All categories

3 years ago

A triangle has side lengths of 34 in., 20 in., and 47 in. Classify it as acute, obtuse, or right.

1 answer:

3 0

34^2 + 20^2 = 1156 + 400 = 1556

47^2 = 2209

because the squares of the 2 smaller sides is less than the square of the longer side the triangle is Obtuse

You might be interested in

Solve the linear programming problem. Minimize and maximize Upper P equals negative 20 x plus 30 y Subject to 2 x plus 3 y great

Alika [10]

Answer:

Maximum = 540 at (6,14)

Minimum = 300 at (0,10) or (12,2).

Step-by-step explanation:

The given linear programming problem is

Minimize and maximize: P = 20x + 30y

Subject to constraint,

$2x+3y\ge 30$ .... (1)

$2x+y\le 26$ .... (2)

$-2x+3y\le 30$ .... (3)

$x,y\geq 0$

The related equation of given inequalities are

$2x+3y=30$

$2x+y=26$

$-2x+3y=30$

Table of values are:

For inequality (1).

x y

0 10

15 0

For inequality (2).

x y

0 26

13 0

For inequality (3).

x y

0 10

15 0

Pot these ordered pairs on a coordinate plane and connect them draw the corresponding related line.

Check each inequality by (0,0).

$2(0)+3(0)\ge 30\Rightarrow 0\ge 30$ False

$2(0)+(0)\le 26\Rightarrow 0\le 26$ True

$-2(0)+3(0)\le 30\Rightarrow 0\le 30$ True

It means (0,0) is included in the shaded region of inequality (2) and (3), and (0,0) is not included in the shaded region of inequality (1).

From the below graph it is clear that the vertices of feasible region are (0,10), (6,14) and (12,2).

Calculate the values of objective function on vertices of feasible region.

Point P = 20x + 30y

(0,10) P = 20(0) + 30(10) = 300

(6,14) P = 20(6) + 30(14) = 540

(12,2) P = 20(12) + 30(2) = 300

It means objective function is maximum at (6,14) and minimum at (0,10) or (12,2).

7 0

3 years ago

Two candidates are randomly selected. a. List all the possible outcomes. b. What is the probability that both are qualified? c.

steposvetlana [31]

Question:

Four candidates are to be interviewed for a job. Two of them, numbered 1 and 2, are qualified, and the other two, numbered 3 and 4, are not.

Answer:

a. S = {12,13,14,23,24,34}

b. 1/6

c. ⅔

Step-by-step explanation:

Let S = Sample Space i.e. total possible outcomes

Given that candidates 1 and 2 are qualified and 3 and 4 are not qualified.

If two candidates are randomly selected. The list of all possible outcomes is as follows

S:{12,13,14,23,24,34}

And the number of outcomes is 6

b. What is the probability that both are qualified?

The event that both are qualified is given as {12} or {21}

From the sample space in (a) above, there's only one occurrence of {12} = 1

So, the probability is calculated as 1/6

c. What is the probability that exactly one is qualified?

The event that one one is qualified is given as {13,14,23,24}

Total = 4

Probability = 4/6

Probability = ⅔

5 0

3 years ago

Four

damaskus [11]

The probability is 50% for heads, so you should expect 2 heads results

4 0

4 years ago

Rose hiked at a constant rate of 13.3 miles per day for 7 days. Estimate the number of miles that Rose hiked during that time by

WARRIOR [948]

I think the answer is A

6 0

3 years ago

Read 2 more answers

A) In a group of 60 students, 15 liked maths only, 20 liked science only and 5 did not like

Paladinen [302]

Part (i)

We have 60 students total, and 5 didn't like any of the two subjects, so that must mean 60-5 = 55 students liked at least one subject.

<h3>Answer: 55</h3>

=========================================================

Part (ii)

We have 15 who like math only, 20 who like science only, and 55 who like either (or both). Let x be the number of people who like both classes.

We can then say

15+20+x = 55

x+35 = 55

x = 55-35

x = 20

This means 20 people liked both subjects

<h3>Answer: 20</h3>

=========================================================

Part (iii)

There are 15 people who like math only, and 20 who like both. Therefore, there are 15+20 = 35 people who like math (and some of these people also like science)

<h3>Answer: 35</h3>

=========================================================

Part (iv)

We'll follow the same idea as the previous part. There are 20 people who like science only and 20 who like both subjects. That yields 40 people total who like science (and some of these people also like math).

<h3>Answer: 40</h3>

=========================================================

Part (v)

We'll draw a rectangle to represent the entire group of 60 students. This is considered the universal set. Inside the rectangle will be two overlapping circles to represent math (M) and science (S).

We'll have 15 go in circle M, but outside circle S to represent the 15 people who like math only. Then we have 20 go in circle S but outside circle M to show the 20 people who like science only. We have another copy of 20 go in the overlapped region between the circles. This is the 20 people who like both classes. And finally, we have 5 go outside both circles, but inside the rectangle. These are the 5 people who don't like either subject.

Note how all of the values in the diagram add up to 60

15+20+20+5 = 60

This helps confirm we have the correct values.

<h3>Answer: See the venn diagram below</h3>

3 0

3 years ago