Check wether the given value is the solution to the equation<br><br> 3(y+8)=2y-6 y=30

The conversion of square feet to square yards can be represented by direct variation. Three square yards are

grandymaker [24]

<h3>The constant of variation is $\frac{1}{9}$ </h3><h3>The equation is $y=\frac{1}{9}x$ </h3>

<em><u>Solution:</u></em>

Given that,

The conversion of square feet to square yards can be represented by direct variation

Let y represent the number of square yards

Let x be the number of square feet

$y \propto x$

y = kx ------ eqn 1

Where, "k" is the constant of variation

Three square yards are equivalent to 27 square feet

Substitute, y = 3 and x = 27 in eqn 1

$3 = k \times 27\\\\k = \frac{3}{27}\\\\k = \frac{1}{9}$

Thus the constant of variation is $\frac{1}{9}$

<em><u>What is the equation representing the direct variation?</u></em>

Substitute k = 1/9 in eqn 1

$y = \frac{1}{9}x$

Thus the equation is found

4 0

3 years ago

Britney lost $450 on investment which was 45% of the money she invested how much money did she invest ?

Whitepunk [10]

She would have invested $1,000 because 1,000x0.45=450. I hope that helped you!

5 0

3 years ago

LMN≅PQR

Tatiana [17]

X = 56°.

Based on the congruence statement, m∠L = m∠P; m∠M = m∠Q; and m∠N = m∠R.

Since m∠L = 72°, m∠P = 72°.
Since m∠N = x°, m∠R = x°.
We are given that m∠Q = 52°.

We can find the value of x by subtracting the given angles from 180:
180-(72+52) = 180-124 = 56°

7 0

3 years ago

Two types of coins are produced at a factory: a fair coin and a biased one that comes up heads 60 percent of the time. We have o

liraira [26]

Answer:

i) 0.1% probability that if the coin is actually fair, we reach a false conclusion.

ii) 0.05% probability that if the coin is actually unfair, we reach a false conclusion

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .