At Ron's Roller Rink, the number of customers has been decreasing at a steady rate of 5% per year. If there were 900 skaters per week in 2010, what is a good estimate for the number of skaters per week in 2006?

Answers

Answer 1

let's say in 2006, year 0, there were "I" amount of customers, and we dunno what "I" is.

now, 4 years later in 2010, t = 4, there are 900 skaters, and the rate of decrease is 5%.

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &900\\ I=\textit{initial amount}\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ t=\textit{elapsed time}\to &4\\ \end{cases} \\\\\\ 900=I(1-0.05)^4\implies 900=I(0.95)^4\implies \cfrac{900}{0.95^4}=I \\\\\\ 1105\approx I\qquad thus\qquad \boxed{A=1105(0.95)^t}[/tex]

[tex]\bf \\\\ -------------------------------\\\\ \textit{now in 2006, 4 years earlier, year 0, t = 0} \\\\\\ A=1105(0.95)^0\implies A=1105\cdot 1\implies A=1105[/tex]

Related Questions

Ann is grouping 38 rocks. She can put them into groups of 10 rocks or as single rocks.what are different ways Ann can group the rocks?

Answers

Answer: 4 ways

To answer this question, you need to make a list based on how much "10 group" of rock can be made.
The possible way to group it should be:
0 pcs of 10 group + 38 pcs of 1 group
1 pcs of 10 group + 28 pcs of 1 group
2 pcs of 10 group + 18 pcs of 1 group
3 pcs of 10 group + 8 pcs of 1 group

The figure has ____ lines of symmetry. A. 0 B. 4 C. 6 D. 8

Answers

Answer = B. 4
a 4 pointed star has 4 lines of symmetry

The star has 4 pairs of symmetry lines

which algebraic expression shows the average melting points of helium, hydrogen, and neon if h represents the melting point of helium, j represents the melting point of hydrogen, and k represents the melting point of neon?

A. h + j + k
B. hjk
c. h+j+k over 3
d. hjk over 3

Answers

Answer:

c. h+j+k over 3

Step-by-step explanation:

We know that,

[tex]\text{Average}=\frac{\text{Sum of observations}}{\text{Total number of observation}}[/tex]

Here, h, j and k represents the melting point of helium, hydrogen and Neon respectively,

Since, the sum of melting points = h + j + k,

Also, the total number of gases = 3,

Thus,

[tex]\text{Average melting points}=\frac{h+j+k}{3}[/tex]

Or (h+j+k) over 3

⇒ Option c is correct.

The algebraic expression which shows the average melting

points of helium, hydrogen, and neon is h+j+k over 3.

What is Average?

This is calculated with the sum of the items divided by the

number of items.

In this scenario, we were given the items as h, j and k. The

total number of items is 3.

The average will therefore be = h+j+k/3

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A pea seller had some peas. He sold 40% of his stock and still had 420 peas. Originally, he had how many peas?

Answers

100-40= 60%

60% = 0.60

420/0.60 = 700

he had 700 peas

420 --------60%
? ------------100%

100 x 420 / 60 = 700

answer
he had 700 peas originally

Which of the following gives all of the sets that contain -1/2?

A.the set of all rational numbers and the set of all real numbers
B.the set of all natural numbers and the set of all irrational numbers
C.the set of all integers and the set of rational numbers
D.the set of all natural numbers, the set of rational numbers, and the set of all real numbers

Answers

i think it might be.... A.the set of all rational numbers and the set of all real numbers

Answer:

Option A is Correct Option.

Step-by-step explanation:

Given: [tex]\frac{-1}{2}[/tex]

[tex]\frac{-1}{2}[/tex] is a rational no.

Option A:

Given no is a rational no.

⇒ Both Set of rational no and real nos. contain rational nos..

Thus, Correct Option.

Option B:

set of natural nos and irrational nos does not contain rational nos.

Thus, Not correct option.

Option C:

Set of integers does not contain rational numbers.

Thus, Incorrect Option.

Option D:

Set of all Natural Nos. does not contain rational nos.

Thus, This option is not correct option

Therefore, Option A is Correct Option.

1 + 2 + 3 + 4 + 5 + . . . is an example of a finite series. True False

Answers

True is my answer hope I helped u

The ellipsis would indicate an infinite series. So I would say false.

(Technically all series are infinite, if they are not infinite they should be referred to as sequences.)

