Evaluate the function as indicated below.

They sold 400 student tickets and 200 student tickets.

And at a certain performance, they sold 100 adult tickets and 200 student tickets.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Given, Let 'x' represents the number of adult tickets and 'y' represent the number of student tickets.

So, The two equations can be formed as,

x + y = 600 and 7.5x + 4.5y = 3300.

Multiplying equation 1 by 7.5x we have 7.5x + 7.5y = 4500 and subtracting it from equation 2 we have,

- 3y = - 1200.

y = 400 and hence x = 200.

At a certain performance, they sold twice as many student tickets as adult tickets.

y = 2x.

x + y = 300.

x + 2x = 300.

3x = 300

x = 100 and hence y = 200.

100×7.5 + 200×4.5 = 750 + 900 = 1650.

So, they were 3300 - 1650 = $1650 short.

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The function f(x) and the number [tex]a[/tex] that satisfies the given equation is:[tex]$$f(x)=x^{3 / 2} \quad \text { and } \quad a=\frac{49}{4} .$$[/tex]

Let's differentiate both sides of the given equation with respect to [tex]x[/tex] obtain

[tex]\frac{d}{d x}\left[5+\int_a^x \frac{f(t)}{t^2} d t\right]=\frac{d}{d x}[2 \sqrt{x}] .[/tex]

The Fundamental Theorem of Calculus combines the concepts of differentiating a function (calculating the slope or rate of change at any point in time) and integrating a function (calculating the area under a graph, or calculating the cumulative effect ) is a combination of of small contributions). 

Using the Fundamental Theorem of Calculus and the Power Rule, we have

[tex]\frac{d}{d x}\left[\int_a^x \frac{f(t)}{t^2} d t\right]=\frac{d}{d x}\left[2 x^{1 / 2}\right][/tex]

Applying the Chain Rule and simplifying, we get

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

Solving for [tex]f(x) \$$, we get $\$ f(x)=x^{\wedge}(3 / 2\}[/tex].

To find a, we can use the given equation with x=1 and simplify:

[tex]$$5+\int_a^1 \frac{f(t)}{t^2} d t=2 \sqrt{1} \Rightarrow \int_a^1 \frac{f(t)}{t^2} d t=-3 .$$[/tex]

Substituting [tex]$ f(x)=\mathrm{x}^{\wedge}[3 / 2\}[/tex], we have

[tex]$$\int_a^1 \frac{f(t)}{t^2} d t=\int_a^1 \frac{t^{3 / 2}}{t^2} d t=\int_a^1 t^{-1 / 2} d t=2(\sqrt{1}-\sqrt{a})=-3$$[/tex]

Solving for a, we obtain [tex]a=\backslash f r a c\{49\}\{4\}[/tex]. Therefore, the function f(x) and the number [tex]a[/tex] that satisfy the given equation are

[tex]$$f(x)=x^{3 / 2} \quad \text { and } \quad a=\frac{49}{4} .$$[/tex]

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Step-by-step explanation: To find the values of l and m, we need to solve the equation 15 - 28i = 3l + (4m)i for l and m.

First, we can move all the terms with i to one side of the equation:

15 = 3l + 4mi

-28i = 4mi

To solve for m, we can divide both sides by 4i:

-28i/4i = m

m = -7

Now that we know the value of m, we can substitute it back into the equation to solve for l:

15 = 3l + 4(-7)i

15 = 3l - 28i

3l = 15 + 28i

To solve for l, we can divide both sides by 3:

l = (15 + 28i)/3

So the values of l and m are l = (15 + 28i)/3 and m = -7

Answer:15

Step-by-step explanation:

At the point of tangency, a tangent to a circle is perpendicular to the radius.

A tangent is a line that extends from a point on the circle to two points that are eternally close to one another. To put it another way, we can say that tangents are lines that precisely cross a circle at a certain location. Where the tangent touches the circle is known as the point of tangency. An angle is tangent to the radius at the point of tangency. This is a key component of geometric constructions and proofs, and as such, it is related to a number of theorems. One by one, we will examine them.

