A theater owner is looking to maximize his profits and needs to increase his ticket
prices. The function P(t) = -50t2 + 100t + 14,400 represents his total profit, P, based on
the amount, in dollars, he raises the ticket price, t.

The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.

What is cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.

In the given box it is given sides are 2, 3 and 4 ft.

So the volume of the rectangular prism is V = 2*3*4 = 24 ft².

So the greater surface area in the given description is 6ft, 2ft and 2ft.

Where the surface area will be 12ft ²

Hence The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.

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Answer:

Step-by-step explanation:

To find the missing side lengths in the given right triangles, use trigonometric ratios.

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the first triangle ABC, we have been given the angle, the side opposite the angle and the side adjacent the angle.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the tangent ratio:

[tex]\implies \tan 18^{\circ}=\dfrac{15}{x}[/tex]

[tex]\implies x\tan 18^{\circ}=15[/tex]

[tex]\implies x=\dfrac{15}{\tan 18^{\circ}}[/tex]

[tex]\implies x=46.165253...[/tex]

[tex]\implies x=46.2\;\;\sf(nearest\;tenth)[/tex]

----------------------------------------------------------------------------------------

Triangle LMN is a right triangle. Interior angles of a triangle sum to 180°.

Therefore, as m∠M = 50° and m∠MLN = 90°, then m∠MNL = 40°.

As KN is perpendicular to NM and m∠MNL = 40° then m∠KNL = 50°.

As KL is parallel to NM, then m∠K = 90°.  Therefore, m∠KLN = 40°.

(Refer to the attached diagram).

For right triangle LMN, we have been given the angle (∠M) and the side adjacent to the angle (LM). To find an expression for the length of the side opposite the angle (LN), use the tangent ratio:

[tex]\implies \tan 50^{\circ}=\dfrac{LN}{45}[/tex]

[tex]\implies LN=45\tan 50^{\circ}[/tex]

LN is the hypotenuse of right triangle KLN.

If we use ∠KNL as θ, then side KN is adjacent to the angle.

Therefore, to find the KN use the cosine ratio:

[tex]\implies \cos 50^{\circ}=\dfrac{KN}{LN}[/tex]

[tex]\implies \cos 50^{\circ}=\dfrac{KN}{45\tan 50^{\circ}}[/tex]

[tex]\implies KN=45\tan 50^{\circ}\cos 50^{\circ}[/tex]

[tex]\implies KN=34.471999...[/tex]

[tex]\implies KN=34.5\;\; \sf (nearest\;tenth)[/tex]

As KL is the side opposite ∠KNL, to find KL use the sine ratio:

[tex]\implies \sin 50^{\circ}=\dfrac{KL}{LN}[/tex]

[tex]\implies \sin50^{\circ}=\dfrac{KL}{45\tan 50^{\circ}}[/tex]

[tex]\implies KL=45\tan 50^{\circ}\sin50^{\circ}[/tex]

[tex]\implies KL=41.0821297...[/tex]

[tex]\implies KL=41.1\;\;\sf (nearest\;tenth)[/tex]

----------------------------------------------------------------------------------------

From inspection of the second triangle ABC, we have been given the angle, the side adjacent the angle and the hypotenuse.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the cosine ratio:

[tex]\implies \cos 70^{\circ}=\dfrac{x}{46}[/tex]

[tex]\implies x=46\cos 70^{\circ}[/tex]

[tex]\implies x=15.732926...[/tex]

[tex]\implies x=15.7\;\;\sf(nearest\;tenth)[/tex]

The solution to the expression ⁴√(-15/16) is (-15/16)^1/4

From the question, we have the following parameters that can be used in our computation:

⁴√(-15/16)

The above expression means that we calculate the 4th root of -15/16

-15 and 16 do not have perfect fourth roots

This means that the expression can only be rewritten as

(-15/16)^1/4

It cannot be evaluated

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The value of the expression xy - x² - 5x - 4 when x = -1 and y = 6 is -6.

Given the expression in the question;

xy - x² - 5x - 4

To find the value of the expression; substitute in x = -1 and y = 6 for all occurrence of x and y in the expression and simplify.

xy - x² - 5x - 4

Plug in  x = -1

(-1)y - (-1)² - 5(-1) - 4

Plug in y = 6

(-1)(6) - (-1)² - 5(-1) - 4

Simplify

-6 - 1 + 5 - 4

Add -6 and -1

-7 + 5 - 4

Add -7 and 5

-2 - 4

Add -2 and -4

-6

Therefore, the value of the expression is -6.

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Answer:

-3

Step-by-step explanation:

you can use elimination to remove y from this equation

your first equation will be

4x+10y=-2; and you can multiply the other one by -10

30x-10y=-100

if you add the two equations, 10y and -10y will cancel out and you'll get

34x = -102

divide both sides by 34

x=-3

So, on solving the provided question, we can say that the equation, we have been provided with is x = 48

The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.

