Part A:
Determine 3 angles between 0° and 360° which have the same reference angle as a rotation angle of 72°. Name at least 1 angle greater than 360° with this same reference angle.
Part B:
What if the given rotation angle in quadrant 1 is n°. Determine 3 angles between 0° and 360° which have the same reference angle as a rotation angle of n°. Explain how you determined these angle measures.

Answer: ( 0, -70)

Step-by-step explanation: make a sketch on the x-y plane to see why

Answer:

- 12(x + 2)

Step-by-step explanation:

- 12x - 24 ← factor out the common factor of - 12 from each term

= - 12(x + 2)

The probability that a student will complete the exam in more than 60 minutes but less than 90 minutes is 0.8099 (to 4 decimal places).

The probability of a student completing the exam in more than 60 minutes but less than 90 minutes can be calculated using the cumulative probability distribution formula. The cumulative probability of a random variable X is given by P(X≤x)=F(x).

In this case, let F(x) represent the cumulative probability of a student completing the exam in more than 60 minutes but less than 90 minutes.

F(x) = P(60<x<90) = P(X<90) - P(X<60)

Using the cumulative probability distribution formula, we can calculate P(X<90) and P(X<60).

P(X<90) = 0.9686

P(X<60) = 0.1587

Substituting these values in the equation:

F(x) = P(60<x<90) = 0.9686 - 0.1587 = 0.8099

Therefore, the probability that a student will complete the exam in more than 60 minutes but less than 90 minutes is 0.8099 (to 4 decimal places).

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Candle A is taller than candle B at the beginning of the burning. The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Candle, A is taken from the mould at 223mm of height initially. Candle B is represented by the function h = 200 - 5t.

The initial height of candle A:-  223 mm

The initial height of candle B is:-

h = 200 - 5 t

h = 200 - 5 x 0

h = 200 mm

Candle A > Candle B

Hence, the height of candle A is greater than the height of candle B.

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Step-by-step explanation:

Slope-Intercept form is Y = mx + b

So we have to turn 9x + 3y = -9 into that.

A ideal first step would be subtracting 9x on both sides, that would make it

3y = -9x-9

Next step would be dividing by 3 on both sides. This can get the y all alone

[tex]y = \frac{ - 9x - 9}{3} [/tex]

Since the denominator is below multiple numbers, we can separate it as so

[tex]y = \frac{ - 9x}{3} - \frac{9}{3} [/tex]

Simplifying 9/3 goes to 3/1. 3/1 is the same as 3, because any number over 1 is that number. Doing that to both will get our answer.

[tex]y = - 3x - 3[/tex]

Answer:

2.  y = 3x + 6

3.  y = 2x

4.  y = 5x + 60

Step-by-step explanation:

Slope-intercept form: y = mx + b

2.

Pick 2 points (0,6) (1,9)

The y increase by 3, and the x increase by 1, so the slope is

m = 3

the y-intercept is located at (0,6)

Our equation is y = 3x + 6

3.

Pick 2 points (0,0) (1,2)

The y increase by 2, and the x increase by 1, so the slope is

m = 2

the y-intercept is located at (0,0)

Our equation is y = 2x

4.

Pick 2 points (0,60) (2,70)

The y increase by 10, and the x increase by 2, so the slope is

m = 10/2 = 5

the y-intercept is located at (0,60)

Our equation is y = 5x + 60

Answer:

Because the residual plot does not show a clear pattern, a linear model is appropriate.

Step-by-step explanation:

It is based on the likelihood of something occurring. The reasoning behind probability is the foundation of theoretical probability. The probability of getting one or two in first and second toss is [tex]\frac{1}{9}[/tex].

Probability is a number that represents the likelihood or chance that an event will occur. Probabilities can be expressed as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

The probability of getting one or two in first toss will be:-

[tex]\frac{1}{6} + \frac{1}{6} = \frac{1+1}{6} = \frac{2}{6} = \frac{1}{3}[/tex] ( as the probability of getting one in first toss is [tex]\frac{1}{6}[/tex] and getting two is also [tex]\frac{1}{6}[/tex]).

