A recipe for oatmeal cookies calls for 5 cups of flour for every 6 cups of oatmeal. How much flour is needed
for a big batch of cookies that uses 24 cups of oatmeal?
cups

The difference in starting Volume is 175 and after 8 minutes both buckets have same volume.

The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time.

Given:

The leakage rate of A

= (2000- 2900)/ (1- 10)

= -900/ (9)

= -100 ml/min

The leakage rate of B

= (2050- 2725)/ (1- 10)

= -675/ (9)

= -75 ml/min

Now, 2900- 100t = 2725 - 75t

25t = 175

t= 7

So, when t= 1 min and after 7 min both buckets have the same volume of water.

So, t= 1+ 7 = 8 mins

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a).north component = 44.0 km/h * sin(40.0°) ≈ 28.31 km/h

East component = 44.0 km/h * cos(40.0°) ≈ 33.71 km/h

The difference between the northern components of the fishing boat and the speedboat is:

North difference = 28.31 km/h - 0 km/h = 28.31 km/h

So the time it takes for the speedboat to intercept the fishing boat is:

Time = North distance / North difference = 6.21 km / (28.31 km/h) = 0.219 hours

Converting to minutes:

Time = 0.219 hours * 60 minutes/hour ≈ 13.1 minutes

Therefore, it takes the speedboat about 13.1 minutes to intercept the fishing boat.

b) tan θ = east component / north component

θ = tan⁻¹(east component / north component)

θ ≈ 51.3°

So the direction in which the speedboat travels is 51.3° east of north. Therefore, the compass bearing with respect to due north is:

Bearing = 90° - 51.3° ≈ 38.7° east of north.

In mathematics, a function is a relationship between two sets of values, such that each input value (also known as the argument or independent variable) is associated with exactly one output value (also known as the value or dependent variable). A function is usually denoted by a symbol such as "f(x)" or "y" and is defined by a rule or formula that specifies how the input value is transformed into an output value.

For example, consider the function f(x) = 2x. This function takes an input value x, multiplies it by 2, and returns the result as the output value. So, for example, when x is 3, the output value is 6. When x is 5, the output value is 10.

Functions can be represented graphically as well. The graph of a function is a set of points in a two-dimensional coordinate system, where the x-coordinate is the input value and the y-coordinate is the output value. For example, the graph of the function f(x) = x^2 is a parabola.

Functions are widely used in many areas of mathematics, science, engineering, economics, and more. They provide a powerful tool for modeling real-world situations, making predictions, and analyzing data.

(a) To find how much time it takes for the speedboat to intercept the fishing boat, we first need to find the position of the fishing boat at the moment the speedboat launches.

From the lighthouse's perspective, the fishing boat is located at a bearing of 15.0° east of north and a distance of 24.0 km. Using trigonometry, we can find the north and east components of the fishing boat's position:

North component = 24.0 km * sin(15.0°) ≈ 6.21 km

East component = 24.0 km * cos(15.0°) ≈ 22.76 km

Now we can use the relative velocity between the fishing boat and the speedboat to find the time it takes for the speedboat to intercept the fishing boat. The speedboat's velocity can be broken down into north and east components:

North component = 44.0 km/h * sin(40.0°) ≈ 28.31 km/h

East component = 44.0 km/h * cos(40.0°) ≈ 33.71 km/h

The difference between the northern components of the fishing boat and the speedboat is:

North difference = 28.31 km/h - 0 km/h = 28.31 km/h

So the time it takes for the speedboat to intercept the fishing boat is:

Time = North distance / North difference = 6.21 km / (28.31 km/h) = 0.219 hours

Converting to minutes:

Time = 0.219 hours * 60 minutes/hour ≈ 13.1 minutes

Therefore, it takes the speedboat about 13.1 minutes to intercept the fishing boat.

(b) To find the direction in which the speedboat travels, we can use trigonometry to find the angle between the speedboat's velocity vector and the north direction.

The north component of the speedboat's velocity is 28.31 km/h, and the east component is 33.71 km/h. Using the tangent function, we can find the angle:

tan θ = east component / north component

θ = tan⁻¹(east component / north component)

θ ≈ 51.3°

So the direction in which the speedboat travels is 51.3° east of north. Therefore, the compass bearing with respect to due north is:

Bearing = 90° - 51.3° ≈ 38.7° east of north.

