6. A hotel has 56 guests.35 of the guests are male.(a) Work out 35 out of 56 as a percentage.

Answers

Answer 1

Answer: The easiest way to work out a percentage is by simple division and then multiplication by 100. 35/56 is 0.625, which then equals 62.5% after mutilplying by 100

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Find the volume, to the nearest m3, of a cylinder with diameter 6 m and height 8 m.a.226 m3 c.207 m3 b.452 m3 d.151 m3

Answers

ANSWER

a. 226m³

EXPLANATION

The volume of a cylinder is calculated using the formula:

$Volume=\pi \: {r}^(2) h$

where r is the radius and h=8m is the height of the cylinder.

The radius is half of the diameter.

This means that:

$r = (d)/(2) = (6)/(2) = 3m$

We plug in the values into the formula to get:

$Volume=\pi * {3}^(2) * 8$

$Volume=72\pi$

$Volume=226.19 {m}^(3)$

To the nearest cubic meters, the volume is 226 m³.

8)What is the equation of a line that goes through the point (3, 12) and is perpendicular to the line given by the equation y = -1/3x - 7?(A) y = -3x - 12
(B )y = -1/3x + 6
(C) y = 3x + 3
(D) = (1/3x) - 6

Answers

The slope of the first line is $m_1=(-1)/(3)$ .
To be perpendicular the slope of the second line must be the negative reciprocal of the first: $m_2=3$
Use the slope-intercept formula:
$y=mx+b$
Substitute known values:
$12=3(3)+b$
Solve for $b$ :
$b=3$
Complete the formula:
$y=3x+3$

THERE ARE A NUMBER of students SITTING IN Acircle. They ARE EVENly spaced and the 7th
STUDENT IS SEATED directly ACROSS FROM THE
18th student
How many students are there altogether

Answers

Answer:

7x18=x

solve for x , X= 127

answer = there are 127 students all together

hope this helpes

Which of the following is a polynomial with roots 4, −5, and 7?Question 4 options:

1) f(x) = x3 − 6x2 − 27x + 140
2) f(x) = x3 − 6x2 − 20x + 27
3) f(x) = x3 − 20x2 − 27x + 35
4) f(x) = x3 − 20x2 − 35x + 140

Answers

If x = 4, then the factor is (x - 4); if x = -5, then the factor is (x + 5); if x = 7, then the factor is (x - 7). We need to FOIL all these together to get a third degree polynomial. (x - 4)(x + 5) = (x^2 + x - 20). Now multiply that by (x- 7): (x^2+x-20)(x-7) = $x^3+x^2-20x-7x^2-7x+140$ . Combine like terms to get $x^3-6x^2-27x+140$ , the first choice above.

Answer: 1) f(x) = x3 − 6x2 − 27x + 140

Which of the following is a polynomial with roots 4, −5, and 7?

Question 4 options:

1) f(x) = x3 − 6x2 − 27x + 140

2) f(x) = x3 − 6x2 − 20x + 27

3) f(x) = x3 − 20x2 − 27x + 35

4) f(x) = x3 − 20x2 − 35x + 140

Step-by-step explanation:

I just did the assignment and the correct answer was 1). f(x) = x3 − 6x2 − 27x + 140. Hope this helps.

Good Luck!!

Factor completely, the expression: 2x^3-2x^2-12x show work please.

Answers

$2x^3-2x^2-12x =2x(x^2-x-6)=2x(x^2-x-2x+2x-6) =\n \n= 2x [(x^2-3x +2x-6)]= 2x [x(x -3 ) +2(x-3) ]=\n \n = 2x (x -3 ) (x+2)$

Extract a 2x from the expression to make it
2x(x^2-x-6).
Factor out x^2-x-6:------------------>must factors must multiply to -6 and add to -1
-3 and 2 fit the criteria therefore
x^2-x-6 factors out to (x-3)(x+2).

But dont forget to put it all back together. The 2x is part of the expression so the full factored expression is:

2x(x-3)(x+2)

Find the indicated term of the given arithmetic sequence. a1 = 45, d = –6, n = 8a. 309
c. 3
b. –3
d. 87

Answers

an = a1+d*(n-1)
a8 = 45 - 6*(8-1) =3

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