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3 years ago

Adnan states if cos30°≈0.866, then sin30°≈0.866.

Mathematics

1 answer:

kiruha [24]3 years ago

8 0

Answer:

Adnan is incorrect because cosx and sin(90 - x) are always equivalent in any right triangle ⇒ first answer

Step-by-step explanation:

In any right triangle there are two acute angles sum of them is 90°

∴ If one of them x°, then the other is (90 - x)°

∵ cos x = adjacent/hypotenuse

∵ sin(90 - x) = opposite/hypotenuse

∵ The opposite of ∠(90 - x) is the adjacent of ∠x

∴ cosx = sin(90 - x)

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A line contains points M(1,3) and N(5,0). what is the slope of MN

garri49 [273]

-3/4 or it could also be -0.75

8 0

3 years ago

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

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

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

What is the IQR (Inter Quartile Range) for the data set?

vladimir2022 [97]

Arrange in ascending order:-

6 7 11 13 14 15 15 19 21

median = 14
lower quartile = mean of 7 and 11 = 9
upper quatile = mean of 15 and 19 = 17

Interquartile range = 17 - 9 = 8

answer is 8

4 0

3 years ago

At a fish market, a pound of salmon costs $12 and a pound of shrimp costs $18. Mrs. Donnelly wants to buy 2 1/3 pounds of salmon

Semmy [17]

Answer:

Yes and she would have $2 left over because all the food costs $91.

Step-by-step explanation:

We should set up an equation so that everything makes sense. A calculator would be wise for this problem, but I am going to lay it out anyhow.

We should convert the mixed numbers to improper fractions to not be confused. 3 1/2 becomes 7/2 or 3.5 and 2 1/3 becomes 7/3.

From your wording, we can assume that the money Mrs. Donnelly has is either greater than or equal to $93.

Thus, we have 12*(7/3) + 18*(7/3) is equal to or greater than 93 (this is an inequality).

The math shows that the food costed 91 and so she only has $2 left.

7 0

3 years ago

I don't know how to do math lol

Nimfa-mama [501]

9514 1404 393

Answer:

(d) 9

Step-by-step explanation:

The relation you're supposed to apply here is ...

an exterior angle of a triangle is equal to the sum of the remote interior angles.

The exterior angle is 17x+7, and it is equal to the sum of the two marked angles inside the triangle.

17x +7 = 13x +3 +40

4x = 36 . . . . . . . . . . . . . subtract 13x+7 from both sides

x = 9 . . . . . . . . . divide both sides by 4

3 0

2 years ago

Read 2 more answers