please help!!

very detailed explanation and answer please!

Answer: one senior ticket is $8 and one student ticket is $14

Hope this helps a little

These intervals were calculated assuming that the differential equation coefficients and initial value are continuous on the intervals. Additional analysis may be required in practice to confirm the precise duration of existence and uniqueness.

The existence and uniqueness theorem for first order linear differential equations states that if the differential equation's coefficients and the initial value are continuous on an interval containing the initial value, then the differential equation has a unique solution on that interval.

It should be noted that these intervals were determined under the assumption that the differential equation coefficients and initial value are continuous on the intervals. In practice, additional analysis may be required to confirm the precise duration of existence and uniqueness.

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The area swept by the blade in model 3 is 66932 square feet.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space. A shape's length and width are used to calculate its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc. But a shape's area is a two-dimensional measurement.

The blade length for model 3 is r = 146.

The area of the circle is given by:

A = pi(r)²

A= (3.14) (146)²

A = 66932

Hence, the area swept by the blade in model 3 is 66932 square feet.

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The weight range is 10 ≤ x < 30.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

For health reasons her doctor advises that she gain weight before her next appointment in 3 months.

She should gain at least 10 pounds but  less than 30 pounds.

let her weight is x pounds then the range for her weight to be healthy.

10 ≤ x < 30.

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The proportion of stocks with returns of less than 10% is 43%.

To find the proportion of stocks with returns of less than 10%, we add up the frequencies of the first two classes in the frequency distribution: 8 + 25 = 33. This number represents the total number of stocks with returns of less than 10%. To find the proportion, we divide this number by the total number of stocks (50) and multiply by 100%: (33/50) * 100% = 66%. This means that 66% of the stocks had returns less than 10%.

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The reason why response scales are generally limited to less than ten options is that anything over this number creates meaningless distinctions.

Response scales are generally limited to no more than ten options because any more than this creates meaningless distinctions. If there are too many options, it becomes difficult to make meaningful comparisons between the responses. Additionally, it becomes more difficult to interpret the data when there are too many options. By having fewer options, it is easier to make more accurate comparisons and more meaningful interpretations. This number helps to make sure that the data collected is accurate and useful. Having fewer options also helps to reduce the amount of time it takes to collect and analyze the data.

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1. a. Probability (X ≤ 7000) = 0.40; b. P(X > 5000) = 0.95; c. P(5000 < X ≤ 7000) = 0.40.

2. a. P(0 < X) = 1; b. P(-0.5 ≤ X ≤ 0.5) = 1; c. P(X < -2) = 0; d. x = -1.645.

3. a. x = 9; b. x = 12; c. x = 7; d. x = 6.

1. a. The probability that the life of a semiconductor laser is less than or equal to 7000 hours can be calculated by subtracting the probability that it is less than or equal to 5000 hours from 1: P(X ≤ 7000) = 1 - 0.05 = 0.40. b. The probability that the life is greater than 5000 hours can be calculated by subtracting the probability that it is less than or equal to 5000 hours from 1: P(X > 5000) = 1 - 0.05 = 0.95. c. The probability that the life is between 5000 and 7000 hours can be calculated by subtracting the probability that it is less than or equal to 5000 hours from the probability that it is less than or equal to 7000 hours: P(5000 < X ≤ 7000) = 0.40 - 0.05 = 0.35.

2. a. The probability that X is greater than 0 can be calculated by subtracting the probability that X is less than or equal to 0 from 1: P(0 < X) = 1 - 0 = 1. b. The probability that X is between -0.5 and 0.5 can be calculated by subtracting the probability that it is less than or equal to -0.5 from the probability that it is less than or equal to 0.5: P(-0.5 ≤ X ≤ 0.5) = 1 - 0 = 1. c. The probability that X is less than -2 can be calculated by simply looking at the upper limit of the function: P(X < -2) = 0. d. The value x such that P(x < X) = 0.05 can be found by solving the equation: x = -1.645.

3. a. The value x such that P(X > x) = 0.5 can be found by solving the equation: x = 9. b. The value x such that P(X > x) = 0.95 can be found by solving the equation: x = 12. c. The value x such that P(3 < X < x) = 0.2 can be found by solving the equation: x = 7. d. The value x such that P(3 < X < x) = 0.8 can be found by solving the equation: x = 6.

