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Len [333]
2 years ago
5

Find the volume of the following rectangular prism HELP PLSSSSSSSS

Mathematics
1 answer:
Advocard [28]2 years ago
4 0

Answer:

\frac{17}{8}  \times 4 \\ 8.5 {units}^{3}

You might be interested in
A computer programming team has 13 members. a. How many ways can a group of seven be chosen to work on a project? b. Suppose sev
Julli [10]

Answer:

1716 ;

700 ;

1715 ;

658 ;

1254 ;

792

Step-by-step explanation:

Given that :

Number of members (n) = 13

a. How many ways can a group of seven be chosen to work on a project?

13C7:

Recall :

nCr = n! ÷ (n-r)! r!

13C7 = 13! ÷ (13 - 7)!7!

= 13! ÷ 6! 7!

(13*12*11*10*9*8*7!) ÷ 7! (6*5*4*3*2*1)

1235520 / 720

= 1716

b. Suppose seven team members are women and six are men.

Men = 6 ; women = 7

(i) How many groups of seven can be chosen that contain four women and three men?

(7C4) * (6C3)

Using calculator :

7C4 = 35

6C3 = 20

(35 * 20) = 700

(ii) How many groups of seven can be chosen that contain at least one man?

13C7 - 7C7

7C7 = only women

13C7 = 1716

7C7 = 1

1716 - 1 = 1715

(iii) How many groups of seven can be chosen that contain at most three women?

(6C4 * 7C3) + (6C5 * 7C2) + (6C6 * 7C1)

Using calculator :

(15 * 35) + (6 * 21) + (1 * 7)

525 + 126 + 7

= 658

c. Suppose two team members refuse to work together on projects. How many groups of seven can be chosen to work on a project?

(First in second out) + (second in first out) + (both out)

13 - 2 = 11

11C6 + 11C6 + 11C7

Using calculator :

462 + 462 + 330

= 1254

d. Suppose two team members insist on either working together or not at all on projects. How many groups of seven can be chosen to work on a project?

Number of ways with both in the group = 11C5

Number of ways with both out of the group = 11C7

11C5 + 11C7

462 + 330

= 792

8 0
2 years ago
I need answers asap... please
aleksandrvk [35]

Answer:

see explanation

Step-by-step explanation:

(4)

consider the left side

factor the numerator

cosx - cos³x = cosx(1 - cos²x)

\frac{cosx(1-cos^2x)}{sinx}[/tex = [tex]\frac{cosxsin^2x}{sinx}

cancel sinx on numerator/denominator

= cosxsinx =right side ⇒ verified

(5)

Consider the left side

expand the factors

(1 + cotΘ)² + (1 - cotΘ)²

= 1 + 2cotΘ + cot²Θ + 1 - 2cotΘ + cot²Θ

= 2 + 2cot²Θ

= 2(1 + cot²Θ) ← 1 + cot²Θ = cosec²Θ

= 2cosec²Θ = right side ⇒ verified

(6)

Consider the left side

the denominator simplifies to

cosxtanx = cosx × \frac{sinx}{cosx} = sinx

\frac{sin^2x(secx+cosecx)}{sinx}

= sinx( \frac{1}{cosx} + \frac{1}{sinx})

= \frac{sinx}{cosx} + \frac{sinx}{sinx}

= tanx + 1 = right side ⇒ verified











3 0
2 years ago
This one is for CATNSIE!!!!! You got this! answer quick!!!!
CaHeK987 [17]

Answer:

OH TY LOL

Step-by-step explanation:

4 0
2 years ago
What does this equal to?
lesantik [10]

Answer:

x = 14

y = 7

z = 22

Step-by-step explanation:

x = # of cucumbers

y = # zucchini

z = # tomatoes

x + y + z = 43

2y = x  or  y = x/2

x + 8 = z

x + x/2 + x + 8 = 43

2x + x/2 = 35

4x + x = 70

5x = 70

x = 14

2y = 14

y = 7

14 + 8 = z

z = 22

Check if these variables are right:

14 + 7 + 22 = 43 ✔️

6 0
2 years ago
Please help with this algebra :)
Dahasolnce [82]
I am gonna go for D is the answer.
8 0
3 years ago
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