the Let number of people = y

Let price = x

Gradient = -200

[tex]\begin{gathered} -200\text{ = }\frac{y\text{ - 800}}{x\text{ - 2}} \\ y\text{ - 800 = -200(x - 2)} \\ y\text{ - 800 = -200x + 400} \\ y\text{ = -200x + 400 + 800} \\ y\text{ = -200x + 1200} \end{gathered}[/tex]Revenue = price X number of people

[tex]\begin{gathered} R(x)\text{ = x }\times\text{ y} \\ R(x)\text{ = x(-200x + 1200)} \\ R(x)=-200x^2\text{ + 1200x} \\ R^{\prime}(x)\text{ = -400x + 1200} \\ To\text{ maximize , R(x) = 0} \\ -400x\text{ + 1200 = 0} \\ 400x\text{ = 1200} \\ x\text{ = }\frac{1200}{400} \\ \text{x = 3} \end{gathered}[/tex]Optimal item price = $3

c(n) = -6 (-1/3) *n-1What is the 2nd term in the sequence ?

We are given the following sequence

[tex]c(n)=-6(-\frac{1}{3})^{n-1}[/tex]We are asked to find the 2nd term of the above sequence

Let us substitute **n = 2** into the given sequence

Therefore, the 2nd term of the given sequence is **2**

A fish tank in the shape of a rectangular prism has a volume of 24 cubic feet. The length of the fish tank is 2 feet less than twice the width w, and the height is 1 foot less than the width. Find the equation, in terms of w, that could be used to find the dimensions of the fish tank in feet. Your answer should be in the form of a polynomial equals a constant.

Answer in the form of a polynomial equals a constant:

2w^3-4w^

I dont know how to answer this pls help

The hedgehog's **total change in weight** is -2.5 ounces.

A relationship is **proportiona**l if the ratio of the variables is constant. The variables can either increase or decrease at a constant rate. A **proportional relationship** can be modelled with a linear equation.

Ratio = change in weight / days of hibernation

-0.18 / 9 = -0.02

-0.56 / 28 = -0.02

-1.44 / 76 = -0.02

-1.96 / 98 = -0.02

Weight when the day of **hibernation **is 125 = number of days x ratio

125 x -0.02 = -2.5

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You are dressing a mannequin for a clothingstore display. You have 4 types of shoes, 5necklaces, 10 tops, and 7 bottoms to choosefrom. How many distinct outfits can youcréate? >

Given:

• Types of shoes = 4

,• Number if necklaces = 5

,• Number of tops = 10

,• Number of bottoms = 7

Let's find how many distinct outfits you can create.

To find the number of distinct outfits you can create, we have:

[tex]\begin{gathered} n=4*5*10*7 \\ \\ n=1400 \end{gathered}[/tex]**Therefore, the number of distinct outfits you can create is **** 1400.**

**ANSWER:**

**1400**

the side opposite the right angle measures 8 in. what is the measurement of the side opposite of the 60 degree angle (draw and label the triangle before solving)

[tex]4\sqrt[]{3}[/tex]

**1) ** The best way to tackle this question is by sketching out the triangle:

**2) **Considering that 60º angle we can write out the following trig ratio:

Note that if we had drawn the 60º angle to the lowe right in that triangle we would find the same measure, by using the cosine of (30º) instead.

**And that's the answer**

Solve tan(x){tan(%) - 1) = 0 O A. x = 5 + 27T7,X = 3 37 + 27 O B. x = -2779,x=37 + X +277, X = +27 2. C. X = +19,X = = tnx +277 O D. X = n,X = x FT 4

**Given the trigonometry equation below,**

**Solving each part separately**

**Therefore, **

**Hence, ****Option D**** is the correct answer.**

Scientific notation of 100+6*10^2

**Answer: The answer is 700 **

**Step-by-step explanation:**

is that the answer you're looking for?

**Answer:**

7e2

**Step-by-step explanation:**

10^2=100

100*6=600

600+100=700

there are 2 zeros in 700 so

7e2

Find the equation of a line perpendicular to y +1 = -x that passesthrough the point (-8, 7).

Two lines are perpendicular if the product of their slopes is equal to -1.