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The total cost for the electric bill is given by the equation A = $ 241

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost for the electric bill be A

Now , the equation will be

The amount of electricity used by Ettienne = 1,895 kWh

And , the standard plan is

8.5 cents/kWh for the first 400 kWh

12 cents/kWh for the next 400 kWh

14.5 cents/kWh for anything over 800 kWh

So , for the first 400 kWh , the cost is = 400 x 8.5 = 3,400 cents

And , for the next 400kWh , the cost is = 400 x 12 = 4,800 cents

And , the remaining units of electricity is = 1,895 - 800 = 1,095 kWh

So , for the next 1,095kWh, the cost is = 1,095 x 14.5 = 15,877.5 cents

Therefore , the total cost for 1,895kWh = 3,400 cents + 4,800 cents + 15,877.5 cents

On simplifying the equation , we get

The total cost for 1,895kWh A = 24,077.5 cents

The total cost for 1,895kWh A = $ 240.77

The total cost for 1,895kWh A = $ 241

Hence , the equation is A = $ 241

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The area of the composite figure is 40.65 cm².

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The composite figure can be made into two shapes.

a) Rectangle with a length of 4 cm and breadth = 3 cm

b) Two semicircles with diameters of 3 cm and 4 cm.

So,

r = 3/2 cm and r = 4 cm

Now,

Area of the rectangle.

= length x breadth

= 4 x 3

= 12 cm²

Area of the one semicircle with r = 3/2 cm

= 1/2 x πr²

= 1/2 x 3.14 x (3/2)²

= 1/2 x 3.14 x 9/4

= 3.53 cm²

Area of the one semicircle with r = 4 cm

= 1/2 x πr²

= 1/2 x 3.14 x 4²

= 1/2 x 3.14 x 16

= 25.12 cm²

Now,

Area of the composite figure.

= 12 + 3.53 + 25.12

= 40.65 cm²

Thus,

The area of the composite figure is 40.65 cm².

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The greater solution of x is x = -12 + 2√3 ÷ 3, and the lesser solution is x = -12 ± 2√3 ÷ 3.

Apart from integration, differentiation is one of the two key ideas in calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a process called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation.

The given function [tex]f(x) = \frac{x}{x + 4}[/tex].

The differentiation of the function is:

[tex]f'(x) = \frac{g(x)f'(x) - f(x)g'(x)}{g(x)^2} \\\\f'(x) = \frac{(x+4)(1) - x(1)}{(x+1)^2}\\\\f'(x) = \frac{x + 4 - x}{(x+4)^2} \\\\f'(x) = \frac{4}{(x+4)^2}[/tex]

The value of f'(x) = 3:

Thus,

3 = 4/ (x + 4)^2

3(x + 4)^2 = 4

3(x² + 8x + 16) = 4

3x² + 24x + 48 - 4 = 0

3x² + 24x + 44= 0

Use the quadratic formula to find the roots of the equation:

x = -12 ± 2√3 ÷ 3

Hence, the greater solution of x is x = -12 + 2√3 ÷ 3, and the lesser solution is x = -12 ± 2√3 ÷ 3.

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Combination X will still have an opportunity cost, society might judge other combinations on the line as preferable to combination X, and it may be allocatively efficient, but it may not be productively efficient.

The Production Possibilities Curve (PPC) is a model used to illustrate the tradeoff between producing two goods. Combination X is a point on the PPC, and is not the same as other combinations on the same line.

A) This statement is not correct. Combination X will still have an opportunity cost associated with it. Opportunity cost is the cost of choosing one option over another, and it is the difference in the total outputs between the chosen combination and the next best combination. For example, if combination X produces 8 units of good A and 10 units of good B, and the next best combination produces 10 units of good A and 8 units of good B, the opportunity cost of combination X is 2 units of good B.

B) This statement is correct. Society might judge other combinations on the line as preferable to combination X because of their comparative advantage in producing one good over another.

C) This statement is correct. Allocative efficiency is the optimal combination of goods and services that maximizes the total benefit of society. Combination X may be allocatively efficient if it maximizes the total benefit of society.

D) This statement is not correct. Productive efficiency is the optimal combination of inputs that maximizes the

output of a good or service. Combination X may not be productively efficient if it does not maximize the output of a good or service.

Combination X will still have an opportunity cost, society might judge other combinations on the line as preferable to combination X, and it may be allocatively efficient, but it may not be productively efficient.

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This expression [tex]t(x) = 4 * \pi * (x/2)^2[/tex]  gives the total area of the four circles as a function of x, the side of the square.

The area of a single circle with radius r can be calculated using the formula:

[tex]A = \pi r^2[/tex]

In this problem, the radius of each circle is the same and equal to r. Therefore, the area of a single circle can be calculated as:

[tex]A = \pi r^2[/tex]

The total area of the four circles, t, can be found by adding the area of each circle:

[tex]t = 4 * \pi r^2[/tex]

The radius of each circle can be expressed as a function of the side of the square, x, as follows:

[tex]r = x/2[/tex]

Substituting this expression for r into the equation for the total area of the four circles, we get:

[tex]t(x) = 4 * \pi * (x/2)^2[/tex]

This expression gives the total area of the four circles as a function of x, the side of the square.

