Mathematics High School

1. In an auditorium, there are 21 seats in the first row and 26 seats in the second row. The number of seats in a row continues to increase by 5 with each additional row.

(a) Write an iterative (explicit) rule to model the sequence formed by the number of seats in each row. Show your work.

(b) Use the rule to determine how many seats are in row 15. Show your work.


2. Rhonda started a business. Her business made $40,000 in profits the first year. Her annual profits have increased by an average of 6% each year since then.

(a) Write an iterative rule to model the sequence formed by the profits of Rhonda’s business each year.

(b) Use the rule to determine what the annual profits of Rhonda’s business can be predicted to be 20 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end. Show your work.

3. The sequence 3, 12, 48, 192, … shows the number of pushups Kendall did each week, starting with her first week of exercising.

(a) What is the recursive rule for the sequence?

(b) What is the iterative rule for the sequence?

Answers

Answer 1
1. Let [tex]s_n[/tex] be the number of seats in the [tex]n[/tex]-th row. The number seats in the [tex]n[/tex]-th row relative to the number of seats in the [tex](n-1)[/tex]-th row is given by the recursive rule

[tex]s_n=s_{n-1}+5[/tex]


Since [tex]s_1=21[/tex], we have

[tex]s_2=s_1+5[/tex]
[tex]s_3=s_2+5=s_1+2\cdot5[/tex]
[tex]s_4=s_3+5=s_1+3\cdot5[/tex]
[tex]\cdots[/tex]
[tex]s_n=s_{n-1}+5=\cdots=s_1+(n-1)\cdot5[/tex]

So the explicit rule for the sequence [tex]s_n[/tex] is

[tex]s_n=21+5(n-1)\implies s_n=5n+16[/tex]

In the 15th row, the number of seats is


[tex]s_{15}=5(15)+16=91[/tex]

2. Let [tex]p_n[/tex] be the amount of profit in the [tex]n[/tex]-th year. If the profits increase by 6% each year, we would have

[tex]p_2=p_1+0.06p_1=1.06p_1[/tex]
[tex]p_3=1.06p_2=1.06^2p_1[/tex]
[tex]p_4=1.06p_3=1.06^3p_1[/tex]
[tex]\cdots[/tex]
[tex]p_n=1.06p_{n-1}=\cdots=1.06^{n-1}p_1[/tex]

with [tex]p_1=40,000[/tex].

The second part of the question is somewhat vague - are we supposed to find the profits in the 20th year alone? the total profits in the first 20 years? I'll assume the first case, in which we would have a profit of


[tex]p_{20}=1.06^{19}\cdot40,000\approx121,024[/tex]

3. Now let [tex]p_n[/tex] denote the number of pushups done in the [tex]n[/tex]-th week. Since [tex]3\cdot4=12[/tex], [tex]12\cdot4=48[/tex], and [tex]48\cdot4=192[/tex], it looks like we can expect the number of pushups to quadruple per week. So,

[tex]p_n=4p_{n-1}[/tex]

starting with [tex]p_1=3[/tex].

We can apply the same reason as in (2) to find the explicit rule for the sequence, which you'd find to be

[tex]p_n=4^{n-1}p_1\implies p_n=4^{n-1}\cdot3[/tex]
Answer 2

Answer:

i will look but i think she was right

Step-by-step explanation:

Related Questions

Find f(-7) if f(x) = 2x + 8.

Answers

Sub in -7 for x to get 2(-7)+8 which is -14+8=-6.  f(-7)= -6

if a train travels 25 miles in 2 hours and 15 minutes, what is it's average speed in miles per hour?
• 10 mph
• 11.1 mph
• 12.5 mph
• 9.1 mph

Answers

2 hours 15 mins = 2 1/4 hours

2 1/4 hours = 25 miles

1 hour = 25 ÷ 2 1/4 = 25 ÷ 9/4 = 25 x 4/9 = 11.1 miles

Answer: 11.1 mph

if a crate contains 25,500 oz of rice , about how many kg does it contains ? 1 pound equals 16 oz & 1 pound equals 0.454 kg

351 kg

724 kg

25500 kg

185000 kg

Answers

You have ounces and you want kilograms, so you need to multiply by a conversion factor that has ounces in the denominator and kilograms in the numerator. In order to keep from changing the value of the quantity you have, the conversion factor must have equivalent quantities in the numerator and denominaotr.

