A group of friends wants to go to the amusement park. They have no more than $280 to spend on parking and admission. Parking is $20, and tickets cost $40 per person, including tax. Write and solve an inequality which can be used to determine

x, the number of people who can go to the amusement park.

Answer:

4. y = -x + 8

9. y = 3/2x + 15

16. y = 1/2x -5

20. y = -3/5x + 16

13. y = -1/2x + 1

14. y =  3/4x - 2

Step-by-step explanation:

4. 5=3(-1)+b = 8

9. 6=-6(3/2)+b=15

16. \(\frac{1--2}{12-6} =\frac{3}{6} = \frac{1}{2}\)

     -2= (1/2)6 + b = -5

20. \(\frac{19-13}{-5-5}= -\frac{6}{10} =-\frac{3}{5}\)

     19 = -3/5(-5) + b = 16

Answer:

I think you need more info

Answer:

Pretty sure the answer is 3 pounds you can pretty much repeatedly take away 8.17 from 80 till you get 55.49

80 - 8.17 = 71.83

71.83 - 8.17 = 63.66

63.66 - 8.17 = 55.49

so 3 Pounds since you took 8.17 three times to get 55.49

Observing the provided right angled triangle and using the trigonometric identities associated with the sides of the right angled triangle. The answers are 9.042 , 18.01 and 61.81 .

A right triangle is a particular kind of triangle with a 90° angle. Trigonometry is based on right triangles and the relationships between their sides and angles.

The study of correlations between triangles' side lengths and angles is known as trigonometry.

for 4) tan(37) = x/12

x= tan(37) * 12 = 9.042

for 6) sin(51) = 14/x

x=14/sin(51) = 18.01

for 8) sin(15) = 16/x

x=16/sin(15) = 61.81

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Answer: 1306.5 m^3

Step-by-step explanation:

1. The formula for the volume of a cylinder is: V=\(\pi\)r^2h

2. If you substitute the values into the equation, you get

V = pi * 5.7^2 * 12.8 = 1306.5

3. 1306.5 is already to the nearest tenth, so that is the answer.

Answer:

Unit price 12.16 for 4.07 pounds is $2.99 per pound

Unit price 14.99 for 5.11 pounds is $2.93 per pound

The best deal is the 14.99 per 4.11 pounds

Step-by-step explanation:

Unit price 12.16/4.07 = 2.99 rounded to the nearest cent

Unit price 14.99/5.11 = 2.93 rounded to the nearest cent.

Answer:

1) $2.99

2)$2.93

The better buy is the 4.07 pound bag

Step-by-step explanation:

To find the unit price you find the cost per pound

$12.16 : 4.07

? : 1

4.07x = 12.16

x = 2.98771499

$2.99

$14.99 : 5.11

? : 1

5.11x = 14.99

x= 2.9334638

Answer:

The formula to find the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder.

Given that the radius of the cylinder is 2 inches and the height is 4 inches, we can substitute these values into the formula to find the volume:

V = πr²h

V = 3.14 x 2² x 4

V = 3.14 x 4 x 4

V = 50.24

Rounding this value to the nearest whole number, the volume of the cylinder is 50 in³.

348.01 rounded to the nearest square centimeter is 348,

To round 348.01 to the nearest square centimeter, we consider the digit immediately after the decimal point, which is 0.01. Since it is less than 0.5, we round down. This means that the tenths place remains as 0. Thus, the number 348.01 becomes 348.

However, it's important to note that square centimeters are typically used to measure area and are represented by whole numbers. The concept of rounding to the nearest square centimeter may not be applicable in this context, as it is more commonly used for rounding measurements of length or distance.

If the intention is to round a measurement to the nearest square centimeter, it would be necessary to provide additional information about the context and the original measurement. Without further context, rounding 348.01 to the nearest square centimeter would simply result in 348.

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Answer:

Step-by-step explanation:

Step one:

Let A be the altitude of the plane

Hence we can define a function that represents this scenario.

the rate at which the plane's altitude decreases is

=33000-17000/8

= 16000/8

=2000

The rate of decrease is 2000 ft per minute.

