The pyramid shown below has a square base, a height of 7, and a volume of 84. what is the length of the side of the base?

Answers

Answer 1
Volume of a pyramid is (length * width * height) / 3

So we plug in the given information and solve. Let x = length and width since it's a square their measurements are the same.

84 = (x * x * 7) or 84 = 7x²

Divide both sides by 7 to isolate the squared variable. 

x² = 12

Now square root both sides to isolate the variable

x = √12 which simplifies to x = 2√3

The measurements for the length and width of the base are 2√3 units or approximately 3.464 units. 
Answer 2

The length of the side of the base is 6 units.

What is the volume of the pyramid?

The volume of the pyramid is;

[tex]\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base[/tex]

The pyramid shown below has a square base, a height of 7, and a volume of 84.

Substitute all the values in the formula

[tex]\rm Volume \ of \ pyramid=\dfrac{1}{3}\times height \times Base\\\\\rm84 =\dfrac{1}{3}\times height \times 7\\\\Height = \dfrac{84\times 3}{7}\\\\ Height = \dfrac{252}{7}\\\\Height =36[/tex]

The length of the side of the base is;

[tex]\rm Side\ length^2=height\\\\ Side\ length^2=36\\\\Side\ length^2=6^2\\\\Side\ length=6[/tex]

Hence, the length of the side of the base is 6 units.

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Related Questions

The domain of {(x, y): y = 2x² + 1 is

Answers

Answer:
Domain: (- ∞, ∞)

Explanation:
The equation y = 2x² + 1 is a somewhat narrow parabola translate up 1 unit on the y-axis from the origin (0, 0). The domain of a graph indicates which x-values the diagram can potentially reach, or how far it can travels on the x-axis.

Because it is a parabola, it goes infinitely in both directions of the x-axis. Therefore, its domain is (-∞ ,∞)

Final answer:

The domain of the function y = 2x² + 1 is all real numbers, which is expressed as [tex]\( (-\infty, +\infty) \)[/tex]

Explanation:

The domain of a function refers to the set of all possible input values for which the function is defined. In the case of the function [tex]\( y = 2x^2 + 1 \)[/tex], it is a quadratic function, meaning it is defined for all real numbers [tex]\( x \).[/tex]

The function[tex]\( y = 2x^2 + 1 \)[/tex] involves squaring [tex]\( x \)[/tex], which can result in any real number. Since there are no restrictions on the values that[tex]\( x \)[/tex] can take, the domain of this function is all real numbers. Mathematically, we denote this domain as[tex]\( (-\infty, +\infty) \)[/tex].

This implies that for any real number you substitute in for [tex]\( x \)[/tex], the function [tex]\( y = 2x^2 + 1 \)[/tex] will produce a corresponding real number for [tex]\( y \).[/tex] There are no values of [tex]\( x \)[/tex] for which the function becomes undefined or non-existent.

Graphically, this function represents a parabola that opens upwards, covering all real values of [tex]\( x \)[/tex] along the x-axis. Therefore, the domain encompasses the entire real number line without any gaps or exclusions.

WHERE MY MATH FOLK AT?!?!

A cylindrical container, which will be used to collect oil, has a circumference of 15.5 in. and a height of 8 in.

Which estimate best approximates the amount of oil the container can hold?

Answers

The vol. of a cyl. is given by V = pi*r^2*h, where r is the radius and h is the height.  If the circumf. of the base of the container is 15.5 in, then the radius is

       15.5 in
r = ------------ = 2.468 in.
          2*pi

Then the vol. of this cyl. is    V = pi*r^2*h = pi * (2.468 in)^2 * (8 in).  Complete the arithmetric and you'll then have your answer.

The equation of the line through ab *write your answer in slope-intercept form

Answers

Sounds as tho' you have a line going thru two points, A and B, but you have not shared those points.  Please do so.

But we can assume that A:(a,b) and B:(c,d), find the slope and then write the equation of the line thru points A and B:
          
          d - b
m = -----------
          c - a
                                                                d - b
then the equation of the line is   y-d = ----------- (x-c)
                                                                c - a

Please ensure that you are sharing all of the info given (e. g., the coordinates of the points A and B).

GIVING AWAY 50 POINTS TO WHOEVER SHOWS LEGIT WORK!
The lengths of the sides of three squares are s, s + 1, and s + 2. If their total area is 365 cm squared (^2), find their total perimeter.

