Zac and Malcolm each wrote short stories. Zac’s story is 273 lines long. Malcolm’s story is 145 lines longer than Zac’s. How long is Malcolm’s story? Explain what operation you used to solve this problem.

The exact value of sin(x + y) is (1 - 2√6) /6. The 2nd option is the answer.

We have sin(x) = -1/2 and cos(y) = -1/3

x is an angle in quadrant III, and y is an angle in quadrant II

For x:

Using trigonometric ratio

sin(x) = -1/2 (sin = opposite/hypotenuse)

adjacent = √(2²-(-1)²) = √3

cos(x) = (-√3)/2  (cos = adjacent/hypotenuse)

Note: adjacent in quadrant III is negative

For y:

Using trigonometric ratio

cos(y) = -1/3  (cos = adjacent/hypotenuse)

opposite = √(3²-(-1)²) = √8 = 2√2

sin(y) = (2√2)/3  (sin = opposite/hypotenuse)

Using trigonometric identity:

sin (x + y) = sin (x)·cos(y) + cos (x)·sin (y)

sin (x + y) = -1/2·(-1/3)  +  [(-√3)/2]·[(2√2)/3]

sin (x + y) = 1/6 - (√6)/3

sin (x + y) = (1 - 2√6) /6

Thus, the exact value of sin(x + y) is  (1 - 2√6) /6

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Answer:

52%

Step-by-step explanation:

Since the question asks about tails, we don't need the information about heads.

So out of 200 flips, 104 were tails. If we put 104 out of 200 in fraction form, you get;

104

-----

200

Now we just divide;

104/200 = 0.52, also known as 52%

Answer:

In probability and statistics, the law of big numbers holds that as a sample size increases, its mean gets closer to the average of the entire population. This is because as the sample size increases, the sample becomes more representative of the population.

According to the law of large numbers, a large entity that is expanding quickly cannot continue doing so indefinitely. Often used as instances of this phenomenon are the largest blue chips, with market values in the hundreds of billions.

Two distinct subjects can be covered by the law of huge numbers. First, there are many topics to which the law of large numbers can be applied in statistical analysis. In order to acquire the necessary amount of data, it may not be practical to survey every member of a given population, but every additional data point has the potential to raise the probability that the result is an accurate representation of the mean.

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By applying the formula of cuboid volume, the volume of the box can be expressed as 225x - 60x² + 4x³.

Cuboid is a 3-D shape formed by three pairs of rectangles (6 sides), 12 edges, and 8 vertices.

The volume of a cuboid can be calculated as follows:

Volume = length * width * height

Initially, we have a 15 x 15-inch piece of metal, then we cut out the four corners so that the sides can be folded up to make a box.

Now we have a shape as the attached image, where x represents the length of the sides of the squares that are to be cut out.

Thus, after the cutting, the length of the new side is 15 - 2x.

This value also represents the length and width of the box, whilst the height is x.

Now we can calculate the volume of the box:

Volume = length * width * height

             = (15 - 2x) * (15 - 2x) * x

             = (225 - 60x + 4x²) * x

             = 225x - 60x² + 4x³

Thus, the volume of the box can be expressed as 225x - 60x² + 4x³.

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The average rate of change for 1.8 < x < 2.5 is given as follows:

121.43.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The change in the output for this problem is given as follows:

325 - 240 = 85.

The change in the input for this problem is given as follows:

2.5 - 1.8 = 0.7.

Hence the average rate of change is given as follows:

85/0.7 = 121.43.

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So, b) and e) are subspaces of R3, and a), c), and d) are not.

a) {(x,y,z) ∈R3 : x = 0} is not a subspace of R3, because it doesn't contain the zero vector (0,0,0) which is a requirement for a subspace. It's also not closed under scalar multiplication.

b) {(x,y,z) ∈R3: x + y = 0} is a subspace of R3, because it's closed under scalar multiplication and addition and it contains the zero vector (0,0,0).

c) {(x,y,z) ∈R3 : xz = 0} is not a subspace of R3, because it's not closed under scalar multiplication and it's not closed under addition

d) {(x,y,z) ∈ R3: y ≥0} is not a subspace of R3, because it's not closed under addition, it doesn't contain the zero vector (0,0,0) and it's not closed under scalar multiplication.

e) {(x,y,z) ∈ R3: x = y = z} is a subspace of R3 because it satisfies all the properties of a subspace, it is closed under addition, scalar multiplication, it contains the zero vector (0,0,0) and the negative of any vector in the set is also in the set. This set contains all the vectors that are multiples of (1,1,1) which forms a subspace.