A mathematical formula explains the connection between the two sentences on either side of a letter. There is typically just one variable, which also acts as the symbol. As an illustration, 2x - 4 = 2.

the equation, we have been provided with is

x + 2 = 50

x = 50-2

x = 48

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Answer:

y=-2x+1

Explanation:

you can see that the x goes up by 1 every time. Y goes down by 2 every time, because 1-2=-1, -1-2=-3, etc. So the -2 goes in your m part of y=mx+b. Then you need to figure out what y is when x is 0, for your y-intercept, or your b part of y=mx+b. The picture makes it simpler, showing that when x is 0, y is 1. Therefore, 1 is your b part of y=mx+b. If you put it all together, it looks like this:

Y=-2x+1

Step-by-step explanation:

It looks Iike the equation is in slope intercept form

[tex]y = mx + b[/tex]

m is the slope

b is the y intercept

Finding B is easy, it's just where X = 0. On this table, Y is 1 when X is 0.

Finding the slope. We'll take two different (X,Y) coordinates. Let's do the first two rows (0,1) and (1,-1)

Next we apply the slope formula. That being

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

So plugging that in

[tex] = \frac{ - 1 - 1}{1 - 0} [/tex]

That gives you -2/1, also known as -2

Now that we have everything, we can put the forumla together

[tex]y = - 2x + 1[/tex]

Where -2 is the answer that belongs in the [?]

Answer:

9.6a + (-2)

Step-by-step explanation:

(6 + 12.5a) - (8 + 2.9a)  Distribute the negative sign

6 + 12.5a - 8 - 2.9a  Combine like terms

12.5a - 2.9a +6 - 8

9.6a + (-2)

Answer:

It should be 8...

Step-by-step explanation:

16 / 8 = 2 and there is no higher number 16 that can be divided by. 56 is dividable by 8 so it makes sense.

Also 56 isn't dividable by 16

Given a parallelogram ABCD with points B and D, we draw two lines such that line BM intersects CD at point M and line DN intersects BC at point N, and BM = DN. The intersection of these lines is point I. Our goal is to prove that IA is a bisector of angle BID.

To prove this, we first note that since ABCD is a parallelogram, AB is parallel to CD and AD is parallel to BC. This means that ∠BAD and ∠CDA are congruent, and ∠BAC and ∠DCB are congruent.

Next, we consider triangle ABM. Since BM is perpendicular to AB, we have ∠BAM = 90°. By the same reasoning, we have ∠BID = 90°. This means that IA is perpendicular to both AB and BD.

Since IA is perpendicular to AB and BD, it follows that IA bisects ∠BAD and ∠BDC. Additionally, we know that AB = BD and ∠BAD = ∠BDC, so it follows that IA bisects ∠BID.

This completes the proof that IA is a bisector of ∠BID. The key idea here is that a line perpendicular to two parallel lines bisects the angles formed by the intersection of the two parallel lines with a third line.

In conclusion, given a parallelogram ABCD with points B and D, the intersection of lines BM and DN, point I, is the bisector of angle BID. This result can be used to prove various geometric theorems and helps to understand the properties of parallelograms and their related figures.

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The error made by the student in the exponential function, y = 48,000(1.03)^x is that the function represented an exponential growth rather than an exponential decay.

An exponential function is written in the form y = abˣ.

In the exponential function, the exponent, x is a variable.

Annual decreasing rate of the fish population = 3% or 0.03

Original population = 48,000

Let the number of years = x

Exponential function: 48,000 (1 - 0.03)^x

= 48,000(0.97)^x

Thus, to represent an exponential decay, the exponential function should have been written as y = 48,000(0.97)^x.

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The table to show the depreciation over time for the first three years is:

Year (x) Depreciation (y)

1         $15,000

2         $13,500

3        $12,000

It should be noted that in order to generate a table to show the depreciation over time for the first three years, we can use the given equation:

y = 16,500 - 1,500x

where y is the depreciation and x is the number of years since the car was purchased new.

Substituting x = 1, 2, and 3 into the equation, we get:

When x = 1, y = 16,500 - 1,500(1) = 15,000

When x = 2, y = 16,500 - 1,500(2) = 13,500

When x = 3, y = 16,500 - 1,500(3) = 12,000

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The recursive rule for the sequence is T(n) = T(n - 2) - T(n - 1)

From the question, we have the following parameters that can be used in our computation:

100, 3 , 97 ,-94 , 191

The above definitions imply that we simply subtract the current from the previous term to get the next term

Using the above as a guide,

So, we have the following representation

T(n) = T(n - 2) - T(n - 1)

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By applying the algebra concept, it can be concluded that p = 3x or p = 2 - 3x.

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.