Answers

S= one length of square 1
S+1 = one length square 2
S+2= one length square 3

Our equation would be
S^2+(S+1)^2+(S+2)^2=365

Idk if it would be called distribute but.. distribute
S^2+S^2+2S+1+S^2+4S+4=365

Add like terms
3S^2+6S-360=0

Divide everything. By 3
S^2+2S-120=0

Factor
(S-10)(S+12)=0

The two solutions are:

S-10=0
S=10

S+12=0
S=-12

Since a length can’t be a negative the only possible solution would be 10

Since a perimeter is all lengths added together we can multiply the length by four to get the perimeter

Square 1
10*4=40
Perimeter is 40cm

Square 2
S+1 =11
11*4=44
Perimeter is 44cm

Square 3
S+2=12
12*4=48
Perimeter is 48cm

Add all the perimeters together to get the total perimeter:

Total perimeter:
40+44+48=132

The total perimeter is 132cm

I hope this helps. Sorry if I messed up anything on here it was kinda hard to keep track of everything. Feel free to ask if you need anything cleared up :)

Which box plot represents the data?
30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40

Answers

your answer would be A after you found the 5 number sequence.
The answer would be A.

) a pair of fair dice is rolled. what is the probability that the sum of the top faces is a number 10 or greater?

Answers

possible number combinations are 1,1  2,1  3,1  4,1  5,1  6,1  1,2  2,2  3,2  4,2  5,2  6,2  1,3  2,3  3,3  4,3  5,3  6,3  1,4  2,4  3,4  4,4  5,4  6,4  1,5  2,5  3,5  4,5  5,5  6,5  1,6  2,6  3,6  4,6  5,6 and 6,6. of those 36 number combinations the ones that add up to more than 10 include: 4,6  5,5  5,6  6,4  6,5  6,6. thats 6 number combinations. 6/36 of the possible sums of the top faces equal out to 10 or more. 6/36=1/6=0.166666666666666666666666(repeating) and to put that in a percentage, 16.7%
the probability is 16.7%
Hope this helps.

A group consists of 6 men and 5 women. three people are selected to attend a conference. in how many ways can 3 people be selected from this group of​ 11? in how many ways can 3 men be selected from the 6​ men? find the probability that the selected group will consist of all men.

Answers

Men = 6
Women = 5
Total number = 6+5 = 11

First question:
This is a question of combination.
Total number of selecting 3 people from the group = 11C3 = 11!/[3!(11-3)!]= 165 ways

Second question:
This is question of combination where only men are considered.
Total number of collecting 3 men from 6 men = 6C3 = 6!/[3!*(6-3)!]= 20 ways

Third question:
The probability that the 3 people selected will all be men is given by:
1st selection: 6/11
2nd selection: 5/10
3rd selection: 4/9
The probability = 6/11*5/10*4/9 = 4/33

1.

[tex] \displaystyle
\binom{11}{3}=\dfrac{11!}{3!8!}=\dfrac{9\cdot10\cdot11}{2\cdot3}=165 [/tex]

2.

[tex] \displaystyle\binom{6}{3}=\dfrac{6!}{3!3!}=\dfrac{4\cdot5\cdot6}{2\cdot3}=20 [/tex]

3.

[tex] |\Omega|=165\\
|A|=20\\\\
P(A)=\dfrac{20}{165}=\dfrac{4}{33}\approx12\% [/tex]

A bag contains 3 red, 4 black and 2 white balls. what is the probability of drawing a red ball and then a white ball, if each ball is returned to the bag immediately after it is drawn? 2/27 1/9 1/3 4/27 2/9

Answers

Total number of balls = 3 + 4 + 2 = 9
red ball = 3
white ball = 2

P(red, then white) = (3/9)(2/9) = 6/81 = 2/27

Answer: 2/27


The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 115 grams of a radioactive isotope, how much will be left after 3 half-lives? Use the calculator provided and round your answer to the nearest gram.

Answers

1st half-life: 115/2 = 57.5 grams
2nd half-life: 57.5/2 = 28.75 grams
3rd half-life: 28.75/2 = 14.375 grams = 14 grams

After 3 half-lives, approximately 14 grams of the radioactive isotope will be left.

We have,

To calculate the remaining mass of a radioactive isotope after a certain number of half-lives, we can use the formula:

Remaining Mass = Initial Mass * (1/2)^(Number of Half-Lives)

Given:

Initial Mass = 115 grams

Number of Half-Lives = 3

Substituting the values into the formula, we get:

Remaining Mass = 115 * (1/2)^3

Calculating this expression:

Remaining Mass = 115 * (1/2)³

Remaining Mass = 115 * (1/8)

Remaining Mass = 14.375

Rounding to the nearest gram, the remaining mass is approximately 14 grams.

