-score is greater than 1.645, we would reject the null hypothesis.

Find the standardized test statistic z

To find the standardized test statistic z, we can use the formula:

z = (p-hat - p0) / (sqrt(p0 * (1 - p0) / n))

where p-hat is the sample proportion of working college students employed as teachers or teaching assistants (6%), p0 is the proportion specified in the null hypothesis (5%), and n is the sample size (400).

z = (0.06 - 0.05) / sqrt(0.05 * (1 - 0.05) / 400)

z = 0.1 / 0.015811388300841898

z = 6.317

Decide whether to reject or fail to reject the null hypothesis and interpret the decision.

Since the calculated z-score (6.317) is greater than the critical value (1.645), we can reject the null hypothesis. This means that there is enough evidence

The work done on the given box from x = 0 m to 4.0 m will be 100 Nm.

Work is performed when an item moves as a result of a force, causing energy to flow from one store to another. Work is measured in Joules, and one joule equals one newton of force on an object traveling one meter.

The graph is given in the question, as shown

We have to determine the work done on the given box from x = 0 m to 4.0 m

As per the given graph, the required solution would be as:

Work done = Force × covered area between the graph and displacement axis

Work done = 1/2 × (30 × 4) + 10 × 4

Work done = 1/2 × 120 + 40

Work done = 100 Nm

The work done on the given box will be 100 Nm.

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Answer:

top right graph

Step-by-step explanation:

5y=-10x+20

y=-2x+4

The p-value of the test hypothesis for each case is given as follows:

b) n = 9: 0.1151.

i. n = 25: 0.0228.

ii. n = 100: 0.

iii. When the sample size increases, the test statistic also increases, and hence the p-value decreases.

Before obtaining the p-value, the first step is obtaining the test statistic for the test.

The z-distribution is used, as the standard deviation for the population is known, and the equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which the parameters are given as follows:

The fixed parameters for this problem are given as follows:

[tex]\overline{x} = 52, \mu = 50, \sigma = 5[/tex]

Hence, for n = 9, the test statistic is given as follows:

z = (52 - 50)/(5/3)

z = 1.2.

We have a right-tailed test, as we are testing if the mean is greater than a value, hence the p-value is of 1 subtracted by the p-value of z = 1.2, that is:

1 - 0.8849 = 0.1151.

With n = 25, we have that:

z = (52 - 50)/(5/5)

z = 2.

z = 2 has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

With n = 100, we have that:

z = (52 - 50)/(5/10)

z = 4.

z = 4 has a p-value of 1.

1 - 1 = 0.

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I preserve shape but not size.

My image and pre-image will be similar.

I am created by using a scale factor that is less than one.

I am Dilation (decrease).

What is scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

The points given are -

1. I preserve shape but not size.

2. My image and pre-image will be similar.

3. I am created by using a scale factor that is less than one.

During dilation if the scale factor is between 0 and 1, then the image shrinks.

The new image will be same but smaller in size than the original image.

The size of the image decreases from its original size but the shape remains the same.

Therefore, this is known as dilation (decrease).

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Answer:

30 = 2·2·3

48 = 2·2·2·2·3

GCF = 6 (2·3)

LCM = 240 (2·3·5·8)

Step-by-step explanation:

Please find attached the drawing, created with MS Word, of the image of the triangle following the reflection across the mirror surface.

1) The object and the image are equidistant from the mirror

2) The object and the image following the reflection across a plane mirror are have the same side lengths and are therefore congruent

3) The image of the triangle is upright, and virtual and inverted from left to right

The laws of reflection are;

1) The angle made by the incident ray and the normal line (the angle of incidence) is equal to the angle made by reflected ray and the normal line

2) The incident ray, the reflected ray and the normal are coplanar

3) The incident ray is on the other side of the normal with regards to the refracted ray

1) The distance of the points on the object from the mirror are the same as the distance of the corresponding point from on the image from the mirror

2) A reflection of an object across a plane mirror is a rigid transformation such that the size of the object and the size of the image are the same.

Therefore, ΔABC ≅ ΔA'B'C'

3) The coordinates of the image formed following the  reflection of a point (x, y) across the y-axis is; (-x, y)

The y-coordinate remains the same, and the x-coordinates changes from positive to negative, and the location of the object on the left of the y-axis, produces an image on the right of the y-axis. Therefore

Therefore, the image is upright and inverted from right to left

The image of the triangle cannot be played on the screen, therefore, the image is virtual

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Answer:

Slope =y2−y1/2−x1 =4−81+3=−1

The function operations are given as follows:

The addition of functions is done combining the like terms, hence:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = x² - 1 + 7 - 3x - x²

(f + g)(x) = -3x + 6.

The multiplication of the functions is done multiplying the terms and then combining the like terms, as follows:

hf(x) = (2x - 1)(x² - 1)

hf(x) = 2x³ - x² - 2x + 1.

The quotient of the functions is quite straightforward, we just replace their definitions, as follows:

(f/h)(x) = (x² - 1)/(2x - 1)

The subtraction of the functions is similar to the addition, combining the like terms, as follows:

(g - f)(x) = 7 - 3x - x² - (x² - 1)

(g - f)(x) = 7 - 3x - x² - x² + 1

(g - f)(x) = -2x² - 3x + 8.

(h - g)(x) = 2x - 1 - (7 - 3x - x²)

(h - g)(x) = 2x - 1 - 7 + 3x + x²

(h - g)(x) = x² + 5x - 8.

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The number of square inches of fabric that Alicia would need to create the logo is equal to 141.135 square inches.

Based on the information provided, we can logically deduce that a mathematical expression that represents the number of square inches of fabric that Alicia would need to create the logo is given by:

s . s + 0.5s . s

where:

s represents the length of the side of the square in inches.