Theorem: 1

By connecting the center with the point of tangency, a radius is produced. A circle's tangent at a given location is perpendicular to its radius. Simply adhere to the diagram below: Here AB⊥OP

Theorem:2  

According to this theorem, two tangents traced to a circle from a single exterior point have equal numbers of tangent segments. Line connecting the exterior point and the point of tangency is referred to as a tangent segment.

Hence the theorem of the tangent of circle mentioned above.

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Complete question:

At the point of tangency, a tangent to a circle is ______ to the radius.

Answer:

Below

Step-by-step explanation:

Domain is the 'x' values a function can have   for this one  {1,3,4,5}

Range is the 'y' values a function has   {6,8,10}

Answer:

4x-6=-5y+9

4×=-5y+9+6

We can substitute the first equation into the second to eliminate [tex]y[/tex] and solve for [tex]x[/tex]

[tex]$$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$[/tex]

An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you'll get both sides equal, hence, it is an infinite solution. Infinite represents limitless or unboundedness. It is usually represented by the symbol ” ∞ “.

Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.

This system of linear equations can be graphed on a [tex]$x-y$[/tex] plane. The first equation represents a line with slope [tex]\frac{1}{4}[/tex] and [tex]$y$[/tex]-intercept [tex]-3[/tex]. The second equation represents another line with slope [tex]-1[/tex] and [tex]$y$[/tex]-intercept [tex]-4[/tex]. The intersection point of the two lines is the solution to the system of linear equations.

To find the solution, we can substitute the first equation into the second to eliminate [tex]y[/tex] and solve for [tex]x[/tex]

[tex]$$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$[/tex]

We can then use either equation to find the value of [tex]y[/tex]

[tex]$$\begin{gathered}y=\frac{1}{4} x-3 \\\Rightarrow \\y=\frac{1}{4} \cdot 3-3 \\= \\y=-2\end{gathered}$$[/tex]

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The measure of angle R is 16.1°

Law of Sines In trigonometry, an equation relating the lengths of the sides of any triangle to the sines of its angles.

Given that, a triangle RST, with one angle S = 39° and RT = 25, ST = 11

We need to measure the angle R,

Using law of sine,

Sin R / TS = Sin T / RS = Sin S / RT

Sin R / 11 = sin 39° / 25

Sin R = 11 × sin 39° / 25

Sin R = 0.2769

R = sin⁻¹(0.2769)

R = 16.1

Hence, the measure of angle R is 16.1°

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Step-by-step explanation:

it is a arithematuc sequence because it has a common difference of 5

so the general term is Tn = 1 + (n-1)5

also the 5th term is T(5) = 1 + (5-1)5 = 21

Answer:

138°

Step-by-step explanation:

∠BCD and ∠CDB are equivalent, meaning they both are 48°.  Together, that is 96°.  Subtract 96° from 180° (the measure of all of the inside angles in a triangle added together.) and you get 84°.  Subtract 84° from 360° (the number of degrees in a circle) and you get 276°.  Divide that by two (∠ABD and ∠ABC) to get 138°.

The cafe served 72 regular coffees.

Here are the steps to find the number of regular coffees served:

The method used for this problem is simple arithmetic calculation, specifically percent calculation.

Percent calculation is used to find the proportion of a number in terms of a percent. To perform a percent calculation, you multiply the original number by the percent (expressed as a decimal) and then round the result to the desired number of decimal places. In this case, the original number is 80 and the percent is 90, which we first convert to 0.90 (by dividing by 100).

You could determine that this method was used because the problem statement asked for the proportion of regular coffee in terms of percent (90%) of the total number of coffees served (80). To find this proportion, you needed to multiply 80 by 0.9, which is equivalent to 80 * 90%.