Therefore,

After 3 half-lives, approximately 14 grams of the radioactive isotope will be left.

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Solve for x: 12(x-7)+3(2x+2)=50x-62

Answers

X= -1/2

Hope this helps
x = -1/2

This is because
12 (-1/2 - 7) + 3 (2 x -1/2 + 2) = 50x - 62
12 x -7.5 + 3 x 1 = -25 - 62
-87 = -87

If a borrower obtains an interest-only loan of $112,500 at an annual interest rate of 6%, what is the monthly interest payment (rounded to the nearest $1)?

Answers

Loan amount = $112,500
Annual interest rate = 6% = 0.06

Interest per year = Principal amount * Annual interest rate = 112,500*0.06 = $6,750

Monthly payment interest = Annual interest/12 = $6,750/12 = $562.50

A certain website averages 4.9 hours of downtime per month with a standard deviation of 0.5 hours. In April, it had 3.5 hours of downtime. What z-score does the 4.5 correspond to?

Answers

The z-score of an observation is a convenient way to compare different distributions to each other. The z-score is defined mathematically as [tex] \frac{x-m}{s} [/tex] where m is the mean and s is the standard deviation. Intuitively, this means that we account for how far off the center of the distribution this observation is, while simultaneously taking into account the spread of the distribution. Substituting x=3.5, m=4.9 and s=0.5, we get that z=-2.8. Negative z-scores imply observations below the mean.

The sum of the squares of two consecutive positive even integers is 100. find the two integers

Answers

The integers are 6 and 8
6^2= 36
8^2=64
36+64=100

Let's denote the two consecutive positive even integers as x and x+2.

We know their squares sum up to 100, represented mathematically as:

x^2 + (x + 2)^2 = 100.

Expanding this equation, we get:

x^2 + x^2 + 4x + 4 = 100.

Combining like terms gives us:

2x^2 + 4x - 96 = 0.

This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = 4, and c = -96.

We can solve this quadratic equation for x using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a.

Substituting a, b, and c into this formula, we find that:

x = [-4 ± sqrt((4)^2 - 4*2*-96)] / 2*2,
x = [-4 ± sqrt(16 + 768)] / 4,
x = [-4 ± sqrt(784)] / 4,
x = [-4 ± 28] / 4.

So the solutions are x = (28 - 4) / 4 = 6 and x = (-28 - 4) / 4 = -8.

Since we are looking for positive even integers, we discard the negative solution.

Therefore, the two consecutive positive even integers are 6 and 6 + 2 = 8.

In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049

Answers

Population in 2010, P(o) = 1,405,233
Rate of decrease, R = 1.1% = 0.011

Applicable formula

P(n) = P(o) *(1-R)^n

Where P(n) = population after n years, n = Number of years
From information given,
1,200,000 = 1,405,233 (1-0.011)^6
1,200,000/1,405,233 = (0.989)^n
0.85395 = (0.989)^n
ln (0.85395) = n ln (0.898)
n = [ln (0.85395)]/[ln (0.989)] = 14.27 years ≈ 14 years
Year in which population will fall below 1,200,000 = 2010+14 = 2024

Then, the correct answer is a.

Answer:

2024

Step-by-step explanation:

took the test

A lucky integer is a positive integer which is divisible by the sum of its digits. what is the least positive multiple of 9 that is not a lucky integer?

Answers

99. 

It is not divisible by 18. Before that they are all added up to 9. 

Solve the problem. 13) from the edge of a 1000-foot cliff, the angles of depression to two cars in the valley below are 21° and 28°. how far apart are the cars? round your answers to the nearest 0.1 ft.

Answers

the cars would be 724.4 feet apart!!
Final answer:

The problem is about finding the distance between the cars using the angles of depression and the height of the cliff. Calculate individual horizontal distances first and then find their difference which gives us the distance between the cars.

Explanation:

This problem can be solved using trigonometry. We've a 1000-foot cliff and a valley below where the two cars are located. From the edge of the cliff, if we draw two lines of sight to the cars, we can get two right triangles. The angles of depression to the cars are 21° and 28°, which are the angles between these lines of sight and a horizontal line.

We can use the tangent of these angles, which is the ratio of the opposite side (the vertical distance from the cliff to the cars) and the adjacent side (the horizontal distance from the cliff baseline to the cars). We know the vertical distance - it's 1000 ft (height of the cliff). So, we can calculate the horizontal distances (D1 and D2) to the cars as D1 = 1000/tan(21°) and D2 = 1000/tan(28°) respectively.