By simplifying the mathematical expression, we have the following:

Number of square inches of fabric = s² + 0.5s²

Substituting the given parameters into the mathematical expression, we have the following;

Number of square inches of fabric = 9.7² + 0.5(9.7)²

Number of square inches of fabric = 94.09 + 0.5(94.09)

Number of square inches of fabric = 94.09 + 47.045

Number of square inches of fabric = 141.135 square inches.

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Complete Question:

Alicia, a graphic designer, is designing a new logo for a company. The logo will contain a square and a triangle. The triangle’s base and height will be the same length as the side of the square. Alicia wants to use fabric to create the shapes to use during her presentation to the company. The expression s · s + 0.5s · s represents the number of square inches of fabric she will need to create the logo, where s is the length of the side of the square in inches.

If a side of the square is 9.7 inches long, how many square inches of fabric will Alicia need?

The total number of relations in the set s = {1,2,3} is given as follows:

9.

The total number of relations in a set is given by the cardinality of the square of the set.

The square of a set is composed by all the possible pairs that can be formed with the elements in the set.

The set for this problem is defined as follows:

s = {1, 2, 3}.

The set has a cardinality of 3, as it has 3 elements, hence the cardinality of the square of the set is given as follows:

3² = 9.

Which is the total number of relations in the set.

These relations are all the ordered pairs with elements of s, hence:

Relations = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}

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The fraction form of the given decimal number [tex]8.3 \overline3[/tex] is 75/90.

Any number with a decimal point in between the full amount and the fractional portion is said to be decimal. These two components of the decimal are separated by the point. It is known as a decimal point as a result the figures following the decimal point are always less than one.

We can covert every decimal number into fractions as follows

Here we have

[tex]8.3 \overline3 = 10F[/tex]  ---- (1)

[tex]- 0.8\overline3 = - F[/tex]  ---- (2)    

Subtract (2) from (1)

=> [tex]8.3 \overline3 - 0.8\overline3 = 10F - F[/tex]  

=> 7.5 = 9F

=> F = 7.5/9

=> F = 75/90    [ Multiplied by 10 on both sides ]

Therefore,

The fraction form of the given decimal number [tex]8.3 \overline3[/tex] is 75/90.

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The mean interest rate of the sample is 3. 92

Mean of values is mathematically described as a quantity having a value that is intermediate between those of the extreme members of a given se of numbers.

From the information given, we have the set of values;

5.7, 1.4, 3.6, 4.9, 4.0

The formula for calculating mean is expressed as;

Mean = sum of numbers/ total number of numbers

Substitute the values

Mean = 5. 7 + 1. 4 + 3. 6 + 4. 9 + 4. 0/5

Add the values

Mean = 19. 6/5

divide through

Mean = 3. 92

Hence, the value is 3.92

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The probability that the two bills together will be worth at least 30 dollars is, 4/7

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Given that,

Marya has 3 bills worth 10 dollars each

4 bills worth 20 dollars each

she chooses two of these bills at random

the probability that the two bills together worth at least 30 dollars =?

So,  total possible combinations  (10, 10, 10, 20, 20, 20, 20) = ⁷C₂ = 21

favorable combinations = ³C₁ × ⁴C₁ = 12

Probability = 12/21

Probability = 4/7

Hence, the probability is 4/7

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The graph that shows that y is less than or equal to 3x - 4 is plotted and attached

The graph is plotted by forming a table of value, then tracing eaching point in the table and marking the points of intersection of the x and y

The points intersections later joined with a line

The table of value is formed for x = -2, 0, and2

y ≤ 3x - 4

for x = -2, y ≤ 3 * -2 - 4 = -10

for x = 0, y ≤ 3 * 0 - 4 = -4

for x = 2, y ≤ 3 * 2 - 4 = 2

table of value

x      y

-2    -10

0     -4

2      2

The graph is attached, the line is a solid line since the inequality is less than or "equal to". The shading is below because it is less than

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The debriefing is an essential part of the informed consent process and is mandatory when the research study involves use of deception.

The debriefing is an essential part of the informed consent process and is mandatory when the research study involves use of deception. The debriefing provides participants with a full explanation of the hypothesis being tested, procedures to deceive participants and the reason(s) why it was necessary to deceive them.

Research in science and technology is important because it contributes to knowledge and understanding of the world. It also contributes to the development of new technologies which are important in science and technology.

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The function is being transformed with a dilation of scale factor of 3 and an upward vertical shift of 4.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given is a function under some transformations, 3 h(x) + 4 ;

If we consider h(x) as a parent function, then the result after the transformation is 3h(x)+4,

We see that, it is being multiplied by 3, we know that if a function is being multiplied by a number greater than 1 in transformation then it is dilated by a scale factor of the number, hence, the function is being dilated by a scale factor of 3.

Also, we see, here is an addition of 4, we know that, when function is added by a certain number then in the transformed function the function is shifted vertically and addition mean it shifted vertically upwards, sine, 4 is added to the function it means, the function is shifted 4 unit vertically upwards.

Hence, the function is being transformed with a dilation of scale factor of 3 and an upward vertical shift of 4.

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Answer:

Domain {-3, 6}

Range: 7, 12}

Not a function

Step-by-step explanation:

Domain

Domain is the set of all x values which result in real and defined values for y

Range

Range is the set of y values that are possible from the values of x in the domain

Both are expressed in the form {min-value, max-value}

For x we see the minimum is -3 and maximum is 6

So domain = {-3, 6}

For y values we see the minimum is 7 and maximum is 12

So range = {7, 12}

A function can have only one output(y) for a specific input(x)

Here we see that for different values of x, x = 4 and x = -3, we get the same y-value

Hence it is not a function