Item 5 What is the explicit rule for the geometric sequence? 500, 100, 20, 4

lys-0071 [83]

2/7 times 2 by 5 and times 7 by 5 also then that would equal 10/35
then you times 3 by 7 and times 5 by 7 to get 21/35 then add 10 and 21 to get 31 then it will be 31/35 then try to reduce it but u cant so the answer is 31/35

8 0

3 years ago

Read 2 more answers

A house was valued at $120,000 in the year 1992. The value appreciated to $160,000 by the year 2007.

pochemuha

Answer:

A) 0.0194

B) 1.94%

C) $ 170,000

Step-by-step explanation:

Value of house in 1992 = P = $ 120,000

Value of house in 2007 = S = $ 160,000

Time difference from 1992 to 2007 = 15 years

Part A)

The formula of compound interest is:

$S=P(1+r)^{t}$

P is the original amount i.e. $ 120,000

t is the time in years which is 15 years

S is the amount after t years which is $ 160,000

r is the annual growth rate

Using the values, we get:

$160000=120000(1+r)^{15}\\\\\frac{160000}{120000}=(1+r)^{15}\\\\ \frac{4}{3}=(1+r)^{15}\\\\(\frac{4}{3} )^{\frac{1}{15}}=1+r\\\\ r=(\frac{4}{3} )^{\frac{1}{15}}-1\\\\ r=0.0194$

Thus, the annual growth rate is 0.0194

Part B)

In order to convert a decimal to percentage, simply multiply the decimal by 100.

So, 0.0194 in percentage would be 1.94%

Part C)

We have to find the value of house in 2010 i.e. after 18 years. So t =18

Using the values in the formula, we get:

$S=120000(1+0.0194)^{18}\\\\ S=169584$

Rounded to nearest thousand dollars, the value of the house would be $ 170,000

7 0

3 years ago

Please help with answer an explain why that is the answer.. Will pick brainliest promise...

andrezito [222]

A negative association means as one increases, the other decreases. For example x goes up 1 and y goes down 1.

Because set B and set D show positive correlation, they can automatically be deleted.

Set A shows a negative correlation, however the change between the x and y value are steady. As x increase one, y decreases one. So the line is straight meaning it is linear.

Leaving our answer to be C

We can check this by looking at the chart, the chart shows a negative correlation between the values, we can also check to see that it is not linear because it begins with x rising a and y decreasing two, however it then changes to f rising one and y decreasing 1. So the equation is non-linear

So your answer is
C. Set C

An outlier in math is a value on a graph that varies greatly from all the others, it is either way higher or way lower than the other values. This is shown by point D because it is far away from the rest of the data on the table.

So your answer is
D. Point D

As the temperature increases, the amount of jackets decreases. This shows a negative association. So because the temperature is increasing the number of jackets decreases, so answer choices A and C can be eliminated because they each say the number of coats will increase. And as previously stated, as the temperature increases the amount of jackets decreases, meaning the association is negative.

So your answer is
B. The number of coats in the coat check will decrease because the graph shows a negative association.

7 0

4 years ago

Find radiuses of circles, if OO1=20cm and 3AK=2BK

Serggg [28]

Answer:

radius of smaller circle on the left = 8 centimeters
radius of larger circle on the right = 12 centimeters

=============================================================

Explanation:

The letter O looks very similar to the number zero, so I'm going to use other letters to avoid confusion. For the smaller circle on the left, it'll have center P. The circle on the right will have center Q. See the diagram below.

Based on that, we can say that PQ = 20 cm.

Let x = length of PK

PK + KQ = PQ

KQ = PQ - PK

KQ = 20 - x

We'll keep this in mind for later. I'll refer to this as "Fact 1" when it does come up later.

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

We're given this equation

3AK=2BK

Let's get the numbers to one side and the letters to the other side like so:

3AK=2BK

3AK/BK = 2

AK/BK = 2/3

We'll use this later as well. I'll refer to this as "Fact 2" when it does come up later.

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

Next, draw a segment from P to A to form triangle PAK (also shown in the diagram below). Do the same for points Q and B to form triangle QBK.

The segments PA and PK are radii of the smaller circle, so PA = PK which leads to triangle PAK being isosceles. Triangle QBK is also isosceles for similar reasoning.

The angles AKP and QKB are vertical angles, so they are congruent.

The facts mentioned so far boil down to the two triangles being similar triangles (use the angle angle method to prove).

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

Now that we know the triangles are similar, we can use a proportion to solve for x.

PK/KQ = AK/KB

PK/KQ = 2/3 .... use fact 2

x/(20-x) = 2/3 .... use fact 1

3x = 2(20-x) .... cross multiply

3x = 40 - 2x

3x+2x = 40

5x = 40

x = 40/5

x = 8

So,

PK = x = 8
KQ = 20-x = 20-8 = 12

The radius of the smaller circle on the left is 8 cm.

The radius of the larger circle on the right is 12 cm.

4 0

2 years ago

Someone please help me

Free_Kalibri [48]

D. y = 3x + 2

Check (-4, -10)
-10 = 3(-4) + 2
-10 = -12 + 2
-10 = -10 :)

Check (-3, -7)
-7 = 3(-3) + 2
-7 = -9 + 2
-7 = -7 :)

Check (-2, -4)
-4 = 3(-2) + 2
-4 = -6 + 2
-4 = -4 :)

Check (-1, -1)
-1 = 3(-1) + 2
-1 = -3 + 2
-1 = -1 :)

Check (0, 2)
2 = 3(0) + 2
2 = 0 + 2
2 = 2 :)

4 0

3 years ago