A tire shop filled 3.5 tires with air. It took 3 3/5 seconds to fill them. How long would it take to fill 10 tires?

Sam counted out loud by 6s . Jorge counted out loud by 8s. What are the first three numbers both Sam and Jorge said

IrinaK [193]

Sam:6,12,18 Jorge:8,16,24

4 0

3 years ago

The common ratio in a geometric series is 0.5 and the first term is 256. Find the sum of the first 6 terms in the series

Svetach [21]

Answer:

The sum of the first 6 terms of the series is 504.

Step-by-step explanation:

Given that,

Common ratio in a geometric series is, r = 0.5

First term of the series, a = 256

We need to find the sum of the first 6 terms in the series. If a and r area the first term and common ratio of a series, then the series becomes:

$a,ar^1,ar^2,ar^3......$

The sum of n terms of a GP is given by :

$S_n=\dfrac{a(1-r^n)}{1-r}$

Here, n = 6

$S_n=\dfrac{256\times (1-(0.5)^6)}{1-0.5}\\\\S_n=504$

So, the sum of the first 6 terms of the series is 504.

4 0

3 years ago

Joe went to the store and bought 4 cans of peanuts for $7.80 .What is the constant of proportionality?

Paladinen [302]

Answer:

$1.95 for one can of peanuts.

Step-by-step explanation:

4 0

3 years ago

Find the lateral surface area of the figure.

Brut [27]

Surface area of the cylinder = 816.4 sq. ft.

Solution:

Height of the cylinder = 21 ft

Diameter of the cylinder = 10 ft

Radius of the cylinder = 10 ÷ 2 = 5 ft

Use the value of $\pi$ = 3.14

Surface area of the cylinder = $2 \pi r h+2 \pi r^{2}$

Substitute the given values in the surface area formula, we get

Surface area of the cylinder $$=2\times3.14\times 5\times 21+2 \times3.14\times 5^2$

$=659.4+157$

$=816.4$ ft²

Hence the surface area of the cylinder is 816.4 sq. ft.

7 0

3 years ago

Read 2 more answers

Find five consecutive integers such that: "the sum of the first and 4 times the third is equal to 60 less than 3 times the sum o

Monica [59]

Consecutive integers are integers that come one after another in order. For example, 2, 3, and 4 are all consecutive integers, as well as 100, 101, and 102. In general, if we have some integer n, the consecutive integers following it will be n + 1, n + 2, n + 3, etc. Here, we have five. If we

Call the first integer n,
Then the second integer will be n + 1,
The third will be n + 2,
The fourth will be n + 3,
And the fifth will be n + 4.

Now, let's break down the equation in English. We'll use #1, #2, #3, #4, and #5 as stand-ins for the five integers just so we can get things set up, then we'll replace them with the expressions we came up with in the first part. Starting from the beginning of the statement, let's translate words to symbols:

"The sum of the first and 4 times the third" → #1 + 4 × #3
"is equal to" → = (maybe obvious, but still!)
"60 less than 3 times the sum of the second, fourth, and fifth" → 3 × (#2 + #4 + #5) - 60

Putting that all together, we get the equation

#1 + 4 × #3 = 3 × (#2 + #4 + #5) - 60.

Replacing our stand-ins for the expressions we came up with, it becomes

n + 4(n + 2) = 3[(n + 1) + (n + 3) + (n + 4)] - 60

We can now start to simplify our equation to find n (the first integer) and the rest will follow easily from that. I'll start by focusing on the left side. We can distribute and combine like terms like so:

n + 4(n+2) = n + 4n + 8 = 5n + 8

Dealing with the right, we can get rid of some redundant parentheses and carry out the same process:

3[(n + 1) + (n + 3) + (n + 4)] - 60 = 3(n + 1 + n + 3 + n + 4) - 60

= 3(3n + 8) - 60 = 9n + 24 - 60 = 9n - 36

Our simplified equation now becomes

5n + 8 = 9n - 36.

Subtracting 5n from either side:

8 = 4n - 36

Adding 36 to either side:

44 = 4n

And dividing either side by 4:

11 = n.

We now know that our first integer is 11, which means that our 5 consecutive integers are 11, 12, 13, 14, and 15.

7 0

3 years ago