We want to express p in terms of x of this equation:

9x² – 6x + 5 = p² – 2p + 5

First, we have to eliminate 5, so we have:

9x² – 6x = p² – 2p

Then we add 1 on each side, so we have:

9x² – 6x + 1 = p² – 2p + 1

       (3x - 1)² = (p - 1)²

            p - 1 = √(3x - 1)²

Thus the solutions are:

p - 1 = 3x - 1      ⇔     p = 3x

or

p - 1 = -(3x - 1)   ⇔     p = 2 - 3x

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The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%. Albinism and hemophilia are both recessive genetic conditions, meaning that both parents must have the recessive gene in order for a child to be born with either condition. Since neither Clara nor Charles have either condition, the probability that their first child will be a boy with both albinism and hemophilia is 0%.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

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Answer: 8 micrograms, y=40-(8)4

Step-by-step explanation: after four hours, 8 (4) micorgrams will stil be in her body

Answer:

the answer is y=40(0.8)^x

16 micrograms

Answer:

To find the sum of two complex numbers on the complex plane, we can simply add their real and imaginary parts separately. The real part of a complex number is the x-coordinate on the complex plane, while the imaginary part is the y-coordinate.

In this case, the two complex numbers are (-4-4i) and (4+2i). To find their sum, we add their real and imaginary parts separately:

Real part: -4 + 4 = 0

Imaginary part: -4 + 2 = -2

So, the sum of (-4-4i) and (4+2i) is 0 - 2i, which can be represented as a point on the complex plane with x-coordinate 0 and y-coordinate -2.

Step-by-step explanation:

Answer:

1. 4

2. $52

3. $20

4. 58

5. 30

6. 2

7. 132

8. 24

Step-by-step explanation:

1. If he needs 10 feet all together, and only has 6, you can put it in an equation as “6+x=10” because 10 would be the final amount, and he already had 6 feet, so he needs x feet. Then you need to get the x alone in the equation, so you would subtract 6 from both sides. 10-6 is 4, which means x=4. So Phil needs 4 more feet of lumber.

2. Emmet paid $64 in total. Within that total, $12 is for the case. You can set up an equation as either 12+x=64 or 64-12=x, both get the same answer, as shown in the first problem. 64-12 is 52, so that would be your answer.

3. So if he paid $x, 6+14=x. 6 from how much money was spent, 14 from how much was returned. 6+14=20. In total, brandy gave the cashier $20.

4. If the temprature dropped 15 degrees, and it is now 43, all you need to do is undo the dropping. If it didnt drop, it rose. To you need to add 15 to 43, giving you 58. The starting temperature was 58.

5. Her rate per hour is $12. That means if she worked x hours, you would set it up as 12x=m, m being the amount of money she earns. If she earns $360, you plug that in, making it look like 12x=360. Then you do the opposite of multiplication, on both sides, so you decide both sides by 12. On the left it cancels out, on the right 360/12 is 30. That means that Cindy worked for 30 hours.

6. If she used 32 cups and there is 16 cups in a gallon, all you need to do is divide 32 by 16. 32/16 is 2. So Mary used 2 gallons of juice.

7. You can write an equation for this one that looks like x/12=11. X is the total number. From there, you multiply 12 on both sides, giving you 132. That means there are 132 students in the gym class.

8. If there are 4 ping-pong balls in each package and there are 6 packages, all you need to do it multiply 6 by 4. 6 times 4 is 24. So Matthew has 24 ping-pong balls.

Answer:

Step-by-step explanation:

The transformations that have been applied to the parent function y = 1/x^2 are:

shift 3 units to the right

shift 5 units down

reflection over the x-axis

So the correct options are:

shift 3 to the right

shift 5 down

reflection over the x-axis

Answer:

600g Butter, 2000g Flour, 200g Sugar

Step-by-step explanation:

First we divide the final number of cakes by the initial

[tex]72 \div 18 = 4[/tex]

Then we multiply each of the ingredients by 4

[tex]150 \times 4 = 600[/tex]

[tex]500 \times 4 = 2000[/tex]

[tex]50 \times 4 = 200[/tex]

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

The ratio for this problem is:

(Ingredients: number of cakes)

Therefore, we need to know how many times 18 can fit into 72.

Now, if we know that 18 can be multiplied by 4 to get 72, we need to multiply all of the ingredients by 4.

Therefore, if the recipe stays proportional, we will need 600g butter, 200g flour and 200g sugar to make 72 cakes.

Answer:i don't realy now so 5 point 3

Answer: $140 each weekend

Step-by-step explanation:

$1250 - $130 = $1,120

$1,120 divided by 8 weekends = $140

A possible formula for the trigonometric function whose values are in the given table is u(x) = 3cos(πx/2)

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Answer:

B

Step-by-step explanation:

cause the premeter is way around the area

Answer:

B. V = pi*r^2*H/6

Step-by-step explanation:

The formula for the volume of a cone is V=pi*r^2*h/3, where h is the height of the cone, and r is the radius of the base. In this case, the hieght of the cone is equal to half the height of the cylinder, so it's h=H/2

If we substitute, we get

V = pi * r^2 * h / 3 = pi * r^2 * (H / 2) / 3 = pi * r^2 * H / 6

The number of terms in the expression -11 - 7c + 5 - 2x - 13b - 7 is 6

Algebraic expressions are defined as expressions that are composed with coefficients, terms, factors, constants and variables.

They are also known to consist of mathematical operations, such as;

From the information given, we have the algebraic expression as;

-11 - 7c + 5 - 2x - 13b - 7

The terms are either single number or variables in the expression. They are six

Hence, the number is 6

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