So, b) and e) are subspaces of R3, and a), c), and d) are not.

Complete Question: For each of the following subsets of R3 determine whether it is a vector subspace of R3 or not. Justify your answer.                                                                                                                                                      

a) {(x,y,z) ∈R3 : x = 0}

b) {(x,y,z) ∈R3: x + y = 0}

c) {(x,y,z) ∈R3 : xz = 0}

d) {(x,y,z) ∈ R3: y ≥0}

e) {(x,y,z) ∈ R3: x = y = z}

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The formula in cell B3 using the VLOOKUP function to find the meaning for the medical abbreviation listed in cell A3, using the "abbreviation" lookup table, would be: =VLOOKUP(A3, "abbreviation", 2, FALSE).

A3 is the cell that contains the medical abbreviation we want to find the meaning for.

"abbreviation" is the name of the lookup table that contains the item names and meanings.

2 is the column number of the lookup table where the meanings are located.

FALSE is used to require an exact match for the abbreviation in cell A3, so that the correct meaning is returned.

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the smallest possible answer in the class is 30.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Mr. Abraham’s is able to divide the learners in his Mathematics class into equal groups of 2, 5 or 6 members without leaving any learners out.

You just need to find the smallest number that can be divided by 2    or  5    or   6    evenly

  The Least Common Multiple

there are various ways to do this  

start with 5    

multiples of 5   are    5   10  15   20  25  30   35    etc.    

see any number in there that is also divisible by 2   and  6

Therefore, 30 is the smallest possible answer in the class.

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Complete question:

Mr. Abraham’s is able to divide the learners in his Mathematics class into equal groups of 2, 5 or 6 members without leaving any learners out. What is the smallest possible number of learners in the class?

Answer:

56

Step-by-step explanation:

The base area will be 4 times the side length

56 units

A counterexample to the statement given in this problem is:

Three colinear points.

The statement for this problem is given as follows:

You can connect any three points to form a triangle.

This statement is false, as for example, three points on a line do not form a function.

The counterexample is the statement that proves that a conjecture(another statement) is false, hence the first option is the correct option in the context of this problem.

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Answer:

Its either .5 or 5

Step-by-step explanation:

im not sure which one though lol

:)

Answer:

No

Step-by-step explanation:

2 * 5 = 10

12 does not equal 10

a) The number of microstates associated with tossing a coin N times and having it come up H times heads and T times tails is given by the binomial coefficient "N choose H" (or "N choose T", as H+T=N), which is equal to N!/(H! * T!)

b) For a series of 1000 tosses, with 50% heads and 50% tails, there are a total of "1000 choose 500" microstates. This is approximately 2.07*10²⁵ microstates.

c) The probability of getting a specific outcome when tossing a coin is given by the binomial probability mass function. The probability of getting 40% heads and 60% tails in 1000 tosses is given by (1000 choose 400)(0.4⁴⁰⁰)(0.6⁶⁰⁰) which is very less probable.

a) The number of microstates associated with a coin flip can be determined using combinatorics. The coin flip can have two possible outcomes: heads or tails. To calculate the number of microstates for N coin flips with H heads and T tails, we use the binomial coefficient formula "N choose H" (or "N choose T", as H+T=N), which is equal to N!/(H! * T!) where ! denotes factorial. This formula gives the number of ways to choose H heads out of N coin flips.

b) To calculate the total number of microstates for a series of 1000 tosses with 50% heads and 50% tails, we use the binomial coefficient formula "1000 choose 500". This is equivalent to (1000!/(500!500!)) which is approximately 2.0710²⁵ microstates.

c) The probability of getting a specific outcome when tossing a coin is given by the binomial probability mass function. The probability of getting 40% heads and 60% tails in 1000 tosses is given by (1000 choose 400)(0.4⁴⁰⁰)(0.6⁶⁰⁰) which is very less probable. We can calculate this using the binomial probability mass function which is ( n choose k ) * p^k * (1-p)^(n-k) where n is the number of trials, k is the number of successful outcomes, p is the probability of success in one trial, 1-p is the probability of failure in one trial.

