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VikaD [51]
3 years ago
10

Find the exact value of tan5x/4

Mathematics
1 answer:
alexandr402 [8]3 years ago
7 0
To evaluate for tan 5x/4 we proceed as follows
5x/4
=5/4*150
=225
which is in quadrant III. 
This implies that the value of tan will be positive, hence:
tan 225=tan (270-225)
tan 225=tan 45
using right angle with length of the legs being unit, then 
tan 45=1
hence
tan 5x/4=1

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For this case we are going to define the original coordinates:
 (x, y): original coordinates.
 We apply the transformation:
 (x, y) -------> (-x, y + k)
 We have:
 -x: reflection on the y axis.
 y + k: translation k units up.
 Answer:
 
The point was reflected over the y-axis and translated up.
6 0
3 years ago
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On average, 28 percent of 18 to 34 year olds check their social media profiles before getting out of bed in the morning. Suppose
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Answer:

0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

Step-by-step explanation:

When the distribution is normal, we use 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:

\mu = 28, \sigma = 5

Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

This is the pvalue of Z when X = 32. So

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

Z = \frac{32 - 28}{5}

Z = 0.8

Z = 0.8 has a pvalue of 0.7881

0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

5 0
3 years ago
The point slope form of the equation of the line that passes through (-5-1) and (10.-7) is
Natalka [10]

Answer:

The standard form of the equation for this line can be:

l: 2x + 5y = -15.

Step-by-step explanation:

Start by finding the slope of this line.

For a line that goes through the two points (x_0, y_0) and (x_1, y_1),

\displaystyle \text{Slope} = \frac{y_{1} - y_{0}}{x_{1} - x_{0}}.

For this line,

\displaystyle \text{Slope} = \frac{(-1) - (-7)}{(-5) - 10} = -\frac{2}{5}.

Find the slope-point form of this line's equation using

  • \displaystyle \text{Slope} = -\frac{2}{5}, and
  • The point (-5, -1) (using the point (10, -7) should also work.)

The slope-point form of the equation of a line

  • with slope m and
  • point (x_{0}, y_{0})

should be l:\; y - y_{0} = m(x - x_0).

For this line,

  • \displaystyle m = -\frac{2}{5}, and
  • x_0 = -5, and
  • y_0 = -1.

The equation in slope-point form will be

\displaystyle l:\; y - (-1) = -\frac{2}{5}(x - (-5)).

The standard form of the equation of a line in a cartesian plane is

l: \; ax + by = c

where

a, b, and c are integers. a \ge 0.

Multiply both sides of the slope-point form equation of this line by 5:

l:\; 5 y + 5 = -2x -10.

Add (2x-5) to both sides of the equation:

l: \; 2x + 5y = -15.

Therefore, the equation of this line in standard form is l: \; 2x + 5y = -15.

7 0
3 years ago
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6 0
4 years ago
If there is a 10% chance of sun tomorrow and a 20% chance of wind and no sun, what is the probability that it is windy, given th
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Since there are two events happening simultaneously (windy and no sun), we can apply the concept of conditional probability here. P(A|B) = P(A∩B)/P(B) where it means that given B is happening, the probability that A is happening as well is the ratio of the chance for A and B to happen simultaneously over the chance of B to happen. For our case, this can be interpreted as P(A|B): it is the probability that it is windy (A) GIVEN that there is no sun (B) P(A∩B) : chance of wind and no sun P(B) : chance that there is no sun tomorrow The chance of P(A∩B) is already given as 20% or 0.20. Since there is 10% or 0.10 chance of sun, then chances of having no sun tomorrow is (1-0.10) = 0.90. Thus, we have P(A|B) = 0.2/0.9 ≈ 0.22 or 22%. So, answer is B: 22%<span>.</span>
5 0
3 years ago
Read 2 more answers
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