a water park sold 1679 tickets for total of 44,620 on a wa summer day..each adult tocket is $35 and each child ticket is $20. how many of each type of tixkwt were sold?

The midline equation of the function is y = 1.5.

The gap between a trigonometric function's highest and least values is known as its amplitude. The difference between the greatest and minimum numbers is, in other words, divided by two. For instance, the amplitude is A in the equation y = A sin(Bx) + C. The amplitude, also known as the average value of the function across a period, denotes the "height" of the function above and below the midline. It gauges the magnitude or intensity of the oscillation of the function's representation of. The oscillation is more prominent and subtler depending on the amplitude, which ranges from higher to lower values.

Given that, the function has minimum point at (1, 1.5) and an amplitude of 1.5.

Using the definition of the amplitude the midline is the given amplitude.

Hence, the midline equation of the function is y = 1.5.

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Answer:

3

Step-by-step explanation:

Khan Academy

When rounded to two decimal places, the radius of the can is approximately 1.6 inches.

Surface fοrmed by a straight line mοving parallel tο a fixed straight line and intersecting a fixed planar clοsed curve. a sοlid οr surface defined by a cylinder and twο parallel planes that cut all οf its elements. See Vοlume Fοrmulas Table, particularly fοr the right circular cylinder.

The volume of a cylinder can be calculated using the following formula:

V = πr²h

where

V denotes volume,

r denotes radius, and

h denotes height.

The cylindrical aluminium can has a height of 7 inches and a volume of 56 cubic inches. We can calculate the radius using the volume of a cylinder formula:

V = πr²h

56 = πr²(7)

56 = (22/7)r²(7)

56 = 22r²

56/22 = r²

2.54 = r²

r = [tex]\sqrt{2.54}[/tex]

r ≈ 1.6

As a result, when rounded to two decimal places, the radius of the can is approximately 1.6 inches.

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The correct option is -C: No, 6 is the geometric mean of 4 and 9, however if the altitude is 6, then the hypotenuse is the geometric mean of the two segments.

An average technique multiplies several values and determines the number's root is known as the geometric mean. You locate the nth root for their product for a collection of n numbers. This descriptive statistic can be used to sum up your data.

Mean Geometric The square root of the product of two numbers is the geometric mean amongst them. The geometric mean of two positive numbers an as well as b is the positive number x as in percentage Cross multiplication results in x² = ab,.

For the given question.

geometric mean of a and b :

From the drawn diagram.

a = 4

b = 9

x = √ab

x = √9*4

x = 6

geometric mean: 6

Applying the altitude rule:

h² = x.y

6² = 9*4

36 = 36

Thus, the geometric mean calculated by friend is correct but the marking on the diagram is wrong.

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The horizontal line at $7.25 on the y-axis of the graph is the one with a slope that most accurately depicts the federal minimum wage of $7.25 per hour as of January 1, 2014.

Although it varies from state to state, the federally mandated minimum wage in the United States is $7.25 per hour. The District of Columbia had the highest minimum wage in the US as of January 1, 2023, at 16.50 dollars per hour.

The variable dearness allowance (VDA) component, which takes into account inflationary trends, such as an increase or fall in the Consumer Price Index (CPI), and, if applicable, the housing rent, are included in the computation of the monthly minimum salary.

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Answer: D. As x → -∞, y → -∞.

Step-by-step explanation:

The graph shows the function approaching negative infinity on the x-axis (left side).  When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.

Answer:

15.8823% error

Step-by-step explanation:

Percent Error Formula

abs([tex]\frac{(a-x)}{x}[/tex]) * 100%

abs:  absolute value

a:  actual value

x:  expected value

Percent Error = abs([tex]\frac{14.3 - 17}{17}[/tex]) * 100%

                       = abs(-0.158823) * 100%

                       15.8823% error

Answer:

A≈1.83m²

Step-by-step explanation:

Using the formulas

A=πr2C=2πr

Solving forAA=C24π=4.824·π≈1.83346m²

Answer:

1.83 (approximate)

Step-by-step explanation:

First, we need to find the radius of the circle.