Your problem statement tells you that both 0.454 kg and 16 oz are equal to a pound, so they are also equal to each other. Their ratio (with kg on top and oz on the bottom) is a suitable conversion factor.

  [tex]25,500\,oz \times \dfrac{0.454\,kg}{16\,oz}=723.5625\,kg[/tex]

The best choice is ...
  724 kg
Final answer:

To find the mass of 25,500 ounces of rice in kilograms, one needs to convert ounces to pounds, then pounds to kilograms. After the conversions, the crate contains approximately 724 kg of rice.

Explanation:

To calculate the mass of 25,500 ounces of rice in kilograms, we first convert ounces to pounds and then pounds to kilograms using the conversion rates provided.

First, we need to find out how many pounds are equivalent to 25,500 ounces. We use the proportion 1 pound = 16 ounces.Divide the total number of ounces by 16 to find the number of pounds:Now, we'll convert pounds to kilograms: 1 pound = 0.454 kg.Multiply the number of pounds by the kilogram equivalent:

When we round this number to the nearest whole number, we get 724 kg, which is the approximate mass of the rice in the crate.

HELPPPPPPPPP and explain why

Answers

Answer: True

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x^2 = x*x
5x = 5*x
Both x^2 and 5x have a factor of x in common

x^2 + 5x = x*x + 5*x
x^2 + 5x = x*x + x*5
x^2 + 5x = x*(x+5) .... use the distributive property in reverse

x^2 + 5x factors to x*(x+5)

As a way to check, you can distribute the x back in
x*(x+5) = x*x + x*5
x*(x+5) = x^2 + 5x
and we get the original expression again

[tex] {x}^{2} + 5x \\ x(x + 5)[/tex]
notice there's no whole number in front of the x^2, so no number can factor out both terms, but both have at least one x, so one x factors out of both

What values of x makes the inequality true? 2(x−4)−9x≤-4x+13

Answers

Answer : x >= -7


On simplifying,

2x - 8 - 9x  <=  -4x + 13

-7x - 8 <= -4x + 13

-3x - 8 < = 13

-3x <= 21

x >= -7

Which regular polygon would have each of its interior angles measure 120°? hexagon heptagon octagon nonagon?

Answers

Hexagon.
____________

Which expression is equal to sin 75°? sin 135° cos 60° – cos 135° sin 60° cos 135° cos 60° + sin 135° sin 60° sin 135° cos 60° + cos 135° sin 60° cos 135° cos 60° – cos 135° cos 60°?

Answers

These are the sum/difference formulas in trigonometry. The first formula is in accordance with sin ( α - β ) = sinα *cosβ - cosα * sinβ. If we combine the first one with this formula, we'll obtain sin 135° cos 60° – cos 135° sin 60° = sin (135-60) = sin75° 

Answer:

The answer is A

The frequency of A4 is 440.00 Hz. What is the frequency of A6, which is two octaves above A4?
A) 110.00 Hz
B) 220.00 Hz
C) 880.00 Hz
D) 1760.00 Hz

Answers

The correct answer is: 1760.00 Hz

Explanation:
The formula to find the unknown frequency is:
(2^n)*f

Where n = Number of octaves above to the known frequency (A4) = 2
f = Known frequency (of A4) = 440 Hz

Hence
(2^2)*(440)
1760 Hz (of A6)

HELP WHOEVER ANSWERS CORRECTLY WILL BE BRAINLIEST!!!!

Answers

Find the surface area:

7.25 x 9.5 x 2 = 137.75 gets the surface area of the two rectangle sides.

To get the bottom rectangle, do 8 x 9.5 = 76

To find the two triangles, do 6 x 8 x 0.5 x 2 = 48

Now add them all together: 137.75+76+48=261.75

So, the answer is 261.75 square feet of material.

Ed and Marge were candidates for the city council. Marge won with 93 more votes than Ed. The total number of votes cast in the election was 587. Find the number of votes received by each candidate.

Answers

587-93=494
so ed had 494 votes
I think it would be 494/2=247 votes

) a quiz consists of 10 true or false questions. to pass the quiz a student must answer at least 7 questions correctly. if the student makes a random selection on each question, what is the probability that the student will pass the quiz? [ you may use distr key. show the command that was typed in to your calculator.]