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The people may easily accept the conclusion of the study described because of a common misunderstanding of correlational studies.

The Correlational Studies are used to examine the relationship between two variables, and a positive correlation suggests that the two variables are related in a certain way .

In this study, the Researchers found a strong positive correlation between sugary snacks and hyperactivity, suggesting that as the amount of sugary snacks offered increased, the number of times children left their seats also increased.

Therefore , people easily accept the conclusion of the study that sugar causes hyperactivity due to a misunderstanding of correlational studies and a lack of knowledge about the need for experimental designs to establish causality.

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The given question is incomplete , the complete question is

Researchers conducted a naturalistic study of children between the ages of 5 and 7 years. The researchers visited classrooms during class party celebrations. As a measure of hyperactivity, they recorded the number of times children left their seats. The researchers found a strong positive correlation between sugary snacks offered at the parties and hyperactivity.

Based on these findings, the researchers concluded that sugar causes hyperactivity.

Explain why people may easily accept the conclusion of the study described above? Include in your explanation a misunderstanding of correlational studies

Darrel's total earning for the week he sold 225 items is $2,805.

We are given that Darrel has a weekly salary of $430.

This means that no matter how many items he sells, he will always earn at least $430 for the week.

However, Darrel also earns an additional $19 for every item he sells in excess of 100 items.

This means that for the first 100 items he sells, he will not earn any additional money beyond his $430 weekly salary.

But for every item he sells beyond 100, he will earn an additional $19.

Now, for selling 225 items, Darrel sold 125 items in excess of the 100 item baseline.

Thus, the additional amount he earned from selling 125 items is:

= 125 items ×  $19 per item

= $2,375

Therefore, his total earnings for the week would be:

$430 (weekly salary) + $2,375 (amount earned from selling items in excess of 100)

= $2,805

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A college finds that 10% of students have taken a distance learning class and that 40% of students are part time students.

a. P(D AND E).= 0.08

b. Find P(E|D).= 0.8

c. Find P(D OR E). = 0.42

A) P (D and E) = 0.4 x 0.2 = 0.08

 explanation: 20% of the part times students are taking distance learning classes (D and E)

B) P (E | D) = P ( D and E) / P (D) = 0.08 / 0.1 = 0.8

C) P (D or E) = 0.4 + 0.1 - 0.08 = 0.42

D and E are not independent, because P (D and E) doesn't equal P(D) x P(E)

D and E are not mutually exclusive

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 incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

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Based on the given option, the correct answer would be; C. 2x - 3y = 6 and 2x + y = -6

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

here, we have,

We are given the system of equations as;

2/3x - y = 2

x + 1/2 y = -3

Here multiply by 3 on both sides;

2x - 3y = 6

Now similarly;

x + 1/2 y = -3

2x + y = -6

The result would be C. 2x - 3y = 6 and 2x + y = -6

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Reason: It fails the vertical line test. It is possible to pass a single vertical line through multiple points on this blue graph.

For instance, we can have a vertical line through x = 1. This vertical line intersects infinitely many points.

In other words, the input x = 1 leads to more than one output, which is a counter-example to show we do not have a function.

A function is only possible if each input in the domain leads to exactly one output in the range.

Since we don't have a function, you don't need to worry about filling in the domain and range boxes.

The graph is a function with a domain of (-infinity, infinity) and a range of (-infinity, infinity).

The graph represents a function because for each value of x, there is exactly one corresponding value of y. As a result, the vertical line test is passed.

The domain of the function is the set of all x-values for which the function is defined. In this case, it appears that the graph extends from x = -infinity to x = infinity, so the domain is (-infinity, infinity).

The function's range is the set of all y-values that the function can yield. According to the graph, the y-values vary from y = -infinity to y = infinite, resulting in the range (-infinity, infinity).

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All the areas of the circles are illustrated below.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know, The area of the circle is πr².

1. The area of the circle with a radius of 2.5 cm is,

= π(2.5)² sq cm.

= 19.625 sq cm.

2. The area of the circle with a radius of 11 in is,

= π(11)² sq in.

= 379.94 sq in.

3. The area of the circle with a radius of 3 mm is,

= π(3)² sq mm.

= 28.26 sq mm.

4. The area of the circle with a radius of 5 in is,

=  π(5)² sq in.

= 78.5 sq in.

5.  The area of the circle with a radius of 6.5 cm is,

= π(6.5)² sq cm.

= 132.665 sq cm.

6.   The area of the circle with a radius of 7.2 yd is,

= π(7.2)² sq yd.

= 162.7776 sq yd.

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Answer:

No solution

Step-by-step explanation:

Given the simultaenous equations:

[tex]\displaystyle{\begin{cases} 3.25x - 1.5y = 1.25 \\ 13x-6y=10 \end{cases}}[/tex]

The first equation can be rewritten as:

[tex]\displaystyle{\dfrac{325}{100} x - \dfrac{15}{10}y = \dfrac{125}{100}}[/tex]

Clear the denominators by multiplying both sides with 100:

[tex]\displaystyle{\dfrac{325}{100} x \cdot 100 - \dfrac{15}{10}y \cdot 100= \dfrac{125}{100} \cdot 100}\\\\\displaystyle{325x - 150y = 125}[/tex]

The whole terms are multiple of 25, so we can simplify even lower by dividing both sides by 25:

[tex]\displaystyle{\dfrac{325x}{25} - \dfrac{150y}{25} = \dfrac{125}{25}}\\\\\displaystyle{13x-6y=5}[/tex]

So now, we have:

[tex]\displaystyle{\begin{cases}13x-6y=5\\ 13x-6y=10 \end{cases}}[/tex]

There are various ways to solve simultaenous equations but I'll use the elimination method. Multiply negative in either first or second equation but I'll choose first:

[tex]\displaystyle{\begin{cases}-13x+6y=-5\\ 13x-6y=10 \end{cases}}[/tex]

Add both equations with like terms:

[tex]\displaystyle{0=5}[/tex]

Since this equation is false. Therefore, there is no solution to the simultaenous equation.

Answer:

Step-by-step explanation:

You want to know what to do first with the system of equations ...

You are taught a couple of strategies for solving systems of linear equations algebraically. The "substitution" strategy requires you use one of the equations to write an expression that can be substituted into the other equation. The purpose of this is to reduce the number of variables in the remaining equation. Usually, that means solving for one of the variables to obtain the expression to substitute.

Another strategy you are taught is the "elimination" strategy. It is also called the "addition" or "combination" strategy. It is executed by adding (or subtracting) some multiple of one of the equations from the other equation, or some multiple of it. The purpose of this is to make the coefficient of one of the variables be zero in the combined equation.

The substitution strategy is easiest to execute if you already have one or both equations in "y=" or "x=" form. It is nearly as easy to execute if the coefficient of one of the variables is +1 or -1, or if that can be easily made to be the case. So, this is what you look for to see if the substitution strategy is an appropriate choice.

The elimination strategy is easiest to execute if the coefficients of one of the variables are the same or opposites. If they are the same, that variable can be eliminated by subtracting one equation from the other. If they are opposites, the variable can be eliminated by adding one equation to the other. So, this relation between coefficients is one of the next things you look for when deciding what your strategy will be.

The elimination strategy can also be effectively used if the coefficients of one of the variables are a nice (integer) multiple of one another. In this problem, we notice that the coefficients of y are -1.5 and -6, which are related by a factor of 4. (It is helpful to be very familiar with multiplication facts.) As it happens, the coefficients of x have the same relation: 13 is 4 times 3.25.

The fact that both sets of coefficients are related by the same factor raises a red flag regarding these equations. It means they are either dependent (have infinite solutions) or are inconsistent (have no solution).

The equations are dependent if one equation is a multiple of the other. Here, we can check that by multiplying the first equation by 4:

  4 × (3.25x -1.5y) = 4 × 1.25

  13x -6y = 5

We notice the other equation is ...

  13x -6y = 10

Values of x and y that make 13x-6y=5 cannot also make that same sum be 10. These are called "inconsistent" equations, and they have No Solution.

