Given: Two is an even integer or three is an even integer. Determine the truth value of this disjunction. Justify you answer.

Answers

Answer 1

Answer: It is TRUE OR FALSE, which gives TRUE.

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Find the median for the following set of numbers. 5, 19, 2, 28, 25 2 5 19 25

Answers

Step 1: List the numbers in order (Least - Greatest): 2, 2, 5, 5, 19, 19, 25, 25, 28
Step 2: Find the middle number: 2, 2, 5, 5, 19, 19, 25, 25, 28
Answer: 19
(Information for further questions): If there are 2 middle numbers, average them. (Add them up and divide by 2)

What is the general solution for (cosX + sinX)(1 - 2sinX)=0

Answers

1. square both sides, a straight forward method.
2. hand plot
3. calculator plot, not recommended.Let Y=sin x + cos x -1
Y=0, find x=?
4. Substitute 1=sin^2(x) + cos^2(x) on the right hand side
Y1=sin^2(x) - sin(x)
Y2=cos^2(x) - cos(x)
Y1 + Y2=0, Y1=0, Y2=0,
a(a-1)=0, so, a=0, a=1, where a=sin(x), or cos(x),
so x=0, pi/2
Have a good day!

Find the range of the data.

76, 72, 81, 71, 73, 89, 83, 75

Answers

Answer:

Range is 18

Step-by-step explanation:

In order: 71, 72, 73, 75, 76, 81, 83, 89

The range is the smallest number subtracted by the largest number:

89-71=18

Answer:

$18$

Step-by-step explanation:

$71, 72, 73, 75, 76, 81, 83, 89$

$\mathrm{The \: range \: is \: equal \: to:}$

$\mathrm{Biggest \: no. - Smallest \: no.}$

$89-71$

$=18$

From 12 prepared songs, a bandchooses 3 to perform on a TV show. One
song will be played at the beginning of
the show, one in the middle, and one at
the end. Tell how many different set lists
are possible. Then tell if the situation
involves permutations or combinations.

Answers

Answer:

1320 different set lists are possible

Step-by-step explanation:

We have a set of 12 elements (12 songs)

There can be NO songs repeatedly

The order of the songs is important because One song will be played at the beginning of the show, one in the middle, and one at the end.

So as the order of selection is important we must use permutations.

The formula for permutations is:

$nPr=(n!)/((n-r)!)$

where n is the number of items you can choose and choose r from them

In this case we know that:

$n=12$ , $r=3$

Then:

$12P3=(12!)/((12-3)!)$

$12P3=(12!)/(9!)$

$12P3=1320$

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 295 square yards. The situation is modeled by the equation h^2 + 5h = 295. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard. A: 17.36 yards
B: 600 yards
C: 14.86 yards
D: 29.71 yards

Answers

Answer:

The height is 14.86 yards ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

- The flower garden in the shape of a trapezoid

- The shorter base to be 3 yards greater than the height

- The longer base to be 7 yards greater than the height

- The area must be 295 square yards

- The situation is modeled by the equation h² + 5h = 295

- We want to find the height that will give the desired area by using

the quadratic formula

- The quadratic formula is $h=\frac{-b+-\sqrt{b^(2)-4ac}}{2a}$ ,

where a is the coefficient of h² and b is the coefficient of h and c

is the numerical term

- The equation of the area is h² + 5h = 295

∵ h² + 5h = 295

- Subtract 295 from both sides

∴ h² + 5h - 295 = 0

- Lets find the values of a , b and c from the equation

∵ a = 1 , b = 5 , c = -295

∴ $h=\frac{-5+-\sqrt{(5)^(2)-4(1)(-295)}}{2(1)}$

∴ $h=(-5+-√(25+1180))/(2)$

∴ $h=(-5+√(1205))/(2)=14.86$

- OR

∴ $h=(-5-√(1205))/(2)=-19.86$

- The dimensions of any figure must be positive value, then we will

neglect the negative value of h

∴ h = 14.86

* The height is 14.86 yards

Answer:

C: 14.86 yards

Step-by-step explanation:

to solve a quadratic equation we need to make it equal to zero and then use the Quadratic Formula

$x= \frac{-b + \sqrt{b^(2)-4ac}}{2a} / \frac{-b - \sqrt{b^(2)-4ac}}{2a}$

having

$h^(2) +5h-295=0$

we have

a=1

b=5

c=-295

the answers for the formula are

h=14.85 and h=-17.36

as we are looking for a distance we can only take the positive answer, then

h=14.85

Solve the logarithmic equation. be sure to reject any value that is not in the domain of the original logarithmic expressions. give the exact answer. log8(5x + 8) = log8(5x + 5)

Answers

this is the answer: false, because the domain is incorrect

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