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Answer: We can use a system of equations to solve this problem. Let x be the number of oranges sold and y be the number of apples sold. Then we know that:

x + y = 15 (the total number of fruits sold)

1x + 2y = 25 (the total cost of the fruits sold)

We can use the first equation to solve for one variable in terms of the other.

For example, we can solve for x:

x = 15 - y

Now we can substitute this expression into the second equation:

1(15 - y) + 2y = 25

15 - y + 2y = 25

3y = 10

y = 10/3 = 3.333

We can round it to 3 apples sold

So we have 3 apples and 12 oranges sold.

This can be represented in a graph with a point (12,3)

Alternatively, we can solve for y:

y = 15 - x

Now we can substitute this expression into the second equation:

1x + 2(15 - x) = 25

1x + 30 - 2x = 25

-x = -5

x = 5

So we have 5 oranges and 10 apples sold.

This can be represented in a graph with a point (5,10)

Both solutions represent the same values, the number of oranges and apples sold, but represented in a different way.

Step-by-step explanation:

Answer: In order to find the number of campgrounds that Montana would expect to have if it was proportional to Nevada in the number of campgrounds to counties, we need to determine the ratio of campgrounds to counties in Nevada and then apply that same ratio to Montana.

First, we'll find the ratio of campgrounds to counties in Nevada by dividing the number of campgrounds (637) by the number of counties (18): 637 / 18 = 35.389

Now we'll apply that same ratio to Montana by multiplying the number of counties in Montana (41) by the ratio of campgrounds to counties in Nevada: 41 x 35.389 = 1458.369

Rounding to the nearest whole number, we get 1458. So if Montana was proportional to Nevada in the number of campgrounds to counties, we would expect to find 1458 campgrounds in Montana.

Step-by-step explanation:

a. Without finding the confidence intervals, the larger margin of error will be the statistics class.

b. The confidence interval is (50.5%, 55.5%)

c. The group that concludes that the outcome is "too close to call is the statistics class.

.

It should be noted that the Without finding the confidence intervals, the larger margin of error will be the statistics class. This is because of the smaller sample size.

The group that concludes that the outcome is "too close to call is the statistics class. This is because the intervals that are obtained contains 50%.

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The correct arrangement regarding the angles of the triangle is;

m∠Y < m∠Z < m∠X

In triangle XYZ, the lengths of sides are;

XY = m + 8

YZ = 2m + 3

ZX = m - 3

If m ≥ 6, then;

m + 8 ≥ 14

2m + 3 ≥ 15

m - 3 ≥ 3

Thus;

m - 3 ≤ m + 8 ≤ 2m + 3

The greatest angle is opposite to the greatest side, the smallest angle is opposite to the smallest side, so;

the greatest side is  YZ = 2m + 3- the greatest angle is ∠X

the smallest side is ZX = m - 3 - the smallest angle is ∠Y

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The required total cost of the two shirts after 6.5% of the tax is given as 2.13s.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Benita buys 2 shirts for the same price s the sales tax rate is 6.5%

1 way, paid the cost of 2 shirts jointly
The total cost of the two shirts becomes,
Total cost = 2[ s + 0.065s]
Total cost = 2.13s

2nd way paid the cost of two shirts individually,
total cost = s + 0.065s + s + 0.065s
               = 2.13s

Thus, the required total cost of the two shirts after 6.5% of the tax is given as 2.13s.

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Since Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, the true statements about the distance which Sam ran are:

A. You know the difference in the distances the boys ran, so this is a subtraction problem.

E. The correct equation is s – 2.3 = 6.8.

In Mathematics, distance can be defined as the total amount of ground that is covered or travelled by a physical object (body) over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Since Dean ran 6.8 km and 2.3 fewer kilometers than Sam, we can logically deduce that this is a subtraction problem. Assuming the variable s represent the distance which Sam ran, Sam's distance can be calculated as follows;

s – 2.3 = 6.8

s = 6.8 + 2.3

s = 9.1 kilometers.