Which is the equation of the line with slope 5 that contains point (-2, -3)

A. y + 2 = 5(x – 3) B. y + 3 = 5(x + 2) C. y – 3 = 5(x – 2) D. y – 2 = 5(x – 3)

Answers

The answer is y = 5x + 7
here's how you get it:

Start with the base y = mx + b
then imput the points and the slope:
-3 = 5 ( -2 ) + b

Then solve for b
-3 = 5 ( -2 ) + b
-3 = -10 + b
-b = -7
b = 7

so the equation is:

y = 5x + 7

The answer is y = 5x + 7

here's how you get it:

Start with the base y = mx + b

then imput the points and the slope:

-3 = 5 ( -2 ) + b

Then solve for b

-3 = 5 ( -2 ) + b

-3 = -10 + b

-b = -7

b = 7

so the equation is:

y = 5x + 7

A rectangular greenhouse has an area of 6480 square meters and a length of 120 meters. How many meters is it in width?

Answers

Area is length x width. If the area is 6480, and you know the length, plug it into the formula to find the width.

120 x width = 6480

So, to solve, you would divide 6480 by 120 to find the width. 6480/120 = 54.

Therefore, the width is 54.

Comment under this post or message me for further help!

A=LW

W=A/L, A=6480 and L=120 so

W=6480/120 m

W=54 m

EASY 5 POINTS!!! A spherical ball just fits inside a cylindrical can, 16 centimeters tall, with a diameter of 16 centimeters. Which expression gives the volume of the sphere in cubic centimeters?

Answers

formula for volume of a sphere is V=4/3 x pi x R63

if diameter = 16 than radius = 16/2 = 8

so the equation would be 4/3 x pi x 8^3

an airline ramp with a base of 50 makes an angle of 27 with the ground. find the distance a person will walk on a ramp round to the nearest foot

Answers

check the picture below.

make sure your calculator is in Degree mode.

find the values of x between 0 and 2pi where the tangent line to the graph of y=sinxcosx is horizontal.

Answers

[tex]\bf \textit{let's recall that }sin^2(\theta)+cos^2(\theta)=1 \\\\\\ sin^2(\theta)=1-cos^2(\theta)\implies sin(\theta )=\sqrt{1-cos^2(\theta)}\\\\ -------------------------------\\\\[/tex]

[tex]\bf y=sin(x)cos(x)\impliedby \textit{now, using the product-rule} \\\\\\ \cfrac{dy}{dx}=cos(x)cos(x)-sin(x)cos(x)\implies 0=cos(x)[cos(x)-sin(x)]\\\\ -------------------------------\\\\ 0=cos(x)\implies \boxed{\measuredangle x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf 0=cos(x)-sin(x)\implies sin(x)=cos(x)\\\\ thus\qquad \sqrt{1-cos^2(x)}=cos(x)\implies 1-cos^2(x)=cos^2(x) \\\\\\ 1=2cos^2(x)\implies \cfrac{1}{2}=cos^2(x)\implies \pm\sqrt{\cfrac{1}{2}}=cos(x) \\\\\\ \pm\cfrac{1}{\sqrt{2}}=cos(x)\implies \pm\cfrac{\sqrt{2}}{2}=cos(x)\implies \boxed{\measuredangle x= \begin{cases} \frac{\pi }{4}\\\\ \frac{3\pi }{4}\\\\ \frac{5\pi }{4}\\\\ \frac{7\pi }{4} \end{cases}}[/tex]

The length of a shadow of a building is
29 m
. The distance from the top of the building to the tip of the shadow is
35 m
. Find the height of the building

Answers

h^2=x^2+y^2

35^2=29^2+y^2

y^2=35^2-29^2

y^2=384

y=√384

y≈19.60 m (to the nearest hundredth of a meter, or nearest centimeter)

Find a_1 and d for an arithmetic sequence with these terms. a_4=9and a_7=18

Answers

[tex]\bf \begin{array}{llll} term&value\\ -----&-----\\ a_4&9\\ a_5&9+d\\ a_6&(9+d)+d\\ &9+2d\\ a_7&(9+2d)+d\\ &9+3d=\underline{18} \end{array}\\\\ -------------------------------\\\\ 9+3d=18\implies 3d=9\implies d=\cfrac{9}{3}\implies \boxed{d=3}[/tex]

[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ n=7\\ d=3 \end{cases} \\\\\\ a_7=a_1+(7-1)d\implies 18=a_1+(7-1)3\implies 18=a_1+18 \\\\\\ 18-18=a_1\implies \boxed{0=a_1}[/tex]

Out of 30 students surveyed 17 have a dog based on these results predict how many of the 300 students in the school have a dog

Answers

17/30 = 0.5666 so about 57% of the sample had dogs

300 x 0.57 = 171 would have dogs

What property describes the number sentence? 6+0=6

Answers

hello :
the property describes the number sentence 6+0=6 is : " 0 Neutral element for addtion"

Find the exact value of cos 105°.