Hypothetical: If the first equation were 3.25x -1.5y = 2.5, then multiplying it by 4 would give 13x -6y = 10, the same as the second equation. In this case, the equations would be called "dependent," and any of the infinite number of solutions to the first equation would also be a solution to the second equation.

After you look at the equations to determine if any of the coefficients are 1, or have nice relations with the coefficients of the other equation, you can formulate a strategy for elimination or substitution. As we saw above, it can be useful to eliminate any fractions to start with. Sometimes, it is also useful to factor out any common factors. For example, 2x + 6y = 8 can be reduced to x +3y = 4 by factoring out 2 from every term.

Then, the variable that you solve for first will be the one that is left after you have done your substitution or elimination.

As we saw above, the given equations can be rewritten as ...

We already know the same coefficients and different constants mean these equations are inconsistent and have No Solution. If we need further convincing we can subtract one from the other. Here, too, we can plan ahead a little bit: subtracting the first from the second will leave a positive constant:

  (13x -6y) -(13x -6y) = (10) -(5)

  0 = 5 . . . . . . . simplify (false)

There are no values of x and y that will make this false statement true, hence no solution.

a) The probability of scoring a one is 1/7, since a one is not the loaded number six and all other scores are equally likely.

b) The probability of scoring a six is 3/7, since a six is the loaded number and occurs three times as often as any other score.

Let p be the probability of scoring any number except six. Then the probability of scoring a six is 3p, since a six is scored three times more often than any other score. Since there are six equally likely possible scores on a die, we have:

p + 3p + p + p + p + p = 1

Simplifying, we get:

7p = 1

Dividing both sides by 7, we get:

p = 1/7

Therefore, the probability of scoring any number except six is 1/7, and the probability of scoring a six is 3/7. We can now answer the questions:

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The equation that can be used to find the year y in which Arizonia became a state is y = x+ 96.

Two expressions that are set equal to one another in a mathematical statement is the definition of an algebraic equation. A variable, coefficients, and constants are the typical components of an algebraic equation.

Both sides have equal weight, therefore it is balanced. Make sure that every modification made to one side of the equation is reflected on the other side to prevent a mistake from throwing the equation out of balance.

Let us suppose the year Indiana became a state = x.

Given that, Arizonia became a state 96 years later than Indiana.

This can be written algebraically as follows:

y = x + 96

Hence, the equation that can be used to find the year y in which Arizonia became a state is y = x+ 96.

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Answer:

Step-by-step explanation:

To find the average speed for the round trip, we can use the formula:

average speed = total distance / total time

We know that Steve drives 5 miles to school and 5 miles back home, so the total distance is:

total distance = 5 miles + 5 miles = 10 miles

To find the total time, we need to calculate the time it takes for Steve to drive to school and the time it takes for him to return home. We can use the formula:

time = distance / speed

For the first part of the trip, Steve drives 5 miles at 10 mph, so the time it takes is:

time to school = 5 miles / 10 mph = 0.5 hours

For the second part of the trip, Steve drives 5 miles at 40 mph, so the time it takes is:

time to home = 5 miles / 40 mph = 0.125 hours

The total time for the round trip is the sum of the time to school and the time to home:

total time = time to school + time to home

total time = 0.5 hours + 0.125 hours

total time = 0.625 hours

Now we can calculate the average speed using the formula:

average speed = total distance / total time

average speed = 10 miles / 0.625 hours

average speed = 16 miles per hour (rounded to the nearest integer)

Therefore, Steve's average speed for the round trip is 16 mph.

Answer:

16 mph

Step-by-step explanation:

A Congruency Proof is a method of proving two figures are congruent by showing that their corresponding sides and angles are equal.

Congruency Proof is important in Math because it provides a rigorous and systematic way to establish that two geometric figures have the same shape and size.

There are three types of congruency proofs.

a) Congruence of side-angle-side (SAS).

Two congruent sets of sides, and the included angle between them is congruent.

b) SSS congruence occurs when two triangles have three pairs of congruent sides.

c) Angle-side-angle congruence (ASA):

The two triangles have two sets of congruent angles and a congruent included side.

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135 in Mayan notation is represented by one dot over four bars, followed by one dot over three bars, and then one dot over five dots.

