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2 years ago

Given that9^-1/2 = 27^1/4 ÷ 3^x+1Find the exact value of x.

Mathematics

1 answer:

nexus9112 [7]2 years ago

5 0

Answer:

Find the exact value using trigonometric identities.

Exact Form: x=34

Decimal Form: x=0.75

Step-by-step explanation:

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Find four consecutive multiples of 3 such that the product of the first, third, and fourth is 1080

Dovator [93]

Answer:

<u>Therefore, we have 6, 9, 12, and 15, that are the first, second, third and fourth consecutive multiples of 3, such the product of 6, 12 and 15 is 1,080.</u>

Step-by-step explanation:

Let's find the factors of 1,080, as follows:

1,080 Dividing by 2 (1,080/2)

540 Dividing by 2 (540/2)

270 Dividing by 2 (270/2)

135 Dividing by 3 (135/3)

45 Dividing by 3 (45/3)

15 Dividing by 3 (15/3)

5 Dividing by 5 (5/5)

In consequence, we have:

5 * 3 * 3 * 3 * 2 * 2 * 2

Let's find out what multiples of 3 there are:

5 * 3 = 15 is a multiple of 3,

And 3 * 3 * 2 * 2 * 2 is remaining.

3 * 2 = 6 is also a multiple of 3,

And 3 * 2 * 2 is remaining

3 * 2 * 2 = 12 is also a multiple of 3.

<u>Therefore, we have 6, 9, 12, and 15, that are the first, second, third and fourth consecutive multiples of 3, such the product of 6, 12 and 15 is 1,080.</u>

7 0

3 years ago

A TV company when purchasing thousands electronic components apply this sampling plan: randomly select 15 of them and then accep

katrin [286]

<h2>Answer with explanation:</h2>

According to the Binomial probability distribution ,

Let x be the binomial variable .

Then the probability of getting success in x trials , is given by :

$P(X=x)=^nC_xp^x(1-p)^{n-x}$ , where n is the total number of trials or the sample size and p is the probability of getting success in each trial.

As per given , we have

n = 15

Let x be the number of defective components.

Probability of getting defective components = P = 0.03

The whole batch can be accepted if there are at most two defective components. .

The probability that the whole lot is accepted :

$P(X\leq 2)=P(x=0)+P(x=1)+P(x=2)\\\\=^{15}C_0(0.03)^0(0.97)^{15}+^{15}C_1(0.03)^1(0.97)^{14}+^{15}C_2(0.03)^2(0.97)^{13}\\\\=(0.97)^{15}+(15)(0.03)^1(0.97)^{14}+\dfrac{15!}{2!13!}(0.03)^2(0.97)^{13}\\\\\approx0.63325+0.29378+0.06360=0.99063$

∴The probability that the whole lot is accepted = 0.99063

For sample size n= 2500

Expected value : $\mu=np= (2500)(0.03)=75$

The expected value = 75

Standard deviation : $\sigma=\sqrt{np(1-p)}=\sqrt{2500(0.03)(0.97)}\approx8.53$

The standard deviation = 8.53

6 0

2 years ago

Rewrite the fraction as a decimal. -82/5

dlinn [17]

You can just multiply the top and the bottom by 2, to get the bottom to be 10. So you get -164/10. From here you can see that 10 goes into 164,16.4 times.

Therefore, -82/5 = -16.4

3 0

2 years ago

Read 2 more answers

I will give brainilest

S_A_V [24]

Answer 19:1

Work:
Students scoring above 80 -
9+18+72+15= 114

Students score exactly 80-
6

114/6 = 19

19 students scored above 80 for every 1 student that scored exactly 80.

3 0

2 years ago

125 A football stadium holds 55,296 people. The seating is divided into

stiks02 [169]

Answer:

1536

Step-by-step explanation:

simply divide 55296 by 36

4 0

3 years ago

Given that9^-1/2 = 27^1/4 ÷ 3^x+1Find the exact value of x. ​

Given that9^-1/2 = 27^1/4 ÷ 3^x+1Find the exact value of x.