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1 year ago

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A group of campers is going to occupy 3 campsites at a campground. There are 17 campsites from which to choose. In how many ways

can the campsites be chosen?

1 answer:

Alexeev081 [22]1 year ago

5 0

Answer:

Campsites be chosen in 680 ways.

Step-by-step explanation:

Given:

Number of campsites= 17

Number of campsites that are to be occupied=3

To Find:

Number of ways can the campsites be chosen=?

Solution:

Combination:

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

nCr = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)!

No of ways in which campsites can be chosen= $\frac{17!}{3!(17-3)!}$ 17C3

=> $\frac{17!}{3!(14!)}$

=> $\frac{15\times16\times17}{3\times 2\times 1}$

=> $\frac{4080}{6}$

=>680

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A circle fits inside a semicircle of diameter 24mm

patriot [66]

Answer:

The shaded are is $113\ mm^{2}$

Step-by-step explanation:

we know that

The shaded area is equal to the area of the semicircle minus the area of the circle inside the semicircle

step 1

Find the area of semicircle

The area of semicircle is equal to

$A=\frac{1}{2}\pi r^{2}$

where

$r=24/2=12\ mm$ ----> the radius is half the diameter

substitute

$A=\frac{1}{2}\pi(12)^{2}=72\pi\ mm^{2}$

step 2

Find the area of the circle inside the semicircle

The area of circle is equal to

$A=\pi r^{2}$

where

$r=12/2=6\ mm$ ---> the radius of circle inside is half the radius of semicircle

substitute

$A=\pi(6)^{2}=36\pi\ mm^{2}$

step 3

Find the shaded area

$72\pi\ mm^{2}-36\pi\ mm^{2}=36\pi\ mm^{2}$

assume

$\pi=3.14$

$36(3.14)=113.04\ mm^{2}$

3 significant figures is

$113\ mm^{2}$

6 0

1 year ago

"Our customer retention rate has decreased 10% from last quarter's goal of 250 consumers retained. We need to increase our curre

Lorico [155]

1. multiply 250 by 10% (250 * .1= 25)
2. Then subtract 25 from 250 (250 -25= 225)
2. Then multiply 225 by 16% (225 * .16 = 36)
3. Add 225 + 36 = 261.
4. 261 is your final answer

6 0

2 years ago

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s = 180(n – 2), where n is the numb

pshichka [43]

S = 180° ( n - 2 )
The equation for n is:
n = s / 180° + 2
s = 1,260°
n = ( 1,260° : 180° ) + 2 = 7 + 2 = 9
Answer:
A polygon has 9 sides.

7 0

1 year ago

Read 2 more answers

If y is the circumcenter is angle STU find each measure

snow_tiger [21]

Answer:

Measures are SV=9 units., SY=14 units, YW= $\sqrt75units$ , YW= $\sqrt27units$

Step-by-step explanation:

Given Y is the circumcenter of ΔSTU. we have to find the measures SV, SY, YW and YX.

As Circumcenter is equidistant from the vertices of triangle and also The circumcenter is the point at which the three perpendicular bisectors of the sides of the triangle meet.

Hence, VY, YW and YX are the perpendicular bisectors on the sides ST, TU and SU.

Given ST=18 units.

As VY is perpendicular bisector implies SV=9 units.

Also in triangle VTY

$YT^{2}=VY^{2}+VT^{2}$

⇒ $14^{2}=VY^{2}+9^{2}$

⇒ VY^{2}=115

As vertices of triangle are equidistant from the circumcenter

⇒ SY=YT=UY=14 units

Hence, SY is 14 units

In ΔUWY, $UY^{2}=YW^{2}+UW^{2}$

⇒ $14^{2}=YW^2+11^{2}$

⇒ $YW^2=196-121=75$ ⇒ YW= $\sqrt75units$

In ΔYXU, $UY^{2}=YX^{2}+XU^{2}$

⇒ $14^{2}=YX^2+13^{2}$

⇒ $YX^2=196-169=27$ ⇒ YW= $\sqrt27units$

Hence, measures are SV=9 units., SY=14 units, YW= $\sqrt75units$ , YW= $\sqrt27units$

4 0

1 year ago

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. A cereal company claims that th

Dmitrij [34]

Answer:

There is not sufficient evidence to warrant the rejection of the claim that the mean weight of cereal is atleast 14 oz

Step-by-step explanation:

The hypothesis for the test above will be stated as follows :

The claim to be tested is the alternative hypothesis, which is the negation of the Null hypothesis

H0 : μ < 14

H1 : μ ≥ 14

If the Null is rejected, then it means that the company's claim that the mean weight of its cereal being atleast 14 is valid ;

Then it means there is significant evidence to support the stance that the mean weight of cereal in the company's packet is atleast 14 oz.

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1 year ago