Solve by writing a proportion.

xYou volunteer to help drive children at a charity event to the zoo, but you can fit only 6 of the 16 children present in your

brilliants [131]

There are 8008 groups in total, in other to drive the children

<h3>How to determine the number of groups?</h3>

From the question, we have

Total number of children, n = 16
Numbers to children at once, r = 6

The number of group of children that could be carried at once is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 16 and r = 6

Substitute the known values in the above equation

Total = ¹⁶C₆

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 16!/10!6!

Evaluate

Total = 8008

Hence, the number of groups is 8008

Read more about combination at

brainly.com/question/11732255

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8 0

1 year ago

Derive the formula for the area of a sector, and then use it to choose all that are correct.

Marina CMI [18]

Answer:

Part A) $A_s=\frac{\pi r^{2}}{360^o}{\theta}$

Part B) option 1,option 4

Step-by-step explanation:

Part A) Derive the formula for the area of a sector

we know that

The area of circle is equal to

$A=\pi r^{2}$

The area of circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector $A_s$ by a central angle of ∅ degrees

$\frac{\pi r^{2}}{360^o}=\frac{A_s}{\theta}$

$A_s=\frac{\pi r^{2}}{360^o}{\theta}$

Part B) Verify each case

case 1) we have

radius = 5 cm

angle = 120°

area = 26.2 cm 2

Find the area of the sector and then compare with the value of the given area

assume

$\pi=3.14$

substitute the given values

$A_s=\frac{(3.14)(5)^{2}}{360^o}{120^o}$

$A_s=26.2\ cm^2$

so

The given value of area is correct

case 2) we have

radius = 4 cm

angle = 105°

area = 16.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

$\pi=3.14$

substitute the given values

$A_s=\frac{(3.14)(4)^{2}}{360^o}{105^o}$

$A_s=14.7\ cm^2$

so

The given value of area is not correct

case 3) we have

radius = 6 cm

angle = 85°

area = 23.7 cm 2

Find the area of the sector and then compare with the value of the given area

assume

$\pi=3.14$

substitute the given values

$A_s=\frac{(3.14)(6)^{2}}{360^o}{85^o}$

$A_s=26.7\ cm^2$

so

The given value of area is not correct

case 4) we have

radius = 7

angle = 75°

area = 32.1 cm 2

Find the area of the sector and then compare with the value of the given area

assume

$\pi=3.14$

substitute the given values

$A_s=\frac{(3.14)(7)^{2}}{360^o}{75^o}$

$A_s=32.1\ cm^2$

so

The given value of area is correct

5 0

3 years ago

Which of the following is a solution of 3x2 = 7x - 3?

dezoksy [38]

3x^2 = 7x - 3
3x^2 - 7x = -3
x^2 - 7/3x = -1
x^2 - 7/3x + 49/36 = -1 + 49/36 = 13/36
(x - 7/6)^2 = 13/36
x - 7/6 = + or - sqrt(13)/6
x = 7/6 + or - sqrt(13)/6
x = (7 + or - sqrt(13))/6

8 0

3 years ago

Read 2 more answers

the sum of the ages of josh and autumn is 88 years 9 years ago josh was 4 times autumn age how old is josh now

forsale [732]

Let
x---------> <span> josh"age
y--------> </span><span>autumn' age

we know that
x+y=88--------> y=88-x---------> equation 1
(x-9)=4*(y-9)--------> equation 2

substitute equation 1 in equation 2
(x-9)=4*(88-x-9)
x-9=4*(79-x)
x-9=316-4x
x+4x=316+9
5x=325
x=65

the answer is
</span>josh"age is 65 years

3 0

3 years ago

What is the number of distinguishable permutations of the letters in the word, POTATO

MaRussiya [10]

Answer:

720

Step-by-step explanation:

Potato has 6 letters

6!/2!×2!

6×5×4×3×2/2×2

6 0

3 years ago