Using the formula:

[tex]C=2 \pi r[/tex]

We have to reorganize terms:

[tex]r=\frac{C}{2\pi}[/tex]

[tex]\frac{4.8}{2 \times \pi}[/tex]

r ≈ 0.76

Now we have the radius and the circumference in order to find the area.

Use the formulas:

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

[tex]C=2 \pi r[/tex]

A = C^2/4[tex]\pi[/tex]  = 4.8^2 / 4 * pi = 1.83

Answer:

g(x)

=6x−4

=3x

2

−2x−10

Escribe (g∘f)(x) como una expresión en términos de x.

Step-by-step explanation:

Primero necesitamos conocer la función f(x). Luego podemos sustituir f(x) en g(x) para obtener (g∘f)(x).

Como la función f(x) no se proporcionó en la pregunta, asumiré que f(x) es:

f(x) = x^2 - 2x + 1

Entonces, podemos sustituir f(x) en g(x) de la siguiente manera:

g(f(x)) = 6f(x) - 4

= 6(x^2 - 2x + 1) - 4 (sustituyendo f(x))

= 6x^2 - 12x + 2

Por lo tanto, (g∘f)(x) = 6x^2 - 12x + 2.

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

we have 2 possible cases for the coin and 6 possible cases for the die.

so, we have 2×6 = 12 combined possible cases :

heads, 1

heads, 2

heads, 3

heads, 4

heads, 5

heads, 6

tails, 1

tails, 2

tails, 3

tails, 4

tails, 5

tails, 6

out of these 12 cases, which ones (how many) are desired ?

all first 6 plus (tails, 3) = 7 cases

so, the correct probability is

7/12

formally that is calculated :

1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12

the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.

Answer: 66

Step-by-step explanation:

all 3 of them should equal to 180

so 79+35 is 114

180-114 will give us the answer which is 66

Answer:

159 proper subsets.

Step-by-step explanation:

Given a set {2, 4, 6, 8...100}, how many proper subsets are there?

First, find how many subsets there are in 2 - 10:

That's 16.

Then because there are 10 10s in 100, multiply by 10:

16 x 10 = 160

Finally, because it says proper subsets, subtract by 1:

160 - 1 = 159 proper subsets.

Therefore, there are 159 proper subsets in {2, 4, 6, 8...100}

Answer:

It means the point x = 5 and y = 10

Answer: The place 5 units right and 10 units up from the center of the graph (the origin).

Step-by-step explanation:

Starting at the origin, the 5 represents moving right 5, and the 10 represents going up 5.

the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.

How to solve and what is graph?

The range of a function refers to the set of all possible output values. Looking at the table, we can see that the output values of g(x) increase rapidly as x increases.

In fact, the output values of g(x) are the result of raising 3 to the power of x, which means that g(x) can never be negative. Therefore, the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.

A graph is a visual representation of data or mathematical functions. It is a diagram made up of points, lines, and curves that show the relationship between different variables or data points.

Graphs are used to display and analyze data, to illustrate trends and patterns, and to communicate complex information in an easily understandable way. There are many different types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more, each suited to different types of data and analysis.

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Answer:

38%

Step-by-step explanation:

I learned in class on Friday.

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

[tex]0.38\times \dfrac{100}{100}[/tex]

[tex]= (0.38 \times 100) \times \dfrac{1}{100} =\dfrac{38}{100}[/tex]

Write in percentage notation: 38%

Answer:

Step-by-step explanation:

[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]

But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.

The function for the value of the account after t years can be written as:

V(t) = 93000(1.08900365)t

The coefficient of 1.08900365 is the annual growth rate (APR) compounded daily. After rounding to four decimal places, it becomes 1.0890.

The percentage of growth per year (APY) is 8.90%. This is the same as APR, but expressed as a percentage.

There are 81 potential outcomes in Andy's sample space.