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The distance that Ann travelled is; 3.61 ft

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

Ann and Elena form the vertical leg of a right angle triangle of length = 3ft. Elena and Rob form the opposite side of the right angle triangle of length = 2 ft.

Using the Pythagorean theorem to find the distance that Anna traveled which is the length of the hypotenuse of the right angle triangle; let that length be x. Then:

x = √(3² + 2²)

x = √ 13

x = 3.61 ft

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The inequality graph is interpreted to have the equation as;

y  > ⁻³/₄x - 3

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From the given graph, the y-intercept is seen to be -3.

The slope is gotten by using two coordinates from the formula;

m = (y₂ - y₁)/(x₂ - x₁)

(0, -3) and (-4,0)

m = (0 - (-3))/(-4 - 0)

m = -3/4

Thus, equation of line is;

y = ⁻³/₄x - 3

Since the upper part of the inequality is shaded and the line is a dashed line, then the symbol is greater than and it is expressed as;

y  > ⁻³/₄x - 3

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Answer:

:)

Step-by-step explanation:

Just divide 1,004.7 by 59.1

If BC = 8 cm, ∠B = 60°and ∠C = 70° then the triangle is an acute triangle and the value of ∠A is 50.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

BC = 8 cm

∠B = 60° and ∠C = 70°.

Now,

The sum of all the angles is 180.

This means,

∠A + ∠B + ∠C = 180

∠A = 180 - 130

∠A = 50

Now,

The triangle is an acute triangle since all the angles are acute.

i.e less than 90.

Thus,

The triangle is an acute triangle.

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Answer:

he would only be able to bring 2 friends

Step-by-step explanation:

250- 100= 150    cost of table

150/ 40=3.75   cost of friends

He was would not be able to bring a .75 of a friend so you would have to round down.

Answer:2 45833333333/50000000000

The equation of the line that passes through (4,2) and is parallel to the line shown is 3x + y = -10

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

The slope intercept form of a line is:

y = mx + b

where m is the slope and b is the y intercept

Two lines are said to be parallel if they have the same slope.

The line shown passes through point (0, 1) and (-1, -2). Hence:

Slope = (-2 - 1) / (-1 - 0) = 3

The line parallel will also have a slope of 3. It then passes through (4, 2). Hence:

y - y₁ = m(x - x₁)

y - 2 = 3(x - 4)

y = -3x - 10

3x + y = -10

The equation of the line is 3x + y = -10

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The total amount of time Michelle's family spends at Mount Rushmore is 93.38 minutes, which is equivalent to 1 hour and 33.38 minutes.

The time Michelle and her family spend watching the movie in the visitor center is 14/60 of an hour or 14 minutes. We are told that this accounts for 15% of the total time they spend at Mount Rushmore, so to find the total amount of time they spent at Mount Rushmore, we need to divide the time spent watching the movie (14 minutes) by the percentage of the total time this accounts for (15%). This gives us the equation:

time = 14 / (15/100)

time = 14 × (100/15)

time = 14 × (6.67)

time = 93.38 minutes or 1 hour and 33.38 minutes.

So the total amount of time Michelle's family spends at Mount Rushmore is 93.38 minutes, which is equivalent to 1 hour and 33.38 minutes.

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Answer:

6/11

Step-by-step explanation:

Mammal - yes

Giraffe - no

Seal - no

Mouse - no

Cat - no

Tiger - no

Bat - yes

Can fly - yes

Swan - yes

Lizard - no

The intersection of the graphs of the inequalities is shown by a compound inequality with a "and" in it.

When two inequalities are separated by "and" or "or," the result is a compound inequality. The intersection of the graphs of the inequalities is shown by a compound inequality with a "and" in it. A number is a compound inequality solution if it also solves the underlying inequality.

Divide a compound inequality into two individual inequalities before solving it. The solution should either be a union of sets ("or") or an intersection of sets ("and"). Inequalities and the graph should then be solved.