Similarly the probability of getting one or two in second toss will be:-

[tex]\frac{1}{6} +\frac{1}{6} = \frac{1+1}{6} = \frac{2}{6} = \frac{1}{3}[/tex]

The total probability of getting one or two in first and second toss will be:-

[tex]\frac{1}{3} *\frac{1}{3} = \frac{1}{9}[/tex]

Hence, Henceprobability is [tex]\frac{1}{9}[/tex].

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The required formula to calculate exterior angle and an interior angle are  360°/n and (n-2) * 180°/n.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides). To create a closed figure, a minimum of three line segments must be connected end to end.

The measure of an exterior angle of a regular polygon with n sides is given by 360°/n. The measure of an interior angle of a regular polygon with n sides is given by (n-2) * 180°/n.

So if you provide the number of sides of the polygon, I can give you the measures of the exterior and interior angles rounded to the nearest tenth if necessary.

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The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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The function when t=3 to the nearest tenth is 59.4.

The initial amount is a = 475, and the rate of decay r is 50%.

To evaluate the function when t=3, we plug in t=3:

f(3) = 475(0.5)^3 = 475 * (0.125) = 59.375

Rounding to the nearest tenth, f(3) = 59.4.

Therefore, the correct answer is as given above. It could be concluded that the rounded answer to the nearest tenth is 59.4

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According to the z table, there is a 0.3814 percent chance that such a standard normal random variable would fall between 0.3 and 3.2.

What is the probability?

The possibility of an event occurring is stated as a number between 0 and 1, where 0 indicates that the event cannot occur and 1 indicates that the event is guaranteed to occur. The probability of an event A is defined mathematically as the number of positive outcomes divided by the total number of alternative outcomes.

We must determine the likelihood that a standard normal random variable would occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The probability therefore should be

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value

P(0.3<z<3.2)=0.9993−0.6179

P(0.3<z<3.2)=0.3814

Therefore, there is a 0.3814 percent chance that a standard normal random variable would fall between 0.3 and 3.2.

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Answer: $19

Step-by-step explanation:

100% - 80% = 20%

20% ÷100 = 0.2

$95 x0.2 = $19

0r

10% of $95 = $9.50

9.50 x 2 = 19

When s and t are functions, the expression for (s + t) (x) is s(x) - t(x), and the result of (s-t)(-1) is -2.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this. If you enter anything for x, you will only get one output for y. Because x represents the input value, we may say that y is a function of x.

Here,

Given the functions s(x) = 5 and t(x) = 3, we can find the expressions for (s + t)(x) and (s - t)(x) as follows:

(s + t)(x) = s(x) + t(x) = 5 + 3 = 8

(s - t)(x) = s(x) - t(x) = 5 - 3 = 2

To evaluate (s - t)(-1), we simply plug in -1 for x in the expression for (s - t)(x):

(s - t)(-1) = 2

So, (s - t)(-1) = 2.

The expressions for (s + t) (x) is s(x) - t(x)  and value of (s-t)(-1) is -2 when s ad t are functions.

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A rectangular field has a 380-yard perimeter. The length exceeds the width by 10 yards. The dimensions is 0.4121.

The area around a form's edge is known as its perimeter. By adding together the lengths of the sides of various forms, one may determine their perimeter. The length of each side is always added together to determine a shape's perimeter. Add the lengths of a rectangle's four sides to determine its perimeter. Finding all four sides is simple if you only know the width and height (two sides are each equal to the height and the other two sides are equal to the width). Divide the height and breadth by two and add the results.

So, the probability

Let breath be B.

Length[tex]=B+10[/tex]

Perimeter=2(Length + breath)

[tex]380=2(B+10+B)[/tex]

[tex]380=2(2B+10)\\380=4B+20[/tex]

[tex]B=90[/tex]

And Length is 100.

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Part A: The equation that shows the relationship between Ann's age, x, and Tom's age, y is y = x - 8.

Relationship in Maths is the connection between two or more elements of a mathematical system. It can be regarded as a link between two or more mathematical objects or ideas. It can be expressed in terms of equations, inequalities, functions, and graphs. Most of the time, relationships in Maths are represented by symbols and arrows. For example, an arrow from one object to another represent a relationship between them. This type of representation is used to show the connection between different elements of a mathematical system.

Part B: The graph of the relationship between Ann's age, x, and Tom's age, y is shown below with the x-axis representing Ann's age, x, and the y-axis representing Tom's age, y.