Answers

[tex] \frac{ \sqrt{2}- \sqrt{6} }{4} [/tex]

Many practical applications require calculations of area. some of these calculations are straightforward, but others are more difficult, and it turns out that the idea of the definite integral can help us with the more difficult cases. let’s start with some familiar shapes. what is the area of a rectangle of length l and width w? express your answer in terms of l and w.

Answers

Area of a rectangle is given by multiplying the length and the width

Let's length be [tex]'l'[/tex] and width be [tex]'w'[/tex], then the area is

A = [tex]l[/tex] × [tex]w[/tex]

The area of a rectangle with length l and width w is given by the product l * w.

what is the area of a rectangle of length l and width w?

The area of a rectangle is calculated by multiplying its length (l) by its width (w).

Therefore, the area (A) of a rectangle can be expressed as:

A = l * w

So, the area of a rectangle with length l and width w is given by the product l * w.

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A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

Answers

check the picture below.

notice, the volume of a cylinder which is the same height(h) and radius(r) as a cone, is three times as much of that of the cone's.

Suppose an isosceles triangle ABC has A = 45° and b = c = 4. What is the length of a2?

Answers

You can use the Law of Cosines (a^2=b^2+c^2-2bc cosA)

a^2=4^2+4^2-2*4*4*cos45°

a^2=32-32cos45°

a^2=32(1-cos45°)

a=√(32(1-cos45°))

a≈3.06 units (to nearest hundredth of a unit)

what is the remainder when 3 is synthetically divided into the polynomial -x^2+5x-9

Answers

-3 is the remainder when you synthetically divide

Answer:

REmainder is -3

Step-by-step explanation:

find remainder when 3 is synthetically divided into the polynomial -x^2+5x-9

In synthetic division we write all the coefficient of the polynomial and divide by 3

3 -1 5 -9

0 -3 6

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

-1 2 -3 ----> Remainder

So the remainder is -3

Find the common ratio of the geometric sequence: −320,80,−20,5,…−320,80,−20,5,… A. −14−14 B. 1414 C. -4 D. 4

Answers

I'm assuming the sequence is: -320, 80, -20, 5

Divide each term by the previous term to get the common ratio r

r = (term 2)/(term 1) = 80/(-320) = -1/4
r = (term 3)/(term 2) = -20/80 = -1/4
r = (term 4)/(term 3) = 5/(-20) = -1/4

No matter which term you pick (as long as it's not the first one) dividing it by the previous term leads to -1/4 or -0.25 as the common ratio

Answer: -1/4

It seems like none of the answer choices have -1/4 but it could be choice A was supposed to show "-1/4" instead of "-14"? Perhaps the division sign didn't show up for some reason?

Expand the fraction 72/125 .so that it has a denominator of 1000.

Answers

x/1000=72/125 multiply both sides by 1000

x=72000/125

x=576

So the fraction is 576/1000

Kathy walked 3 1/2 miles per hour for 1 1/4 hours. During 1/2 of her walking time it rained. How many miles did she walk while it was raining?

Answers

I think it's 2.2 miles walking in the rain

1 1/4 = 5/4 * 1/2 = 5/8

3 1/2 = 7/2 * 5/8 = 35/16 = 2 3/16 miles

Evaluate the limit using the appropriate limit law(s). (if an answer does not exist, enter dne.) lim x → 1 2x2 + 4 x2 + 4x − 4

Answers

Presumably, the limit to be evaluated is

[tex]\displaystyle\lim_{x\to1}\frac{2x^2+4}{x^2+4x-4}[/tex]

Since the given function is continuous at [tex]x=1[/tex], the limit of function is equal to the value of the function at [tex]x=1[/tex]:

[tex]\displaystyle\lim_{x\to1}\underbrace{\frac{2x^2+4}{x^2+4x-4}}_{f(x)}=f(1)=\frac{2+4}{1+4-4}=6[/tex]

If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour.