The difference between D1 and D2 will give the distance between the cars.

The calculations might give the distance in decimals, and the problem asks to round the answer to the nearest 0.1 ft.

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A regular pentagonal prism has 9-cm base edges. A larger, similar prism of the same material has 36-cm case edges. How does each indicated measurement for the larger prism compare to the same measurement for the smaller prism? A)volume B) weight

Answers

To compare the volumes of the prism we used the scale factor:
volume scale factor=(linear scale factor)³
the linear scale factor of the prism is:
(length of larger prism)/(length of smaller prism)
=36/9
=4
thus the volume scale factor will be:
4³=64
hence the volume of the larger prism is 4 times that of the smaller prism.
Do you have the answers to this quiz?

Please help! Vectors and angles
A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). The current has a velocity of 5 knots along a bearing of 213°. Find the resultant velocity and direction of the ship. (Remember that bearing is measured clockwise from the north axis).
1) 25 knots at 166.5 degree
2) 27 knots at 350 degree
3) 166.5 knots at 25 degree
4) 350 knots at 27 degree

Answers

The answer is A. I am doing Pearson Connexus and had this same question. It showed A was the correct answer to this question.

We have been given that a ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157°.

Further we have been given that current has a velocity of 5 knots along a bearing of 213°.

Therefore, angle between the direction of ship and direction of current will be

[tex]\theta = 213 - 157 = 56^{0}[/tex]

We can find the magnitude of resultant by using parallelogram law of vectors.

[tex]R=\sqrt{P^{2}+Q^{2}+2PQcos(\theta)}[/tex]

Upon substituting [tex]P=22, Q = 5 \text{ and }\theta = 56[/tex] in this formula, we get

[tex]R=\sqrt{22^{2}+5^{2}+2\cdot 22\cdot 5cos(56)}\\ R=\sqrt{484+25+220\cdot0.55919}\\ R=\sqrt{632.0224}\\ R=25.14 \text{ knots}[/tex]

Therefore, resultant velocity of the ship is 25.14 knots.

We find the angle of resultant from P, that direction of ship using the formula

[tex]\alpha = arctan(\frac{Qsin(\theta)}{P+Qcos(\theta)})[/tex]

Upon substituting the values, we get

[tex]\alpha = arctan(\frac{5sin(56)}{22+5cos(56)})\\ \alpha = arctan(\frac{4.14518}{24.79596})\\ \alpha = arctan(0.16717)\\ \alpha = 9.49^{0}[/tex]

Therefore, bearing of the resultant is [tex]157+9.49 = 166.49^{0}[/tex]

Hence, option (A) is the correct choice!

Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.

Answers

The additive inverse property states that when you add a number and its opposite (rational numbers), the result is zero. The reason is that the inverse of a number is the opposite, so if you have a number and when do the opposite with it (add the opposite), the result will be zero. This applies to adding!!!

Hope This Helped =3

Anyone help please!!!!

Answers

We are to verify the identity:

cos(α-B)-cos(α+B) = 2 sinα sinβ

Left hand side = cos(α - B)-cos(α + B) 

= cosα cosβ + sinα sinB - (cosα cosB - sinα sinβ)

= cosα cosβ + sinα sinB - cosα cosB + sinα sinβ)

= sinα sinβ + sinα sinβ

= 2 sinα sinβ

= Right Hand side

cos(a-B)-cos(a+B)
cosucosv - sinusinv = cos(u+v)
cosucosv + sinusinv = cos(u-v)

cos(a-B)-cos(a+ B) = cosa cosB + sina sinB - (cosa cosB - sina sinB)= cosa cosB + sina sinB - cosacosB + sinb sinB= 2 sina sinB

Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of height H and length L. What is the height of a wall that is 30 feet long and that requires 2,310 bricks to build? a. 12 ft c. 11 ft b. 10 ft d. 20 ft

Answers

plug in 30ft for L and 2310 for n so you will get 2310=7(30)(h)... h would equal 11ft

WILL GIVE BRAINLIEST IF YOU HAVE THE REST OF THE ANSWERS

Answers

Hey, I remember this. Connexus, right? 

I completed this a few months ago but don't remember the rest of the answers. Message me and I'll be able to find them for you, but anyway, I'm positive the answer is A.