Potential Outcomes is a list of every scenario that could happen as a result of an occurrence. For instance, while rolling a dice, the possible results are 1, 2, 3, 4, 5, and 6. 6. Favorable Result - the intended outcome. For instance, if you roll a 4 on a dice, the only possible result is 4.

The total number of cards (i.e., 4 + 3 + 2 = 9) determines the number of outcomes that can occur in each draw.

We must multiply the total number of results for each draw in order to determine the total number of possible outcomes for the two draws.

For two draws with replacement, there are exactly as many outcomes available as the product of the amount of outcomes that could occur in each draw.

9 × 9 = 81.

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Answer:

B is correct

Step-by-step explanation:

If it is spun twice then the probability of it landing on 2 and then an odd number is:

Pr(2,1) or Pr(2,3) or Pr(2,5) or Pr(2,7)

1/49 * 4

4/49

Answer:

Step-by-step explanation:

i think it B

Answer:

To find the integral of f(x) = 2x + 5/3 over the interval [0, 5], we can use the definite integral formula:

∫[a,b] f(x) dx = F(b) - F(a)

where F(x) is the antiderivative of f(x).

First, we find the antiderivative of f(x):

F(x) = x^2 + (5/3)x + C

where C is the constant of integration.

Next, we evaluate F(5) and F(0):

F(5) = 5^2 + (5/3)(5) + C = 25 + (25/3) + C

F(0) = 0^2 + (5/3)(0) + C = 0 + 0 + C

Subtracting F(0) from F(5), we get:

∫[0,5] f(x) dx = F(5) - F(0)

= 25 + (25/3) + C - C

= 25 + (25/3)

= 100/3

Therefore, the definite integral of f(x) = 2x + 5/3 over the interval [0, 5] is 100/3.

Therefore , the solution of the given problem of function comes out to be f(x) = sec(x) has a period of 2. 2 is the answer.

The midterm test questions will cover all of the topics, including actual as well as fictitious locations and arithmetic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox has a particular spot that might be used as a haven.

Here,

=> F(x) = sec(x) has a 2 phase.

Because the secant function is periodic, its values recur after a predetermined amount of time.

This interval's length is equal to the secant function's duration.

The formula for the secant function is

=> sec(x) = 1/cos.(x).

The cosine function repeats its values every 2 units of x, which is known as its period.

Consequently, the secant function has a period of 2 as well.

Therefore, f(x) = sec(x) has a period of 2. 2 is the answer.

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A company manufactures rubber balls, random variable X in words is diameter of the rubber ball, standard deviation is -1.5 and z-score of the x = 2 is 2.123.

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. Random variables are frequently identified by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.

In probability and statistics, random variables are used to measure outcomes of a random event, and hence, can take on various values. Real numbers are often used as random variables since they must be quantifiable.

1) X denotes the diameter of the rubber ball.

So the correct option was A. (option A)

Therefore,  the random variable X in words is diameter of the rubber ball.

2) For 1.5 Standard deviations left to the mean , Z score will be -1.5

option(A)

So, standard deviation to the left of the mean is -1.5.

3) [tex]Z=\frac{(x-\mu)}{\sigma}[/tex]

x=2

sigma = √2

Z = 2-(-1)/ √2

Z = 3/√2

Z = 2.123

Hence, the z-score of the x = 2 is 2.123.

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Complete question:

A company manufactures rubber balls. The mean diameter of a rubber ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X

diameter of a rubber ball

rubber balls

mean diameter of a rubber ball

12 cm

Question 2 What is the z-score of x=9, if it is 1.5 standard deviations to the left of the mean? Hint: the z-score of the mean is =0 −1.5 1.5 9 Question 3 Suppose X∼N(−1,2). What is the z-score of x=2 ? Hint: z=(x−μ)/σ 1.5 −1.5 0.2222

The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.

The given equation is [tex](e - 2\sqrt{3} )^2[/tex] = f - 20√3.