Find the slope of the given line. Then, use that result to find the slope of a line perpendicular to it. Use the slope of the line perpendicular to the given line to find the equation of the one that passes through the point (-8,7).

To find the slope of the given line, write it in **slope-intercept** form by isolating **y**:

The coefficient of **x** is **-1**. Then, the slope of the given line is **-1.**

Let **m** be the line perpendicular to y+1=-x.

Since the product of the slopes of perpendicular lines is equal to -1, then:

[tex]\begin{gathered} -1\times m=-1 \\ \Rightarrow m=\frac{-1}{-1} \\ \therefore m=1 \end{gathered}[/tex]The equation of a line with slope **m** that passes through the point **(a,b)** in **slope-point** form is:

Replace m=1, a=-8 and b=7 to find the equation of the line perpendicular to y+1=-x that passes through the point (-8,7):

[tex]\begin{gathered} y=1(x-(-8))+7 \\ \Rightarrow y=(x+8)+7 \\ \therefore y=x+15 \end{gathered}[/tex]**Therefore, the equation of the line perpendicular to y+1=-x that passes through (-8,7) is:**

Find the indicated angle 0. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 120 and c = 136. Round your answer to two decimal places.)

Base on the given data, the triangle is shown below.

Apply law of sine to this triangle implies,

[tex]\sin \theta=\frac{a}{c}[/tex]Given that, *a=*120 and *c=*136. Thefore, the given equation becomes,

Take the inverse to find the the measure of indicated angle.

[tex]\begin{gathered} \theta=\sin ^{-1}0.88 \\ \theta=61.64 \end{gathered}[/tex]Therefore, the angle is 61.64 degree.

Jolie is redesigning a water bottle to fit better in her cup holder. The diameter will have to be no larger 2.5 in. The water bottle is straight up and down. What would the height of the bottle be if she wants it to have a 99.34 in3 volume. (Round to nearest whole number)

Answer:

20in

Explanations:The water bottle in question is known to be **cylindrical in shape.** The formula for calculating the** volume of a cylinder** is expressed as:

where;

r is the **radius**

h is the **height**

**Given the following** parameters

diameter = 2.5in

radius = 2.5/2 = 1.25in

volume = 99.34 in^3

**Required**

Height of the water bottle

**Substitute the given parameters** intothe formula

The **height** of the water bottle will be** 20in**

2. A membership to the theme park is $48 per year. Marcos cancelled his membership early and is only required to pay for 0.25 of a year. How much will he need to pay?

**Marcos** needs to pay $12 for 0.25 of a year due to **cancelling** the **membership**

Membership cost to the **theme** park per year = $48

**Payment** required to be made by Marcos = 0.25 of a year

When we divide a whole into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a **decimal** number has the same decimal place value system as the complete number. However, as we proceed to the right following the decimal point, we obtain the fractional portion of the decimal number.

Converting the decimal into a fraction we get:

=0.25

= 25/100

= 1/4 of a year

So, Marcos needs to pay the membership fees for only 1/4 of a year

According to which we get: 48*1/4 = $12

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To rent a certain meeting room, a college charges a reservation fee of $46 and an additional fee of $6.70 per hour. The math club wants to spend less than$106.30 on renting the meeting room.What are the possible amounts of time for which they could rent the meeting room?Use t for the number of hours the meeting room is rented, and solve your inequality for t.

As given by the question

There are given that the college charges a reservation fee of $46.

Now,

According to the question, the inequality is:

[tex]46+6.70t<106.30[/tex]Then,

To solve the above inequality, collect the constant terms on the right side

So,

[tex]\begin{gathered} 46+6.70t<106.30 \\ 6.70t<106.30-46 \\ 6.70t<60.3 \\ t<\frac{60.3}{6.70} \\ t<9 \end{gathered}[/tex]Hence, t**he room could be rented for up to 9 hours less than the stated amount.**

Given l ∥ m ∥ n, find the value of x.

**Answer:**

[tex]x = \frac{ - 23}{3} [/tex]

**Step-by-step explanation:**

everything u need is in the picture

can you help me factor the expression x^2+4x-21

To factor this expression we need to find two numbers which sum is 4 and the product is -21.