Thus for anytime "t" the expression for the altitude is

S=33000-2000t-------where t is the time in minute.

say we want to find altitude after 12 minutes

then t=12

substitute  in the expression we have

S=33000-2000(12)

S=33000-24000

S=9000ft

Answer:

Part 1)  Descending Rate = -2,000 ft/min

Part 2)  Starting altitude value is 33,000 ft

Part 3)  The linear equation for the plane's altitude (y) as a function of time (x) is:  

Part 4)  The information not used for the equation is that the plane was travelling for 4 hours to cover 1800 miles before starting the descent

Step-by-step explanation:

Part 1)

The rate at which the airplane descends is given by the difference between final and initial altitude (17,000 ft-33,000 ft) divided the elapsed time (8 minutes):

Part 2)

When graphing the descent (that is the plane's altitude as a function of time), the starting value for the altitude should be 33,000 ft

Part 3)

We can build the equation of the plane's altitude as a function of time in slope y-intercept form y = m x + b

by noticing that the slope "m" stands for the rate of descent that we found in part 1), and then using the information that at time zero (when the plane starts its descent), its altitude is 33000 ft:

with this information about the intercept "b", we can write the final expression for the plane's altitude as a function of time during its descent as:

Part 4)

The information that was not used to write the descent equation was the initial details about how long the plane traveled (4 hours) and for 1800 miles.

Step-by-step explanation:

The money paid to the secretary is $14000 and the money paid to mathematician is $22000.

A mathematical statement that establishes the equality of two mathematical expressions is the called an equation.

Total money available for hiring = $36000

Let the money given to secretary = X

Money given to the mathematician = X + 8000

X + (X + 8000) = 36000

2X = 28000

X = 14000

Money given to secretary is $14000.

Money given to the mathematician is $22000.

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The term "mean" or "average" refers to a statistical measure that describes the central value of a set of data.

It is found by adding all the numbers in a set and dividing the sum by the total number of items in the set. The mean is a valuable tool in interpreting and comparing sets of data. Given below are the solutions to the problems presented:

a. Mean (average) = (24 + 45 + 38 + 56 + 27)/5= 190/5= 38

b. Mean (average) = (24 + 31 + 17 + 39 + 9 + 17)/6= 137/6= 22.83

c. Mean (average) = (125 + 136 + 174 + 116 + 164)/5= 715/5= 143

d. Mean (average) = (3.8 + 9.2 + 6.7 + 11.5)/4= 31.2/4= 7.8e.

Mean (average) = (7.3 + 7.5 + 7.0 + 8.1 + 8.0)/5= 38.9/5= 7.78

Therefore, the mean (average) of the given sets of numbers is:

a. 38 b. 22.83 c. 143 d. 7.8 e. 7.78

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It should be noted that the probability for P(X ≥ 14) rounded to 5 decimal places is approximately 0.17026.

P(X ≥ 14) = P(X = 14) + P(X = 15) + ... + P(X = 22)

Let's calculate P(X ≥ 14):

P(X = 14) = (22 choose 14) * (0.20^14) * (0.80^8)

P(X = 15) = (22 choose 15) * (0.20^15) * (0.80^7)

P(X = 16) = (22 choose 16) * (0.20^16) * (0.80^6)

P(X = 17) = (22 choose 17) * (0.20^17) * (0.80^5)

P(X = 18) = (22 choose 18) * (0.20^18) * (0.80^4)

P(X = 19) = (22 choose 19) * (0.20^19) * (0.80^3)

P(X = 20) = (22 choose 20) * (0.20^20) * (0.80^2)

P(X = 21) = (22 choose 21) * (0.20^21) * (0.80^1)

P(X = 22) = (22 choose 22) * (0.20^22) * (0.80^0)

Calculating each probability and summing them up:

P(X ≥ 14) = P(X = 14) + P(X = 15) + ... + P(X = 22)

= 0.17026

Therefore, P(X ≥ 14) rounded to 5 decimal places is approximately 0.17026.

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Upper

daysThe(a) The time for an individual to recover from an infectious disease, is estimated to be between 4.02 and 5.98 days. (d) The structured SIR model assumes homogeneous mixing, constant population, recovered immunity.

(a) To calculate the time for an individual to recover with a 95% confidence level, we can use the properties of the normal distribution. The 95% confidence interval corresponds to approximately 1.96 standard deviations from the mean in both directions.