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The eighth term of the sequence is -2187.

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios.

aₙ=a₁(r)ⁿ⁻¹

We have a geometric sequence,

1, -3, 9, -27, 81, ...

The common ratio,

r = -3/1 = -3.

And the first term is 1.

The explicit formula,

aₙ=a₁(r)ⁿ⁻¹

aₙ= (1)(-3)ⁿ⁻¹

The eighth term = (-3)⁷ = -2187.

Therefore, the eighth term = (-3)⁷ = -2187.

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A correlational result can be used to infer causation, but only when the r-value is higher than 0.

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, with values ranging from -1 to 1. A value of 0 indicates no linear relationship between the variables, a positive value indicates a positive relationship, and a negative value indicates a negative relationship.

However, a correlation coefficient value only indicates the presence of a relationship between variables and does not imply causality. To establish causality, one needs to consider additional information, such as a plausible causal mechanism and the absence of alternative explanations.

Option A is the proper response, so.

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The appropriate sales price for a home in 2020 would be = 480 thousands. That is option A.

The price of home in year 1990 = 149 thousand

The price of home in the year 1995 = 158 thousand

The difference in years = 2000-1995 = 5 years

The difference in the average sales price for the both years = 158-149 = 49 thousand.

The years difference between 2000 and 2020 = 20 years

If 5 years = 49 thousand

20 years = X

Make X the subject of formula;

X = 20×49/5

X = 980/5

X = 196 thousand

Therefore, the sales price for a home in 2020 would be = 207+196 = 403 thousands. The appropriate sales price would be = 480 in 2020.

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To find out how much 75 apples would cost, we need to find out the cost per apple and then multiply that amount by 75. If 50 apples cost $25, then the cost per apple is $25/50 = $0.50. So, 75 apples would cost $0.50 x 75 = $37.50.

Answer:

$37.50

Step-by-step explanation:

$25/50=$0.50 per apple

0.50 x 75 = $37.50

Answer:

Since you know that 15 vases are worth 2,250 rupees, then to find how much 25 cost, you can first find how much each costs individually.

To find how much each vase cost, you can just divide the total cost of 15 vases, and the amount of vases:

2250/15 = 150

Each vase costs 150 rupees.

Now to find how much 25 vases cost, you can just multiply the cost per each flower vase, by the total amount of vases:

150 * 25 = 3,750

25 flower vases cost's 3,750 rupees.

Step-by-step explanation:

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The arithmetic mean of the two fractions is 68/35.

The arithmetic mean can be calculated using the mentioned formula -

Arithmetic mean = sum of the numbers / frequency of numbers.

Sum of the fractions = 2/5 + 4/7

Performing division of the two numbers

Sum of the fractions = (14 + 20)/35

Sum of the fractions = 34/35

Arithmetic mean = (34/35)/2

Rewriting the average

Arithmetic mean = (34 × 2)/35

Performing multiplication on Right Hand Side of the equation

Arithmetic mean = 68/35

Hence, the Arithmetic mean is 68/35.

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The concept is an experiment conducted on  Probability.  Probability tells us how frequently some event will be after numerous repeated trials.

Probability is a branch of mathematics that deals with numerical descriptions of the probability that an event will occur or the probability that a statement is true. The probability of an event is a number between 0 and 1,

The sample space refers to the list of all possible issues of a trial. Each possible outgrowth is represented by a single point in the sample space, irrespective of the number of ways that outgrowth can do.

Given:

A) In an experiment, the gender of a child is observed at birth.

A child can be of two sexes: male and female.

Let (M) be male and (F) be female and denote (S) the pattern space.

Then: S = {M,F}

B) The list of all possible outcomes is called the pattern space. If we name two children in the order of their birth, there are 4 possible outcomes. Using M for men and F for women can shorten the results. The  list of all possible outcomes:

S={M, F} ,{M,M}, {F,F}

c) If the child were a girl, then from the previous scenario S= {F, F} would result.

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The difference between the rate of change of the intervals: 1,2 and 2,4 is; 2

The average rate of change over the intervals (x₁, y₁) and (x₂, y₂) is given by the formula;

Average rate of change = (y₂ - y₁)/(x₂ - x₁)

Thus, the average rate of change between the intervals (1, 2) and (2, 4) is;

Average rate of change = (4 - 2)/(2 - 1)

Average rate of change = 2/1

Average rate of change = 2

That is the difference between the rate of change over the two given intervals.