Answers

3 out of 10 or 30% becasue if he is guessing and he has to get 7 out of 10 right then it would be 3 out of 10

2. The robot was initially placed at position (6,9), and at = 2 seconds, its position is (10,15).
a. How far did the robot travel in 2 seconds?

b. What is the speed of the robot?
Could you work it out

Answers

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 6 &,& 9~) % (c,d) &&(~ 10 &,& 15~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(10-6)^2+(15-9)^2}\implies d=\sqrt{4^2+6^2}\implies d=\sqrt{52} \\\\\\ d\approx 7.2[/tex]

what's its speed?  well, it traveled √(52) in 2 seconds, so is simply √(52)/2, which is about 3.6 units per second.

What are the zeros of f(x) = x(x – 8)?

A. x = 0 and x = 8
B. x = 0 and x = –8
C. x = 0 only
D. x = 8 only

Answers

f(x) will = 0 when either x = 0 or x = 8. Here's how you know.
if x = 0 then 0 * (x - 8) = 0 because anything multiplied by 0 is zero.

if x = 8 then 8 * (8 - 8) = 8 * 0 = 0

A <<<<<< Answer

The zeros of the function f(x) = x(x – 8) are x = 0 and x = 8, which correspond to each factor of the equation being set equal to zero. Therefore, the correct answer is option A.

To identify the zeros of the function f(x) = x(x – 8), we should solve for x when f(x) is set to zero. Setting the function equal to zero gives us the equation 0 = x(x – 8).

We can find the zeros by looking for the values of x that make each factor in the equation equal to zero. The first factor is x, and it is equal to zero when x = 0. The second factor is (x – 8), which is equal to zero when x = 8.

Therefore, the zeros of the function f(x) are x = 0 and x = 8.

Selection A is the correct answer: The zeros of the function x(x – 8) are x = 0 and x = 8.

Select the objects that hold the same amount of liquid as a 98 fluid ounce jug

Answers

To answer this question, you need to know how many fluid ounces are in a pint and in a quart.  None of the choices reflect 98 fl oz, so I showed the ones that would hold 96 fluid ounces.

1 cup = 8 fl oz
2 cups = 16 fl oz
1 pint = 2 cups, so 1 pint also equals 16 fl oz.

2 pints equal 1 quart, so 16 x 2 = 32 oz (the number of fluid ounces in a quart)

1 pint - 16 fl oz
1 quart = 32 fl oz

Choice A: 3 quarts x 32 =96 fl oz.
Choice B: 2 quarts x 32 = 64 fl oz
Choice C: 2 quarts  x 32 + 2 pints x 16 = 64 + 32 (96 fl oz)
Choice D: 1 quart x 32 + 8 cups x 8 = 32 + 64 (96 fl oz)
Choice E: 2 cups x 8 + 2 pints x 16 = 16 + 32 (48 fl oz)

Change -40° to radians.


A). 2π/9

B). -2π/9

C). 4π/9

D). -4π/9





Answers

To solve this, we are going to multiply our degrees by a conversion factor. Remember that 1°=[tex] \frac{ \pi }{180} [/tex], so to convert -40° to radians, we are going to multiply -40° by the conversion factor [tex] \frac{ \pi }{180} [/tex]; that way we can cancel degrees and express our answer in radians:

(-40°)[tex] (\frac{ \pi }{180} )= -\frac{2 \pi }{9} [/tex]

We can conclude that the correct answer is: B). -2π/9

A recipe calls for 5 8 pound of cheese per batch. Assuming you have enough of the other ingredients, how many batches of the recipe can you make with 5 pounds of cheese?

Answers

I assume you mean 5/8 of a pound not 58 pounds. In that case convert your total number of pounds into eights to make it easier to calculate. 5 pounds is equal to 40/8 pounds of cheese. Now divide this by 5/8. That equals 8. SO you can make 8 batches.

what percentage does the third quartile represent?

Answers

Since the data is split, the third quartile would represent 25% of the total data, but the top 75%. It depends what the problem is asking.
The third quartile (also called the upper quartile) has 75 percent of the data below it and the top 25 percent of the data above it on a box and whisker plot! Hope this helps!