Given:

Mean (μ) = 5 days

Standard deviation (σ) = 0.5 days

The confidence interval can be calculated as follows:

Lower limit = Mean - (1.96 * Standard deviation)

Upper limit = Mean + (1.96 * Standard deviation)

Lower limit = 5 - (1.96 * 0.5)

= 5 - 0.98

= 4.02 days

Upper limit = 5 + (1.96 * 0.5)

= 5 + 0.98

= 5.98 days

Therefore, the time for an individual to recover from the infectious disease with a 95% confidence level is between approximately 4.02 and 5.98 days.

(b) To simulate the epidemic using the SIR model, we need additional information about the transmission rate and the duration of infectivity.

(c) Without the transmission rate and duration of infectivity, we cannot determine the fraction of the total population that will have come down with the infectious disease once the epidemic is over.

(d) The structured model in this case is the SIR (Susceptible-Infectious-Recovered) model, which is commonly used to study the dynamics of infectious diseases. The major assumptions associated with the SIR model include:

Homogeneous mixing: The model assumes that individuals in the population mix randomly, and each individual has an equal probability of coming into contact with any other individual.

Constant population: The model assumes a constant population size, without accounting for birth, death, or migration rates.

Recovered individuals develop immunity: The model assumes that individuals who recover from the infectious disease gain permanent immunity and cannot be reinfected.

No vaccination or intervention: The basic SIR model does not incorporate vaccination or other intervention measures.

These assumptions simplify the model and allow for mathematical analysis of disease spread dynamics. However, they may not fully capture the complexities of real-world scenarios, and more sophisticated models can be developed to address specific contexts and factors.

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Answer:

Step-by-step explanation:

Caution! Don't Use "AAA"

AAA means we are given all three angles of a triangle, but no sides.

Answer:

There is no congruency theorem

Step-by-step explanation:

We don't know that the triangles are congruent.  We know that the angles are the same that makes the triangles similar.  We need at least one side being equal to make the triangles congruent

Answer:

P(-5) = 109

Step-by-step explanation:

     If the polynomial p(x) is divided by the linear polynomial (x-a), the remainder is p(a).

   Dividend = divisor * quotient + remainder.

   p(x) = (x-a) * q(x) + p(a)

Here, q(x) is the quotient and p(a) is the remainder.

      P(x) = 4x² - x + 4

     P(-5) = 4*(-5)² - 1*(-5) + 4

              = 4*25 + 5 + 4

              = 100 + 5 + 4

              = 109

Answer:

The candidate won 266  votes

A sampling distribution is the probability distribution of a statistic for all random samples of n observations from a population. The term "sampling distribution" refers to the probability distribution of a statistic, such as the mean or standard deviation, that arises from random sampling of a fixed-sized sample from a population.

It is essential to understand this concept because it allows us to make inferences about the population parameter using information from the sample statistic. The standard deviation of the sampling distribution is known as the standard error of the statistic, and it measures how much the statistic varies across all possible samples of the same size from the population. In short, the sampling distribution is a theoretical distribution that helps us to understand the properties of the statistic and make inferences about the population parameter based on sample data.

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Answer

Step-by-step explanation:

B - 8-7-6-5-4-3-2-1-0 234 567 8 8

- 8-7-6-5-4-3-2-1-0 234 567 8 8 is the number line that represents the solutions to -2]x1 = -6. Therefore, the correct option is option B.

A number line is a pictorial portrayal of numbers on a straight line. It serves as a guide for comparing and arranging numbers. It can be used to depict any real number, including natural and whole numbers. Comparing numbers becomes simpler when they are written on a number line.

As can be seen from the preceding illustration, the integers on the left are smaller than those on the right. For instance, 0 is under 1, - 1 is under 0, - 2 is not exactly - 1, etc.  - 8-7-6-5-4-3-2-1-0 234 567 8 8 is the number line that represents the solutions to -2]x1 = -6.

Therefore, the correct option is option B.

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The midpoint of AB has coordinates (9, -1.5), the gradient of line L is -3 and the point (100, -302) doesn't lie on L.

What is a coordinate?

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space (3D). Mathematicians, physicists, and engineers employ a variety of coordinate schemes.

(a) Given point A (5, -4) and point B (13, 1)

Therefore, midpoint of AB is \((\frac{x1+x2}{2},\frac{y1+y2}{2})\)

                                          \(or,(\frac{5+13}{2},\frac{-4+1}{2})\)

                                          \(or, (\frac{18}{2},\frac{-3}{2} )\)

                                          \(or,(9, -1.5)\)

(b) In the equation \(y=2-3x\), -3 is the gradient of line L.  

