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1 year ago

What is the formula for the nth term of the given sequence 100, 20, 4, …

Mathematics

1 answer:

Naily [24]1 year ago

6 0

Answer:

$a_n=100 \left(\dfrac15\right)^{n-1}$

Step-by-step explanation:

General equation of geometric sequence: $a_n=ar^{n-1}$

Given:

a₁ = 100
a₂ = 20
a₃ = 4

$\implies a_1=a=100$

$\implies a_2=100 \cdot r=20$

$\implies a_3=100 \cdot r^2=4$

Common ratio:

$r=\dfrac{a_3}{a_2}=\dfrac{4}{20}=\dfrac15$

Therefore:

$a_n=100 \left(\dfrac15\right)^{n-1}$

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A TV that usually sells for $186.67 is on sale for 20% off. If sales tax on the TV is 8%, what is the price of the TV, including

Furkat [3]

Answer:

$161.28288 or $161.28 if rounded

Step-by-step explanation:

first find 10% of the original cost

186.67/10 =18.667

18.667 x 2 = 37.334 (20%)

186.67 - 37.334 = 149.336

to find the tax, mulitple 149.336 x 1.08

1.08 because, 100% of the cost, plus 8% of the cost for tax

= 161.28288

5 0

2 years ago

An ice cream shop sells cones at the volume of 94.2 cubic meters they want to double the volume of the cones without changing th

marin [14]

The volume of a cone is $V=\pi r^2\frac{h}3$ where r = radius and h = height. If the cone has a volume of 94.2 cm³ (I assume you didn't mean m³ because that would be ridiculously huge) and a height of 10 cm, we can plug these values into the formula to find the radius. Don't do any rounding.

$94.2 = \pi r^2\frac{10}3 \\ 282.6 = \pi r^2 *10 \\ 28.26 = \pi r^2 \\ 8.99543738355 = r^2 \\ 2.99923946752=r$

Now we know that's going to be the radius of our new cone as well since we're keeping the diameter the same. The volume is going to be double 94.2 which is 188.4. Let's solve for the height.

$188.4 = \pi (2.99923946752)^2\frac{h}3 \\ 188.4 = \pi(8.99543738355)\frac{h}3 \\ 188.4 = 28.26\frac{h}3 \\ 565.2 = 28.26h \\\\ \boxed{h = 20, r\approx 3}$

5 0

2 years ago

HELP: I need help on multiple questions for a quiz before tomorrow night. If all is answered, you will get 40+ points and marked

Vinil7 [7]

Answer:

1. $33,000

2. $6077.53

a) 2.72 seconds

b) 0.96 seconds

4. 189 square meters

a) Average Rate of Change = 4 pounds per week, or -4

b) 160 pounds (after 5 weeks)

Independent Variables = p, A, and H

Dependent Variable = T

141 beats per minute (rounded to nearest whole number)

Step-by-step explanation:

The value of a tractor V(t) decreases over time, t. Its value is given by:

$V(t)=55000-5500t$

To find value of tractor after 4 years, we would need to substitute "4" into t and calculate. It is shown below:

$V(t)=55000-5500t\\V(4)=55000-5500(4)\\V(4) =33000$

The value of the tractor after 4 years is $33,000

The value of investment that is growing each year, is given by:

$f(n)=5000(1.05)^{n}$

Where

5000 is the initial investment (deposit)

1.05 means a 5% growth rate per year

n is the time in years

We want the investment's value after 4 years, so n would be 4. Substituting we get our answer:

$f(n)=5000(1.05)^{n}\\f(4)=5000(1.05)^{4}\\f(4)=6077.53$

To the nearest cent, the value of the investment would be:

$6077.53

The time it takes of pendulum to make one swing is given by the formula:

$T(L)=2\pi \sqrt{\frac{L}{32}}$

Where L is the length of the pendulum in feet

If L = 6ft, the time it will take is:

$T(6)=2\pi \sqrt{\frac{6}{32}}\\T(6)=2.72$

About 2.72 seconds

Now, the length is 9 inches, we convert it to feet first:

9/12 = 0.75 feet

So, the time it will take:

$T(0.75)=2\pi \sqrt{\frac{0.75}{32}}\\T(0.75)=0.96$

So, it will take about 0.96 seconds

The area of weed after t days can be modeled by:

$A(t)=0.006 \pi t^2$

Where t is number of days

Now, we want to find area after 100 days, so let t = 100, we get:

$A(t)=0.006 \pi t^2\\A(100)=0.006 \pi (100)^2\\A(100)=188.5$

Rounded to nearest sq. m, we have the area to be:

189 square meters

The avg. rate of change is basically how much the program is advertising that someone can loose in a week. It says "4 pounds per week". Since decrease, we give the value of "4" and negative sign So:

Average Rate of Change = 4 pounds per week, or -4

Initial weight is 180 pounds, we know 4 pounds is decreased every week when going through the program course. So, after 5 weeks,

5 * 4 = 20 pounds will be less

So, he will be:

180 - 20 = 160 pounds (after 5 weeks)

The Karvonen formula is given as:

$T=p(220-A)+H(1-p)$

Where

T is target heart rate (in bpm)

p is the percent intensity (expressed as decimal)

A is the age (in yrs)

H is the resting heart rate (in bpm)

We need to identity the independent and dependent variables. Now, lets that a simple example:

y = 2x

Here,

x is the independent variable

y is dependent on x, so y in dependent

Similarly, if you look at the formula, you can see:

p, A, and H are all independent

T depends on them

So,

p, A, H are independent variables

T is the dependent variable

Independent Variables = p, A, and H

Dependent Variable = T

We are given

A = 35

H = 60

p = 65% = 65/100 = 0.65

Now, we want T, lets substitute and find:

$T=0.65(220-35)+60(1-0.65)\\T=141.25$

The target heart rate should be: 141 beats per minute (rounded to nearest whole number)

3 0

2 years ago

In a class of 50 students, everyone has either a pierced nose or a pierced ear. The professor asks everyone with a pierced nose

Tems11 [23]

Answer: 3

Step-by-step explanation:

Let E be the event of that student pierces ear and N be the event of that student pierces nose.

Given: $n(E\cup N=50)$

$n(E)=46\\\\n(N)=7$

For any two event A and B, we have

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

Similarly , $n(E\cup N)=n(E)+n(N)-n(E\cap N)$

$50=46+7-n(E\cap N)\\\\\Rightarrow\ n(E\cap N)=53-50=3$

Hence, 3 students have piercings both on their ears and their noses.

7 0

2 years ago

Determine if (-2,6) and (4,12) are solutions to the system of equations:

kykrilka [37]

Answer:

Both $(-2,6)$ and $(4,12)$ are solutions to the system.

Step-by-step explanation:

In order to determine whether the two given points represent solutions to our system of equations, we must "plug" thos points into both equations and check that the equality remains valid.

Step 1: Plug $(-2,6)$ into $y=x+8$