Plsss help this is for math

Six distinct integers are picked from the set {1, 2, 3,…, 10}. How many selections are there, in which the second smallest integ

Ksivusya [100]

Answer:

1680 ways

Step-by-step explanation:

Total number of integers = 10

Number of integers to be selected = 6

Second smallest integer must be 3. This means the smallest integer can be either 1 or 2. So, there are 2 ways to select the smallest integer and only 1 way to select the second smallest integer.

2 ways 1 way

Each of the line represent the digit in the integer.

After selecting the two digits, we have 4 places which can be filled by 7 integers. Number of ways to select 4 digits from 7 will be 7P4 = 840

Therefore, the total number of ways to form 6 distinct integers according to the given criteria will be = 1 x 2 x 840 = 1680 ways

Therefore, there are 1680 ways to pick six distinct integers.

6 0

3 years ago

If the smallest angle of a triangle is 20° and it is included between sides of 4 and 7, then (to the nearest tenth) the smallest

lawyer [7]

Answer:

$3.5$

Step-by-step explanation:

The smallest side of a triangle is formed by the smallest angle in the triangle.

To find the side opposite (formed by) the 20 degree angle, we can use the Law of Cosines. The Law of Cosines states that for any triangle, $c^2=a^2+b^2-ab\cos \gamma$ , where $a$ , $b$ , and $c$ are the three sides of the triangle and $\gamma$ is the angle opposite to $c$ .

Let $c$ be the side opposite to the 20 degree angle.

Assign variables:

$a\implies 4$
$b\implies 7$
$\gamma \implies 20^{\circ}$

Substituting these variables, we get:

$c^2=4^2+7^2-2(4)(7)\cos 20^{\circ},\\c^2=16+49-56\cos 20^{\circ},\\c^2=12.377213236,\\c=\sqrt{12.377213236}=3.51812638147\approx \boxed{3.5}$

Therefore, the shortest side of this triangle is 3.5.

5 0

3 years ago

Evaluate the expression for the given value of the variable.

MatroZZZ [7]

Answer:

17

Step-by-step explanation:

24/t + t^2

Let t=3

24/3 + 3^2

8 + 9

17

5 0

3 years ago

Read 2 more answers

Maureen earned some money doing odd jobs last summer and put it in a savings account that earns 9% interest compounded quarterly

ivolga24 [154]

Answer:

Maureen earned $123.19 doing odd jobs

Step-by-step explanation:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

In this question:

Compounded quarterly means that $n = 4$