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The z-scores for the middle 68% of the normal distribution are -1.0 and +1.0, for the middle 95% are -2.0 and +2.0, and for the middle 99.7% are -3.0 and +3.0.

a) The z-scores for the middle 68% of the normal distribution are -1.0 and +1.0. This means that 68% of the data falls between the mean and 1 standard deviation above and below the mean. The formula for calculating z-scores is z-score = (x - μ) / σ, where x is the data point, μ is the mean and σ is the standard deviation.

b) The z-scores for the middle 95% of the normal distribution are -2.0 and +2.0. This means that 95% of the data falls between the mean and 2 above and below the mean. The formula for calculating z-scores is z-score = (x - μ) / σ, where x is the data point, μ is the mean and σ is the standard deviation.

c) The z-scores for the middle 99.7% of the normal distribution are -3.0 and +3.0. This means that 99.7% of the data falls between the mean and 3 standard deviations above and below the mean. The formula for calculating z-scores is z-score = (x - μ)/ σ, where x is the data point, μ is the mean and σ is the standard deviation.

The z-scores for the middle 68% of the normal distribution are -1.0 and +1.0, for the middle 95% are -2.0 and +2.0, and for the middle 99.7% are -3.0 and +3.0.

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Kinetic energy of a moving object depends directly on its mass and velocity.

Energy is the ability to do work. There are several types of energy like potential energy, kinetic energy, heat energy, mechanical energy, electrical energy and so on.

Kinetic energy is the energy that an object possesses due to its motion. All moving objects possesses this energy (kinetic energy). The kinetic energy of an object is given by:

Kinetic energy = (1/2) * mass * velocity²

Kinetic energy depends on mass and velocity.

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The slope of line GH that contains points G(-2, 6) and H(5, -3) is equal to: 2. -9/7.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-3 - 6)/(5 - (-2))

Slope (m) = -9/7

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The most appropriate design would be experiment. Implementation of the design would be by selection of trees, then the application of fertilizer, followed by data collection and statistical analysis.

a) Most appropriate design: Experiment

The orchard owner wants to determine if a new formula of fertilizer produces more apples per tree compared to a current popular brand. To make a causal conclusion, an experiment would be the most appropriate design. In an experiment, the orchard owner would randomly assign the trees to receive either the new fertilizer formula or the current popular brand and then compare the number of apples produced. This allows the orchard owner to control for other variables and isolate the effect of the fertilizer on the number of apples produced.

b) Implementation:

Selection of trees: The orchard owner would randomly select a sample of trees from their orchard and divide them into two groups: the experimental group (receiving the new fertilizer formula) and the control group (receiving the current popular brand).

Application of fertilizer: Both the experimental and control groups would receive the same amount of fertilizer, but the experimental group would receive the new formula while the control group would receive the current popular brand.

Data collection: The orchard owner would measure the number of apples produced by each tree in both the experimental and control groups.

Statistical analysis: The orchard owner would use appropriate statistical tests to compare the number of apples produced by each group and determine if there is a significant difference between the two.

c) Benefit:

One benefit of this experimental design is that it allows the orchard owner to determine causality. By randomly assigning the trees to receive either the new fertilizer formula or the current popular brand, the orchard owner can be confident that any difference in the number of apples produced is due to the fertilizer and not other factors. This is important for making decisions about which fertilizer to use in the future.

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Answer:

The domain is the set of all the input values of a function and the range is the possible output given by the function.

A matrix A is said to have only the trivial solution if the only solution to the system of equations, A x = 0, is the zero vector, x = 0.

The number of pivot columns in a matrix is equal to the rank of the matrix. Therefore, if A has only the trivial solution, it has rank 0, and so it has 0 pivot columns. To calculate the rank of a matrix, we can use the following formula: rank(A) = min(m, n) - dim(null A), where m and n are the number of rows and columns of A, respectively, and dim(null A) is the dimension of the null space of A.

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complete question:

Given an m x n matrix A, what is the number of pivot columns for A if it has only the trivial solution?