Proof:
A=(123-55)/2=34

If x varies directly with y and x=3.5 when y=14 find x when y=18

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{x} varies directly with \underline{y}}\qquad \qquad x=ky\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} x=3.5\\ y=14 \end{cases}\implies 3.5=k14\implies \cfrac{3.5}{14}=k \\\\\\ \cfrac{1}{4}=k\qquad therefore\qquad \boxed{x=\cfrac{1}{4}y} \\\\\\ \textit{when y = 18, what is \underline{x}?}\qquad x=\cfrac{1}{4}(18)[/tex]

Which of the following is not needed when making a box plot?
A - Mean
B - Minimum
C - Median
D - Third Quartile

Answers

The mean is not needed to make a box plot.

I hoped this helped!
Answer: A) Mean

You use the median as the center of the boxplot. The first and third quartiles (Q1 and Q3) make up the left and right edges of the box. The min and max are the furthest points on the left and right side of each whisker. The mean is not used at all. With outliers, the mean is skewed. If you have any outliers then its best to use the median instead.

At a particular music store, CDs are on sale at $14.00 for the first one purchased and $12.00 for each additional disc purchased. Maria spends $86.00 on CDs. How many CDs has Maria purchased?

Answers

To calculate the answer, we subtract $ 14 from the first CD to the total amount spent, which is $ 86.
 So:
 $ 86- $ 14 = 72
 The rest of the CDs cost $ 12.
 Then we divide $ 72 between $ 12
 $ 72 / $ 12 = 6.
 That means that 6 CDs were bought at $ 12 plus the first one bought at $ 14.
 So the number of CDs that María bought was 7

Answer: 7

Step-by-step explanation:

Simplify 2y (3-x) + 7 (x-2y)

Answers

Hi there!
Let's simplify step by step.


[tex]2y(3 - x) + 7(x - 2y) = [/tex]
First we work out the parenthesis (for instance possible by using rainbow technique).

[tex] 2y \times 3 + 2y \times - x + 7 \times x + 7 \times - 2y = \\ 6y - 2xy + 7x - 14y = [/tex]
Finally we collect the common terms.

[tex] - 2xy + 7x - 8y[/tex]
~ Hope this helps you!


The first step for solving this expression is to distribute 2y through the first parenthesis.
6y - 2xy + 7(x - 2y) 
Now distribute 7 through the second set of parenthesis.
6y - 2xy + 7x - 14y
Lastly,, collect the like terms with y.
-8y - 2xy + 7x
Since we cannot simplify any further,, -8y - 2xy + 7x is the correct answer to your question.
Let me know if you have any further questions.
:)

WILL GIVE BRAINLIEST... HELP ASAP!!!!!!



1. Circle A with center at (3, 4) and radius 2 is similar to circle B with center at (−4, −5) and radius 3. Below is an incorrect informal argument for proving two circles are similar:


Step 1 Translate circle B to the right 9 units and up 7 units to form concentric circles.
Step 2 Dilate circle B to be congruent to circle A using scale factor of k = r sub two over r sub one equals two over three
Step 3 When an object is dilated, the dilated object is similar to the pre-image, thus the two circles are similar.


What is the first incorrect step, and how can it be fixed?

A. All steps are correct
B. Step 1, translate circle B to the right 7 units and up 9 units
C. Step 2, use scale factor of K= r^2/r^1=3/2
D. Step 3, replace dilated with translated.

An image of two concentric circles is shown with r2 = 8 and r1 = 3:

2. Image shows a pair of concentric circles. The radius of the smaller circle is r sub 1 and the radius of the second is r sub 2.


In order to prove the two circles are similar, the radius r1 was increased to make the circles congruent. What is the scale factor used in the above image?

A. k=8/3
B. K=3/8
C. K=1/5
D. K=5

Answers

The anwser is B, k= 3/8

First one is B. Because if you're moving from -4 to 3 you don't move 9 units right instead you move 7.

If f is a function such that f(b)-f(a)/b-a=2, then which of the following statements must be true?

Answers

Based on the type of equation, f(b) relates to y2, f(a) relates to y1, b relates to x2, and a relates to x1.  If we change those around we now get:
(y2 - y1)/(x2 - x1) which is the slope formula, or the average rate of change.  thus your answer would be C

Use a coordinate grid to create a map of a town with at least five different locations, such as a house, a post office, a school, a library, and a mall. Each location must be plotted where two grid lines cross. In addition, no two locations can lie on the same vertical grid line or the same horizontal grid line.

A. Post your diagram.
B. Use the Pythagorean theorem to find the distance between two of your locations.

Answers

see attached picture:

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

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:

i will look but i think she was right

Step-by-step explanation:

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