Express the fraction in simplest form.
9/12

a.2/3
b.3/4
c.12/16
d.10/13

Answers

[tex]\dfrac{9}{12}=\dfrac{9:3}{12:3}=\dfrac{3}{4}[/tex]


[tex]Answer:\ \boxed{b.\ \dfrac{3}{4}}[/tex]

A radio station wants to determine whether its audience would like to listen to more rap music. It asks its listeners to call in and participate in a survey. Each listener is asked: “Do you want us to play more rap music or less rap music?” One hundred fifty listeners call in, and their responses are recorded.
What is the focus of the study?


The type of music listeners want to hear.


The playing of rap music.


The number of listeners who respond.


The response of the listeners.

Answers

A radio station made a survey of their listeners to determine whether the audience would like to listen to more rap music. They asked the question “Do you want us to play more rap music or less rap music?” The station recorded one hundred fifty listeners who call in.

The focus of the study is about the playing of the rap music because it is what the question is about. Not the type of music listeners want to hear, nor the number of listeners who respond nor the response of listeners.

the response of listeners to give opinion on to play more or less rap music

which undefined geometric term is described as a two dimensional set of points that has no beginning or end

Answers

is a Line

It is a series of 2 points that has no beginning or an end and is two-dimensional.

NEED HELP ASAP!!!
find the equation that goes through points (18,3) and (21,1) find slope and y-intercept

Answers

To effectively and correctly answer this and help we'll need a photo diagram for the question. We need to see a graph of some sort to even know where to start this off. It'd probably be solvable without a diagram if you don't have one, but I don't think that many people have the skill to do so (at least I don't). I know how terrible I feel when no one answers my questions, so I thought I'd let you know why others might not be answering this for you. I'm pretty sure you can update the question and attach a photo (an actual photo or a screenshot) to it, via the paperclip icon. Have a great day! :)

Find the length of the third side of a right triangle with a hypotenuse of 17 and a leg of 10.

Answers



You need to use the Pythagorean theorem.
[tex]{a}^{2} + {b}^{2} = {c}^{2} [/tex]
The hypotenuse is "c" and each leg is either "a" or "b".
[tex] {10}^{2} + { x}^{2} = {17}^{2} [/tex]
[tex]100 + {x}^{2} = 289 \\ {x}^{2} = 189 \\ x = 13.7477270849[/tex]

Dylan opened a credit card account with $675.00 of available credit. Now that he has made some purchases, Dylan's account only has $384.75 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?

Answers

The percent decrease would be 43%:

675-384.75=290.25

290.25/675=.43*100%=43%

Gary number has 6 in thousands and a7 in hundred and a 5 in ones. when rounded to the nearest ten, the number is 6760. what is gary's number

Answers

Gary’s number is 6755.

If a number is 5 or more, round up.

If a number is 4 or less, round down.

I hope this helps!

A park in a subdivision has a triangular shape. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53 degrees. Find the area of the park to the nearest square foot.

Answers

Answer:

The area of the park is 1,11,739 square feet.

Step-by-step explanation:

Since, the area of a triangle is,

[tex]A=\frac{1}{2}\times s_1\times s_2\times sin\theta[/tex]

Where, [tex]s_1[/tex] and [tex]s_2[/tex] are the adjacent sides and [tex]\theta[/tex] is the included angle of these sides,

Here, the two adjacent sides of the park are 533 feet and 525 feet, while, the angle included by these sides is 53°.

That is,  [tex]s_1[/tex] = 533 ft, [tex]s_2[/tex] = 525 ft and [tex]\theta[/tex] = 53°,

Hence, the area of the park is,

[tex]A=\frac{1}{2}\times 533\times 525\times sin 53^{\circ}[/tex]

[tex]=\frac{279825\times 0.79863551004}{2}[/tex]

[tex]=\frac{223478.181599}{2}=111739.090799\approx 111739\text{ square ft}[/tex]

a newspaper carrier earns a fixed amount for each newspaper he delivers, and yesterday his average hourly wage was 7.50 an hour. If he worked 4 hours yesterday and delivered 120 newspapers, how much does he earn for each newspaper delivered?

Answers

 answer would be; $0.25

I keep getting 70 but that's not an answer??

Betty's bite size candies are packaged in bags the number of candies per bag is normally distributed with a mean of 50 candies and a standard deviation of 3. At a quality control checkpoint a sample of bags is checked and 12 bags contain fewer than 47 candies how many bags were probably taken as samples?

a) 15
b) 75
c) 36
d) 24

Answers

The standard deviation is 3 , so 50 -47 = 3, means the 47 candies is 1 deviation below the mean.