Compound inequality comes in two flavors. Both conjunction and disjunction issues are present. Sometimes, the two simple inequalities in these compound inequalities will be separated by the words AND or OR. When resolving compound "and/or" inequalities, start by resolving each inequality separately.

Therefore, the correct answer is option D.

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Aaron should answer 3 open-ended questions and 0 multiple-choice questions to get a maximum of 3 * 20 points/question = 60 points

Aaron has 45 minutes to answer the questions, so he has 45 minutes / 15 minutes/question = 3 open-ended questions that he can answer.

For the remaining questions, he has 45 minutes - (3 * 15 minutes) = 45 minutes - 45 minutes = 0 minutes.

So he cannot answer any more open-ended questions.

He can answer 0 minutes / 1 minute/question = 0 multiple-choice questions.

Therefore, Aaron should answer 3 open-ended questions and 0 multiple-choice questions to get a maximum of 3 * 20 points/question = 60 points.

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The  temperature when the plane reaches an altitude of ​3000ft is 51.8 F

Temperature is the degree of hotness or coldness of an object.

Given here: the temperature drops every 1.2 F for every thousand feet ascend.

Thus if the temperature on the ground is 55.4 F

When the plane ascends to 3000 feet the number of temperature drops would be 3 .

Thus drop in temperature is 1.2×3=3.6 F

Therefore the temperature at an altitude at an altitude of 3000 ft. is

55.4-3.6=51.8 F

Hence, The  temperature when the plane reaches an altitude of ​3000ft is 51.8 F

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At the haunted mansion, 6114 people were  scared by a group of 135 ghosts and 273 witches.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

According to the question each ghost must scare 19 people that means 135 ghost will scare:

135 ghosts x 19 people = 2,565 people......................(i)

And each witch must scare 13 people-no more and no less i.e 273 witches will scare:

273 witches x 13 people = 3,549 people.....................(ii)

Adding (i) and (ii) we get;

2,565 + 3,549 = 6114 people

Therefore, 6114 people were scared by a group of 135 ghosts and 273 witches.

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Answer:

in 2014=4100 in 2008=6800 last question=2020

Step-by-step explanation:

multiply (-5+i) and 2i with 2i

2i × 2i = 4i^2 ➡-4

2i × (-5+i) = -10i + 2i^2 ➡-10i -2

then do the division

(-10i -2)/-4 = (5i + 1)/2

There are 4 steps to build a VI to compute the variance of an array x.

Here is a VI in LabVIEW to compute the variance of an array x:

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When determining sample size for the first test, it is most important to Weigh the potential consequences of a test that does not lead to improvement against the belief in success.

When evaluating a patient, a patient assessment form is used to evaluate the patient's potential diagnosis and the appropriate course of therapy. To prevent misdiagnosis and ensure that the right therapy is given, it is crucial to gather relevant data. In order to register patients for operations provided by medical institutions, patient registration forms are utilised. Our free patient registration forms will efficiently capture patient information online, streamlining the registration and onboarding process whether you need to register new patients for your hospital, clinic, health centre, or private practise. Usability testing may find and support data-driven design decisions that have been drawn from practitioner usage of the system in a hectic office setting. Health care safety may be improved by using human factors understanding of HCI design and its effects on human performance.

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Answer: It will take 63 minutes for the group to make a wood pile of 45 sticks

Step-by-step explanation:

i hope this helps if so pls mark brainliest !!

The Triangle ABC having perimeter 22cm and AB = 8cm and BC =5cm is not a right angled triangle.

A triangle to have a right angle triangle it should follow the basic theorem of Pythagoras,

If perimeter of ΔABC is 22cm

P = AB + BC + AC

22 = 8 + 5 + AC

AC = 9

By using Pythagoras theorem ,

AC² = AB² + BC²

9² = 8² + 5²

81 ≠ 89

Therefore its not a right angle triangle.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle. The right triangle or 90-degree triangle is another name for this triangle. In trigonometry, the right triangle is significant.

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