Now, 21 has only 2 factors (besides 1 and 21), 7 and 3, se we need to write them in a way such that they sum 4, so

[tex]x^2+4x-21=(x+7)(x-3)[/tex]we see that 7-3=4 and 7(-3)=-21, so the factorization is correct.

Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?

As per the given **percentage**, there are **147** **students **are not take French their freshman year.

**Students**:

The students are the person formally engaged in **learning**, especially one enrolled in a **school or college.**

Given,

Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students.

Here we need to find the number of students who are not take French as their freshman year.

Let x be the total number of students in the **freshman **year.

So according to the given question, we know that,

72% of x = 378

Therefore, we have to find the value of x, so we have to move the others,

Then we get,

x = 378/72%

x = 378 x 100/72

x = 525

So, the total number of students are 525.

Then the students who are not taken French is,

=> 525 - 378 = 147

Therefore, the students who are not taken French is 147.

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The product of the digits of a five-digit number is 6! (factorial). How many such numbers are there

There are 720 of such numbers that consists of five-digits which their product is 6! by **permutation**.

The mathematical term **permutation** can simply be defined as a process of **arrangement** or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.

We can apply the formula for **permutation**;

[tex]p(n,r) = \frac{n!}{(n - r)!} [/tex]

where n = total number of object and r = number of objects selected.

We can calculate the **arrangement** by applying the **permutation** formula as follows

[tex]p(6,5) = \frac{6!}{(6- 5)!}[/tex]

[tex]p(6,5) = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{1!}[/tex]

[tex]p(6,5) = \frac{720}{1}[/tex]

[tex]p(6,5) = 720[/tex]

Hence, with good application of the formula for **permutation**, we can say that there are 720 **arrangement** of such numbers which their product is 6!.

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Identify the pre-image and the image. Then determine if the transformation is a rigid motion or not

The pre-image is the figured formed by the points VWUST and the image is V'W'U'S'T'.

To produce the image from the pre-image a rotation is performed around the point (2, -2). A rotation doesn't change the dimensions of the figure, therefore** it is not a rigid motion**.

Use inverse matrices to find the solution to the system of equations represented by this matrix equation

[tex]\frac{1}{detA}\begin{bmatrix}{d} & {-b} \\ {-c} & {a}\end{bmatrix}[/tex]

if you replace it in that order, it should give you the answer

[tex]\begin{bmatrix}{2} & {-3} \\ {-3} & {5}\end{bmatrix}[/tex]Identify a solution to the system of equation

-4x+ 3y=23

x - y =7

**x = - 44 and y = - 51**

**How are the linear equations solved?**

-4x+ 3y=23 ---(1)

x - y =7 ----(2)

4*(2) => 4x- 4y =28 ---- (3)

(3) + (1)

4x- 4y =28 (+)-4x+ 3y=23

- y = 51

** y = -51**

Substituting y in (2)

x - y =7

x + 51 = 7

**x = -44**

**What are linear equations ?**

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**Answer: x = -2**

** y = 5**

**Step-by-step explanation:**

-4x+3y=23

x-y= -7

First take x-y= -7 and make it x=-7+y place it into the first equation

-4 (-7+y)+3y = 23

28-4y+3y = 23

28-y = 23

+y +y

28=23+y

-23 -23

5=y

Not that you have y you can replace it into the original

-4x+3(5)=23

-4x+15=23

-15=-15

-4x = 8

x= -2

The answer would be (-2,5)

PLS HELP WILL MARK YOU BRAINLIEST!!

Point B is the midpoint of AC. AB=2x and AC=3x+20.

What is the value of x?

x=-20

x=20

x=4

x=6

**Answer:**

X=4

**Step-by-step explanation:**

i got the answer on a different app

**Answer: The correct answer is 20 or -20**

**Step-by-step explanation:**

its between 20 and -20 since i selected x=6 and x=4 and they were both wrong lol

(Solve the problem down below & simplify the answer. Round to the nearest hundredth as needed.)

