Ask question

Ask question

All categories

3 years ago

12

In a set of five consecutive integers, the smallest integer is more than $\frac23$ the largest. What is the smallest possible va

lue of the sum of the five integers?

2 answers:

Goryan [66]3 years ago

4 0

Answer:

55

Step-by-step explanation:

Let x represent the middle integer. Then the smallest is x-2 and the largest is x+2. Your requirement is that ...

(x-2)/(x+2) > 2/3

3x -6 > 2x +4 . . . . cross multiply

x > 10 . . . . . . . . . . .add 6-2x

The smallest integer satisfying this requirement is x=11. The sum of the 5 integers is 5x = 55.

The smallest sum is 55.

miv72 [106K]3 years ago

4 0

Answer:

55

Step-by-step explanation:

You might be interested in

Don’t remember how to do this , ?

andriy [413]

28. The ratio of games they won to total games played = 12: 14 = 6: 7.

29. Max's pay rate is 9.50 dollars per hour.

30. The value of n is 9.

Step-by-step explanation:

Step 1; Heather's team won 12 games out of 14. To find the ratio of games won to the total number of games we divide the number of games won to the number of games played.

The ratio of games won to games played = 12: 14, dividing both sides by 2 we simplify the ratio. So the simplified ratio is 6: 7.

Step 2; Max earns $380 for working 40 hours. So to find how much he earns an hour we divide the total money earned in n hours divided by n number of hours.

Money earned per hour = $\frac{380}{40}$ = $9.50. So Max's pay rate per hour is $9.50.

Step 3; The given proportion is

$\frac{n}{12}$ = $\frac{18}{24}$ , to solve this we keep n on the left-hand side while we multiply the 12 on to the other side

n = $\frac{18}{24}$ × 12 = $\frac{3}{4}$ × 12 = $\frac{36}{4}$ = 9.

7 0

3 years ago

I found the interval of convergence, but I am not sure how to do the second part, finding the sum of the series as a function of

antiseptic1488 [7]

The given series is geometric with common ratio $6^x - 9$ , which converges if $|6^x - 9|$ (i.e. the interval of convergence). We have the well-known result

$\displaystyle |r| < 1 \implies \sum_{n=0}^\infty ar^n = \frac{a}{1-r}$

If you're not familiar with that result, it's easy to reproduce.

Let $S_N$ be the $N$ -th partial sum of the infinite series,

$\displaystyle S_N = \sum_{n=0}^N \left(6^x - 9\right)^n = 1 + \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \cdots + \left(6^x - 9\right)^N$

Multiply both sides by the ratio.

$\left(6^x - 9\right) S_N = \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \left(6^x - 9\right)^3 + \cdots + \left(6^x - 9\right)^{N+1}$

Subtract this from $S_N$ to eliminate all the powers of the ratio between 0 and $N+1$ .

$\left(1 - \left(6^x - 9\right)\right) S_N = 1 - \left(6^x - 9\right)^{N+1}$

Solve for $S_N$ .

$S_N = \dfrac{1 - \left(6^x - 9\right)^{N+1}}{10-6^x}$

Now as $N\to\infty$ , the exponential term converges to 0 and we're left with

$\displaystyle \sum_{n=0}^\infty \left(6^x-9\right)^n = \lim_{N\to\infty} S_N = \boxed{\frac1{10-6^x}}$

7 0

2 years ago

What is the equation of the line??

Wittaler [7]

Answer:

x = 0

Step-by-step explanation:

This is a vertical line, in fact the y- axis

The equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through

All of the x- coordinates on the y- axis are zero, then

x = 0 ← equation of line

7 0

3 years ago

This is pre calculus please help !Describe three ways to determine the measure of segment YZ.

Dmitry [639]

(1) Using trigonometric ratios:
$sin(30) = \frac{YZ}{50}$
$YZ = 25$

(2) Using Pythagoras' Theorem:
$cos(30) = \frac{XY}{50}$
$50cos(30) = XY$
$50^{2} - 50^{2}cos^{2}(30) = YZ^{2}$
$2500 - 2500cos^{2}(30) = YZ^{2}$
$YZ = 25$

(3) Using sine rule:
$\frac{50}{sin(90)} = \frac{YZ}{sin(30)}$
$50 = \frac{YZ}{sin(30)}$
$50sin(30) = YZ$
$YZ = 25$

7 0

4 years ago

Read 2 more answers

-5a to the second power-7a

kakasveta [241]

-5a^2 - 7a = -a x (5a + 7)
let me know if you have any other questions
:)

7 0

4 years ago