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The value of P(A|B) from the given data is 1/6 ≅ 0.17    

The term P(A/B) is known as a conditional probability which indicates the probability of an event A that depends on another event B.  

The probability of an event or outcome occurring due to the existence of a prior event or outcome is known as conditional probability.  

P(A/B) is used to find this conditional probability.

The formula for P(A/B) is given by

Here we have

A ven diagram which shows sports played by 10 students

From given figure

Number of students who play basketball, p(A) = 3

Number of students who play soccer, p(B) = 2  

Number of students who play both games, A∩B = 3  

As we know, P(A/B) = P(A∩B)/P(B)    

= 1/3 [2]

= 1/6 ≅ 0.17    

Therefore,

The value of P(A/B) from the given data is 1/6 ≅ 0.17      

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The Venn diagram that represents the description on Events A and B would be the A. First Diagram.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other.

This means that Events A and B cannot happen at the same time and therefore cannot share circles on the Venn diagram.

Events B and C are non - mutually exclusive however and so will share a circle on the Venn Diagram as shown below.

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Answer: D

last one

Step-by-step explanation: just did the test

Answer:

DCBA

Step-by-step explanation:

It's just reverse look closely and you'll notice

The number of servings that Sam has would be = 18.67 servings.

A fraction is part of a whole value that is being represented in a form of numerator and denominator.

The number of cups that Sam has = 9 1/3 = 28/3

The number of cups used for each serving = 2/4

That is ;

1 serving = 2/4 cups

X servings = 28/3 cups

Make X the subject of formula;

X servings = 28/3 ÷ 2/4

= 28/3 × 4/2

= 112/ 6

= 18.67 servings.

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The side length of the cube is 1/6 and the volume is 1/216

From the question, we have the following parameters that can be used in our computation:

Face area = 1/36

This means that

Side length = √(1/36)

Evaluate

Side length = 1/6

From the question, we have the following parameters that can be used in our computation:

Side length = 1/6

This means that

Volume = (1/6)^3

Evaluate

Volume = 1/216

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The height of the tree is 29 feet.

A measure of an angle formed which an object is viewed above the horizontal plane is termed angle of elevation.

Let the distance from the top of the tree to the student's eyes be represented by x. Thus, applying the required trigonometric function;

Tan θ = opposite/ adjacent

Tan 50 = x/ 20

x = 20*Tan 50

  = 23.8351

x = 24 ft

So that;

the height of the tree = 24 + 5

                                    = 29 feet

Therefore, the height of the tree is 29 feet.

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The statement 2( g = f + a) and 5(c = f) are true where as statement 3(a = d), 4(d = g - c), and 6(a = -b) are false.

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Since it is possible to drive a fraction of a mile, so it will be appropriate to use fractions; however, it is not possible to drive a negative number of miles, so only positive rational numbers are appropriate.

A rational number is said to be positive if its numerator and denominator are both positive.

Now, we are told that lian's truck uses 0.05 gallon of gas for every mile driven. Thus;

Rate of consumption of gas = 0.05 gallons per mile

The function for number of gallons is;

y = -0.05x + 25

where;

x is number of miles

y is number of gallons

We can use a fraction for the number of miles because it is possible but then the number of miles must be positive rational numbers because number of miles cannot be negative.

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well, we know that π is 180°, so what's 11π/6?

[tex]\begin{array}{ccll} radians&degrees\\ \cline{1-2} \pi &180\\\\ \frac{11\pi }{6}&x \end{array}\implies \cfrac{\pi }{ ~~ \frac{11\pi }{6} ~~ }~~ = ~~\cfrac{180}{x}\implies \cfrac{ ~~ \frac{\pi}{1} ~~ }{\frac{11\pi }{6}}~~ = ~~\cfrac{180}{x} \\\\\\ \cfrac{6\pi }{11\pi }=\cfrac{180}{x}\implies \cfrac{6 }{11 }=\cfrac{180}{x}\implies 6x=1980\implies x=\cfrac{1980}{6}\implies x=330[/tex]