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The simplified form of the expression 3/4 (z+2/5) + 2z is (37z + 6)/20.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

An expression,

3/4 (z+2/5) + 2z.

Simplifying,

= 3/4 (5z + 2)/5 + 2z.

= (15z + 6)/20 + 2z

= (37z + 6)/20

Therefore, the expression is  (37z + 6)/20.

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Open-ended questions are often used in market research, customer satisfaction surveys, and other social sciences research to gather in-depth information from respondents.

Open-ended questions are a type of qualitative research method that seeks to gather unrestricted comments or opinions from respondents. These questions are usually framed in a way that allows the respondent to express their thoughts and feelings without being limited by pre-determined response options. This method can provide valuable insights into the perspectives, experiences, and motivations of the individuals being studied. Open-ended questions are often used in market research, customer satisfaction surveys, and other social sciences research to gather in-depth information from respondents.

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The spring constant for the stretched spring is 62.86 N/m.

The formula to be used for calculation of spring constant is -

W = 1/2kx², where W is work done, k is spring constant and x refers to stretched distance. For the mentioned question, x will be -

x = (final x² - initial x²)

Keep the values in formula to find the value of k

1100 × 2 = k (6² - 1²)

Performing multiplication on Left Hand Side and taking square on Right Hand Side of the equation

2200 = k (36 - 1)

k = 2200/35

Performing division on Right Hand Side of the equation

k = 62.86 N/m

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The correct statement is: "E and F are independent if after selecting the first ball we do not place it back in the urn (without replacement)."

An event is independent if the occurrence of one event does not affect the probability of the other event.

In this case:

E and F are not always independent, because the occurrence of E (the first ball is blue) does affect the probability of F (the second ball is blue).

E and F are independent if after selecting the first ball we do not place it back in the urn (without replacement). In this case, the probability of F remains constant, regardless of the occurrence of E.

E and F are not independent if after selecting the first ball we place it back in the urn (with replacement). In this case, the occurrence of E affects the number of blue balls in the urn, and hence affects the probability of F.

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The number of ways you can draw n chords in a circle combination with 2 x n points such that no 2 chords intersect is n! / (2! * (n - 2)!).

Given a number n, the number of ways you can draw n chords in a circle with 2 * n points such that no two chords intersect is given by n choose 2. This is because you have 2 * n points, and for each chord, you must choose two of these points to be its endpoints.

The number of ways to choose two points out of 2 * n points is given by the binomial coefficient (n choose 2), which is equal to n! / (2! * (n - 2)!). This formula counts the number of combinations of n chords that can be drawn in a circle without any intersections.

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The minimum value of the function f(x) = 2x^2 + 8.1x + 15.4 is 15.96 to the nearest hundredth.

Minimum value is the lowest y-value the function reaches.

The minimum value of a parabolic function like f(x) = 2x^2 + 8.1x + 15.4 is achieved at the vertex of the parabola.

The x-coordinate of the vertex is given by the formula:

x = -b / (2a

where a = 2, b = 8.1, and c = 15.4.

Plugging in these values, we get:

x = -8.1 / (2 * 2) = -2.05

So, the x-coordinate of the vertex is -2.05. To find the y-coordinate (i.e., the minimum value of the function), we plug in this x-coordinate and solve for y:

y = f(-2.05) = 2(-2.05)^2 + 8.1(-2.05) + 15.4 = 15.96

So, the minimum value of the function f(x) = 2x^2 + 8.1x + 15.4 is 15.96 to the nearest hundredth.

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The 12-inch pieces the dressmaker can cut from 10 of these rolls of ribbon will be 30 strips.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given a dressmaker has a ribbon of 3 feet in length,

and he has a total of 10 rolls,

total length of ribbon = 10*3 = 30 feet

and 1 feet = 12 inches

30 feet = 12*30 inches

30 feet = 360 inches

the dressmaker has 360 inches of ribbon.

The dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 3 feet in length.

The number of rolls she has =  10 rolls

so,

12 inches strips from 360 inches of ribbon

= 360/12 = 30 strips.

Hence the dressmaker can make 30 strips of 12 inches from 360 inches of total ribbon.

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10 < n < 12 gives the equivalent solution to the given system of equation.

Inequality expressions are expressions not separated by an equal sign.

From the given expression, the equivalent inequalities are given as:

n > 0

2n > 20

5n > 60

For the expression 2n > 20

n > 20/2

n > 10

Similarly;

5n < 60

n < 60/5

n < 12

Hence the solution to the given expressions are 10 < n < 12

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The ordered pairs in table T. (3, 4) and (3, - 4) are the same, indicating that it is not a function.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is a function if it is one-to-one and many-to-one.

And, A relation is not a function if it is one to many meaning no two distinct ordered pairs have the same first coordinate.

Observing the given tables we conclude that in table T the ordered pairs

(3, 4) and (3, - 4) have the same first coordinate so it is not a function.

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171 is 1.8 standard deviations below the mean.

Using the 68-95-99.7 rule, approximately 5.5% of the population scored 171 or lower. This translates to 66 people.

1. Calculate the z-score: z = (171 - 225) / 18 = -1.8

2. Use the 68-95-99.7 rule to calculate the percentage of the population that scored 171 or lower: 5.5%

3. Calculate the number of people that scored 171 or lower: 66 (5.5% of 1200) mean

The complete question is :

What is the population of people who scored 171 out of a population of 1200 with a mean of 225 and a standard deviation of 18?

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No, I don't agree with Sundeep. The mixture wont simply add up

When two liquids are mixed together, their volumes don't simply add up to equal the total volume of the mixture.

When sugar is mixed with water, the total volume of the mixture is usually slightly greater than the volume of the water alone, because the sugar particles take up space between the water molecules.

The volume of the mixture will be equal to the sum of the individual volumes only if the two liquids are completely immiscible, meaning they don't mix together at all. In this case, the total volume of the mixture will be equal to the sum of the volumes of water and sugar, which is 400 mL.

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The value of the stock at 10 percent is given as 88 dollars

The value of a stock can be estimated using the Gordon Growth Model, which takes into account the company's future growth rate, recent dividends, and the required return of the investor. The formula for the Gordon Growth Model is:

Stock Price = Dividend / (Required Return - Growth Rate)

Plugging in the given values, we have:

Stock Price = 1.76 / (0.10 - 0.08)

Stock Price = 1.76 / 0.02

Stock Price = 88

Therefore, the estimated value of the Safeco stock is $88 when the required return is 10%. This estimate assumes that the company's future growth rate and dividends will remain constant at 8% and 1.76, respectively.

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In a case whereby three friends got the prize money worth 120000 The first friend would get three times the amount of the third friends portion. the third friend would get twice the amount of the second friends  the amount that each friend would receive are:$10909, $21818 and $87272 respectively.

The concept that willbe used here is simplification.

Let assume that the amount that is gotten by the second friend be $X,

then the amount that is gotten by the third friend be $2X

then the amount that is gotten by the third friend be $8X

Then perform the summation as $X+$2X+ $8X=120000

11X= 120000

X=120000/11 = 10909

X=$10909

$2X= 2*10909=$21818

$8X=8*10909=$87272

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now, we're making the assumption that the monthly payments Ricky is doing are at the beginning of every month.

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 400\\ r=rate\to 1\%\to \frac{1}{100}\dotfill &0.01\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &28 \end{cases}[/tex]

[tex]A=400\left[ \cfrac{\left( 1+\frac{0.01}{12} \right)^{12 \cdot 28}-1}{\frac{0.01}{12}} \right]\left(1+\frac{0.01}{12}\right) \\\\\\ A=400\left[ \cfrac{\left( \frac{1201}{1200} \right)^{336}-1}{\frac{1}{1200}} \right]\left(\frac{1201}{1200}\right) \implies \boxed{A \approx 155157.45}[/tex]

We will use six square tables and eight round tables.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's call the number of square tables used "x". Then, the number of round tables used would be x + 2.

We know that the total number of people that can be seated is represented by 8 × number of round tables + 10 × number of square tables, or 8(x + 2) + 10x = 124.

Expanding and solving for x, we get 18x + 16 = 124.

Subtracting 16 from both sides, we get 18x = 108.

Dividing both sides by 18, we find that x = 6.

So, we will use 6 square tables and 8 round tables.

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The circumference of the larger circle is 94.3 inches.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

Let's call the radius of the larger circle "R" and the radius of the smaller circle "r".

Since the circumference of the smaller circle is 20% of the circumference of the larger circle, we have:

2πr = 0.2 × 2πR

Dividing both sides by 2π:

r = 0.2 × R

Since the diameter of the smaller circle is 6 inches, we have:

2r = 6

So:

r = 3

And, since r = 0.2 R:

3 = 0.2 × R

Solving for R:

R = 15

So the circumference of the larger circle is:

C = 2πR = 2π × 15 = 94.25

Rounding to the nearest tenth, the circumference of the larger circle is 94.3 inches.

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