(c) The point with coordinates (100, -302) doesn't lie on L as it doesn't satisfy the equation \(y=2-3x\)

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Answer:

-3

Step-by-step explanation:

-8(1-4x)=-104

1-4x=-104/-8

1-4x=13

4x=1-13

4x=-12

x=-12/4

x=-3

Answer:B 66.72

Step-by-step explanation:

complementary means if two angles are added up they will equal 90. we and eliminate d cause 23.28+23.28=46.56 so d is wrong now let's try c 46.56+23.28=69.84 so c is wrong cause it doesn't equal 90 now let's try a 156.72+23.28=180 its wrong since we are using complementary angles instead of supplementary angles Supplementary are angle two angles that add up to 180. so that just leaves b cause 23.28+66.72=90. i hope this helps and i made sure to explain it as best as i can have a great day

The solution is Option B.

The measure of the complementary angles are 66.72° and 23.28°

When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.

Let the first angle and second angle be a and b respectively such that

a + b = 90°

Given data ,

Let the first angle be represented as A

Now , the value of A is = 23.28°

Let the second angle be represented as B

Now , the value of B is = B

The angles A and B are complementary ,

So , A + B = 90°   be equation (1)

Substituting the values in the equation , we get

23.28° + B = 90°

On simplifying the equation , we get

Subtracting 23.28° on both sides of the equation , we get

B = 90° - 23.28°

B = 66.72°

Therefore , the value of B is 66.72°

Hence , the measure of the angle is 66.72°

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Thus, to determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can use a statistical analysis of the daily rate of return for each stock over a 50-day period. However, the small sample size means that we must be cautious when interpreting the results.

To determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can conduct a statistical analysis using the sample data collected. The sample size of 50 days is relatively small, so we must be cautious when interpreting the results.

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The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.

We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.

Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).

The left/right opening of the hyperbola indicates that the primary axis is horizontal.

The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.

The primary axis' 195 m length and the diameter at its highest point are matched.

The hyperbola's highest point is 80 metres above the centre.

These characteristics allow us to write the hyperbola's equation in standard form:

(x - h)²/a² - (y - k)²/b² = 1

Where (h, k) represents the center of the hyperbola.

Substituting the given values:

Center: (h, k) = (0, 0)

Minor axis: 2a = 180 m, so a = 90 m

Major axis: 2b = 195 m, so b = 97.5 m

Vertical shift: c = 80 m

Now we can write the equation of the hyperbola:

x²/90² - y²/97.5² = 1

Simplifying, we have:

x²/8100 - y²/9506.25 = 1

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The statement that best describes the composition of most foods is: "They contain mixtures of the three energy nutrients, although only one or two may predominate."

Most foods contain mixtures of the three energy nutrients, namely carbohydrates, proteins, and fats. However, the relative proportions of these nutrients can vary significantly from one food to another. In some foods, one or two of these nutrients may predominate, while others may contain relatively equal amounts of all three.

Carbohydrates are a primary source of energy for the body and can be found in various forms such as sugars, starches, and fibers. Foods like grains (e.g., rice, wheat, oats), fruits, vegetables, and legumes tend to be rich in carbohydrates. However, the specific types and amounts of carbohydrates can vary widely.

Proteins are crucial for building and repairing tissues, as well as for various metabolic functions. Foods like meat, poultry, fish, eggs, dairy products, legumes, nuts, and seeds are excellent sources of protein. Again, the protein content in different foods can vary.

Fats, also known as lipids, are an important energy source and provide essential fatty acids. Foods such as oils, butter, avocados, nuts, and fatty meats are high in fats. Like carbohydrates and proteins, the fat content in foods can differ significantly.

It's worth noting that some foods may predominantly consist of one specific nutrient. For example, pure sugar is almost entirely composed of carbohydrates, while pure oil is almost entirely composed of fats. However, most whole foods, such as fruits, vegetables, grains, meats, and dairy products, contain a mixture of these energy nutrients.

Furthermore, a balanced diet typically includes a combination of these nutrients in appropriate proportions. A varied diet that incorporates a range of foods from different food groups helps ensure an adequate intake of carbohydrates, proteins, and fats, along with other essential nutrients required for optimal health.

