Systematic random sampling is used to interveiw residents in 25% of 80 apartments in a building. The sampling interval would be

The sum of two integers is 26. the sum of the squares of the two integers is 340. what is the product of the two numbers?

Phoenix [80]

Lets say that the two unknown integers are $n$ and $m$ .

We know the following things about $n$ and $m$ :

$n+m=26$
$n^2+m^2=340$

And, we want to find $nm$ .

To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:

$(n+m)^2=n^2+2nm+m^2$

So, given what we know about the unknown integers, the previous can be written as:

$(26)^2=340+2nm$

We can easily solve for $nm$ :

$nm= \frac{(26)^2-340}{2}= \frac{676-340}{2}= \frac{336}{2}=168$

The answer is 168.

Another approach to solve the problem is, from the two starting equations, compute the values of $n$ and $m$ , which are 12 and 14, and directly compute their product; however, the approach described is more elegant.

5 0

3 years ago

If triangles have the ratio of 2:3 adn the smaller traingle has a aside length of 7 what si length of the correspodning sides

REY [17]

$2:3=7:x\\\\\dfrac{7}{x}=\dfrac{2}{3}\ \ \ \ |cross\ multiply\\\\2x=7\cdot3\\\\2x=21\ \ \ |:2\\\\\boxed{x=10.5}$

5 0

3 years ago

Vernon tossed a coin 20 times. The results were 8 head s and 12 tails. What is the experimental probability of tossing heads?

solmaris [256]

Answer:

2/5

Step-by-step explanation:

The experimental probability is

P (heads) = number of heads/ total tosses

= 8/20

= 2/5

8 0

3 years ago

What is the measure of the vertex angle of an isosceles triangle if one of its base angle measures 34° and it’s congruent sides

KIM [24]

Let the vertex angle be x.

Base angles in the isosceles triangle are congruent.

Let the base angles be α=34°

Total sum of the inner angles in the triangle is 180°.

We can make equation

2α+x=180° => x=180-2α=180-68=112

The measure of the vertex angle is 112°

Good luck!!!

4 0

3 years ago

The cost per hour of running an assembly line in a

nlexa [21]

Answer:

the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

Step-by-step explanation:

if there is no mistake in the problem description, I read the following function :

C(x) = y = 0.3x² - 1.2x + 2

I don't know if you learned this already, but to find the extreme values of a function you need to build the first derivative of the function y' and find its solutions for y'=0.

the first derivative of C(x) is

0.6x - 1.2 = y'

0.6x - 1.2 = 0

0.6x = 1.2

x = 2

C(2) = 0.3×2² - 1.2×2 + 2 = 0.3×4 - 2.4 + 2 = 1.2-2.4+2 = 0.8

so, the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.

5 0

2 years ago