The circumference of a circular table top is 283.48 inches. Find the area of this table top. Use 3.14 for piπ

A political polling organization wishes to select a smaller focus group from a group of 7 Republicans, 10 Democrats, and 2 Indep

Alina [70]

Answer:

a) 1470 ways

b) 2835 ways

Step-by-step explanation:

the question is not correct, in the correct question The number of independents should be 3 not 2

there are 7 republicans, 10 democrats and 3 independents.

C(n,r) is the number of different combinations of n distinct objects taken r at a time.

C(n,r) = $\frac{n!}{(n-r)!r!}$

a) it will consist of 1 Republican and 4 Democrats

The number of ways this can be chosen is = C(7,1) × C(10,4) = $\frac{7!}{(7-1)!1!} * \frac{10!}{(10-4)!4!}$ = 7 × 210 = 1470 ways

(b) it will consist of 2 Republicans, 2 Democrats, and 2 Independents (consist of 2 independents not 3)

The number of ways this can be chosen is = C(7,2) × C(10,2) × C(2,2)

= $\frac{7!}{(7-2)!2!} * \frac{10!}{(10-2)!2!}* \frac{3!}{(3-2)!2!}$ = 21 × 45 × 3 = 2835 ways

7 0

3 years ago

What is the weight, in Newtons, of a person on Earth whose mass is 90 kilograms? Gravity near the Earth's surface is 9.8 m/s2.

valentinak56 [21]

Answer:

W = 882 N

Step-by-step explanation:

Given that,

The weight of a person, W = 90 kg

The value of acceleration due to gravity, g = 9.8 m/s²

We need to find the weight of the person on Earth. The formula for the weight of an object is given by :

W = mg

Substitute all the values,

W = 90 kg × 9.8 m/s²

W = 882 N

So, the weight of the person is equal to 882 N.

8 0

2 years ago

What is the answer to -3k-(-8)+2

NISA [10]

Answer:

-3k + 10

Step-by-step explanation:

-3k - (-8) + 2

-3k + 8 + 2 !!

-3k + 10 → simplified version of the given expression

!! → We got rid of the parenthesis by combining the two negative signs. The rules state that any 2 identical signs combined (in this case, - and -) equal a positive sign (+).

Hope it helped,

BiologiaMagister

6 0

2 years ago

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What is the intermediate step in the form (x + a)2 = b as a result of completing the

Eddi Din [679]

Answer:

(x + 7)^2 = 64

Step-by-step explanation:

x^2 + 23x – 19 = 9x - 4

x^2 + 23x - 9x = -4 + 19

x^2 + 14x = 15 = 0

Completing the square:

(x + 14/2)^2 - (14/2)^2 = 15

(x + 7)^2 - 49 = 15

(x + 7)^2 = 64

8 0

2 years ago

What is the sum or difference?

dlinn [17]

1. Ans: Option (B) $-6x^4$

Explanation:
Given: $2x^4 - 8x^4$
Take the common out:
=> $x^4(2 - 8)$

Hence: => $[tex]-6x^4$ [/tex] (Option B)

2. Ans: Option (D) $-3y^5$

Explanation:
Given: $6y^5 - 9y^5$
Take the common term(s) out:
=> $y^5(6-9)$

Hence: => $-3y^5$ (Option D)

3. Ans: Option (B) $9x^2 - 12x + 6$ quadratic trinomial

Explanation:
Given: $6 - 12x + 13x^2 - 4x^2$

The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.

=> $13x^2 - 4x^2 - 12x + 6$
=> $9x^2 - 12x + 6$ (Option B)

4. Ans: Option (C) $7.3x^2 + 0.8x + 1.3$

Explanation:
In order to find the total number of Common and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:

Common guppies: $3.1x^2 +6.0x + 0.3$ 
Endler's guppies: $4.2x^2 - 5.2x + 1.0$
(add both)
-----------------------------------------------------------------
Total number: $7.3x^2 +0.8x + 1.3$
-----------------------------------------------------------------
Hence the ans is Option(C) $7.3x^2 + 0.8x + 1.3$

5. Ans: Option (D) $2x^2(133 - 18 \pi )$

Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x = $266x^2$

Now the area of the circular fountain:
Area of the Circular Fountain = $\pi r^2$
Since, r=6x
Therefore,
Area of the Circular Fountain = $\pi (6x)^2 = 36 \pi x^2$

Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = $266x^2$ - $36 \pi x^2$
=> Final area of the Yard = $2x^2(133 - 18 \pi)$ (Option D)

6. Ans: Option (A) $56x^2$

Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x = $60x^2$

Now the area of the stadium:
Area of the stadium = 1x * 4x = $4x^2$

Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= $60x^2$ - $4x^2$
=> Final area of the lot = $56x^2$ (Option A)

-i

4 0

3 years ago

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