A normal distribution, 68% of the sample falls within 1 standard deviation, which means 100-68 = 32 is out side the mean. Half of that, 32 / 2 = 16% is above and the other half (16%) would be below.

 12 bags were below, so we would do a ratio, with the percentages as a whole number, so 16% = 16 and 100% = 100:

12/16 = X/100

Cross multiply: 16x = 1200

Divide both sides by 16:
X = 1200/16
X = 75
 

The answer is 75 bags were tested.


Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given XY = WZ and XW = YZ
a.

No; you cannot determine that the quadrilateral is a parallelogram.


b.

Yes; two opposite sides are both parallel and congruent.


c.

Yes; opposite sides are congruent.


d.

Yes; diagonals of a parallelogram bisect each other.

Answers

The best answer is Letter C - Yes, opposite sides are congruent.

If both pairs of opposite sides of a quadrilateral are congruent, then you'll always have two opposite pairs of parallel sides. Congruent means that they measure the same. Since two congruent sides separating the other pair of opposite sides must always keep those opposite lines the same distance apart, then, the opposite sides are also parallel.

From the information provided a.  No; you cannot determine that the quadrilateral is a parallelogram.

A parallelogram is a quadrilateral (has four sides and four angles) in which opposite sides are parallel and congruent to each other. The diagonals of a parallelogram bisect each other.

Given XY = WZ and XW = YZ, this means that the opposite sides are congruent.

Just from the information provides,  we cannot determine that the quadrilateral is a parallelogram.

Find out more at: https://brainly.com/question/555469

what is the solution to the following system of equations (3x-4y=-25)( 3x+ 4y=5)? PLEASE HURRY!!!!!!!!!!!

Answers

[tex]\underline{+\left\{\begin{array}{ccc}3x-4y=-25\\3x+4y=5\end{array}\right}\\.\ \ \ \ \ \ 6x=-20\ \ \ \ |:6\\\\x=-\dfrac{20}{6}\\\\x=-\dfrac{10}{3}[/tex]
substract the value of x to the second equation:
[tex]3\cdot\left(-\dfrac{10}{3}\right)+4y=5\\\\-10+4y=5\ \ \ |+10\\\\4y=15\ \ \ \ |:4\\\\y=\dfrac{15}{4}[/tex]
[tex]\left\{\begin{array}{ccc}x=-\dfrac{10}{3}\\\\y=\dfrac{15}{4}\end{array}\right[/tex]

algebra mid-unit review quiz Unit 3 lesson 5

1. simplify the rational expression; 2m^2 - 72/ m - 6.

A. 2 ( m+6)
B. 2
C. 2 ( m-6)
D. m + 12

2. simplify the rational expression; -8z^2/ z^4 - z^2.

A. -8z
B. -8
C. -8/ z^2
D. -8/ z^2 - 1

3. simplify the rational expression; 6x-54/ 7x-63.

A. - 6/7
B. 6/7
C. 6(x-9)/ 7
D. 6/ 7 (x-9)

Answers

Please check, i'm not entirely sure but i'm decent enough. 
1 is A 2 is D3 is B
Good luck. 
Final answer:

The solutions to the problems in the mid-unit review quiz for Algebra Unit 3 Lesson 5 are A(2(m+6)), D(-8/(z^2-1)), and B(6/7). These are found by factoring out common factors and simplifying the expressions.

Explanation:

Let's solve the algebra mid-unit review quiz Unit 3 lesson 5 one by one.

To simplify the rational expression 2m^2 - 72/ m - 6, first factor out a 2 from the numerator to obtain 2(m^2 - 36). This can be further broken down as 2(m - 6)(m + 6). Given the denominator is (m - 6), we cancel out (m - 6) from both the numerator and denominator to get the answer as 2(m+6) hence option A is correct.To simplify the rational expression -8z^2/ z^4 - z^2, first take out -8z^2 from the numerator to get -8*z^2/z^2*(z^2 - 1). On simplifying, we are left with -8/(z^2-1), i.e. option D is correct. To simplify the rational expression 6x-54/ 7x-63, we factor out a 6 from the numerator and a 7 from the denominator. This gives us 6(x - 9)/7(x - 9). By cancelling out the common factor, (x - 9), we get 6/7, i.e., option B is correct.

Learn more about Algebra simplification here:

https://brainly.com/question/34472544

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