Of the tangent is 15/20 what’s the sine of the angle

If pq = 23 and uv = 1/23, find the value of u×q×v×p. Explain which properties you used

zhannawk [14.2K]

Remember that multiplication is commutative, which means the order in which we multiply things doesn't matter.

The order of u × q × v × p (which we can abbreviate uqvp) isn't as important as the fact that we're multiplying all four values together. We could just as easily rewrite the expression as pquv, and it'd represent the same value.

To find this value then, we can simply multiply pq and uv - the values we already know - together.

If we start with the expression pq = 23, we can multiply either side by uv (taking advantage of the multiplication property of equality) to get

pquv = 23uv

And since we know that uv = 1/23, we can use the substitution property of equality to replace the uv on the right side with 1/23:

pquv = 23(1/23)

The inverse property of multiplication states that any number multiplied by its inverse (its reciprocal) gives us 1. 23 and 1/23 are reciprocals of each other, so 23(1/23) = 1, which means

pquv = 1

Finally, going back to the second paragraph, we can use the commutative property of multiplication to rearrange the left side of the equation, giving us the solution

uqvp = 1

3 0

3 years ago

ACT mathematics score for a particular year are normally distributed with a mean of 27 and a standard deviation of 2 points.

mel-nik [20]

Answer:

A: 16%

B: 95%

C: 97.5%

Step-by-step explanation:

According to the empirical rule:

68% of a normal distribution is between -1 and +1 standard deviations.

95% of a normal distribution is between -2 and +2 standard deviations.

99.7% of a normal distribution is between -3 and +3 standard deviations.

Given μ = 27 and σ = 2.

Part A

29 is one standard deviation above the mean. We can show this by calculating the z-score:

z = (x − μ) / σ

z = (29 − 27) / 2

z = 1

We know that 68% is between -1 and +1 standard deviations. Since normal distributions are symmetrical, we can also say that 34% is between 0 and +1 standard deviations.

P(0 < Z < 1) = 68%/2 = 34%

We can also say that 50% is less than 0 standard deviations.

P(Z < 0) = 50%

Therefore, P(Z < 1) = 34% + 50% = 84%.

Which means P(Z > 1) = 100% − 84% = 16%.

Part B

Like before, calculate the z-scores:

z₁ = (23 − 27) / 2

z₁ = -2

z₂ = (31 − 27) / 2

z₂ = 2

From the empirical rule, we know this is 95% of the normal distribution.

Part C

We found in part B that the z-score is 2.

P(0 < Z < 2) = 95%/2 = 47.5%

P(Z < 2) = 50% + 47.5% = 97.5%

5 0

4 years ago

Aeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Kobotan [32]

Answer:

oooooooffff

Step-by-step explanation:

3 0

3 years ago

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Can someone please tell me what I'm doing wrong? I think I know how to do quadratic formula, and I know all the steps, but the l

Nata [24]

Okay, so first you set equal to 0:
$6-6x^{2}=3x\\-6x^{2}-3x+6=0$

Next simplify the equation so that the leading coefficient is positive:
$\frac{-6x^{2}-3x+6}{-3}=\frac{0}{3}\\2x^{2}+x-2=0$

Looking at the quadratic equation you can't easily simplify it, so plug it into the quadratic equation and simplify:
$x=\frac{-b\ -+\ \sqrt{b^{2}-4ac}}{2a}\\\\x=\frac{-(1)\ -+\ \sqrt{(1)^{2}-4(2)(-2)}}{2(2)}\\\\x=\frac{-1\ -+\ \sqrt{1+16}}{4}\\\\x=\frac{-1\ -+\ \sqrt{17}}{4}*\frac{-1}{-1}\\\\x=\frac{1\ -+\ \sqrt{17}}{-4},\ or\ B.$

I noticed a couple mistakes in your work, so if you want me to I can explain them in the comments section :)

5 0

3 years ago

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Divide. Write your answer using the smallest numbers possible.

Ilya [14]

Answer:

30660

Step-by-step explanation:

8 0

3 years ago