From the given information, we know that the decreasing function values is

[tex]V(t)=3600(3^{-0.15t})[/tex]and we need to find the time t when V(t) is equal to $1200. Then by substituting this values into the function, we have

[tex]1200=3600(3^{-0.15t})[/tex]By dividing both sides by 3600, we get

[tex]3^{-0.15t}=\frac{1200}{3600}=\frac{1}{3}[/tex]So we have the equations

[tex]3^{-0.15t}=\frac{1}{3}[/tex]From the exponents properties, we know that

[tex]3^{-0.15t}=\frac{1}{3^{0.15t}}[/tex]so we have

[tex]\frac{1}{3^{0.15t}}=\frac{1}{3}[/tex]or equivalently,

[tex]3^{0.15t}=3[/tex]This means that

[tex]0.15t=1[/tex]Then, by dividing both sides by 0.15, we obtain

[tex]t=\frac{1}{0.15}=6.6666[/tex]So, by rounding to the nearest hundreadth, **the answer is 6.67 years**

need help for mathhh

Using **implicit differentiation,** the rates are given as follows:

**2.** dV/dt = 144π cm³/sec.

**3. **dh/dt = 2/5π cm/s.

**4. **dr/dt = -0.2/π cm/day.

The volume of an sphere of **radius r **is given by the following equation:

[tex]V = \frac{4}{3}\pi r^3[/tex]

Applying implicit differentiation, differentiating both variables relative to t, the **rate of change** is given as follows:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

For **item 2,** the parameters are given as follows:

[tex]\frac{dr}{dt} = 2, r = 4[/tex]

Hence the **rate **is given as follows:

dV/dt = 4π x 4² x 2 = 144π cm³/sec.

For** item 4,** the **parameters **are:

[tex]\frac{dV}{dt} = -0.2, r = 5[/tex]

Negative because the orange is shrinking.

Hence the **rate **of the radius can be found as follows:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

[tex]-0.2 = 4\pi (5)^2\frac{dr}{dt}[/tex]

dr/dt = -0.2/100π

dr/dt = -0.2/π cm/day.

What is the rate of change of the volume of an cylinder?The volume of a cylinder of **radius r and height h** is given as follows:

[tex]V = \pi r^2h[/tex]

The **rate of change** of the volume as a function of time is given by:

[tex]\frac{dV}{dt} = 2\pi rh\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]

For **item 3**, the parameters are given as follows:

[tex]r = 5, \frac{dV}{dt} = 10, \frac{dr}{dt} = 0[/tex]

The radius is of 5 as r² = 25, due to the area of the base.

Hence the **rate **of change of the **height **is found as follows:

[tex]\frac{dV}{dt} = \pi r^2\frac{dh}{dt}[/tex]

10 = 25π dh/dt

dh/dt = 10/25π

dh/dt = 2/5π cm/s.

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Find f(g(3)).f(x)=2x-5g(x) = 1 + x²f(g(3)) = [?]

[tex]\begin{gathered} f(x)=2x-5 \\ g(x)=1+x^2 \end{gathered}[/tex]

To find the value of the given composition of functions you follow the next steps:

1. Find g(3):

[tex]\begin{gathered} g(3)=1+3^2 \\ g(3)=1+9 \\ g(3)=10 \end{gathered}[/tex]2. Find f(g(3)) or f(10):

[tex]\begin{gathered} f(g(3))=f(10) \\ f(g(3))=2(10)-5 \\ f(g(3))=20-5 \\ f(g(3))=15 \end{gathered}[/tex]Then, f(g(3)) is equal to 15Choose the equation that represents a line that passes through points (−3, 2) and (2, 1)

5x + y = −13

5x − y = 17

x − 5y = −13

x + 5y = 7

The **equation** that represents a line that passes through points (−3, 2) and (2, 1) is x + 5y = 7.

The **equation of the line** passes through the points (−3, 2) and (2, 1). The **equation of the line** can be represented as follows;

y = mx + b

where

m = slopeb = y-interceptTherefore, let's find the slope using (−3, 2) and (2, 1)

m = slope = 1 - 2 / 2 + 3

m = - 1 / 5

Therefore,

slope = - 1 / 5

Let's find the y-intercept of the line using (2, 1)

y = - 1 / 5 x + b

1 = - 1 / 5 (2) + b

b = 1 + 2 / 5

b = 5 + 2/ 5

b = 7 / 5

Therefore, the **equation of the line** can be represented as follows:

y = - 1 / 5 x + 7 / 5

5y = -x + 7

5y + x = 7

x + 5y = 7

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Write the inequality shown by the shaded region in the graph with the boundary line y = -3x +5

Inequality is an inequality comparison of numbers or expressions.