Answers

[tex]\bf \textit{arc's length}\\\\ s=rw\qquad \begin{cases} r=radius\\ w=\textit{angular speed} \end{cases}\qquad w=\cfrac{50 rev}{min}\cdot \cfrac{2\pi }{rev} \\\\\\ w=\cfrac{100\pi }{min}\qquad s=80in\cdot \cfrac{100\pi }{min}\implies s=\cfrac{8000\pi\ in}{min}\\\\ -------------------------------\\\\ \textit{now to convert it to miles/hr} \\\\\\ \cfrac{8000\pi\ in}{min}\cdot \cfrac{ft}{12in}\cdot \cfrac{mile}{5280ft}\cdot \cfrac{60min}{hr}\implies \cfrac{8000\pi \cdot 60\ in}{12\cdot 5280\ hr}[/tex]

What is the greatest common factor of 4k, 18k4, and 12?

Answers

factor each
4k=2*2*k
18k⁴=2*3*3*k*k*k*k
12=2*2*3

GCF=2

the greatest common factor is 2

the great common factor is 2

The table below represents the distance of a train from its destination as a function of time: Time (hours) x Distance (miles) y 0 665 1 570 2 475 3 380 4 285 Part A: What is the y-intercept of the function, and what does this tell you about the train? (4 points) Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, and tell what the average rate represents. (4 points) Part C: What would be the domain of the function if the train continued to travel at this rate until it reached its destination? (2 points)

Answers

A. y=-95x+665 y-intercept is 665
B. Ave rate of change is -95
C. y=0 so x=7 Domain is [0,7]

You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 5 days later you determine that it has decayed down to 0.7 grams. What is its half-life? (Round your answer to three significant digits.)

Answers

The half-life of a given radio active material is given by:
t(1/2)=[tln2]/[lnN-lnN(t)]
where;
t=time
N=initial amount
N(t)=final amount
thus the half-life of our material will be as follows:
t=5 days
N=1 g
N(t)=0.7 g
N(1/2)=[5*ln2]/[ln1-ln0.7]
=9.717

A new cruise ship line just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the Mediterranean Paradise.
The Caribbean Paradise has 29 more than the Pacific Paradise. The Mediterranean Paradise has 30 fewer deluxe staterooms than twice the number of deluxe staterooms on the Pacific Paradise. Find the number of deluxe staterooms for each of the ships if the total of deluxe staterooms for the total of the three ships is 719.

Answers

c = caribbean, p = pacific, m = mediterranean

c = p + 29
m = 2p - 30
c + m + p = 719

(p + 29) + (2p - 30) + p = 719
4p - 1 = 719
4p = 719 + 1
4p = 720
p = 720/4
p = 180 <=== pacific paradise deluxe staterooms

c = p + 29
c = 180 + 29
c = 209 <=== caribbean paradise deluxe staterooms

m = 2p - 30
m = 2(180) - 30
m = 360 - 30
m = 330 <=== mediterranean paradise deluxe staterooms

Final answer:

To find the number of deluxe staterooms for each of the three ships, we can set up and solve an equation based on the given information.

Explanation:

Let's represent the number of deluxe staterooms on the Pacific Paradise ship as x.

The number of deluxe staterooms on the Caribbean Paradise is 29 more than the Pacific Paradise, so it can be represented as x + 29.

The number of deluxe staterooms on the Mediterranean Paradise is 30 fewer than twice the number of deluxe staterooms on the Pacific Paradise, so it can be represented as 2x - 30.

We can form an equation with the sum of the deluxe staterooms on all three ships: x + (x + 29) + (2x - 30) = 719.

Simplifying the equation gives us 4x - 1 = 719.

By adding 1 to both sides and dividing by 4, we can find the value of x which represents the number of deluxe staterooms on the Pacific Paradise ship.

Finally, we can substitute the value of x into the expressions for the other two ships to find their number of deluxe staterooms.

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Which of the following is not an appropriate method of proving triangles congruent a) AAA b)SSS c) AAS D) SAS

Answers

Answer:

a) AAA.

Step-by-step explanation:

Triangles which are of the same shape and size are called congruent triangles. Triangles of same shape are similar triangles.

Two triangles can be proved congruent by SSS ,SAS AAS ,ASA ,HL postulates.

Two triangles can be proved similar by AAA method.

All congruent triangles are similar but all similar triangles are not congruent.

Hence option a) AAA is not an appropriate method of proving triangles congruent.

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