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PolarNik [594]
3 years ago
8

2x — бу = 12 х+ 10 = — 9

Mathematics
1 answer:
Serggg [28]3 years ago
5 0

Answer:

x = -19; y = 25/3

Step-by-step explanation:

Step 1: solve the equation with only one variable

Isolate the variable (x)

x + 10 = -9

x = -9 - 10

x = -19

Step 2: input new information into the other equation

If x = -19, then:

2(-19) - 6y = 12

Isolate the variable (y)

-38 - 6y = 12

-6y = 12 + 38

-6y = 50

y = 50 ÷ 6

y = 50/6

Simplify

y = 25/3

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Answer:

B) 0.02

Step-by-step explanation:

<u>Use the Binomial Theorem</u>

\displaystyle P(X=x)=\binom{n}{x}p^xq^{n-x}\\\\P(X=4)=\binom{30}{4}(0.30)^4(1-0.30)^{30-4}\\\\P(X=4)=\frac{30!}{4!(30-4)!}(0.30)^4(0.70)^{26}\\ \\P(X=4)=\frac{30!}{4!(26)!}(0.30)^4(0.70)^{26}\\ \\P(X=4)=\frac{30*29*28*27}{4*3*2*1}(0.30)^4(0.70)^{26}\\ \\P(X=4)=27405(0.30)^4(0.70)^{26}\\\\P(X=4)\approx0.0208

We have the probability of success, p=0.30, and the probability of failure, q=1-0.30=0.70. The binomial coefficient, \binom{n}{k}, represents the amount of possible combinations that k items can be chosen out of n items, with its respective formula \frac{n!}{k!(n-k)!}.

Hence, the best choice for the probability that 4 students chosen at random from the class of 30 that want the next test to be on Monday will be option B, 0.02

7 0
2 years ago
The angle measures associated with which set of ordered pairs share the same reference angle? (Negative StartFraction StartRoot
Katarina [22]

Answer:

(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)

Step-by-step explanation:

The reference angle is the angle that the given angle makes with the x-axis.

For an ordered pair to share the same reference angle, the x and y coordinates must be the same or a factor of each other.

From the given options:

(A)\left(-\dfrac{\sqrt{3} }{2} ,-\dfrac{1 }{2}\right)$ and \left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)\\\\(B)\left(\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(-\dfrac{\sqrt{3} }{2}, \dfrac{1 }{2}\right)\\\\(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)\\\\(D)\left(\dfrac{\sqrt{3} }{2},\dfrac{1 }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)

We observe that only the pair in option C has the same x and y coordinate with the second set of points being a negative factor of the first term. Therefore, they have the same reference angle.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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