Given inequality:

y < -3x+5, y < x+2, y < -1

Graph the above inequality using Geogebra's online graphing calculator.

**Answer:**

...................... Hoffe er u

In the distribution shown, state the mean and the standard deviation. Hint: The vertical lines are 1 standard deviation apart.

We are given a distribution graph.

The mean of the distribution is the center that is **125.**

The **standard deviation** is given by

**Therefore, the mean of the distribution is 125 and the standard deviation is 28.**

All eleven letters from the word MATHEMATICS are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having a vowel written on it?

Let:

A = Get a paper having a vowel written on it

N = Total number of letters = 11

a = Number of vowels = 4

so:

[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{4}{11} \\ P(A)\approx0.36 \end{gathered}[/tex]**Answer:**

**36%**

Four of the twelve members of the panel were late for

the meeting. What fraction of the members were on

time?

**Answer:**

2/3

**Step-by-step explanation:**

If 4 were late, then 8 were on time.

8/12 Divide the top and bottom by 4

2/3

Find sinθ, tanθ, and secθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.sinθ=tanθ=secθ=

[tex]undefined[/tex]

1) We have here a right triangle, so we can use the Pythagorean Theorem to find the adjacent leg. Note that the hypotenuse is leg opposite to the right angle. In this case, a=4.

a²=b²+c²

4²=b²+3²

16=b²+9

16-9=b²

b=√7

2) Let's find the trigonometric functions. The first one is the sine (θ), which relates the opposite side and the hypotenuse:

[tex]\sin (\theta)\text{ =}\frac{3}{4}[/tex]2.2)Moving on, we can deal with the tangent of theta, relating the opposite side over the adjacent, for this one we have to rationalize it:

[tex]\begin{gathered} \tan (\theta)\text{ =}\frac{3}{\sqrt[]{7}} \\ \tan (\theta)=\frac{3\sqrt[]{7}}{7} \end{gathered}[/tex]Finally, let's find the reciprocal function of the cosine function by setting this as the reciprocal of the cosine, and then calculating it:

[tex]\begin{gathered} \sec \text{ (}\theta)=\frac{1}{\cos(\theta)}\Rightarrow\sec (\theta)=\frac{1}{\frac{\sqrt[]{7}}{4}}\Rightarrow\sec (\theta)\text{ =}\frac{4}{\sqrt[]{7}} \\ \sec (\theta)\text{ =}\frac{4\sqrt[]{7}}{7} \end{gathered}[/tex]on a map where each unit represents one kilometer two marinas are located at p(4,2) and q(8,12). if a boat travels in a straight line from one marina to the other how far does the boat travel. Answer choices: 14 kilometers 2sqrt296 kilometer 2sqrt5 kilometers

Solution:

Given the points below

[tex]p\left(4,2\right)and\text{ }q\left(8,12\right)[/tex]To find the distance between two points, the formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where point p represents coordinates 1 and point q represents coordinates 2

Substitute the coordinates into the formula above

[tex]\begin{gathered} d=\sqrt{(8-4)^2+(12-2)^2} \\ d=\sqrt{4^2+10^2} \\ d=\sqrt{16+100} \\ d=\sqrt{116} \\ d=\sqrt{4\times29} \\ d=2\sqrt{29}\text{ units} \end{gathered}[/tex]Since, 1 unit represents 1 kilometer on the map,

**Hence, the answer is**

1. Inconsistency #1Jay is the "criminal element of Woodlawn"Version 1:Version 2: He isn't really a criminal (just a small time weed dealer)Is Jay forgetting, fibbing, lying, or something else? Why would he change this part of his story?
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Anis a noteworthy deed. The KingArthur legends are full of stories of theof the Knights of the Round Table, includinLancelot and King Arthur himself.
If (-1, y) is a solution to the equation y = x + 5, determine the value of y.HELP I WILL MARK BRAINLIEST
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