Expanding the left side of the equation we have:

[tex](e - 2\sqrt{3} )^2[/tex] = (e - 2√3)(e - 2√3)

= [tex]e^2[/tex] - 2e√3 - 2e√3 + 12

= [tex]e^2[/tex] - 4e√3 + 12

Substituting back in the function

[tex]e^2[/tex] - 4e√3 + 12 = f - 20√3

[tex]e^2[/tex] - 4e√3 - f + 20√3 - 12 = 0

Using the quadratic formula:

e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2

e = [4√3 ± √(4f - 64√3)] / 2

e = 2√3 ± √(f - 16√3)

Now for,

(e - 2√3)² = f - 20√3

(2√3 + √(f - 16√3) - 2√3)² = f - 20√3

f - 20√3 = f - 16√3

f = 4√3

Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

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Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.

The above statement is True.

In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.

A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.

Sometimes the term linear function has the same meaning as linear map, but not in analysis.

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Answer:

................................

The gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]

What is gravitational force?

Gravitational force is the force of attraction that exists between any two objects in the universe with mass. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between their centers.

The gravitational force that the moon produces on the Earth can be calculated using the formula:

[tex]F = G \cdot \frac{m_1 \cdot m_2}{r^2}[/tex]

where:

[tex]G$ = gravitational constant = $6.67430 \times 10^{-11}\ \mathrm{N(m/kg)^2}$[/tex]

[tex]m_1$ = mass of the moon = $7.34 \times 10^{22}\ \mathrm{kg}$[/tex]

[tex]m_2$ = mass of the Earth = $5.97 \times 10^{24}\ \mathrm{kg}$ (approximate)[/tex]

[tex]r$ = distance between the centers of the Earth and the moon = $3.88 \times 10^8\ \mathrm{m}$[/tex]

Substituting these values into the formula, we get:

[tex]F &= 6.67430 \times 10^{-11} \cdot \frac{7.34 \times 10^{22} \cdot 5.97 \times 10^{24}}{(3.88 \times 10^8)^2} \&= 1.98 \times 10^{20}\ \mathrm{N}[/tex]

Therefore, the gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]

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The correct options are:

The data contain a sample of multiple individuals.

The data are collected  are approximately at  the same point in time.

Cross-sectional data sets are a type of research design used in statistical analysis. They consist of a sample of multiple individuals or entities observed at a single point in time. One of the characteristics of cross-sectional data sets is that they do not involve any observation or measurement over time, making them different from longitudinal or time-series data sets.

One advantage of cross-sectional data sets is that they are relatively easy and inexpensive to collect. It can be assumed that the data were obtained through a random sampling of the underlying population, making them representative of the larger population. However, these data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.), as the timing of data collection can impact the results.

Overall, cross-sectional data sets can provide a snapshot of a population or phenomenon at a specific point in time, making them useful for a wide range of research questions in social, economic, and political sciences.

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Because g(x) is continuous on the interval, we can see that the correct option is the last one (counting from the top)

Here we have the function g(x), and we know that it is continuous on the interval [1, 6], and that:

g(1) = 18

g(6) = 11

If it is continuous, then g(x) covers all the values between 18 and 11 in the given interval, this means that there must exist a value c in the given interval such that when we evaluat g(x) in that value c, we get the outcome 12, and we know this by the intermediate value theorem.

So the correct optionis the last one.

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When three dices are rolled.

Total number of outcomes =  = 216

Sum of 13 can be achieved in the following ways:

From the digits 6,4,3

So, there are 3! ways =  = 6

From the digits 6,2,5

So, there are 3! ways =  = 6

From the digits 5,4,4

So, there are  ways = 3

From the digits 6,6,1

So, there are  ways = 3

From the digits 3,5,5

So, there are  ways = 3

So, total numbers whose sum is 13=

So, Probability = .

Therefore, the probability of getting sum as 21 on rolling three dice =   .

The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.

Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.

The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.

Given that, K = 5/9 (F - 459.67).

To obtain F in term of K we isolate the value of F as follows:

K = 5/9 (F - 459.67)

Multiplying both sides by 9/5, we get:

(9/5) K = F - 459.67

Adding 459.67 to both sides, we get:

F = (9/5) K + 459.67

Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.

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