the central angle of a sector is 60 degrees and the area of the circle is 144 pi. What is the area of the sector

Lisa makes a cherry pie and an apple pie. She cuts the cherry pie into six equal wedges and she cuts the apple pie into eight eq

ale4655 [162]

Both the pies at first have 360* as their initial complete angles.

The Cherry Pie is cut into 6 parts equal and the angular width of each piece will be 360/6=60*...therefore, each piece is 60*.

the Apple Pie is cut into 8 parts and the angle of each piece would be 360/8=45*...therefore, each piece is 45*.

Now the angular difference between the pieces of the 2 pies is 60*-45* = 15*.

Therefore the Cherry pie's piece is 15* greater than the Apple pie's piece.

5 0

3 years ago

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The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it

brilliants [131]

Answer:

(a) 11.25 and 1.68

(b) 0.1651

(c) 0.3903

(d) 0.6865

Step-by-step explanation:

We are given that GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 75% of the cases and suppose the 15 cases reported today are representative of all complaints.

This situation can be represented through Binomial distribution as;

$P(X=r)= \binom{n}{r}p^{r}(1-p)^{n-r} ; x = 0,1,2,3,....$

where, n = number of trials (samples) taken = 15

r = number of success

p = probability of success which in our question is % of cases in

which customer problems are resolved on the same day, i.e.;75%

So, here X ~ $Binom(n=15,p=0.75)$

(a) Expected number of problems to be resolved today = E(X)

E(X) = $\mu$ = n * p = 15 * 0.75 = 11.25

Standard deviation = $\sigma$ = $\sqrt{n*p*(1-p)}$ = $\sqrt{15*0.75*(1-0.75)}$ = 1.68

(b) Probability that 10 of the problems can be resolved today = P(X = 10)

P(X = 10) = $\binom{15}{10}0.75^{10}(1-0.75)^{15-10}$

= $3003*0.75^{10} *0.25^{5}$ = 0.1651

(c) Probability that 10 or 11 of the problems can be resolved today is given by = P(X = 10) + P(X = 11)

= $\binom{15}{10}0.75^{10}(1-0.75)^{15-10}+\binom{15}{11}0.75^{11}(1-0.75)^{15-11}$

= $3003*0.75^{10} *0.25^{5} + 1365*0.75^{11} *0.25^{4}$ = 0.3903

(d) Probability that more than 10 of the problems can be resolved today is

given by = P(X > 10)

P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

= $\binom{15}{11}0.75^{11}(1-0.75)^{15-11}+\binom{15}{12}0.75^{12}(1-0.75)^{15-12} + \binom{15}{13}0.75^{13}(1-0.75)^{15-13}+\binom{15}{14}0.75^{14}(1-0.75)^{15-14} + \binom{15}{15}0.75^{15}(1-0.75)^{15-15}$

= $1365*0.75^{11} *0.25^{4} + 455*0.75^{12} *0.25^{3}+105*0.75^{13} *0.25^{2} + 15*0.75^{14} *0.25^{1}+1*0.75^{15} *0.25^{0}$

= 0.6865

3 0

3 years ago

How many whole-number solutions does the inequality |x-5|≤8 have?

-BARSIC- [3]

The answer is -3 to 13

6 0

3 years ago

One card is randomly selected from a deck of cards find the odds against drawing a seven

Stella [2.4K]

Answer:

$\frac{3}{4}$

Step-by-step explanation:

Probability of getting a 7 + Probability of not getting a 7 = 1.

Odds against drawing a 7 = Probability of not getting a 7.

We could calculate the probability of getting a 7 and subtract 1 from it to get the answer.

There a four sevens in a deck of card, one of each kind.

Probability of getting a 7 = $P(7) = \frac{4}{52} = \frac{1}{13}$

$\implies P(not \hspace{1mm} getting \hspace{1mm} a \hspace{1mm} 7) = 1 - P(7)$

$\implies$ P(not getting a 7) $= 1 - \frac{1}{13} = \frac{12}{13}$

4 0

3 years ago

Which pair of triangles is congruent?

stiv31 [10]

Answer:

The first pair.

Step-by-step explanation:

3 corresponding parts must be congruent for two triangles to be congruent. The first pair has 3 congruence markings; two angles and one side are congruent. Additionally, they are congruent by the ASA postulate because two angles and the included side are congruent.

7 0

3 years ago

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