When the smaller of two consecutive integers is added to two times the larger, the result is 35. Find the integers.

Is second term of a geometric series is 48 and it's fifth term is 6 then find the sum of the first 6 terms.

AlekseyPX

Answer:

the sum of the first 6 terms =189

Step-by-step explanation:

the first 6 terms-

96,48,24,12,6,3

I found them easily by dividing 48 with random small numbers until I got 6 for the fifth term. So here I divided 48 by 2 which is = 24(3rd term), then divided 24 by 2 which is =12(4th term) and then again decide the answer by 2 and finally got 6 for the 5th term. So the ratio is 1/2. For the first term I did the opposite, multiply 48 by 2 which is = 96. And lastly find the sixth term and add them up which is = 189

I tried my best to explain it in simple terms, hope this helps:)

5 0

2 years ago

An investment of 100,000 AED increases at a rate of 16% per year. What is

stepan [7]

Answer:

1,946,075.95 AED

Step-by-step explanation:

Firstly, we write the general formula for an exponential increase as follows;

V(t) = A( 1 + r)^t

where V(t) is the value after some number of years t

A is the investment amount which is 100,000 AED

r is the rate of increase which is 16% = 16/100 = 0.16

t is the number of years which is 20

substituting these values;

V(20) = 100,000( 1 + 0.16)^20

V(20) = 100,000(1.16)^20

V(20) = 1,946,075.95 AED

7 0

2 years ago

t hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular regio

masha68 [24]

Given:

Required:

To find the probability that the dart land will be in the shaded region.

Explanation:

Area of the circle is given by the formula:

$A=\pi r^2$

Where r = radius

Thus the area of the circular region

$\begin{gathered} =(3.14)\times(2)^2 \\ =3.14\times4 \\ =12.56\text{ square in.} \end{gathered}$

The area of the square is given by the formula:

$=(side)^2$

Thus the area of the given square

$\begin{gathered} =(6)^2 \\ =36\text{ square in.} \end{gathered}$

The probability of an event is given by the formula:

$P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}$

The probability that the dart land will be in the shaded region

$=\frac{Area\text{ of the shaded region}}{Area\text{ of the square}}$

Thus probability

$\begin{gathered} P=\frac{12.56}{36} \\ P=0.3488 \\ P=0.349 \end{gathered}$

Final answer:

Thus the probability that the dart land will be in the shaded region is 0.349.

6 0

1 year ago

Amy needs to mail a gift card to a friend. She uses 47-cent stamps and 6-cent stamps to pay $2.42 in postage. How many of each s

AVprozaik [17]

Answer:

Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.

Step-by-step explanation:

Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.

41 cents = 41/100 = $0.41

6 cents = 6/100 = $0.06

She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that

0.41x + 0.06y = 2.12

Multiplying through by 100, it becomes

41x + 6y = 212

6y = 212 -41x

We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.

If x = 3,

6y = 212 - 41 × 3 = 89

y = 89/6 = 14.8333

If x = 4,

6y = 212 - 41 × 4 = 48

y = 48/6 = 8

Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.

Step-by-step explanation:

Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.

41 cents = 41/100 = $0.41

6 cents = 6/100 = $0.06

She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that

0.41x + 0.06y = 2.12

Multiplying through by 100, it becomes

41x + 6y = 212

6y = 212 -41x

We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.

If x = 3,

6y = 212 - 41 × 3 = 89

y = 89/6 = 14.8333

If x = 4,

6y = 212 - 41 × 4 = 48

y = 48/6 = 8

8 0

2 years ago

Read 2 more answers

87 POINTS PLZ HELP Aman is adding –17 + 9. He wants to write –17 as the sum of two numbers so that one of the numbers, when adde

Pie

Consider number 17. You know that

17=9+8.

Then for negative numbers you have the same rule (with respect to sign -):

-17=(-9)+(-8).

Since (-9)+9=9+(-9)=9-9=0, you have that

-17+9=(-9)+(-8)+9=(-9+9)+(-8)=0+(-8)=-8.

Answer: -17=(-9)+(-8).

5 0

2 years ago

When the smaller of two consecutive integers is added to two times the​ larger, the result is 35. Find the integers.

When the smaller of two consecutive integers is added to two times the larger, the result is 35. Find the integers.