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3 years ago

What is the value of x rounded to the nearest tenth

Mathematics

2 answers:

Digiron [165]3 years ago

8 0

Use the trigonometric function

$\sin63^o=\dfrac{x}{85}\\\\\sin63^o\approx0.891\\\\\dfrac{x}{85}=0.891\ \ \ |\cdot85\\\\x=75.735\to x\approx75.7\ cm$

Alika [10]3 years ago

7 0

To find x, the function would be sine because from starting from the given angle, I can see x is the opposite and its gives me the hypotenuse. The formula to find sine is opposite over hypotenuse. sine(x)= opp/hyp

Now we plug in the given.

sin(63) = x / 85

To get x by itself we need to multiply 85 on both sides of the equation.

sin(63) x 85 = 7<span>5.73
</span>
So, 'x' is <span>75.73
</span>
Make sure your calculator is in DEGREES

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Given a bag of 5 blue, 3 green, and 8 red marbles.. What is the probability of picking a blue

Anvisha [2.4K]

$b = 5, \: g = 3, \: r = 8$

$total = 5 + 3 + 8 = 16$

$p(b) = \frac{5}{16}$

$p(g |without \: replacement|) = \frac{3}{16 - 1} = \frac{3}{15} = \frac{1}{5} \\$

$p(b \: and \: g) = \frac{5}{16} \times \frac{1}{5} = \frac{1}{16}$

6 0

3 years ago

Find four distinct complex numbers (which are neither purely imaginary nor purely real) such that each has an absolute value of

Luda [366]

Answer:

0.5 + 2.985i
1 + 2.828i
1.5 + 2.598i
2 + 2.236i

Explanation:

Complex numbers have the general form a + bi, where a is the real part and b is the imaginary part.

Since, the numbers are neither purely imaginary nor purely real a ≠ 0 and b ≠ 0.

The absolute value of a complex number is its distance to the origin (0,0), so you use Pythagorean theorem to calculate the absolute value. Calling it |C|, that is:

$|C| = \sqrt{a^2+b^2}$

Then, the work consists in finding pairs (a,b) for which:

$\sqrt{a^2+b^2}=3$

You can do it by setting any arbitrary value less than 3 to a or b and solving for the other:

$\sqrt{a^2+b^2}=3\\ \\ a^2+b^2=3^2\\ \\ a^2=9-b^2\\ \\ a=\sqrt{9-b^2}$

I will use b =0.5, b = 1, b = 1.5, b = 2

$b=0.5;a=\sqrt{9-0.5^2}=2.958\\ \\b=1;a=\sqrt{9-1^2}=2.828\\ \\b=1.5;a=\sqrt{9-1.5^2}=2.598\\ \\b=2;a=\sqrt{9-2^2}=2.236$

Then, four distinct complex numbers that have an absolute value of 3 are:

0.5 + 2.985i
1 + 2.828i
1.5 + 2.598i
2 + 2.236i

4 0

4 years ago

Lance and Alex have 70 pencils. Lance has 4 times as many pencils as Alex. Alex's pencils are shared equally among 2 children. H

gogolik [260]

let l = lance, and a = alex.

so: l + a = 70

and l = 4a

Putting the value for l in the first equation:

4a +a = 70

5a = 70

a = 14.

So Alex has 14 pencils. And Lance has (70-14) 56 pencils.

And if each child gets half of Alex' pencils, then each child will have 7 pencils.

6 0

3 years ago

A professor's son, having made the wise decision to drop out of college, has been finding his way in life taking one job or anot

Trava [24]

Answer:

88.88% probability that it endures for less than a year and a half

Step-by-step explanation:

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.

In this question, we have that:

$\mu = 66, \sigma = 10$