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The least common multiple of the given two integers is 24804834 if the product of two integers is 27 x 38 × 52 × 711 and their greatest common divisor is 23 x 34 x 5.

We can use the formula

LCM(a, b) = (a * b) / GCD(a, b)

where LCM(a, b) is the least common multiple of a and b, and GCD(a, b) is their greatest common divisor.

We are given that the product of the two integers is

27 x 38 x 52 x 711

We can factor this into its prime factors

27 x 38 x 52 x 711 = 3^3 x 2 x 19 x 2^2 x 13 x 3 x 59 x 79

The greatest common divisor of the two integers is

23 x 34 x 5 = 2^2 x 5 x 23 x 17

We can now use the formula to find the least common multiple

LCM = (27 x 38 x 52 x 711) / (23 x 34 x 5)

LCM = (3^3 x 2 x 19 x 2^2 x 13 x 3 x 59 x 79) / (2^2 x 5 x 23 x 17)

Simplifying, we can cancel out the common factors of 2, 5, 23, and 3

LCM = 3^2 x 2 x 19 x 13 x 59 x 79 x 17

LCM = 24804834

Therefore, the least common multiple of the two integers is 24804834.

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Answer:

Red, Yellow, Blue

Step-by-step explanation:

They are the primary colors,

or you can use Violet, Green, And Orange

These are secondary colors

Answer:

12 + 4√6

Step-by-step explanation:

xy = 48, x + y = 24

\(x + \frac{48}{x} = 24\)

\( {x}^{2} + 48 = 24x\)

\( {x}^{2} - 24x + 48 = 0\)

\( {x}^{2} - 24x + 144 = 96\)

\( {(x - 12)}^{2} = 96\)

x - 12 = + 4√6

x = 12 + 4√6, y = 12 - 4√6

When every length in the cylinder is decreased by 60%, the volume of the cylinder decreases by approximately 85.6%.

Let's assume the original diameter and height of the cylinder are both represented by "d". The original volume of the cylinder can be calculated as V = π * (d/2)^2 * d.

When every length in the cylinder is decreased by 60%, the new diameter and height become 0.4d (40% of the original value). The new volume of the cylinder can be calculated as V' = π * (0.4d/2)^2 * (0.4d).

To find the percent decrease in volume, we can calculate (V - V') / V * 100.

Substituting the values, we have:

Percent decrease in volume = [(V - V') / V] * 100

Percent decrease in volume = [(π * (d/2)^2 * d - π * (0.4d/2)^2 * (0.4d)) / (π * (d/2)^2 * d)] * 100

Simplifying further, we get:

Percent decrease in volume = [(1 - 0.4^3) / 1] * 100

Evaluating the expression, we find:

Percent decrease in volume ≈ 85.6%

Therefore, the volume of the cylinder decreases by approximately 85.6% when every length is decreased by 60%.

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                                                Question 1)

Answer:

The slope between  (-5, -20) and (9, 9) is:

\(m=\frac{29}{14}\)

Step-by-step Explanation

Given the points

Finding the slope between (-5, -20) and (9, 9)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(-5,\:-20\right),\:\left(x_2,\:y_2\right)=\left(9,\:9\right)\)

\(m=\frac{9-\left(-20\right)}{9-\left(-5\right)}\)

Refine

\(m=\frac{29}{14}\)

Therefore, the slope between  (-5, -20) and (9, 9) is:

\(m=\frac{29}{14}\)

                                        Question 2

Answer:

the slope between (18, -5) and (18, 20) is undefined.

Step-by-step Explanation

Given the points

As the x-values of the points are the same. It indicates that the given line is vertical.

Finding the slope between (18, -5) and (18, 20)

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [20 - (-5)] / [18 - 18]

               = [20+5] / [0]  

               = 25/0

               = ∞ or undefined

Thus, the slope between (18, -5) and (18, 20) is undefined. It indicates that the line is vertical.

Hence, the slope between (18, -5) and (18, 20) is undefined.

Answer:

C) 2

fοf(2) =2

Step-by-step explanation:

Explanation

Given f(x) = 3 x-4 and g(x) = -x²

given f(x) = 3 x-4

fοf (2) = f(f(2))

         = f(3 (2)-4)) ( ∵ put x=2 in f(x))

        = f(2)

       = 3(2) -4

      =  6-4

      =2

∴  fοf (2) =2