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2 years ago

∠F and ∠G are supplementary angles. If m∠F is two less than six times the measure of ∠G, find the measures of both angles

Mathematics

1 answer:

Mnenie [13.5K]2 years ago

4 0

Answer:

∠ G = 26°, ∠ F = 154°

Step-by-step explanation:

Express ∠ F in terms of ∠ G, that is

F = 6G - 2

and since the angles are supplementary, then

G + 6G - 2 = 180, that is

7G - 2 = 180 ( add 2 to both sides )

7G = 182 ( divide both sides by 7 )

G = 26

Thus

∠ G = 26° and ∠ F = 6(26) - 2 = 156 - 2 = 154°

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Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability,

Maurinko [17]

Answer:

0.1662 = 16.62% probability that exactly 2 will stay with the same company for more than five years

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they stay for the same company for more than five years, or they do not. Graduates are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Eight percent of all college graduates hired by companies stay with the same company for more than five years.

This means that $p = 0.08$

Sample of 11 college graduates:

This means that $n = 11$

The probability, rounded to four decimal places, that in a random sample of 11 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is: the absolute tolerance is +-0.0001

The tolerance means that the answer is rounded to four decimal places.

The probability is P(X = 2). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{11,2}.(0.08)^{2}.(0.92)^{11} = 0.1662$

0.1662 = 16.62% probability that exactly 2 will stay with the same company for more than five years

4 0

3 years ago

Find the length of l on the curve r(t)=5cos(3t)i-5sin(3t)j+3tk over the interval [3,7]

stealth61 [152]

$\mathbf r(t)=5\cos3t\,\mathbf i-5\sin3t\,\mathbf j+3t\,\mathbf k$
$\mathrm d\mathbf r(t)=\mathbf r'(t)\,\mathrm dt=(-15\sin3t\,\mathbf i-15\cos3t\,\mathbf j+3\,\mathbf k)\,\mathrm dt$

$\displaystyle\int_C\mathrm d\mathbf r(t)=\int_{t=3}^{t=7}\|\mathbf r'(t)\,\mathrm dt\|=\int_{t=3}^{t=7}\sqrt{225\sin^23t+225\cos^23t+9}\,\mathrm dt$
$=\displaystyle3\sqrt{26}\int_{t=3}^{t=7}\mathrm dt$
$=12\sqrt{26}$

4 0

3 years ago

Suppose you flip 3 quarters, one at a time. What is the probability that you will

Semenov [28]

Answer:

The probability of the combination {H, T and H} is 0.125.

Step-by-step explanation:

The sample space of flipping a quarter is:

S = {H and T}

The probability of both outcomes is same, i.e. P (H) = P (T) = 0.50.

It is provided that three quarters are flipped one at a time.

The outcomes of all the three quarters are independent of each other.

Compute the probability of the combination {H, T and H} as follows:

$P(\text{H},\text{T and H}) = P(\text{H})\times P(\text{T})\times P(\text{H})$

$=0.50\times 0.50\times 0.50\\=0.125$

Thus, the probability of the combination {H, T and H} is 0.125.

7 0

3 years ago

Find the standard deviation of

Kruka [31]

Answer:

11.5

The sample standard deviation measures the spread of a data distribution of the sample. It is usually used to estimate the population standard deviation

7 0

2 years ago

What is 1/5 × -3/2 +4/5 × -2/7 × -1/6 × -2/7

velikii [3]

Answer:

$\frac{-457}{1470}$