To convert 135 to Mayan notation, we repeatedly divide by 20 and use the remainders to determine the number of dots and bars in each position. First, we divide 135 by 20 to get a quotient of 6 with a remainder of 15. The remainder of 15 corresponds to 1 dot over 5 dots and 2 bars (10 + 5).

Next, we divide 6 by 20 to get a quotient of 0 with a remainder of 6. The remainder of 6 corresponds to 1 dot over 3 bars (15). Finally, we have a quotient of 0 with a remainder of 6, which corresponds to 1 dot over 4 bars (20).

Putting these together, we get the Mayan representation of 135 as one dot over four bars, followed by one dot over three bars, and then one dot over five dots.

Complete question:

Convert the following numbers to Mayan notation. Show your calculations used to get your answers. 135?

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The correct responses are:

If you have SSA, the triangle is determined by the third side. It does not form a triangle if it is too short to intersect the other side. A triangle can also be formed if the third side is the ideal length to connect to the other two sides. Last but not least, the third side may be long enough to intersect the opposite side twice, forming two triangles.

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complete question:

When using the law of sines, why can the SSA case result in zero, one, or two triangles?

Vogel's approximation method is used to find an initial feasible solution to a transportation problem.

The method is based on the observation that if there is a row or a column in the transportation tableau having the same minimum positive difference (or penalty) between the costs of two cells, it is likely that one of these cells will get a positive allocation in the optimal solution.

Calculate the penalty for each cell by subtracting the smaller of the two adjacent cells from the larger.

D1 D2 D3 D4 A B C D

5 1 3 3 34 3 6 4

Penalty 0 2 0 1 31 2 2 -1

3 3 5 4 15 3 4 -1

Penalty 0 0 2 1 12 2 2 2

6 4 4 3 12 4 3 2

Penalty 2 1 1 0 6 1 0 1

4 -1 4 2 19 2 3 2

Penalty 5 5 2 0 17 2 0 0

Identify the row and column having the maximum penalty. In this case, the maximum penalty is 5 in row 1 and column 4.

Allocate as much as possible to the cell in the intersection of the row and column with the maximum penalty. The allocation should not exceed the demand or the supply of that row or column.

D1 D2 D3 D4 A B C D

5 1 3 2 34 3 6 4

Penalty 0 2 0 1 31 2 2 -1

3 3 5 3 15 3 4 -1

Penalty 0 0 2 1 12 2 2 2

6 4 4 3 12 4 3 2

Penalty 2 1 1 0 6 1 0 1

4 -1 4 2 19 2 3 2

Penalty 5 5 2 0 17 2 0 0

Repeat the process until all demands are met or all supplies are exhausted.

D1 D2 D3 D4 A B C D

5 1 2 2 34 3 6 3

Penalty 0 2 0 0 32 2 2 -1

3 3 5 3 15 3 3 0

Penalty 0 0 2 0 12 2 1 2

6 4 4 3 12 4 0 1

Penalty 2 1 1 0 6 1 0 0

4 -1 4 2 19 2 3 1

Penalty 5 5 2 0 17 2 0 0

The above table shows an initial feasible solution to the transportation problem using Vogel's approximation method. The total cost of this solution is 34 + 15 + 12 + 19 = 80, which is the same

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Answer:

Part A: length = 4x - 5

Part B: See explanation below

Step-by-step explanation:

Part A

Area of a rectangle = length x width

Given area and width we can find the length as

[tex]length = \dfrac{area}{width}[/tex]

[tex]Area = 12x^2 - 15x\\\\Width = 3x\\\\Length = \dfrac{12x^2 - 15x}{3x}\\\\= \dfrac{12x^2}{3x} - \dfrac{15x}{3x}\\\\= 4x - 5\\\\[/tex]

Answer to Part A

Part B

[tex]length = 4x- 5\; (from part A)}[/tex]

[tex]width = 3x \;(given)}[/tex]

[tex]area = length \times width[/tex]

[tex]=(4x - 5)(3x)\\\\= 4x(3x) - 5(3x)\\\\= 12x^2 - 15x\\\\[/tex]

Hence verified

Answer:

To construct a 90% confidence interval for the mean amount of juice in all such bottles, we first need to find the sample mean and sample standard deviation:

Sample mean, x = (15.2 + 15.5 + 15.9 + 15.5 + 15.0 + 15.7 + 15.0 + 15.7)/8 = 15.4375

Sample standard deviation, s = s = sqrt[((15.2-15.4375)^2 + (15.5-15.4375)^2 + (15.9-15.4375)^2 + (15.5-15.4375)^2 + (15.0-15.4375)^2 + (15.7-15.4375)^2 + (15.0-15.4375)^2 + (15.7-15.4375)^2)/7] = 0.339

Using a t-distribution with degrees of freedom (n-1) = 7 and a 90% confidence level, we can find the t-value as 1.895.

The 90% confidence interval can then be calculated as:

x plus or minus (t-value)*(s/sqrt(n))

= 15.4375 plus or minus (1.895)*(0.339/sqrt(8))

= (15.16, 15.72)

Therefore, the answer is A.

To find a 99% confidence interval for the mean monthly income for all workers at the plant, we use the formula:

x plus or minus (z-value)*(σ/sqrt(n))

where x is the sample mean, σ is the population standard deviation, n is the sample size, and z-value is the critical value from the standard normal distribution for a 99% confidence level, which is 2.576.

Plugging in the given values, we get:

x  plus or minus (z-value)*(σ/sqrt(n))

= 2150  plus or minus (2.576)*(250/sqrt(18))

= (2096, 2204)

Therefore, the answer is A.

The hypothesis tested are given as follows:

[tex]H_0: \mu = 500, H_a: \mu < 500[/tex]

The claim for this problem is given as follows:

"Bags are consistently underweight".

At the null hypothesis, we consider that the claim is false, that is, there is not enough evidence to conclude that the bags are underweight, hence:

[tex]H_0: \mu = 500[/tex]

At the alternative hypothesis, we test if there is enough evidence to conclude if the claim is true, hence:

[tex]H_a: \mu < 500[/tex]

The problem asks for the null and for the alternative hypothesis.

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The 22 half-pieces Kristin had from cutting the sheets she started with and the 7 pieces she found, indicates, that the solution to the word problem is that the number of sheets of paper Kristin started with are;

A word problem is a mathematical question in which the scenario of the question is described using verbal terms, or complete sentences, rather than mathematical symbols or expressions, but which are solved using mathematical calculations.

Let x represent the initial number of paper Kristin had.

The extra number of papers Kristin found = Seven more pieces

The size in which Kristin cut each piece of paper = In half

The number of pieces she had after cutting the papers = 22 half-pieces

Therefore, the following equation can be used to find the number of sheets of paper, x, she started with;

2 × (x + 7) = 22

2 × (x + 7)/2 = 22 ÷ 2 = 11

x + 7 = 11

x = 11 - 7 = 4

The number of sheets of paper Kristin started with, x = 4 sheets of paper

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Step-by-step explanation: A stem and leaf plot is a way to plot data where the data is split into stems (the largest digit) and leaves (the smallest digits). They were widely used before the advent of the personal computer, as they were a fast way to sketch data distributions by hand.

The dependent and independent variables are b and t respectively.

A variable is a mathematical symbol, which do not have any fixed value, it can be a function, which changed according to the property given.

Given that, a committee is organizing a music festival in Jefferson County,

The time which reserved by venue, gives the number of band that will play at there,

We need to determine the dependent and independent variables,

Dependent variable :-

Dependent variable is a kind of variable which depends on the factors given, and do not change by its own.

Independent variables :-

The independent variable in the given study is the cause by which the dependent variable works, it does not manipulate by any other variable given.

Here,

The number of bands depends upon the amount of the time that the venue has been reserved for.

Therefore, the number of band is a dependent variable.

Hence, the dependent and independent variables are b and t respectively.

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The Exact values for the sine and cosine of the given angles are : sin(120°) = √3/2, cos(120°) = -1/2

Given that the terminal ray of an angle with measure of 120 degrees intersects a unit circle at the point (-1/2, √3/2), we can use the definition of sine and cosine to find the exact values of these trigonometric functions for the given angle.

The sine of an angle is defined as the y-coordinate of the point on the unit circle that the terminal ray of that angle intersects. So, for this angle, the sine is:

sin(120°) = √3/2

The cosine of an angle is defined as the x-coordinate of the point on the unit circle that the terminal ray of that angle intersects. So, for this angle, the cosine is:

cos(120°) = -1/2

So, the exact values for the sine and cosine of the angle with measure of 120 degrees are:

sin(120°) = √3/2

cos(120°) = -1/2

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The area of the circle in discuss as required to be determined is; 44/7.

It follows that the radius of a circle is the distance between its center and any point on the circumference.

In this case, center, = (0, 0) and point in circumference= (-1, -1).

Therefore, the radius is;

r = √( (-1 -0)² + (-1-0)² )

r = √2.

Consequently, since area of a circle is given by;

Area = πr²

A = (22/7) × (√2)²

A = 44/7.

Ultimately, the area of the circle is; 44 / 7.

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The probability of a positive test result given that the subject actually lied is 0.962

In simple terms, probability is the measure of the likelihood of an event occurring. In this question, we are asked to find the probability of a positive test result given that the subject lied.

Let's break down the question and use the formula for conditional probability. Conditional probability is the probability of an event occurring, given that another event has already occurred.

P(A|B) = P(A and B) / P(B)

In this case, A represents the event of a positive test result, and B represents the event of the subject lying.

From the question, we know that 2% of the subjects lie, and 90% of those who lie test positive. This means that out of the 98 subjects, 2% or 1.96 subjects lied. And out of those 1.97 subjects, 90% or 1.78 subjects tested positive.

So, the probability of a positive test result given that the subject lied is

=> P(A|B) = 1.78/1.97 = 0.962.

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Complete Question:

If one of the 98 test subjects is randomly selected, find the probability that the subject had a positive test result GIVEN

POSITIVE TEST RESULT      13            40

NEGATIVE TEST RESULT    34            11

that the subject actually lied.

A 0.962

B 0.654

C 0.784

D 0.456

Answer:

Step-by-step explanation:

a

The probability density function for the average length of life of the two components is fU(u) = (1/7)[tex]e^{(-u/7)}[/tex], u ≥ 0

The length of life of each component is governed by an exponential distribution with a mean of 7, which means that the probability density function for the length of life of each component is given by:

fX(x) = (1/7)[tex]e^{(-x/7)}[/tex], x ≥ 0

The average length of life of the two components is given by:

U = (X1 + X2)/2

where X1 and X2 are the lengths of life of the two components.

To find the probability density function for U, we can use the convolution formula:

fU(u) = ∫fX(x)fX(2u-x)dx

where the limits of integration are from 0 to u if u ≤ 7, and from u-7 to 7 if u > 7.

Plugging in the expressions for fX(x) and fX(2u-x), we get:

fU(u) = ∫(1/7)[tex]e^{(-x/7)}[/tex](1/7)[tex]e^{-(2u-x/7)}[/tex]dx

= (1/49)∫[tex]e^{-(2u-2x/7)}[/tex]dx

= (1/49)∫[tex]e^{(-t/7)}[/tex]dt (where t = 2u - 2x)

= (1/49)(-7[tex]e^{(-x/7)}[/tex])|0 to 2u

= (1/7)[tex]e^{(-u/7)}[/tex], u ≥ 0

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The ratio of games won to games played is options A and E, 16/20 or 4/5 in fraction form and 0.8 in decimal form.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

For every 16 games the football team won, they lost four.

Games won = 16

Games lost = 4

Total games played = 16 + 4 = 20

Ratio of games won to total games in fractional form = 16 / 20 = 4/5

Ratio of games won to total games in decimal form = 0.8

The correct options are A and E.

Hence the ratio of games won to total games is 16/20 or 4/5 in fraction form and 0.8 in decimal form.

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Your question is incomplete. The complete question is given below.

Manchester Football team participates in a tournament. For every 16 games the football team won, they lost four. Represent the ratio of games won to games played in fraction form and decimal form.

Select TWO correct answers.

A. 4/5, 0.8

B.  1/2, 0.5

C.  2/4, 0.5

D. 1 /4, 0.25

E.  16/20, 0.8